Development index: analysis of the basic instrument of Croatian regional policy
ANA PERIŠIĆ, mag. math.* VANJA WAGNER, mag. math.*
Preliminary communication** JEL: R1, C18, C43 doi: 10.3326/fintp.39.2.4
* The authors would like to thank Dubravka Šišak Jung, PhD as well as to two anonymous referees for their useful comments and suggestions. ** Received: June 1, 2014 Accepted: November 21, 2014 The article was submitted for the 2014 annual award of the Prof. Dr. Marijan Hanžeković Prize. Ana PERIŠIĆ Polytechnic of Šibenik, Trg Andrije Hebranga 11, 22000 Šibenik, Croatia e-mail: [email protected] Vanja WAGNER University of Zagreb, Faculty of Science, Department of Mathematics, Bijenička cesta 30, 10000 Zagreb, Croatia e-mail: [email protected] ------for a i X (1) ), (3) unem- 2 ), (5) educational attain- 4 per capita (X ), (2) budget revenue 1 c is calculated using the formula per capita (X ), (4) change in population number (X 3 ), relative to the national average. The value of the development in 5 X , i = 1,2..., 5 represent the normalized value of a sub-indicator ic x INTRODUCTION territorial unit c. The indicators, their corresponding weights and other issues are determined by a government decree (Decree on Development Index, Ac 2010). cording to the values of their development indices, LGUs are categorized into 5 ment (Puljiz, 2009). This prompted several groups of authors to propose that the state grants and subsidies are unclear and non-transparent for allocating criteria (Ott and Bajo, 2001; Bronić, 2008, 2010). Therefore, in 2009, a new Law on Regional Development inaugurated a new cat egorization of local (LGU) and regional (RGU) government units based on the index is a composite indicator The development index. of a development value indi- socio-economic normalized basic five of average weighted the as calculated cators: (1) income The State has a constitutional obligation to promote the economic development of development economic the promote to obligation constitutional a has State The economic progress all the regions in Croatia and to promote and the social welfare units territorial of development of level the of assessment Accurate citizens. all of and is a key criterion for is crucial for regional planning and development policy, the allocation of various structural funds and national subsidies (Cziraky et al., making capacities, fiscal low entail units local in situations economic Poor 2005). of pursuing their own develop incapable them dependent on state subsidies and Abstract re and local of Croatian categorization and assessment level The development the main in index which is of the development is based on the value gional units The index is development a indi composite policy. regional strument of Croatian cator calculated as a weighted average of five socio-economic indicators. The development of the and sensitivity uncertainty the paper is to analyze goal of this This used in its construction. and indicators the procedures arise from index that The impovements. for future guidelines useful used to propose analysis is then index has development been critically re regional methodology of the Croatian An of outliers. existence and the of multicollinearity problems revealing viewed, - for weight selec approach multivariate objective more empirical and relatively conducted analysis were and sensitivity uncertainty The tion has been proposed. Instead of a simulations and variance-based techniques. using Monte Carlo units an alternative of territorial level for the development estimate unique point was considered. approach confidence interval un indicators, multivariate analysis, development index, composite Keywords: Croatia certainty analysis, sensitivity analysis, 1 ployment rate (X dex for a territorial unit where ment rate (
financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy 39 (2) 205-236 (2015) 206 financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy
207 39 (2) 205-236 (2015) ------Sensitivity analysis examines the effects of variability
the development index and to propose an improved method for its Poorly constructed or may composite indicators misinterpreted send misleading importance, major of is models such of validation the Therefore, messages. policy and many methods and approaches of model validation have been devised. Since 1994), al., et (Oreskes true proven being of sense the in validated be cannot models Rosen (1991) proposed that the justification for a composite indicator liesin its fitness for the intended purpose and in peeracceptance. a However, group of au groups, while RGUs are classified into 4 groups. LGUs classified in groups I or II, I or groups in classified LGUs groups. 4 into classified are RGUs while groups, and development, in behind lagging as rated are I group into classified RGUs and The level. support from the state are granted special a special status and thus have development the of basis the on RGUs and LGUs of classification and evaluation years. conducted every three index are The main goal of this study is to examine the existing methodology of the con- methodology the existing goal of this study is to examine The main struction of thors (Saisana and Saltelli, 2008) report that it is more defensible and correct to ca be corroborated if it passes say that a model can tests that assess the model’s pacity to explain or “system” in a predict the convincing and parsimonious way. indicators composite misuse, their minimize and utility their maximize to order In transparently, documented evidence, available best the using developed be to need and validated using appropriate uncertainty and sensitivity analyses. Uncertainty analysis focuses on how the uncertainty in the input factors propagates through indica the values of the composite and affects indicator of the composite structure tor (Saisana et al., 2005). in most While as possible sources of instability. of indicators and interactions cases the sensitivity and the uncertainty a analysis syn are conducted separately, of during the development analysis and a sensitivity use of an uncertainty ergistic a composite indicator could improve the structure (Nardo et al., 2005; Saisana et al., 2005; et Tarantola al., 2000; Gall, 2007). For example, Saisana et al. (2005) conducted uncertainty and sensitivity analyses using Monte Carlo simulation and variance-based techniques. Furthermore, Paruolo et al. (2013) suggest Pearson correlation coefficient as Also, a they measure conducted of variable importance. techniques and applied these methods to sensitivity analysis using variance-based various composite indicators. On the other hand, Hoyland et al. (2012) criticize index without incorporat into a composite variables the approach in aggregating ing uncertainty. They suggest a Bayesian approach when assessing uncertainty Another group of authors indicators. and apply this method to three composite (Nardo et al., 2008) provide directions for the construction of composite indica of sensitivity and uncertainty for implementation tors and give recommendations Apart analyses. from the papers analyzing regional disparities in Croatia and the develop- socio-economic to according RGUs and LGUs Croatian of classification 2005; 2003, al., et Cziraky 2002; Filipić, and Grčić 1992; al., et Rimac (e.g. ment Perišić, 2014) there is a lack of related work regarding sensitivity of categoriza- tion and uncertainty in the construction of the development index. - - - - - vice with re-
per capita, per capita, , change in population in change per capita, DevelOpmeNT l DevelOpmeNT ODellINg RegIONA DevelOpmeNT pOlICy The RegIONAl DevelOpmeNT The DevelOpmeNT Of The DevelOpmeNT gyThe meThODOlO Of m IN CROATIA spect to the indicators involved in its construction. Uncertainty and sensitivity Uncertainty and in its construction. indicators involved spect to the in an important role analyses play of the construction and composite indicators because of their generality these methods can be applied in wide-ranging fields. methods. using multivariate of data structure also includes the analysis The study and experts in in this paper can be useful to policymakers The methods presented of the composite indicators. assessing the reliability 2 duced in 2002, comprises local units that are lagging behind in development ac cording to four criteria: economic development, structural graphic, and difficulties, a demo- special criterion (Bronić, 2008). The introduction of Eleven indicators in developing regional policy. was a step forward nomic criteria socio-eco- were used for the designation of the third category ASSC: of income share of population earning an income, municipality (direct) income aid social rate, employment rate, unemployment number, educational attainment rate, population density, age index and vitality socio-economic aforementioned four the to addition In 2005). al., et (Puljiz index criteria, two special criteria related to border position and mine area status were used. In