Competitive Tendering Versus Performance-Based Negotiation in Public Transport

Research Collection

Doctoral Thesis

Essays on Efficiency Measurement in Network Industries

Author(s): Koller, Martin

Publication Date: 2012

Permanent Link: https://doi.org/10.3929/ethz-a-007558848

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ETH Library DISS. ETH NO. 20501

ESSAYS ON

EFFICIENCY MEASUREMENT IN NETWORK INDUSTRIES

A dissertation submitted to

ETH ZURICH

for the degree of

Doctor of Sciences

presented by

MARTIN KOLLER

lic. oec. publ., University of Zurich

born 1st of December 1978

citizen of Appenzell AI, Switzerland

accepted on the recommendation of

Prof. Dr. Massimo Filippini, examiner

Prof. Dr. Helmut Dietl, co-examiner

2012

PREFACE

I am glad to say that the time spent on this dissertation was not a solitary endeavor, but very much a collective effort. I owe an enormous debt of gratitude to all the extraordinary people who have taken time to teach me what I know about economics.

First and foremost, I am deeply indebted to my supervisor, Prof. Dr. Massimo Filippini, not only for giving me the opportunity to write this dissertation at his chair at the Centre for Energy

Policy and Economics (CEPE), but also for his academic guidance, his close support and many challenging discussions. I enjoyed a high level of his confidence working on a project on behalf of the Swiss Federal Ministry of Energy1 and was given the pleasure of travelling to Vancouver for a visiting stay at the University of British Columbia (UBC). Thank you! I would also like to thank

Prof. Dr. Helmut Dietl, who kindly agreed to act as co-examiner, for his trust and his time in re- viewing my dissertation. I owe special thanks to Prof. Dr. Mehdi Farsi, who showed great patience in teaching me different subjects in econometrics and economics and without whom this dissertation would not have reached its present form. He inspired me in many ways.

Similarly important, but in a different way was the trust and backing of Dr. Urs Trinkner, who introduced me to the scientific world and whom I owe, among other things, my position with the General Secretary of Swiss Post during the first years and herewith the topic of this dissertation.

Thank you! I thank the following colleagues at Swiss Post: my former bosses, Lukas Bruhin and

Ronny Kaufmann for their professional confidence and scientific freedom, Dr. Christian Jaag for his demanding and inspiring thoughts on economics and Martin Mägli for his companionship.

Swiss Post made this dissertation possible by providing resources and data.2

I also enjoyed scientific assistance on particular points in my dissertation. Therefore, I thank

Prof. Dr. William Greene, Prof. Dr. Michael Crew, Prof. Dr. Paul Kleindorfer, Prof. Dr. Sumeet

Gulati, Prof. Dr. Per Agrell and Prof. Dr. Robert Windle. I have been fortunate to work at CEPE

1 Filippini et al. (2012). 2 Please note that the views and opinions expressed in this dissertation are mine and do not necessarily reflect those of Swiss Post or those of ETH. 4 PREFACE

and thank my colleagues Dr. Aurelio Fetz, Dr. Silvia Banfi, Dr. Souvik Datta, Dr. Martin Jakob,

Dr. Jelena Zoric, Dr. Andrea Horehájová, Dr. Mozghan Alaeifar, Fabian Heimsch, Céline

Ramseier, Markus Bareit, Laura Di Giorgio, Florian Landis, Jan Imhof, Justin Caron, Renger van

Nieuwkoop, Thomas Geissmann, Nina Boogen, Andrea Gossweiler and Rina Fichtl for having shared a great time in my life. I also thank Dr. Ina Kaufmann and Dr. Aline Bütikofer for their friendship and support.

Finally, I wish to thank my parents and my six siblings as well as my friends outside of aca- demia for their moral support in the many things I do, and especially Regula Holenstein for her encouragement and understanding during the final stage of this dissertation.

Martin Koller, June 2012, Zurich

ABSTRACT

During the last two decades, several countries around the world have been gradually liberalizing their postal markets. The key objectives of these reforms are improved efficiency within the sector, an increase in product innovation, higher quality levels, and affordable postal products while maintaining the provision of a minimum universal postal service.

The postal market in Switzerland also underwent a fundamental change with the reform of the Postal Organizations Act (POG (1997)). In the ensuing years, the letter market was gradually liberalized while maintaining a residual monopoly for Swiss Post in order to finance the public service, and the parcel market was fully liberalized. The public passenger bus transport branch of

Swiss Post was corporatized and the corresponding market put under competitive pressure by applying incentive regulation schemes.

Essay one examines economies of scale and scope in Swiss Post’s postal outlet network.

This network consists mainly of self-operated post offices and some franchised postal agencies.

Apart from making use of economies of scale for considerations concerning optimal size, we calculate economies of scope to answer strategic questions such as how the optimal output should be produced – whether jointly within the same infrastructure or in separate outlets. The postal outlets conduct letter and parcel collection, banking operations and sales activities. An important characteristic of the postal outlet network is regulated accessibility and, to some extent, politically negotiated opening hours to enhance public service and customer comfort. Consequently, the duty to operate a comprehensive postal outlet network implies minimum opening hours. Frequently, these hours exceed the time necessary to operate local demand, which gives rise to standby time. We propose to introduce standby time as an indicator of public service in the cost model. We show that for the estimation of the optimal size of postal outlets it is important to account for the impact of the public service obligation in the empirical cost analysis. The results of essay one confirm the existence of increasing unexploited economies of scale and scope in the Swiss Post office network.

Essay two examines cost efficiency in Swiss Post’s postal delivery network. Swiss Post is obliged to deliver letters and parcels in every year-round occupied residential area in the entire 6 ABSTRACT

country every working day (PG (1997)). In the course of market liberalization, the reserved services were limited to letters below 50 grams as a compromise in order to secure the financing of these universal services (PV (2004)). For the improvement of competitiveness as well as for future discussions on the extent of the universal service and its financing, it is important to gain information on cost efficiency through the implementation of an internal benchmarking system in the delivery process of Swiss Post. Therefore, this paper addresses the formulation of suitable econometric cost efficiency measurement models. From a methodological point of view, this requires the estimation of a cost frontier and the formulation of a model specification that adequately reflects the supply of the postal delivery. Thereby, special attention is paid to the consideration of unobserved time-invariant factors attributed to unobserved heterogeneity, as the delivery bases are subject to many different factors such as landscape, weather, traffic, output-mix, culture, etc., which cannot all be controlled perfectly in the models. Therefore, we apply different panel data models and some extensions that are suitable to control unobserved heterogeneity. Following the idea of Farsi et al. (2005b), we extend the Pooled model of Aigner et al. (1977) and the True Ran- dom Effects model of Greene (2005b) by the formulation of Mundlak (1978) to avoid the heterogeneity bias. For comparability reasons, we also estimate a True Fixed Effects model and the familiar Random Effects model of Pitt and Lee (1981). In this context, we also discuss the identification problem of inefficiency and unobserved heterogeneity. The results of essay two show that assumptions on unobserved heterogeneity are decisive and that results of econometric cost efficiency measurement models have to be interpreted with corresponding caution.

Essay three examines the differences in the levels of cost efficiency of bus lines operated on the basis of competitively tendered contracts and of bus lines operated with performance-based negotiated contracts using data from Postbus Switzerland. The public passenger transport market underwent a fundamental reform with the revision of the Swiss railway act (EBG) and its legal ordinances in 1996. Previous to the revision, passenger transportation companies were compensated for deficits after the operating period, i.e. regulated tariffs existed with automatic ex post coverage guarantee of the deficit by the state. According to the revised acts, however, companies were given the opportunity to declare anticipated deficits ex ante, subject to required quality and performance constraints. If the anticipated deficit was justifiable by certain benchmarking indicators, the public authorities could negotiate and finally procure the service. Furthermore, the public authorities were given the opportunity of putting lines out to tender in order to impose competitive 7

pressure on the passenger transportation companies. Therefore, with the revision of the acts, the public authorities were given a choice between two different contractual regimes to procure public passenger transport services: one relying on competitively tendered contracts and the other relying on performance-based negotiated contracts. Both contractual regimes are incentive regulation schemes. During the last fifteen years, the governments of most of the Swiss cantons have exercised their right and put some bus lines out to tender. However, despite this possibility, the majority of the bus lines are procured on performance-based negotiated contracts. In this study, we empirically estimate the differences in the levels of cost efficiency of bus lines operated under competitively tendered contracts and bus lines operated under performance-based negotiated contracts.

The study highlights the importance of separating the impact of changes of the institutional form or changes of ownership from impacts of the contractual regimes. The results of essay three indicate that the levels of cost efficiency of these contractual regimes are not statistically different from each other.

ZUSAMMENFASSUNG

In den vergangenen beiden Dekaden haben viele Länder ihre Postmärkte schrittweise liberalisiert. Die Hauptziele dieser Reformen waren Steigerung der Effizienz, Zunahme der Produktin- novationen, Erhöhung der Qualität und Erschwinglichkeit postalischer Produkte unter Aufrechter- haltung eines minimalen postalischen Universaldienstes.

Der schweizerische Postmarkt unterlag mit der Reform des Postorganisationsgesetzes (POG

(1997)) einer fundamentalen Änderung. In den darauffolgenden Jahren wurde der Briefmarkt schrittweise unter Beibehaltung eines Restmonopols der Schweizerischen Post zur Finanzierung des Universaldienstes liberalisiert, und der Paketmarkt wurde vollständig liberalisiert. Die Abtei- lung des öffentlichen Personenbustransportes der Schweizerischen Post wurde in eine Aktienge- sellschaft überführt und im entsprechenden Markt Wettbewerb mittels Anreizregulierungen einge- führt.

Der erste Aufsatz untersucht Skalen- und Verbundeffekte im Poststellennetz der Schweize- rischen Post. Dieses Netzwerk besteht hauptsächlich aus selbst betriebenen Poststellen und einigen konzessionierten Postagenturen. Neben von der Verwendung der Skaleneffekte zu Erwägungen bezüglich optimaler Grösse berechnen wir Verbundeffekte zur Beantwortung strategischer Fragen wie beispielsweise wie der Output produziert werden sollte – gemeinsam mit derselben Infrastruk- tur oder über separate Kanäle. In den Poststellen werden Brief- und Paketannahme abgewickelt,

Bankgeschäfte getätigt und Verkaufsaktivitäten durchgeführt. Eine wichtige Eigenschaft der Post- stellen sind regulierte Erreichbarkeit und, in gewissem Ausmass, politisch verhandelte Öffnungs- zeiten, um die Grundversorgung und den Kundenkomfort zu erhöhen. Folglich impliziert der Auf- trag, ein flächendeckendes Poststellennetz zu betreiben, gewisse Öffnungszeiten. Oft überschreiten diese Öffnungszeiten die notwendige Zeit zur Befriedigung der lokalen Nachfrage, was zu Bereit- schaftszeit führt. Wir schlagen in diesem Aufsatz vor, diese Bereitschaftszeit als Indikator für die

Grundversorgung im Kostenmodell zu einzuführen. Wir zeigen, dass es zur Schätzung der optima- len Grösse der Poststellen wichtig ist, die Auswirkungen der Grundversorgungsverpflichtung in der empirischen Kostenanalyse zu berücksichtigen. Die Resultate dieses ersten Aufsatzes bestäti- 10 ZUSAMMENFASSUNG

gen die Existenz von steigenden Skalen- und Verbunderträgen im Poststellennetz der Schweizeri- schen Post.

Der zweite Aufsatz untersucht die Kosteneffizienz im Zustellungsnetzwerk der Schweizeri- schen Post. Die Schweizerische Post ist verpflichtet, Briefe und Pakete in jedem ganzjährlich be- wohnten Gebiet der Schweiz jeden Werktag zuzustellen (PG (1997)). Im Rahmen der Marktlibera- lisierung wurden die reservierten Dienste als Kompromiss limitiert auf Briefe unter 50 Gramm, um die Finanzierung der Grundversorgung sicherzustellen (PV (2004)). Zur Erhöhung der Wettbe- werbsfähigkeit sowie für künftige Diskussionen um den Umfang des Universaldienstes und seiner

Finanzierung ist es wichtig, Information zur Kosteneffizienz durch die Implementierung eines internen Benchmarking-Systems in der Zustellung der Schweizerischen Post zu haben. Dieser

Aufsatz befasst sich darum mit der Formulierung geeigneter ökonometrischer Kosteneffizienzmes- sungsmodelle. Aus methodologischer Sicht bedingt das die Schätzung einer Kostengrenze und die

Formulierung einer Modellspezifikation, welche die postalische Zustellung adäquat abbildet. Da- bei wird ein spezielles Augenmerk auf die Berücksichtigung unbeobachteter, zeitinvarianter Fakto- ren gerichtet, die der unbeobachteten Heterogenität zugeschrieben werden können, da die Vertei- lungszentren vielen verschiedenen Faktoren wie Landschaft, Wetter, Verkehr, Output-Mix, Kultur, etc. unterliegen, die in den Modellen nicht perfekt kontrolliert werden können. Darum verwenden wir verschiedene Paneldaten Modelle sowie einige Erweiterungen, die sich zur Berücksichtigung unbeobachteter Heterogenität eignen. In Anlehnung an die Idee von Farsi et al. (2005b) erweitern wir das gepoolte Modell von Aigner et al. (1977) und das True Random Effects Modell von

Greene (2005b) um die Formulierung von Mundlak (1978), um eine Verzerrung durch die unbeo- bachtete Heterogenität zu vermeiden. Aus Vergleichbarkeitsgründen schätzen wir auch ein True

Fixed Effects Modell und das gewöhnliche Random Effects Modell von Pitt and Lee (1981). In diesem Zusammenhang diskutieren wir auch das Identifizierungsproblem von Ineffizienz und unbeobachteter Heterogenität. Die Resultate dieses zweiten Aufsatzes zeigen, dass die Annahmen bezüglich unbeobachteter Heterogenität entscheidend sind und dass die Resultate der ökonometri- schen Kosteneffizienzmessungsmodelle mit der entsprechenden Vorsicht zu interpretieren sind.

Der dritte Aufsatz untersucht mittels Daten von Postauto Schweiz die Unterschiede der Kos- teneffizienz von Buslinien basierend auf Ausschreibeverträgen und von Buslinien basierend auf

Leistungsvergleichsverträgen. Der öffentliche Personentransportmarkt unterlag einer fundamentalen Reform 1996 mit der Revision des Schweizerischen Eisenbahngesetzes (EBG) und den ent- 11

sprechenden Verordnungen. Vor der Revision wurden Personentransportunternehmen nach dem

Geschäftsjahr für Defizite entschädigt, d.h. es gab regulierte Tarife mit einer automatischen ex post

Deckungsgarantie durch die öffentliche Hand. Gemäss revidiertem Gesetz konnten die Unterneh- men die antizipierten Verluste ex ante unter Berücksichtigung erforderlicher Qualitäts- und Leis- tungsauflagen deklarieren. Wenn das antizipierte Defizit unter Berücksichtigung bestimmter Ver- gleichsindikatoren zu rechtfertigen war, konnte die öffentliche Hand den Dienst bestellen. Im Wei- teren bekam die öffentliche Hand das Recht, Linien öffentlich auszuschreiben, um Wettbewerb unter den Personentransportunternehmen einzuführen. Mit der Revision des Gesetzes bekam die

öffentliche Hand also die Wahl zwischen zwei unterschiedlichen Vertragsarten zur Bestellung

öffentlicher Personentransportleistungen: eine basierend auf Ausschreibungen und eine basierend auf Leistungsvergleichen. Beide Vertragsarten sind Anreizregulierungen. In den letzten anderthalb

Dekaden haben die Regierungen der meisten Schweizer Kantone ihr Recht genutzt und Linien

öffentlich ausgeschrieben. Trotz dieser Möglichkeit wurde aber der Grossteil der Buslinien basierend auf Leistungsvergleichsverträgen bestellt. In diesem Aufsatz schätzen wir empirisch die Un- terschiede der Niveaus der Kosteneffizienz von Buslinien mit Ausschreibeverträgen und von Bus- linien mit Leistungsvergleichsverträgen. Wir betonen die Wichtigkeit, Einflüsse durch die Ände- rung der institutionellen Form oder Einflüsse durch die Änderung der Eigentümerverhältnisse von den Einflüssen der Vertragsarten zu separieren. Die Resultate dieses dritten Aufsatzes indizieren, dass sich die Niveaus der Kosteneffizienz der Vertragsarten statistisch nicht voneinander unter- scheiden.

CONTENTS

PREFACE ...... 3 ABSTRACT ...... 5 ZUSAMMENFASSUNG ...... 9 CONTENTS ...... 13 LIST OF FIGURES ...... 15 LIST OF TABLES ...... 17 1 INTRODUCTION ...... 19 1.1 ISSUES AND GOALS ...... 19 1.2 METHODOLOGY ...... 22 1.3 ABSTRACTS ...... 24 1.4 CONTRIBUTIONS ...... 26 2 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS ...... 29 2.1 INTRODUCTION ...... 29 2.2 PREVIOUS STUDIES ON ECONOMIES OF SCALE AND SCOPE ...... 30 2.3 COST MODEL SPECIFICATION AND ESTIMATION METHODS ...... 34 2.3.1 Cost model specification ...... 34 2.3.2 The choice of the functional form of the cost function ...... 36 2.4 DATA ...... 41 2.5 ECONOMETRIC APPROACHES ...... 44 2.5.1 Unobserved heterogeneity ...... 44 2.5.2 Heteroskedasticity ...... 46 2.6 RESULTS ...... 47 2.6.1 Regression results and classification of the sample ...... 47 2.6.2 Results for economies of scale and scope ...... 51 2.7 SUMMARY AND CONCLUSIONS ...... 57 2.8 APPENDIX ...... 59 2.8.1 Acknowledgements ...... 59 2.8.2 Additional Figures and Tables ...... 60 14 CONTENTS

3 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS ...... 65 3.1 INTRODUCTION ...... 65 3.2 PREVIOUS STUDIES ON COST EFFICIENCY MEASUREMENT ...... 67 3.3 MEASUREMENT OF COST EFFICIENCY ...... 73 3.3.1 Theoretical definitions of cost efficiency ...... 73 3.3.2 Introduction on econometric approaches to measure cost efficiency ...... 74 3.3.3 Stochastic frontier models ...... 76 3.4 COST MODEL SPECIFICATION AND METHODOLOGY ...... 83 3.5 DATA ...... 89 3.6 RESULTS ...... 93 3.7 SUMMARY AND CONCLUSIONS ...... 102 3.8 APPENDIX ...... 104 3.8.1 Acknowledgements ...... 104 3.8.2 Short introduction to deterministic frontier models ...... 104 3.8.3 Additional Figures and Tables ...... 105 4 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION IN PUBLIC TRANSPORT ...... 107 4.1 INTRODUCTION ...... 107 4.2 PREVIOUS STUDIES ON THE EFFECTS OF COMPETITIVE TENDERING .... 110 4.2.1 General literature ...... 111 4.2.2 Empirical literature ...... 113 4.3 COST FRONTIER MODEL SPECIFICATION AND ESTIMATION METHODS 116 4.4 DATA ...... 120 4.5 RESULTS ...... 123 4.6 SUMMARY AND CONCLUSIONS ...... 127 4.7 APPENDIX ...... 128 4.7.1 Acknowledgements ...... 128 4.7.2 Additional Tables ...... 129 APPENDIZES ...... 133 REFERENCES ...... 135 CURRICULUM VITAE ...... 149

LIST OF FIGURES

Figure 2–1: The postal value chain: collection process ...... 33

Figure 2–2: Post offices and agencies considered in this paper ...... 42

Figure 2–3: Box plots of important characteristics in latent classes 1 and 2 ...... 50

Figure 2–4: Sample economies of scale and scope with 6 vs. 5 outputs ...... 60

Figure 3–1: The postal value chain: delivery process ...... 68

Figure 3–2: Decomposition of cost efficiency ...... 74

Figure 3–3: Econometric frontier methods ...... 75

Figure 3–4: Stochastic frontier cost function ...... 77

Figure 3–5: Delivery units considered in this paper...... 90

Figure 3–6: Distribution of efficiency scores ...... 99

Figure 3–7: Comparison of efficiency scores of two models ...... 105

LIST OF TABLES

Table 2–1: Relevant previous literature on economies of scale and scope in the postal sector ...... 33

Table 2–2: Comparison of the most important functional forms ...... 39

Table 2–3: Regression results ...... 48

Table 2–4: Prior class probabilities ...... 50

Table 2–5: Economies of scale (OLS-, WLS-, and LC-model) ...... 54

Table 2–6: Economies of scope (OLS-, WLS-, and LC-model) ...... 56

Table 2–7: Kruskal-Wallis equality-of-populations test ...... 57

Table 2–8: Regression results of the quantile regression model ...... 61

Table 2–9: Economies of Scale of the quantile regression model ...... 62

Table 2–10: Economies of Scope of the quantile regression model ...... 62

Table 2–11: Regression results of the WLS model with quasi-correction ...... 63

Table 2–12: Economies of Scope of the WLS model with quasi-correction ...... 64

Table 3–1: Relevant previous literature on cost efficiency measurement in the postal sector ...... 71

Table 3–2: Overview of different stochastic frontier models ...... 82

Table 3–3: Econometric specifications ...... 86

Table 3–4: Treatment of unobserved heterogeneity ...... 89

Table 3–5: Regression results (Models I, II and VI) ...... 95

Table 3–6: Regression results (Models III – V) ...... 96

Table 3–7: Hausman test statistics ...... 98

Table 3–8: Efficiency scores ...... 100

Table 3–9: Correlations of efficiency scores and Spearman rank correlations ...... 101

Table 3–10: Pair-wise deviation measures ...... 102

Table 4–1: Econometric specifications ...... 119

Table 4–2: Regression results ...... 125

Table 4–3: Cost efficiency scores ...... 126

Table 4–4: Kruskal-Wallis equality-of-populations test (cost efficiency scores) ...... 127

Table 4–5: Kruskal-Wallis equality-of-populations test (variables) ...... 129 18 LIST OF TABLES

Table 4–6: Regression results of preliminary models ...... 130

Table 4–7: Correlation of cost efficiency scores and Spearman rank correlation ...... 131

1 INTRODUCTION

This dissertation is composed of three essays on efficiency measurement in network industries. Essay one aims at measuring economies of scale and scope in postal outlets. Essay two im- merges into cost efficiency measurement in postal delivery units. Essay three seeks the differences in cost efficiency between the contractual regimes of competitive tendering and performance- based negotiation in public transport.

This short introduction discusses, in line with the detailed regulations for doctoral studies of

D-MTEC (2009), the general issues and the main goals of the dissertation. Further, it briefly outlines the methods applied in the empirical analysis. Finally, it includes the abstracts and the main contributions of the individual essays.

1.1 ISSUES AND GOALS

European Postal Directive (2008)). One of the most challenging tasks for the universal service providers in this process is to improve efficiency given the universal service obligations they face.

The postal market in Switzerland underwent also a fundamental change with the reform of the Postal Organizations Act (POG (1997)) and its following market liberalization processes. The former PTT3 was split up into the two public enterprises Swiss Post and Swisscom, the latter being corporatized and not focused in this dissertation. In the ensuing years, the letter market was gradually liberalized while maintaining a residual monopoly for Swiss Post in order to finance the pub-

3 PTT was the acronym for “Post, Telephon, Telegraph”. Hence, the postal markets including the letter, parcel, financial service and public bus passenger transport market as well as the telecommunications markets were served by one company that was provided with legal monopolies for most of these markets. Its predecessor organization was founded one year after the Federal State of Switzerland in 1849. 20 INTRODUCTION

lic service, and the parcel market was fully liberalized. The public passenger bus transport branch of Swiss Post was corporatized and the corresponding market put under competitive pressure by applying incentive regulation schemes. In addition to the institutional changes, there were considerable market upheavals due to electronic substitution.

Swiss Post owns a nationwide network of postal outlets, consisting mainly of self-operated post offices and some franchised postal agencies. In the course of the reorganization of the postal market, it is important to gain information on economies of scale and scope, along with the impact on cost of a predefined universal postal service. Apart from making use of economies of scale for considerations concerning optimal size, we calculate economies of scope to answer strategic questions such as how the optimal output should be produced – whether jointly within the same infrastructure or in separate outlets. These outlets conduct letter and parcel collection, banking operations and sales activities. An important characteristic of the postal outlet network is regulated accessibility and, to some extent, politically negotiated opening hours to enhance public service and customer comfort. Consequently, the duty to operate a comprehensive postal outlet network implies minimum opening hours. Frequently, these hours exceed the time necessary to operate local demand, which gives rise to standby time. We propose to introduce standby time as an indicator of public service in the cost model. We show that for the estimation of the optimal size of postal outlets it is important to account for the impact of the public service obligation in the empirical cost analysis.

Goal for essay one: Estimation of economies of scale and scope in the postal outlet network under consideration of opening hours and unobserved heterogeneity.

Besides the operation of a nationwide network of postal outlets, Swiss Post is obliged to deliver letters and parcels in every year-round occupied residential area in the entire country every working day (PG (1997)). In the course of market liberalization, the reserved services were limited to letters below 50 grams as a compromise in order to secure the financing of these universal services (PV (2004)). However, today, physical letters are also in competition with electronic mail, and the decline in letter volumes is ascribed mainly to electronic substitution (see e.g. Nikali (2008) or Dietl et al. (2011)). In order to increase the level of productive efficiency, the internal organization of Swiss Post has also undergone extensive restructuring. Two of these changes were the organizational separation of the collection and delivery processes and the commissioning of new, 1.1 ISSUES AND GOALS 21

more centralized sorting centers. The intention of these measures was to benefit from considerable scale effects through merger of delivery bases and centralized sorting centers while losing some economies through vertical disintegration.

Inefficiencies in the delivery process are of particular importance, as about half of total costs of letters and more than one third of total costs of parcels accrue in this process (NERA (2004b)).

For the improvement of competitiveness as well as for future discussions on the extent of the universal service and its financing, it is important to gain information on cost efficiency through the implementation of an internal benchmarking system in the delivery process of Swiss Post. There- fore, this paper addresses the formulation of suitable econometric cost efficiency measurement models. From a methodological point of view, this requires the estimation of a cost frontier and the formulation of a model specification that adequately reflects the supply of the postal delivery.

Thereby, special attention is paid to the consideration of unobserved time-invariant factors attributed to unobserved heterogeneity, as the delivery bases are subject to many different factors such as landscape, weather, traffic, output-mix, culture, etc., which cannot all be controlled perfectly in the models. Therefore, we apply different panel data models and some extensions that are suitable to control unobserved heterogeneity. Following the idea of Farsi et al. (2005b), we extend the Pooled model of Aigner et al. (1977) and the True Random Effects model of Greene (2005b) by the formulation of Mundlak (1978) to avoid the heterogeneity bias. For comparability reasons, we also estimate a True Fixed Effects model and the familiar Random Effects model of Pitt and

Lee (1981). In this context, we also discuss the identification problem of inefficiency and unobserved heterogeneity.

Goal for essay two: Estimation of cost efficiency in the postal delivery network under consideration of unobserved heterogeneity.

Swiss Post also holds a corporation operating in the Swiss public passenger bus transport market, Postbus Switzerland Ltd. This market underwent a fundamental reform with the revision of the Swiss railway act (EBG) and its legal ordinances in 1996. Previous to the revision, passenger transportation companies were compensated for deficits after the operating period, i.e. regulated tariffs existed with automatic ex post coverage guarantee of the deficit by the state. According to the revised acts, however, companies were given the opportunity to declare anticipated deficits ex ante, subject to required quality and performance constraints. If the anticipated deficit was justi- 22 INTRODUCTION

fiable by certain benchmarking indicators, the public authorities could negotiate and finally procure the service. Furthermore, the public authorities were given the opportunity of putting lines out to tender in order to impose competitive pressure on the passenger transportation companies.

Therefore, with the revision of the acts, the public authorities were given a choice between two different contractual regimes to procure public passenger transport services: one relying on competitively tendered contracts and the other relying on performance-based negotiated contracts.

Both contractual regimes are incentive regulation schemes. During the last fifteen years, the governments of most of the Swiss cantons have exercised their right and put some bus lines out to tender. However, despite this possibility, the majority of the bus lines are procured on performance-based negotiated contracts. In this study, we empirically estimate the differences in the levels of cost efficiency of bus lines operated under competitively tendered contracts and bus lines operated under performance-based negotiated contracts. The study highlights the importance of separating the impact of changes of the institutional form or changes of ownership from impacts of the contractual regimes.

Goal for essay three: Estimation of the differences in cost efficiency of bus lines operated on the basis of competitively tendered contracts and of bus lines operated with performance-based negotiated contracts.

1.2 METHODOLOGY

Economic literature has developed three different paradigms to empirically measure cost efficiency. The first is based on non-parametric, linear programming techniques, the second on

Bayesian theory and the third on an econometric approach.4 The linear programming and the econometric are established approaches in both theory and practice, whereas the Bayesian approach is only little-known in applied science. In this dissertation, we focus on the use of econometric approaches to estimate a cost function. 5 There have been numerous general survey studies

4 The econometric approach is sometimes also called parametric approach. 5 Readers interested in linear programming models such as Data Envelopment Analysis (DEA; Farrell (1957), Charnes et al. (1978)), Full Disposable Hull (FDH; Deprins et al. (1984)) or index methods are referred to Thanassoulis et al. (2008) and to Färe et al. (2008) for a comprehensive overview on these models and their developments. Readers interested in Bayesian stochastic frontier models (sometimes also characterized as non-parametric models) are referred to van den Broeck et al. (1994). Readers interested in a comparison of Bayesian models and classical econometric approaches are referred to Kim and Schmidt (2000). 1.2 METHODOLOGY 23

and books on frontier literature and on econometric approaches during the last three decades.

Among the more recent are, for example, Kalirajan and Shand (1999), Murillo-Zamorano (2004),

Coelli et al. (2005), Cornwell and Smith (2008) and Greene (2008).

Most of the econometric approaches include estimating an empirical cost function,6,7 where the observed variables should include a vector of outputs and a vector of input prices. Hence, the cost function describes a relationship between costs, input prices and outputs. Its explaining variables can be used to calculate economies of scale, scope (based on the seminal work of Baumol et al.

(1982)) and density (based on the work of Caves et al. (1984)). The remaining unobserved part of the cost function, the residual, is used to create the cost frontier and measure cost efficiency, based on the works of Winsten (1957) and Afriat (1972) for deterministic and on Aigner et al. (1977) and

Meeusen and van den Broeck (1977) for stochastic frontier models.

The concept of global economies of scale measures the degree of global returns to scale in a multiproduct company, whereas the concept of global economies of scope measures the relative additional costs incurring from unbundling the production of a multiproduct company in independent single-product companies (Filippini and Farsi (2008)). These two concepts, together with a latent class model to reduce unobserved heterogeneity, have been applied in essay one. The concept of economies of density measures the degree of returns to density, i.e. the changes in output with fixed network characteristics.

