CC BY
58
For citation: López Rodriguez M. I., Barac M. (2019). Inequality of Spanish Household Expenditure for the 2006-2016 Period — Are We Converging? Ekonomika Regiona [Economy of Region], 15(3), 780-790
doi 10.17059/2019-3-12 UDC: 332.1
M. I. López Rodríguez, M. Barac
Universitat de Valencia (Valencia, Spain; e-mail: Maja.Barac@uv.es)
INEQUALITY OF SPANISH HOUSEHOLD EXPENDITURE FOR THE 2006-2016 PERIOD - ARE WE CONVERGING? 1
The depth and persistence of the Great Recession that started in 2008 had a considerable impact on income distribution and inequality. Therefore, studies of living standards and evolution of income inequality are trend topics nowadays.
Our goal was to estimate the impact of the economic crises on household expenditure and the trends and evolution of regional inequality. We applied our analysis to the Spanish case based on Household Budget Survey data from Instituto Nacional de Estadística (INE, the National Statistics Institute) and the period of eleven years between 2006 and 2016. A model that showed good results in modelling income was the bipar-ametric gamma model, which is further very useful to estimate inequality. First, we tested the validity of the model, which allowed us to obtain the inequality data. Second, we extended our analysis studying the evolution of inequality, as well as household living standards, by examining the impact of the Great Recession on household expenditures. For the second part of the paper, we conducted longitudinal and transversal studies. The main results show that, in general, expenditure inequality reduces during the period studied. Moreover, given that average spending decreases in most regions, the tendency is for them to equalize on the downside, especially for the period of the economic crisis (2008-2013).
Keywords: household expenditure, inequality, regional data, Autonomous Communities, biparametric Gamma, longitudinal analysis, transversal studies
1. Introduction
Having a suitable income explanatory model is key for policy makers when designing policies for improving social welfare at both the regional and national level. Relative to income, inequality is one of the dimensions that directly affects policy makers' performance, as more inequality is usually associated with more economic, political and social instability. Income modelling has been widely studied in literature [1] and [2] Singh and Maddala, [3] and [4] Dagum, 1977 and 1980; 1976 and 1978; [5] Baró, 1982; [6] Esteban et al., 1994; [7] Callealta et al., 1996; [8] Herrerías et al., 1996; [9] Klein et al., 2015, [10] Nartikoev and Peresetsky, 2019, as well as the economic interpretation of the parameters of the proposed model [11] Dagum, 1980; [12] Rojo, 1993; [13] Lafuente, 1995; [14] Martín-Guzmán, 1996; [15] López Rodríguez, 1997; [16] García et al., 2006. The main reason for such interest lies in the fact that when finding a proper model which can explain the evolution of income, we will be able to make comparisons between regions and among time that can help design more accurate economic policies. Moreover, modelling income also allows us to better analyse inequal-
1 © López Rodriguez M. I., Barac M. Text. 2019.
ity, which is key in the study of the evolution of social welfare.
Studying income evolution also helps to identify inequalities and their evolution over time. In this topic, regional disparities have been in the spotlight of much research. For instance, [17] Diez-Minguela et al. (2018) analyse Spanish long-term income evolution for the period 1860-2015 using GDP per capita. They find the well-known inverted U shaped curve with an initial period of increasing inequality between 1860 and 1930.This is followed by a converging period until 1980 and an increasing polarization between the north and the regions of the south and south-west. [18] De la Fuente, 2019, also focuses on regional inequalities through GDP per capita, but for the period 1955-2016. A similar pattern with a reduction in regional disparities was found at the beginning of the period, that smoothens afterwards and even reverts in the last decade.
The present work follows this line of analysis and the main questions that this study aims to answer are: What has been the evolution of household expenditure, bearing in mind that the period includes the recent Great Recession? Is inequality increasing or decreasing among the regions? And finally, what is the relative evolution of expenditure in the different regions, that is,
has the regional inequality undergone changes in composition or have their relative positions been maintained?
Relationships between income inequality and consumer inequality are not always clear, and there is no consensus on which variables are more accurate to better identify inequalities among people or regions. Decisions on choosing income or consumption (expenses) can rely on different aspects.
On the one hand, their capacity to estimate a utility function:
"Much of the debate over the rising levels of inequality in the United States and other developed countries is phrased in terms of income, or in terms of components of income like wages and earnings. But for economists, a basic utility function of individuals typically refers to consumption and leisure, not income." ([19] Attanasio and Pistaferri, 2016, p. 3)
On the other hand, the availability and data quality. Apparently, income analysis can underestimate inequality and the opposite happens when the chosen variable has to do with expenses. This can be due to different patterns in savings and credit access within groups ([20] Aguiar and Bils, 2015, [21] Krueger and Perri, 2006), but according to [22] Brewer and O'Dea, 2012, a household's long-term standard of living should be better predicted by current consumption rather than current income. Additionally, as we are focusing on regional and not individual inequalities, these differences attributed to the variable choice might be attenuated.
We applied this analysis to the evolution of income on the side of the expenses of Spanish households for the 2006-2016 period. Data are obtained from the Household Budget Survey of Instituto Nacional de Estadística (INE, the National Statistics Institute), and inequality is analysed at the regional level. Spain has a decentralized unitary state with 17 Autonomous Communities (AA. CC.) plus two autonomous cities, which are Ceuta and Melilla. The regional study is interesting because the Autonomous Communities have a certain level of self-government and have some distinctive particularities.
