Assessing the Value of Museums with a Combined Discrete Choice / Count Data Model Jan Rouwendal, Jaap Boter
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Assessing the value of museums with a combined discrete choice / count data model Jan Rouwendal, Jaap Boter To cite this version: Jan Rouwendal, Jaap Boter. Assessing the value of museums with a combined discrete choice / count data model. Applied Economics, Taylor & Francis (Routledge), 2009, 41 (11), pp.1417-1436. 10.1080/00036840601019240. hal-00582083 HAL Id: hal-00582083 https://hal.archives-ouvertes.fr/hal-00582083 Submitted on 1 Apr 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Submitted Manuscript For Peer Review Assessing the value of museums with a combined discrete choice / count data model Journal: Applied Economics Manuscript ID: APE-06-0127.R1 Journal Selection: Applied Economics D61 - Allocative Efficiency|CostÂBenefit Analysis < D6 - Welfare Economics < D - Microeconomics, R53 - Public Facility Location JEL Code: Analysis; Public Investment; Capital Stock < R5 - Regional Government Analysis < R - Urban, Rural, and Regional Economics Keywords: museums, travel cost method Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Page 1 of 29 Submitted Manuscript 1 2 3 4 5 6 7 8 Assessing the value of museums with a combined discrete choice / count data 9 10 model 11 12 Jan Rouwendal * 13 14 15 Department of Spatial Economics 16 Vrije Universiteit Amsterdam 17 De Boelelaan 1105 18 1081 HV Amsterdam For Peer Review 19 The Netherlands 20 21 22 and 23 24 Jaap Boter 25 Department of Marketing 26 Vrije Universiteit Amsterdam 27 28 De Boelelaan 1105 29 1081 HV Amsterdam 30 The Netherlands 31 32 33 This version: July 17, 2006 34 35 36 37 Keywords: museums, travel cost method 38 JEL Classification Codes: D61, Z11, R41, R53. 39 40 Abstract 41 42 This paper assesses the value of Dutch museums using information about destination choice as 43 well as about the number of trips undertaken by an actor. Destination choice is analyzed by 44 means of a mixed logit model, and a count data model is used to explain trip generation. We use a 45 utility-consistent framework in which the discrete choice model for destination choice is linked to 46 an indirect utility function. The results are used to compute the compensating variation of 47 particular museums and of the total group of museums in the sample. 48 49 50 51 52 53 54 * 55 Corresponding author. E-mail: [email protected] ; tel. +31.20.4986093; fax +31.20. 56 5986004. Jan Rouwendal is also affiliated to the Tinbergen Institute. 57 58 59 60 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Page 2 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 For Peer Review 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Page 3 of 29 Submitted Manuscript 1 2 3 1 Introduction 4 5 Museums, theaters, recreation sites, or nature reserves often rely on government funding, as they 6 are valued by the population but unable to survive in an open market. Such government funding 7 is believed justified as long as its level does not exceed the total value the population adheres to 8 such collective goods. As the services provided by these amenities are not traded in an open 9 market, standard methods cannot be used to determine their value. Ever since Hotelling suggested 10 the ‘travel cost method’ in 1947, transportation costs have been used in economics to assess the 11 12 value of location-specific services. The essential idea is that the travel cost can be interpreted as 13 the price of using the facility and that the demand function can be obtained by plotting the 14 number of visitors as a function of their distance to the facility. The empirical demand function 15 may then be used as the basis for welfare calculations. The travel cost method was further 16 developed and refined in the 1950s and 1960s by Clawson (1959) and Clawson and Knetsch 17 (1966), among others. In the 1970s the economic analysis of discrete choice (see McFadden 18 For Peer Review 19 1974, 1981), enabled researchers to analyze a trip to a particular facility as the best choice among 20 a number of alternatives that are explicitly taken into account. The next and most recent 21 improvement of the travel cost method is the model of Hausman, Leonard and McFadden (1995) 22 that covers trip generation as well as destination choice in a single utility maximizing framework. 23 The method proposed by Hausman, Leonard and McFadden (HLM) is a major step forward. Its 24 25 significance is not confined to applications of the travel cost method, but extends to the field of 26 transportation economics, where trip generation and trip distribution tend to be studied 27 separately. However, it will be shown in this paper that a problem is associated with the use of 28 the logit model (and generalizations like the nested logit) in the HLM framework. Moreover, an 29 inherent limitation of their method is that effects of income on destination choice are excluded. 30 31 For these reasons, we propose an alternative. Like HLM, we use a logit model for destination 32 choice and integrate it with a count data model for the number of trips. However, whereas the 33 HLM framework is based on separability of the direct utility function, our approach assumes 34 separability of the indirect utility function. We show that the logit model for destination choice 35 fits naturally in this framework and that effects of income on destination choice can be 36 incorporated. The model we develop is consistent with the determination of the number of trips 37 38 and destination choice as two stages in a utility maximizing planning procedure, just as the one 39 proposed by HLM. Also, empirical implementation can start with estimating the sub-model that 40 explains destination choice and the results can be used in estimating the count data model for trip 41 generation in a second stage of the estimation process. In the discrete choice/count data model 42 developed in this paper the total change in welfare that results from disappearance of a facility is 43 44 (apart from special cases) a nonlinear function of the change in the logsum. In our model the 45 change in the logsum can be interpreted as the approximation of the welfare effect that results 46 from ignoring the substitution between museum trips and other commodities and is therefore 47 biased upward. 48 We demonstrate the alternative model in an application of museum visiting. So far the use of 49 travel-cost based procedures to determine the value of cultural goods has been limited. To our 50 51 knowledge, there have been three applications of demand functions based on travel costs. Forrest, 52 Grime and Woods (2000), and Poor and Smith (2004) show that the use value of, respectively, a 53 local theater and a heritage site alone exceed public funding. Martin (1994) uses travel costs as 54 part of assessing the overall value of a local museum, whereby non use value is determined 55 through Contingency Valuation. Rather than determining the value of a single cultural institution 56 57 or site, Boter, Rouwendal and Wedel (2005) show how multiple museums may be compared by 58 the different willingness to travel of their visitors. They use a discrete choice approach, 59 60 1 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Page 4 of 29 1 2 3 employing information on destination choice only. Heterogeneity among consumers is taken into 4 5 account by means of five latent classes of consumers and there is no welfare analysis, only a 6 comparison of the estimated attractiveness of the museums. In the empirical work in this paper 7 we use a full-fledged discrete choice/count data approach. Moreover, we account for 8 heterogeneity among the decision makers by adopting a mixed logit approach. Our mixed logit 9 destination choice model implies that the logsum, which is the welfare indicator related to 10 destination choice, is a random variable. Since the logsum plays a role in the count data model, 11 12 this randomness has to be taken into account in estimating the latter model. 13 14 2 The two-stage budgeting model 15 16 2.1 Introduction 17 Much travel behavior has at least two aspects: how many trips to make and which destination to 18 For Peer Review 19 choose on each trip. In transportation analysis these two aspects are often described as, 20 respectively, trip generation and trip distribution and the two tend to be studied relatively 21 independent of each other. The separation between these two aspects is more or less analogous to 22 the two stage budgeting procedure in applied consumer theory. Two-stage budgeting allows a 23 researcher to study the determination of the budget for expenditure on a group of commodities 24 25 (for instance, those to be bought during a particular period) separately from the way this budget is 26 distributed over particular commodities.