The concept of cost efficiency in the stochastic frontier models of Aigner et al. (1977) and

Meeusen and van den Broeck (1977) divides the residual under some distributional assumptions into two parts: one is reflecting inefficiency and the other is capturing the random noise. This model with slight adaptations has been applied in essay three. As the basic stochastic model neglects the time dimension, it is often referred to the pooled stochastic frontier model. It does not distinguish between efficiency and time-invariant unobserved effects, i.e. it is affected by a heterogeneity bias if the unobserved effect is correlated with the regressors. In the following years, many developments for panel data evolved from the pooled stochastic frontier model.8 Among the most important are the random effects models of Pitt and Lee (1981) and the true effects models of

6 The evidence is (under a set of regularity conditions) analogously valid for its dual, the production function and hence productive efficiency (see Shepard (1953) and Nerlove (1963)). 7 For an overview on different functional forms and its implications, see Subsection 2.3.2. 8 For an overview on different developments of the stochastic frontier model, see Section 3.3. 24 INTRODUCTION

Greene (2005b). Comparing efficiency estimates of these models, Greene (2008) states explicitly that the ‘truth’ doubtless lies somewhere between the two extremes, as these models form a lower and an upper bound of efficiencies. The model of Pitt and Lee assumes the time-invariant individual effects, which should capture the unobserved heterogeneity, to be uncorrelated with the explanatory variables, and interprets it as inefficiency. As long as this assumption holds, the estimators are not affected by a heterogeneity bias. The true effects models of Greene include a random and a fixed effects model and introduce time-invariant, unit-specific constants to capture the unobserved effect, so that the remaining elements in the residual, including inefficiency, vary freely over time. Still, correlation between the individual effects and the explanatory variables in the random effects model might cause a heterogeneity bias.

To overcome the unobserved heterogeneity problem, these models can be extended by the auxiliary equation proposed by Mundlak (1978) and first applied to stochastic frontier models by

Farsi et al. (2005b). This auxiliary equation considers possible correlation between the unobserved heterogeneity and the explanatory variables using the group-means of the explanatory variables.

These models have been applied in essay two, some of them including Mundlak’s extension.

The econometric software packages of Stata® 11 and LIMDEPTM 9.0 have been employed for the econometric application of these methodologies to data. Reference work for these packages are the modeling guides of Kohler and Kreuter (2006) and Cameron and Trivedi (2009) for Stata® and Greene (2007) for LIMDEPTM.

1.3 ABSTRACTS

Essay one: Economies of scale and scope in postal outlets

The purpose of this study is to analyze the cost structure of Swiss Post’s postal outlets. In particular, the idea is to assess economies of scale and scope in post offices and franchised postal agencies. Information on their optimal size and production structure is of importance from the policy-makers’ point of view because this hypothetical situation may be a basis for calculation of reimbursements when providing the universal service. Two important novelties are introduced in this study. First, the latent class model accounts for postal outlets with different underlying production technologies, caused by unobserved factors. Second, the cost model includes standby time as an indicator of public service because regulated accessibility and negotiated opening hours that 1.3 ABSTRACTS 25

enhance public service frequently lead to opening hours that exceed the time necessary to operate the demand. Overall, this analysis confirms the existence of increasing unexploited economies of scale and scope with falling outputs in the Swiss Post office network. Furthermore, the results for the latent class model point to the existence of unobserved heterogeneity in the industry.

Keywords: economies of scale, economies of scope, postal outlet network, unobserved heterogeneity, latent class model, opening hours, standby time

JEL classification: C21, C81, D24, H42, L87

Essay two: Cost efficiency measurement in postal delivery units

The purpose of this study is to analyze the cost structure of Swiss Post’s postal delivery units. In particular, the idea is to evaluate different panel data models in order to assess cost efficiency in these units in due consideration of unobserved heterogeneity. Information on cost efficiency is important from the policy makers’ as well as from Swiss Post’s point of view with regard to further market changes. The main novelty in this study is a differentiated treatment of unobserved heterogeneity applying Mundlak’s formulation to the Pooled stochastic frontier model. The results provide evidence that this model is not affected by a heterogeneity bias and that the cost efficiency values lie within a lower and upper bound of the other recent and familiar econometric models. Overall, the analysis has shown that assumptions on unobserved heterogeneity are decisive and that results of econometric cost efficiency measurement models have to be interpreted with corresponding caution.

Keywords: cost efficiency, stochastic frontier models, unobserved heterogeneity, Mundlak, postal delivery network

JEL classification: C33, D24, H42, L87

Essay three: Competitive tendering versus performance-based negotiation in public transport

The purpose of this study is to analyze the cost structure of Swiss Post’s public passenger transportation bus lines. In particular, the idea is to assess the differences in the levels of cost efficiency between bus lines operated on the basis of competitively tendered contracts and bus lines operated with performance-based negotiated contracts. Information on the effects of these contractual regimes on total costs is of importance from the policy makers’ as well as from the purchasers’ 26 INTRODUCTION

view, as the legislation governing procurement of public passenger transport services is currently under revision. This is one of the first studies directly comparing the impact of competitively tendered contracts and of performance-based negotiated contracts on cost efficiency operated by one single company at the same time. The overall results show that the differences in the levels of cost efficiency between bus lines with competitively tendered contracts and bus lines with performance-based negotiated contracts are not significant. This finding is in line with a recent study that found a tendency of cost convergence of competitive tendering and performance-based negotiation and another that attributed many of the same advantages to yardstick competition as to competitive tendering.

Keywords: public bus contracts, comp. tendering, performance-based negotiation, cost efficiency

JEL classification: C21, D24, H57, L92

1.4 CONTRIBUTIONS

This dissertation contributes in different ways to the literature of cost efficiency measurement in network industries. The most important contribution of each essay is listed below.

Essay one: Public service

We include standby periods of opening time in the cost model specification. This variable allows us to consider production process situations in which an office must remain open even if demand is zero due to regulated accessibility and politically negotiated opening hours to enhance public service and customer comfort. To the best of our knowledge, this is the first study that considers this seemingly unproductive time as an output in the form of a public service.

Essay two: Unobserved heterogeneity

We apply panel data on different elaborated cost model specifications that take the unobserved heterogeneity into account. Most importantly and following the idea of Farsi et al. (2005), we extend the Pooled model of Aigner et al. (1977) by the formulation of Mundlak (1978). The estimators of this auxiliary equation absorb the correlated components of the unobserved heterogeneity and therefore avoid a heterogeneity bias. To the best of our knowledge, this is the first study that combines the Pooled model with the formulation of Mundlak.

Essay three: Incentive regulation schemes 1.4 CONTRIBUTIONS 27

We estimate the differences in the levels of cost efficiency of bus lines operated under competitively tendered contracts and bus lines operated under performance-based negotiated contracts.

Both contractual regimes are incentive regulation schemes. The study highlights the importance of separating the impact of changes of the institutional form or changes of ownership from impacts of the incentive regulation schemes. To the best of our knowledge, this is the first empirical study that examines the differences in the levels of cost efficiency of this two incentive regulation schemes.

2 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

This chapter is based on Filippini et al. (2010b), Filippini et al. (2010a) and on Filippini and

Koller (2012b).

2.1 INTRODUCTION

European Postal Directive (2008)). One of the most challenging tasks for the universal service providers in this process is to improve efficiency given the universal service obligations they face.9

In Switzerland, the postal market is also affected by such regulatory changes. The largest and most important provider of postal services in the country is the incumbent Swiss Post, a publicly owned company. Besides the delivery of letters and parcels in the entire country, Swiss Post owns a nationwide network of postal outlets, consisting mainly of self-operated post offices and some franchised postal agencies. These postal outlets conduct letter and parcel collection, banking operations and sales activities. An important characteristic of the postal outlet network is regulated accessibility and, to some extent, politically negotiated opening hours to enhance public service and customer comfort. Consequently, the duty to operate a comprehensive postal outlet network implies minimum opening hours. Frequently, these hours exceed the time necessary to operate local demand, which gives rise to standby time. The supply of such a service is financially unat- tractive, especially in rural areas, where post offices are characterized by a relatively high percentage of standby time.

9 The provision of universal services in a liberalized market is challenging as potential market distor- tions are higher with increasing universal service obligations (Dietl et al. (2009)). Free market and universal service are two conflicting concepts (Trinkner (2007)). 30 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

To promote the reorganization of the postal market successfully, it is important to gain information on economies of scale and scope, along with the impact on cost of a predefined universal postal service. From a methodological point of view, this requires the specification of a cost model that adequately reflects the supply of the universal postal service. We propose to introduce standby time as an indicator of public service in the cost model. We show that for the estimation of the optimal size of postal outlets it is important to account for the impact of the public service obligation in the empirical cost analysis.

Apart from making use of economies of scale for considerations concerning size, we calculate economies of scope to answer strategic questions such as how the optimal output should be produced – whether jointly within the same infrastructure or in separate outlets. Among others, this question arises specifically for banking services and the sale of further products.

The paper is organized as follows. Section 2.2 outlines the main contribution of this paper with regard to the relevant literature available on the subject. Section 2.3 presents the model specifications. Section 2.4 introduces the data, Section 2.5 addresses the econometric approaches for heteroskedasticity and unobserved heterogeneity and Section 2.6 provides the estimation results and measures for economies of scale and scope for different model specifications. We draw the conclusions in Section 2.7, which is followed by the appendix containing further figures and tables, mostly uncommented.

2.2 PREVIOUS STUDIES ON ECONOMIES OF SCALE AND SCOPE

During the last decades, various studies have investigated economies of scale and scope in network industries such as the energy and transport sector, healthcare, the banking industry, or even in higher education. Only few studies have been concerned with the postal market. Therefore, we first have a look at an assortment of the studies of non-postal industries.

For the energy sector, an early but seminal paper was published by Nerlove (1963) that investigates returns to scale in electricity supply. Estimating a total cost function derived from a

Cobb-Douglas production function, Nerlove arrayed the 144 observations in five groups with respect to their size, attempting to approximate the cost function at different segments. He found evidence of a marked degree of increasing returns to scale, that turned out to vary inversely with the output. The study by Fraquelli et al. (2004b) supports the hypothesis of increasing economies 2.2 PREVIOUS STUDIES ON ECONOMIES OF SCALE AND SCOPE 31

of scale and scope for small and medium firms, comparing the estimates of a composite cost function of a sample of public utilities providing a combination of gas, water and electricity with estimates of traditional forms as standard translog, generalized translog and separable quadratic.

The study by Preyra and Pink (2006) analyzes large scale restructuring, closures and mergers of Canadian hospitals. Using a total cost function with several econometric specifications, they concluded that efficiency gains are noteworthy at least in the long run, but vary considerably by assumptions about capital to changes in size and product mix. In the short run, however, these gains do not necessarily occur. The paper of Farsi et al. (2007) analyzes the cost structure of a sample of Swiss multi-modal urban transport operators in order to assess economies of scale and scope, which could be affirmed by the results. Farsi et al. (2008a) also investigated economies of scale and scope in multi-utilities estimating several econometric specifications including a random-coefficient model for a sample of firms distributing electricity, gas and/or water to the Swiss population. While indicating considerable economies of scale and scope overall, the results suggest a significant variation in scope economies across companies due to unobserved heterogeneity.10

As far as postal services are concerned, however, most empirical studies pay attention to economies of scale and scope in delivery or combined activities (see Wada et al. (1997), Cohen and Chu (1997), Mizutani and Uranishi (2003), Cazals et al. (2005), Filippini and Zola (2005),

Bradley et al. (2006), and Farsi et al. (2006b)).11 With the exception of Mizutani and Uranishi’s contribution, their results correspond well to intuition and confirm the existence of economies of scale and scope. Wada et al. (1997) estimated a multiproduct total cost function of the Japanese mail service by treating the delivery of letters and that of parcels as two independent outputs. Us- ing a translog specification and panel data, they found evidence for the existence of overall economies of scale. Furthermore, their study highlights significant product-specific economies of scale for letters, but not for parcels. Cohen and Chu (1997) examined the issue of whether the postal services were natural monopolies, and estimated the total cost impact of splitting the U.S. Postal

10 For more studies on economies of scale and scope in non-postal industries, see for example Caves et al. (1981), Caves et al. (1984) or Cambini and Filippini (2003) (transport sector), Koshal and Koshal (1999) or Sav (2004) (higher education), Fu and Heffernan (2008) (banking sector), Filippini (2001) or Farsi et al. (2008b) (health sector), Kaserman and Mayo (1991), Filippini (1996) or Farsi et al. (2007) (electricity distribution), Filippini and Luchsinger (2007) (hydropower). 11 See also NERA (2004a) for an overview on the relevant empirical literature. 32 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Service into two equally sized but separate organizations. They found the sum of the costs under the new arrangement to be greater than the costs of single-firm delivery and attributed the cost difference to scale economies in street delivery. Cazals et al. (2005) found evidence for economies of scale estimating a log-linear cost model of panel data of 509 delivery offices of Royal Mail operating in 2001 and 2002. In their paper, the authors emphasize the importance of treating the heterogeneity between delivery offices.

Bradley et al. (2006) built a structural model including delivery street time in a two step process and estimated a quadratic model of 145 delivery offices of U.S. Postal Service. They found evidence for both large scale and scope economies. Filippini and Zola (2005) estimated a

Cobb-Douglas cost frontier function for a small sample of post offices in Switzerland with combined collection and delivery processes and found empirical evidence for economies of scale.

Their results suggested that efficiency gains could have resulted from merging smaller post offices operating in the same or in a small adjacent service area. Farsi et al. (2006b) examined a subset of

327 delivery offices in Switzerland and have evidence for economies of scale, density and scope, especially for units in remote areas with low mail volume.

Apart from delivery, only a few studies are available on economies of scale and scope in postal services. Bradley and Colvin (1999) focused on mail sorting and estimated a multiproduct total cost function for 250 US sorting centers between 1988 and 1996. They found evidence for substantial economies of scale and enhanced productivity within the observed time span. The most recent investigations relevant for this study are those by Cazals et al. (2002) and Gazzei et al.

(2002) on economies of scale in postal collection. Cazals et al. (2002) applied a multiproduct log- log cost function to analyze a cross-sectional dataset consisting of 9’168 French post offices operating in the year 1999. The results of their empirical analysis provide evidence of the existence of economies of scale, at least for small- and medium-sized post offices. No estimation of economies of scope is provided because the deployed functional form impedes straightforward computation.

Gazzei et al. (2002) have implemented parametric (translog cost function) and non-parametric techniques to analyze a cross-sectional dataset consisting of 11’415 Italian post offices operating in the year 2000. They addressed the problem of unsaturation in post offices and its impact on the estimation of economies of scale. Their empirical analysis indicates the presence of economies of scale irrespective of the size of the offices. Table 2–1 recapitulates the most important studies on economies of scale and scope in the postal sector. 2.2 PREVIOUS STUDIES ON ECONOMIES OF SCALE AND SCOPE 33

Table 2–1: Relevant previous literature on economies of scale and scope in the postal sector

Authors Process Data Cost function Scale Scope Wada et al. (1997) delivery panel, m.p. translog *,**,*** n.c. Cohen and Chu (1997) delivery cross-s. m.p. quadratic *,**,*** n.c. Bradley and Colvin (1999) sorting panel, m.p. quadratic *,**,*** n.c. Cazals et al. (2002) collection cross-s.; m.p. log-log *,**,*** n.c. Gazzei et al. (2002) collection cross-s.; s.p. translog *,**,*** n.c. Mizutani and Uranishi (2003) delivery pooled; s.p. translog n.c. Cazals et al. (2005) delivery panel; s.p. log-log *,**,*** n.c. Filippini and Zola (2005) collection / delivery cross-s.; m.p. log-log *,**,*** n.c. Bradley et al. (2006) collection / delivery cross-s.; m.p. quadratic *,**,*** *,**,*** Farsi et al. (2006) delivery cross-s.; m.p. quadratic *,**,*** *,**,*** *,**,***: large, medium and small units; n.c.: not calculated; m.p.: multi-product; s.p.: single-product

In this paper, we raise the question of economies of scale and scope of Swiss Post’s collection network. Unlike earlier, when post office clerks conducted the processes of collection and delivery, both of these are now separated from each other organizationally and in most of the cases geographically. This restructuring measure was a trade-off between gaining economies of scale through merger of delivery bases and losing economies through vertical disintegration of the collection and delivery processes. The whole restructuring process was driven by the commissioning of new, more centralized sorting centers enabling the disentanglement of collection and delivery.

As depicted in Figure 2–1, the postal value chain can be segmented into the four main processes collection, sorting, transportation and delivery. The collection process includes collection of letters from letter drop boxes as well as collection of mail, financial consulting and sale activities at the post office.

Figure 2–1: The postal value chain: collection process

Collection Transport Sorting Transport Delivery (centralized) Letter Post Drop Office / Box Agency

Clients Consolidators

Source: own illustration. 34 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Generally, the reviewed studies present some limitations. First and most importantly, the issue of unobserved heterogeneity remains mainly undiscussed. Only Bradley and Colvin (1999) and Cazals et al. (2005) address this problem in the delivery process using panel data models, respectively, but none of the studies on the collection process takes a closer look on this issue. Se- cond, Gazzei et al. (2002) indeed allude to the problem of unsaturation12 in post office networks in their paper, but neither they nor other authors propose a satisfying solution to quantify the impact of unsaturation.

We therefore introduce these two points as main novelties into the discussion of economies of scale and scope in postal collection networks. First, Swiss Post’s collection units are characterized by considerable observed and, possibly, unobserved heterogeneity of the environmental and production situation. The unobserved part of the heterogeneity could cause biased estimators and, as a consequence, incorrect values for economies of scale and scope. In order to take this unobserved unit-specific heterogeneity into account, we apply a latent class model. Second, we include standby periods of opening time in the cost model specification. This variable will allow us to consider production process situations in which an office must remain open even if demand is zero.

Moreover, we control heteroskedasticity using a weighted least squares model. With these specifications, we expect more meaningful results than from crude approaches such as ordinary least squares.

2.3 COST MODEL SPECIFICATION AND ESTIMATION METHODS

Subsection 2.3.1 discusses the cost model specification with the parameters to be estimated.

Subsection 2.3.2 presents the most important functional forms in the literature together with the selection criteria in order to guarantee theoretical requirements.

2.3.1 Cost model specification

We specify a cost model that explains total costs of Swiss Post’s collection network with six aggregated output variables, one input variable, and two environmental characteristics. Under the assumption of cost-minimizing behavior of postal outlets and convex production technology, we write this model as follows:

12 This term describes situations, in which a post office must remain open even if demand is zero. 2.3 COST MODEL SPECIFICATION AND ESTIMATION METHODS 35

CfQQQQQQPdBMdRA (,123456 , , , , ,C , , ) (2–1),

where the dependent variable C represents total cost of a postal outlet. The first five outputs (Q1 –

Q5) are measured by the following parameters: letters, parcels, payment services, account management services, and sale of further products.

The sixth output, Q6, is the variable that represents standby periods during the opening time of these post offices. This variable allows us to account for situations in which a post office counter must remain open even if demand is zero. In these situations, the employees at the counters are not performing any specific tasks but are waiting to serve the next customers. Gazzei et al. (2002) classify this time as ‘unsaturation’ and point out that its presence causes misleading efficiency estimates and biased results for economies of scale. This (upward) bias arises due to the cost of unsaturation. In a saturated process, either costs are lower or outputs higher. Hence economies of scale in saturated processes are lower than in unsaturated processes. Standby time that causes this bias is not a priori a negative economic phenomenon such as inefficient organization or laziness of the employees, but it can be commercially optimal or politically desired. In the latter case, it might be set indirectly as a constraint by the universal service obligation regulations that require a comprehensive postal network.13 Consequently, the duty to operate such a network would imply a certain number of opening hours, even though the time absorbed by local demand might be lower.

Our analysis has shown that the share of standby time is negatively correlated with opening hours; hence, it is relatively large in post offices with short opening hours. Note that post offices with short opening hours are usually small ones located in rural areas. Hence, despite short opening hours, these post offices still exhibit relatively high standby times.

In short, standby time arises due to the difference in the time absorbed by local demand and the opening time. As argued above, the provision of long opening hours is a service that is indirectly politically desired. Consequently, standby time is to a large extent a result of political obligations. I therefore interpret, unlike previous authors, this seemingly unproductive time as an output in the form of a public service.14 A comparison might be drawn with emergency services char-

13 According to the Postal Regulator’s interpretation of the Swiss Postal Law (PG (1997) and PV (2004)), at least 90 percent of the population should be able to reach a post office within 20 minutes by foot or public transport. 14 Standby time as a public service is not a pure public good because it is characterized only by nonrivalry, but not by nonexcludability. Standby time might appear to be an input to provide the oth- 36 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

acterized by a considerable number of standby hours. The standby time of fire brigades, for example, is widely accepted as public service.

For comparability reasons, we estimate the same model with the quadratic cost function specified in Equation (2–2) (below) with the first five outputs (Q1 – Q5) and treat Q6 as a hedonic characteristic of every single observation instead of standby time.

PC is the price of capital, measured by the cost of physical capital. The price of labor was not included in the model because it is set by a collective labor agreement and therefore does not vary significantly among units and regions.

Swiss Post’s postal outlets differ considerably. Therefore, the dummy variables dBM (franchising business model, where the franchisees run a core business other than postal operations within the same infrastructure) and dRA (peripheral rural areas and alpine tourist center regions) are introduced in the model as environmental characteristics.15 For a complete description of the variables with the corresponding data see Section 2.4.

2.3.2 The choice of the functional form of the cost function

According to Jehle and Reny (2001), a proper cost function C(P,Q) should exhibit the following characteristics to conform with neoclassical microeconomic theory:16

1. Non-negative: C(P,Q) > 0 for all P > 0 and Q > 0.

2. Non-decreasing in input prices: C(P’,Q) ≥ C(P,Q) for P’ ≥ P.

3. Non-decreasing in outputs: C(P,Q’) ≥ C(P,Q) for Q’ > Q.

4. Linear homogeneous (homogeneous of degree one): C(tP,Q) = tC(P,Q) for t > 0.

5. Concave and continuous in P.

er outputs, but the other outputs are provided without standby time, which is an independent service derived from the input labor. In general, Elsenbast (1999) classifies postal universal services as mixed goods. 15 We are aware that the cost model specified in Equation (2–1) does not completely capture the heterogeneity that characterizes the production process in postal outlets. However, the specification of six outputs should reduce the potential unobserved heterogeneity bias. Additionally, we use econometric approaches that minimize the residual bias (see Subsection 2.5.1). 16 The same textbook offers a closer look on duality (a proper cost function contains the same information as a production function) and on Shephard’s Lemma (factor demand can be deduced from the estimated, twice differentiable proper cost function). 2.3 COST MODEL SPECIFICATION AND ESTIMATION METHODS 37

Current literature offers a wide variety of different functional forms to approximate the true, but unknown cost function.17 The choice of the functional form is therefore a delicate task that should be exercised with reasonable accuracy. According to Baumol et al. (1982), a functional form should meet the following properties in addition to the characteristics mentioned above:18

6. Substantial flexibility: the form of the cost function should be consistent with both econ-

omies of scale and scope as well as with super and subadditivity; hence it should exhibit

a flexible functional form and impose no restrictions on the values of the first and second

partial derivative.

7. Number of parameters: the cost function should not require estimation of values of an

excessive number of parameters.

8. Zero output values: the cost function should yield a reasonable cost figure for output vec-

tors that involves zero values of some outputs.

Table 2–2 recapitulates the most important algebraic functional forms and its characteristics.

The first algebraic functional forms were linear in parameters and had to be easy to estimate due to computational restrictions. Most of them were inflexible in the sense that they were first-order approximations to any arbitrary function. The best known empirical cost function of this class is the Cobb-Douglas, developed by Cobb and Douglas (1928) and still used in applied work. Compu- tational advances led to the use of more flexible functional forms as e.g. the quadratic (Lau (1974)), which is still popular because of its straightforward handling of zero values in multiproduct cost functions, the transcendental logarithmic (translog, Christensen et al. (1973)), the generalized Le- ontief (Diewert (1971)), and the composite cost function, a composed form for multiproduct firms as a special case of the generalized Box-Cox (both Pulley and Braunstein (1992)). These functional forms are locally flexible in the sense that they provide second-order local Taylor- approximations to any arbitrary, twice differentiable cost function. Most of these cost functions have been developed over the years, so that many derivative cost functions exist. For instance, the quadratic has been developed further to the flexible fixed cost quadratic (Mayo (1984), Panzar

(1989)) to adapt different fixed cost using dummy variables or to the normalized quadratic, used by Jara-Diaz et al. (2003). Development of the translog are the generalized translog (Caves et al.

17 Kuenzle (2005) provides a comprehensive discussion on the most important empirical cost functions with their characteristics. 18 Lau (1986) provides a comprehensive discussion on the requirements of functional forms. 38 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

(1980)), where only zero values are transformed using Box-Cox transformations or the hybrid translog, where outputs are not logarithmic to allow for zero values, used by Eakin et al. (1990).

The generalized Leontief was refined to a version of Diewert and Wales (1987) to impose linearity and to the hybrid Diewert joint cost function (Hall (1973)).

As a main drawback, locally flexible functions can impose large errors moving away from the approximation point. Therefore, Gallant (1981; 1984) introduced the Fourier flexible form to achieve global approximation. His idea was to use a Fourier series to approximate the true function in the so-called Sobolev-norm, which is a generalization of the quadratic norm. Therefore, the

Fourier form consists of two parts, the first being the usual translog, while the second is a nonparametric Fourier-expansion. However, higher flexibility comes at the cost of higher information, as it requires more parameters to estimate. Hence, it reduces degrees of freedom and gives rise to multicollinearity. As these are serious problems in applied work, higher flexibility is therefore oftentimes renounced.

As noted, a proper cost function should exhibit the characteristics mentioned above. The characteristics one to three (non-negative, non-decreasing in input prices and outputs) can be easily verified ex-post with the estimation results, and characteristic five requires a negative semi- definite Hessian matrix. Whether the cost function complies with the remaining four characteristics (linear homogeneity, substantial flexibility, number of parameters and zero output values), can be checked with Table 2–2 below.

Table 2–2: Comparison of the most important functional forms

Linear Flexi- Number of Zero Name Functional from homo- Further comments and critique bility parameters outputs geneity Cobb PM Constant returns to scale and elasticities of lnCPQ ( , ) ln P   ln Q yes* no α 0 , γ p , β m no Douglas 0 p pmm substitution; linearly homogenous if ? γ=1 . pm11 MMM 1 α 0 , β m , CQ()0 mm Q   mnmn QQ no local yes Input prices not included mmn1112 β mn PPP1 Quadratic CPQ(, ) P   PP 0 pp pqpq α 0 , γ p , ppq1112 Symmetry restrictions: γ pq =γ qp , β mn =β nm , MMMPM yes* local γ pq , β m , yes 11  λ pm =λ mp mmQQQPQ mnmn  pmpm β mn, λpm mmnpm1111122 PPP1 lnCPQ ( , ) ln  P  ln P ln P Generalization of Cobb-Douglas; 0 pp pqpq α0 , γ p , ppq1112 corresponds to generalized Box-Cox with Translog yes* local γ , β , no MMMPM11  pq m ?=0 , τ=1 , and π=0 ; symmetry restrictions: mmlnQQQPQ mnmn ln ln  pmpm ln ln β mn, λpm  γ pq =γ qp , β mn =β nm , λ pm =λ mp mmnpm1111122 0.5 PP Locally flexible if h(·) known; single output; CPQ(, ) hQ pq PP p q yes no γ pq yes Generalized pq11 symmetry restriction: γ pq =γ qp >0 Leontief PP0.5 P PM 2 γ pq , γ p , Single output; symmetry restrictions: CPQ(, ) Qpq PP p q p P p mm pm P p Q m yes local yes    γ =γ >0 , β =β , λ =λ pq11 p  1 pm  11 β mn , λ pm pq qp mn nm pm mp ()  MMMMP ()  ()11 () () () α0 , α m , Non-linear estimation procedure; CQP(,) exp0 m Q m  mn QQ m n  mp QP m p 22 α mn , λ mp , Box-Cox transformation in brackets: Generalized  mmnmp11111 yes local β , β , yes (?) ? () 0 p C (Q,P):=(C -1)/? for ??0 and lnC for Box-Cox PPPMP   11()  β pq , γ mp , ?=0 by application of de l'Hopital's rule ; *exp0 pp lnPPPQP pqp ln ln q  mpmp ln   ?, τ, π all other transformations apply accordingly ppqmp1111122 MMMMP ()  '11 ' ' ' α 0 , α m , CQP(,)0 mm Q    mnmn QQ  mpmp QP 22 α mn , λ mp , Non-linear estimation procedure; Composite mmnmp11111 () yes local β 0 , β p , yes corresponds to generalized Box-Cox with cost function  PPPMP    11'  β pq , γ mp , τ=1, π=0 and Q'= Q - 1 *exp 0 pp lnPPPQP pqp ln ln q  mpmp ln  22  ppqmp11111   ? Fourier translog in combination with fourier expansion yes global more no High number of parameters to estimate flexible * Linear homogeneity implies for any t>0 : C(tP,Q)=tC(P,Q) . Therefore, to impose linear homogeneity, set one of the inputs, say P , t=1/P . Then one obtains C(P,Q)/P =C(P/P ,Q). 1 1 1 1 40 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

For the estimation of the cost model specified in Equation (2–1), we apply a quadratic functional form as it is locally flexible, straightforward to estimate and as it has the advantage of being able to take zero values into account.19 As Section 2.4 will show, zero outputs occur in about one third of all observations for payment and/or account management services in agencies and in small post offices. The quadratic cost function was widely used by previous studies on economies of scale and scope in network industries, for example in Baumol et al. (1982), Jara-Diaz et al. (2003) or Farsi et al. (2007). In the non-homothetic form,20 it can be written as:

MM1 MM CQQQQQ     i0  m mi2 mm mi mi  mn mi ni mm11 mnm  1 (2–2), 1 M   PPPPQdBMdRA PCiCCC PPCiCi mCimi12 i i i 2 m1

where subscript i denotes postal outlet i = 1, 2, ..., I. εi is the error term and subscripts m and n are product indices. As the quadratic function is a second order Taylor-approximation, the values of the explanatory variables must be normalized to the approximation point. For this purpose, we chose the median value of the variables.21

19 Other functional forms such as Cobb-Douglas or translog require adjustments, for instance through a Box-Cox transformation, because logarithms are not defined for non-positive arguments (see Box and Cox (1964)). In combination with the latent class model, such (non-linear) transformations might cause problems that lie far beyond the scope of this paper. As an alternative, the zero values could be replaced with small values for example 0.00001 (small value transformation). But according to some authors (e.g. Pulley and Braunstein (1992) or Pulley and Humphrey (1993)), this transformation may lead to strongly biased results for economies of scope. Further alternatives are non-linear econometric approaches such as e.g. the composite cost function of Pulley and Braunstein (1992). 20 A cost function is non-homothetic, if input prices depend on output levels, hence if input prices and output levels are not separable. In contrast, a homothetic cost function is separable in the sense:

C(P,Q) = h(Q)c(P). Further properties of the quadratic functional form: symmetry (βmn = βnm), posi-

tivity (βm ≥ 0) and non-linearity in input prices. Linearity (linear homogeneity) in input prices (C(tP,Q) = tC(P,Q) for any t > 0) cannot be imposed by parametric restrictions without scarifying the flexibility of the quadratic functional form (Caves et al. (1980)). 21 The median value is better suited as an approximation point than the mean value, as it is less affected by outliers. 2.4 DATA 41

2.4 DATA

This study is based on a cross-sectional dataset of the year 2006 with information on 2,466 postal outlets, which is more than 99 percent of all postal outlets operating in Switzerland.22 These outlets consist of two groups according to their business model. The major part, namely 2’348 common post offices, is run by Swiss Post, whereas 118 agencies are run by franchisees.23 The variable for the business model (dBM) takes the value 1 for agencies, and 0 for common post offices. Approximately one-fifth of the post offices and one-third of the agencies are located in peripheral rural areas and alpine tourist center regions. These outlets are indicated by the value 1 of the corresponding dummy variable dRA. The reference region takes the value 0 and consists of urban areas and extended agglomerations.24 Figure 2–2 gives an overview of the 2,466 post offices and agencies considered in this paper. Obviously, these two business models are unequally distributed among the country.