The methodology proposed to explain the expenses of Spanish households in recent years is the biparametric gamma model. The main advantage of this model is that it has a remarkable property, that is, it allows to parameterize the evolution of inequality. Is the biparametric gamma model always adequate for modelling income? In the literature there is no consensus. This model was proposed by [23] Salem and Mount, 1974, rejected by
[24] Dagum, 1991, then validated for the Spanish case by [27] Rojo, 1993, who considered the data on income provided by the Household Budget Survey (H. B. S.) for the period 1980-81, aggregated in deciles. Later, the model was also validated by [25] Lafuente, 1998 and [15] López Rodríguez, 1997, who considered as empirical information the aggregated data from the same 1990-91 income survey, and for disaggregated income and expenses of 1980-81 and 1990-91, respectively. More recently [26] López Rodríguez, 2016 and [27] López Rodríguez, 2016, also ratified the model regarding the information of expenses provided by the H. B. S. (base 2006).
The article is structured in the following way. The first section presents the justification of the methodology used in the paper, that is, the bipar-ametric model applied on household expenditure, and the study of the correlation between model parameters and the well-known Gini's inequality index. The next section, section 2, sets the results of the analysis by validating the adequacy of the model chosen, and once inequality is estimated we can apply longitudinal and transversal studies. The first studies explore the annual evolution of inequality and average expenditure. The evolution of household expenditure reflects the same trend as experienced by the economic cycle during the period. The second studies are aimed at establishing clusters within the AA. CC. regarding its relative position in household expenditure, and extending the results from the sample to the population level. The last section concludes.
2. Data and Methods
The empirical analysis is based on more than 225.000 data from the H.B.S. of INE for eleven years that make up the period 2006-2016 [28]. Thus, table 1 contains the sample size for each Autonomous Community and year. In the same table, it can be seen that the information collected by the INE about Ceuta and Melilla appears aggregated between 2006 and 2010, and broken down as of 2011. In order to properly perform the longitudinal analyses, we will proceed to deflate the expenses. For this we will use the Consumer Price Index (CPI) for each AA.CC with base 2016, also provided by the INE.
With regard to statistical techniques, and taking into account what was stated in the introduction, the model proposed to explain family expenses will be the biparametric Gamma, with density function:
la -lxxa-1
f (x) =-—-, Vx e 10, «i, a > 0, l > 0, (1)
r(a)
Table 1
Sample sizes of Expenditures by community and year. Period 2006-2016
AA.CC. 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Andalusia 2106 2274 2336 2379 2379 2403 2436 2451 2424 2410 2417
Aragon 849 885 927 915 935 956 969 992 964 986 989
Asturias 649 801 820 824 829 825 839 868 875 889 879
Balearic Islands 793 809 809 801 794 815 824 807 780 777 763
Canary Islands 907 960 986 1016 1026 996 1015 1039 1066 1018 983
Cantabria 531 704 750 763 757 768 773 776 768 762 761
Castille and León 1376 1416 1441 1449 1436 1422 1441 1464 1471 1482 1449
Castille-La Mancha 1160 1103 1101 1168 1181 1175 1202 1204 1206 1221 1195
Catalonia 1949 1989 2050 2048 1982 1969 1939 2009 2008 2028 2016
Valencian Com. 1564 1644 1646 1701 1685 1727 1722 1718 1723 1712 1694
Extremadura 902 942 949 962 944 973 984 1002 993 1002 983
Galicia 1311 1317 1369 1368 1327 1322 1322 1352 1361 1350 1355
Madrid 1172 1380 1461 1585 1550 1565 1571 1568 1634 1643 1653
Murcia 874 991 1002 971 942 917 905 904 893 910 912
Navarre 676 1409 1436 1407 1391 1183 766 757 766 740 747
Basque Country 1783 1995 2058 2018 2093 2136 2123 2167 2222 2220 2237
La Rioja 623 705 706 733 718 718 730 733 737 732 739
Ceuta and Melilla/Ceuta 209 218 228 235 234 117 116 119 120 122 118
Melilla 130 129 124 129 123 118
where r(a) is Euler's Gamma function, and the estimation method used to obtain the estimators a and 1 will be the maximum-likelihood method. The use of the maximum-likelihood method leads to the need to solve the following system of equations:
X
ln (a )-¥(a ) = ln
Г'(а)
(2)
D =
max
e{1,2,......-
,{1-^ 1}
D =
- ln (a/2) 2n '
(4)
2.1 Properties of the Estimators and Inequality Indicator
As a result of the method applied to obtain the model estimators, the properties of the maximum-likelihood estimators are applicable, that is: a) They are asymptotically normally distributed, and it can be demonstrated that
( \
v1 /
■+N
where T (a) = ^ ^ is the digamma function, and r(a)
X and X are the arithmetic and geometric means of the sample data. Since this system has no analytical solution, the Newton-Raphson and Gauss-Laguerre methods will be used in combination for its resolution. As for the goodness-of-fit test, the Kolmogorov-Smirnov test will be used, whose statistic is:
" " (3)
(a v1
where
d2 ln Г (a)
5a2
(5)
(6)
with n being the sample size and F and FT the
Oj 1 j
functions of the empirical and the theoretical distribution, respectively.
On the other hand, the critical value, for a level of significance a, responds to the following expression:
which would allow us to elaborate tests about the parameters.
b) They are invariant, that is, taking into account that the mean, variance, mode and median of a biparametric gamma respond to the following expressions:
; CT2 =4; Mo = 2-1; Me = ^ (7)
11 1 31
The maximum-likelihood estimators of said measures will be:
a
a
A = -; a2 ; Mo =
a-1
Me =
1
12
3a -1 31 '
(8)
Regarding the selection of the inequality indicator, taking into account the "desirable compliance properties" of the indices used for this purpose ([29] Kakwani, 1980; [7] Callealta et al., 1996 and [14] Martin-Guzman, 1996) and the classification that is usually made of them ([29] Kakwani, 1980; [5] Baro, 1982; [7] Callealta et al., 1996 and [14] Martin-Guzman, 1996) the indicator of inequality selected for the present study will be the parameter a of the gamma model.