total, 185 LGUs enjoyed a special status; of these, 50 were classified in ASSC. of category third the in 74 and category, second the in 61 category, first the to related not were ASSC of designation for criteria the that appeared it However, the real socio-economic indicators. Bajo and Primorac (2013) report that prefer (above aver more developed ential status was also given to some economically age) LGUs. Furthermore, a group of authors (Maleković et al., 2011) conclude that the regional development approach, inherited from central planning, was in regional The instruments. and actors, goals, defined clearly lacking and consistent policy has been often conducted within the scope of fiscal equalization and clashed, often policies these of objectives the and instruments the whereby versa, and the effects were neutralized at a high cost to the state budget. Consequently, of a simple The introduction to regional policy needed to be changed. laws related fis- and criteria appropriate on based equalization fiscal of system transparent and 2.1 af- areas of renewal the on focused was policy regional Croatian beginning, its In fected by war. Some progress was made when the Law on the Areas of Special to order in established were areas These implemented. was (ASSC) Concern State status in the a special and thus they have more rapid development their encourage in adopted ASSC on Law the to According 2001). Bajo, and (Ott regime financing defined were categories two first The formed. were units of categories three 1996, on the basis of damage caused by the war in Croatia. The third category, intro - the categori of and sensitivity the uncertainty into account taking by calculation zation of LGUs and RGUs. Uncertainty of the development sensitivity is methodology and the construction considering evaluated index is assessed
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------equitable support system. The establishment of a comprehensive and coherent regional development policy development and coherent regional of a comprehensive The establishment on system based of the principles with policy started along regional contemporary Union to the European of Croatia for the accession activities the preparatory the was policy regional of implementation the for basis The 2012). al., et (Sumpor adoption of the Law on Regional Development in 2009. This Law regulates re cal instruments remains a challenge for the Government 2013). (Bajo and Primorac, Supported areas were supposed to replace the ASSC, but instead, a parallel exist Supported areas were supposed to replace the gional policy by introducing the development index as a basis for the development index as a basis gional policy by introducing socio-eco the nomic development assessment and categorization of territorial units. In addition According level of to that, the development LGUs was assessed for the first time. to the Ministry of Regional Development and EU Funds (MRRFEU), the single transpar and to the simplicity index contributes development system based on the ency of the whole system, enabling the better direction of incentives and the ac the of units from or exclusion inclusion the basis for of a high-quality quisition 2012). supported areas (MRRFEU, This perennial categories of underdeveloped areas occurred. ence of different of a new Law on Regional Development. problem will be solved by the adoption Furthermore, this new Law will introduce a uniform The application to the whole state. units applicable level assessment of territorial system for development novelties the of Some 2015. in expected is law new the by introduced measures of of the new Law are introduction of the category of urban area (and additionally, among such areas, agglomeration centers), the formation of the Council for re which index, development to measures future all binding and development gional assessment of LGUs and RGUs level for development acts as the basic instrument Devel- Regional on Law the ASSC, on Law the changing By 2013c). (MRRFEU, opment, the Law on Hill and Areas Mountain and the Act, Personal Income Tax the Government endeavors to harmonize tax reliefs and distribution of grants to The index. by the development LGUs level measured with their development the grants from to LGUs involve redirecting main changes in the grant distribution the state budget to LGUs, according to the development index, in the amount of corporate income tax generated in their area, and changes in the and basic I categories personal in classified LGUs this, By 2013). Primorac, and (Bajo allowance collected revenue tax income corporate (100%) entire the to right the obtain will II in and 60%, IV group in 75%, of amount the in aid to III category in area, their in category limitation IV A 40%. of this distribution can be presented by following having the development index value of 74.82%, municipality, Tovarnik example: will obtain the right to Governmental support in the amount of 100%, while the City of Ozalj, with a development index value of 75.08%, will obtain the right to aid in the amount of 75%. These two marginal examples show that more legiti mate support is needed. For example, would contribute to an introducing partially linear deductions ------), average N), , revenues from the dis along with standard deviation (in along with standard deviation 5 (with the reduction by 0 points for (with the reduction by per capita (without the reduction by 0 points (without the reduction KV V I I ,.., X 1 X along with standard deviation (in brackets). 5 ,..., X 1 X egORIZATION Of lgUs AND Of Rg TOgUs ACCORDIN egORIZATION The CAT INDeX DevelOpmeNT According to the value of the development index, LGUs groups (table 1). 1 Table are also provides the classified number of LGUs intoclassified into each 5 group (N), average values of indicators 2.2 Adopting the new Law on Regional Development will stop there being two laws being two stop there will Development Regional Law on the new Adopting that define supported areas. ASSCHowever, again have a special status during to the Decree Amendments The Decree on of assessment level. the development on development index implies that the the Development index value of the LGUs ASSC will be reduced by 10 points (the adjusted index) if their in original the in Develop on Decree the to Amendments on (Decree 75% than higher is value dex ment index, 2013). In this paper, two indices will be obtained for the local level (LGU): the unadjusted development index brackets). Large standard deviations indicate heterogeneity within the group. standard deviations brackets). Large According to the development index, RGUs are classified into4 groups (table 2). ( group each into classified LGUs of number the provides also 2 Table values of indicators LGUs classified into categories I or II, and RGUs classified in category I are rated I are category in classified RGUs and II, or I categories into classified LGUs there Croatia, In status. special a have thus and development in behind lagging as are 556 LGUs, composed of 429 municipalities and 127 towns, with the City of Zagreb, the capital of Croatia, having the status of both county and town. More development the to according while ASSC, on located are LGUs of third one than index, almost one half of LGUs and more than a half of RGUs are categorized as areas lagging behind in development. for ASSC) and adjusted development index development adjusted and ASSC) for ASSC). The methodology for construction of the development index for the period 2010- on Decree the 2013, In 2006-2008. period the for used that from different is 2012 Amendments to the Decree on Index the Development two introduced main mod ifications: when calculating budget revenue posal of non-financial assets are excluded; also, the value of the development in dex is reduced by 10 points for LGUs from the firstor second ASSC category of that have a value of the development index greater than 75%. The first modifica tion prevented the impact of short-term funding sources in budget revenues on the value of development index. The second modification was introduced in order to area for undeveloped LGUs assure the retention of the status of supported that were By by affected this the modification,war. 24 LGUs from the first or second ASSC category are, of according to the adjusted development index, categorized as supported areas, although according to the unadjusted development index they development level. belong to categories of middle or higher