22 This is an updated version of the data used by Jaag et al. (2009). We had to exclude four of the post offices and seven of the agencies due to missing values for total costs. Four more post offices turned out to be severe outliers with a Cook’s Distance (Cook (1977)) exceeding the mean by a factor of more than 300. We excluded them as well. 23 ‘Agency’ is a generic term for different types of franchisee models; most of the franchisees run gro- cery stores or other retail businesses. 24 Classification implemented by the Federal Office of Statistics (2009). The other data were provided by Swiss Post. 42 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Figure 2–2: Post offices and agencies considered in this paper

Data source: Federal Office of Statistics (2008b), Federal Office of Topography (2011) and Swiss Post, own illustration.

Note: Post offices are marked in blue and agencies in red.

The postal outlets cover a wide range of costs and outputs. Total costs (C) include all fixed costs such as capital costs or rental fees, and all variable costs such as labor cost or costs originating from counter activities. Total costs vary by a factor of more than one thousand among the postal outlets. All of these outlets collect letters and parcels and sell further products, whereas zero outputs may occur for payment and account management services in agencies and small post offices. These first four outputs are weighted sums of different subproducts of the corresponding output. We use the internal standards of performance as the weighting factor. As all postal outlets must comply with the same internal quality guidelines and principles, we assume comparable quality levels for all units.

Letter output (Q1) is a generic term for regular, express and registered letters including single piece and mass mail. It is calculated as the weighted sum of thousand letter items collected.

Parcel output (Q2) is also measured in thousands, but incorporates more diverse products. Due to the similar nature of the processes involved, the weighted number of either single or bulk parcels collected is added to the weighted number of items picked up at the postal outlets by the clients.

The output of payment services (Q3) is measured in million Swiss Francs transacted and can be 2.4 DATA 43

understood analogously.25 The weighted volume of incoming payments is added to the weighted volume of outpayments. The fourth output, account management services (Q4), is the weighted number of thousand account openings (closings) and the weighted number of related consulting services. The fifth output, sale of further products (Q5), is measured by sales volumes of postage and further products such as mobile phones, prepaid cards, tickets or stationery, measured in thousand Swiss Francs.

The variable representing standby time (Q6) is an important cost driver at least for smaller post offices, measured in hours. This variable allows us to consider production process situations in which a post office counter must remain open even if local demand is zero. As standby time is neither directly observable nor measurable, we derived it in the following way:

M Qtmi m m1 Standby time OHi (2–3), ni

hence we multiplied the standard performance value tm necessary to completely operate one item or transaction m with the corresponding number of items or transactions Qm occurring in a postal outlet and added it up.26 We divided this value by the number of active counters n and subtracted the result from the opening hours OH. In the case of zero demand we assume that all counters close down except for one. Hence, we assume that at most one employee is confronted with standby time at the same time.27 For the reasons provided in Section 2.3, we interpret standby time as public service and hence as output. It takes the value 0 in post offices working at full capacity and in all agencies because neither is confronted with unsaturated processes (time not spent on servicing postal customers would presumably be absorbed by complementary activities of the core business). The share of standby time is negatively correlated with OH and positively with dRA.

25 Alternatively, payment services could be measured by the number of transactions or by the number of customers doing transactions instead of by the volume transacted. However, the volume transacted reflects the fact that higher volumes induce more capacious anti-money-laundering inquiries and safety measures. 26 The standard performance values are equal for all post offices, irrespectively of size and technology, since Swiss Post does not distinguish. We are aware that this might cause biased values for standby time. 27 This is of course a strong assumption for very short periods of zero demand, but it certainly holds during off-peak hours. 44 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

The cost of physical capital (PC) is measured by the rental fee per square meter (ratio of the rental fee and rented surface area). These costs are, as expected, clearly higher in urban areas and agglomerations than in rural areas.

2.5 ECONOMETRIC APPROACHES

The estimation of the quadratic cost function specified in Equation (2–2) can be complicated by at least two econometric problems, that is unobserved unit-specific heterogeneity across postal units and heteroskedasticity. Subsections 2.5.1 and 2.5.2 discuss these problems and their solutions using a latent class model and different specifications of the error terms, respectively.

2.5.1 Unobserved heterogeneity

We anticipate unobserved unit-specific heterogeneity across the postal outlets, for example originated by other output or environmental characteristics that are not included in the model. It is further conceivable that operational procedure differs among various units because they might use different technical equipment or serve more high-volume customers in relative terms. Such unobserved factors could influence the marginal effects of the observed variables and therefore affect the estimates of economies of scale and scope.

These possible effects can be taken into account with common approaches like random effects or random coefficients models, if panel data are available. With cross-sectional data, however, other methods such as clustering, latent class estimation or quantile regression techniques are suited to capture unit-specific effects.28,29 Latent class analysis, originally introduced by Lazarsfeld and Henry (1968), is a stochastic procedure for identifying distinctive class membership among subjects regarding their cost structure and estimating a separate cost function for each of these categories simultaneously. This technique has lately been applied in different fields of science and

28 Quantile regression, originally introduced by Koenker and Basset (1978), is actually well suited to capture unobserved heterogeneity. It has also been used to calculate economies of scale and scope, for example by Christensen (2004). But disadvantageously, the coefficients have to be estimated sep- arately for every quantile. The resulting economies of scale and scope are therefore not comparable to economies of scale and scope calculated from coefficients effective for the entire dataset. 29 For results on a supplemental quantile regression analysis without comments, see Table 2–8 to Table 2–10 in the Appendix. 2.5 ECONOMETRIC APPROACHES 45

industry sectors.30 Latent class estimation involves maximizing a log-likelihood function and out- plays many of the cluster analysis methods because no decisions about the scaling of mixed measurement levels are necessary. Furthermore, rigorous statistical tests and diagnostic statistics such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) are included in the model setting to estimate the optimal number of classes.

The primary problem of latent class models is that their estimation requires a large number of parameters. The current latent class model specified in Equation (2–4) contains 37 independent variables and one constant per class. This might cause severe numerical problems maximizing the likelihood function with increasing number of classes and uses a taxing number of degrees of freedom. The higher the expected unit-specific heterogeneity among postal outlets, the higher the required number of classes. With a sufficiently large number of classes, the model approximates a full random-parameters model (Greene (2008)). The estimation of a homothetic model could solve the problem, as the number of parameters is less. However, separability of the cost function is a strong assumption in the actual case31 such that the results of homothetic models might differ severely from non-homothetic models.

We therefore estimate a non-homothetic latent class model using the cost model specified in

Equation (2–1) with the quadratic cost function specified in Equation (2–2) for each class j in J:

MM1 MM C Q   QQ   QQ i0 i mi mi2 mmi mi mi  mni mi ni mm mmnn() (2–4). 1 M  PPPPQdBMdRA     PCCCi Ci P P i Ci Ci mi Ci mi12 i i i i i 2 m

The subscript i in the quadratic functional form specified in Equation (2–4) for the latent

2 class model denotes the postal outlets and ii N(0, ) . i , i ,  i , i , i and  i are discrete random parameters identified in j = 1, 2, …, J classes, endowing each observation with the class-

30 For example in the banking industry (Orea and Khumbhakar (2004), Greene (2005b)), in the energy sector (Cullmann (2010)) or in agriculture (Corral et al. (2009)). The book Applied Latent Class Analysis, edited by Hagenaars and McCutcheon (2002), shows further applications of latent class models in marketing, psychology and other social sciences. 31 Especially outputs that are not covered by the Universal Service Obligation, for instance account management or the sale of further products are not independent of the location hence not of the capital price of a post office as there is competition for banking services and retail goods. 46 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

specific characteristics. These random parameters are distributed among the classes by the following rule:

{iiiiii,,,,,} = { jjjjjj,,,,,} with probability p j and  p j 1 (2–5). j1

Hence, each observation belongs to class J with a certain probability pj, which has been obtained using Bayes Theorem. For estimation, the number of classes J is assumed to be known, but, as the ongoing discussion in literature shows, there is no reason to expect this (Greene (2008)). A likelihood ratio test could in principle be used to test a model with J classes against one with J–1 classes, but the accurate number of degrees of freedom remains unclear. J is, therefore, typically chosen on the basis of diagnostic criteria as the AIC or the BIC. The smaller these statistics, the more likely is the corresponding model.32

2.5.2 Heteroskedasticity

As expected, a preliminary econometric analysis showed that the data is affected by heteroskedasticity. We expected heteroskedasticity due to a wide range of costs and outputs between ‘small’ and ‘large’ postal outlets (see Section 2.4). In order to account for this problem, an advanced econometric specification of the error term have been considered and compared to the ordinary least squares (OLS) model. The weighted least squares (WLS) model is a version of a robust regression, where variances of the error terms are calculated in an iteratively accomplished process and assumed to be proportional to the square of the dependent variable. The process starts with the variance predicted by the OLS model and stops when changes in the variances fall below a certain limit. The specifications of the error terms of these two models can be summarized as follows:33

32 These statistics are the values of -2*ln(likelihood) corrected by 2*M for the AIC and M*log(N) for the BIC, respectively, where M denotes the number of parameters and N the number of observations. 33 In a preliminary stage of the analysis, we additionally inspected a third, multiplicative heteroscedastic regression model, where the variances of the error terms are assumed to be an exponential function of 6 22 2 the outputs (QQ16 :iiimmi iid (0, ), exp( Q )) . Unfortunately, the standby time (Q6) m1 caused prohibitive effects to the variance, as it is relatively long in very small post offices. 2.6 RESULTS 47

OLS model: iid(0,2 ) i (2–6). 222iterativelyweighted 2 WLS model:iiii iid(0, ), ( C )

The latent class model is estimated using heteroskedasticity-robust standard errors (see

White (1980)). These specifications allow a better comparability of the outcomes of the two models concerning unobserved heterogeneity.

2.6 RESULTS

This section shows the regression results of the two basic models (OLS and WLS) and of the latent class model as well as considerations to the distribution of the class memberships of the latent class model in Subsection 2.6.1 and the corresponding values for economies of scale and scope in Subsection 2.6.2.

2.6.1 Regression results and classification of the sample

We first throw light on the regression results of the two basic models (OLS and WLS) and of the latent class model with two classes, listed in Table 2–3. 48 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–3: Regression results

OLS WLS Latent Class (classes 1 and 2) VariableCoefficient (SE) Coefficient (SE) Coefficient (SE) Coefficient (SE)

Letter output (Q 1 ) 1'081 *** (56.14) 1'290 *** (34.04) 1'465 *** (103.2) 1'003 *** (43.85)

Parcel output (Q 2 ) 15'781 *** (1190) 14'073 *** (723.1) 8'307 ** (3381) 20'653 *** (856.7)

Payment services (Q 3 ) 3'689 *** (162.2) 2'776 *** (98.24) 3'372 *** (354.5) 2'674 *** (107.1)

Account mgmt (Q 4 ) 263'643 *** (46023) 330'065 *** (28068) 482'166 *** (102604) 230'989 *** (28683)

Further sales (Q 5 ) 361.864 *** (79.67) 458.407 *** (48.3) 423.533 ** (208.4) 378.957 *** (53.39)

Standby time (Q 6 ) 162.346 *** (18.18) 147.879 *** (11.05) 118.418 * (62.99) 130.328 *** (12.11)

Price capital (P C ) 1'206.521 * (684.9) 2'398.950 *** (415.1) -2'452.424 (2490) 2'562.538 *** (446.1)

(Q 1 Q 1 ) -0.284 *** (0.028) -0.137 *** (0.017) -0.763 *** (0.138) -0.186 *** (0.026)

(Q 2 Q 2 ) 270.193 *** (59.37) 370.084 *** (35.97) 71.873 (189.1) -422.570 *** (74.48)

(Q 3 Q 3 ) -2.225 ** (1.116) 2.947 *** (0.702) -7.519 *** (2.51) 1.053 (0.966)

(Q 4 Q 4 ) 166'741 *** (49260) 72'800 * (42261) -348'950 ** (148525) -153'969 *** (35230)

(Q 5 Q 5 ) -0.165 (0.411) 0.062 (0.25) 0.813 (1.037) -1.159 *** (0.308)

(Q 6 Q 6 ) -0.055 (0.054) 0.002 (0.033) -0.042 (0.161) -0.010 (0.037)

(Q 1 Q 2 ) -7.173 *** (1.304) -17.260 *** (0.791) 0.869 (4.799) -8.743 *** (1.506)

(Q 1 Q 3 ) -0.066 (0.213) -0.933 *** (0.129) -0.613 (0.44) 2.028 *** (0.171)

(Q 1 Q 4 ) 101.108 ** (49.52) -157.718 *** (30.04) 100.279 (91.1) -143.249 *** (53.51)

(Q 1 Q 5 ) 0.538 *** (0.167) 2.313 *** (0.101) 0.663 ** (0.336) 0.032 (0.144)

(Q 1 Q 6 ) 0.255 *** (0.087) 0.493 *** (0.053) 0.144 (0.168) 0.211 *** (0.065)

(Q 2 Q 3 ) -29.226 *** (7.641) 24.566 *** (4.645) 6.760 (17.11) 36.581 *** (6.799)

(Q 2 Q 4 ) -2'571.837 (1867) -2'227.768 * (1151) 1'499.923 (3927) -4'587.311 ** (1917)

(Q 2 Q 5 ) -3.248 (4.949) -39.607 *** (2.999) -28.384 *** (10.23) -10.776 ** (4.703)

(Q 2 Q 6 ) 2.162 (1.676) -5.662 *** (1.015) 8.723 ** (3.899) -8.893 *** (1.257)

(Q 3 Q 4 ) 664.912 *** (184.1) 766.183 *** (133) 1'769.239 *** (510.7) -889.885 *** (175.1)

(Q 3 Q 5 ) 2.448 *** (0.542) -1.726 *** (0.33) 3.706 *** (0.997) -4.716 *** (0.443)

(Q 3 Q 6 ) -0.473 ** (0.198) 0.216 * (0.12) -0.219 (0.441) 0.091 (0.149)

(Q 4 Q 5 ) -591.450 *** (142.1) 24.648 (87.56) -673.928 *** (258.3) 2'061.495 *** (129.5)

(Q 4 Q 6 ) 114.372 ** (49.72) 141.790 *** (30.15) 112.909 (107.6) 194.126 *** (39.47)

(Q 5 Q 6 ) 0.168 (0.12) 0.103 (0.073) -0.238 (0.275) 0.267 *** (0.09)

(P C P C ) -75.603 (67.5) 75.375 * (41.01) 82.441 (132.3) 101.775 ** (48.99)

(P C Q 1 ) 4.404 ** (2.095) 4.118 *** (1.272) 22.617 *** (4.742) -17.846 *** (1.811)

(P C Q 2 ) 317.738 *** (70.2) 193.145 *** (42.53) 224.946 * (123.9) 319.082 *** (58.47)

(P C Q 3 ) -18.072 ** (7.805) -54.306 *** (4.736) -42.283 *** (14.93) 60.766 *** (5.213)

(P C Q 4 ) -3'873.413 ** (1919) -940.279 (1163) -5'287.129 (3912) -195.553 (1347)

(P C Q 5 ) -1.629 (4.26) 19.047 *** (2.583) -5.085 (7.731) -5.442 ** (2.571)

(P C Q 6 ) 7.089 *** (1.309) 2.528 *** (0.793) 9.506 ** (3.903) 2.361 *** (0.9) Business model (dBM ) -88'620 *** (22906) -82'305 *** (13888) -166'146 ** (72677) -60'071 *** (17774) Region (dRA) 61'920 *** (13548) 30'339 *** (8208) 187'400 *** (46158) 17'337 * (9454) Constant 715'180 *** (6912) 706'515 *** (4195) 750'465 *** (31734) 715'141 *** (4953) Sigma 259'649 *** (6476) 90'167 *** (2345) ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets; values not in CHF. n = 2'466

2.6 RESULTS 49

Irrespective of the model, the entire first and most of the second-order coefficients of the output variables have the expected sign and are highly significant. In particular, the values for the standby time confirm the expectation that unsaturated processes occur and increase cost substan- tially. The input price of capital shows that part of the differences among postal outlets can be explained by higher capital costs. Further, the coefficients for the business model and the region leave no doubt: firstly, agencies generate considerable cost reductions compared to common post offices, and secondly, postal outlets in sparsely populated and touristic regions increase costs.

As expected, the results of the OLS model differ strongly from the WLS model. These differences suggest that ignoring heteroskedasticity may cause bias in the calculation of economies of scale and scope. Therefore, the WLS model is more relevant for the empirical analysis of the economies of scale and scope. Nevertheless, we use both of them to compute the economies of scale and scope at the approximation point (sample median) and at the quartiles in the sample to shed light on the impact of the magnitude and the composition of the output.34

To test the hypothesis if postal outlets in Switzerland operate with different methods, we estimate a latent class model. Within this framework we allow post offices to have different underlying methods or even production technologies, caused by unobserved factors or variations in customer structure. Estimating a latent class model requires an à priori determination of the number of classes (see Subsection 2.5.1). Applying the AIC, the empirical analysis with two up to four classes favors the definition of two classes, as the maximum likelihood estimation with three and four classes did not converge to meaningful solutions. Two classes are appropriate to test the hypothesis of unobserved heterogeneity for smaller and larger postal outlets. The estimation results of the two classes support this hypothesis, as most of the variables differ significantly in terms of level and significance.

The prior class probabilities in Table 2–4 show a latent sorting of the postal outlets into the classes with just under one third (31 percent) belonging to the first and the remaining (69 percent) to the second class. With little exceptions, which are all located in urban areas, agencies belong to the second class whereas post shops (integrated stores, mostly in intra-urban post offices) occur disproportionately often in the first class.

34 Taking into account the experiences from other studies, the levels of the variables listed in Table 2–5 and Table 2–6 should be treated with caution because of the lack of panel data. 50 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–4: Prior class probabilities

p (class) (se) n dBM dRA dBM & dRA P-Shop Class 1 0.311 *** (0.018) 375 8 35 0 37 Class 2 0.689 *** (0.018) 2'091 110 274 38 39 1.000 2'466 118 309 38 76 ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets.

To gain deeper insights into the characterization of both classes, we compare important economic and physical data. Figure 2–3 shows the box plots for total costs and the outputs of both classes, normalized to the median of the respective variables in the second class. We can derive one clear trend: class 1 incorporates larger post offices with considerably higher costs and outputs; class 2 seems to include smaller post offices and agencies. Especially, the demand of cost- intensive and complex services subsumed under “account management” is higher, its median value triples in class 1 compared to class 2, and even the difference in the sale of further products is obvious. Only the output standby time does not correspond to this pattern as it is smaller in class 1 than in class 2. However, this observation is in line with our argumentation in Section 2.4 where we stated that the share of standby time is negatively correlated with opening hours, hence that larger offices have relatively low standby time.

Figure 2–3: Box plots of important characteristics in latent classes 1 and 2

values normalized to the median of the respective variable in latent class 2

grey: latent class 1 white: latent class 2

outside values excluded

total letter parcel payments account optional standby capital cost mgmt products time price

Source: own illustration. 2.6 RESULTS 51

To summarize, the post offices in class 1 can be characterized as larger concerning total costs, volume and opening hours than post offices in class 2, and they further exhibit a higher share of post shops and a lower share of agencies, whereas the standby time of post offices in class 2 is superior. Hence, class 1 subsumes large and class 2 small postal outlets. In Subsec- tion 2.6.2, we will test if economies of scale and scope differ significantly between these two classes.

2.6.2 Results for economies of scale and scope

The results of the econometric estimation of the quadratic cost function specified in Equa- tion (2–2) can be used to compute economies of scale and scope.

The concept of economies of scale investigates whether or not a company operates at an economically reasonable size. Economies of scale are measured by the ratio between average and marginal costs, and the optimal size of a unit is reached if this ratio equals unity. In the presence of

(dis)economies of scale, ray average costs increase (decrease) when all outputs increase propor- tionately. In such a situation, postal outlets would be oversized (undersized).

The concept of economies of scope examines whether or not a company operates with an optimal product mix. If (dis)economies of scope are present between the different products and services offered in postal outlets, it is advantageous to offer them jointly in the same unit (sepa- rately in different units). Economies of scope can arise from two sources: first, the spreading of fixed costs over an expanded product mix (e.g. the sale of further products in the same infrastructure as the collection of letters and parcels), and second, cost complementarities among product categories in production (e.g. the provision of payment services reduces the cost to provide account management services, as the first is often conditioned on having an account at Swiss Post).35

Widely used definitions of economies of scale and scope of multi-output companies go back to Baumol et al. (1982). According to these definitions, the values of (global) economies of scale can be computed as follows:

35 Pulley and Humphrey (1993) have expounded different functional forms distinguishing between these two sources. Disadvantageously with the quadratic functional form, fixed cost and cost complementarities are not distinguishable. Therefore, economies of scope are quite sensitive to the constant and have to be interpreted with caution. An alternative specification when having single-output outlets in the sample would be a flexible fixed cost model, which includes several intercepts depending on the outlet’s output combination, suggested by Mayo (1984) and Panzar (1989). 52 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

C Economies of scale  i (2–7), M Ci Qmi m1 Qmi

C where  denotes the partial derivative operator and, hence, i the marginal cost of output m. Qmi

Accordingly, the values of (global) economies of scope are given by:

M CQimi( ,0,0,0,0,0) CQQQQQQ i (123456 iiiiii , , , , , ) Economies of scope  m1 (2–8), CQQQQQQiiiiiii(,123456 , , , , )

where Ci(Qmi,0,0,0,0,0) represents the cost of specialized and Ci(Q1i,Q2i,Q3i,Q4i,Q5i,Q6i) of integrated postal outlets. Note that none of the outlets in our sample is highly specialized such that it only produces one of the six outputs. However, as Pulley and Braunstein (1992) argue, measuring economies of scope requires estimating the cost function at points with some empirical support, hence simulating situations really occurring in the data. Consequently, they suggest the estimation of quasi economies of scope, where firm specialization is imperfect, as it stands for producing basi- cally one output and the others to a very small extent μ.36 Nevertheless, we focused on economies of scope as proposed by Baumol et al. (1982) for two reasons: firstly, partially specialized postal outlets with at least some of the outputs being zero occur in the sample, and secondly, previous analysis has shown that the differences between the two methods are marginal.37,38

36 To simulate such situations, they extended the formula for economies of scope in the following way:

M CQ(mi ,(1(1))) M Q mi  CQQQQQQ (,,,,,)123456 i i i i i i Quasi economies of scope  m1 . Thus, μ must be CQ(,123456iiiiii Q , Q , Q , Q , Q ) smaller than 1/M to achieve post office specialization. 37 For results of this previous analysis of quasi economies of scope without comments, see Table 2–11 and Table 2–12 in the Appendix. We choose μ = 0.05, which seems to be reasonable with 1/M = 0.167. 38 Caves et al. (1984) propose a refinement of the analysis of economies of scale in network industries. A variable representing the density of the network is used to distinguish between economies that stem from expanding the outputs and the network size by the same factor (economies of scale) and those that stem from expanding the output in the existing network (economies of density). This differentiation is of no relevance in the case of postal collection networks, because unlike letter and parcel delivery, railways or energy distribution, only the nodes of the network cause costs, the network itself is of a virtual nature. 2.6 RESULTS 53

The results of the economies of scale and scope are provided in Table 2–5 and Table 2–6.

We distinguish between economies stemming from simulation and from sample data. In the first four lines of each model, we depict the values of economies of scale and scope for simulated postal outlets with all outputs set at the sample median and the sample mean at the first or third quartiles, respectively. Of course, a unit exhibiting exactly these values might hardly or merely coinci- dentally exist in the data, but representative points are best suited for comparison reasons. As an exception, the values for Q6 (standby time) are set at the sample median throughout all representative points. The standard errors for the latent class model were not computed due to calculation restrictions on the one hand and due to uncertainties on interdependencies between the two classes on the other.39 The four subsequent lines belong to representative postal outlets in the sample, sep- arately for post offices in urban and rural regions, for agencies and for all of the postal outlets existing in the data set. As these are mean values of the economies of each observation, standard errors do not exist.

39 The standard errors have been calculated using the delta method: se(SC) = ((Avar(SC))*n-1)-0.5, where Avar(SC) = [δSC/δβ]’[VCE(β)][ δSC/δβ] with [δSC/δβ] as a #p×1 and [VCE(β)] as a #p×#p matrix. For more details on the delta method, see Hayashi (2000). For the latent class model the number of parameters and hence the number of partial derivatives to be calculated (#p = 79 for the model with two classes) is prohibitive for a sensible estimation of the errors using the available software. Besides that, one has to decide whether the classes should be considered as independent from each other or not. On the one hand, if so, only the second and the fourth quadrant of the VCE(β) with all the variances and the intra-class covariances should be considered, i.e. the inter-class covariances in the first and third quadrant are assumed to be zero. This is a very strong assumption and might entail misleading results. On the other hand, if the classes are considered as dependent, the standard errors of one class are affected by the parameters, variances and covariances of both classes to the same degree, which might be wrong, too. As the assumption on the dependence of the two classes is arbitrary, we did not calculate the standard errors for the economies of scale and scope of the latent classes. 54 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–5: Economies of scale (OLS-, WLS-, and LC-model)

Economies of Scale OLS WLS WLS Latent Class 5 Outputs Class 1 Class 2 1.018 *** 1.020 *** 1.098 *** 1.037 *** 1.120 *** 1st quartile, post office (0.008) (0.005) (0.005) (n.c) (n.c) 1.001 *** 1.030 *** 1.333 *** (1.163) *** 1.107 *** Median, post office (0.043) (0.027) (0.020) (n.c) (n.c)

rd 1.278 *** 1.190 *** 1.608 *** (1.578) *** 1.163 ***

Simulation 3 quartile, post office (0.074) (0.038) (0.042) (n.c) (n.c) 1.043 *** 1.048 *** 1.102 *** 1.071 *** 1.079 *** Mean, post office (0.010) (0.006) (0.005) (n.c) (n.c) Mean, post offices urban 1.085 *** 1.115 *** 1.286 *** 1.270 *** 1.228 *** Mean, post offices rural 1.292 *** 1.349 *** 1.924 *** (1.481) *** 1.257 ***

Sample Mean, agencies 1.815 *** 0.981 *** 0.981 *** (1.692) *** 1.114 *** Mean, all postal outlets 1.143 *** 1.140 *** 1.372 *** 1.299 *** 1.220 *** ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets, n. c.: not calculated. Several values of latent class 1 are given in brackets as hardly offices of this size or type occurs in the data. n = 2'466

These results suggest that the postal outlet network in Switzerland is considerably affected by unexploited economies of scale, irrespective of the model, of the number of outputs or of the simulated and sample outlets.

The results for the simulated offices show for the heteroskedasticity-corrected WLS model that economies of scale increase with falling outputs and therefore with smaller post offices, even though we did not vary the magnitude of the standby time. Therefore, this finding is more pronounced in the same model with five outputs, as the share of standby time is negatively correlated with opening hours and hence with the size of an office. In other words, the difference between five and six outputs is highest in smaller offices (simulated in the third quartile) as these offices are most affected by standby time. The two latent classes display a different pattern: economies of scale of the first class increases fast, whereas it is almost stable in class 2. However, the median and third quartile offices in class 1 get hardly empirical support in real data and are put in brackets, as most of them are large. Therefore, only the value of the first quartile is representative for post offices in class 1.40 Interestingly, simulated offices with mean values exhibit similar values for economies of scale, irrespective of the model.

40 The results of the latent class analysis argue for a supplemental quantile regression analysis. Due to the lack of comparability (see Subsection 2.5.1), we dispense with it. For results on a supplemental quantile regression analysis without comments, see Table 2–8 to Table 2–10 in the Appendix. 2.6 RESULTS 55

The results for the sample offices show that rural offices are more affected by unexploited economies of scale than the ones located in urban and suburban regions. The mean value of the agencies in the WLS model is the only one that falls below one and is of the same magnitude for five and six outputs because agencies do not exhibit standby time. In general, sample mean values must be interpreted with caution, especially for agencies, as they are strongly influenced by outliers. For example, only eight out of the 118 agencies and 35 of the rural post offices are in class 1

(see Table 2–4). Again, as in the simulated case, these values are put into brackets.

The overall findings on economies of scale are well authenticated through the scatter plots of the WLS model for every post office in the sample with five and six outputs (see Figure 2–4 in the appendix, scatter plots on the left hand side). The postal outlet network in Switzerland is considerably affected by unexploited economies of scale and the smaller the office (approximated through the regulator’s ranking), the higher the value for the economies of scale.

Like the results for economies of scale, considerable economies of scope appear in almost every category of postal outlets. Hence, the models suggest that it is generally favorable to provide postal products and services jointly within the same infrastructure. Again, for the simulated offices, economies of scope increase with falling outputs and therefore with smaller post offices, and the specification with five outputs is less favorable in terms of economies of scope. Overall, rural post outlets appear to face higher economies of scope than urban or suburban outlets. At large, sample mean values must be interpreted with caution, especially for agencies, as they are strongly influenced by outliers. Besides, note that in agencies economies of scope do not arise primarily between postal products themselves, but mainly between postal products and all other products such as groceries etc., see Buser et al. (2008). As we analyze agencies from Swiss Post’s point of view, such third-party further products are not included in the dataset and hence our measures of economies of scope are limited to postal products. However, economies of scope between groceries and postal products might be reflected indirectly by dBM which can be interpreted as Swiss Post’s share of cost savings that are realized by the agency model by exploiting economies of scope between postal services and groceries. 56 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–6: Economies of scope (OLS-, WLS-, and LC-model)

Economies of Scope OLS WLS WLS Latent Class 5 Outputs Class 1 Class 2 0.225 *** 0.471 *** 0.623 *** 0.223 *** 0.088 *** 1st quartile, post office (0.060) (0.039) (0.030) (n.c) (n.c) -0.177 *** 0.402 *** 1.553 *** (0.775) *** 0.244 *** Median, post office (0.131) (0.077) (0.051) (n.c) (n.c)

rd 0.028 *** 0.690 *** 2.157 *** (1.854) *** 0.618 ***

Simulation 3 quartile, post office (0.236) (0.135) (0.064) (n.c) (n.c) 0.262 *** 0.528 *** 0.584 *** 0.380 *** 0.117 *** Mean, post office (0.068) (0.043) (0.032) (n.c) (n.c) Mean, post offices urban 0.241 *** 0.655 *** 1.018 *** 0.710 *** 0.549 *** Mean, post offices rural 0.893 *** 1.154 *** 1.731 *** (0.134) *** 0.531 ***

Sample Mean, agencies -2.399 *** 1.097 *** 0.194 *** (0.838) *** -5.362 *** Mean, all postal outlets 0.173 *** 0.736 *** 1.123 *** 0.659 *** 0.415 *** ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets, n. c.: not calculated. Several values of latent class 1 are given in brackets as hardly offices of this size or type occurs in the data. n = 2'466

Astonishingly, economies of scope are more accentuated in latent class 1. At first glance, this result is somewhat contra-intuitive, as the offices in this class are larger concerning outputs and therefore an office specialization seems to be more legitimate than in offices with lower outputs. However, latent classes might comprise information that is not enclosed output data, but refers to further heterogeneity that raises the level of economies of scope in class 1. This argument is supported by the fact that economies of scope in both classes follow an expected pattern as they increase with falling outputs.