The advantages of this indicator are several. First, it is dimensionless, so easily comparable among years and regions. Second, given its high negative correlation with the index of Gini ([30] Esteban et al., 2000), it is easy to interpret and therefore helps us answer our research questions. Third, as a is one of the parameters of the model that explains household expenditures, it verifies that when considered as an estimator it has (in asymptotic terms) a known distribution, and as previously exposed, it is asymptotically Normal. This last property will allow us to conduct hypothesis testing that will let us compare inequalities between different geographical areas and/or different periods of time.
3. Results
First of all, we need to prove the validity of the gamma biparametric model as an explanation of household expenses of the AA. CC., with the data provided by the INE for the 2006-2016 period. The Kolmogorov — Smirnov test is used as a method-
ological tool. Due to the fact that no option has been found in the commercial statistical software which would allow this validation to be carried out, it has been necessary to develop specific programs that solve both the manipulation of the data and the calculations necessary to obtain the results. In the elaboration of these programs, it has been taken into account that the maximum-likelihood estimation of the parameters of the model were not analytically deductible, so numerical calculation techniques have been used, specifically, a combination of the Newton-Raphson and Gauss-Laguerre methods.
Thus, Table 2 shows the results in detail (value of the level of significance, statistic and estimated parameters of the model) corresponding to the 11 years considered (2006-2016) and for each AA. CC. Except for the years of the cells marked in black, that is, 2010 for Andalusia, 2013 for the Valencian Community, 2016 for Madrid, 2014 and 2015 for Navarre and 2010 and 2011 for the Basque Country, the adherence test is supported for levels of significance within the valid range in any data analysis (between 1 % and 10 %). Therefore, in general, the biparametric gamma model fits with our data.
3.1. Inequality Evolution of Household Expenditure for the Period 2006-2016
To examine the evolution of inequality, the a parameter on household expenditure was estimated. Taking into account that this parameter
Table 2
AA.CC. 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Andalusia 0.4033 0.1863 0.1442 0.1279 0.0028 0.1770 0.031 0.0113 0.0211 0.0148 0.0271
Aragon 0.8714 0.6013 1.0259 1.3114 0.2834 0.5807 0.5011 0.8798 0.5169 0.3558 0.2421
Asturias 0.2004 0.5306 1.2583 0.2866 0.7650 0.7384 0.1240 0.2339 0.7732 0.2181 0.5413
Balearic Islands 0.9803 0.1681 0.7694 0.3089 0.8647 0.9257 0.8019 0.0833 0.1424 0.1999 0.3799
Canary Islands 0.3316 0.2515 0.1569 0.7393 0.3828 0.0250 0.0373 0.4025 0.5299 0.6191 0.3911
Cantabria 0.1019 1.1954 0.7082 1.1393 0.6292 0.2013 0.2421 0.4921 0.4669 0.3839 0.1258
Castille and León 0.5348 0.2787 0.8563 1.1370 0.5203 0.4676 0.1798 0.3822 0.0412 0.0130 0.3166
Castille-La Mancha 0.7047 0.7461 0.76755 0.1759 0.09619 0.57218 0.2464 0.1645 0.2242 0.3508 0.7881
Catalonia 0.3309 0.4971 0.6686 0.3348 0.31359 0.2963 0.0695 0.12848 0.0376 0.0510 0.0527
Valencian Com. 0.4122 0.0120 0.2454 0.0398 0.31316 0.0774 0.04346 0.00155 0.05778 0.1755 0.0144
Extremadura 0.5771 0.5248 0.4279 0.0411 0.2466 0.1327 0.1089 0.2731 0.0819 0.7634 0.5868
Galicia 0.4508 0.2126 0.3364 0.5347 0.4903 0.4629 0.2182 0.4299 0.3634 0.0212 0.0421
Madrid 0.2866 0.4089 0.0541 0.0428 0.0853 0.0622 0.4821 0.1205 0.0551 0.0228 0.0068
Murcia 0.6787 0.0957 0.4097 0.5048 0.0654 0.2664 0.1114 0.3924 0.6436 1.1149 1.2334
Navarre 0.5684 1.3027 1.0805 0.6404 0.6941 0.6844 0.8321 0.5514 0.0071 0.0061 0.3333
Basque Country 0.9364 0.4961 0.0491 0.4877 0.0008 0.0063 0.0482 0.0264 0.0890 0.0127 0.0169
La Rioja 0.8194 0.3300 0.2565 0.5746 0.2918 0.4941 0.3385 0.3248 0.1710 0.7151 0.5515
Ceuta and Melilla/ Ceuta 0.0442 0.3705 0.5414 0.7830 0.6024 0.2307 0.8913 0.0948 0.1340 0.1436 0.7274
Melilla n.a. n.a. n.a. n.a. n.a. 1.4629 0.2831 0.2913 1.0895 0.4560 0.2651
Adhesion contrast of expenses to the biparametric gamma model. Period 2006-2016
Table 3
Estimating a parameter on household expenditure. Period 2006-2016
AA. CC. 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Andalusia 1.9099 2.17971 2.28689 2.47752 2.5432 2.4521 2.3864 2.4117 2.5477 2.6052
Aragon 2.0363 2.05827 2.61065 2.54666 2.69340 2.6699 2.5562 2.7332 2.6035 2.4903 2.5612
