Personal income distribution and inequality at the local level. An estimation for Spain using a tax microdata-based model

Personal income distribution and inequality at the local level. An estimation for Spain using a tax microdata-based model. Miriam Hortas-Ricoa,b Jorge Onrubiaa Daniele Pacificoc January, 2013 Abstract Local income data is a key element to analyze residents’ standard of living and wellbeing as well as an important economic indicator, very used in a wide range of studies related to regional convergence, urban economics, fiscal federalism and spatial welfare analysis. Despite its importance, there is a lack of official data on local incomes and, most importantly, on local income distributions. In this paper we use official data on personal income tax returns and a reweighting procedure to derive a representative income sample at the local level. Unlike previous attempts in the literature to get local income estimates, the results obtained allow us to derive not only an average value of income but its local distribution, a valuable and informative tool for distributional and income inequality analysis. We apply this methodology to Spanish micro-data and illustrate its potential use in income inequality analysis by means of computed Gini and Atkinson coefficients for a set of municipalities. Keywords: local income distribution, sample reweighting, income inequality. JEL classification codes: C42, C61, D31, D63, O15 a Universidad Complutense de Madrid, Spain. b Institut d’Economia de Barcelona (IEB), Spain. c Department of the Treasury – Italian Ministry of Economy and Finance; Centre for North-South Economic Research, University of Cagliari, Italy Corresponding author: [email protected] 2 1. Introduction Local income data is a key element to analyze residents’ standard of living and wellbeing as well as an important economic indicator, very used in a wide range of studies related to regional convergence, urban economics, fiscal federalism and spatial welfare analysis. Despite its importance, local income data remains a key missing element within Spanish official statistics. This absence of official estimates of local income has led its measurement to direct or indirect methods by other research institutions, such as the Lawrence R. Klein Institute or the Research Department of La Caixa-Savings Bank. The direct method calculates the disposable income directly considering a production function and sectorial employment matrices with municipal data while the second approach relies on an econometric procedure where local income is estimated as a function of a set of socioeconomic indicators linked to the municipality. Nonetheless, both approaches present several limitations. On the one hand, they proxy personal income through territorialized macroeconomic magnitudes which could not adequately represent residents’ ability to pay taxes or their share of disposable income allocated to consumption or saving, as these magnitudes include capital income under the criteria of where production activity is located instead of where their owners reside. On the other hand, these methods do not allow the researcher to obtain local income distributions as their result is a unique value without information about its dispersion. Hence, in this paper we develop a model of sample reweighting intended to overcome these problems, particularly in the context of distributional and income inequality analysis. The reweighting procedure proposed here adapts the calibration approach proposed in Deville and Särndal (1992), Creedy (2003) and Creedy and Tuckwell (2004) for survey reweighting and allows us to derive local income distributions from micro-data of personal income tax returns. These local income distributions are a valuable and informative tool for distributional and income inequality analysis. They do not only summarize the information contained in thousands of observations (i.e. average taxable income) but provide us with useful inequality indexes drawn from these distributions (i.e. Gini and Atkinson indexes). Thus, the objectives of the paper are twofold. On the one hand, we seek to provide a representative income sample at the local level based on official tax statistics. To that aim, we adapt a methodology for sample reweighting to the case of Spanish micro-data of personal income tax returns. On the other hand, we use this representative local income sample to derive local income distributions. Unlike previous attempts to get local income 3 estimates, in this paper we obtain not only an average value of income for each Spanish municipality but its local distribution, allowing us to carry out income inequality analysis. The article is organized as follows. In the next section we present the problem of estimating personal income at the local level and we review the related literature and data sources. The tax microdata-based model and the calibration approach implemented in the paper to get the new sample weights used to derive local income distributions is presented in the third section. Data used, main findings and the validation of estimates are presented in the fourth section. In the fifth section we report an illustration of income inequality analysis for the case of the Spain. Finally, in the last section, we conclude. 2. The problem of measuring the local income In Spain, as in many other countries, there are not official statistics of personal income for territorial areas smaller than the provinces or the regions. However, the household income estimation is essential information to know the standard of living and wellbeing of the population of the municipalities. In our opinion, local personal income can be considered as one of the most important economic indicators, very used in a wide range of studies related to regional convergence, urban economics, fiscal federalism or spatial welfare analysis, among other topics, not forgetting the entrepreneurial, financial or commercial issues. 