The overall findings on economies of scope are well authenticated through the scatter plots of the WLS model for every post office in the sample with five and six outputs (see Figure 2–4 in the appendix, scatter plots on the right hand side). The postal outlet network in Switzerland is considerably affected by unexploited economies of scope and the smaller the office (approximated through the regulator’s ranking), the higher the value for the economies of scope.

Where economies of scope are concerned, global values are somewhat unnatural measures.

Product-specific measures could improve the explanatory power of the analysis. For example, a comparison of offices partly specialized in logistics (letter and parcel) and in banking (payment services and account management) with fully integrated offices would be more enlightening. Nev- ertheless, we desisted from it, because the allocation of the sale of further products and particularly of the standby time was arbitrary. 2.7 SUMMARY AND CONCLUSIONS 57

Last but not least, the question arises whether the two classes of the latent class model are statistically different. This can be confirmed by means of the Kruskal-Wallis equality-of- populations test (Kruskal and Wallis (1952)), which examines the null hypothesis that there is no statistical difference between the two samples. The results of this test indicate that we can reject the hypothesis of equal distribution of the classes. We can, therefore, conclude that accounting for unobserved heterogeneity in the econometric specification of the model leads to more robust results than common techniques as we adapt differences in methods and technologies more accurate- ly. Table 2–7 summarizes these test results.

Table 2–7: Kruskal-Wallis equality-of-populations test

Economies of Scale Economies of Scope Class 1 Class 2 Class 1 Class 2 Average rank 1'361 1'211 1'356 1'212

H0: scale(class 1) = scale(class 2) rejected -

H0: scope (class 1) = scope(class 2) - rejected P-value 0.000 *** 0.000 *** Lower values of economies of scale and scope are assigned to lower ranks. ***, **, *: significant at 1%, 5% and 10%. n = 2'466

2.7 SUMMARY AND CONCLUSIONS

The purpose of this study was to analyze the cost structure of Swiss Post’s postal outlets, and in particular to assess economies of scale and scope in post offices and franchised postal agencies. Information on the optimal size and production structure is of importance from a policy- makers’ point of view, as this hypothetical situation may be a calculation basis of reimbursements for providing the universal service. Furthermore, from a company’s perspective, the question of the optimal organization of the network also arises. Important questions are the optimal size of post offices, whether and where common post offices should be transformed into agencies, or whether product lines should be offered in post offices or agencies operated by partners.

Two important novelties are introduced in this study. First, the latent class model accounts for postal outlets with different underlying methods or even production technologies, caused by unobserved factors. Second, the cost model includes standby time as an indicator of public service 58 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

because regulated accessibility and negotiated opening hours that enhance public service frequently lead to opening hours that exceed the time necessary to operate the demand.

A quadratic total cost function was estimated using a cross-section consisting of 2’466 post offices and agencies operating in the year 2006. The estimation results with two latent classes and the corresponding equality-of-populations test support the hypothesis of unobserved heterogeneity: many of the variables vary significantly in level, but scarcely concerning significance. The seg- mentation of the data reveals one class with high outputs and one with high standby time. Moreo- ver, the empirical analysis shows that standby time has an important effect on cost and hence on economies. Overall, the subsequent empirical results indicate the presence of strong economies of scale and economies of scope, especially for postal outlets with low output volumes.

The empirical results suggest that the postal outlet network in Switzerland is considerably affected by unexploited economies of scale, irrespective of the model, of the number of outputs or of the simulated and sample outlets. Rural offices are more affected by unexploited economies of scale than the ones located in urban and suburban regions, and agencies more than post offices.

Furthermore, the results of the latent class analysis accounting for unobserved heterogeneity point to different values for economies of scale in the two classes. Beyond that and even more importantly, economies of scale of the simulated offices increase with falling outputs, even though the share of standby time is larger in smaller offices. This gives rise to a more pronounced increase of economies of scale with falling outputs in the model without standby time. Therefore, Swiss

Post would benefit from merging smaller post offices in rural regions. Transforming smaller post offices in rural regions into agencies might be an alternative second-best strategy for merging post offices in case of political opposition. This change of the business model would also reduce standby time and, therefore, cost.41

Considerable economies of scope appear in almost every category of postal outlets, much like the results for economies of scale. Hence, the models suggest that it is generally favorable to provide postal products and services jointly within the same infrastructure. However, the results for economies of scope do not reveal a likewise accentuated pattern as for economies of scale because its values in latent class 1 are higher than in class 2. However, economies of scope follow an expected pattern in both classes because they increase with falling outputs, as is the case in the

41 Note that standby time is not meaningful for agencies as time not spent on servicing postal customers would presumably be absorbed by complementary activities of the core business. 2.8 APPENDIX 59

other models. Again, rural post offices are more affected by unexploited economies of scope than the ones located in urban or suburban regions. These results support Swiss Post’s policy to offer postal and financial services as well as the sale of further products within the same infrastructure.

Sales expansion of further products and other services might be an alternative second-best strategy for transforming common post offices into agencies in the case of political or regulatory opposition.

Opposition to post office closures (or replacements by third-party agencies) is mainly based on two factors in Switzerland. Firstly, agencies do not provide payment services in cash due to security and anti-money-laundering measures. Therefore, they fail to fulfill a small part of the universal service. For this situation, the issue of the legitimate extent of the universal service needs to be discussed and, if necessary, properly reimbursed. Secondly, common post offices appear to contribute to the identity of villages, especially in remote areas. Closing down other retail businesses and small enterprises may foster resistance against post office conversions. On the other hand, joint use of infrastructure in the case of agencies could help to ensure continuing postal and other services in rural areas, which would otherwise be too costly for a dedicated post office, as well as providing more convenient opening hours.

2.8 APPENDIX

2.8.1 Acknowledgements

I am indebted to my supervisor, Prof. Dr. Massimo Filippini (ETH Zurich and University of

Lugano), to Prof. Dr. Mehdi Farsi (ETH Zurich and University of Neuchatel) and to Dr. Urs

Trinkner (University of Zurich) for their helpful comments and support. I thank Prof. Dr. Michael

A. Crew (Rutgers University, New Jersey) and Prof. Dr. Paul R. Kleindorfer (University of Penn- sylvania and INSEAD) for their help on a conference follow-up (Filippini et al. (2010b)) as well as two anonymous referees for their contributions to the working paper (Filippini et al. (2010a)) and the published version (Filippini and Koller (2012b)) of this essay. Furthermore, I thank different participants of the 17th Conference on Postal and Delivery Economics 2009 in Bordeaux and of the

SSES Annual Meeting 2011 in Lucerne for their notes. I thank also Martin Buser (Swiss Post) for his explanations on industry backgrounds and Swiss Post for access to their data. Any remaining errors are my own. 60 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

2.8.2 Additional Figures and Tables

Figure 2–4: Sample economies of scale and scope with 6 vs. 5 outputs 2 2.5 1.5 2 1 1.5 .5 1 0 Economies of scale, 6 outputs (WLS) outputs 6 scale, of Economies Economiesof scope, 6 outputs (WLS) .5 -.5 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Regulator's ranking in respect of size (largest office: rank 1) Regulator's ranking in respect of size (largest office: rank 1) 2 2.5 2 1.5 1 1.5 1 .5 Economies of scale, 5 outputs (WLS) 0 Economies of scope, 5 outputs (WLS) outputs 5 of scope, Economies .5 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Regulator's ranking in respect of size (largest office: rank 1) Regulator's ranking in respect of size (largest office: rank 1)

Source: own illustration. Note: agencies excluded, rural offices red. 2.8 APPENDIX 61

Table 2–8: Regression results of the quantile regression model

0.25 Quantile Median 0.75 Quantile VariableCoefficient (SE)Coefficient (SE) Coefficient (SE)

Letter output (Q 1 ) 905.543 *** (33.01) 1'125.347 *** (29) 1'162.929 *** (41.99)

(Q 1 Q 1 ) -0.226 *** (0.013) -0.243 *** (0.013) -0.295 *** (0.016)

Parcel output (Q 2 ) 16'024.22 *** (675.2) 15'723.12 *** (610) 18'508.11 *** (850.9)

(Q 2 Q 2 ) 21.721 (28.07) 201.564 *** (24.21) 140.090 *** (38.85)

Payment services (Q 3 ) 2'950.936 *** (94.61) 3'211.820 *** (84.35) 3'219.894 *** (124.7)

(Q 3 Q 3 ) -3.909 *** (0.603) -1.385 *** (0.518) -1.776 ** (0.739)

Account mgmt (Q 4 ) 352'538 *** (26390) 294'590 *** (23964) 387'675 *** (33423)

(Q 4 Q 4 ) 158'248 *** (22015) 360'544 *** (18939) 324'837 *** (26428)

Further sales (Q 5 ) 417.690 *** (45.05) 406.546 *** (41.01) 376.068 *** (60.07)

(Q 5 Q 5 ) -0.613 *** (0.205) -0.014 (0.2) 0.766 *** (0.273)

Standby time (Q 6 ) 157.091 *** (10.64) 158.584 *** (9.555) 145.506 *** (13.74)

(Q 6 Q 6 ) -0.016 (0.03) -0.012 (0.027) 0.019 (0.042)

(Q 1 Q 2 ) -3.498 *** (0.672) -7.076 *** (0.626) -6.832 *** (0.784)

(Q 1 Q 3 ) 0.422 *** (0.116) -0.168 (0.106) -0.383 *** (0.129)

(Q 1 Q 4 ) 55.923 ** (23.29) 87.600 *** (24.67) 244.599 *** (27.77)

(Q 1 Q 5 ) 0.196 ** (0.084) 0.613 *** (0.083) 0.441 *** (0.117)

(Q 1 Q 6 ) 0.444 *** (0.047) 0.536 *** (0.045) 0.498 *** (0.063)

(Q 2 Q 3 ) 0.748 (4.746) -5.772 (3.874) 17.103 *** (5.231)

(Q 2 Q 4 ) -9'936.746 *** (872.5) -4'016.165 *** (886.6) -5'550.145 *** (1081)

(Q 2 Q 5 ) 13.975 *** (2.648) -9.930 *** (2.469) -26.468 *** (3.282)

(Q 2 Q 6 ) -1.873 ** (0.937) -3.120 *** (0.866) -2.915 ** (1.226)

(Q 3 Q 4 ) 1'077.794 *** (100.5) 303.663 *** (89.16) -23.864 (109.5)

(Q 3 Q 5 ) -0.318 (0.25) 2.549 *** (0.247) 3.160 *** (0.33)

(Q 3 Q 6 ) -0.007 (0.103) 0.165 * (0.096) -0.422 *** (0.124)

(Q 4 Q 5 ) -167.580 ** (69.6) -763.858 *** (69.45) -660.093 *** (98.02)

(Q 4 Q 6 ) 72.863 *** (27.25) 45.937 * (24.53) 151.636 *** (30.81)

(Q 5 Q 6 ) 0.072 (0.062) 0.075 (0.06) 0.194 ** (0.086)

Price capital (P C ) 1'611.953 *** (376.1) 2'003.218 *** (361.7) 3'105.997 *** (516.3)

(P C P C ) -25.070 (34.7) 12.731 (35.2) 38.088 (57.84)

(P C Q 1 ) 0.997 (1.084) 2.285 ** (1.006) -0.066 (1.298)

(P C Q 2 ) 212.270 *** (39.97) 216.141 *** (35.58) 483.580 *** (46.82)

(P C Q 3 ) -8.333 * (4.683) -33.037 *** (4.023) -10.060 * (5.367)

(P C Q 4 ) -5'162.180 *** (980.2) -505.599 (975.9) -13'386.21 *** (1147)

(P C Q 5 ) 4.643 * (2.635) 9.465 *** (2.143) 9.770 *** (2.714)

(P C Q 6 ) 4.446 *** (0.745) 3.062 *** (0.661) 2.465 ** (0.966) Business model (dBM ) -74'568 *** (13354) -81'033 *** (12132) -89'472 *** (17510) Region (dRA) 25'743 *** (7670) 28'003 *** (7207) 47'450 *** (10717) Constant 631'262 *** (3788) 700'663 *** (3599) 783'361 *** (5373) ***, **, *: significant at 1%, 5% and 10%, respectively; se given in brackets; values not in CHF. n = 2'466

Note: the 0.1 and 0.9 quantiles are excluded. 62 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–9: Economies of Scale of the quantile regression model

Economies of Scale 0.1 quantile 0.25 quantile 0.5 quantile 0.75 quantile 0.9 quantile 1.045 *** 1.076 *** 1.007 *** 1.034 *** 1.081 *** # quantile, post office (0.120) (0.037) (0.022) (0.005) (0.010) 0.997 *** 0.999 *** 1.033 *** 1.071 *** 1.109 *** Mean, post office (0.009) (0.006) (0.005) (0.007) (0.011) Mean, post offices urban 0.971 *** 1.000 *** 1.091 *** 1.164 *** 1.101 *** Mean, post offices rural 0.860 *** 0.956 *** 1.383 *** 1.604 *** 1.468 ***

SampleMean, Simulation agencies (-2.000) *** (0.071) *** 0.926 *** 2.339 *** 6.243 *** Mean, all postal outlets 0.792 *** 0.931 *** 1.127 *** 1.294 *** 1.408 *** ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets. n = 2'466 Agencies of 0.1 and 0.25 quantiles in brackets as no agencies in these quantiles in the data occur.

Table 2–10: Economies of Scope of the quantile regression model

Economies of Scope 0.1 quantile 0.25 quantile 0.5 quantile 0.75 quantile 0.9 quantile -1.784 *** -1.007 *** -0.105 *** 0.350 *** 0.691 *** # quantile, post office (0.653) (0.172) (0.066) (0.038) (0.042) -0.086 *** -0.140 *** 0.260 *** 0.436 *** 0.743 *** Mean, post office Simulation (0.060) (0.042) (0.034) (0.043) (0.061) Mean, post offices urban -0.344 *** -0.315 *** 0.253 *** 0.549 *** 0.977 *** Mean, post offices rural -0.121 *** -0.167 *** 0.610 *** 1.159 *** 1.871 ***

Sample Mean, agencies (5.154) *** (-2.681) *** 0.495 *** 0.667 *** 2.973 *** Mean, all postal outlets -0.021 *** -0.372 *** 0.305 *** 0.624 *** 1.186 *** ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets. n = 2'466 Agencies of 0.1 and 0.25 quantiles in brackets as no agencies in these quantiles in the data occur.

2.8 APPENDIX 63

Table 2–11: Regression results of the WLS model with quasi-correction

WLS WLS (Quasi) VariableCoefficient (SE) Coefficient (SE)

Letter output (Q 1 ) 1'290.086 *** (34.04) 1'829.071 *** (50.93)

(Q 1 Q 1 ) -0.137 *** (0.017) -0.243 *** (0.03)

Parcel output (Q 2 ) 14'073.19 *** (723.1) 19'357.79 *** (1104)

(Q 2 Q 2 ) 370.084 *** (35.97) 657.928 *** (63.94)

Payment services (Q 3 ) 2'775.712 *** (98.24) 3'170.523 *** (133.9)

(Q 3 Q 3 ) 2.947 *** (0.702) 5.240 *** (1.247)

Account mgmt (Q 4 ) 330'065 *** (28068) 452'654 *** (39590)

(Q 4 Q 4 ) 72'800 * (42261) 129'424 * (75130)

Further sales (Q 5 ) 458.407 *** (48.3) 785.045 *** (71.67)

(Q 5 Q 5 )0.062(0.25) 0.110 (0.444)

Standby time (Q 6 ) 147.879 *** (11.05) 254.522 *** (15.55)

(Q 6 Q 6 )0.002(0.033) 0.003 (0.058)

(Q 1 Q 2 ) -17.260 *** (0.791) -30.684 *** (1.406)

(Q 1 Q 3 ) -0.933 *** (0.129) -1.659 *** (0.229)

(Q 1 Q 4 ) -157.718 *** (30.04) -280.387 *** (53.41)

(Q 1 Q 5 ) 2.313 *** (0.101) 4.112 *** (0.18)

(Q 1 Q 6 ) 0.493 *** (0.053) 0.876 *** (0.094)

(Q 2 Q 3 ) 24.566 *** (4.645) 43.673 *** (8.258)

(Q 2 Q 4 ) -2'227.768 * (1151) -3'960.497 * (2046)

(Q 2 Q 5 ) -39.607 *** (2.999) -70.413 *** (5.331)

(Q 2 Q 6 ) -5.662 *** (1.015) -10.065 *** (1.805)

(Q 3 Q 4 ) 766.183 *** (133) 1'362.101 *** (236.5)

(Q 3 Q 5 ) -1.726 *** (0.33) -3.068 *** (0.587)

(Q 3 Q 6 )0.216*(0.12) 0.384 * (0.214)

(Q 4 Q 5 ) 24.648 (87.56) 43.818 (155.7)

(Q 4 Q 6 ) 141.790 *** (30.15) 252.071 *** (53.6)

(Q 5 Q 6 )0.103(0.073) 0.183 (0.13)

Price capital (P C ) 2'398.950 *** (415.1) 5'170.160 *** (570.3)

(P C P C ) 75.375 * (41.01) 134.001 * (72.9)

(P C Q 1 ) 4.118 *** (1.272) 7.321 *** (2.261)

(P C Q 2 ) 193.145 *** (42.53) 343.368 *** (75.61)

(P C Q 3 ) -54.306 *** (4.736) -96.544 *** (8.419)

(P C Q 4 ) -940.279 (1163) -1'671.618 (2067)

(P C Q 5 ) 19.047 *** (2.583) 33.861 *** (4.592)

(P C Q 6 ) 2.528 *** (0.793) 4.495 *** (1.41) Business model (dBM ) -82'305 *** (13888) -82'305 *** (13888) Region (dRA) 30'339 *** (8208) 30'339 *** (8208) Constant 706'515 *** (4195) 956'664 *** (5886) ***, **, *: significant at 1%, 5% and 10%, resp.; se in brackets; not in CHF.n = 2'466

Note: µ = 0.05. 64 ECONOMIES OF SCALE AND SCOPE IN POSTAL OUTLETS

Table 2–12: Economies of Scope of the WLS model with quasi-correction

Economies of Scope WLS WLS (Quasi)

st 0.471 *** 0.505 *** 1 quartile, post office (0.039) (0.220)

Median, post office 0.402 *** 0.397 *** (0.077) (0.123)

rd 0.690 *** 0.622 *** 3 quartile, post office (0.135) (0.055)

Mean, post office 0.528 *** 0.679 *** (0.043) (0.061) Mean, post offices urban 0.655 *** 0.768 *** Mean, post offices rural 1.154 *** 1.250 *** +++

SampleMean, agencies Simulation 1.097 *** 0.171 Mean, all postal outlets 0.736 *** 0.758 +++ ***, **, *: significant at 1%, 5% and 10%, respectively; se in brackets. +++ : excludes one severe outlier. n = 2'466

Note: µ = 0.05.

3 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

This chapter is based on Filippini and Koller (2012a).

3.1 INTRODUCTION

European Postal Directive (2008)). One of the most challenging tasks of the universal service providers in this process is to improve efficiency given the universal service obligations they face.42

In Switzerland, the postal market is also affected by such regulatory changes. The largest and most important provider of postal services in the country is the incumbent Swiss Post, a publicly owned company. Besides the operation of a nationwide network of postal outlets, Swiss Post is obliged to deliver letters and parcels in every year-round occupied residential area in the entire country every working day (PG (1997)). These universal services traditionally were subject to the legal monopoly of Swiss Post. Today, some services are still reserved for Swiss Post, whereas in respect of other services, Swiss Post is competing on the open market. In the course of market liberalization, the reserved services were first limited to letters below 100 grams and then below

50 grams as a compromise in order to secure its financing (PV (2004)). However, today, physical letters are also in competition with electronic mail, and the decline in letter volumes is ascribed

42 The provision of universal services in a liberalized market is challenging as potential market distor- tions are higher with increasing universal service obligations (Dietl et al. (2009)). Free market and universal service are two conflicting concepts (Trinkner (2007)). 66 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

mainly to electronic substitution (see e.g. Nikali (2008) or Dietl et al. (2011)). In this context of increasing competition, it is important for Swiss Post to increase the level of productive efficiency.

In order to increase efficiency, the internal organization of Swiss Post has also undergone extensive restructuring. One of these changes was the organizational and in most of the cases geographical separation of the collection and delivery processes. The commissioning of new, more centralized sorting centers came along with this disentanglement. The intention of these measures was to benefit from considerable scale effects through merger of delivery bases and centralized sorting centers while losing some economies through vertical disintegration.

Inefficiencies in the delivery process are of particular importance, as about half of total costs of letters and more than one third of total costs of parcels accrue in this process (NERA (2004b)).

For the improvement of competitiveness as well as for future discussions on the extent of the universal service and its financing, it is important to gain information on cost efficiency through the implementation of an internal benchmarking system in the delivery process of Swiss Post.43 There- fore, this paper addresses the formulation of suitable econometric cost efficiency measurement models. From a methodological point of view, this requires the estimation of a cost frontier and comparing different model specifications that adequately reflect the supply of the postal delivery.

Thereby, special attention is paid to the consideration of unobserved time-invariant factors attributed to unobserved heterogeneity44, as the delivery bases are subject to many different factors such as landscape, weather, traffic, output-mix, culture, etc., which cannot all be controlled perfectly in the models. Therefore, we apply different panel data models and some extensions that are suitable to control unobserved heterogeneity. Following the idea of Farsi et al. (2005b), we extend the Pooled model of Aigner et al. (1977) and the True Random Effects model of Greene (2005b) by the formulation of Mundlak (1978) to avoid the heterogeneity bias. For comparability reasons,

43 In other industries, benchmarking systems are used for incentive regulation schemes such as price- or revenue cap (Littlechild (1983)) or yardstick regulation (Shleifer (1985)). However, these regulation schemes are not suited in the postal market, as the monopoly situation no longer exists with liberalization (except for light letters below 50 grams). Moreover, there was only one monopoly and not several regional monopoly companies that could be benchmarked against each other. In liberalized markets without monopoly situations, price setting and market allocation are a function of competition. 44 The general term “unobserved heterogeneity” refers to unobserved, time-invariant and time-varying factors that affect the dependent variable. Other names can be found in the literature as well, such as unobserved effect, individual heterogeneity, or unobserved individual-specific effect. In the present study, the term unobserved heterogeneity refers mainly to time-invariant factors. 3.2 PREVIOUS STUDIES ON COST EFFICIENCY MEASUREMENT 67

we also estimate a True Fixed Effects model and the familiar Random Effects model of Pitt and

Lee (1981). In this context, we also discuss the identification problem of inefficiency and unobserved heterogeneity.

The paper is organized as follows. Section 3.2 outlines the main contribution of this paper with regard to the relevant literature available on the subject. Section 3.3 addresses the econometric approaches and stochastic frontiers and Section 3.4 presents the model specifications. Sec- tion 3.5 introduces the data and Section 3.6 provides the estimation results and measures of cost efficiency for different model specifications. We draw the conclusions in Section 3.7. The appendix, finally, contains further figures and tables, mostly uncommented.

3.2 PREVIOUS STUDIES ON COST EFFICIENCY MEASUREMENT

During the last decades, various studies have investigated cost efficiency measurement in network industries such as the energy and transport sector, healthcare, the banking industry, or even in the sector of higher education.45 As far as postal services are concerned, only few studies exist on empirical cost efficiency measurement. Therefore, we also include studies on production efficiency due to the similar nature of production and cost efficiency. The first three of the reviewed studies analyze the collection and delivery process jointly, and the second three uniquely the delivery process.

In this paper, we raise the question of econometric cost efficiency measurement in Swiss

Post’s delivery network. Unlike in earlier studies, the separate inspection of the delivery process is unproblematic, as these days, this process is organizationally and geographically separated from other main processes of the postal value chain (collection, sorting, transportation and delivery, see

Figure 3–1). The delivery process includes manual sequencing of all items according to the planned delivery route as well as their delivery to the mailboxes, post office boxes and to the door- steps.

45 For recent studies on cost efficiency measurement using stochastic models in non-postal industries, see for example Kopsakangas-Savolainen and Svento (2008) and Farsi and Filippini (2009a) (energy sector), Farsi et al. (2006a) and Cullmann et al. (2012) (transport sector), Filippini et al. (2008) (water distribution), Greene (2004) and Farsi (2008) (health care sector), and Johnes and Johnes (2009) (higher education). 68 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Figure 3–1: The postal value chain: delivery process

Collection Transport Sorting Transport Delivery (centralized) Mailbox Manual sequen- P.O . B ox zing Doorstep

Source: own illustration.

An early but remarkable study was conducted by Perelman and Pestieau (1994) and aimed at comparing productive performance of national postal services in 16 OECD industrial countries, using a panel data set containing 15 years (1975 – 1989). In the first step, they estimated technical efficiency applying a translog production function to the Pooled model proposed by Aigner et al.

(1977). Number of items plus that of transactions were used as output, and labor, number of post offices and vehicles as inputs. The average efficiency ranged from about 39 percent to 90 percent

(excluding the values of countries that were not observed over the whole time span). As remarked by the authors, this wide spread was the result of the very simple model neglecting any geographical and institutional differences and thus excluding a good portion of heterogeneity among countries. Therefore, in the second step, the estimated efficiency scores were regressed on mailbox density, on inhabitants per letter drop, on an index of tendering (share of post offices run by private franchisees) and on an index of autonomy (degree of regulatory constraints) to explain the inefficiency at least partly by heterogeneity. The question remains, why these geographical and institutional variables were not included in the frontier equation in order to reduce unobserved heterogeneity ab initio. Such an approach would have been more appropriate to obtain accurate efficiency estimates.

The study by Borenstein et al. (2004) analyzed tree groups of totally 113 post offices operating in the year 2000 in Brazil concerning their specific postal services provided: collection (‘client service stores’), delivery (‘distribution stores’), or both (‘integrated stores’). Using five input and six output variables and applying it to a data envelopment analysis model, they found about

44 percent of the offices located on the frontier, thus be fully efficient. However, applying cross- sectional, obviously highly heterogeneous data on this model might result in a heterogeneity bias that should not be neglected. Further, the integrated stores appear to be relatively inefficient, a fact the authors trace back to the ‘hybrid nature’ of these offices. This result is not intuitively clear at 3.2 PREVIOUS STUDIES ON COST EFFICIENCY MEASUREMENT 69

first sight, as one could expect economies of scope resulting from the spreading of fixed costs on more activities. However, economies of scope between collection and delivery processes probably play only a minor role, as many postal operators organizationally disentangled these processes in the last century.

Filippini and Zola (2005) estimated a Cobb-Douglas stochastic cost frontier function for a small sample of post offices operating in the year 2001 in Switzerland and combined collection and delivery processes. Explaining total costs by collected and delivered mail and the factor prices for labor and physical capital as well as by the population density, they found more than

50 percent of the sampled offices having mean inefficiency scores lower than twelve percent. The fact that the majority of the postal offices are operating relatively close to the fully efficient cost frontier can be explained, notwithstanding the very simple model and small sample, by the relatively similar environmental conditions, as all offices are small and located in the same region of

Switzerland. Hence, unobserved heterogeneity in this sample can be expected as relatively low.

Nevertheless, the authors suggest using panel data for future research.

The paper of Moriarty et al. (2006) is the first in the field of cost efficiency measurement in the postal sector which distinguishes between processes. Using cross-sectional data of more than

1100 delivery offices of Royal Mail and a Cobb-Douglas total cost function, the authors estimated the stochastic frontier model of Aigner et al. (1977) with a half-normal normal distribution and a type of corrected OLS that shifts the frontier not to the lowest observation, but to the lowest decile, allowing at least for some unobserved effects. Nine different explanatory variables were employed, including volumes, density, local wages, and business penetration in the region as well as five additional dummy variables indicating the degree of the region’s urbanization. Unfortunately, the authors did only report the estimation results, but not the efficiency scores. However, they indicated that the initial results of the stochastic and the deterministic model were within five percent of each other and that they remained close after some model adjustments suggested by Royal Mail’s consultants. As a policy implication for the regulator authority, they overtaxed the scope of interpretation of the results and valued the savings potential of more than one quarter billion pounds simply by applying best practices within the delivery network. This implication neglects the fact that on the one hand the unobserved heterogeneity is only insufficiently respected in these simple, cross-sectional models and on the other that the adaption rate on new practices is limited. However, the results can help to find best practices and to provide an informative basis for adaption. 70 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Cost efficiency of Royal Mail’s delivery offices was also under investigation in the paper of

Horncastle et al. (2006). Based on the same cross-sectional data as the paper of Moriarty et al.

(2006), the authors removed about one fourth of the observations due to limitations of accuracy.

Presumably, this process also removed a considerable amount of unobserved heterogeneity out of the data. Applying Cobb-Douglas and translog functional form and specifying different distributions of the inefficiency term of the stochastic frontier model suggested by Aigner et al. (1977), they compared the results with results from a variable returns to scale model in the context of a data envelopment analysis. For the DEA model, different stratifications of the data were conducted, because dummy variables cannot be included. In general, the average inefficiency was higher in the DEA models than in the SFA models, especially for the Cobb-Douglas specification. This is because the latter two models allow for random noise in the data, whereas the former assess the whole distance to the frontier as inefficiency. The inefficiency in the DEA models monotonically decreased as the number of data sets from the stratification of the data increased due to decreasing heterogeneity in every single data set. Talking about the pros and cons of DEA and SFA in their conclusions, the authors emphasized that both the linear programming and the econometric para- digm have their advantages; however, they highlighted the ability of SFA to detect random noise in the data.

The paper of Harman et al. (2010) analyses the effects of falling volumes in delivery offices on cost efficiency estimates. The authors use constructed data with 1000 delivery offices, of which all are assumed to be cost efficient in the first period, and estimate it with a stochastic frontier model after a volume shock in the second period. These shocks are assumed to reduce volume at five percent, ten percent, and 30 percent. As one would expect, inefficiency arises in the second period depending on the level of these shocks and on the ability of the delivery offices that are outside of management control to adjust labor to the new volumes. They conclude that SFA is erroneous when delivery offices experience volume declines and their ability to adjust labor to lower volume is limited. Therefore, regulators should consider when ability to adjust labor is limited and use panel data techniques that have the potential to identify inefficiencies while address- ing labor adjustment under different assumptions.

The motive of calculating cost efficiency of Visco Commandini et al. (2010) was the state aid regulation in the European antitrust law. The cornerstone of the analysis is the European Jus- tice’s Altmark decision, which defined four conditions so that compensation for public services 3.2 PREVIOUS STUDIES ON COST EFFICIENCY MEASUREMENT 71

(for example in the context of universal service obligations) is not considered to be state aid. The fourth condition says that the level of compensation is determined on the basis of an analysis of the cost of a typical, well-run company to discharge such public services. Hence, costs stemming from inefficient performance are not to be compensated. In their study, the authors estimated a ten year panel data set with 13 European countries that includes data on operating cost, mail volume, labor costs, and number of households and percentage of population living in urban areas. Unfor- tunately, they pooled the data to shape it for their models and neglected the panel dimension; hence they abstained from an obvious possibility to control unobserved heterogeneity. They specified a translog functional form and estimated a corrected OLS, a corrected GLS, and DEA model and found considerable differences between countries and models.