Asturias 1.8554 1.83550 2.19750 2.13977 2.33080 2.4546 2.3979 2.5098 2.4430 2.3307 2.5841
Balearic Islands 2.5398 2.3967 2.5352 2.7635 2.6477 2.8276 2.9063 3.0824 2.8691 2.7532 3.0493
Canary Islands 2.0241 1.9833 2.4037 2.4894 2.6515 2.1615 2.3490 2.4748 2.2268 2.2550 2.3538
Cantabria 1.9174 2.1327 2.3056 2.5037 2.4893 2.4614 2.3380 2.4170 2.1754 2.1654 2.7188
Castille and León 1.8667 1.7465 2.0436 2.3157 2.2219 2.4391 2.4823 2.4930 2.4975 2.4192 2.5238
Castille-La Mancha 1.8433 1.9521 2.0107 2.2802 2.4968 2.6032 2.6478 2.3032 2.3598 2.3003 2.3011
Catalonia 2.1828 2.2993 2.4160 2.4631 2.6330 2.6732 2.8116 2.6039 2.5299 2.5117 2.6325
Valencian Com. 1.9657 2.1760 2.4499 2.6107 2.6040 2.6622 2.4687 2.3462 2.4037 2.4689
Extremadura 1.6789 1.7912 2.1960 2.0542 2.0991 2.2522 2.2173 2.2255 2.1326 2.0468 2.1427
Galicia 1.8991 2.1603 2.2069 2.1473 2.2001 2.1862 2.1869 2.2582 2.3311 2.0899 2.1074
Madrid 2.4282 2.4182 2.6482 2.8146 2.6556 2.7205 2.7669 2.6922 2.4993 2.6615
Murcia 2.0068 2.1037 2.2622 2.3845 2.4389 2.4884 2.4501 2.3424 2.4736 2.5154 2.6080
Navarre 2.2321 2.2891 2.4422 2.5102 2.5951 2.7281 2.5781 2.784 2.9235
Basque Country 2.4479 2.4196 2.5863 2.8365 2.6678 2.7660 2.7558 2.6172 2.5775
La Rioja 2.0955 1.9187 2.4509 2.5407 2.6764 2.4338 2.4911 2.7265 2.6838 2.6834 2.3953
Ceuta and Melilla/Ceuta 2.1532 2.1848 2.02972 2.0754 2.2563 2.3636 2.6764 2.3389 1.9091 2.2499 2.4067
Melilla n.a. n.a. n.a. n.a. n.a. 2.0342 1.8815 1.9707 2.5381 2.8250 2.6531
Table 4
Annual difference on expenditure inequality. Period 2006-2016
AA. CC. 2007-2006 2008-2007 2009-2008 2010-2009 2011-2010 2012-2011 2013-2012 2014-2013 2015-2014 2016-2015 No. / % A
Andalusia 0.270 0.107 0.191 -0.091 -0.066 0.025 0.136 0.058 6/75.0
Aragon 0.022 0.552 -0.064 0.147 -0.024 -0.114 0.177 -0.130 -0.113 0.071 5/50.0
Asturias -0.020 0.362 -0.058 0.191 0.124 -0.057 0.112 -0.067 -0.112 0.253 5/50.0
Balearic Islands -0.143 0.139 0.228 -0.116 0.180 0.079 0.176 -0.213 -0.116 0.296 6/60.0
Canary Islands -0.041 0.420 0.086 0.162 -0.490 0.188 0.126 -0.248 0.028 0.099 7/70.0
Cantabria 0.215 0.173 0.198 -0.014 -0.028 -0.123 0.079 -0.242 -0.010 0.553 5/50.0
Castille and León -0.120 0.297 0.272 -0.094 0.217 0.043 0.011 0.004 -0.078 0.105 7/70.0
Castille-La Mancha 0.109 0.059 0.269 0.217 0.106 0.045 -0.345 0.057 -0.060 0.001 8/80.0
Catalonia 0.117 0.117 0.047 0.170 0.040 0.138 -0.208 -0.074 -0.018 0.121 7/70.0
Valencian Com. 0.210 0.274 0.161 -0.007 0.058 -0.194 0.058 0.065 6/75.0
Extremadura 0.112 0.405 -0.142 0.045 0.153 -0.035 0.008 -0.093 -0.086 0.096 6/60.0
Galicia 0.261 0.047 -0.060 0.053 -0.014 0.001 0.071 0.073 -0.241 0.017 7/70.0
Madrid -0.010 0.230 0.166 -0.159 0.065 0.046 -0.075 -0.193 0.162 5/55.6
Murcia 0.097 0.159 0.122 0.054 0.050 -0.038 -0.108 0.131 0.042 0.093 8/80.0
Navarre 0.057 0.153 0.068 0.085 0.133 -0.150 0.206 6/85.7
Basque Country -0.028 0.167 0.250 0.098 -0.010 -0.139 -0.040 3/42.9
La Rioja -0.177 0.532 0.090 0.136 -0.243 0.057 0.235 -0.043 0.000 -0.288 5/50.0
Ceuta and Melilla/Ceuta 0.032 -0.155 0.046 0.181 0.107 0.313 -0.337 -0.430 0.341 0.157 7/70.0
Melilla n.a. n.a. n.a. n.a. n.a. -0.153 0.089 0.567 0.287 -0.172 3/60.0
is negatively correlated with the index of Gini, we are going to study how it progresses through the period studied to find the evolution on inequality. In table 3, we show the a estimates. As we are analysing expenditure and not income, we are expecting to find that inequality reduces in economic crises, but should increase in expansive periods.
Observing table 4 we find that, in general, the parameter a increases. That is, the levels of inequality decrease, especially for the case of Andalusia, Castille-La Mancha, Murcia and Navarra. In all AA. CC., the inequality decreases in half of the period studied at least, except for the Basque Country where there is more evidence of a decrease in a, i.e. increase in inequality. The effect of a growth is more regular among AA. CC. for the beginning of the crisis, so in 2008 and 2009, but also in the last year 2016. However, in the period associated with the economic recovery (2014 and 2015) we can find more evidence of intensification of inequality in terms of expenditure of Spanish
families. The evidence seems to show that at the beginning of the economic shock, the negative impact on expenditures was quite uniform. However, as the policy makers adopted measures to recover growth, the impact of these measures has not had an even effect on different regions, showed by the increase in inequality.