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211 39 (2) 205-236 (2015) - (%) (%) 72 5 5 (5.1) (4.9) (8.1) (8.7) 80.35 83.32 62.17 54.07 84.23 79.51 69.38 78.84 (6.78) (3.14) (3.71) (3.93) (4.32) X X 4 4 94.1 (2.4) 108.1 99.92 92.83 86.20 100.3 (9.27) (8.91) (2.55) (2.67) (3.57) 119.48 119.48 101.77 106.53 (11.01) (12.15) (28.22) 8 (%) X (%) X 3 3 (3.1) (3.6) (4.5) (6.3) 10.84 14.89 22.89 37.67 10.37 20.47 16.43 13.20 (6.59) (2.46) (4.78) (3.58) (1.95) X X 2 2 (682) (506) (337) (472) 5,213 3,166 1,912 2,597 748.87 (472.4) 1,912.6 (288.98) 7,060.54 3,556.06 1,020.29 (1,359.8) (1,179.26) (1,064.74) The CONSTRUCTION X X 1 1 (785) 35,662 25,460 27,156 22,798 (5,655) (2,746) (2,494) 18,095.3 28,557.11 28,557.11 29,938.73 23,355.31 13,049.28 (6,000.14) (4,426.46) (3,668.74) (3,333.85) (2,146.69) NX NX ASpeCTS Of <50 47 < 75 12 >125 26 >125 3 <50, 75> 217 <75, 100> 173 <100, 125> 93 Development Development Development index value (%) index value (%) index value 2 1 meThODOlOgICAl Of COmpOSITe INDICATORS Of able able V IV III II Cate- gory Cate- gory I IV I IIIII <75, 100> <100, 125> 3 3 The categorization of RGUs according to development index The categorization of RGUs according The categorization of LGUs according to development index development to according of LGUs The categorization In the indicators literature there is a fundamental division between those who there is a fundamental In the indicators literature choose to aggregate variables into a composite indicator, the aggregators, those who and do not, the non-aggregators. The aggregators believe that composite indicators can capture reality and are meaningful. Moreover, they believe composite indicators are extremely useful in garnering media interest and hence that emphasize non-aggregators the hand, other the On makers. policy of attention the are combined by which the variables process of the weighting nature the arbitrary and indicators select to how to as exist also disagreements Certain 2004). (Sharpe, techniques for measuring disparities. Relying solely on economic indicators is questionable due to the fact that development either leaves behind, or in ways even some creates, large areas and of stagnation, actual poverty, marginality, ex 3 Source: Authors’ calculation. Authors’ Source: T Source: Authors’ calculation. Authors’ Source: T ------per and unemployment rate became key indica- per capita INDICATORS SeleCTION INDICATORS torial units. Thereby, income Thereby, units. torial basis the on excluded were indicators some while disparities, socio-economic of tors and too high of or their too weak low credibility, correlation with the key economic indicators (Puljiz et al., 2005). For instance, infrastructural indicators were rated as not reliable; the indicators “share of persons earning an income” and “income capita” were highly correlated (coefficient of correlation was 0.93); the indicators In the process of the construction of new composite indicator, the development in- dex, the main criterion for variable selection was the estimation of the contribution to the objective variable’s estimation of socio-economic differences among terri jectivity. The use of multivariate analysis jectivity. helps to identify the data structure, and Multivariate results. final of interpretability the and accuracy the both increase can methods can also help to investigate the presence of Multicol multicollinearity. variables position because multicollinear linearity causes an unequal variable measure the same phenomenon, which in turn has a multiple contribution to the value of An the additional composite problem indicator. is the difficulty of inter pretation, while it is hard to assess the impact of the individual variable. If two be may model the in them of both of inclusion the correlated, highly are variables redundant (Salzman, 2003). 3.1 qual- from the derived are indicator The strengths and weaknesses of a composite basis of their should be selected on the Variables ity of the underlying variables. relevance, analytical etc. The soundness, choice timeliness, of accessibility, indi- sub developer’s the limiting framework, theoretical the by guided be must cators The main pros of using composite indicators are the ability of summarizing com- plex, multi-dimensional realities, an easy and direct interpretation, facilitation of of a set of indicators amount the and reducing public with general communication main cons are related to a The base. underlying information without dropping the problem of if the indicators are poorly misleading policy messages constructed or misinterpreted, they can invite simplistic policy conclusions, the selection of indi clusion from economic and social progress is too obvious and too urgent to be to urgent and too obvious is too progress and social from economic clusion the for indicators more including for need The 1969). Nations, (United overlooked purpose of resulted in a considerable development socio-economic measuring composite indicators. number of inappropriate to lead and dispute political of subject the be could weight and cator policy (Nardo et al., 2005). If the construction process is not transparent and/or lacks sound statistical or conceptual principles, composite indicators can be mis The to support preferred policy. in order can be manipulated used and index values theoretical framework of composite indicators are: basic steps in the construction nor analysis, multivariate data, missing of imputation selection, data construction, malization, weighting and aggregation, uncertainty analysis, sensitivity analysis, al., 2005). and visualization (Nardo et linking to other variables, presentation
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213 39 (2) 205-236 (2015) , - - - - - per per a skew per capita is calculated ), standard deviation standard x), per capita (GDP per capita) was capita) per (GDP per capita ˉx has the largest dispersion both on local and has the largest 2 X , unemployment rate, change in population number, and and “unemployment rate” (Puljiz, 2007). Due to some 4.5 54.48 18.94 9.24 0.86 223 10,115 1,981.59 1,695.36 1.96 41.3 247.8 98.3 13.8 2.72 7,105 42,175 21,609.14 6,088.6 0.38 per capita per capita” as an indicator on the local level because it is calculated on because it is calculated on the local level as an indicator per capita 3 (%) (%) 31.65 90.41 68.58 11.07 -0.36 3 4 5 2 able X X X Indicator min. max. X X The effect of an outlier, when the outlier is excluded, asymmetry coefficient is 0.65. The effect of an outlier, T regional level. Indicators LGU a calculation. Authors’ Source: () and asymettry coefficient (skew) are presented in tables 3and 4 for the LGUs Variable and RGUs respectively. Minimum value (min), maximum value (max), mean value ( ˉ ( value mean (max), value maximum (min), value Minimum “vital “vital index” and “age index” had a too low correlation coefficient with the indica tors “income tors “income not involved in the construction of the development index. However, the GDP - that the reliabil it is expected while indicator as a potential capita is still considered ity it of will is grow the not estimation (Puljiz, of possible 2007). GDP to However, use the GDP the regional and state level. The Decree on The Decree on Index the Development prescribes the the regional and state level. income index: of the development used in the construction indicators methodological difficulties, gross domestic product domestic gross difficulties, methodological educational attainment rate. The indicator values have been acquired from MRR budget revenue FEU (2013a, 2013b, 2010a, 2010b). Local/regional income by dividing the total income in a tax period (one calendar year), generated by taxpay- by generated year), calendar (one period tax a in income total the dividing by ers, persons domiciled or habitually resident, in the territory of the local/regional unit, by the total population number of a local/regional unit. Budget revenue capita is calculated by dividing the realized reduced local/regional budget revenue by the population number of a local/regional unit. Budget revenue pur is derived receipts transfers, and reduced subsidies aid, foreign by: and domestic from receipts suant to special contracts (co-financing by citizens), additional share in income tax, equalization aid for the decentralized functions and disposal of non-financial assets. by dividing the total number of unemployed per rate is determined Unemployment sons by the sum of unemployed and employed persons in the area of the local/re of of the number number is expressed as the ratio unit. Change in population gional the population in a local/region unit according to the last two consecutive censuses. as the number of persons with secondary rate is calculated attainment Educational education and higher, aged over 15 years, as a proportion of the LGU/LRU. population aged 16-65 in the area of the total number of
0 ------i is i vis- X (2) (3) (4) skew
across all units c; x across is the minimum value
i i,min