Table 3–1 recapitulates the characteristics of the most important studies on cost efficiency measurement in the postal sector.

Table 3–1: Relevant previous literature on cost efficiency measurement in the postal sector

Functional form / Output Unobserved Authors Process Data model measures heterogeneity collection / translog production f. / del. mail, correcting reg- Perelman and Pestieau (1994) pooled; m.p. delivery SFA transactions ression 2nd step collection / - production f. / del. mail, Borenstein et al. (2004) cross-s.; m.p. neglected delivery DEA clients served collection / C-D. cost f. / coll. and del. Filippini and Zola (2005) cross-s.; m.p. regional data delivery SFA mail C-D. cost f. / Moriarty et al. (2006) delivery cross-s.; s.p. del. mail neglected SFA, COLS C-D., translog cost f. / Horncastle et al. (2006) delivery cross-s.; s.p. del. mail exclusion of obs. SFA, DEA C-D. cost f. / Harman et al. (2010) delivery pooled; s.p. del. mail neglected SFA translog cost f. / Visco Commandini et al. (2010) delivery pooled; s.p. del. mail neglected OLS, GLS, DEA m.p.: multi product; s.p.: single product; f.: function; C-D.: Cobb-Douglas; obs.: observations

Generally, as already mentioned, the issue of unobserved heterogeneity remains mainly undiscussed in the reviewed studies. Perelman and Pestieau (1994) circumvent this problem rudi- mentarily regressing the inefficiency scores on some environmental variables in a second stage.

Horncastle et al. (2006) excluded a good deal of the observations in order to reduce heterogeneity.

Filippini and Zola (2005) refer to the problem and suggest using panel data in addition to environmental characteristics in order to capture the unobserved heterogeneity. However, they use 72 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

regional data where the unobserved heterogeneity can be expected to be relatively low. Even though in some of the other studies panel data was available, none of the authors made use of so- phisticated panel data models in order to separate unobserved heterogeneity from inefficiency. As hardly any attention has been paid to the unobserved heterogeneity, the identification problem of inefficiency and unobserved heterogeneity has, to the best of our knowledge, not been discussed in the postal context. Furthermore, none of the studies focused on the choice of methods that are suitable for an internal benchmarking.

One of the main contributions of this paper is to discuss and consider the observed heterogeneity problem within the context of cost efficiency measurement in postal delivery networks.

The unobserved heterogeneity problem is considered in two ways. First, by introducing a selective set of variables in the model specification and distinguishing sharply from different ancillary production processes that are carried out additionally in a small number of delivery units (e.g. interof- fice mail delivery). Second, by applying econometric models for panel data that takes the unobserved heterogeneity into account. For this purpose, we apply the panel data on different elaborated cost model specifications. Most importantly and following the idea of Farsi et al. (2005b), we extend the Pooled model of Aigner et al. (1977) and the True Random Effects model of Greene

(2005b) by the formulation of Mundlak (1978). The estimators of this auxiliary equation absorb the correlated components of the unobserved heterogeneity and therefore avoid a heterogeneity bias. For comparability reasons, we also estimate a True Fixed Effects model and the familiar

Random Effects model of Pitt and Lee (1981). Coming to the identification problem of unobserved heterogeneity and inefficiency, we argue that uncorrelated unobserved heterogeneity in the postal delivery process should be considered as inefficiency. Second, many of the methods proposed in econometric efficiency measurement are rather complex and bear the inherent risk of non- convergence. In order to be able to estimate cost efficiency in an internal benchmarking process repeatedly using new data waves, we propose with the Pooled model and Mundlak’s formulation an elementary but powerful tool that can be estimated with almost any econometric software. 3.3 MEASUREMENT OF COST EFFICIENCY 73

3.3 MEASUREMENT OF COST EFFICIENCY

This section briefly outlines the theoretical backgrounds of cost efficiency measurement, but makes no claim to be complete, as the body of literature is huge and still growing.46 Even though the focus is on cost efficiency and with it on cost functions, the evidence is (under a set of regularity conditions) analogously valid for its dual, the production functions and hence productive efficiency (see Shepard (1953) and Nerlove (1963)). This Section proceeds as follows: the first Sub- section, 3.3.1, defines the theoretical concepts of cost efficiency and Subsection 3.3.2 introduces economic approaches to empirically measure cost efficiency. Subsection 3.3.3 discusses various stochastic frontier models, respectively.

3.3.1 Theoretical definitions of cost efficiency

In general, producers are characterized as cost efficient in microeconomic theory, if they produce one or more outputs at minimal costs. Cost efficiency requires both maximizing the outputs given the inputs (technical efficiency) and choosing the optimal input combination (allocative efficiency) and is therefore a blend of the two measures.47 Following Kumbakhar and Lovell

(2000), cost efficiency (CE) can be defined as

CE(q,w,p)  c(p,q) / p’w (3–1),

where w and q are input and output vectors, p the input price vector and c the minimal reference cost. Cost efficiency is thus the ratio of minimal and observed cost and 0  CE  1. This relation is shown in Figure 3–2 with an isoquant curve and an isocost line p’p representing input price ratios.48 Technical efficiency is  with the input vector wA normalized to one. However, this measure understates the degree of cost efficiency, as a technical efficient producer in wA could reduce its cost producing the same output by reallocating inputs in favor of w1, moving to w*.

Thus, producer A is both technically and allocatively inefficient, and its cost efficiency is .

46 The microeconomic production theory is extensively documented in the literature (see e.g. Jehle and Reny (2001) or Chambers (1988)) and will not be repeated here. 47 The measure of technical efficiency goes back to the seminal papers of Debreu (1951) and Farrell (1957) (Debreu-Farrell-measure) and marks the beginning of economic efficiency literature. 48 Figure 3–2 deduced from Kumbakhar and Lovell (2000). 74 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Figure 3–2: Decomposition of cost efficiency

w2 L(q)

wA p wA w*

p‘ w 1

Source: adapted from Kumbakhar and Lovell (2000), own illustration.

The empirical decomposition of cost efficiency into technical and allocative efficiency, also referred to the “Greene problem” (Greene (1993)), is complex and not solved properly in the literature. We therefore concentrate our analysis on the estimation of cost efficiency.

3.3.2 Introduction on econometric approaches to measure cost efficiency

Economic literature has developed three different paradigms to empirically measure cost efficiency. The first is based on non-parametric, linear programming techniques, the second on

Bayesian theory and the third on an econometric approach.49 The linear programming and the econometric are established approaches in both theory and practice, whereas the Bayesian approach is only little-known in applied science. In this study, we focus on the use of econometric approaches to estimate a cost function with special attention to panel data models. 50 There have been numerous general survey studies and books on the frontiers literature and on econometric approaches during the last three decades. Among the more recent are, for example, Kalirajan and

Shand (1999), Murillo-Zamorano (2004), Coelli et al. (2005), Cornwell and Smith (2008) and

49 The econometric approach is sometimes also referred to the parametric approach. 50 Readers interested in linear programming models such as Data Envelopment Analysis (DEA; Farrell (1957), Charnes et al. (1978)), Full Disposable Hull (FDH; Deprins et al. (1984)) or index methods are referred to Thanassoulis et al. (2008) and to Färe et al. (2008) for a comprehensive overview on these models and their developments. Readers interested in Bayesian stochastic frontier models (sometimes also characterized as non-parametric models) are referred to van den Broeck et al. (1994). Readers interested in a comparison of Bayesian models and classical econometric approaches are referred to Kim and Schmidt (2000). 3.3 MEASUREMENT OF COST EFFICIENCY 75

Greene (2008). Figure 3–3 therefore presents a general classification on the most important econometric approaches.

Figure 3–3: Econometric frontier methods

Econometric Methods

Deterministic Semi-parametric Stochastic Winsten 1957 (COLS) Koenker & Bassett Afriat 1972 (MOLS) 1978 (QR)

Pooled Models (SFA) FE and RE Models (SFA) True FE and RE Latent Class Aigner et al. 1977 Pitt & Lee 1981 and RC Models (SFA) Models (LC) Meeusen & vd Broeck Schmidt & Sickles 1984 Kumbhakar 1991 Lazarsfeld & Henry 1977 Battese & Coelli 1988, 1992 Polacheck & Yoon 1996 1968 Cornwell et al. 1990 Greene 2005b

Source: adapted from Filippini et al. (2012), own illustration.

Most of the econometric approaches include estimating an empirical cost function, where the observed variables should include a vector of outputs (q) and a vector of input prices (p). The remaining unobserved part, the residual, is completely (in deterministic models) or partially (in stochastic models) assigned to inefficiency. Full efficiency is therefore limited to a selection of units identified as best practice producers, which form the cost frontier. All other units are assumed to operate above the cost frontier.

Deterministic models are similar to DEA and other linear programming models in that the best practice (the cost frontier) is a fixed function that does not vary across observations or units.

As main drawback, these models attribute the residual to inefficiency, i.e. they do not account for other sources of stochastic variation such as measurement errors. Nevertheless, deterministic models are still widely used in applied economic literature and in regulation (see e.g. Filippini et al.

(2012)).51

51 These models are the Corrected and Modified OLS (COLS, MOLS). See Appendix for a short introduction. 76 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Semi-parametric frontier models such as quantile regression (Koenker and Bassett (1978)) sometimes count as deterministic models. Unlike least squares methods, quantile regression techniques do not approximate the conditional mean of the response variable, but either its median or quantiles and offer therefore a systematic strategy for examining the entire distribution of the population.52 In stochastic models, however, the residuals are decomposed into two or three parts, one of which is assumed to represent the inefficiency. In these models, the inefficiency is usually identified as non-linear functions of the residuals. The following subsection describes the most important stochastic frontier models.

3.3.3 Stochastic frontier models

To overcome the drawback of deterministic models, Aigner et al. (1977) and Meeusen and van den Broeck (1977) proposed a stochastic frontier model, which divides the residual it into two parts: uit is reflecting inefficiency, and vit is capturing the random noise. The basic cost function of the stochastic frontier model can be written as

ln Cit = f(qit,pit;β) +  + uit + vit (3–2).

With certain distribution assumptions on uit and vit, this model can be estimated using the Maximum Likelihood (ML) estimation method. Typically, it is assumed that the inefficiency term uit has a one-sided non-negative distribution that is, a normal distribution truncated at zero:

2 53 2 uit  |N(0, u )| , and the random noise term vit is normally distributed: vit  N(0, v ). Additionally, uit and vit are considered as being independently distributed from each other. As in the models above, one would expect the most efficient unit to take uit = 0, and the efficiency value to be calculated according to Equations (3–1) and (3–2) above as exp(-uit). Unfortunately, E(uit) cannot be calculated for an individual unit. Jondrow et al. (1982) proposed therefore a different estimator to measure efficiency. This estimator is based on the conditional expectation function of the residual,

54 (E[uit|it]), and is known as the JLMS estimator referring to the authors. This is a highly non-

52 Readers interested in applied quantile regression models for efficiency measurement are referred to Behr (2010) and to Knox et al. (2007). 53 Other extensions of the stochastic frontier model have considered exponential, gamma, or truncated normal distributions for the inefficiency term. 54 J. Jondrow, C.A.K. Lovell, I.S. Materov, and P. Schmidt in Jondrow et al. (1982). 3.3 MEASUREMENT OF COST EFFICIENCY 77

linear function that only slightly increases the inefficiency for units close to the frontier leaving no unit with full efficiency. The other estimator proposed by these authors is based on the conditional mode (M[uit|it]) that normally assigns full efficiency to several units. It has been used much less in the empirical literature than the JLMS estimator.

Figure 3–4 depicts the intuition behind the stochastic frontier model, where we consider

55 output and cost levels for units i and j, each indicated by a dot. The symmetric random noise vi is positive, whereas vj is negative, reflecting a more challenging production environment or a positive measurement error for unit i, thus unit i has higher costs than it would have under regular conditions (reflected by the deterministic cost function) and much higher costs than it would have under unit j’s conditions.

Figure 3–4: Stochastic frontier cost function

Cost j i uit ujt

vit vjt

Deterministic Cost Function Output

Source: adapted from Kuenzle (2005), own illustration.

The models described so far can be applied either to cross-sectional or panel data. However, the panel structure in the data is ignored, as these models require pooling all observations and treating them as being independent from each other. Temporal variations can be captured using time trends or time-interactions. Moreover, these models are not suited to account for unmeasured, i.e. unobserved heterogeneity. This is due to the fact that with pooled data, each observation is considered as a single, discrete unit. With only one observation per unit, it is not possible to disen- tangle efficiency and time-invariant, unit-specific heterogeneity. Therefore, the presence of unobserved heterogeneity influences the estimation results of the regressors in case of correlation, or

55 To avoid confusion, the time dimension t is omitted in Figure 3–4. 78 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

the residuals (referred to heterogeneity bias, Chamberlain (1982)). The structure of panel data offers the opportunity to apply models that account for the individual effect that should capture the unobserved heterogeneity and hence free from the heterogeneity bias. The time dimension in panel data sets allows us to observe the same unit repeatedly over a certain time span. This enables us to extract time-invariant factors such as unit-specific characteristics that do not necessarily accrue to the unit’s inefficiency, but do affect the costs across different networks.56 Especially structural inefficiencies (inefficiency that is constant over time) and inefficiencies following a certain time path can be better identified using panel data. Most of the developments of the panel data models go back to the stochastic frontier models of Aigner et al. (1977) and Meeusen and van den Broeck

(1977) expressed in Equation (3–2).

An early application to panel data of this stochastic frontier model was the Random Effects

(RE) model by Pitt and Lee (1981) which was estimated by ML and assumed that the inefficiency

2 57 uit is fixed through time, but still half-normally distributed: ui  |N(0, u )|. Battese and Coelli

(1988) formulated a similar model, but with a normally distributed inefficiency component truncated at zero.

To overcome the problem of specifying a particular distribution assumption of the inefficiency component in the Pitt and Lee (1981) model, Schmidt and Sickles (1984) suggested another

RE model, which can be written as

ln Cit = f(qit,pit;β) +  + ui + vit = f(qit,pit;β) + ( + ) + ui* + vit = f(qit,pit;β) + i + vit (3–3),

with  = E(ui) > 0. As ui* = ui –  has zero mean by definition, usual Generalized Least

Squares (GLS) panel data techniques apply and the model can be rewritten as with i =  + ui. The estimate of inefficiency ûi is then given as the distance from the unit-specific intercept to the minimal intercept in the sample, and the unit-specific intercept is the mean of the residuals of the unit.

Besides this RE model, Schmidt and Sickles (1984) proposed also a Fixed Effects (FE)

58 model, where i =  + ui is the common unit effect of the FE model. As in the RE model, the

56 See, for instance, Greene (2005b) or Farsi and Filippini (2009b) for cases of heterogeneity and various modeling approaches. 57 In their paper, this model was called Model 1. 58 See Hayashi (2000) for details on the Fixed Effects and the Random Effects estimator. 3.3 MEASUREMENT OF COST EFFICIENCY 79

estimate of efficiency is given from the unit-specific intercept to the minimal intercept in the sample. Consequently, any deviation from the smallest intercept is interpreted as inefficiency. This model is estimated performing the within transformation and does not require any distributional assumptions on the individual effect i. Therefore, the heterogeneity bias does not exist. Unfortu- nately, FE models require a certain within-variation (variation within one unit) over time, hence, it does not allow for time-invariant variables.

One of the drawbacks of models with time-invariant efficiency is that time-varying components of heterogeneity are entirely interpreted as random noise. Therefore, Cornwell et al. (1990),

Kumbhakar (1990) and Battese and Coelli (1992) suggested the first stochastic models which allow the cost efficiency to vary over time. The model of Cornwell et al. (1990) for cost efficiency can be written as follows:

ln Cit = f(qit,pit;β) + 0t + uit + vit = f(qit,pit;β) + it + vit (3–4),

where 0t is the intercept of all units in period t and it = 0t + uit is the intercept for unit i in period t. As it is not possible to estimate it (it would require N  T coefficients), they proposed a

2 simplified form: it = i1 + i2t + i3t , which reduces the model to estimating N  3 parameters in addition to the ones contained in f(qit,pit;β). However, estimation with numerous parameters might cause multicollinearity and is inapplicable to many, especially short datasets. The models of

Kumbhakar (1990) and Battese and Coelli (1992) assume that uit = (t)ui, where in the former case,

2 –1 (t) = [1 + exp(b1t + b2t )] , and (t) = [–b(t – T)] in the latter. On the one hand, this reduces the additional parameters to two or one, respectively, but prescribes the inefficiency term a deterministic functional form over time on the other.

The main restriction of all of the models presented above is that unobserved factors are assumed to be random over time. This implies that time-invariant factors such as physical network and environmental characteristics are not considered as heterogeneity. The family of ‘true’ panel data models (Kumbhakar (1991) and Polachek and Yoon (1996) as precursor models of Greene

(2005b) extend the original stochastic frontier model as it is formulated in Equation (3–2) by adding a unit-specific time-invariant factor accounting for the individual effect.59 Hence, apart from

59 The term ‘true‘ refers to the Fixed and Random Effects models fully described in Greene (2005b) and applied in Greene (2004) and Greene (2005a). 80 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

the random noise component, these models include two stochastic terms for unobserved heterogeneity, one for time-varying and one for time-invariant individual effects. This model can be written as

ln Cit = f(qit,pit;β) + i + uit + vit (3–5),

where i is the time-invariant unit-specific factor and the model is estimated by Maximum

Simulated Likelihood (MSL). In a RE framework, i is an iid random component and must not be correlated with the observed variables. In a FE framework, i is a constant parameter for every unit.60 As in all ML models, the inefficiency component can be measured by the JLMS estimator of Jondrow et al. (1982). Assuming that physical network and environmental characteristics do not vary considerably over time and that the inefficiency is time-varying, these models help to separate unobserved time-invariant effects from efficiency estimates. However, if inefficiency is persistent over time, these models underestimate the inefficiency systematically, e.g. if managers take wrong decisions in every period or make the same mistakes again and again, the according inefficient effects are detected as time-invariant unit-specific heterogeneity and not as inefficiency. As noted in Greene (2008), the ‘truth’ doubtless lies somewhere between the two strong assumptions.

The idea of observed parameter variability was early applied to a precise indication of heterogeneity of the production environment by Kalirajan and Obowona (1994) in the stochastic frontier context. A similar random parameter (RP) model was also formulated by Greene (2005b), which is a generalization of the True Effects models in that not only the constant but also the parameters of the observed variables are unit-specific indicating the effect of different environments or technologies. It is, hence, no longer assumed that the cost frontier of the units have exactly the same core. This model is estimated by MSL, and the cost efficiency is measured by the conditional mean of the unit-specific parameter vector. As noted by Greene (2008), the estimation of the MSL of this model can be numerically cumbersome.

60 An alternative version of the True Fixed Effects model uses dummy variables for every unit. Howev- er, this specification may be affected by the ‘incidental parameter problem’, especially in short panel data sets. For details on this problem, see Lancaster (2000). 3.3 MEASUREMENT OF COST EFFICIENCY 81

Another approach to accommodate heterogeneity among units into the model is followed by latent class (LC) models.61 Originally introduced by Lazarsfeld and Henry (1968), LC identifies distinct class membership among subjects regarding their cost structure and estimates a separate cost function for each of these classes simultaneously.62 LC models can be regarded as the discrete counterparts of RP models. With a sufficient large number of classes, LC approximates a fully parameterized RP model (Greene (2008)). The LC model can be written as:

ln Cit = f(qit,pit;βj) + j + uit|j + vit|j (3–6).

The subscript i denotes the unit, and uit and vit are defined as above. j is the constant and βj is a vector of discrete random parameters identified in j = 1, 2, …, J classes, endowing each observation with the class-specific characteristics. Prior class membership probabilities (Pij) are specified by the researcher or using a Bayesian approach, and posterior class membership probabilities

(P(j|i)) are calculated using the prior class membership probability and the likelihood function (see

Greene (2005b) for these functions). For the calculation of the efficiencies ûit two different approaches exist: the first assigns unit i to the frontier of class j with the highest posterior class membership probability, whereas the second approach evaluates the efficiency score as the aver- ages weighted by the posterior class membership probability:

J ˆˆ uujPjiit  it ()*( |) (3–7), j1

where ûit(j) is the efficiency score of unit i at time t when it belongs to class j. For estimation, the number of classes J is assumed to be known, but, as the ongoing discussion in literature shows, there is no reason to expect this (Greene (2008)). J is typically chosen on the basis of diagnostic criteria such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion

(BIC). The smaller these statistics, the more likely the model with the corresponding number of classes is.

61 Sometimes, LC models are placed under the heading of ‘finite mixture models’, see Greene (2005b). 62 Latent class analysis has been applied in different fields of science and industry sectors, e.g. in the banking sector (Orea and Khumbhakar (2004)) or more recently in the electricity distribution (Cullmann (2010)). 82 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

So far, different stochastic frontier models for pooled and panel data have been discussed.

Table 3–2 outlines the major characteristics of the most important of these models. This table makes no claim to be complete.63

Table 3–2: Overview of different stochastic frontier models

Authors Name Residual Estimation Assumptions Distribution

Aigner et al. (1977) Pooled model u it + v it ML panel structure neglected i.i.d. half normal

Pitt & Lee (1981) Model 1 u i + v it ML eff time-invariant i.i.d. half normal

Schmidt & Sickles (1984) FE model u i + v it FE eff = u i - min{u i }no

Schmidt & Sickles (1984) RE model a i + v it GLS a i =  + u i normal - half normal

Cornwell et al. (1990) a t + u it ML functional form of residual no

Battese & Coelli (1992) a t + u it ML functional form of residual i.i.d. half normal

Greene (2005b) True FE u it + v it ML random constant several proposed

Greene (2005b) True RE u it + v it MSL random constant several proposed

Greene (2005b) RP u it + v it MSL all parameters random several proposed

Greene (2005b), LC u it | j + v it | j ML J different classes u it | j half normal EFF: Efficiency term; i.i.d.: identically and independently distributed; FE: Fixed Effects; RE: Random Effects; RP: Random Parameters LC: Latent Class; GLS: Generalized Least Squares; ML: Maximum Likelihood; MSL: Maximum Simulated Likelihood

Handling of (unobserved) heterogeneity is one of the most dominating challenges in the frontier literature. Especially when unobserved heterogeneity is correlated with regressors, RE models suffer from a heterogeneity bias (see above). The first formulation for the consideration of the correlated heterogeneity in a RE model was found by Mundlak (1978).64 He assumed that the unobserved factors that are correlated with the explanatory variables x (consisting of variable vectors p and q) can be absorbed by group-means of the explanatory variables x and suggested modeling this correlation in an additional auxiliary equation:

Ti 1 2 iii xxx,,(0,) i  iti N  (3–8), Ti t1

which can be incorporated in a RE cost function:

ln Cit = f(qit,pit;β) + xi + i + uit + vit (3–9).

63 For a more comprehensive overview, see Greene (2008). 64 His idea has first been applied to the stochastic frontier models (Random Effects and True Random Effects models) by Farsi et al. (2005b). 3.4 COST MODEL SPECIFICATION AND METHODOLOGY 83

This formulation divides the unit-specific stochastic term into two components. The first component with the estimators  absorbs the unobserved heterogeneity that is correlated with the explanatory variables; hence it can be explained by exogenous variables. The second component is orthogonal to explanatory variables and is interpreted in some models as the unit’s (time-invariant) inefficiency. Mundlak showed that his formulation of the general GLS model results in estimators equivalent to the FE estimators of the original equation, thus it is unbiased even when unobserved heterogeneity is correlated with explanatory variables.65 However, his argument does not strictly apply to stochastic frontier models estimated by ML, as these models possess an asymmetric composite error term i. As the model captures the correlation between the individual effects and the explanatory variables at least partly, the resulting heterogeneity bias is expected to be minimal.

The choice of the econometric models presented so far is usually not straightforward. For instance, Farsi and Filippini (2009b) have found several studies that report discrepancies in efficiency estimates between different models and approaches.66 Such discrepancies are partly due to methodological sensitivity in the estimation of individual efficiency scores and partly due to different consideration of unobserved factors. The discussion on the choice of the econometric models to use in this study will be introduced in the next section.

3.4 COST MODEL SPECIFICATION AND METHODOLOGY

We specify a cost model that explains total costs of Swiss Post’s delivery network with three aggregated output variables, two input variables and five environmental characteristics. Un-

65 This can be seen easily extending Equation (3–9) with the term ±βxi. For more details on Mundlak’s approach and a comparison with other estimators, see Wooldridge (2010). 66 See e.g. Jensen (2000), Jamasb and Pollitt (2003), Street (2003), Estache et al. (2004), Farsi and Filippini (2004). The results show substantial variations in estimated efficiency scores and, for some of them, in efficiency rankings across different approaches (econometric and non-parametric) and among model specifications. To overcome these problems, Bauer et al. (1998) have proposed a series of criteria to evaluate whether efficiency estimates from different methods lead to comparable scores and ranks, what they call ‘mutual-consistency conditions’. However, empirical results suggest that these criteria are not satisfied in many cases in network industries. Given the fact that the results of different models directly punish or reward units depending on the regulation scheme, the benchmarking models have been criticized in several studies. In practice, mostly cross-sectional models have been applied. Recent panel data models can be used to overcome some of the shortcomings in that they better control unit- or network-specific unobserved heterogeneity extracting the individual effects, which is an important source of discrepancy across different models. 84 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

der the assumption of cost-minimizing behavior of postal delivery units and convex production technology, we write this model as follows:

C  f (,Q123 Q , Q ,, PLC P ,, D dA , dH , dS S ,) T (3–10),

where the dependent variable C represents total costs of a delivery unit. The three outputs (Q1 – Q3) are measured by the following parameters: letters, parcels, and post office box delivery. The model incorporates two different inputs: PL is the price of labor and PC the price of capital, respectively.

Furthermore, in order to capture the heterogeneity of Swiss Post’s delivery units, additional variables have been included to the model. D represents the mailbox density in the delivery area by the ratio of street time and number of mailboxes. The dummy variable dA accounts for geographical disadvantages in alpine regions originating from atmospheric exposure such as snowfall or low temperatures. It is approximated by the height above sea level, averaged and weighted by the total output on zip code level. The dummy variable dH measures the share of addresses with

‘doorstep service’, where postmen provide households with postal services at the doorstep upon request. This service is offered in remote regions with few post offices or third-party owned agencies. The variables dSS are dummies denoting the seasons, as the data is on quarterly basis (see Section 2.4) and subject to strong seasonal fluctuation, especially concerning output volumes. Fi- nally, a time trend T has been introduced to capture the neutral technical progress. For a complete description of the variables with the corresponding data see Section 2.4.

The estimation of the cost model in Equation (3–10) requires the specification of a functional form. Proposed by Christensen et al. (1973) and applied in numerous empirical studies in production economics, we specify a translog functional form for the purpose of flexibility and the straightforward imposition of the linear homogeneity restriction.67,68 In the non-homothetic form,69 it can be written as:

67 The following restrictions are necessary to guarantee linear homogeneity in inputs: ∑rγPr = 1,

∑r=1∑s=1γPCrPCs = 0, and ∑rλrm = 0 for all values m. Linear homogeneity implies for any t > 0:

C(tP,Q) = tC(P,Q). Therefore, to impose linear homogeneity, one of the inputs, say PC, might be arbi-

trarily chosen and set t = 1/PC. Then one obtains C(P,Q)/PC = C(P/PC,Q). 68 Following Jehle and Reny (2001), a proper cost function should exhibit the following characteristics to conform with neoclassical microeconomic theory: (a) non-negative and non-decreasing in input prices and outputs, (b) linearly homogeneous, concave and continuous in input prices. 3.4 COST MODEL SPECIFICATION AND METHODOLOGY 85

33 33 Cit 1 ln0 m lnQQQQQ mit   mm ln mit ln mit    mn ln mit ln nit PLit mm112 mnm  1 PPP11 lnCit ln Cit ln Cit   lnDDD ln ln PPPP22 PP D it DD it it Lit Lit Lit (3–11), 33 PPCit Cit PDln lnDQDQ it Pm ln ln mit   Dm ln it ln mit PPLitmm11 Lit

PCit AitHdA dH itS   dS SiTtT TTTTtt  i it PDitln ln D PLit where subscript i denotes postal delivery unit i = 1, 2, ..., I, subscript t 16 quarters from 1/2007 –

4/2010, and subscripts m and n outputs m = 1, 2, 3 and n = 2, 3. i stands for the individual effects that should capture the time-invariant unobserved heterogeneity, and εit is the composite error term, consisting of the inefficiency uit and the random error vit. As the translog functional form is a second order Taylor-approximation, the values of the explanatory variables must be normalized to the approximation point. For this purpose, we chose the median value of the variables.70 Finally, a time trend has been introduced in a neutral, non-linear way accounting for technological progress- es.

The identification problem of unobserved heterogeneity and inefficiency is studied by a comparative analysis of pooled cross-sections and Random and Fixed Effects models. All models are based on the specification in Equation (3–11). The differences among the models are related to assumptions on the individual effect i and the composite error term i. Table 3–3 summarizes the econometric specifications of the six models used in this paper.71

69 A cost function is non-homothetic, if input prices depend on output levels, hence if input prices and output levels are not separable. In contrast, a homothetic cost function is separable in the sense:

C(P,Q) = h(Q)c(P). Further properties of the translog functional form: symmetry (βmn = βnm) and pos-

itivity (βm ≥ 0). The translog functional form requires every unit to have strictly positive outputs. 70 The median value is better suited as an approximation point than the mean value, as it is less affected by outliers. 71 In addition to the models summarized in Table 3–3, we also formulated a random coefficient and a latent class model in a previous stage of this study, but the models either did not converge or the results were of questionable quality. 86 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Table 3–3: Econometric specifications

Model I Model II Model III Model IV Model V Model VI Pooled RE (ML) True RE True RE + FE Pooled + Mundlak's Mundlak's equation equation

   x   iii    x Ti ii Individual 2 2 1 xx Ti none iid(0, ) N(0, ) iit  fixed 1 effect α i Ti t1 xxiit  2 Ti t1 i  N(0,  )

 ituv it it ituv i it  ituv it it  ituv it it  ituv it it  ituv it it Composite  2  2  2  2  2  2 uNit (0, u ) uNiu (0, ) uNit (0, u ) uNit (0, u ) uNit (0, u ) uNit (0, u ) error ε it 2 2 2 2 2 2 vNit (0, v ) vNit (0, v ) vNit (0, v ) vNit (0, v ) vNit (0, v ) vNit (0, v ) Inefficiency E[u |ε ]E[u |ε ]E[u |α + ε ]E[u |δ + ε ]E[u |ε ]E[u |ε ] it it i it it i it it i it it it it it

Model I is the conventional Pooled model of Aigner et al. (1977), which does not account for the individual effects, i.e. the time-invariant unobserved heterogeneity. In case of correlation of these effects with the explanatory variables, this model might exhibit biased coefficients. Model II is a Random Effects (RE) model as proposed by Pitt and Lee (1981). As in any RE model, the individual effects ui, that should capture the unobserved heterogeneity, are assumed to be uncorrelated with the explanatory variables. As long as this assumption holds, the estimators are not affected by a heterogeneity bias. Furthermore, this model interprets the individual effects ui as inefficiency. Model III is based on the True RE model of Greene (2005b). It estimates unit-specific constants that are designed to capture unobserved heterogeneity by maximum simulated likelihood, so that the remaining elements in the error term, including inefficiency, vary freely over time.72

Still, correlation between the individual effects and the explanatory variables might cause a heterogeneity bias. Model IV, therefore, extends Model III using the auxiliary equation proposed by

Mundlak (1978) and first applied to stochastic frontier models by Farsi et al. (2005b) and subse- quently by Farsi et al. (2005a). This equation considers possible correlation between the unobserved heterogeneity and the explanatory variables with the group-means of the explanatory variables:

Ti 1 2 iii xxx,,(0,) i  iti N  (3–12). Ti t1

72 This model is a special case of the random parameter model of Greene (2005b), where only the intercept is random. It is therefore also known as the random constant model. 3.4 COST MODEL SPECIFICATION AND METHODOLOGY 87

This auxiliary equation can directly be incorporated into the cost model specification in

Equation (3–11) above, which divides the unobserved heterogeneity term into two components.