3.2 Average Expenditure Evolution for the Period 2006-2016
In this subsection we carry out a longitudinal, as well as a transversal study of the evolution of the average household expenditure. The first aims to study the evolution of average expenditure of households in the AA. CC. throughout the time period considered. To this end, the data have been deflated to 2016 constant euros before obtaining the differences in average expenditures by region. It can be seen in Table 5 that, in the periods where household expenditure declined, cells are marked in grey and otherwise in white.
Table 5
Annual difference on average expenditure (in 2016 constant euros). Period 2006-2016
AA.CC. 20072006 20082007 20092008 20102009 20112010 20122011 20132012 20142013 20152014 20162015 % A
Andalusia 478.41 -879.22 -2021.45 -1018.89 -1868.12 -2246.56 -1548.61 170.64 175.95 1520.25 60
Aragon -325.38 -1142.27 -1171.72 -815.65 -827.45 -890.68 -723.32 -430.05 653.65 1089.04 80
Asturias -196.20 91.82 -907.99 223.70 -3890.05 -2602.92 -505.05 389.35 1139.78 0.32 50
Balearic Islands 1374.67 -3326.75 -3591.84 -3.52 -1722.49 -1198.04 -888.28 1217.98 597.85 2229.52 60
Canary Islands 628.93 -2520.96 -2066.18 -1558.22 -221.38 -2665.17 -771.83 1124.57 139.80 720.38 60
Cantabria 1811.22 -1862.67 -456.52 -1692.17 -1819.40 -1779.28 -2032.94 -14.27 1180.53 -185.84 80
Castille and León 747.96 -932.89 -2587.55 -907.66 -914.33 -1677.11 -919.60 346.97 1023.20 253.59 60
Castille-La Mancha 1122.35 -1860.70 -1042.38 -209.54 -1396.41 -2440.52 -166.05 175.50 777.68 70.94 60
Catalonia -560.77 -1741.95 -1079.94 -1574.98 -1201.35 -2235.22 -630.39 556.86 509.76 537.23 70
Valencian Com. 581.23 -2781.73 -1557.57 -1527.51 -1431.64 -656.95 -1424.80 -156.53 584.44 1071.02 70
Extremadura 383.57 -1698.38 -847.30 -453.76 -1380.94 -2550.23 -174.94 62.05 -124.43 412.27 70
Galicia 56.01 -614.17 -1257.24 -1263.41 -733.21 -1798.01 -1347.32 -269.99 613.02 339.29 70
Madrid 689.96 -1382.53 -2059.87 -454.60 -685.08 -1793.87 -2259.40 -613.12 290.27 1415.36 70
Murcia 1134.71 -3182.99 -3153.97 -715.98 -982.61 -426.30 -1451.40 -101.46 496.36 1764.93 70
Navarre -227.87 -327.86 -1635.30 -770.45 -2271.42 -1849.75 -1239.86 884.22 352.64 906.92 70
Basque Country -471.06 -1748.85 -1254.31 421.66 -1538.28 -927.06 -745.47 -717.11 1230.08 590.02 70
La Rioja 1552.98 -1641.12 -111.73 -1064.35 -597.03 -2972.09 -213.05 51.61 524.14 626.76 60
Ceuta and Melilla/ Ceuta 1623.27 -1585.59 -135.60 -1425.75 873.65 -1261.60 -5488.83 4190.35 -3153.30 3683.17 60
Melilla n.a. n.a. n.a. n.a. n.a. -4989.61 1342.39 -1905.07 3581.34 675.48 40
786 COm/IA-nbHO-flEMOrPAQMHECKMM nOTEH^Afl PErMOHA^bHORO PA3BMTMÍI
It can be concluded that, in general, the annual rate of variation has been positive in the pre-crisis period from 2006 to 2007 and the post-crisis period from 2013 to 2016. The AA. CC. where expenditure tends to decrease in at least seven over ten periods (at least 70 % of the cases) are Aragon, Cantabria, Catalonia, Valencian Community, Extremadura, Galicia, Madrid, Murcia, Navarre and the Basque Country. The "reversed J" shape of the evolution of average household expenditure (except for Melilla) can be observed in Figure 1. Therefore, when the
Ranking of the AA. CC. by its average h
economic recovery started, from 2013 onwards, average household expenditure also began to grow in many AA. CC., following a parabolic form. Despite the recovery, the average expenditure in levels is still low and far from the levels achieved by the AA. CC. at the beginning of the period studied (in the pre-crisis period). In any case, if the trend continues as it has been up to now, it seems that, unfortunately, it will take a long time to reach the standards of living that households enjoyed at the beginning of the period.
Table 6
usehold expenditure. Period 2006-2016
2006 2007 2008 2009 2010 2011
Madrid Madrid Madrid Madrid Madrid Madrid
Navarre Balearic I. Navarre Navarre Navarre Ceuta
Catalonia Navarre Catalonia Catalonia Basque C. Melilla
Balearic I. Catalonia Balearic I. Ceu.-Mel. Catalonia Navarre
Basque C. Murcia Ceu.-Mel. Cantabria Ceu.-Mel. Basque C.
Murcia Cantabria Cantabria Basque C. Asturias Catalonia
Ceu.-Mel. Ceu.-Mel. Basque C. Asturias Cantabria Cantabria
Andalusia Basque C. Andalusia Andalusia Balearic I. La Rioja
Val. Com. Andalusia Murcia La Rioja Andalusia Galicia
Cantabria Val. Com. Asturias Galicia La Rioja Balearic I.
