iẳ1 > > > K > P > l > c¼0 : f yi ị log yi iẳ1 The similar behavior of polarization (ER and FW) and inequality measures was also reported in Fedorov (2002) for Russian regions He proposed to modify the KZ index and to define the index as the ratio of between-group inequality to total inequality for the following two reasons: (i) if within-group inequality is small, then www.ebook3000.com 62 On Polarization in Russia even small changes in within-group inequality from one period to another will lead to large swings in the results; (ii) the modified measure has an intuitive interpretation as the share of between-group inequality in the total one 5.1.3 Decomposition of Polarization Indices Araar (2008) proposed to decompose the DER index (5.1.6) by population groups as follows: Pẳ X g /g1 ỵ a w1a g Rg Pg ~ ỵP R Rg ẳ where ag yịpg yịfg yị1 ỵ a dy R /g ag yịfg yị1 ỵ a dy 5:1:8ị ~ denotes the DER index when the within-group polarization or inequality is P ignored, /g is the population share of group g, wg is the income share of group g, fg is the density function for group g, ag ðyÞ is the alienation for the individual at the level of its group g and pg ðyÞ is the local proportion of individuals belonging to group g and having income y If the groups of incomes not overlap, Rg = When α = 0, then Rg = and this decomposition is similar to that of the Gini index Araar (2008) also proposed to decompose the DER index by income sources: P¼ l1Àa Z f yị 1ỵa ayịdy ẳ X R wk k f yị1 ỵ a ak yịdy X ẳ wk CPk wak laÀ1 k ð5:1:9Þ where CPk is the pseudo-polarization index of income source k 5.2 5.2.1 Empirical Results Measuring Polarization The results of the DER index, based on (5.1.6) with α = 0.5 are given in Table 5.1 and Fig 5.1 To make the comparison easier, Duclos, Esteban and Ray (2004) suggested dividing all indices by two, so that if α = 0, the DER index is equal to the Gini coefficient Table 5.2 summarizes the main changes in the DER-index The DER increased between 1992 and 1996 and then decreased Over the whole period, the DER changed significantly only when working with individual incomes Table 5.3 gives the components of the DER index (see Eq 5.1.6b), namely the average alienation, average identification and the normalized covariance between 5.2 Empirical Results 63 Table 5.1 The DER-index (α = 0.5) Year Individuals CI 95% Households CI 95% Equivalent incomes [CI 95%] 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 0.317 0.320 0.367 0.393 0.505 0.456 0.406 0.399 0.384 0.379 0.352 0.324 0.339 0.309 0.305 0.271 0.284 0.291 0.289 0.311 0.294 0.294 0.293 0.285 0.278 0.280 0.278 0.292 0.273 0.282 0.251 0.261 0.271 0.272 0.298 0.272 0.266 0.256 0.251 0.247 0.250 0.244 0.255 0.241 0.244 [0.311 [0.314 [0.358 [0.384 [0.493 [0.445 [0.397 [0.384 [0.375 [0.371 [0.345 [0.319 [0.332 [0.305 [0.300 0.322] 0.326] 0.376] 0.402] 0.517] 0.468] 0.416] 0.414] 0.393] 0.387] 0.359] 0.330] 0.345] 0.314] 0.310] [0.265 [0.274 [0.279 [0.278 [0.302 [0.283 [0.284 [0.281 [0.273 [0.271 [0.266 [0.269 [0.276 [0.267 [0.270 0.277] 0.295] 0.302] 0.299] 0.320] 0.304] 0.304] 0.305] 0.298] 0.285] 0.294] 0.288] 0.308] 0.279] 0.294] [0.245 [0.251 [0.261 [0.260 [0.289 [0.263 [0.254 [0.247 [0.242 [0.241 [0.240 [0.234 [0.243 [0.235 [0.232 0.257] 0.271] 0.282] 0.284] 0.308] 0.282] 0.278] 0.265] 0.261] 0.253] 0.261] 0.253] 0.268] 0.248] 0.256] 0.60 0.55 DER-index 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 year individual incomes households equivalent incomes Fig 5.1 DER-index, a = 0.5 them The alienation component is equal to the Gini index and its plot is given in Fig 2.5 (Chap 2); the identification component is illustrated in Fig 5.2 The results show that the increase in the DER for individual incomes during the 1992–1996 period was due to the changes in both the alienation and identification components In the case of household and equivalent incomes, however, the identification component decreased during this period www.ebook3000.com 64 On Polarization in Russia Table 5.2 The main significant changes in the DER-index (α = 0.5) over time Type of incomes Period Difference P > |t| CI 95% Individual incomes 1992/1996 1996/2005 2005/2006 2006/2007 1992/2008 1992/1996 1996/2005 1992/1996 1996/2005 0.188 –0.181 