; x i The calculation represents the average value of indi average value the represents i ˉx (formula 5) i X for a local unit c; unit for a local i is the maximum value of indicator X . i i,max is the standard deviation of indicator X is the standard i 7.80 25.90 17.41 5.54 0.17 90.7 109.1 97.86 5.42 0.50 1,368 5,997 2,660.48 1,248.45 1.36 19,455 42,175 25,638.19 5,262.95 1.66 across all units c; x across i is the value of indicator X ci across all units c; across 5 4 i NORmAlIZATION NORmAlIZATION (%) 62.49 86.93 74.30 7.01 0.15 (%) 5 3 4 2 able able X Min-max Distance to a reference Standardization (z-score) Normalization methods X Indicator min. max. X X X is the reference value for indicator X is the reference Evaluated normalization methods Indicators RGU Indicators cator X Remark: x a as selected was method min-max the Index, Development the on Decree the By suitable normalization method. The min-max normalization of an indicator 3.2 Data normalization is often required because the indicators in a data set have dif standard devia in their means or differences units or large ferent measurement The tions. normalization phase can be crucial for the accuracy of a composite in tech normalization simplest The units. of ranking the for accordingly and dicator con- or Standardization, outliers. by affected not is method This ranking. is nique verting to z-scores, on the other hand, is one of the most popular normalization by outliers since indicators with extreme values have a methods. It is affected on greater the effect composite The indicator third value. widely used normaliza tion method is the min-max method, which normalizes the indicators so that they position to a reference measures the relative range. Distance have an identical value, minimum value, average the be could reference (the point reference a à-vis by the expert decision). maximum value or some other value determined T Source: Authors’ calculation. Authors’ Source: T of indicator X conducted by subtracting the minimum value and dividing by the range of the in- dicator values. Furthermore, this normalized value is divided by the normalized state average value of the indicator
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215 39 (2) 205-236 (2015) ------(5) when there is
determination of weights for various components implies the exist a priori determination ggRegATION WeIghTINg AND A Since the extreme values are usually outliers, this normalization method should be should method normalization this outliers, usually are values extreme the Since revised (in the sense of excluding outliers or even changing the method). Changing normalization the minimum value of an indicator can affect the composite indicator values of all units. The normalization defined in formula 5 reduces the nominal value of each indicator to a distance to the value relative to minimum the average to the minimum value. distance of the national An ticians, like budget allocation processes, analytic hierarchy processes and conjoint and processes hierarchy analytic processes, allocation budget like ticians, the reflect to order in selected often are weights The 2008). al., et (Nardo analysis ap This to be measured. for the phenomenon of the indicator importance relative proach is often criticized as too arbitrary since weighting can have a significant effect on composite index value and ranking of units. On the other hand, multi variate techniques present an empirical and relatively more objective option for weight selection, allowing for no control over the selection of weighting scheme. This is due to the fact that the weights are selected based on the data themselves. weight weights is often bypassed by equal an indicator’s of selecting The problem ing, i.e. all variables are given equal weights. Composite indices generally seem to be additive, with equally weighted components (Booysen, 2002). This essen could it but composite, the in same the “worth” are variables all that implies tially also disguise the absence of a statistical or an empirical basis, e.g. or a lack of consensus insufficient knowledge of causal relationships on the alter native (Nardo et al., 2005). When a few highly correlated indicators equal exist weighting and is applied, double counting may be introduced into the index. Thus, it is desirable to perform correlation analysis prior to weight selection and correlation analysis. to adjust weights according to results of ence of a universally acceptable human welfare/development function, which is not the case (Noorbakhsh, 1998). Thus, the empirical approach, as an alternative approach to weight setting, is worth pursuing. In order to generate a set of non- subjective weights, has PCA been applied for the calculation of development in- reduction the enables PCA 2010-2012. for and 2008-2010 period the for both dex of the variables by a small number of their linear combinations. The objective is 3.3 Perhaps the most difficult aspect of constructingchoosing weights a multidimensional for the components index is (Tofallis, 2013). analysis, A factor as number such models, of statistical from derived weighting are Some exist. techniques principal component analysis (PCA), data envelopment analysis, or from partici- patory methods that incorporate various stakeholders – experts, citizens and poli
j ------Y (6) are 5 linear combinations k ≤ k.
SIS ANAly , is the linear combination of the variables that Y AND SeNSITIvITy a priori criterion, scree test and proportion of variance criterion are chosen, maximizing the variance of the original data. of the original maximizing the variance are chosen, i X UNCeRTAINTy individual indicators. An undesirable feature of linear aggregation is that it implies is that it implies feature of linear aggregation An undesirable indicators. individual compen be can indicators some in performance poor that such compensability, full sated for by sufficiently high values in other indicators. Geometric aggregation is degree of non-compensability. better suited if the modeller wants some
has the greatest possible variance. Various guidelines have been developed on the guidelines Various possible variance. has the greatest k combinations linear issue of how many should be retained. For instance: the la than greater an eigenvalue (only components that have tent root criterion retained), the (Hair et al., 1995). In practice, very few composite indices use PCA weights, in part because it is difficult to explain the process to non-statisticians, in part be cause the weights themselves change as the data changes over time, but mainly sub weights tend not to differ and PCA weights the results using equal because 2011). Tanner, stantially (Foa and 3.4 methods aggregation and weights determine to way “objective” an of absence The does not necessarily lead to rejection of the validity of composite indicators, as and sensi- of uncertainty combination A transparent. process is long as the entire and im indicator the robustness of the composite analysis can help gauge tivity prove transparency (Nardo et The al., methodological 2008). choices, such as the method normalization the choosing selection, indicator data, missing of treatment as well as the aggregation method, and the weighting scheme have a major influ The goal of the uncertainty analysis is to evaluate ence on the composite indicator. in confidence the in reflected are modeller the by taken choices subjective the how the model. Since the development level of a territorial unit measured, it cannot is be not possible directly exactly to determine how well validated. the be to composite needs index indicator composite a However, phenomenon. this describes Thus, each construction of a composite index needs to involve uncertainty analy sis and sensitivity analysis. uncertainties Generally, during the development of a composite indicator are associated with a number choice of of factors: data error, indica- of transformation the exclusion, and inclusion indicator for mechanism the espe and method aggregation method, normalization of choice data, missing tors, compos a of uncertainty The 2005). al., et (Nardo scheme weighting the of cially Because the composite indicators describe multidimensional phenomena by a uni- dimensional construct, it is necessary to find an appropriate aggregation method. of out method and is independent simplest aggregation is the Additive aggregation weighted of summation the is method, widespread most the aggregation, Linear liers. - of the origi combinations linear a few through data of the variance the to explain nal data minimizing the information Therefore, loss. of variables of variables The first principal component,
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- - - - is (7) (9) (8) 0 i (10) x , (11) to the total output to the total output Y and the individual 1 X . Higher values of the sensitiv- the of values Higher .
i , the first-order sensitivity index sensitivity first-order the , X k . In order to compute a variance- i X
. . needs to be fixed to a specific value i ,…, X 1 X X is obtained; this is determined by their sum. Ti and the variance of the resulting function of function of the resulting and the variance
S ., 2004). In general, Y and indicators , i X . indicate a higher dependance between the index between a higher dependance indicate i i S X V(Y), in its range. Then the mean of the output is computed by averaging over all fac in its range.