Canary I. Canary I. Galicia Balearic I. Galicia Aragon
Asturias Galicia C. León Aragon Aragon Andalusia
Galicia Asturias Val.Com. Murcia Murcia Asturias
Aragon La Rioja Aragon Val. Com. C.Mancha Murcia
C.León C.León Canary I. Canary I. Val.Com. C. Mancha
La Rioja Aragon La Rioja C.León C. León C.León
C. Mancha C. Mancha C. Mancha C. Mancha Extremad. Val.Com.
Extremad. Extremad. Extremad. Extremad. Canary I. Canary I.
Extremad.
The Continion of Table 6
2012 2013 2014 2015 2016
Madrid Madrid Ceuta Basque C. Madrid
Ceuta Basque C. Navarre Melilla Navarre
Navarre Navarre Madrid Navarre Melilla
Basque C. Melilla Catalonia Madrid Balearic I.
Catalonia Catalonia Basque C. Catalonia Basque C.
Cantabria Aragon Balearic I. Balearic I. Ceuta
Murcia Balearic I. Melilla Cantabria Catalonia
Melilla Murcia Aragon Aragon Murcia
Balearic I. Cantabria Murcia Ceuta Aragon
Aragon La Rioja Cantabria Murcia La Rioja
Galicia Ceuta La Rioja Asturias Cantabria
La Rioja Galicia Asturias La Rioja Asturias
Val. Com. Asturias Galicia Galicia Galicia
Andalusia Val. Com. C.León C.León Andalusia
Asturias C. León Andalusia C. Mancha Val.Com.
C.León C. Mancha C. Mancha Val.Com. C.León
C. Mancha Andalusia Val.Com. Andalusia C.Mancha
Canary I. Extremad Canary I. Canary I. Canary I.
Extremad Canary I. Extremad. Extremad. Extremad.
2006 2007 « 2008 2009 «2010 «2011 «2012 «2013 «2014 «2015 2016
Fig. 1. Average household expen
Regarding the transversal analysis, this is useful in exploring which Autonomous Communities are among the best placed in terms of average expenditure and which are in a worse position, that is, the "richest" and the "poorest". Moreover, it is interesting to check the impact of the Great Recession on their relative positions. Thus, a ranking of the Autonomous Communities has been established based on the average expenses (in this case we use no deflated data, as it is a cross-sectional analysis). In table 6 we can see the AA. CC. ordered from highest to lowest average expenditure for each of the 11 years, and the results show two well-differentiated clusters that are maintained throughout the whole period. Among the best situated we find Madrid, Navarra and Catalonia, that is, in more than half of the period they are situated between the four best positioned, and for the whole period they are never situated in the lower half of the ranking. Among the worst positioned, we meet the Canary Islands, Castille and León, Castille-La Mancha and Extremadura (opposite to the best situated, these AA. CC. can be found in at least 6 of the ten years between the four last positions, and they are not situated in the first half of the ranking during the period). In this analysis we cannot have a clear picture of the effects of economic crises, as some positions such as Madrid on the top or Extremadura on the bottom, are quite stable. However, the Canary Islands seems to lose
ture evolution. Period 2006-2016
positions through the period, worsening its performance. A more extended analysis that considers particular economic policies conducted by the AA. CC. should be done to obtain clearer implications of these results.
3.3. Evolution of Variability at the Population Level. Period 2006-2016
To close the analysis, a study of the representativeness of average expenditure at the population level is carried out. For this purpose, the Pearson variation coefficient is used (estimated by applying the invariance property of the estimators of the model parameters). Thus, Table 9 contains the value of said coefficient for the years of the period of time considered. In order to quantify this variation, table 7 reflects the absolute variation rates between each pair of Pearson coefficients of consecutive years, where negative rates are emphasized in grey. From this analysis, we infer that in most periods the variation rates have been negative, implying a decrease in the population variation coefficient. In other words, for each AA. CC. except for the Basque Country, in at least half of the cases the average expense grew in representativeness.