2.1. Background in personal disposable income estimation: the case of Spanish municipalities The aforementioned absence of official estimates of local income has led its measurement to direct or indirect methods. The first proceeding calculates the disposable income directly, considering a production function and sectorial employment matrices with municipal data. This direct approach is based on the aggregation of the monetary flows of goods and services produced in each subsector of the municipal economy. Alternatively, it can be calculated by way of income, adding wages, interest, profits and other income earned by households in the municipality. From this first estimation, wage ratios and gross operating surplus are added to provide an estimate of the value for each element of the matrix (defined by the intersection of each activity with each municipality). It is a complex method that requires a large information database generally difficult to obtain and not always precise. Its main weakness is that it cannot reflect the underground economy of Spanish municipalities, even when estimating agricultural gross added value. 4 That is why the direct methodology has always needed to be complemented by indirect proceedings. Thus, the estimation method most commonly used is the indirect one, given the complexity of the direct method discussed above. This methodology consists of an econometric estimation, in which municipal income for a given year is the dependent variable, using as explanatory variables selected socioeconomic indicators linked to the municipality, in addition to the aggregate size of the territorial level closer to municipality, usually the gross value added (GVA) of the province of reference1. Since 1992, the Lawrence R. Klein Institute of the Autónoma University of Madrid estimates personal disposable income for a sample of Spanish municipalities2. These data have been published, firstly in the “Atlas Comercial de España 1994” (Spanish Trade Atlas), and subsequently in the “Anuario Económico de España” (Spanish Economic Yearbook) sponsored and published by the Barcelona Pensions and Savings Bank, La Caixa, from 1999 to 20033. This information about the personal income of each municipality was displayed on several levels, each of which is ranked in a set of thresholds4. This way of presenting information represents an important limitation for empirical work. Furthermore, the aggregate nature of the data prevents us from obtaining inequality measures. Other contributions from the academic field that have also estimated the municipal income usually with a regional scope should be mentioned: Arcarons et al. (1994) and Oliver et al. (1995) in Catalonia, Esteban and Pedreño (1992) in the Valencia Community, Fernández and Sierra (1992) in La Rioja, De las Heras (1992) and De las Heras and Murillo (1998) in Cantabria and Herrero (1998) in Castile and Leon. Some of them have introduced more complex estimation methods, such as multivariate factor and cluster analysis or econometric multiequational models. Likewise, Alañón (2002) offers an interesting study with estimates of gross value added for the Spanish municipalities using spatial econometric techniques. The identification of the local income with some territorialized macroeconomic magnitude such as the GVA or even the gross domestic product (GDP) seriously limits the analysis of issues related to personal income distribution. Regardless of the problem of 1 For a detailed description of the content of these models see Fernández-Jardón and Martínez-Cobas (2002). 2 Only municipalities with more than 1,000 inhabitants are considered (i.e. around 3,200 out of 8,111 municipalities). 3 http://www.anuarieco.lacaixa.comunicacions.com/java/X?cgi=caixa.le_RightMenuHemeroteca.pattern 4 In particular, 10 income thresholds are defined: 1. From 0.01 € to 7,200 €; 2. From 7,200.01 € to 8,300 €; 3. From 8,300.01€ to 9,300 €; 4. From 9,300.01€ to 10,200 €; 5. From 10,200.01 € to 11,300 €; 6. From 11,300.01 € a 12,100 €; 7. From 12,100.01 € to 12,700 €; 8. From 12,700.01 € to 13,500 €; 9. From 13,500.01 € to 14,500 €; 10. From 14,500.01 onward. From 2003, this income variable was no longer available in the Spanish Economic Yearbook. 5 territorial assignation, these macroeconomic magnitudes do not adequately represent residents’ ability to pay taxes or their share of disposable income allocated to consumption or saving, as they include capital income under the criteria of where production activity is located instead of where their owners reside. In fact, as the GAV is the value of output (goods and services) produced in an area less the value of intermediate consumption, it is a measure of the contribution to GDP made by an individual producer, industry or sector. In other words, GVA is the source from which the primary incomes of the National Accounts System (SNA) are generated and is therefore carried forward into the primary distribution of income account. Thereby, territorial GVA includes the return on capital income under the criteria of where production activity is located, instead of where their owners reside. For instance, we can think of a residential municipality with a high standard of living where owners of enterprises locate their activities in other municipalities, even in other regions or countries. Of course, there will also be municipalities whose residents do not have a high standard of living but where very profitable companies are located due to, for example, their lower wage costs. A second limitation of using macro aggregates to estimate local income is related to the impossibility to obtain distributions of income for municipalities and, consequently, measures of inequality. Whatever the statistical or econometric method used to estimate the income of each municipality, the result is a unique value, which prevents having information about the dispersion of the magnitude. 