is a good model-free sensitivity measure, and it always gives the expected re- 0 i i ity index due to the uncertainty in is the variance of Y due to the uncertainty
tor (interactions) and then to compute high-order sensitivity indices. When additive model is concerned (a model without interactions) the contribution of an an first- the by obtained entirely is composite a of variance the to indicator individual (9) is valid. order sensitivity index and therefore formula Analogously, it is possible to compute conditional variance to more than one fac Analogously, tors but factor
variance High sensitivity to small changes in input information makes the composite index index composite the makes information input in changes small to sensitivity High Thus, when unstable a and composite unreliable. index is being created, it is nec ite index can be assessed by exploring the main sources of with uncertainty, the (Nardo input factors uncertain among effects synergy possible all of capturing aim Carlo simulation. directly or by Monte et al., 2008), For the composite index composite the For essary to determine the effect of the variation in the individual indicator on the indicator individual in the of the variation the effect determine essary to overall index value. Therefore, methods that are not based on the assumptions of et al., 2008). techniques, are used (Satelli the model, such as variance-based
where averaged over all possible values of the indicator averaged over all possible values of the is assessed of an individual indicator as the contribution
dividual indicator (Saltelli et al duction of the variance of the output that one would obtain if one could fix an in For a non-additive model, instead of computing higher-order sensitivity indices, sensitivity index the total effect S based sensitivity measure, the first factor x indicator - - Y per 5 5 X X Y due to the 4 4 X X ) it is possible to compute the Ti . However, unlike the first-order 3 3 i , S i X X X . As in . the first-order sensitivity indi i X indicate a higher dependence of the index dependence a higher indicate Ti S 2 2 X X AND TeSTINg OUTlIeR pReSeNCe of the variance represents index composite the 1 1 X X 0.51 0.250.73 0.51 0.55 -0.39 -0.55 0.51 0.92 0.440.79 0.55 0.81 -0.59 -0.57 0.66 -0.67 -0.48 -0.68 -0.67 and budget revenue per capita, per capita and budget revenue and also budget revenue 7 6 mUlTICOllINeARITy 3 4 5 2 2 3 4 5 ReSUlTS ReSUlTS able able X X X X X X X X X X uncertainty of all indicators but indicator indicators but indicator of all uncertainty sensitivity indices, this sensitivity approach considers all possible with interactions - other in dicators. Therefore, by comparing the pairs (S Correlation matrix RGU Correlation Correlation matrix LGU Correlation Source: Authors’ calculation. Authors’ Source: index. condition and factor inflation variance using assessed was Multicollinearity It can be is concluded that multicollinearity present since the value of variance and (Bahovec 13.8 is index condition of value and 7 than higher is factor inflation by solved be can multicollinearity of problem The 2004). Gujarati, 2009; Erjavec excluding one of the indicators or by replacing it with another For indicator. ex T and educational attainment rate are problematic in the sense of too high are problematic rate attainment capita and educational correlation. T calculation. Authors’ Source: Correlation matrices of indicators on the local and regional level are presented in level regional and on the local of indicators matrices Correlation (at significant statistically and high is indicators of correlation The 7. and 6 tables indicators of coefficients correlation level, regional the On 1%). level significance income 4.1 where where on the variability of an individual indicator indicator of an individual on the variability intensity of indicator interaction. intensity of indicator 4 ces, high values of the total effect
financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy 39 (2) 205-236 (2015) 218 financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy
219 39 (2) 205-236 (2015)
- - - - per capita per capita. . In that pe- . In that LGU per capita (b) Period 2010-2012 0 100 200 300 400 500 600 8 6 4 2 0 12 0 d is expected. Furthermore, local revenues depend mostly on mostly depend revenues local Furthermore, expected. is LGU ) corresponding to LGUs for the period (a) 2006-2008, and (b) and 2006-2008, (a) period the for LGUs to corresponding d) of the average of all LGUs. Dugopolje municipality is an example an is municipality Dugopolje LGUs. all of average the of per capita 1 per capita 0 100 200 300 400 500 600 igure 0 d 0 In both periods one outlier can be detected in the upper right side of the figure. For figure. the of side right upper the in detected be can outlier one periods both In - larg the has which Dugopolje municipality the is outlier the 2006-2008 period the budget revenue high and extremely index est development calculation. Authors’ Source: (a) Period 2006-2008 Outliers were detected using Mahalanobis distance, where observations with large large with observations where distance, Mahalanobis using detected were Outliers Maha Squared 2005). Gal, (Ben outliers as indicated were distances Mahalanobis F and income and income tax revenues, especially on income tax and surtax the when especially redundant, be may on indicators both of inclusion the Therefore, income tax (Ott, 2009). This issue level. regional on a is available per capita key economic indicator GDP can be circumvented by introducing realized local/regional budget revenue in the independence and strength of indicator alternative an LGU/RGU: of income total be should revenue budget local/regional realized the case, that In budgets. local of reduced by receipts from domestic and foreign aid, subsidies and transfers, re ceipts derived pursuant to special contracts (co-financing by citizens), additional share in income tax, equalization aid for the decentralized functions and disposal of non-financial assets. lanobis distances ( 2010-2012 are presented in figure 1. ample, ample, for the development index calculated for the period 2006-2008, the prob lem of multicollinearity was was lem of solved by multicollinearity revenue per budget the indicator excluding capita, of indicators also by and regional with alternative this indicator replacing budget strength high (Perišić, A correlation 2014.). of budget revenue Detection of outliers in LGUs using the squared Mahalanobis distance (d) for the of outliers in LGUs squared Detection using the period (a) 2006-2008 and (b) 2010-2012 riod, the second largest development index corresponds to Kostrena municipality. municipality. Kostrena to corresponds index development largest second the riod, has a however, three This times municipality, smaller budget revenue rev budget the times twenty than more has municipality Dugopolje Furthermore, enue of the failure of aggregation methods, since the deficit in one dimension can be - - - 74 55 66 62 (%) variance variance explained CA p 5 rate 0.22 w attainment educational - priori only one linear combi A CA p 4 0. 0.17 0.22 w number Change in population SIS ReSUlTS CA p 3 rate w Unemployment CA p 2 w Budget revenue revenue CA p 1 0.24 0.24 0.2 0.21 0.22 0.19 0.17 0.21 0.23 0.18 0.21 0.15 0.23 0.21 0.2 0.2 w Income 8 NT ANAly COmpONeNT pRINCIpAl pCA able Index RGU 2006-2008 Index RGU 2010-2013 Index LGU 2006-2008 Normalized weights w Index LGU 2010-2013 Normalized indicator weights according to PCA, LGU and RGU level Normalized indicator weights according nation was selected (k = 1), representing an alternative to the development index. It is statistically justified to retain only one component since only one principal component has the eigenvalue greater than 1, which satisfies the latent root crite lated for both periods, 2006-2008 and 2010-2012. 2010-2012. and 2006-2008 periods, both for lated rion. Indicator weights have been calculated on the basis of PCA, and afterwards note to important is It 8. table in represented are weights resulting The normalized. performing the PCA. that outliers have been excluded prior to T Principal component analysis Principal component is conducted for the development index, and calcu 4.2 compensated by a surplus in another and thus create a false image on the unit’s on the unit’s image a false thus create and in another by a surplus compensated municipality Dugopolje of revenue budget high extremely The level. development situation similar A land. of sale as such sources, funding short-term of result the is occurred with other LGUs. For the period 2010-2012 stands out as number in the population high change outlier with an extremely an the municipality of Vir (247.8). These examples show that outliers create a false image of the develop the ment value level of of the a development index territorial unit, and also affect of all units. This effect, as well as the effect of different data range, is removed and normalization of the data. with transformation One of the weaknesses of the weights derived from PCA is the minimization of the of minimization the is PCA from derived weights the of weaknesses the of One contribution of individual indicators which do not move along with other indi- vidual indicators. In case of development index, the indicator change in popula- because this indicator tion number has the smallest weight determined by PCA exhibits the weakest correlation with other indicators. weights However, derived than those determined are higher indicators to demographic assigned from PCA by the government decree, at both a local and a regional level. Source: Authors’ calculation. Authors’ Source:
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------PCA ), in (12) (13) w PCA I and cor i c I determined by the unad determined NV c . R . is calculated as the weighted average of as the weighted average c is calculated The DevelOpmeNT INDeX The DevelOpmeNT = (0.2, 0.2, 0.2, 0.2, 0.2)). Indices computed with (c = 1,..., 556), the development index E c w . v c I SIS Of , of a local unit ; weights derived from PCA for the period 2010-2012 ; weights derived from PCA c V I w were calculated. Figure 2 shows the smallest, greatest and the and greatest smallest, the shows 2 Figure calculated. were ANAly i c R y UNCeRTAINT AlTeRNATIve NORmAlIZATION meThOD NORmAlIZATION AlTeRNATIve total 57 LGUs are classified intovalue categoryindex the (reducing I, index development andadjusted the 211using When LGUsII. category are classified into for 10 points for the undeveloped LGUs on ASSC), the category II contains 239 development the by II or I categories into classified LGUs three only Also, LGUs. index are now, according to PCA-derived index, classified intohigher groups development level. withOn the a regional level, there is no difference between the classification of RGUs according to government decree and derived the PCA indices are presented in table 0. derived The values of PCA index. justed development index nize weights and normalization method selection as the main sources of uncer In tainty. total, 12 models have been obtained: 3 normalization methods are pre- sented in table 5 and the normalization method determined by the government decree (formula 5); 3 weighting methods (weighting method determined by the government decree Taking into Taking account analogous indices of countries in the region, one can recog 4.4 development index 4.4.1 Uncertainty analysis of the lgU 4.3 Development index, According to the index computed with the use of PCA-derived weights ( weights of PCA-derived with the use index computed to the According different different normalization methods are not mutually comparable. Thus, the uncer tainty was obtained due to i = 1,...,12 and for each LGU the corresponding LGU ranks. For each model relative to the rank median rank value for a LGU c relative (table 8); and equal weights
Section 3.2 gives a critical review of the normalization method used in the con of value maximum the of influence direct The index. development the of struction an individual indicator on the LGU/RGU development index can be removed by combining the min-max normalization and averaging relative to the development index of Croatia (formula 13). The calculation of the development weighted average of the same indicators, but on the state level, would result with index as a an indicator less sensitive to extreme values.