4. Conclusions
Based on the proposed objectives and regarding the evolution of inequality, it can be concluded
The End of Table 7
Table 7
Variation of the estimated population Pearson coefficient. Period 2006-2016
AA.CC. 2007-2006 2008-2007 2009-2008 2010-2009 2011-2010 2012-2011
Andalusia -0.046 -0.016 -0.026 0.012
Aragon -0.004 -0.078 0.008 -0.017 0.003 0.013
Asturias 0.004 -0.064 0.009 -0.029 -0.017 0.008
Balearic Islands 0.018 -0.018 -0.027 0.013 -0.020 -0.008
Canary Islands 0.007 -0.06S -0.011 -0.020 0.066 -0.028
Cantabria -0.037 -0.026 -0.027 0.002 0.004 0.017
Castille and León 0.02S -0.0S7 -0.042 0.014 -0.031 -0.006
Castille-La Mancha -0.021 -0.011 -0.043 -0.029 -0.013 -0.00S
Catalonia -0.017 -0.016 -0.006 -0.021 -0.00S -0.01S
Valencian Com. -0.03S -0.039 -0.020 0.001 -0.007 0.024
Extremadura -0.02S -0.072 0.023 -0.008 -0.024 0.00S
Galicia -0.04S -0.007 0.009 -0.008 0.002 0.000
Madrid 0.001 -0.029 -0.018 0.018 -0.007 -0.00S
Murcia -0.016 -0.02S -0.017 -0.007 -0.006 0.00S
Navarre -0.008 -0.021 -0.009 -0.010 -0.01S 0.017
Basque Country 0.004 -0.021 -0.028
La Rioja 0.031 -0.083 -0.011 -0.016 0.030 -0.007
Ceuta and Melilla/Ceuta -0.00S 0.02S -0.008 -0.028 -0.01S -0.039
Melilla n.a. n.a. n.a. n.a. n.a. 0.028
AA.CC. 2013-2012 2014-2013 2015-2014 2016-2015 % А
Andalusia 0.009 -0.003 -0.017 -0.007 7S.0
Aragon -0.021 0.01S 0.014 -0.009 S0.0
Asturias -0.01S 0.009 0.01S -0.033 S0.0
Balearic Islands -0.017 0.021 0.012 -0.030 60.0
Canary Islands -0.017 0.034 -0.004 -0.014 70.0
Cantabria -0.011 0.03S 0.002 -0.073 S0.0
Castille and León -0.001 -0.001 0.010 -0.013 70.0
Castille-La Mancha 0.044 -0.008 0.008 0.000 80.0
Catalonia 0.023 0.009 0.002 -0.01S 70.0
Valencian Com. -0.008 -0.009 7S.0
Extremadura -0.001 0.014 0.014 -0.016 60.0
Galicia -0.011 -0.010 0.037 -0.003 70.0
Madrid 0.008 0.023 -0.020 SS.6
Murcia 0.01S -0.018 -0.00S -0.011 80.0
Navarre -0.023 8S.7
Basque Country -0.011 0.001 0.016 0.00S 42.9
La Rioja -0.028 0.00S 0.000 0.036 S0.0
Ceuta and Melilla/Ceuta 0.043 0.070 -0.0S7 -0.022 70.0
Melilla -0.017 -0.08S -0.033 0.019 60.0
that the inequality of household expenditure has decreased in most of the regions during the Great Recession, as a generalised tendency towards an increase in equality has been detected (except for the Basque Country). Additionally, this tendency has been more intense in the worst years of the economic crisis: 2008-2009, 2011, as well as in the last period, with 2016 changing this trend in the recovery period 2013-2015. This trend is probably a consequence of the loss of purchasing power of
the population caused by high unemployment, and the policy of wage devaluation carried out by the Government as a measure to recover price competitiveness during the Great Recession. These results are obtained by fitting household expenditures to the biparametric Gamma model for the period 2006-2016 and using the parameter a as an estimator of inequality.
By using a descriptive longitudinal analysis, a similar decreasing trend was found in av-
erage expenditure at the beginning of the crisis, which coincides with the second year of our study. This is the case in most Autonomous Communities, especially Aragon, Cantabria, Catalonia, Valencian Community, Extremadura, Galicia, Madrid, Murcia, Navarre and the Basque Country. However, as the recovery period begins from 2013 onwards, the trend is reversed, although we are still far from the levels of expenditure that we had at the end of the expansive cycle. Data show a convergent trend produced at the bad cycle period, where heterogeneity reduction is due to a quite general lowering in households' expenditure. As for the "intergroup" changes, two differentiated clusters are observed throughout the period: Madrid, Navarre and Catalonia as the best positioned Autonomous Communities, and Extremadura, the Canary Islands, Castille and Leon and Castille-La Mancha as the worst positioned. Despite the apparent convergence found in the previous analyses, looking at the dichotomy between the north and centre on one side, and periphery on the other, heterogeneities seem to be persistent to cyclical income variations. Consequently, further research should be conducted to connect economic policy decisions and
structural characteristics with the final relative position of the different regions.
Finally, to analyse the strength of the conclusion obtained, the representativeness of the average expenditure of the population is studied by an inferential analysis through the Pearson coefficient of variation value. It should be pointed out that dispersion decreased in most of the AA. CC., especially in Andalusia, Canary Islands, Castille and León, Castille-La Mancha, Catalonia, Galicia, Murcia, Navarre and Ceuta and Melilla/Ceuta. Therefore, the lower variability of expenditure means that the average expenditure better represents the expenditure of all households for these regions, which, together with the fact that said average expenditure tended to decrease, allows us to infer that for these Autonomous Communities, most households have tended to spend less. On the other hand, for the Autonomous Communities which have a percentage of cases with greater variability (less representativeness of the average), such as the Basque Country, the conclusions of the study at the population level are weaker. Further extension will require a deeper analysis of the political-economic causality between the evolution and the results of household expenditure.
References
1. Singh, S. K. & Maddala G. S. (1976). A Function for Size Distribution of Incomes. Econometrica, 44(5), 963-970. DOI: 10.2307/1911538.
2. Singh, S. K. and Maddala G. S. (1978). A Function for Size Distribution of Incomes: Reply. Econometrica, 46(2), 461. DOI: 10.2307/1913915.
3. Dagum, C. (1977). A New Model of Personal Income-Distribution-Specification and Estimation, Economie Appliquée, 30(3), 413-436.
4. Dagum, C. (1980). Sistemas Generadores de Distribución del Ingreso y la Ley de Pareto. El Trimestre Económico, 47, 188(4), 877-917.
5. Baró, J. (1982). Distribución personal de la renta. Medidas y leyes de desigualdad. Doctoral dissertation, Universidad Central de Barcelona, 515.
6. Esteban, J., Bachero, J. M., Rojo, C. & Ruiz, F. (1994). La distribución de la renta en Castilla y León. 4° Congreso de Economía Regional de Castilla y León. Universidad de Burgos. 24-26.11.1994, 1493-1505.
7. Callealta Barroso, F. J., Casas J. M., Mederiz A., Núñez J. & Pena Trapero J. B. (Dir.) (1996). Distribución Personal de la Renta en España: correción y modelización de la información básica: desigualdad y análisis. Madrid: Ed. Pirámide, 981.