2.2. Personal income estimation for municipalities using micro data As argued above, the study of local income inequality, either directly or through its consideration in other analyzes in which it acts as an explanatory variable, is a matter of undoubted interest in economic research. Therefore, we believe it is necessary to try to find alternatives to overcome this shortfall. Furthermore, these alternatives should try to overcome the above limitations related to the need of approximating a more precise notion of personal income. In this regard, the recent availability of data on personal income tax returns turns out to be a feasible approach to address this problem. Nevertheless, the utilization of micro-data from personal income tax returns to estimate local income tax involves using a tax definition of income. Given that our interest is in the estimation of personal income at the local level, we believe this is not a matter for concern. Usually, the taxable income for 6 this kind of taxes includes all incomes obtained by residents in a territory regardless of its source (labor income, capital income -both financial and real estate incomes-, and income from personal business activities). Available information comes from the tax forms according to the rules of taxation and, as such, the income reported includes all essential components of personal income in an economic sense, with the exception of certain exemptions of income that are not taxed. The main limitation arises from the measurement criteria of some kinds of the incomes taxed, as it is the case of income from business activities (largely estimated by means of objective methods) or real estate imputed rents for homeowners, and the capital gains. However, when we look at the measurement of aggregated household disposable income at the national level we observe that it often offers lower income levels than the tax data5. Another limitation is related to the unit of analysis used. According to legislation applicable for the Spanish Personal Income Tax (PIT hereinafter), the observation units are not the taxpayers of the tax but rather the income tax returns presented by them. These tax returns can be of two types: individual returns with a sole taxpayer and joint returns with more than one taxpayer. Joint returns can be of two types: those filed by both spouses in a married couple when they decide to file jointly and those filed by a single parent, widow/widower or divorcees together with their under-age or disabled children. In accordance with tax cost of the family unit, married couples who opt for joint taxation have only one income earner. Therefore, in any case, the information contained in the tax returns limits the unit of analysis for the taxpayer unit, not being possible to integrate the tax information at the economic household level, as it is usual in the surveys conducted by statistical agencies (for instance, the household budget survey or the living conditions survey). After comparing the advantages and limitations of using micro-data from personal income tax returns, this option turns out to be the most suitable one, to the extent that the use of micro-data is indispensable for conducting distributional analysis. The representativeness of these tax micro-data is appropriate for small territorial estimates, as in the case of municipalities. Perhaps the most controversial issue is the use of the individual as the unit of analysis. However, it has been widely used in the related literature on income inequality and redistribution and, therefore, we believe it is a reasonable choice. 5 For instance, see the analysis made by Picos (2006) for the Spanish case. 7 3. Tax microdata-based model 3.1. The model Let  be the personal income distribution (measured by the variable taxable income) for a given year  (the year 2007 in our case) corresponding to the reference population . In turn,  is the distribution function of the same variable for the sample obtained from population administrative census of tax returns. For each of  tax units, micro-data sample contains information on this income variable and other variables of territorial identification, such as provincial and municipal codes. Insofar as the sample has been obtained using minimum variance stratification under Neyman allocation, a sample weight  was assigned to each observation  extracted. The strata used in the sampling are: a) the province6; b) 12 income levels; c) the type of return (separate or joint filing). So, this “original weight” was calculated as the ratio between the size of the population of the strata  and its sample size,  ⁄. Let  be the taxable income corresponding to sample tax unit . The estimated population total of taxable income  can be obtained using the original weights provided in the sample, such that7: ∑   [1] In so far as the spatial stratification variable was fixed at the provincial level, both the population estimates for the provinces and for the whole national population keep the stated confidence level in the sample design. However, to obtain estimates at the municipal level is necessary to calculate new population weights, to the extent that our estimates would face now smaller spatial areas used as a strata sample extraction. We define this “new weight” as,, such that the total population income estimated for the municipality  can be obtained as follows: |∑,,   [2] Following Creedy and Tuckwell (2004), we use the distance criterion to assess the closeness between , and , in each of  spatial areas. In general terms, let denote this distance through the function, ,,,, what must verified in aggregate terms that: 6 48 Spanish provinces with common fiscal regime, plus the Autonomous Cities of Ceuta and Melilla, as well as an additional group of Spanish non-resident taxpayers that paid taxes in Spain (article 10 of the Law 35/2006). 7 For the sake of simplicity, the superscript h corresponding to each stratum is discarded from now on. 8 ,,,, ∈"# [3] Therefore, the method to obtain the new weights that allow estimates of income at the municipal level using micro-data sample consists in solving the following optimization program: to minimize distance function [3] subject to municipality restriction [2]. To carry out this reweighting we need information on true population totals for the taxable income variable, for each  municipality, so that the estimated value | can be replaced in [2]. This information is taken from administrative census of personal income tax8. 