The first component with the estimators  absorbs the unobserved heterogeneity that is correlated with the explanatory variables. The second component (i) is orthogonal to the explanatory variables and accounts for the unit-specific constants. If this formulation is applied to a normal RE model, it results in estimators equivalent to the Fixed Effects (FE) estimator, thus it is unbiased even when unobserved heterogeneity is correlated with explanatory variables.73,74 Model V is an alternative to the True FE model of Greene (2005b),75 in that it estimates the unit-specific con-

76 stants i by brute force, i.e. it includes dummy variables. As any model with FE estimators,

Model V should not be affected by a heterogeneity bias. As mentioned, the coefficients and hence also the inefficiencies should be equal to that of Model IV (True RE with Mundlak’s auxiliary equation). A requirement for this is, however, a certain within variation in the variables, as time- invariant variables cannot be included in FE models.

Irrespective of the possible heterogeneity bias in the RE models and the negligence of unobserved heterogeneity in the Pooled model, Models I – V presented above exhibit an important limi- tation identifying and separating inefficiency and unobserved heterogeneity. It is indeed true that all of the Models I and III – V use the JLMS estimator of Jondrow et al. (1982) and Model II a special joint density function to separate the inefficiency component from the random error. How- ever, in Model II, the one-sided disturbance term ui, which is interpreted as inefficiency, complete-

73 This argument holds for RE models, which are based on normality, but does not strictly apply to stochastic frontier models estimated by ML, as these models possess an asymmetric composite error

term i. As the model captures the correlation between the individual effects and the explanatory variables at least partly, the resulting heterogeneity bias is expected to be minimal. 74 This can be seen easily by extending the equation yit x+x it i it with  xi  on the right hand

side of the equation. It leads to yit ()()xx+x it i i   it . Therefore,  is the within and () the between estimator. 75 This model is not to be confused with an LSDV model in the stochastic frontier context, as it is estimated by maximum likelihood and as it is not based on normality. In order to avoid confusion, we therefore hereafter refer this model to the FE model. However, it uses more degrees of freedom than the usual FE model. 76 Greene (2005b) mentions two problems likely to arise using the brute force approach, especially if N and hence the number of parameters becomes large. First, the number of parameters might cause estimation problems, which, though, did not arise in this study. Second, a bias could result from the ‘incidental parameter problem’ (Lancaster (2000)). However, this possible bias is expected to be negligible, because the panel data set is relatively long (T = 16) compared to the limited number of units (N = 77). 88 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

ly contains the unobserved heterogeneity. It has been shown in several papers (e.g. in Bagdadioglu and Weyman-Jones (2007) or in Farsi and Filippini (2009a)), that this model tends to overstate inefficiency or at least forms an upper bound. By contrast, the composite errors of Models III – V are exempt from the time-invariant unobserved heterogeneity, which results in relatively low inefficiencies that can be interpreted as a lower bound. Comparing these models, Greene (2008) states explicitly that the ‘truth’ doubtless lies somewhere between the two extremes of Model II and

Models III – V. He also remarks that this identification problem only can be resolved by non- sample information, i.e. by additional assumptions.

Model VI therefore extends the Pooled model of Aigner et al. (1977) (Model I) with

Mundlak’s auxiliary equation also used in Model IV.77 With this specification, the correlated components of the unobserved heterogeneity are absorbed by the group-means of the explanatory variables, whereas the uncorrelated components are stuck in the composite error. The additional assumption that underlies Model VI is that only uncorrelated, i.e. separable components of unobserved heterogeneity are in the composite error and, therefore, can be absorbed by the inefficiency term. The correlated, i.e. non-separable components of unobserved heterogeneity are considered in the coefficients of the auxiliary equation and thus not interpreted as inefficiency. This assumption is in line with Bagdadioglu and Weyman-Jones (2007) and Cullmann et al. (2012) in that time- invariant non-separable factors are assumed to be an integrated part of the production process and therefore not inefficiency. This seems to be reasonable in our cost model, because it takes into account various time-invariant environmental variables and because the data only contains observations that belong to the same superordinate company following the same guidelines and principles and conduct the same processes. Hence, heterogeneity in the production technologies is captured to a high degree in the cost model. As in the Models IV and V, the unobserved heterogeneity bias is avoided in Model VI. To the best of our knowledge, this specification has not yet been used in the context of stochastic frontier models.

Table 3–4 summarizes these explanations on the identification of inefficiency in the six models.

77 The Pooled estimator is consistent and asymptotically identical to the RE estimator, but not necessarily efficient. 3.5 DATA 89

Table 3–4: Treatment of unobserved heterogeneity

Model I Model II Model III Model IV Model V Model VI Pooled RE (ML) True RE True RE + FE Pooled + Mundlak's Mundlak's equation equation Unobs. heterogeneity possible possible possible no no no bias Time-variant in ε in ε in ε in ε in ε in ε unobs. heterogeneity it it it it it it Time-inv. uncorrelated in ε in ε in α in α in α in ε unobs. heterogeneity it it i i i it Time-inv. correlated in β in β in β in γ in α in γ unobs. heterogeneity i

3.5 DATA

This study is based on an unbalanced panel dataset from 2007 – 2010 with quarterly observations on 77 postal delivery units operating in Switzerland at the beginning of the observation period and 73 at the end.78 Figure 3–5 gives an overview on the delivery units considered in this paper. These units cover the whole delivery area of Swiss Post’s mail division; the difference in numbers is due mainly to consolidation of units.

78 This dataset might be interpreted as a pseudo panel, as the obvious temporal delimitation would be one year. However, working with quarters allows for absorbing systematic seasonal variation caused by weather influences or quantity changes. 90 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Figure 3–5: Delivery units considered in this paper

Data source: Federal Office of Statistics (2008b) and Swiss Post, own illustration.

Each of these units belongs to one of the nine superordinate delivery zones and includes about one and a half dozen subordinate delivery areas on average, where postmen start their delivery routes. For a small share of these delivery routes in urban areas, parcels are delivered separate- ly by Swiss Post’s logistics division. However, the aggregated number of delivered parcels is high enough for robust conclusions on delivery unit level. On average, these delivery units stretch across a small area in the more densely populated midland and especially in major cities, whereas they are larger-scale in the alpine and more sparsely populated regions.

The delivery units cover a wide range of outputs and geographical characteristics. Total costs (C) are measured in Swiss Francs and vary only by a factor of approximately four among delivery units. All of these units deliver letters and parcels in post- and post office boxes and offer payment services. The outputs are weighted sums of different subproducts of the corresponding output. As all delivery units must comply with the same internal quality guidelines and principles, we assume comparable quality levels for all units.79

79 In fact, customer satisfaction varies sparsely and on a high quality level. It is indeed surveyed for every delivery unit, but it is to some extent affected by public perception of the umbrella brand Swiss 3.5 DATA 91

Letter output (Q1) is a generic term for all categories of addressed and direct mail including catalogues that can be readily dropped into the mailbox at the street or at the doorway. In contrast, parcel output (Q2) includes all categories of registered mail, parcels and express items that entail more and costlier processes than Q1, for example dismounting from the motorcycle or getting out of the car, knocking at the door to submit for signature and ensuring traceability of the items. If the consignee is out, a pickup notice has to be filled in and the item brought to the closest postal out-

80,81 let. Both Q1 and Q2 are calculated as the weighted sum of the number of delivered letters and parcel, respectively.82 The output of payment services is measured and to be understood analogously. The weighted number of outpayments is added to the weighted number of incoming payments. Except for cash on delivery and doorstep service (see below), payment transactions have been decreasing steadily in the last years. Due to very similar production processes and quantitative negligibility, these services are subsumed under Q2. The last output, post office box delivery

(Q3), includes all items delivered in a post office box, again measured as a weighted sum. Com- pared to Q1 and Q2, most of the process steps fall away with post office box delivery.

Two different inputs prices, defined as factor expenditures per factor unit, are included in the model. As postal delivery is still labor intensive to a high degree, the most important input is

83 the price of labor (PL). It is measured by average full-time equivalents per-capita expenses and varies by attributes such as age, type of contract, experience and special qualification of the post- man. The second input is a residual price that has been considered for the approximation of the price of capital (PC), following the idea of Friedlaender and Wang Chiang (1983). It is measured as the ratio of non-labor expenses to a measure of real estate capital. The measure of real estate capital is approximated by the rented surface of the postal delivery unit in square meters. We did not include the price of movables such as motorcycles or cars, as the vehicle service is provided by a central division; hence all delivery units face the same prices for movable capital.

Post, which includes the mail, logistics, finance, bus transport, international and the technical solutions divisions. Furthermore, the survey is published only once a year and on a retrospective view. 80 Postal outlet is a general term for post office and post agency. In the majority of the cases, postal outlets and postal delivery units are not located at the same place. 81 The professional risk of getting bitten by angry dogs is a further characteristic of products subsumed

in output Q2. However, this risk is highly overrated in public perception. 82 For weighting factors, we use the internal standards of performance. 83 More than 80 percent of total costs originate from labor expenses. In the forthcoming years, this rate is likely to decline due to a substitution by capital, as automated sorting and sequencing processes will be established. 92 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

As indicated in Section 3.4 and illustrated in Figure 3–5, Swiss Post’s delivery units are heterogeneous, in terms of geographical preconditions such as density, urbanity and alpine exposure as well as in terms of organizational differences such as doorstep service in remote parts of the delivery area. The most important geographical characteristic is density (D) of the delivery area, which depends on time on the road on the one hand and on the number of stops at the other. Deliv- ery costs are clearly higher in dispersed settlements than in densely populated areas with a high share of multiple-family dwellings having several mailboxes located at the same place. Therefore, the variable D is calculated by the ratio of time spent on the road and the number of mailboxes served. It varies by a factor of more than ten among delivery units. In addition to D, one could also think of a variable accounting for urbanity of the delivery area, representing characteristics such as personnel turnover, traffic lights and jams and different customer behavior. The idea behind is that also rural villages may be dense with respect to the definition of D, depending on the landscape and on the housing settlement structure. However, a pretest with such a variable has shown that it is highly correlated with D on the aggregation level of delivery units used in this analysis.

The second variable accounting for geographical influences is alpine exposure (dA). In general and both in summer and in winter, topographic conditions are more challenging in alpine regions than in the remaining parts of Switzerland. In particular, snowfall and low temperatures have an effect on the delivery process as they cause traffic jams, scarcely passable streets or limitedly accessible mailboxes. Furthermore, the use of motorcycles is more dangerous and sometimes im- possible, and mounting snow chains time consuming. These influences are therefore approximated by the height above sea level, weighted by the total output on zip code grade.84 Weighting the height by output is important, because height and output vary considerably between delivery units and subordinate delivery areas. Altogether, the weighted height of the lowest delivery unit lies about 200, the highest almost 1’700 meters above sea level. However, as the distribution of heights shows a discontinuous pattern at 700 meter, dA is defined as a dummy variable taking the value 1 in about 13 percent of all observations lying above this threshold.

The dummy variable dH accounts for organizational differences and indicates if there are addresses with ‘doorstep service’ in the delivery unit. Households with doorstep service are provided by the postmen with postal services and products at the doorstep upon request, indicated by

84 Data on height above sea level on zip code grade was provided by the Federal Office of Statistics (2008a). The other data was provided by Swiss Post. 3.6 RESULTS 93

a sign at the mailbox. This service is offered in remote regions with few post offices or third-party owned agencies.85 The highest share of routes with doorstep service is 42 percent, the lowest zero.

The variables dSS are dummies denoting the season, as the data is on quarterly basis and subject to strong seasonal fluctuation, especially concerning output volumes. The reference season includes the last three months in the year, hence the time before Christmas, where outputs achieve their maximum. The first six months in the year are represented in the first two seasons. July, Au- gust and September build the third season including summer vacations, where outputs achieve their minimum. The variables T and TT, finally, form a neutral, non-linear time trend it that it does not interact with the other explanatory variables. Hence, it captures only technical progress, but not labor or capital savings.

3.6 RESULTS

Table 3–5 and Table 3–6 list the regression results of the six stochastic frontier models as specified in Equation (3–11) and listed in Table 3–3. Generally, the estimated coefficients of the first-order terms have the expected signs and are statistically significant. Since the dependent and independent variables are in natural logarithms, the estimated coefficients can be interpreted as cost elasticities at the approximation point.86 For example, a volume rise of one percent of items delivered in post office boxes (Q3) increases total costs by about 0.04 to 0.05 percent in most of the models.

The first order coefficients of the three output variables (letter (Q1), parcel (Q2), and post office box delivery (Q3)) are of similar magnitude, except for Q3 in Model I. The cost elasticity of Q1 is much higher than of Q2 and Q3 reflecting the relative importance in terms of volumes. The coefficients for the input price ratio (P) show that parts of the differences in total costs among delivery units can be explained by higher input prices, either capital or labor. An exception with this variable is again Model I that exhibits an insignificant value. The negative signs of the coefficients for

D confirm that in densely populated areas costs are lower. An exception with this variable is Mod- el III that exhibits an insignificant value. As argued above, the effects of the urbanity of the area

85 For more background information and especially on the political implications of doorstep service, see Buser et al. (2008), Filippini et al. (2010b) or Filippini and Koller (2012b). 86 Cost elasticities with respect to the dummy variables d (dA, dH and dSS) are calculated as [exp(d)-1]. Thus, a shift from conventional postal delivery to doorstep service raises costs about 5.52 (4.23) percent in Model I (II). 94 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

should be captured by the coefficient of D. The coefficients for the dummy variable dA accounting for alpine exposure are positively significant throughout all models, hence alpine exposure increase costs for the delivery. The coefficients for the dummy variable dH denoting doorstep services is not significant for the Models IV, V and VI, hence in the models with Mundlak’s auxiliary equation and in the FE model that avoid the unobserved heterogeneity bias. The coefficients for the seasonal dummy variables (dSS) do not vary considerably among models, but among seasons: all of them are significantly positive and of similar magnitude. This implies that the costs in the reference season including the months before Christmas can be explained by high outputs. Also and not unexpected, the third season, with the months July until September including summer vacation, exhibits the highest coefficient. The coefficients for the variables T and TT, finally, confirm a neutral, non-linear time trend that is positive but decreasing for all models except for Mod- el I. This means that the technical progress was highest negative at the beginning of the observation period and became positive by the end, when all automated sorting centers have overcome their initial technical problems. The unit-specific constants of Model V are not reported due to space restrictions. They are mainly significant and positive. The signal-to-noise ratio λ is significant, indicating skewness of the composite error term and hence existence of inefficiency. It lies, except for Model II, between 1.26 and 1.73, meaning that the standard errors of the efficiency terms are slightly higher than that of the noise terms, but of similar magnitude.

As mentioned above, the coefficients of Q3, P and T (Model I) and D (Model III) exhibit suspicious values that can possibly be attributed to a heterogeneity bias. This presumption will be confirmed later by testing of correlation between unobserved heterogeneity and explanatory variables.

Finally, only three of the six cost functions (Models I, II, and VI) are concave in input prices

(labor and capital) at the approximation point.87 This means that the management’s strategies are not strictly responsive to changes in input prices, i.e. they do not show completely unconstrained

87 With a translog cost function, the concavity condition is satisfied if the Hessian matrix of the second 2 lnTC derivatives of total costs with respect to the input prices, , is negatively semi-definite, i.e. if lnPj ln Pi the eigenvalues of the matrix are non-positive. In the actual analysis with two input prices and im-  posed linear homogeneity, the Hessian matrix reduces to H  PP PP . However, one could al- PP PP so argue that the concavity condition is fulfilled since none of the second derivatives are significantly different from zero, i.e. the eigenvalues are zero. 3.6 RESULTS 95

cost-minimizing behavior as theory might predict. According to Farsi and Filippini (2009a), the reason could lie in constraints in input choices by regulations, e.g. labor contracts or quality restrictions. Furthermore, substitution of capital and labor is in many cases not feasible in the postal delivery sector.

Table 3–5: Regression results (Models I, II and VI)

Model II Model I Model VI RE (ML) Pooled Pooled + Mundlak's equation Main equation Auxiliary equation VariableCoefficient (SE) Coefficient (SE) Coefficient (SE) Coefficient (SE)

Letter output (Q 1 ) 0.5787 *** (0.019) 0.6605 *** (0.013) 0.5502 *** (0.027) 0.1162 *** (0.032)

Parcel output (Q 2 ) 0.1672 *** (0.016) 0.1358 *** (0.010) 0.1578 *** (0.022) -0.0198 (0.025)

P.O. box output (Q 3 ) 0.0394 *** (0.011) 0.1155 *** (0.007) 0.0471 *** (0.015) 0.0863 *** (0.018) Input price ratio (P) 0.0609 *** (0.009) 0.0069 (0.010) 0.0641 *** (0.013) -0.1042 *** (0.021) Density (D) -0.0879 *** (0.024) -0.1217 *** (0.012) -0.0874 ** (0.036) -0.0881 ** (0.038)

(Q 1 Q 1 ) 0.1276 *** (0.045) 0.0895 * (0.050) 0.0340 (0.063) 0.0206 (0.099)

(Q 2 Q 2 ) 0.0720 * (0.040) 0.1102 *** (0.040) 0.0352 (0.059) 0.1424 * (0.081)

(Q 3 Q 3 ) 0.0387 *** (0.015) 0.0168 (0.019) 0.0563 *** (0.020) -0.1867 *** (0.036) (PP) -0.0155 (0.029) -0.0073 (0.039) -0.0053 (0.041) -0.0145 (0.092) (DD) -0.1600 *** (0.056) 0.0701 (0.047) -0.1418 * (0.077) -0.0059 (0.101)

(Q 1 Q 2 ) -0.0267 (0.036) -0.1203 *** (0.039) 0.0586 (0.049) -0.2770 *** (0.076)

(Q 1 Q 3 ) -0.0827 *** (0.021) -0.0339 (0.022) -0.0981 *** (0.028) 0.1355 *** (0.041)

(Q 1 P) 0.0027 (0.025) 0.0257 (0.029) 0.0085 (0.035) 0.0041 (0.065)

(Q 1 D) -0.1860 *** (0.040) -0.0654 * (0.037) -0.1334 ** (0.059) 0.0516 (0.073)

(Q 2 Q 3 ) 0.0278 (0.018) 0.0551 *** (0.017) 0.0246 (0.025) 0.0679 ** (0.033)

(Q 2 P) -0.0655 *** (0.022) -0.0917 *** (0.027) -0.0854 *** (0.029) -0.2025 *** (0.066)

(Q 2 D) 0.1355 *** (0.040) 0.0981 *** (0.029) 0.0545 (0.056) -0.0105 (0.065)

(Q 3 P) 0.0264 * (0.015) 0.0364 * (0.019) 0.0271 (0.020) 0.2512 *** (0.047)

(Q 3 D) 0.0148 (0.025) 0.0290 (0.028) 0.0047 (0.035) 0.2080 *** (0.055) (PD) -0.1208 *** (0.028) -0.0713 ** (0.032) -0.1202 *** (0.039) -0.2540 *** (0.072) Alpine exposure (dA) 0.0642 *** (0.021) 0.0408 *** (0.010) 0.0269 *** (0.009) - Doorstep service (dH) 0.0537 *** (0.013) 0.0273 *** (0.010) 0.0107 (0.010) -

Season 1 (dS 1 ) 0.0442 *** (0.005) 0.0433 *** (0.007) 0.0471 *** (0.007) -

Season 2 (dS 2 ) 0.0656 *** (0.005) 0.0739 *** (0.007) 0.0670 *** (0.007) -

Season 3 (dS 3 ) 0.1053 *** (0.005) 0.1206 *** (0.007) 0.1027 *** (0.007) - Time trend (T) 0.0067 ** (0.003) -0.0068 ** (0.003) 0.0097 *** (0.003) - (TT) -0.0003 ** (0.000) 0.0005 *** (0.000) -0.0004 ** (0.000) - Constant 4.8026 *** (0.023) 4.9612 *** (0.019) 4.9400 *** (0.021) - 2 2 2 (0.011) (0.001) (0.001) σ = σu +σv 0.0511 *** 0.0133 *** 0.0110 *** -

λ = σu/σv 4.0514 *** (0.116) 1.5887 *** (0.011) 1.7277 *** (0.011) - ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets. n = 1'177

96 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Table 3–6: Regression results (Models III – V)

Model III Model IV Model V True RE True RE + Mundlak's equation FE Main equation Auxiliary equation VariableCoefficient (SE) Coefficient (SE) Coefficient (SE) Coefficient (SE)

Letter output (Q 1 ) 0.6257 *** (0.007) 0.5654 *** (0.015) 0.0752 *** (0.019) 0.5656 *** (0.019)

Parcel output (Q 2 ) 0.1408 *** (0.006) 0.1688 *** (0.014) -0.0343 ** (0.017) 0.1687 *** (0.015)

P.O. box output (Q 3 ) 0.0410 *** (0.005) 0.0357 *** (0.010) 0.1212 *** (0.012) 0.0358 *** (0.010) Input price ratio (P) 0.0502 *** (0.006) 0.0628 *** (0.008) -0.1007 *** (0.014) 0.0632 *** (0.009) Density (D) -0.0109 (0.008) -0.0717 *** (0.015) -0.1146 *** (0.017) -0.0701 *** (0.025)

(Q 1 Q 1 ) 0.0918 *** (0.034) 0.0963 ** (0.045) -0.2853 *** (0.071) 0.0946 ** (0.043)

(Q 2 Q 2 ) 0.0347 (0.025) 0.0531 (0.040) 0.0283 (0.056) 0.0528 (0.040)

(Q 3 Q 3 ) 0.0256 ** (0.012) 0.0367 ** (0.016) -0.1747 *** (0.027) 0.0365 ** (0.014) (PP) 0.0146 (0.019) 0.0032 (0.021) -0.0765 (0.063) 0.0037 (0.028) (DD) 0.0837 *** (0.025) -0.1157 *** (0.045) 0.0022 *** (0.067) -0.1122 ** (0.055)

(Q 1 Q 2 ) 0.0172 (0.025) 0.0287 (0.033) -0.0571 (0.053) 0.0295 (0.034)

(Q 1 Q 3 ) -0.0932 *** (0.015) -0.0979 *** (0.026) 0.1661 *** (0.035) -0.0985 *** (0.020)

(Q 1 P) 0.0204 (0.019) 0.0008 (0.025) 0.0137 (0.047) 0.0020 (0.024)

(Q 1 D) -0.1461 *** (0.023) -0.1684 *** (0.033) 0.1940 *** (0.048) -0.1682 *** (0.040)

(Q 2 Q 3 ) 0.0609 *** (0.012) 0.0364 (0.028) 0.0063 (0.032) 0.0370 ** (0.017)

(Q 2 P) -0.0949 *** (0.016) -0.0752 *** (0.021) -0.1905 *** (0.047) -0.0757 *** (0.021)

(Q 2 D) 0.0763 *** (0.020) 0.0630 (0.039) -0.0035 (0.048) 0.0634 (0.039)

(Q 3 P) 0.0104 (0.010) 0.0234 * (0.014) 0.2450 * (0.035) 0.0233 * (0.014)

(Q 3 D) 0.0304 ** (0.015) 0.0211 (0.025) 0.1423 (0.039) 0.0221 (0.024) (PD) -0.0647 *** (0.019) -0.1130 *** (0.024) -0.2669 *** (0.050) -0.1114 *** (0.027) Alpine exposure (dA) 0.0805 *** (0.006) 0.0363 *** (0.006) - 0.0409 * (0.022) Doorstep service (dH) 0.0414 *** (0.006) 0.0107 (0.007) - 0.0111 (0.014)

Season 1 (dS 1 ) 0.0473 *** (0.008) 0.0460 *** (0.009) - 0.0461 *** (0.005)

Season 2 (dS 2 ) 0.0688 *** (0.012) 0.0662 *** (0.012) - 0.0663 *** (0.005)

Season 3 (dS 3 ) 0.1120 *** (0.009) 0.1041 *** (0.011) - 0.1043 *** (0.005) Time trend (T) 0.0092 *** (0.002) 0.0095 *** (0.003) - 0.0096 *** (0.002) (TT) -0.0004 *** (0.000) -0.0005 *** (0.000) - -0.0005 *** (0.000) Constant 4.8712 *** (0.014) 4.9846 *** (0.016) - 4.8745 *** (0.026) Unit-specific constant 0.7860 *** (0.019) 0.0579 *** (0.002) - † 2 2 2 (0.000) (0.000) (0.000) σ = σu +σv 0.0052 *** 0.0046 *** - 0.0044 ***

λ = σu/σv 1.4607 *** (0.203) 1.2601 *** (0.197) - 1.3281 *** (0.095) ***, **, *: significant at 1%, 5% and 10%, respectively; standard errors are given in brackets. n = 1'177 †: unit-specific constants are estimated as dummies. ***+(-): 43(4) units, **+(-): 5(1) units, *+(-): 2(2) units, insignificant: 19 units

In GLS models, the coefficients of Mundlak’s main equation result in the FE (within) estimators. The coefficients of the auxiliary equation cannot be interpreted directly, but adding to the coefficients of the main equation, they result in the between estimator (Mundlak (1978)). Hence, it 3.6 RESULTS 97

gives cross-sectional information reflected in the changes between units. As argued above, we apply Mundlak’s extension to stochastic frontier models, where these arguments do not strictly hold. However, we expect the thereby emerging error to be minimal.

In Table 3–5 and Table 3–6 we presented the estimation results obtained using several models. The first three of these considered the unobserved heterogeneity bias, the other three did not.

Unfortunately, there are no standard statistical tests for frontier models with panel data to identify the best suitable model, as the composite error terms of frontier models are not normally distributed. For this reason, we decided to proceed as follows: First, we estimated the cost model without using the frontier approach and then applied standard statistical tests to identify the best model. 88

Then, second, we estimated the same cost models with the frontier approach and applied standard statistical tests, based on certain assumptions. Therefore, these test results have to be interpreted with corresponding caution.

The Breusch-Pagan Lagrange multiplier test proposed by Breusch and Pagan (1980) applied on the RE model (with and without Mundlak’s extension) based on normality confirms the presence of unobserved heterogeneity. 89 The test statistics of the specification test proposed by

Hausman (1978) to verify the consistency of the models are shown in Table 3–7. Among the models based on normality, both the RE and the Pooled OLS models are biased; hence the null hypothesis of no statistical difference between the coefficients is rejected. As theory predicts, these biases can be eliminated adding Mundlak’s auxiliary equation to the two models. Even though the

Hausman test is based on normality, these results are confirmed also with the frontier models:

Models I – III seem to be biased, whereas Models IV and VI (with Mundlak’s auxiliary equation) are consistent.90 In other words, the coefficients of the Pooled model with Mundlak’s extension and especially the coefficients of the True RE model are not significantly different from the coefficients of the Model V with FE estimators.

88 Hereafter, these models are referred to as models based on normality. As these models are estimated only on testing purposes, we do not report the estimation results. 89 The test statistics are 1’773 and 2’165, respectively, each based on a χ2(1) distribution. 90 The negative signs in the test statistic of Model IV and VI might arise from the non-normality of the error term. However, the Hausman test is known to sometimes produce slightly negative test statistics in small samples, and even asymptotically (Schreiber (2008)). This author proposes using the absolute value as a remedy in finite samples. 98 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Table 3–7: Hausman test statistics

Model comparisonTest statistic H0: no difference between models Fixed vs. random effects 111.40 *** rejected, random effects biased Models Fixed vs. random effects with Mundlak 0.00 not rejected based on normality Fixed effects vs. pooled OLS 1118.25 *** rejected, pooled OLS biased Fixed effects vs. pooled OLS with Mundlak 0.01 not rejected V vs. II Fixed vs. random effects 40.81 *** rejected, random effects biased V vs. III Fixed vs. true random effects 58.50 *** rejected, true random effects biased V vs. IV Fixed vs. true random effects with Mundlak -0.19 not rejected V vs. I Fixed effects vs. pooled model 929.20 *** rejected, pooled model biased V vs. VI Fixed effects vs. pooled model with Mundlak -4.84 not rejected ***, **, *: significant at 1%, 5% and 10%; test statistics based on χ2(27) distribution n = 1'177

These test results are also confirmed by Likelihood ratio tests comparing the model fit with and without Mundlak’s extension (unrestricted vs. restricted models).91 In both cases (Model III vs.

IV and Model I vs. VI), the unrestricted model cannot be rejected in favor of the restricted model at the one percent significance level. Hence, the models with Mundlak’s extension (Models IV and VI) fit the data better than the corresponding models without the extension. Another, intuitive way to see this is by the significance of 13 Mundlak terms out of 20 in each of these two models. A simple Wald test finally approves the joint significance of all coefficients of Mundlak’s extension in both models.92 Of course, one should keep in mind that the use of classical statistical tests for panel data in the frontier framework is not straightforward. Therefore, the test results have to be interpreted with corresponding caution.

Figure 3–6 shows the distribution of efficiency scores and emphasizes some of the main findings of the results graphically.93 The six models can be formed in three groups. Only Model II belongs to the first group. It is different from the other models as it assumes time-invariant efficiency. The Pooled models (Models I and VI) belong to the second group, even though in Mod- el VI Mundlak’s extension becomes noticeable in the results. Models III – V are in the third group, in which the congruence of Model IV and V is consistent with theory. Furthermore and except for

91 The Likelihood ratio (LR) is given by –2(L unrestricted model) +2(L restricted model) with df(unrestricted model) – df(restricted model) degrees of freedom. The test statistics are 371 and 256, respectively, each based on a χ2(20) distribution. 92 The test statistics are 1’057 and 280, respectively, each based on a χ2(20) distribution. 93 In addition, Figure 3–7 in the appendix compares the efficiency scores obtained from Models IV, V and VI with the True RE model (Model III), the models with Mundlak’s extensions (Models IV and VI) with the Pooled model (Model I) and with each other, respectively. 3.6 RESULTS 99

Model II, all models indicate a clearly negatively skewed distribution of efficiencies corresponding to positively skewed distribution of inefficiencies, which is in line with the usual assumption of a normally – half-normally distributed composite error term (for more on this argumentation, see

Farsi and Filippini (2009a)).94

Figure 3–6: Distribution of efficiency scores

A descriptive summary of the inefficiency scores obtained from the Models I – VI is given in Table 3–8. As found by several previous authors and perhaps not surprisingly, the RE model produces the lowest and the True RE and the FE models the highest mean and minimum efficiency scores. According to the latter models, the postal delivery units exhibit on average about four percent of excess costs compared to a fully efficient unit. The efficiency scores of the Pooled model lie clearly below the ones of the True RE and FE models. As already mentioned, the reason is that the True RE and FE models do not account for persistent (time-invariant) inefficiencies. Therefore,

Farsi and Filippini (2009a) argue that these models should provide a reasonable upper bound for the efficiency to the extent that there are certain sources of time-invariant inefficiencies. The same

94 If the skewness of the error term is in the wrong direction, the results are not those of a frontier, but 2 2 OLS for the slope and for σv and zero for σu (Waldman (1982), cited in Greene (2007)). In that case, the software used for this analysis (LIMDEPTM 9.0) would have produced full cost efficiency for all units und shown a warning message. 100 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

argument applies for the Model II in that it can be considered to produce a reasonable lower bound for the inefficiency. The median efficiency score is higher than mean in all models suggesting a right-skewed distribution of the scores. The maximum score tends to one in all models, which is a known characteristic of the JLMS estimator. As expected, the efficiency scores of Model VI are higher than in Model I indicating that the coefficients in Mundlak’s extension absorb the factors of the unobserved heterogeneity that are correlated with the explanatory variables.