five basic normalized socio-economic indicators five basic normalized responding rank - - (14) possible values of the max c I NV j R and maximum min c I Weights were chosen from the Weights interval . [0.1, 0.6] and scaled c, the minimum and certain jumps of the median rank for the middle region. This 0 100 200 300 400 500 0 100 200 NV 0 500 400 300 200 00 2 j i igure ior. This the inability of indicates a model to estimate the concisely development ior. catego the in disparities significant to leads this Furthermore, units. these of level rization based on development index compared to the categorization based on other models. the relative is determining key issue in the construction of a composite indicator A This weights. indicator choosing appropriate and by that of indicators importance is especially important because the sensitivity of the composite indicator, due to change in weights, opens up the possibility of manipulation of the categorization weights in change to due uncertainty Thus, development. in behind lagging units of is analyzed. For every LGU behavior may indicate a possible overestimation, or underestimation of certain LGUs, especially LGUs with medium development level. On the units, it can same be observed that a wider range of indicator values follow this behav set of Source: Authors’ calculation. Authors’ Source: Analysis of the data presented in figure 2 shows good agreement in low and high regions of R max R min R F
index are calculated to a unity sum. Uncertainty analysis due to LGU rank, LGU level LGU to LGU rank, due analysis Uncertainty
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(15) represent represents v i PCA i
w
w and
, k = 1,2,...,500 were where , where c,k I ) which have the probabil- the have which ) w the probability was estimated
, 3
is analyzed. More than 43% of S min c I . Afterwards, . weights were scaled to and , where , 1 S . PCA c I was conducted by generating 2500 weights from weights 2500 generating by conducted was higher than 0.45:
2 S (c) was conducted by generating 2500 weights from the from weights 2500 generating by conducted was 1 w S p was conducted by generating 2500 weights from the 3 S , the probability of incorrect categorization was estimated was categorization incorrect of probability the , 2 S is calculated for each simulation and each unit. The average is calculated for each simulation and each unit. V . Also, for . simulations . and V 1 c , etermined from PCA. I S PCA determined by the government decree. frequency of incorrectly classified units (n units classified incorrectly of frequency was used, i.e. 56% of the units from the supported areas are not rated not are areas supported the from units the of 56% i.e. used, was form distribution, max c weights uniform distribution, weights d uniform distribution, uni a unity sum. The latter ensured for a unity weights sum. to range between 0.1 and 0.35, of an individual indicator over others. preventing domination (c) Third simulation (c) (a) The first simulation first The (a) (b) The second simulation second The (b) , and PCA, w v due to a categorization based on calculated The first simulation is almost nonrestrictive, while the second and third and second the while nonrestrictive, almost is simulation first The calculated determined by simulation generate weights around values the government decree w Uncertainty analysis on the LGU level was performed using due to the distribution of types of simulations were performed Three simulation. the Monte Carlo weights: units classified into categories III, IV andV bythe development index are now nt. that are lagging behind in developme classified into categories The percentage of simulations resulting in a classification corresponding to the development index I as the relative frequency of incorrect categorization of LGUs due to the categori- zation based on For simulations For simulated indices are the maximum and minimum value in each simulation. Additionally, table 9 provides the Results Results obtained by formula (14) were compared to the results obtained by using the development index. The comparison showed that 56% of units classified into or IV III, categories into classified are index development the by II or I categories when I V ity of wrong classification
After being generating, all weights were scaled to unity sum. For each simulation, each For sum. unity to scaled were weights all generating, being After and for every LGU c, 500 values of development index percentage for each category is provided in table 9, as well as the average range of range average the as well as 9, table in provided is category each for percentage as lagging behind in development. Similar results occur when the classification according to minimum possible index value,
------V V I 0.14 max–min - I
a b w n 71 31 . . V PCA is less confident than the PCA catego PCA the than confident less is V Category retention (%) Category retention I II III Iv v 96 94 94 95 98 6 0.08 87 9296 80 94 82 94 98 96 96 9 0.08 , which is the least restrictive in the choosing of weights, re 1 S two types of development indices were computed: the develop the were computed: indices c, two types of development resulted in the categorization of this municipality in the group of using weights determined by the government decree and the index decree by the government using weights determined 1 V c S . This is a significantly lower number. than the number of incorrect cat PCA . 9 PCA
1 2 3 able Number of incorrect categorizations according to I to categorizations according Number of incorrect S S Simulation S Number of incorrect categorizations according to I to categorizations according Number of incorrect supported units. A supported similar A units. situation occurs with more than 20 LGUs (see appen dix). Due to the large number of LGUs, interval estimations are presented only at only presented are estimations interval LGUs, of number large the to Due dix). a regional level (table 10). Monte Carlo simulations open up the possibility of employing confidence inter vals for the estimation of the development level of territorial of incorrect cat the probability estimate when using simulations it is possible to units. Moreover, egorization for every unit. This is particularly beneficial in the case of marginal value index development to according municipality, Lećevica instance, For units. (75.36%), is not categorized in the group of supported units. However, 84% of simulations Simulation result, LGU level LGU result, Simulation a b The simulation T 4.4.2 Uncertainty analysis of RgU development index 4.4.2 Uncertainty analysis of RgU development of the development for the construction the methodology says that The Decree index on the local level is the same as that for the regional level (Decree on the Development Index, 2010). However, one can pose the question methodology can whether be one reliably applied to two different cases? In particular, justified to select the same weights at a local and a regional level? is it RGU every For rization. In addition to that, a greater confidence of the PCA-categorization can be can PCA-categorization the of confidence greater a that, to addition In rization. values of w of weights around the perturbations smaller by considering obtained Source: Authors’ calculation. Authors’ Source: (71 LGUs incorrectly categorized). Thus, it can (71 be LGUs concluded that incorrectly categorized). the categoriza index I to the development tion according or w egorizations resulting from the categorization based on the development index sulted in 31 LGUs being incorrectly categorized due to the categorization based on the I ment index I