3.2. Computational settlement: the calibration approach In this section we overview the method we use to adjust the original micro-data sample weights provided by the Spanish Tax Administration (AEAT hereinafter) so as to make them representative with respect to both the average income and the aggregate number of taxpayers in each Spanish municipality. The methodology closely follows Creedy (2003), Creedy and Tuckwell (2004) and Deville and Särndal (1992) and it was coded in Stata 12. Following Creedy (2003), let us consider a sample of n taxpayers and K individuallevel variables, both monetary (as taxable income or tax liability) and non-monetary (as age, sex, province and municipality of residence). We collect these variables for the generic taxpayer i in the following vector: $%$,$&,…,$()′. If we define the original sample weight with the vector %,&,…,,…,), the estimated population values of each K individual-level variable is given by: +(|,∑$(   [4] The AEAT provided us with the true population totals for some of these K variables+(. Specifically, we managed to obtain from the AEAT the aggregate income and the total number of taxpayers in each j Spanish municipality. With this information in hands it is possible to compute a new vector of sample weights for each municipality, -,…,. , where ∑ / , that is as close as possible to the original sample weights, while satisfying the set of K calibration equations: +(∑$(   [5] 8 This population data have been provided by Spanish Tax Administration Agency (hereafter AEAT). 9 where +( is the true population value of each K individual-level variable in each j municipality. Indeed, if we denote the distance between the original and the new sample weights with the function ,,,, the new sample weights can be obtained by minimizing the following Lagrangian function with respect to z: 0∑,,,1∑2(3+(4∑$(   5 6 (   [6] where [ ] 1 2 K λ = λ ,λ ,...,λ ´ are the Lagrange multipliers. Clearly, the solution of the minimization problem strongly depends on the property of the distance function ,,, and, in what follows, we require the function ,,, to respect two fundamental properties: - The first derivative of ,,, with respect to , must be expressed as a function of the ratio between the new and the original weights: 78,9,,9, 79,′:9, ,9,; [7] - The inverse of the first derivative of ,,, must be invertible explicitly. If these properties hold, then the n first order conditions for the problem in [6] are: ′:9, ,9,;4$<201,2,…, [8] The new weights can be obtained as: ,,′@$<21,2,…, [9] and given a solution for the Lagrange multipliers, which can be obtained through an iterative procedure (Newton’s method) after some algebraic manipulations of equations [9], [5]and [4]. Specifically, if we substitute equation [9] into equation [5] and then subtract from both sides equation [1] after some rearrangements we obtain: +(4+(|,4∑3<@$<2415$   0 [10] The root of this function can be computed by means of the following iterative recursion: 2A#2A4-7BC 7C .@D2 [11] where D2 is given by the left hand side of equation [10] and, at each iteration I+1th, is 16 Figure 3 shows the income distribution for the entire sample, i.e. all municipalities included, before and after reweighting. As expected, the overall income distribution derived from the new sample weights replicates the overall income distribution when using the original sample weights. In general terms, differences are expected in local income distributions, as original weights were just representative at the provincial level while the new sample weights are now representative at the municipal level. In any case, the sample is always representative of the entire population, i.e. the weights are used for grossing up from the sample in order to obtain estimates of population values. [Insert Figure 3 around here] In Figures 4 and 5 we present some of the results obtained for the Spanish municipalities included in the sample. In particular, we display some local income distributions of poor and rich municipalities. In every graph, the local income distribution derived from the original sample weights is illustrated by the dash line, whereas the redefined local income distribution according to the new calibrated sample weights is given by the solid line. [Insert Figure 4 around here] [Insert Figure 5 around here] 5. Personal income inequality in Spanish municipalities The estimated local income distributions obtained in the previous section are a valuable and informative tool for distributional and income inequality analysis. As an illustration, in this section we perform an analysis of local inequality for a sample of Spanish municipalities based on the computation of two of the most common measures of inequality, the Gini and the Atkinson indexes. The Gini coefficient (Gini, 1912) is probably the standard in the income inequality literature. This index is defined as the area between the 45°(which indicates perfect equality) and the Lorenz curve M142N0O;QO  R [15] where the Lorenz curve of income 0O; at such p-values of ranked relative cumulatedpopulation (so that, O∈0,1) can be defined mathematically by the expression, 17 OS⟹0O;NDQ UV ⁄ W R [16] Accordingly, the Gini coefficient takes values between zero (perfect equality) and one (complete inequality). As it is well known, we can infer income distribution  if we know mean income UV and the shape of the Lorenz curve of income0O;16. Alternatively, the Gini coefficient can be calculated in terms of the covariance between income levels and their ranks, so that, M2UV ⁄cov[,\ [17] An alternative formula for the Gini coefficient for the discrete approach of income distribution is, M∑ ∑ |V]@V^| &_`ab cd [18] where a and b are two generic observations of N-observations size income distribution y. There are several plausible alternatives to calculate this expression when using microdata. In particular, we use the Stata’s do file provided by Haughton and Khandker (2009) and adapted for our stratified sample of micro-data. The second income inequality measure used in our analysis is the Atkinson index (Atkinson, 1970). This index differs from the Gini index in its explicitly ethical foundation. In fact, the Atkinson index is based upon a social welfare function, including a weighting parameter ε which measures aversion to inequality, so that the index becomes more sensitive to changes at the lower end of the income distribution as approaches to 1, while if the level of inequality aversion falls (that is, as approaches to 0) the index becomes more sensitive to changes in the upper end of the income distribution. For e0 the equally distributed equivalent income is simply the average level of income, while for e→∞ the Rawlsian criterion is used (that is, social welfare function is close to the maximum concavity). From a continuous approach of the income distribution, the Atkinson index is defined as, hi14jN:V ab;@iDQ k Rlm mno [19] for ep0 and eq1, while if e1, the expression is, 16 