0.014 –0.030 –0.012 0.040 –0.033 0.047 –0.054 0.000 0.000 0.001 0.000 0.002 0.000 0.000 0.000 0.000 [0.175 0.202] [–0.194 –0.167] [0.006 0.023] [–0.038 –0.022] [–0.019 –0.005] [0.029 0.050] [–0.046 –0.019] [0.036 0.058] [–0.068 –0.041] Household incomes Equivalent incomes Table 5.3 The components of the DER-index (α = 0.5) Equivalent incomes Alienation Identification Correlation Individual incomes Alienation Identification Correlation 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 0.415 0.446 0.481 0.492 0.540 0.491 0.468 0.445 0.435 0.426 0.423 0.409 0.432 0.399 0.404 –0.207 –0.223 –0.239 –0.232 –0.204 –0.210 –0.231 –0.221 –0.202 –0.187 –0.208 –0.201 –0.215 –0.184 –0.191 0.524 0.539 0.609 0.631 0.706 0.669 0.646 0.647 0.621 0.615 0.582 0.569 0.562 0.543 0.539 –0.182 –0.188 –0.217 –0.225 –0.261 –0.242 –0.246 –0.252 –0.222 –0.217 –0.190 –0.179 –0.176 –0.165 –0.171 identification Year 0.762 0.753 0.742 0.722 0.694 0.702 0.739 0.738 0.723 0.713 0.747 0.746 0.753 0.743 0.746 0.739 0.731 0.769 0.802 0.968 0.900 0.833 0.824 0.795 0.787 0.746 0.694 0.732 0.682 0.683 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 year individual incomes total household income Fig 5.2 Identification component of the DER-index equivalent incomes 5.2 Empirical Results 5.2.2 65 Decomposition of Polarization Measures by Income Sources In the previous subsection the DER-index for the different years was computed The purpose of this subsection is to estimate the contribution of different income sources to the changes in this measure Firstly, the DER-index will be broken down using the so-called Shapley decomposition procedure Then, it will be decomposed using the approach proposed by Araar (2008) Since a decomposition by income sources analysis can include only positive incomes, we first compute the DER-index when only positive incomes are taken into account Table 5.4 and Fig 5.3 give these results Table 5.5 summarizes the main (largest) changes for the DER-index for individual (positive) incomes The significant changes over time can be divided into two sub-periods in two ways: an increase between 1992 and 1996 and a decrease between 1996 and 2005 (first decomposition in Tables 5.9 and 5.10) or an increase between 1992 and 2001 and a decrease between 2001 and 2005 (second decomposition) The shares of the various income sources in total income and the values of the Gini for each income source are given in Chap (Tables 4.8 and 4.9) Table 5.6 gives the values of the DER-index for each income source and various years Positive incomes, as expected, are less unequal and polarized The largest differences between the measures for all incomes and for positive ones were found for 1996, when the percentage of zero-incomes was the highest The lowest DER-index was found for transfers Self-employment incomes are more polarized than incomes from salaried work Other sources have the highest degree of polarization Table 5.4 The DER-index for positive incomes (α = 0.5) 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 Individuals [CI 95%] Households [CI 95%] Equivalent incomes [CI 95%] 0.284 0.279 0.301 0.310 0.320 0.316 0.330 0.331 0.316 0.315 0.291 0.275 0.282 0.274 0.279 0.271 0.285 0.292 0.289 0.293 0.289 0.296 0.294 0.286 0.279 0.280 0.279 0.293 0.273 0.283 0.251 0.262 0.272 0.271 0.274 0.262 0.266 0.256 0.251 0.248 0.250 0.244 0.255 0.242 0.244 [0.279 [0.274 [0.293 [0.302 [0.311 [0.306 [0.322 [0.316 [0.308 [0.308 [0.286 [0.270 [0.277 [0.271 [0.274 0.289] 0.284] 0.309] 0.317] 0.329] 0.326] 0.339] 0.346] 0.324] 0.322] 0.297] 0.279] 0.288] 0.278] 0.284] [0.265 [0.275 [0.280 [0.278 [0.283 [0.277 [0.286 [0.282 [0.274 [0.272 [0.266 [0.269 [0.277 [0.267 [0.271 0.277] 0.296] 0.303] 0.300] 0.303] 0.300] 0.306] 0.306] 0.299] 0.286] 0.294] 0.288] 0.308] 0.279] 0.295] www.ebook3000.com [0.245 [0.252 [0.261 [0.258 [0.264 [0.251 [0.253 [0.248 [0.241 [0.241 [0.240 [0.234 [0.243 [0.235 [0.232 0.257] 0.272] 0.282] 0.283] 0.284] 0.272] 0.278] 0.265] 0.261] 0.255] 0.261] 0.253] 0.268] 0.248] 0.256] 66 On Polarization in Russia 0.40 DER-index 0.35 0.30 0.25 0.20 0.15 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008 year individual incomes households equivalent incomes Fig 5.3 DER-index for positive incomes