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225 39 (2) 205-236 (2015) - 3 S c for I for 90% CI 2 S c for I for 90% CI 1 S c for I for (%) 90% CI pCA c (%) I v c (%) I 1 S c 7.18 (1) 5.56 (1) 7 (1) <0.06, 0.08> 0.06> <0.05, <0.06, 0.08> I ¯ 62.78 (12) 73.24 (12) 61.45 (11) <0.56, 0.69> <0.68, 0.78> <0.58, 0.66> 52.63 (8) 59.19 (9) 51.64 (8) <0.46, 0.59> <0.55, 0.64> <0.48, 0.56> 39.75 (6) 38.70 (6) 41.54 (6) <0.35, 0.44> <0.36, 0.42> <0.39, 0.44> 30.25 (5) 33.81 (5) 29.01 (5) <0.26, 0.34> <0.31, 0.36> <0.27, 0.31> 21.96 (2) 23.29 (4) 21.84 (3) <0.21, 0.23> <0.23, 0.24> <0.21, 0.22> 22.65 (3) 18.73 (3) 21.74 (2) 0.26> <0.19, <0.17, 0.21> <0.20, 0.24> 24.03 (4) 18.43 (2) 22.42 (4) 0.29> <0.19, <0.16, 0.21> <0.20, 0.25> 112.62 (16)112.62 106.39 (16) 109.13 (16) <1.04, 1.23> <1.01, 1.12> <1.04, 1.14> 185.45 (21) 186.44 (21) 188.5 (21) <1.76, 1.93> <1.81, 1.92> <1.83, 1.93> 154.36 (20) 156.80 (20) 154.20 (20) <1.5, 1.59> <1.54, 1.6> <1.51, 1.57> 139.69 (19) 139.21 (19) 141.71 (19) <1.35, 1.44> <1.37, 1.41> <1.39, 1.44> 121.21 (17) 124.23 (18) (17) 118.03 <1.15, 1.28> <1.21, 1.28> <1.14, 1.22> 123.62 (18) 120.84 (17) 122.31 (18) <1.2, 1.28> <1.18, 1.23> <1.20, 1.25> 10 c , computed using weights derived from PCA. Based on indices values, cor able PCA c City of Zagreb Istria Primorje- Gorski kotar Zagreb Dubrovnik- Neretva Zadar Split-Dalmatia 102.55 (15) 93.75 (15) 101.2 (15) <0.97, 1.09> <0.90, 0.98> <0.98, 1.05> Varaždin 78.81 (13) 86.34 (14) 77.39 (13) <0.73, 0.84> <0.82, 0.90> <0.74, 0.81> Šibenik-Knin 83.04 (14) 80.93 (13) 82.14 (14) <0.80, 0.87> <0.79, 0.83> <0.80, 0.84> MeđimurjeKrapina- Zagorje 64.79 (12) 69.65 (11) 62.03 (12) <0.58, 0.72> <0.64, 0.75> <0.58, 0.66> Lika-Senj 59.61 (10) 64.82 (10) 61.04 (10) <0.54, 0.65> <0.61, 0.68> <0.58, 0.64> Koprivnica- Križevci Karlovac 53.28 (9) 56.34 (8) 54.47 (9) <0.49, 0.57> <0.54, 0.59> <0.52, 0.57> Osijek-Baranja (7) 49.11 46.07 (7) 49.21 (7) <0.47, 0.52> <0.44, 0.48> <0.48, 0.51> Sisak- Moslavina Požega- Slavonia Bjelovar- Bilogora Vukovar- Sirmium Slavonski Brod-Posavina County of Virovitica- Podravina Comparison of the index value and corresponding rank (in brackets) and corresponding of the index value Comparison CI – interval estimation. calculation. Authors’ Source: I T responding responding ranks were determined. The results are presented in table 10, where are presented in brackets. the ranks
------per 5 are calcu- i T S 4 Similarly, the comparison . Similarly, 3 underestimates the develop underestimates V I and S 1 3 c, 1,000 values of development index and total effect sensitivity indices and total effect i 2 he DevelOpmeNT INDeX The DevelOpmeNT S and the upper bounds of estimations indi- the interval V SIS Of = 1,2,3 were calculated. For 21 RGUs, interval estimations interval RGUs, 21 For calculated. were 1,2,3 = , i=1, 2,..., 5. The results on the LGU level are presented in i j X and every RGU and every j 1 ANAly shows that the development index per capita and unemployment rate. 0.0840.394 0.145 0.485 0.087 0.390 0.021 0.155 0.022 0.216
, 3 1,2,..., 1000, 1,2,..., . and S 1 11 S k =
SeNSITIvITy Ti i able I S S of development index, based on percentile index values, are computed with 90% level. confidence simula- obtained by estimations lower bounds of the interval The comparison of tions of the development index I Sensitivity indices (LGU level) Source: Authors’ calculation. Authors’ Source: the val affects of a single indicator in the value a change that It can be concluded 4.5 index, lgU level 4.5.1 Sensitivity analysis of the development First order sensitivity indices lated for indicators inter a single indicator that This is due to the fact index. ues of the development is observable on the value acts with other indicators and thus effect the cumulative of development index. Significantly higher values of sensitivity total index effect budget revenue between economic indicators: stronger interactions indicate capita, income Due to the selection of weights, uncertainty analysis was conducted using Monte 5,000 level, local the on conducted analysis the to Analogously simulations. Carlo For generated. were distributions uniform of types three from weights of samples S each simulation ment level for following Slavonski counties: Virovitica-Podravina, Brod-Posavi na, Vukovar-Sirmium, Bjelovar-Bilogora, Osijek-Baranja and Split-Dalmatia. lower than the lower bounds of index value a development These counties have provided interval estimations by S simulations cates a possible overestimation of the development level for the following coun level for the following of the development cates a possible overestimation ties: Bjelovar-Bilogora, Koprivnica-Križevci and Varaždin since the development the since Varaždin and Koprivnica-Križevci Bjelovar-Bilogora, ties: The selection of weights doesn’t index is higher than the upper interval bounds. significantlyaffect the categorization of RGUs determined by the government decree, but it has an impact on the units ranking. According to the development index, the county of Split-Dalmatia is categorized in the second group, while ac cording to the average simulated index and derived PCA index is categorized in level. the group having a higher development table T
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227 39 (2) 205-236 (2015) - - - and vari- ci x 7 – 19 12 12 category (%) Advancing into higher Advancing into higher = 1,..., 5 were generated from generated were 5 1,..., = i
, i X LGU and interval estimations. 12 Table pro- V – 9 8 I 15 15 category (%) falling into lower falling into lower , 100 values of the indicator the of values 100 , c 400 500 0 100 200 300 3 equal to the quarter of the sample variance. This way the simulation is limitedThis way the simulation variance. quarter of the sample equal to the 2 12 i 1.4 1.2 .0 0.8 0.6 0.4 0.2
v Development index Development abel igure Category according to I I II III IV V vides the percentages of shifts between groups. LGUs switching between catego- of shifts between groups. LGUs switching between vides the percentages Category changed (%) sponding interval estimations, are presented on figure The 3. interval estimations are assessed via simulations at the 95% confidence level. The LGUs that shift to categories with lower or upper development levels are determined by intersec tions of level boundaries according to Source: Authors’ calculation. Authors’ Source: The values of the development indices on the LGU level, together with corre T Source: Authors’ calculation. Authors’ Source: F The effect of small changes in the values of economic indicators on the sensitivity of the sensitivity on indicators of economic in the values changes of small The effect the development index was examined directly by using the Monte Carlo simulations. unit regional every For ance the normal distribution with a mean equal to the observed indicator value indicator value equal to the observed distribution with a mean the normal only to small perturbations of the parameters, which can appear as the result of impre of result the as appear can which parameters, the of perturbations small to only to change over time. indicator values tend or the fact that cise measurement Interval estimates - - - 5
- are calcu
i T XXI
S
XVIII
VIII I
4
XIX
XIII
XVII
V
3 XV
II
XX
IX RGU VI
2 and total effect sensitivity indices sensitivity effect and total i IV
S
XIV
III XI
, i=1, 2,...,5. The results at the RGU level are presented in i VII
1
0.0840.439 0.039 0.322 0.119 0.481 0.021 0.239 0.022 0.221 XVI
XII X 4 13 . This indicates a possible underestimation of the specified counties. Thus, V I 1.25 0.75 i
i T able igure Development index Development S S I Sensitivity indices (RGU level) Sensitivity indices (RGU dex Interval estimations of the development index for the counties Krapina-Zagorje, catego- the in placed partially are Zagreb and Dubrovnik-Neretva Split-Dalmatia, ries of by higher development level according to the category determined the in Source: Authors’ calculation. Authors’ Source: ment index on the RGU level. The values of RGU the development indices on the ment index on the RGU level. on figure 4. estimations are presented level together with corresponding interval Similar to the results obtained with the sensitivity analysis of LGUs, the interaction the LGUs, of analysis sensitivity the with obtained results the to Similar of the develop main source of variability as the of economic indicators emerges F Source: Authors’ calculation. Authors’ Source: ries should be analyzed in more detail due to the possibility of incorrect classifica incorrect of possibility the to due detail more in analyzed be should ries tion. RgU level Development index, analysis of the 4.5.2 Sensitivity First order sensitivity indices X lated for indicators table 13. T Interval estimations (RGU level)