For a demonstration of this lemma see Lambert (2001:32) 18 h14exp:N:V ab;DQ k R; [20] In both cases, the Atkinson index takes a value between 0 (if the income is distributed equally) and 1 (if the inequality is the highest). We also use the Stata’s do file included in Haughton and Khandker (2009) to calculate the Atkinson index with micro-data, according to the following expression in discrete terms (for N observations)17: hi14j _∑:V9 ab;@i _  lm mno [21] for ep0 and eq1. In particular, we have chosen for our calculations the value 0.5 for the e inequality aversion parameter. Confidence intervals via bootstrap re-sampling methods (Mills and Zandvakili, 1997) have been calculated for both inequality measures. In particular, two types of bootstrap confidence intervals are obtained, using respectively the alpha-percentile method and the normal-distribution method. In the first case, the percentile confidence interval is defined as 3uv & ⁄ ∗,u@v & ⁄ ∗5, where u∗ is the inequality coefficient (Gini or Atkinson index) estimated from a bootstrap sample and x is (100−confidence level)/100. In the second case, the normal approximation confidence interval is defined as 3uym ∗,uy` ∗5, so that, uymUAV4zmn{ `∙a}b √ and uy`UAV4z{ `∙a}b √, where UAV is the mean of inequality coefficients obtained from B bootstrap re-samples implemented, and z represents the standard normal distribution values. Then for a 95% confidence interval based on the normal approximation is, 3uym ∗,uy` ∗5%UAV1.96a}b √ [22] Given the large size of the micro-data sample used in our analysis, the number of bootstrap replicates has been set at 100. Likewise, we have calculated the standard errors for both inequality indexes. 17 For e1 the above expression transforms into: h114∏1  ⁄  1 U 19 Using the AEAT micro-data and the new sample weights, we calculate these two different income inequality measures at the municipality level. The results for both income inequality indexes are reported in Figures 6 and 7, respectively. Detailed results on these indexes as well as their bootstrapped standard errors and confidence intervals are presented in Appendix 2 and 3. [Insert Figure 6 around here] [Insert Figure 7 around here] To the purpose of this empirical exercise we have selected a small sample of Spanish municipalities. In particular, only the results for the 56 municipalities with a population above 100,000 inhabitants are reported. For the sake of clarity and according to their size, this sample of municipalities has been divided into three groups. Two main finding arise from the results. On the one hand, the Gini coefficient has a wide range of variation, as it takes values from 0.38 to 0.52. On the other hand, there exists a clearly positive correlation between the Gini coefficient and the average taxable income of the municipality, with a correlation coefficient of 0.65. This result suggests that richer cities have more income inequality (more unequal income distributions) than the poorer ones. This result also holds for the Atkinson coefficients, whose results exhibit a very similar pattern of variation than those presented for the Gini coefficient. 6. Concluding remarks Local income data is a key element to analyze residents’ standard of living and wellbeing as well as an important economic indicator, very used in a wide range of studies related to regional convergence, urban economics, fiscal federalism and spatial welfare analysis. Despite its importance, there is a lack of official data on personal incomes for territorial areas smaller than the provinces or regions. This paper makes use of official data on personal income tax returns and a reweighting procedure to derive a representative income sample at the local level. The methodology implemented here relies on the calibration approach proposed in Deville and Särndal (1992), Creedy (2003) and Creedy and Tuckwell (2004) for survey reweighting. In doing so, we adjust the original micro-data sample weights so as to make them representative at the local level, given that our estimates would face now smaller spatial areas used as a strata sample extraction. 20 Unlike previous attempts in the literature to get local income estimates, the results obtained allow us to derive not only an average value of income but its local distribution, a valuable and informative tool for distributional and income inequality analysis. We apply this methodology to Spanish micro-data and illustrate its potential use in income inequality analysis. In particular, in this paper we use the micro-data contained in the Spanish Personal Income Tax annual sample for the year 2007, which includes 1,351,802 records extracted from a population of 18,702,875 personal income tax returns. As a result, we obtain local income distributions for 5,328 out of 7,024 Spanish municipalities with common fiscal regime. Next, we perform an analysis of local income inequality for a sample of those municipalities based on the computation of two of the most common measures of inequality, the Gini and the Atkinson indexes. Two main findings arise from the results. On the one hand, the Gini coefficient has a wide range of variation, as it takes values from 0.38 to 0.52. On the other hand, there exists a clearly positive correlation between the Gini coefficient and the average taxable income of the municipality, with a correlation coefficient of 0.65. This result suggests that richer cities have more unequal income distributions than the poorer ones. This result also holds for the Atkinson coefficients, whose results exhibit a very similar pattern of variation than those presented for the Gini coefficient. Overall, the methodology presented here represents a starting point for income inequality analysis at the local level. A wide range of implementations arise from these results and should be addressed in future research. The illustration presented here could be extended to the whole set of municipalities, so as to get a picture of income inequality within municipalities in Spain. Besides, recent availability of PIT annual samples for several years would allow us to perform both cross-section and longitudinal income inequality analysis. References Arcaróns, J., Castells, A., García, G. and Parellada, M. (1992). Estimació de la renda familiar disponible a les comarques i municipis de Catalunya.1989. Generalitat de Catalunya, Departement d’Economia i Finances, Barcelona. Alañón, A. (2002). “Estimación del valor añadido per cápita de los municipios españoles en 1991 mediante técnicas de econometría espacial”, Ekonomiaz, 51: 172-194. 