Table 3–8: Efficiency scores

Model II Model III Model IV Model V Model I Model VI RE (ML) True RE True RE + FE Pooled Pooled + Mundlak's Mundlak's equation equation Mean 0.829 0.954 0.959 0.959 0.926 0.931 Standard deviation 0.088 0.023 0.019 0.020 0.038 0.037 Minimum 0.610 0.812 0.835 0.829 0.731 0.759 10th Percentile 0.711 0.924 0.935 0.933 0.877 0.880 1st Quantile 0.770 0.944 0.951 0.951 0.909 0.914 Median 0.840 0.960 0.963 0.964 0.935 0.941 3rd Quantile 0.888 0.970 0.972 0.972 0.954 0.958 90th Percentile 0.928 0.977 0.977 0.978 0.966 0.969 Maximum 0.995 0.992 0.993 0.993 0.986 0.988 n = 1'177

The pair-wise correlations between the efficiency scores of the six models and the corresponding Spearman rank correlations are listed in Table 3–9 in the lower and upper triangle of the matrix, respectively. Models IV and V exhibit almost perfect correlation, consistent with theory; it is generally high among the Models III – V and among the two Pooled models due to similar model assumptions, at least in the latter case. More surprisingly, the correlations between the models of these two groups are also remarkable. The weakest correlation with all other models shows Mod- el II, especially with the True RE models; it is even not significantly different from zero with

Model V. The reason for this island position is obvious: Model II assumes the time-invariant individual effects to be inefficiency, whereas it freely varies over time in all other models. The only moderate correlation is with the Pooled model, which neglects unobserved heterogeneity. The

Spearman rank correlations in the upper triangle of the matrix present a similar pattern. 3.6 RESULTS 101

Table 3–9: Correlations of efficiency scores and Spearman rank correlations

Model II Model III Model IV Model V Model I Model VI RE (ML) True RE True RE + FE Pooled Pooled + Mundlak's Mundlak's equation equation Model II 1 0.035 0.012 -0.018 0.459 *** 0.371 *** Model III 0.078 *** 1 0.959 *** 0.966 *** 0.649 *** 0.664 *** Model IV 0.065 ** 0.966 *** 1 0.998 *** 0.641 *** 0.698 *** Model V 0.037 0.959 *** 0.997 *** 1 0.603 *** 0.657 *** Model I 0.489 *** 0.594 *** 0.589 *** 0.543 *** 1 0.886 *** Model VI 0.374 *** 0.633 *** 0.670 *** 0.620 *** 0.898 *** 1 Note: correlations of efficiency scores are listed in the lower, Spearman rank correlations in the upper triangle of the matrix. ***, **, *: significantly different from 0 at 1%, 5% and 10%, respectively. n = 1'177

However, correlation measures are not satisfactory to assess the potential errors in efficiency at the individual level. In order to evaluate individual differences between models, we calculated the deviations of the individual efficiency scores from each pair of models. These deviations are listed in Table 3–10 below. The lower triangle of the matrix shows mean absolute deviations between two models. As expected, the mean absolute deviations are low among the Models III – V and the Pooled models, whereas it is high with Model II. For example, the mean absolute deviation between Model IV and V of 0.001 stands for a mean absolute deviation between these two models of 0.1 percentage points. Here again, the mean absolute deviations between the True RE and FE models and the Pooled models are remarkably low. The upper triangle of the matrix shows the mean deviations between two models. The mean deviation is based on the row model’s score minus the column model’s score. Thus, a negative value implies that on average the row model understates the column model. Therefore, the mean deviation can be considered as a measure of bias of one model with respect to the other. For example, the mean deviations that belong to Model II are without exception negative, hence, the mean deviations of the efficiency scores in Model II are lower than in any other model. The mean deviation of 0.000 between Model IV and V indicates that there is no or only a very low bias between the two models in direct comparison and that one model could be used as a substitute of the other. 102 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

Table 3–10: Pair-wise deviation measures

Model II Model III Model IV Model V Model I Model VI RE (ML) True RE True RE + FE Pooled Pooled + Mundlak's Mundlak's equation equation Model II 0 -0.125 -0.130 -0.130 -0.097 -0.102 Model III 0.129 0 -0.005 -0.005 0.028 0.023 Model IV 0.132 0.006 0 0.000 0.033 0.028 Model V 0.132 0.006 0.001 0 0.032 0.028 Model I 0.102 0.031 0.034 0.034 0 -0.005 Model VI 0.106 0.026 0.029 0.029 0.013 0 Note: M ean absolute deviations are listed in the lower triangle of the matrix. M ean deviations are listed in the upper triangle. Mean deviations are based on the Row model’s score minus the Column model’s score. Thus, a negative value implies that on average the Row model understates the Column model.

3.7 SUMMARY AND CONCLUSIONS

The purpose of this study was to analyze the cost structure of Swiss Post’s postal delivery units, and in particular to assess cost efficiency among these units. Information on cost efficiency is important from a policy makers’ as well as from Swiss Post’s view, as the postal market is fac- ing increasing competition due further steps of liberalization, a market upheaval due to electronic substitution and process changes due to progressive automation of letter sorting.

The main contribution of this study is the consideration of the unobserved heterogeneity problem of cost efficiency measurement in the postal sector. In this context, we have proposed to extend the conventional Pooled model of Aigner et al. (1977) by the formulation of Mundlak

(1978) and compared it to several recent models suggested by Greene (2005b) and to the well- established model of Pitt and Lee (1981). The intention of this model extension was first to avoid the unobserved heterogeneity bias and second to separate parts of unobserved heterogeneity from efficiency. The underlying assumption for the latter was that time-invariant, non-separable unobserved heterogeneity should be interpreted as part of the production process, whereas time- invariant, separable unobserved heterogeneity should be ascribed to inefficiency.

A translog total cost function was estimated using an unbalanced panel data set consisting of

1’177 observations consisting of 77 postal delivery units in 16 quarters of the years 2007 until

2010. The estimation results of the six models support the hypothesis of unobserved heterogeneity in the data and the corresponding bias in the three models that do not avoid it. The coefficients of 3.7 SUMMARY AND CONCLUSIONS 103

the other three models that avoid the unobserved heterogeneity bias are – under some assumptions on the testing procedure for stochastic frontier models – statistically indifferent from each other and are thus in line with econometric theory. This is in particular a remarkable result as these three models consist of one Random Effects, one Fixed Effects and one Pooled model.

The empirical results for the cost efficiency confirm, as shown in several papers, that the values of the model of Pitt and Lee form a lower and the values of the three True Effects models of

Greene an upper bound (range of average cost efficiency values: 82.9% – 95.9%). The reason for this high range is the completely different treatment of unobserved heterogeneity in the two model groups. Correspondingly, the pair-wise deviation measures between the two model groups are high.

Furthermore, there is also almost no correlation either of the cost efficiency and the Spearman ranks. However, there is hardly any difference among the tree True Effects models, in particular not among the two unbiased models: their cost efficiencies as well as the Spearman ranks are highly correlated and the pair-wise deviations measures tend towards zero. The cost efficiency values of the Pooled models (92.6% and 93.1% on average) lie well within the range. Thereby, especially the results of the latter model with the Pooled model and Mundlak’s extension are interesting, as it is unbiased and allows for a differentiated treatment of unobserved heterogeneity. Not surprising, the correlation of this model to the model of Pitt and Lee is extremely weak and the pair-wise deviations high, whereas these values with respect to the True Effects models are remarkably good.

The implications of this study are threefold. First, the treatment of unobserved heterogeneity is of crucial importance, even when relatively homogeneous data is applied. Thereby, considerable industry knowledge is required to make realistic and adequate assumptions on unobserved heterogeneity. Second, as many of the methods in econometric efficiency measurement are complex and bear the inherent risk of non-convergence, the proposed Pooled model with Mundlak’s formulation is an elementary but powerful tool for internal benchmarking process repeatedly using new data waves. And third, finally, the results of a benchmarking process should be interpreted and used with corresponding caution. We do not recommend using them to mechanically reward or punish, e.g. in an internal compensation scheme or in a financing system for the universal service. 104 COST EFFICIENCY MEASUREMENT IN POSTAL DELIVERY UNITS

3.8 APPENDIX

3.8.1 Acknowledgements

I am indebted to my supervisor, Prof. Dr. Massimo Filippini (ETH Zurich and University of

Lugano), to Prof. Dr. Mehdi Farsi (ETH Zurich and University of Neuchatel), to Dr. Urs Trinkner

(University of Zurich) and to Dr. Christian Jaag (University of St.Gallen) for their helpful comments and support. I thank Prof. Dr. William Greene (New York Stern University) as well as different other participants of the XII European Workshop on Efficiency and Productivity Analysis

2011 (EWEPA) in Verona for their notes on the testing procedure. I thank also Yves Zimmermann

(Swiss Post) for his explanations on industry backgrounds and Swiss Post for access to their data.

Any remaining errors are my own.

3.8.2 Short introduction to deterministic frontier models

The first econometric frontier models that appeared in the literature were deterministic and estimated by OLS. Usually, their cost function is expressed in logarithms as

ln Cit = f(qit,pit;β) +  + it (3–13),

where Cit is total cost incurred by the unit i at time t, f(.) is a parametric cost function, qit and pit are vectors of outputs and input prices, respectively, β is the vector of parameters and  the intercept to estimate, and it is the residual. As the error term in deterministic models only reflects the inefficiency, it is assumed to be non-negative. Therefore, Winsten (1957) suggested shifting the estimated intercept down by the minimal residual value. This model is called Corrected OLS

(COLS). The cost efficiency of unit i in the COLS model is thus given by exp(-uit) with uit = it –

min(it) ≥ 0. Afriat (1972) proposed a slightly different model, usually referred to as Modified

OLS (MOLS), where the OLS intercept is shifted by the expected value of the inefficiency term that is, E(uit). The cost efficiency of unit i at time t in the MOLS model is thus given by exp(-uit) with uit = it + E(uit). The efficiency term uit is not necessarily positive (some units are below the cost frontier). Truncation at 0 assigns the respective units with full efficiency. 3.8 APPENDIX 105

3.8.3 Additional Figures and Tables

Figure 3–7: Comparison of efficiency scores of two models 1 1 1 .9 .9 .9 True RE Pooled SFA .8 .8 .8 True RE with Mundlak RE True .7 .7 .7 .7 .8 .9 1 .7 .8 .9 1 .7 .8 .9 1 Pooled SFA with Mundlak Pooled SFA with Mundlak Pooled SFA with Mundlak 1 1 1 .9 .9 .9 True FE True RE Pooled SFA .8 .8 .8 .7 .7 .7 .7 .8 .9 1 .7 .8 .9 1 .7 .8 .9 1 True RE with Mundlak True RE with Mundlak True RE with Mundlak

Source: own illustration.

4 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION IN PUBLIC TRANSPORT

4.1 INTRODUCTION

The Swiss public passenger transportation industry underwent a fundamental reform with the revision of the Swiss railway act (EBG) and its legal ordinances in 1996.95 The purpose was, amongst others, to rearrange financing schemes and to introduce market mechanisms, in order to enhance productivity, improve customer satisfaction, heighten quality levels and to keep public transport services affordable, similar to other changes in this industry throughout the world. Previ- ous to the revision, passenger transportation companies were compensated for deficits after the operating period, i.e. regulated tariffs existed with automatic ex post coverage guarantee of the deficit by the state. According to the revised acts, however, companies were given the opportunity to declare anticipated deficits ex ante, subject to required quality and performance constraints. If the anticipated deficit was justifiable by certain benchmarking indicators including quality and financial aspects, the public authorities could negotiate and finally procure the service. Further- more, the public authorities were given the opportunity of putting lines out to tender in order to impose competitive pressure on the passenger transportation companies.96 Therefore, with the revision of the acts, the public authorities were given a choice between two different contractual regimes to procure public passenger transport services: one relying on competitively tendered contracts and the other relying on performance-based negotiated contracts.

95 The Swiss railway act and the later concretized Swiss passenger transportation act (PGB) apply for public passenger transportations on railway tracks, on the road, on water routes, as well as with cable cars and with lifts. 96 In this study, we use the term competitive tendering. The terms competitive contracting, competitive bidding and franchise bidding (or similar versions) are synonyms. 108 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

In Switzerland, the cantonal governments are responsible for the organization of the regional public bus transportation services.97 Hence, the cantons define the bus lines linking urban transportation networks, railway lines and rural villages that are part of the public transportation network and stipulate a contract with a passenger transportation company for the supply of the transport services on a specific bus line. This bus line network is widely ramified and operated by more than hundred companies. However, the sector is dominated by one large bus company, Post- bus Switzerland Ltd.98 This by far largest company operates more than one thousand bus lines throughout the whole country, whereof about ten percent have gone through a competitive tendering process during the last decade.

All over the world, competitive tendering for the provision of public bus services has by and by become a common mean to establish competitive pressure among public or private monopoly passenger transportation companies. The idea goes back to Demsetz (1968), who argued that competition for the market is the only way to enhance efficiency when competition in the market is not possible.99 Success in many countries applying some form of competitive tendering seems to prove him right, expressed by about 20 percent lower unit costs compared to an unchallenged public monopoly setting (Preston (2005)).100 However, as Hensher and Wallis (2005), Amaral et al.

(2009), and many of other authors in their studies emphasize, the success of competition for the field depends on numerous factors like its organization, the rules chosen, the number of companies and the institutional setting.

During the last fifteen years subsequent to the revision of the Swiss railway act, the governments of most of the Swiss cantons have exercised their right and put some bus lines out to tender.101 This measure is believed by Swiss authorities (Bundesversammlung (2010)) to have

97 Switzerland is a confederation composed of 26 cantons and about 2500 municipalities. 98 Further on, Postbus Switzerland Ltd. is referred to Postbus. 99 Therefore, it is also known as Demsetz-competition. The idea was originally developed by Chadwick (1859). 100 Other authors as e.g. Hensher and Stanley (2010) are much vaguer and give a wide span of possible savings (10–50 percent). 101 The railway act leaves the organization and the design of the competitive tendering process open to the cantonal general submission laws, or, in the absence of it, to the interpretation of cantonal authorities. In order to provide a minimum of legal certainty for the bus companies, the federal authorities provided corresponding guidelines (BAV (2003)). These guidelines are not normative de jure, but they achieved de facto some normative character in competitive tendering processes, as the important contents and subjects of these guidelines are usually listed as conditions in the competitive tendering documents. However, these guidelines will be displaced by legal ordinances in the context of the on- 4.1 INTRODUCTION 109

heightened efficiency and quality levels. Competitive tendering processes in Switzerland aim at finding a passenger transportation company that operates a bus line or a bundle of contiguous bus lines at best value for money, i.e. at the best price-performance ratio. Price criteria comprise variable and fixed compensation payments and have an impact of 40 percent on the contractual decision.

Usually, the levels of the variable compensation payments are relatively rigid. The remaining

60 percent on the decision of the contractual regime pertain to performance criteria and quality aspects that comprise the following main dimensions: driving training as well as language skills and local knowledge of the employees; security, convenience, maintenance and ecologic aspects of the bus fleet; and finally company management, marketing aspects and the overall picture of the applicant. Several further performance criteria such as certain environmental or working standards as well as willingness to participate in tariff and timetable systems are mandatory for all applicants.

Other important rules apply for a possible transfer of employees and buses and other capital equipment in case of operator change. Thereby, main focus is usually put on employee protection as well as on avoidance of stranded investments. The winning company of the competitive tendering process is provided with a license to exclusively operate the according bus lines usually for ten years. It is bound to its offer at least for the first four years of the contract. For the later phase of the contract, it can assert changes of external factors as e.g. changes in demand, etc.

However, despite the possibility to put bus lines in a competitive tendering process, the majority of the bus lines are procured on performance-based negotiated contracts. These contracts must be renewed annually and are subject to simple benchmarking indicators including the most important quality aspects and operating ratios such as total costs, revenues per passenger kilometers, revenue-to-cost ratio, compensations payments (yearly and per passenger kilometers), average passengers on a bus, etc. The renewal of the performance-based negotiated contract depends on the justification of these ex-ante planned benchmarking indicators. By the end of the year, bus companies have to give account ex-post of the benchmarking indicators.

going reform on the acts concerning railways and public passenger transportations (“Bahnreform II”, see Bundesversammlung (2010)). This reform will not fundamentally change the competitive tendering processes, but increase its legal certainty. 110 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

This study aims at quantifying the impact on cost and cost efficiency of the bus lines operated by Postbus under competitively tendered contracts and under performance-based negotiated contracts.102 For this purpose, we use a total cost frontier approach.

The paper is organized as follows. Section 4.2 outlines the main contribution of this paper with regard to the relevant literature available on the subject. Section 4.3 presents the model specifications and the econometric approaches. Section 4.4 introduces the data and Section 4.5 provides the estimation results and measures for the levels of cost efficiency for different model specifications and contracts. We draw the conclusions in Section 4.6, which is followed by the appendix containing further tables, mostly uncommented.

4.2 PREVIOUS STUDIES ON THE EFFECTS OF COMPETITIVE TENDERING

During the last decades, various studies have investigated the differences in the levels of cost efficiency determined by several factors as e.g. contracting (tendered vs. negotiated), ownership (public vs. private) or institutional settings in the public transportation industries such as railways, bus or ferry lines. The huge body of literature on these effects includes studies either on theoretical and on empirical basis. To the best of our knowledge, however, only few studies have made an attempt to empirically isolate the effect of the contractual regime from other effects that usually came at the same time with regulatory changes and market restructurings in the bus industry using econometric tools. The outcome of new contractual regimes such as competitive tendering depends greatly on these effects and also on several other organizational issues. Therefore, we first give a general overview on competitive tendering and public-private agreements in the bus passenger transportation industry in Subsection 4.2.1, based on the recapitulating study by

Hensher and Wallis (2005). After that, we discuss empirical studies measuring the effect of competitive tendering and different other factors on the level of cost efficiency in the sector in Subsec- tion 4.2.2.

102 Unfortunately, no information on cost is available for other bus companies. However, as we will discuss later, the use of data of one single company that operates bus lines with different contracts is interesting from an empirical point of view. 4.2 PREVIOUS STUDIES ON THE EFFECTS OF COMPETITIVE TENDERING 111

4.2.1 General literature

The study by Hensher and Wallis (2005) gives an overview on international successes and failures of competitive tendering mechanisms in some European countries, in the US, in Australia and in New Zealand not only as a strategy to reduce costs and subsidies in the bus industry, but also under consideration of other relevant aspects of service provision.103 Compiling several other studies on these countries, the authors found evidence on considerable cost savings in the short and medium term through the imposition of competitive tendering mechanisms. However, they made some important caveats, of which we highlight four. First, the measurement of savings is inconsistent, as countries start from different legal backgrounds (pre-competitive tendering models, ownership, funding settlements, etc.) and as the introduction of competitive tendering is accompa- nied by changes in service and quality levels and by institutional restructurings. Furthermore,

Hensher and Wallis presume that the results on savings of competitive tendering are often upwards biased by preconceptions of the authors. Second, in most of the cases, only first round effects net of administrative costs are reported. This comprises two limitations: on the one hand, effects of competitive tendering seem to occur uniquely or much more distinctively in the first round compared to retendering. Costs seem to increase in retendering due to unreasonable low initial tender prices and to a decreasing number of competitors (see e.g. Wallis et al. (2010) or Hensher and

Stanley (2010)). On the other hand, competitive tendering generates administrative costs to operators and regulators, according to Hensher and Wallis typically about five percent of the initial savings (call for tenders, offer, assessment of offers, contract, possible renegotiations, etc.; see e.g.

Hensher (1988), Saussier et al. (2009), Gil and Marion (2012), or Yescombe (2007)). Third, most of the studies are focused primarily on cost saving and not on value for money. This leads to un- wanted incentives, as cost minimizing does not take external benefits into account to maximize social surplus. Additionally, single focus on costs leads the authority to accept the tender of the bus company that underestimates the true operating costs most severely (winner’s curse, see e.g.

Armstrong and Sappington (2006)). Saussier et al. (2009) list different criteria besides lowest price.

And finally fourth, Hensher and Wallis demur that competitive tendering might be exposed to regulatory capture by powerful providers. As competitive tendering fosters market concentration

103 For international successes and failures of competitive tendering in the railway sector, see e.g. Alexandersson and Hultén (2006), Smith et al. (2010) or Merkert (2010); for tendering of European ferry lines, see e.g. Baird and Wilmsmeier (2011). For a general overview on the economics of public bus transportation, see Hensher (2007). 112 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

(see e.g. Mathisen and Solvoll (2008), Amaral et al. (2009), Amaral et al. (2010), Yvrande-Billon

(2006), Augustin and Walter (2010)), this risk becomes more severe in the long run.104

Hensher and Wallis also shed light on negotiated contracting as an alternative to competitive tendering.105 Negotiated contracts should be benchmarked to best practice context-specific costs to prevent, amongst others, the asymmetric information problem and to approximate competitive tendering outcomes. With the approach of performance-based negotiation, some of the drawbacks that may come along with competitive tendering (e.g. asymmetric information, high transaction costs or lack of trust) can be avoided. Competitive tendering can then be utilized as fallback mechanism in cases when bus companies with performance-based negotiated contracts do not achieve the expected performance (Wallis et al. (2010)) or when the regulator’s commitment powers are limited (Armstrong and Sappington (2007)). The former authors for instance stated a tendency for cost convergence of competitively tendered contracts and performance-based negotiated contracts in Australia. This underlines the importance of negotiation as an alternative approach (Hensher and Stanley (2010)). Also Armstrong and Sappington (2006) mention that yardstick competition as proposed by Shleifer (1985) can lead to many of the same advantages as competitive tendering when different monopolists operate in distinct geographic areas. Moreover, an appropriate benchmarking system alleviates the effects of the asymmetric information or the hold-up problem between incumbent and public authorities in case of necessary modifications of running or renegotia- tion at the end of contracts. In particular, issues relating to service quality seem to be much more difficult to specify in competitive tendering contract requirements than price (Hensher and Stanley

(2010), for similar arguments see e.g. Armstrong and Sappington (2006) or Wallis et al. (2010)).

104 However, market concentration is characterized by a trade-off between gaining efficiency through working competition with a lot of bidders and small tenders and losing economies of scale. Cambini and Filippini (2003) found economies of scale in the Italian bus market and conclude that the optimal tender should include an area of given size and not necessarily only one bus line. Cambini et al. (2007) additionally found economies of density, suggesting that a suitable network should include a large urban centre. The study by von Hirschhausen and Cullmann (2010) supports these results for the German bus market. Farsi et al. (2007) found economies of scope between different transportation systems such as motor-bus, tramway, and trolley-bus in the Swiss urban public transport sector. Hence, their results provide evidence in favor of multi-mode tendering as opposed to regulatory unbundling. Alternatively, the authors suggest introducing incentive regulation schemes such as yardstick competition. Di Giacomo and Ottoz (2010) found economies of scope between the Italian urban and intercity bus markets. Fraquelli et al. (2004a) found economies of scale and scope in the Italian bus market and concluded that progression of mergers and urban-intercity diversifications have con- sequences about the network configuration that should be competitively tendered. 105 See also Stanley and van de Velde (2008) or Yvrande-Billon (2006) for similar arguments. 4.2 PREVIOUS STUDIES ON THE EFFECTS OF COMPETITIVE TENDERING 113

Wallis et al. (2010) underline that the choice of these two approaches depend on specific circumstances and that ‘one size does not fit all’.106 Among other things, the authors highlight the necessity of periodic market testing through competitive tendering in order to provide outside information on benchmarking costs as input to any negotiation strategy. They conclude for the public bus market of Adelaide, that negotiation with competitive tendering as fallback mechanism is the preferrable strategy. Moreover, they mention a lack of good empirical evidence on the relative outcomes from the two contractual regimes.

4.2.2 Empirical literature

In the following review, we will discuss some studies on the impact of ownership, competitively tendered contracts and performance-based negotiated contracts on costs. To note that in order to analyze the impact of the contractual regime on the cost efficiency of bus companies, it is important to define an empirical setting that makes it possible to isolate the impact of other institutional changes, such as changes of ownership. As we will see, most of the studies consider the impact on costs of several changes, which of course may lead to an identification problem.

The differences in performance between public and private ownership have been much de- bated, especially between private and public companies operating in a monopoly situation. The study by Roy and Yvrande-Billon (2007) estimates the level of technical efficiency for a panel of

French urban transportation networks to measure at the same time the impacts of ownership and contractual regimes. The results indicated modest, but significant differences between ownership categories. Private bus companies, which have been competitively tendered, were the most efficient, followed by public bus companies under fixed contracts and public bus companies under cost-plus contracts.107 It can be assumed that the effect of ownership for private bus companies is biased by the effect of competitive tendering. As mentioned before, in several empirical studies it was not possible to separate the impact on costs of ownership or institutional form from the impact of different types of contracts in a proper way. The study by Pestana Barros and Peypoch (2010) examines the level of cost efficiency of a panel of Portuguese bus companies. The results indicate

106 This argument is valid also for other industries, as e.g. Bajari et al. (2009) show in their study for procurement in the public sector. 107 Piacenza (2006) came to the same conclusion for the Italian bus market and argues in favor of mod- ern, high powered incentive regulation. This finding can be explained by the Averch-Johnson effect (Averch and Johnson (1962)). 114 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

no differences between public and private bus companies. However, this result might be biased, as public bus companies are prevalent in densely populated, urban areas, whereas private bus companies operate mainly on the outskirts. The study by Filippini and Prioni (2003) estimates a total cost function of a panel of regional bus companies in Switzerland characterized by different forms of ownership. The results do not completely support the hypothesis that private bus companies perform better than public companies. The specifications of the output and network variables used in the cost model specification of this study might have had an influence on the ownership parameter.

The study by Mizutani and Urakami (2003) estimates a cost function of a sample of Japanese bus companies. They found that public bus companies are much less efficient than private ones, with costs exceeding that of private bus companies of about 20 percent. The empirical study by

Cambini et al. (2011) investigates the effect of the corporatization process on production costs.108

The authors build their hypothesis upon the theoretical argument of Stiglitz (2000), that even without privatization, corporatization is an effective way to improve efficiency. They estimated a cost function using panel data of local bus companies in Italy. The results of the study show that corporations have a reducing impact on costs compared to common public enterprises.

In the literature, we also find some studies on the effect of subsidies on costs. Filippini and

Prioni (1994) studied a sample of Swiss bus companies under the, at that time still unreformed

Swiss railway act (EBG), and found that tariff subsidies have a negative influence on cost efficiency. A similar result was found by Nieswand and Walter (2010), who analyzed the effect of deficit- balancing subsidies on the level of cost efficiency of a panel of local public bus companies in

Germany. They found that the range of cost inefficiency increases with the share of subsidies on total costs and that non-subsidized bus companies perform best in terms of cost efficiency.

One important study for our empirical analysis is the one performed by Bekken et al. (2006).

In fact, these researchers examined the effect of competitive tendering in the Norwegian bus industry on operating costs and subsidies paid. Using pooled data with a rich set of variables, the authors found that competitive tendering reduces total costs by about ten percent. The authors assess these savings as low compared to savings in other countries. They attributed this to institutional

108 Corporatization refers to the transformation of public enterprises to limited liability public companies. Other than with public enterprises, limited liability companies are responsive to incentive schemes, as the control rights do not lie with politicians but with managers, who can be made responsible for the performance of the company. 4.2 PREVIOUS STUDIES ON THE EFFECTS OF COMPETITIVE TENDERING 115

changes and substantial efficiency improvements in the industry already before competitive tendering was introduced (see also Dalen and Goméz-Lobo (2003)).

Generally, the reviewed studies highlight the importance to be able to separate the impact of changes of the institutional form or changes of ownership from impacts of the introduction of new contractual regimes such as competitive tendering or performance-based negotiation on costs and cost efficiency. Moreover, several researchers mention the importance of taking the problem related to unobserved heterogeneity into account in the empirical analysis. The reviewed studies on the effects of competitive tendering on costs do not seem to have considered these two issues on effective ways.

To the best of our knowledge, there is no empirical study that has examined the difference in the levels of cost efficiency of bus lines operated under competitively tendered contracts and bus lines operated under performance-based negotiated contracts.

With respect to previous studies, we are able to improve the empirical analysis in our study in two directions. First, we only use data of bus lines from Postbus in 2009. Postbus was formerly a division of the public company Swiss Post, but turned into a limited liability company, held by

Swiss Post, in 2006. According to the work of Cambini et al. (2011), most of the efficiency gains on the way from public to private ownership seem to occur in the intermediate stage of corporatization. In this way, effects on costs stemming from the privatization or corporatization process on the contractual regime are excluded in our analysis. Furthermore, we do not compare bus companies before and after the introduction of competitive tendering, but only bus lines of the same company and of the same year that have gone through a competitive tendering process with bus lines that have been procured on performance-based negotiation. Hence, all conditions of the compared bus lines are held constant except for the fact, that some are featured with competitively tendered contracts and the other with performance-based negotiated contracts. The consideration of bus lines instead of bus companies is also an improvement compared to earlier studies as the conclusion of contracts and hence the accruement of total costs and possible compensations are based on the level of bus lines.

Second, we use relatively homogeneous data of only one bus company and a relatively rich set of explanatory variables in the cost model specification. Furthermore, we cleaned the data of

Postbus from lines that are not operated year-round and not on seven days per week. This means 116 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

that in the data used in this study there are no school bus lines, no night lines, no pure touristic lines, no ski-bus lines, no dial-a-bus lines, no extra trip lines and no substitution lines for temporarily interrupted railway lines (see also Section 4.4). The data consists almost exclusively of rural bus lines that are sometimes linked to suburbs and, in very few cases, to intra-urban public passenger transportation nodes. Furthermore and in addition to usual variables such as input prices, output and load factor, we include in the model variables for average travelling speed, trip length and network length which account for a good portion of the remaining heterogeneity in the data.

Therefore, in our empirical analysis the problem of unobserved heterogeneity as e.g. discussed by

Farsi et al. (2006a) or by Cullmann et al. (2012) should not be so severe.