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229 39 (2) 205-236 (2015) ------. This problem can be bypassed by excluding . per capita CONClUSION The analysis of the model determined by the Government decree indicated strong indicated by the Government decree The analysis of the model determined of the the variability affect indicators which dominantly of economic interactions development index, both on the local and the regional level. Because even small perturbations of input variables can significantlyaffect the categorization out gation methods and selecting indicators and corresponding weights, play an im portant role in the construction of a composite index. Thus, it is necessary to de main the of One consequences. their analyze to and uncertainty of sources all tect is the lack of consensus con indicators of composite features of the construction cerning relative weights selection. In a this development study, index derived di component analysis was proposed as a reference rectly from the data by principal index. The uncertainty of the development index, especially due to the selection, weight was analyzed using Monte Carlo simulations. This analysis indicated the inability of the development index to rank source LGUs main the uniformly, particularly is for selection weight Because III. and II groups in categorized LGUs revealed was index development the of basis the on categorization uncertainty, of to be less confident compared to the PCA-categorization. come, a special emphasis was placed on the inclusion of these methods in the The researchers’ subjective decisions, such as choosing normalization and aggre The researchers’ Prior to the implementation of the development index, the categorization process of territorial units was often criticized as unbalanced and fragmented. A turna or by correcting indicator weights. or replacing one of the collinear indicators these these counties should be analyzed in more detail. Using interval estimates allows of an in the estimation considering units these marginal of briefer analysis for a 5 The main goals of to assess this paper were uncertainty of the development index sensitivity considering methodology and to evaluate considering the construction guide useful account, to this taking By construction. its in involved indicators the correct classification of territorial units. of territorial correct classification devel- indices as a basis for the of composite employment round started with the index is The development calcu of opment level assessment LGUs and RGUs. lated as the weighted average of normalized indicator values relative to the state catego the development, in behind lagging are that units local many For average. rization based on the development index is crucial for further development as it benefits and incentive intensity. provides it different method- the Furthermore, proposed. be can index the of improvement the for lines ology of is presented. In order to exam the construction of the development index ine the data structure, multivariate analysis was conducted, indicating the pres the at out carried analysis multivariate of results the particular, In outliers. of ence income per between indicators the presence of collinearity level indicate regional revenue capita and budget ------construction of composite indicators. The inclusion of uncertainties in the model in the model of uncertainties The inclusion indicators. of composite construction data indicators, some for and frequent, are errors measurement the since needed is proposed are estimations interval purpose, this For time. on provided not often are in uncertainties incorporate to possible is it Therefore, estimation. point of instead the This model. also enables some units to be closely analyzed (for example, ter ritorial units having the development index values 5 points away from the mar of the categories). ginal values was authors the of intention the subject, this on papers scientific of lack the to Due to emphasize the need for analyzing the sensitivity and the uncertainty of the de- velopment index and of composite indicators in general. Since composite indica tors are increasingly used, this study provides useful guidelines for the applica- aca of variety wide a in indicators composite of development, for as well as tion, fields. demic and professional In three years a new of is calculation the development index It will be expected. interesting to observe the development of the construction methodology, espe- cially the as indicator well selection as process the and assessment quality, of the the With conditions in the state. relative importance due to the socio-economic improve to necessary is it index, development the of acceptance general the of aim methodology of the new calcu The the transparency of the construction process. changes in the dynamics of indicators and their should follow the expected lation a modern approach to the assessment of in order to ensure the develop interaction ment level of territorial units.
financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy 39 (2) 205-236 (2015) 230 financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy
231 39 (2) 205-236 (2015) - - -
(see section per capita, as a key and budget revenue per capita and budget per capita (see section 4.4.1).
gorization in groups II and III from MC simulations S Furthermore, LGUs listed in table A2 should be considered for inclu- sion into group III, i.e. exclusion from supported A2 areas. also Table of the cate index values and the percentage provides the development 4.4.1). should be considered for inclusion into group II, i.e. into supported ar also provides values of the development index and the A also provides values of the development eas. Table percentage of the categorization in groups II and III from MC simula tions S a) correction of weights, a) correction indicator, b) excluding an individual an alternative indicator. c) replacement with 5.2) 5.1) In particular, 5.1) regarding simulation results, LGUs listed in table A1 economic indicator, should be considered. economic indicator, On the regional level, the inclusion of the indicator GDP An inclusion/exclusion of marginal units in/from supported areas should be considered. This can be achieved by using Monte Carlo simulations and esti- (see section 4.4). mating the probability of (incorrect) categorization alternative normalization method we propose normalization with formula 13). index value (given state’s relative to the should be corrected in one of the following ways: corrected in one of should be analysis and sensitivity analysis should be conducted in order to improve the in order to improve analysis should be conducted and sensitivity analysis index. transparency and the quality of the development Interval estimations of the development index should be provided prior to the development of the Interval estimations categorization of LGUs and RGUs. LGUs/RGUs with the interval estimates supported groups should be more closely with one of the partially overlapping analyzed in order to avoid incorrect categorization. AppeNDIX 5) 4. 3) Alternative weighting methods should be considered. Furthermore, uncertainty Furthermore, considered. be should methods weighting Alternative 3) 2) The outliers should be excluded when using the min-max normalization. As an As normalization. min-max the using when excluded be should outliers The 2) 1) The correlation of indicators income 1) Basic guidelines for improving the methodology of the development index methodology of the the improving for Basic guidelines - III III 0.474 0.438 0.244 0.430 0.450 0.234 0.198 0.416 0.074 0.128 0.138 0.324 0.258 0.058 0.454 0.212 0.020 0.240 0.140 0.098 0.124 0.824 0.794 0.544 0.608 II 0.526 0.562 0.756 0.570 0.550 0.766 0.802 0.584 0.926 0.872 0.862 0.676 0.742 0.942 0.546 0.788 0.980 0.760 0.860 0.902 0.876 II Categorization into group (%) into group Categorization 0.176 0.206 0.456 0.392 Categorization into group (%) Categorization into group index 0.8231 0.7901 0.7856 0.7829 0.7775 0.7728 0.7700 0.7695 0.7689 0.7688 0.7683 0.7681 0.7671 0.7624 0.7612 0.7543 0.7537 0.7525 0.7522 0.7517 0.7508 Development Development 0.728 0.735 0.741 0.743 index Development a a1 a2 Although this study did not involve the analysis of alternative aggregation the analysis of alternative Although this study did not involve methods, this would also be worth pursuing. In particular, one could consider the geometric aggregation as the compensability between varia it delimitates bles. able able Veliki Bukovec Veliki Bedenica Breznički Hum Đurmanec Jalžabet Mače Kraljevec na Sutli Lepoglava Đelekovec Pregrada Hrašćina Vratišinec Klenovnik Krašić Donji Miholjac Petrijanec Lećevica Sveti Martin na Muri Jesenje Donji Vidovec Donji lgU Vrsi Imotski Nova Gradiška Beli Manastir lgU Ozalj AASC, not categorized into supported areas on the basis of unadjusted development index. on the basis of AASC, not categorized into supported areas Proposal for the inclusion of LGUs into supported areas supported into of LGUs the inclusion for Proposal Proposal for the exclusion of LGUs from the supported areas the supported areas for the exclusion of LGUs from Proposal T a 6) T
financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy 39 (2) 205-236 (2015) 232 financial theory and ana perišić, vanja wagner: practice development index: analysis of the basic instrument of croatian regional policy
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