21 Atkinson, A. B. (1970). “On the measurement of inequality”, Journal of Economic Theory, 2: 244-263. Creedy, J. (2003). Survey reweighting for tax microsimulation modelling. New Zealand Treasury Working Paper Series, 17/03. Creedy, J. and Tuckwell, I. (2004). Reweighting household surveys for tax microsimulation modelling: An application to the New Zealand household economic survey. Australian Journal of Labour Economics 7 (1), 71–88. De las Heras, A. (1992). “Un Modelo General de Estimación Indirecta de la Renta Familiar Disponible Municipal. Su Aplicación a la Comunidad Autónoma de Cantabria”. Tesis Doctoral. Universidad de Cantabria. De las Heras, A. and C. Murillo (1998). “Información fiscal y estimación indirecta de la renta familiar disponible municipal en España”. I Congreso de Economía Aplicada. Barcelona. Deville, J. and Särndal, C. (1992) Calibration estimators in survey sampling. Journal of the American Statistical Association, 87: 376–382. Esteban, J. and A. Pedreño (1992). “La Articulación Territorial de la Economía Valenciana”. Estructura Económica de la Comunidad Valenciana. Madrid: Espasa Calpe, pp. 73- 112. Fernández, C. and Sierra, Y. (1992). “Estimación de la Renta Familiar Disponible a Nivel Municipal. Una Aplicación a La Rioja. Año 1985”. Actas de la VI Reunión Asepelt España. Granada. Fernández-Jardón, C. M. and Martínez-Cobas, F. X. (2002). “Un método de estimación de la renta en unidades espaciales pequeñas”, Revista Asturiana de Economía, 23: 91-112 Gini, C. (1912) “Variabilità e mutabilità, contributo allo studio delle distribuzioni e relazioni statistiche”, Studi Economico-Giuridici dell’ Universiti di Cagliari, 3, (2): 1- 158. Herrero, L. C. (1998). “Perspectivas de Desarrollo Territorial: Renta Municipal y Desarrollo Económico en las Comarcas de Castilla y León”. Junta de Castilla y León, Consejería de Economía y Hacienda. Haughton, J. H. and Khandker, S. R. (2009). Handbook on poverty and inequality. Washington DC: The World Bank. 22 Lambert, P. J. (2001). The distribution and redistribution of Income, 3rd edition. Manchester: Manchester University Press. Mills J. A and Zandvakili, A. (1997). “Statistical inference via bootstrapping for measures of inequality”, Journal of Applied Econometrics, 12: 133-150. Oliver, J., Busóm, I. and Trullén, J. (1995). “Estimació de la renda familiar disponible per càpita de Barcelona, els seus districtes i els 27 municipis de la Corporació Metropolitana de Barcelona”, Ajuntament de Barcelona, Barcelona. Picos, F. (2006). “Microsimulación mediante fusión de Phogue y Panel de Declarantes para evaluar reformas fiscales”. Revista de Economía Aplicada, 41: 33-60. Picos, F., Pérez, C. and González, M. C. (2011). “La muestra de declarantes de IRPF de 2007: descripción general y principales magnitudes”, Documentos de Trabajo del Instituto de Estudios Fiscales, 01/11. Särndal, C. (2007): The calibration approach in survey theory and practice. Survey Methodology 33 (2), 99–119. 23 Tables and Figures Table 1. Different distance functions D  w , z   1. Chi-squared   4   & 2  2. Minimum Entropy 4      1  4  3. Modified Minimum Entropy   E     4  4  4. Deville and Sändal (1992)  G 4     E  G 4   G 4 E  1    4 E   E    4 E 1 4 E  1 G 4 E x  Note: u and l are known constants in the interval EF1FG;x @ @@. Table 2. Final micro-data sample sizes and their distribution by Province Province Province Code Number of sample observations (used in estimations) Álava 1 - Albacete 2 19,784 Alicante 3 44,072 Almería 4 24,353 Ávila 5 12,534 Badajoz 6 28,710 Balears (Illes) 7 32,885 Barcelona 8 86,880 Burgos 9 18,131 Cáceres 10 22,842 Cádiz 11 34,890 Castellón 12 25,682 Ciudad Real 13 21,542 Córdoba 14 33,076 Coruña (A) 15 37,749 Cuenca 16 14,172 Girona 17 24,974 Granada 18 33,254 Guadalajara 19 12,594 Guipúzcoa 20 - Huelva 21 21,255 Huesca 22 14,167 Jaén 23 30,891 León 24 23,201 Lleida 25 20,342 Rioja (La) 26 16,820 Lugo 27 21,261 Madrid 28 110,208 Málaga 29 40,883 Murcia 30 38,140 Navarra 31 - Ourense 32 19,439 Asturias 33 36,084 Palencia 34 12,065 Palmas (Las) 35 31,743 24 Table 2 (continued) Province Province Code Number of sample observations (used in estimations) Pontevedra 36 33,238 Salamanca 37 18,651 Santa Cruz de Tenerife 38 30,891 Cantabria 39 23,579 Segovia 40 11,297 Sevilla 41 44,700 Soria 42 8,624 Tarragona 43 27,661 Teruel 44 11,822 Toledo 45 24,773 Valencia 46 53,361 Valladolid 47 22,904 Vizcaya 48 - Zamora 49 14,452 Zaragoza 50 36,454 Ceuta 51 5,244 Melilla 52 5,068 Non residents 99 615 Total of observations 1,337,957 Source: own elaboration using data drawn from the Spanish Personal Income Tax 2007 annual sample. Table 3. Spanish municipalities according to population size, 2007. Population threshold Number of municipalities % of Total Population < 1,000 inhab. 4,877 3.37% 1,000 – 5,000 inhab. 1,968 10.06% 5,000 – 20,000 inhab. 895 19.37% 20,000 – 50,000 inhab. 235 15.50% 50,000 – 100,000 inhab. 77 12.05% > 100,000 inhab. 59 39.66% Source: Own elaboration using population counts from the Spanish National Statistics Institute. Table 4. Percentage of municipalities for which a new non-negative vector of weights was obtained Distance function Percentage Chi-squared 82.2% Minimum Entropy 91.6% Modified Minimum Entropy 94.8% Deville and Sändal (1992) 73.3% Source: Own elaboration 25 Table 5. Chosen distance function for each municipality Distance function Number of municipalities % Chi-squared 1,607 31.65% Minimum Entropy 2,496 49.15% Modified Minimum Entropy 473 9.31% Deville and Särndal (1972) 502 9.89% Total: 5,078 100 Source: Own elaboration Table 6. Distribution of the ratio of new to original sample weights. Percentiles Ratio z/w 1% 0.06013 5% 0.31796 10% 0.62805 25% 0.91277 50% 0.99691 75% 1.04968 90% 1.14317 95% 1.24089 99% 1.80791 Mean 0.97445 St. Dev. 0.98183 Source: Own elaboration Province Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities pop Province / total pop Álava 29 4,25% 19 11,36% 2 9,26% 0 0,00% 0 0,00% 1 75,13% 51 0,68% Albacete 40 5,23% 39 21,86% 4 10,22% 3 20,67% 0 0,00% 1 42,02% 87 0,87% Alicante 50 1,17% 35 4,88% 33 18,91% 16 25,49% 5 19,70% 2 