4.3 COST FRONTIER MODEL SPECIFICATION AND ESTIMATION METHODS

In order to analyze the impact of the contractual regime on costs and cost efficiency of bus lines, we decided to use a cost frontier approach. Within this approach, we apply two empirical strategies. The first strategy is characterized by two stages. In the first stage, a stochastic cost frontier model as proposed by Aigner et al. (1977) is estimated, whereas in the second stage the levels of cost efficiency of the contractual regimes are compared using a Kruskal-Wallis equality-of- populations test (Kruskal and Wallis (1952)). The second empirical strategy is based on the estimation of a stochastic cost frontier model as proposed by Battese and Coelli (1995), where the mean of the cost inefficiency term is a function of a dummy variable indicating the contractual regime.

We specify a cross-sectional total cost frontier model where the total costs of operating a bus line is a function of one output variable, two input variables, two output characteristic variables, and a dummy variable indicating the contractual regime. Under the assumption of cost- minimizing behavior of the bus lines’ managers and convex production technology, we write this model as follows:

C  f (,QPLC , P ,,,, LSTNdT , ) (4–1), where the dependent variable C represents total costs of a bus line. The output Q is measured by passenger kilometers. The model incorporates two different input variables: PL is the price of labor and PC the price of capital, respectively. To capture possible heterogeneity among the bus lines, 4.3 COST FRONTIER MODEL SPECIFICATION AND ESTIMATION METHODS 117

additional variables have been included into the model. L is a load factor and S represents the average travelling speed. The variables T and N stand for the average trip length and network length, respectively. The dummy variable dT, finally, indicates the contractual regime, i.e. it indicates if a bus line is operated under a competitively tendered contract or under a performance-based negotiated contract. See Section 4.4 for a complete description of the variables with the corresponding data.

As discussed previously, the estimation of the total cost model in Equation (4–1) requires the specification of a functional form. Proposed by Christensen et al. (1973) and applied in numerous empirical studies in production economics, we specify a translog functional form for the purpose of flexibility and the straightforward imposition of the linear homogeneity restriction.109,110 In the non-homothetic form,111 the total cost frontier model with translog functional form can be written as:

CPPPiCiCiCi11 ln0 Qi lnQQQ   QQii ln ln  PPPLi ln   ln ln   ln L PPPPLi22 Li Li Li

111PCit LLiiSilnLL ln ln S SSiiTi ln SS ln ln T TTii ln TT ln ... 222PLit

1 PCi TilnNNNQ TTiiQ ln ln  P ln i ln   QL ln QLQS i ln i   QS lnln i i 2 PLi (4–2),

PPCi Ci QTlnQT i ln i QN ln QN i ln i   PL ln ln L i   PS ln ln S i PPLi Li

PPCi Ci PTln lnTNLSLTLN iPN ln ln iLSiiLTiiLNi   ln ln ln ln ln ln i PPLi Li

PCit STln ST iln i SN ln SN i ln i   TN ln T i ln N i   i ... PLit

109 The following restrictions are necessary to guarantee linear homogeneity in inputs: ∑rγPr = 1,

∑r=1∑s=1γPCrPCs = 0, and ∑rλrm = 0 for all values m. Linear homogeneity implies for any t > 0:

C(tP,Q) = tC(P,Q). Therefore, to impose linear homogeneity, one of the inputs, say PC, might be arbi-

trarily chosen and set t = 1/PC. Then one obtains C(P,Q)/PC = C(P/PC,Q). 110 Following Jehle and Reny (2001), a proper cost function should exhibit the following characteristics to conform with neoclassical microeconomic theory: (a) non-negative and non-decreasing in input prices and outputs, (b) linearly homogeneous, concave and continuous in input prices. 111 A cost function is non-homothetic, if input prices depend on output levels, hence if input prices and output levels are not separable. In contrast, a homothetic cost function is separable in the sense:

C(P,Q) = h(Q)c(P). Further properties of the translog functional form: symmetry (βmn = βnm) and pos-

itivity (βm ≥ 0). The translog functional form requires every unit to have strictly positive outputs. 118 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

where subscript i denotes bus line i = 1, 2, …, I, and εi is the composite error term, consisting of the inefficiency ui and the random error vi. As the translog functional form is a second order Tay- lor-approximation, the values of the explanatory variables must be normalized to the approximation point. For this purpose, we chose the median value of the variables.112

The effect of competitively tendered contracts on total costs compared to performance- based negotiated contracts is studied applying a cost frontier approach involving two different empirical strategies.113,114 The first empirical strategy (Model I) is based on the estimation of a stochastic cost frontier model as proposed by Battese and Coelli (1995). Within this strategy, we evaluate the differences in the levels of cost efficiency between the contractual regimes, where the corresponding dummy variable (dT) allows certain heterogeneity in the mean of the cost efficiency according to the contractual regime. This dummy variable enters the mean of the cost inefficiency

+ 2 u such that it is distributed in the following way: ui ~ N (βdTdT,σu ). This strategy is estimated in one stage as opposed to several earlier studies (e.g. Kalirajan (1989)) estimating similar models to analyze the effect of environmental factors in two stages. In these studies, the first stage includes the estimation of the stochastic frontier model and the prediction of cost inefficiencies. The second stage includes the regression of the environmental factors on cost inefficiency. However, as noted by Battese and Coelli (1995), the two-stage approach is inconsistent, because two different distributions are assumed in the first and second stage.

112 The median value is better suited as an approximation point than the mean value, as it is less affected by outliers. 113 In a preliminary step of the analysis, we additionally estimated a stochastic cost frontier model including a dummy variable indicating competitively tendered bus lines in the deterministic core of the total cost frontier model specification, allowing for a shift of the total cost frontier. The within-group cost inefficiencies resulted from the distance of total costs to the own, group-specific frontier, the between-group cost inefficiencies from the distance between the frontiers, which was measured by the coefficient of the dummy variable. The resulting cost inefficiencies were interpreted as performance indicators net of the effect of competitive tendering. Gross cost efficiencies were obtained reevaluat-

ing net cost efficiencies as proposed by Coelli et al. (1999): CEiidTi E[exp( u   ) | ]

 Eu[exp(ii ) | ]*exp( dT ) . This means that all bus lines were compared to the lower of the two best practice frontiers. However, as the coefficient of the dummy variable was insignificant, there was no sense in using this model. The estimation results of this model are provided in Table 4–6 in the Ap- pendix. 114 We additionally estimated a common regression model for comparability purposes including a dummy variable for competitively tendered bus lines in the total cost model specification. The effect of competitively tendered contracts compared to performance-based contracts is directly measured by the coefficient of this dummy variable. The estimation results of this model are also provided in Ta- ble 4–6 in the Appendix. 4.3 COST FRONTIER MODEL SPECIFICATION AND ESTIMATION METHODS 119

The second strategy (Model II) is characterized by two stages. In the first stage, a stochastic cost frontier model as proposed by Aigner et al. (1977) is estimated assuming that all bus lines share the same total cost function. This assumption is reasonable as the production technology does not depend on the underlying contract. The question remains whether the levels of the cost efficiency depend on the contractual regime, i.e. whether the levels of the cost efficiency of the competitively tendered and the performance-based negotiated bus lines are statistically different.

This can be evaluated in the second stage by means of the Kruskal-Wallis equality-of-populations test (Kruskal and Wallis (1952)).

The inefficiency ui is estimated using the conditional expectation function, E(ui|εi), as proposed by Jondrow et al. (1982). The level of cost efficiency of bus line i (CEi) can be obtained in the following way:

ln C frontier CEiiiexp( E [ u | ]) (4–3), ln Ci

where Cfrontier illustrates the costs of an efficient company. Hence, CEi takes a value between 0 and 1, where a value of 0.8 implies a level of cost efficiency of 80%. Table 4–1 summarizes the econometric specifications of the two models used in this study.

Table 4–1: Econometric specifications

Model I Model II

SFA + dummy f(u i ) SFA dT function of the mean inefficiency not included

iiiuv iiiuv  2  2 Composite error (ε i ) uNidTu (,) dT uNiu (0, ) 2 2 vNiv (0, ) vNiv (0, )

Inefficiency E[u i |ε i ] E[u i |ε i ]

Level of efficiency exp(-E[u i |ε i ]) exp(-E[u i |ε i ]) Kruskal-Wallis test no yes

120 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

4.4 DATA

This study is based on cross-sectional data with information on 568 bus lines operated by

Postbus in Switzerland under the Swiss railway act (EBG) in the year 2009.115 All of these bus lines are operated year-round and on seven days a week. This means that there are no school bus lines, no night lines, no pure touristic lines, no ski-bus lines, no dial-a-bus lines, no extra trip lines and no substitution lines for temporarily interrupted railway lines in the data. The data consists almost exclusively of rural bus lines that are sometimes linked to suburbs, and, in very few cases, to intra-urban public traffic transportation nodes. The bus lines considered in this study consist of two groups according to the contractual regime. The major part of them, namely 522 bus lines, is operated with performance-based negotiated contracts, whereas 46 are featured with a competitively tendered contract. The dummy variable indicating the contractual regime, dT, takes the value 1 for competitively tendered bus lines and 0 for bus lines with a performance-based negotiated contract.

The data covers one output, two inputs and a range of further variables characterizing the output and geographic conditions of the bus lines. Total costs (C) include expenditure for buses and infrastructure as well as for labor, fuel and depreciation and are measured in Swiss Francs.

Total costs vary by a factor of about fifteen among the bus lines. The output Q reflects demand and is measured by passenger kilometers, following the studies of Windle (1988) and Deb and

Filippini (2011).116 Many other authors have applied supply-related output measures such as seat or bus kilometers.117,118 Supply-related output measures do not consider consumed, but produced

115 In the year 2009, Postbus operated about 630 bus lines under the Swiss railway act (EBG) that were first considered in this analysis. Some of them had to be excluded due to missing values in the variables of interest and in some cases due to indistinct differentiation from normal bus lines and dial-a- bus and night lines, respectively. In total, Postbus operates more than one thousand bus lines including school bus lines, night lines, pure touristic lines, ski-bus lines, dial-a-bus lines, extra trip lines and substitution lines for temporarily interrupted railway lines. From the remaining 568 bus lines, none could be identified as outlier due to a too high Cook’s Distance (Cook (1977)). 116 This output has further been used in the studies of Bhattacharyya et al. (1995) and Jha and Singh (2001). Similarly, the number of passenger trips has been used in an earlier study by Berechman (1987). 117 See e.g. Farsi et al. (2006a), Cambini et al. (2011), Walter (2010) or Walter (2011), for seat kilometers and e.g. Wang Chiang and Chen (2005), Ottoz et al. (2009) or Sakai and Shoji (2010) for bus kilometers. Sometimes, the choice of outputs is restricted by data availability. 118 De Borger and Kerstens (2008) note that both supply and demand related output measures are relevant. 4.4 DATA 121

outputs. This distinction is important measuring the output of companies operating low frequented bus lines. However, a load factor can also be applied to control such situations. Demand is an important cost driver, e.g. by bus cleaning or by operational asset depreciation. Therefore, in this study we use a demand-related output measure and argue that production should be adapted to real demand unless reserve capacity is desired by the public authorities to guarantee a certain quality level, also when short-term demand is exceptionally much higher than in business as usual. Oth- erwise, an inadequate choice of means of transportation would not be identified as cost inefficiency. Even worse, the most efficient bus companies would be those operating large empty buses

(Roy and Yvrande-Billon (2007)). It is certainly the case that intra-day excess capacities also arise due to fluctuating demand caused by commuter flows (peak load) and that it would be uneconomic to replace buses several times a day. However, we consider this constraint with the input price variable for capital and, as mentioned above, with a load factor.

Two different input prices, defined as factor expenditures per factor unit, are included in the model. The input price of labor (PL) is defined by the labor expenses per full-time equivalent. In this sample, labor expenses are an average about half of total costs. The input price of capital (PC) is a residual price and approximated by the non-labor expenses per kilometer, following the idea of

Friedlaender and Wang Chiang (1983). These non-labor expenses consist mainly of costs related to the capital expenditures of buses such as interests, depreciation and maintenance. The capital stock apart from the rolling stock is negligible and the fuel price is constant through all observations, so that the residual price method is justifiable for approximation the input price for capital.

In addition to the output and two inputs, we include four further variables, two characterizing the output and two geographic conditions of the bus lines. The first variable characterizing output is defined as a load factor (L), measured by passenger kilometers per seat kilometers, as proposed by Windle (1988) and used by most of the authors modeling output by passenger kilometers. It accounts for situations where buses are scheduled but demand is low, e.g. for possible intra- day excess capacities or for remote areas with constantly low demand. Therefore, we expect L to have a negative influence on total costs. The second output characteristic variable is the average trip length (T). The longer the average trip of the passengers, the lower the costs associated with stopping for an additional passenger and transporting it, i.e. we expect the sign of the according 122 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

coefficient to be negative.119 The first variable characterizing geographic conditions is the average travelling speed (S), as used in Fraquelli et al. (2004a) and in Piacenza (2006). It is measured by operative bus kilometers per operative working hours of the bus drivers. It reflects different local traffic conditions and geographic situations and is a typical quality indicator, predetermined by the schedule. S affects not only demand with transfer time as important criterion for the choice of transportation modes, but also supply with the amount of working hours and capital requirements

(Gagnepain (1998)). Therefore, a higher S is expected to influence total costs negatively (Fraquelli et al. (2004a)). The second variable characterizing geographic conditions and scale effects is the network size, measured by the network length (N). It is used in many studies as e.g. in Cullmann et al. (2012) or in Roy and Yvrande-Billon (2007) and accounts for either the boundaries of the natural situation or the public service obligations determined by the authorities.120 The effect of N on total costs is expected to be positive.

We conducted a preliminary analysis to clarify three issues concerning data. First, we additionally included the year of the tender into the model specification, as some of the tenders took place a few years before 2009. The idea was to capture the diminishing effect of the tender over the years due to possible modifications in length of the bus line, number of courses, off-peak supply, passenger frequency, etc. as we expected the ensuing renegotiations to possibly having a weakening effect on the contract (see also, e.g. Dalen and Goméz-Lobo (2003)). However, as this effect could not be substantiated, we desisted from including this variable.

Second, we additionally included different dummy variables to account for further geographical situations (alpine regions) as well as for cultural differences (linguistic regions)121 in the bus lines. However, as most of these differences are already considered in some of the other variables and the preliminary results were not robust, we also desisted from including such variables.

Third, we tested the null hypothesis that there is no statistical difference in the variables included in the model, between tendered and negotiated bus lines by means of a Kruskal-Wallis equality-of-populations test (Kruskal and Wallis (1952) in order to avoid a selection bias. The

119 Mohring (1972) showed this relationship in his article on scale effects and the dependency of demand, waiting time and frequency. 120 Other authors such as Jara-Díaz et al. (2001) argue that the number of stops is the appropriate measure to account for scale effects. 121 Switzerland consists of four linguistic regions (the German, the French, the Italian and the Romanic speaking parts) including about 50, 25, 10 and 15 percent of the bus lines. 4.5 RESULTS 123

results of this test indicate that we cannot reject the hypothesis of equal distribution except for the input price of labor. This means that the differences in the variables of the two groups concerning total costs, output and output characteristics are statistically insignificant, i.e. there is no selection bias in the data, and differences in the estimated cost efficiency values between the two groups do not accrue from differences in the bus lines such as network size, etc. Table 4–5 in the Appendix shows the detailed results of this test.

4.5 RESULTS

Table 4–2 lists the regression results of the two models as specified in Equation (4–2) and presented in Table 4–1. Generally, the estimated coefficients and the first-order terms have the expected signs and are statistically significant. Furthermore, the coefficients are of similar magnitude in all models. Since the dependent and the independent variables are in natural logarithms, the estimated coefficients can be interpreted as cost elasticities at the approximation point. For example, a rise of one percent in average travelling speed (S) reduces total costs of about 0.34 percent in both models.

The coefficients of the output Q are about 0.68, which is of similar magnitude as the coefficients of other studies using passenger kilometers as output. This shows, together with the low standard errors in both models, that passenger kilometers are a reasonable choice for the output variable. The coefficients for the input price ratio (P) show that parts of the differences among the bus lines can be explained by higher input prices, either capital or labor. Furthermore, all of the total cost functions are concave in input prices at the approximation point.122 This means that the management’s strategies are responsive to changes in input prices, i.e. they do show cost- minimizing behavior as theory predicts. As both homogeneity in input prices and symmetry of the

122 With a translog cost function, the concavity condition is satisfied if the Hessian matrix of the second 2 lnC derivatives of total costs with respect to the input prices, , is negatively semi-definite, i.e. if lnPj ln Pi the eigenvalues of the matrix are non-positive. In the actual analysis with two input prices and im-  posed linear homogeneity, the Hessian matrix reduces to H  PP PP . PP PP 124 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

second order terms were imposed, the estimated total cost frontiers satisfy all regularity conditions of a theoretically valid total cost frontier model.123

The negative signs of the coefficients of S confirm that in bus lines with higher average travelling speed total costs are lower, with negative second order coefficients even amplifying the effect with increasing average travelling speed. The coefficients of the load factor L are also negative, however, with much higher cost elasticity and positive second order coefficients. Together with the coefficients of the output, this is a sign of high returns to passenger density.124 The coefficients of the trip length T are negative as predicted. The coefficients of the network length N are small, but positive as predicted. Together with the coefficients of the output, this is a sign of relatively low returns to scale.125 The signal-to-noise ratio λ is about 0.76 and significant in both models, meaning that the standard errors of the cost efficiency terms are slightly larger than that of the noise terms.

In Model I, the coefficient of the dummy variable indicating the contractual regime (dT) is positive, but not significant. This means that the results obtained using this empirical strategy show that the level of cost efficiency is not influenced by the contractual regime.

123 The regularity conditions are: non-negative and non-decreasing in input prices and outputs; linear homogeneity and concavity in input prices. 124 Following Windle (1988), at the approximation point, returns to passenger densities with a translog 1 lnCC ln cost function are given by the inverse of the sum of both coefficients, i.e. by  = lnQL ln (0.686-0.502)–1 = 5.42 for Model II. 125 Following Windle (1988), at the approximation point, returns to scale with a translog cost function 1 lnCC ln –1 are given by the inverse of the sum of both coefficients, i.e. by  = (0.686+0.133) = lnQN ln 1.22 for Model II. 4.5 RESULTS 125

Table 4–2: Regression results

Model I Model II

SFA + dummy f(u i ) SFA Coefficient(SE) Coefficient (SE) Passenger km (Q) 0.6862 *** (0.016) 0.6864 *** (0.014) Input price ratio (P) 0.7932 *** (0.058) 0.7931 *** (0.045) Average speed (S) -0.3432 *** (0.058) -0.3437 *** (0.049) Load factor (L) -0.5015 *** (0.040) -0.5020 *** (0.038) Trip length (T) -0.1278 *** (0.046) -0.1291 *** (0.037) Network length (N) 0.1323 *** (0.039) 0.1330 *** (0.029) (QQ) 0.1256 *** (0.018) 0.1251 *** (0.016) (PP) -0.1350 ** (0.064) -0.1327 *** (0.048) (SS) -0.3492 * (0.204) -0.3450 * (0.205) (LL) 0.2936 *** (0.049) 0.2920 *** (0.049) (TT) -0.1599 (0.145) -0.1513 (0.137) (NN) -0.0396 (0.094) -0.0347 (0.084) (QP) -0.0929 ** (0.040) -0.0955 *** (0.032) (QS) -0.0081 (0.050) -0.0059 (0.039) (QL) -0.1649 *** (0.031) -0.1644 *** (0.028) (QT) -0.0309 (0.039) -0.0314 (0.033) (QN) 0.0299 (0.041) 0.0299 (0.029) (PS) 0.5663 *** (0.153) 0.5621 *** (0.148) (PL) 0.1813 *** (0.053) 0.1834 *** (0.059) (PT) -0.0919 (0.102) -0.0889 (0.112) (PN) 0.0835 (0.075) 0.0868 (0.063) (SL) 0.1013 (0.064) 0.1001 (0.068) (ST) 0.0012 (0.094) 0.0000 (0.114) (SN) -0.2019 ** (0.087) -0.2096 ** (0.096) (LT) 0.0663 (0.061) 0.0649 (0.063) (LN) -0.0141 (0.057) -0.0150 (0.060) (TN) 0.1005 (0.076) 0.0984 (0.077)

dT as f(u i ) (dT) 0.0433 (0.110) Constant 11.7335 *** (0.051) 11.7340 *** (0.060) 2 2 2 σ = σu +σv 0.0683 *** (0.012) 0.0687 *** (0.015)

λ = σu/σv 0.7632 ** (0.342) 0.7672 *** (0.089) ***, **, *: significant at 1%, 5% and 10%; standard errors are given in brackets. n = 568

A descriptive summary of the level of cost efficiency obtained from the two models and differentiated by the contractual regimes is given in Table 4–3. Generally, the average level of cost efficiency obtained in both models is relatively high. However, the minimum values and the values of the 10th percentile indicate the presence of bus lines characterized by a relatively low level of 126 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

cost efficiency. In both models, the differences of the values of cost efficiency between the bus lines operating under different contractual regimes are relatively small.

Table 4–3: Cost efficiency scores

Model I Model II

SFA + dummy f(u i ) SFA performance-based competitive performance-based competitive Contractual regime negotiation tendering negotiation tendering Mean 0.8822 0.8757 0.8818 0.8791 Standard deviation 0.0360 0.0401 0.0363 0.0367 Minimum 0.6356 0.7652 0.6321 0.7756 10th Percentile 0.8401 0.8347 0.8394 0.8419 1st Quantile 0.8694 0.8568 0.8688 0.8618 Median 0.8886 0.8778 0.8881 0.8828 3rd Quantile 0.9040 0.8976 0.9036 0.8989 90th Percentile 0.9171 0.9292 0.9168 0.9279 Maximum 0.9653 0.9470 0.9652 0.9432 n = 568

It should be noted that the second empirical strategy used in this paper to test the impact of the different contractual regimes is based on the results of Model II and on the application of the

Kruskal-Wallis equality-of-populations test (Kruskal and Wallis (1952)) on the ranks of the level of cost efficiency. The null hypothesis in this test is that there is no statistical difference between the two samples. The test results indicate that we cannot reject the hypothesis of equal distribution of the groups in Model II. This result confirms the result obtained in Model I using the first empirical strategy. Therefore, we can conclude that the level of cost efficiency of competitively tendered bus lines in Switzerland is not statistically different from that of performance-based negotiated bus lines. Table 4–4 summarizes the test results for Model II. 4.6 SUMMARY AND CONCLUSIONS 127

Table 4–4: Kruskal-Wallis equality-of-populations test (cost efficiency scores)

Model II SFA performance-based competitive Contractual regime negotiation tendering Average rank 282 305

H0: eff(dT =0) = eff(dT =1) not rejected P - value 0.349 Lower efficiency values are assigned to higher ranks. ***, **, *: significant at 1%, 5% and 10%, respectively.

Table 4–7 in the Appendix shows that the cost efficiency scores produced by the two models are highly correlated with each other.

4.6 SUMMARY AND CONCLUSIONS

The revision of the Swiss railway act (EBG) and its legal ordinances in 1996 induced a fundamental change of the public passenger transportation market. Among other things, the regional public authorities were given the choice between two different contractual regimes to procure public passenger transport services: one relying on competitively tendered contracts and the other relying on performance-based negotiated contracts. Current revisions of these acts (“Bahnreform

II”, see Bundesversammlung (2010)) address, among other things, procurement processes of public passenger transportation services. Therefore, information on the effect of these contractual regimes on costs is important from a policy makers’ as well as from the purchasers’ view. For this reason, the purpose of this study was to analyze the levels of cost efficiency of bus lines operated in the Swiss public bus transportation sector as well as the impact of the different contractual regimes on the level of cost efficiency of these bus lines.

For this purpose, a translog total cost frontier model was estimated using cross-sectional data consisting of 568 bus lines operated by Postbus in the year 2009. We applied two different empirical strategies. The strategy in Model II was characterized by two stages. In the first stage, a stochastic cost frontier model was estimated. In the second stage, a Kruskal-Wallis equality-of- populations test was applied to assess the differences in the rankings of the levels of cost efficiency between the two contractual regimes. The empirical strategy in Model I was based on the estimation of a stochastic cost frontier model. Within this strategy, we evaluated the differences in the 128 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

levels of cost efficiency between the contractual regimes with a dummy variable that entered the mean of the cost inefficiency.

Generally, the empirical results show that the average levels of cost efficiency are relatively high and that there are no statistical significant differences in the levels of cost efficiency in either of the two models. In Model I, the dummy variable indicating the contractual regime was statistically insignificant. In Model II, the average ranks in the levels of cost efficiency of the two contractual regimes were statistically insignificant.

Both contractual regimes enforced in Switzerland, competitive tendering and performance- based negotiation, are incentive regulation schemes. The current practice of using both contractual regimes is challenging for the operators of bus lines in terms of competitive pressure. As stated by

Hensher and Wallis (2005), some of the negative effects of both approaches can be avoided, such as too high compensation payments with negotiation and too high administrative costs with competitive tendering. The possibility of bus lines being competitively tendered has a disciplining effect on negotiation, as it is a credible threat. This threat prevents bus companies from bargaining an inadequate rent for a bus line and creating advantages of asymmetric information. This connec- tion was confirmed by Hensher and Stanley (2010), who found a tendency for cost convergence of competitive tendering and negotiated contracting in Australia. It is also mentioned by Armstrong and Sappington (2006) that yardstick competition can lead to many of the same advantages as competitive tendering.

4.7 APPENDIX

4.7.1 Acknowledgements

I am indebted to my supervisor, Prof. Dr. Massimo Filippini (ETH Zurich and University of

Lugano) and to Dr. Souvik Datta (ETH Zurich) for their helpful comments and support. I thank

Prof. Dr. Sumeet Gulati (University of British Columbia (UBC), Vancouver) for his critical remarks to an earlier version of this study during my visiting stay at UBC in autumn 2011. Further, I thank Prof. Dr. Robert Windle (University of Maryland) for his explanations on the load factor and

Kaspar Weilenmann (Postbus Switzerland Ltd.) for his explanations on industry backgrounds and

Postbus for access to their data. Any remaining errors are my own. 4.7 APPENDIX 129

4.7.2 Additional Tables

Table 4–5: Kruskal-Wallis equality-of-populations test (variables)

Variable CQPL P C Average rank (dT = 0) 281 281 275 283 Average rank (dT = 1) 305 301 372 282

H0: variable (dT =0) = variable(dT =1) not rejected not rejected rejected not rejected P - value 0.337 0.437 0.000 *** 0.968 Variable LSTN Average rank (dT = 0) 282 282 280 283 Average rank (dT = 1) 289 289 310 281

H0: variable (dT =0) = variable(dT =1) not rejected not rejected not rejected not rejected P - value 0.791 0.770 0.239 0.941 Lower values of the variables are assigned to higher ranks. ***, **, *: significantly different at 1%, 5% and 10%, respectively. n = 568

130 COMPETITIVE TENDERING VERSUS PERFORMANCE-BASED NEGOTIATION

Table 4–6: Regression results of preliminary models

OLS + dummy SFA + dummy Coefficient (SE)Coefficient (SE) Passenger km (Q) 0.6797 *** (0.012) 0.6861 *** (0.014) Input price ratio (P) 0.7929 *** (0.046) 0.7930 *** (0.045) Average speed (S) -0.3307 *** (0.048) -0.3432 *** (0.049) Load factor (L) -0.4848 *** (0.032) -0.5015 *** (0.038) Trip length (T) -0.1367 *** (0.036) -0.1283 *** (0.037) Network length (N) 0.1354 *** (0.030) 0.1324 *** (0.029) (QQ) 0.1230 *** (0.015) 0.1253 *** (0.016) (PP) -0.1338 *** (0.050) -0.1344 *** (0.048) (SS) -0.3448 (0.210) -0.3503 * (0.206) (LL) 0.2897 *** (0.050) 0.2927 *** (0.049) (TT) -0.1607 (0.142) -0.1582 (0.138) (NN) -0.0390 (0.088) -0.0382 (0.085) (QP) -0.0872 *** (0.032) -0.0940 *** (0.032) (QS) -0.0063 (0.040) -0.0077 (0.039) (QL) -0.1571 *** (0.027) -0.1646 *** (0.028) (QT) -0.0352 (0.033) -0.0313 (0.033) (QN) 0.0354 (0.030) 0.0303 (0.030) (PS) 0.5753 *** (0.154) 0.5666 *** (0.149) (PL) 0.1849 *** (0.061) 0.1817 *** (0.059) (PT) -0.1062 (0.114) -0.0907 (0.112) (PN) 0.0857 (0.065) 0.0847 (0.064) (SL) 0.1159 * (0.067) 0.1020 (0.068) (ST) -0.0029 (0.117) 0.0014 (0.114) (SN) -0.2138 ** (0.100) -0.2038 ** (0.098) (LT) 0.0614 (0.064) 0.0663 (0.063) (LN) -0.0240 (0.061) -0.0153 (0.060) (TN) 0.1031 (0.079) 0.0999 (0.077) Comp. tendering (dT) 0.0144 (0.039) 0.0126 (0.038) Constant 11.8616 *** (0.017) 11.7343 *** (0.061) 2 2 2 σ = σu +σv 0.0684 *** (0.015)

λ = σu/σv 0.7593 *** (0.091) ***, **, *: significant at 1%, 5% and 10%; standard errors are given in brackets. n = 568

4.7 APPENDIX 131

Table 4–7: Correlation of cost efficiency scores and Spearman rank correlation

Model I Model II SFA SFA +

dummy f(u i ) Model I 1 0.9994 *** Model II 0.9992 *** 1 Correlation of efficiency scores in the lower, Spearman rank correlation in the upper triangle matrix. n = 568 ***, **, *: significant at 1%, 5% and 10%, respectively.

APPENDIZES

ABBREVIATONS

AIC Akaike Information Criterion

BIC Bayesian Information Criterion

CE Cost Efficiency

COLS Corrected Ordinary Least Squares

DEA Data Envelopment Analysis

EBG Eisenbahngesetz

FDH Full Disposal Hull

FE Fixed Effects

GLS Generalized Least Squares

JLMS Jondrow, Lovell, Materov, Schmidt

LC Latent Class

ML Maximum Likelihood

MSL Maximum Simulated Likelihood

MOLS Modified Ordinary Least Squares

OLS Ordinary Least Squares

PG Postgesetz

POG Postorganisationsgesetz

PV Postverordnung

PTT Post, Telephon, Telegraph

QR Quantile Regression 134 APPENDIZES

RE Random Effects

RP Random Parameter

SFA Stochastic Frontier Analysis

TFE True Fixed Effects

TRE True Random Effects

WLS Weighted Least Sqares

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CURRICULUM VITAE

I was born on the 1st of December 1978 in Switzerland as the third of seven children of Agnes and

Franz Koller-Keller.

Education

2008 – 2012: Doctoral studies at Centre for Energy Policy and Economics (CEPE), ETH Zürich

2002 – 2006: Master of Arts in Economics at University of Zürich

1999 – 2002: Grammar school at Interstaatliche Maturitätsschule für Erwachsene, St.Gallen

1998: Military service

1994 – 1998: Apprenticeship as electrician

1985 – 1994: Basic education

Work experience

2011 – 2012: Economist at CEPE, ETH Zürich

2007 – 2010: Economist at Swiss Post, Bern

2007: Management consultant at b&m management, Zürich

2006: Assistant at CEPE, ETH Zürich

2002 – 2005: Partner at Thailandvolunteering, Rapperswil

2001 – 2005: Teacher at different private and public schools

1999 – 2001: Technician at Netstal Maschinen AG, Näfels

1994 – 1998: Apprenticeship as electrician