8. Herrerías R., Palacios, F. & Callejón, J. (1996). Distribución de la Renta en la Comunidad de Castilla y León: dos Métodos de Estimación. In Actas del 5° Congreso de Economía Regional de Castilla y León. Universidad de Ávila, 2, 978-990.
9. Klein, N., Kneib, T., Lang, S., & Sohn, A. (2015). Bayesian structured additive distributional regression with an application to regional income inequality in Germany. The Annals of Applied Statistics, 9(2), 1024-1052.
10. Nartikoev, A. & Peresetsky, A. (2019). "Modeling the dynamics of income distribution in Russia," Applied Econometrics 54, 105-125.
11. Dagum, C. (1980). The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Appliquée, 33, 327-367.
12. Rojo Olivas, C. (1993). Análisis de la Distribución de la Renta en España. Doctoral dissertation, Universitat de València, 254.
13. Lafuente Lechuga, M. (1995). Dos Familias de Medidas de Desigualdad y la Distribución Gamma. Estadística Española, 37(139), 239-260.
14. Martín-Guzmán, P., Toledo, M. I., Bellido, N., López Ortega, J., & Jano, D. (1996). Encuesta de Presupuestos Familiares. Desigualdad y pobreza en España. Estudio basado en las Encuestas de Presupuestos Familiares de 1973-74, 1980-81 y 1990-91. Instituto Nacional de Estadística y Universidad Autónoma de Madrid, 381.
15. López Rodríguez, M. I. (1997). La Desigualdad en España desde la Perspectiva de los Ingresos y los Gastos. Evolución en el Periodo 1980-1990. Doctoral dissertation, Universitat de Valencia, 473.
16. García Pérez, C., Callealta Barroso, F. J. & Núñez Velázquez, J. J. (2006). La Interpretación de los parámetros de los Modelos Probabilísticos para la Distribución Personal de la Renta. Una Aplicación al Caso Español. Estadística Española, 48(163), 433-462.
17. Díez-Minguela A., Martinez-Galarraga J., Tirado-Fabregat D. A. (2018) What Explains the Long-term Evolution of Regional Income Inequality in Spain? In Regional Inequality in Spain. Palgrave Studies in Economic History. Palgrave Macmillan, Cham, 149-179.
18. de la Fuente, A. (2019). La dinámica territorial de la renta en España, 1955-2016: una primera aproximación, Studies on the Spanish Economy eee2019-14, FEDEA, 1-12.
19. Attanasio, O. P., & Pistaferri, L. (2016). Consumption inequality. Journal of Economic Perspectives, 30(2), 3-28.
20. Aguiar, M., & Bils, M. (2015). Has consumption inequality mirrored income inequality? American Economic Review, 105(9), 2725-56.
21. Krueger, D. & Perri F. (2006), Does Income Inequality Lead to Consumption Inequality? Evidence and Theory, Review of Economic Studies, 73(1), 163-193.
22. Brewer, M. & O'Dea, C. (2012), Measuring living standards with income and consumption: evidence from the UK, ISER working paper series, 2012-05.
23. Salem, A. B. & Mount, T. D. (1974). A Convenient Descriptive Model of Income Distribution: the Gamma Density. Econometrica, 42(6), 1115-1127. DOI: 10.2307/1914221.
24. Dagum, C. (1991). Renta y Distribución de la Riqueza, Desigualdad y Pobreza: Teoría, Modelos y Aplicaciones. Cuaderno 22. Seminario Internacional de Estadística en Euskadi. Guipúzcoa. Ed: Instituto Vasco de Estadística, Eustat, 75.
25. Lafuente Lechuga, M. (1998). La Distribución Gamma como Modelo para Analizar la Distribución de Renta: una Aplicación a la EPF 1990-91. Revista de Estudios Regionales, 50, 161-186.
26. López Rodríguez, M. I. (2016). Modelización de los gastos familiares en el periodo 2006-2013. XXX Congreso Internacional de Economía Aplicada. Universitat de Valencia. In Anales de Economía Aplicada. ASEPELT. Murgui, S., Pavía, J. M., Casino, A. and García-Cárceles, B. (Cond.), 75-88. ISSN: 2174-3088.
27. López Rodríguez, M. I. (2016). Mapa de la economía familiar valenciana en el periodo 2006-2014. I Workshop d'Economia Valenciana. Universitat Politécnica de Valencia, 1-19, ISBN: 978-84-9048-581-1, DOI: http://dx.doi. org/10.4995/EC0NVAL16.2016.451.
28. Encuesta de Presupuestos Familiares de 2006-2016. Instituto Nacional de Estadística (INE) Retrieved May 2018 from https://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736176806&menu=resulta-dos&idp=1254735976608.
29. Kakwani, N. C. (1980). Income Inequality and Poverty. Methods of Estimation and Policy Applications. A World Bank Research Publication. New York: Oxford University Press, 416.
30. Esteban, J., López, M. I. & Ruiz, F. (2000). Una Revisión de los Sistemas Generadores y Modelos de Probabilidad Descriptivos de la Distribución de la Renta. Estudios de Economía Aplicada, 14(1), 47-72.
Authors
Maria Isabel López-Rodríguez — Doctor of Economics, Professor, Department of Applied Economics, Faculty of Economics, University of Valencia; Scopus Author ID: 57189250351; https://orcid.org/0000-0002-1739-0573 (Campus dels Tarongers, Av. Dels Tarongers, s/n, 46022 — Valencia, Spain, e-mail: Maria.I.Lopez@uv.es).
Maja Barac — Doctor of Economics, Professor, Department of Applied Economics, Faculty of Economics, University of Valencia; Scopus Author ID: 57159424700; https://orcid.org/0000-0002-1984-3644 (Campus dels Tarongers, Av. Dels Tarongers, s/n, 46022 — Valencia, Spain, e-mail: Maja.Barac@uv.es).