29,86% 141 4,04% Almería 50 3,44% 32 12,75% 14 21,05% 3 10,79% 2 23,10% 1 28,87% 102 1,43% Asturias 16 0,86% 31 6,62% 24 23,96% 4 15,16% 1 7,75% 2 45,65% 78 2,38% Ávila 226 31,16% 17 22,04% 4 14,90% 0 0,00% 1 31,90% 0 0,00% 248 0,37% Badajoz 52 4,40% 84 26,72% 23 25,98% 3 13,40% 1 8,09% 1 21,41% 164 1,50% Baleares 7 0,43% 23 6,09% 26 24,54% 10 31,77% 0 0,00% 1 37,17% 67 2,28% Barcelona 98 0,73% 86 4,08% 83 15,55% 25 14,00% 12 14,96% 7 50,69% 311 11,80% Burgos 345 18,78% 21 10,87% 2 3,55% 2 19,22% 0 0,00% 1 47,57% 371 0,81% Cáceres 144 16,54% 63 29,34% 10 22,34% 1 9,72% 1 22,06% 0 0,00% 219 0,91% Cádiz 3 0,17% 9 1,95% 17 13,71% 7 15,65% 5 31,64% 3 36,88% 44 2,67% Cantabria 30 2,62% 54 20,71% 14 24,73% 2 10,53% 1 9,67% 1 31,74% 102 1,27% Castellón 88 5,60% 28 10,43% 11 16,81% 7 37,05% 0 0,00% 1 30,11% 135 1,27% Ceuta 0 0,00% 0 0,00% 0 0,00% 0 0,00% 1 100,00% 0 0,00% 10,17% Ciudad Real 39 4,25% 39 15,78% 19 37,68% 3 18,41% 2 23,89% 0 0,00% 102 1,13% Córdoba 11 0,90% 35 12,19% 21 23,40% 7 22,67% 0 0,00% 1 40,85% 75 1,75% Coruña, A 0 0,00% 37 9,49% 46 34,02% 8 20,01% 2 14,91% 1 21,57% 94 2,51% Cuenca 202 26,58% 29 25,90% 6 22,46% 0 0,00% 1 25,06% 0 0,00% 238 0,47% Girona 131 7,44% 60 19,36% 22 29,41% 7 30,74% 1 13,05% 0 0,00% 221 1,56% Granada 56 3,49% 76 18,54% 29 32,01% 5 12,62% 1 6,62% 1 26,72% 168 1,96% Guadalajara 258 15,54% 24 23,06% 4 14,06% 1 12,56% 1 34,78% 0 0,00% 288 0,50% Guipúzcoa 32 1,72% 25 8,60% 25 38,78% 4 15,85% 1 8,69% 1 26,35% 88 1,54% Huelva 25 2,43% 34 18,44% 16 36,72% 3 13,04% 0 0,00% 1 29,37% 79 1,10% Huesca 171 23,20% 24 19,04% 6 35,13% 1 22,63% 0 0,00% 0 0,00% 202 0,49% Jaén 14 1,43% 53 20,52% 24 33,33% 4 17,99% 1 9,22% 1 17,51% 97 1,47% León 138 13,28% 62 25,11% 8 15,21% 1 5,81% 1 13,44% 1 27,15% 211 1,10% Lleida 163 15,19% 53 24,76% 14 29,30% 0 0,00% 0 0,00% 1 30,75% 231 0,92% Lugo 4 0,75% 51 39,48% 11 33,34% 0 0,00% 1 26,42% 0 0,00% 67 0,79% Madrid 54 0,38% 50 2,06% 45 6,86% 12 6,84% 9 10,57% 9 73,29% 179 13,45% 5.000 - 20.000 Population thresholds Appendix 1. Spanish municipalities by province and population size, 2007. < 1.000 1.000 - 5.000 Total> 100.00050.000 - 100.00020.000 - 50.000 33 Province Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities % of total provincial population Number of municipalities pop Province / total pop Málaga 25 0,86% 50 8,66% 10 6,71% 7 13,95% 6 24,50% 2 45,32% 100 3,36% Melilla 0 0,00% 0 0,00% 0 0,00% 0 0,00% 1 100,00% 0 0,00% 10,15% Murcia 2 0,12% 7 1,18% 21 18,74% 11 24,00% 2 10,70% 2 45,27% 45 3,08% Navarra 187 9,08% 64 23,94% 18 25,80% 2 9,01% 0 0,00% 1 32,17% 272 1,34% Ourense 10 2,12% 72 41,31% 9 24,76% 0 0,00% 0 0,00% 1 31,81% 92 0,75% Palencia 170 20,46% 16 16,49% 4 15,56% 0 0,00% 1 47,49% 0 0,00% 191 0,38% Palmas de G.C. 1 0,07% 3 0,73% 19 21,79% 7 20,73% 3 20,49% 1 36,20% 34 2,31% Pontevedra 1 0,08% 23 8,42% 29 32,59% 7 19,33% 1 8,46% 1 31,11% 62 2,10% Rioja, La 144 9,90% 21 14,92% 7 20,28% 1 7,69% 0 0,00% 1 47,21% 174 0,68% Salamanca 334 25,76% 20 11,08% 7 18,78% 0 0,00% 0 0,00% 1 44,38% 362 0,78% S.C. Tenerife 0 0,00% 17 4,99% 24 22,77% 9 27,76% 1 7,35% 2 37,13% 53 2,18% Segovia 187 27,79% 18 22,16% 3 14,87% 0 0,00% 1 35,18% 0 0,00% 209 0,35% Sevilla 5 0,18% 37 5,98% 49 27,02% 11 19,09% 1 3,57% 2 44,16% 105 4,09% Soria 170 24,89% 10 22,67% 2 11,62% 1 40,82% 0 0,00% 0 0,00% 183 0,21% Tarragona 98 5,58% 57 16,81% 20 24,11% 6 21,97% 0 0,00% 2 31,54% 183 1,68% Teruel 214 32,38% 19 27,37% 2 16,48% 1 23,77% 0 0,00% 0 0,00% 236 0,32% Toledo 89 6,96% 92 38,01% 21 29,36% 0 0,00% 2 25,67% 0 0,00% 204 1,42% Valencia 84 1,65% 107 9,91% 48 20,63% 22 24,68% 4 11,06% 1 32,08% 266 5,50% Valladolid 182 8,25% 33 13,27% 7 9,74% 2 8,06% 0 0,00% 1 60,68% 225 1,15% Vizcaya 42 1,94% 37 7,77% 22 19,36% 8 24,38% 2 15,61% 1 30,94% 112 2,53% Zamora 225 38,18% 20 13,85% 2 14,44% 0 0,00% 1 33,53% 0 0,00% 248 0,44% Zaragoza 231 6,50% 52 12,46% 8 8,61% 1 2,26% 0 0,00% 1 70,18% 293 2,06% Total: 4877 3,37% 1968 10,06% 895 19,37% 235 15,50% 77 12,05% 59 39,66% 8111 Own elaboration using population counts from the Spanish National Statistics Institute. Appendix 1 (continued) Population thresholds < 1.000 1.000 - 5.000 5.000 - 20.000 20.000 - 50.000 50.000 - 100.000 > 100.000 Total Municipality Gini Index Lower limit Upper limit Lower limit Upper limit Mean of the estimator Standard error Madrid 0.52257 0.51587 0.52970 0.52162 0.52319 0.52241 0.00400 Barcelona 0.53002 0.51815 0.54292 0.52832 0.53073 0.52953 0.00615 Valencia 0.50176 0.48732 0.51690 0.49874 0.50158 0.50016 0.00722 Sevilla 0.48521 0.47665 0.49368 0.48377 0.48564 0.48470 0.00477 Zaragoza 0.46188 0.45531 0.46840 0.46112 0.46264 0.46188 0.00388 Málaga 0.46565 0.45852 0.47294 0.46455 0.46638 0.46547 0.00467 Murcia 0.48116 0.47327 0.48950 0.48010 0.48196 0.48103 0.00474 Palma de Mallorca 0.47876 0.47032 0.48634 0.47716 0.47904 0.47810 0.00480 Palmas G.C. 0.49246 0.47945 0.50908 0.49088 0.49424 0.49256 0.00857 Córdoba 0.47483 0.46449 0.48709 0.47337 0.47577 0.47457 0.00614 Alicante 0.47337 0.46262 0.48560 0.47246 0.47484 0.47365 0.00607 Valladolid 0.45337 0.44518 0.46234 0.45224 0.45412 0.45318 0.00481 Vigo 0.46074 0.45238 0.46750 0.45978 0.46140 0.46059 0.00414 Gijón 0.46088 0.45174 0.47114 0.45975 0.46176 0.46076 0.00512 Hospitalet Llobregat 0.37441 0.35401 0.39218 0.37091 0.37528 0.37309 0.01116 Coruña (A) 0.50698 0.49446 0.52088 0.50636 0.50941 0.50788 0.00777 Granada 0.46257 0.45335 0.47053 0.46172 0.46356 0.46264 0.00469 Elche 0.47830 0.46342 0.49019 0.47645 0.47956 0.47801 0.00792 Santa Cruz de Tenerife 0.46752 0.45935 0.47626 0.46676 0.46848 0.46762 0.00438 Oviedo 0.45946 0.44686 0.46998 0.45845 0.46093 0.45969 0.00634 Badalona 0.39552 0.37485 0.41643 0.39473 0.39916 0.39695 0.01130 Cartagena 0.45181 0.43910 0.46380 0.45000 0.45296 0.45148 0.00755 Móstoles 0.39790 0.34810 0.46170 0.38667 0.39975 0.39321 0.03339 Jerez de la Frontera 0.45574 0.44634 0.46740 0.45422 0.45642 0.45532 0.00562 Terrassa 0.44346 0.40923 0.47609 0.43578 0.44377 0.43977 0.02038 Sabadell 0.46838 0.44227 0.49242 0.46355 0.46905 0.46630 0.01402 Alcalá de Henares 0.40751 0.38397 0.43487 0.40802 0.41361 0.41081 0.01425 Fuenlabrada 0.37292 0.34778 0.39975 0.37048 0.37648 0.37348 0.01531 Almería 0.45299 0.44288 0.46273 0.45205 0.45394 0.45300 0.00482 Leganés 0.40992 0.37374 0.43635 0.40179 0.40862 0.40521 0.01741 Santander 0.47659 0.46458 0.48536 0.47498 0.47732 0.47615 0.00596 Burgos 