Table 5.5 The main changes over time in polarization for individual positive incomes Polarization index Period Difference P > |t| CI 95% Polarization for total population (DER) 1992/1996 1996/2005 1992/2001 2001/2005 1992/2007 0.036 –0.045 0.047 –0.056 –0.010 0.000 0.000 0.000 0.000 0.004 [0.025 0.046] [–0.055 –0.035] [0.031 0.062] [–0.072 –0.040] [–0.016 –0.003] Table 5.6 The DER-index (α = 0.5) for the various income sources Income source 1992 1996 2001 2005 2007 Salaried work 0.243 [0.240 0.246] 0.280 [0.271 0.289] 0.280 [0.273 0.288] 0.260 [0.255 0.266] 0.247 [0.243 0.251] Self-employment 0.304 [0.262 0.345] 0.310 [0.295 0.325] 0.363 [0.334 0.392] 0.289 [0.272 0.305] 0.293 [0.280 0.305] State transfers 0.204 [0.200 0.208] 0.195 [0.189 0.201] 0.204 [0.198 0.209] 0.213 [0.206 0.219] 0.199 [0.194 0.203] Other incomes 0.379 [0.361 0.397] 0.386 [0.356 0.415] 0.501 [0.396 0.606] 0.456 [0.424 0.487] 0.348 [0.332 0.364] Total population 0.284 [0.279 0.289] 0.320 [0.311 0.329] 0.331 [0.316 0.346] 0.275 [0.270 0.279] 0.274 [0.271 0.278] Note Confidence intervals 95% are in the brackets 5.2 Empirical Results 67 Table 5.7 Decomposition of the DER-index (α = 0.5) by income sources using the Shapley decomposition technique Income source 1992 1996 Salaried work 0.040 0.067 (0.141) (0.209) Self-employment 0.086 0.086 (0.303) (0.269) State transfers 0.039 0.049 (0.137) (0.153) Other incomes 0.119 0.118 (0.419) (0.369) Total 0.284 (1) 0.320 (1) Note The relative contributions to the overall index 2001 2005 0.049 0.056 (0.148) (0.204) 0.100 0.069 (0.302) (0.251) 0.028 0.022 (0.085) (0.080) 0.154 0.128 (0.465) (0.465) 0.331 (1) 0.275 (1) are in the parentheses 2007 0.061 (0.223) 0.076 (0.277) 0.036 (0.131) 0.101 (0.369) 0.274 (1) Tables 5.7 and 5.8 give the contribution of various income sources to the DER index: Table 5.7 gives the results based on the Shapley decomposition procedure (see Appendix A) and Table 5.8 is derived from the approach of Araar (2008) and is based on (5.1.9) When implementing the Shapley decomposition procedure it appears that all income sources have a positive impact on the DER index, but state transfers have the smallest effect Other incomes, like in the case of bipolarization, provide the largest contribution to polarization When using Araar’s method, it appears that state transfers not make the DER greater (in some periods they reduce polarization and in others they not make any contribution) and incomes from salaried work represent the highest relative contribution Note that Shapley procedure is based on marginal changes, while that of Araar on average changes Tables 5.9 and 5.10 give the results of the decomposition of changes in the DER index as a function of changes in the income sources Both the Shapley and Araar approaches show that over the whole period the decrease in the DER was mostly due to a decrease in the absolute contribution of self-employment and other incomes, while the contribution of salaried work increased Table 5.8 Decomposition of the DER-index (α = 0.5) by income sources using the Araar (2008) method Income source Salaried work 1992 1996 0.215 0.176 (0.756) (0.548) Self-employment 0.028 0.078 (0.099) (0.243) State transfers –0.019 0.001 (–0.066) (0.003) Other incomes 0.060 0.066 (0.211) (0.206) Total population 0.284 (1) 0.320 (1) Note The relative contributions to the overall index 2001 2005 0.225 0.225 (0.680) (0.818) 0.056 0.025 (0.169) (0.091) –0.006 0.000 (–0.018) (0.000) 0.056 0.025 (0.169) (0.091) 0.331 (1) 0.275 (1) are in the parentheses www.ebook3000.com 2007 0.239 (0.869) 0.017 (0.062) –0.009 (–0.033) 0.027 (0.098) 0.274 (1) ... in the median income and in the shape of the distribution of income The purpose of Chap (“Bipolarization and the Middle Class in Russia ) is to analyze the determinants of changes in income bipolarization... 1995 and 2000 and then declined sharply between 2000 and 2005, whatever the limits of the range selected Then the size of the middle class grew significantly in 2008 and then again in 2010 While in. .. the two main factors in the creation and sustenance of a middle class are higher education and stable and secure well-paid jobs 1.2 The Russian Middle Class 1.2 The Russian Middle Class Remington