0.42545 0.41916 0.43236 0.42547 0.42696 0.42621 0.00381 Castellón de la Plana 0.47092 0.46264 0.48400 0.47051 0.47250 0.47150 0.00509 Alcorcón 0.41525 0.38455 0.44873 0.41365 0.42109 0.41737 0.01897 Albacete 0.46965 0.44891 0.49192 0.46642 0.47145 0.46894 0.01282 Getafe 0.42737 0.39226 0.47757 0.41994 0.42826 0.42410 0.02122 Salamanca 0.45741 0.44467 0.46758 0.45601 0.45842 0.45722 0.00615 Huelva 0.43721 0.42823 0.44446 0.43542 0.43719 0.43630 0.00451 Logroño 0.45804 0.44844 0.46776 0.45700 0.45928 0.45814 0.00583 Badajoz 0.45968 0.44474 0.47278 0.45680 0.45960 0.45820 0.00715 San Cristóbal de La Laguna 0.44123 0.42915 0.45562 0.43962 0.44235 0.44099 0.00698 Appendix 2. Gini indexes for selected Spanish municipalities* (new weights used) α-percentile method at 95% Normal method at 95% Bootstrap (100 replications) 35 Municipality Gini Index Lower limit Upper limit Lower limit Upper limit Mean of the estimator Standard error León 0.44852 0.44068 0.45604 0.44703 0.44884 0.44793 0.00464 Tarragona 0.45087 0.43762 0.46264 0.44877 0.45183 0.45030 0.00780 Cádiz 0.44729 0.43584 0.46181 0.44650 0.44954 0.44802 0.00774 Lleida 0.46426 0.45379 0.47694 0.46298 0.46560 0.46429 0.00669 Marbella 0.51489 0.49542 0.53378 0.51384 0.51782 0.51583 0.01014 Mataró 0.43900 0.40682 0.47274 0.43706 0.44389 0.44048 0.01741 Dos Hermanas 0.45715 0.43225 0.48305 0.45317 0.45907 0.45612 0.01504 Santa Coloma de Gramenet 0.40724 0.36949 0.43502 0.40030 0.40757 0.40393 0.01856 Jaén 0.44532 0.43571 0.45539 0.44412 0.44629 0.44520 0.00554 Algeciras 0.42852 0.41106 0.44498 0.42719 0.43047 0.42883 0.00836 Torrejón de Ardoz 0.39015 0.35569 0.42681 0.38661 0.39372 0.39017 0.01816 Ourense 0.47292 0.46388 0.48239 0.47239 0.47457 0.47348 0.00558 Alcobendas 0.63962 0.59375 0.68292 0.63307 0.64368 0.63838 0.02707 Reus 0.44789 0.42813 0.46723 0.44524 0.44932 0.44728 0.01040 Own elaboration * Spanish municipalities with population size above 100,000 inhabitants. α-percentile method at 95% Normal method at 95% Bootstrap (100 replications) Appendix 2. (continued) 36 Municipality Atkinson Index (risk aversion 0.5) Lower limit Upper limit Lower limit Upper limit Mean of the estimator Standard error Madrid 0.25433 0.24676 0.26296 0.25332 0.25510 0.25421 0.00454 Barcelona 0.26068 0.24821 0.27294 0.25872 0.26129 0.26001 0.00658 Valencia 0.23535 0.21870 0.25485 0.23179 0.23549 0.23364 0.00944 Sevilla 0.22003 0.21044 0.23141 0.21855 0.22058 0.21957 0.00520 Zaragoza 0.19791 0.19106 0.20548 0.19721 0.19887 0.19804 0.00424 Málaga 0.20113 0.19356 0.20867 0.20008 0.20185 0.20097 0.00452 Murcia 0.21130 0.20264 0.21888 0.20998 0.21184 0.21091 0.00474 Palma de Mallorca 0.20897 0.20085 0.21754 0.20738 0.20921 0.20829 0.00469 Palmas de G.C. 0.22352 0.20792 0.24505 0.22166 0.22561 0.22363 0.01009 Córdoba 0.20989 0.19815 0.22441 0.20827 0.21102 0.20964 0.00701 Alicante 0.20666 0.19614 0.21989 0.20579 0.20815 0.20697 0.00603 Valladolid 0.19275 0.18450 0.20281 0.19165 0.19362 0.19263 0.00503 Vigo 0.19503 0.18812 0.20100 0.19436 0.19573 0.19505 0.00350 Gijón 0.19978 0.19219 0.20894 0.19887 0.20072 0.19980 0.00472 Hospitalet de Llobregat 0.13554 0.11949 0.14914 0.13368 0.13686 0.13527 0.00810 Coruña (A) 0.23380 0.22032 0.25179 0.23325 0.23671 0.23498 0.00885 Granada 0.19664 0.19044 0.20332 0.19609 0.19758 0.19683 0.00382 Elche 0.21167 0.19789 0.22326 0.21015 0.21299 0.21157 0.00726 Santa Cruz de Tenerife 0.19853 0.19223 0.20512 0.19793 0.19934 0.19864 0.00359 Oviedo 0.19538 0.18559 0.20562 0.19470 0.19686 0.19578 0.00549 Badalona 0.14829 0.13433 0.16373 0.14778 0.15134 0.14956 0.00907 Cartagena 0.19198 0.17959 0.20360 0.19022 0.19310 0.19166 0.00734 Móstoles 0.16316 0.11659 0.22770 0.15284 0.16608 0.15946 0.03378 Jerez de la Frontera 0.19317 0.18419 0.20390 0.19206 0.19408 0.19307 0.00517 Terrassa 0.18991 0.15886 0.22967 0.18353 0.19107 0.18730 0.01923 Sabadell 0.19984 0.17976 0.22228 0.19611 0.20105 0.19858 0.01260 Alcalá de Henares 0.15428 0.14122 0.17341 0.15507 0.15859 0.15683 0.00896 Fuenlabrada 0.13051 0.11700 0.14503 0.12992 0.13324 0.13158 0.00845 Almería 0.19054 0.18139 0.20137 0.18959 0.19148 0.19053 0.00481 Leganés 0.15910 0.13560 0.18868 0.15348 0.15907 0.15627 0.01426 Santander 0.20738 0.19686 0.21523 0.20622 0.20822 0.20722 0.00510 Burgos 0.16743 0.16192 0.17438 0.16732 0.16869 0.16800 0.00351 Castellón de la Plana 0.20238 0.19481 0.21275 0.20197 0.20383 0.20290 0.00474 Alcorcón 0.16207 0.13903 0.19147 0.16056 0.16665 0.16361 0.01555 Albacete 0.21249 0.18764 0.24197 0.20854 0.21464 0.21159 0.01556 Getafe 0.17527 0.14739 0.22481 0.16930 0.17733 0.17332 0.02048 Salamanca 0.19092 0.18216 0.19950 0.18993 0.19196 0.19095 0.00518 Huelva 0.17553 0.16770 0.18066 0.17392 0.17545 0.17469 0.00392 Logroño 0.19412 0.18432 0.20456 0.19312 0.19545 0.19429 0.00593 Badajoz 0.19456 0.18199 0.20826 0.19203 0.19467 0.19335 0.00673 Appendix 3. Atkinson indexes for selected Spanish municipalities* (new weights used) α-percentile method at 95% Normal method at 95% Bootstrap (100 replications) 37 Municipality Atkinson Index (risk aversion 0.5) Lower limit Upper limit Lower limit Upper limit Mean of the estimator Standard error San Cristóbal de La Laguna 0.17644 0.16596 0.18881 0.17479 0.17733 0.17606 0.00648 León 0.18236 0.17576 0.18959 0.18126 0.18284 0.18205 0.00402 Tarragona 0.18595 0.17317 0.20232 0.18420 0.18738 0.18579 0.00810 Cádiz 0.18780 0.17836 0.20154 0.18746 0.18990 0.18868 0.00621 Lleida 0.19822 0.18769 0.21085 0.19709 0.19960 0.19834 0.00638 Marbella 0.24560 0.22362 0.26428 0.24445 0.24849 0.24647 0.01029 Mataró 0.17865 0.15747 0.20410 0.17882 0.18396 0.18139 0.01309 Dos Hermanas 0.20014 0.17631 0.22948 0.19627 0.20216 0.19922 0.01504 Santa Coloma Gramanet 0.15343 0.13244 0.17526 0.14963 0.15473 0.15218 0.01301 Jaén 0.18025 0.17312 0.18923 0.17926 0.18108 0.18017 0.00464 Algeciras 0.16941 0.15827 0.18310 0.16863 0.17136 0.16999 0.00697 Torrejón de Ardoz 0.14753 0.12319 0.17403 0.14526 0.15086 0.14806 0.01428 Ourense 0.20149 0.19238 0.21193 0.20102 0.20313 0.20207 0.00540 Alcobendas 0.37615 0.31233 0.43396 0.36849 0.38257 0.37553 0.03592 Reus 0.18472 0.17021 0.19876 0.18266 0.18591 0.18429 0.00831 Own elaboration * Spanish municipalities with population size above 100,000 inhabitants. α-percentile method at 95% Normal method at 95% Bootstrap (100 replications) Appendix 3. 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