Unravelling Declining Income Inequality in Bolivia: Do Government Transfers Matter?

Transcription

1 Unravelling Declining Income Inequality in Bolivia: Do Government Transfers Matter? Werner L. Hernani-Limarino (Fundación ARU, Bolivia) Ahmed Eid (Fundación ARU, Bolivia) Paper Prepared for the IARIW-IBGE Conference on Income, Wealth and Well-Being in Latin America Rio de Janeiro, Brazil, September -4, 23 Session 3: Taxation and Redistribution I Time: Thursday, September 2, 4:-5:3

2 Unravelling Declining Income Inequality in Bolivia: Do Government Transfers Matter? Final draft Werner L. Hernani-Limarino Ahmed Eid Fundación ARU Abstract This paper documents and explains the remarkable decline in income inequality observed during the last decade in one of the most unequal countries in the world, Bolivia. Regarding the changes in the income distribution, we find significant differences in annual growth rates by quantile during the period, much more related to the growth performance of the last half of the decade, i.e. the 25-2 period. While the first half was a period of relatively no growth for almost all quantiles; the second half was a period of high growth (6 on average), pro-poor growth (with average growth rates close to 8 for the bottom 3 deciles and rates around 6 for the middle quantiles); but not shared by everybody: the top experienced growth rates below and some Pen s giants even negative annual growth rates, as low as -6. These uneven growth patterns have caused a remarkable decline in income inequality during the last half of the decade. During the 25-2 period, the bottom 2 has increased its income share in more than 4 while the top has reduced as much as 4 of its income share, causing the Gini index to drop in percentual points, from a level of.5 to. To analyze the proximate determinants of Bolivia s income inequality decline, we perform a counterfactual á la Barros decomposition of inequality changes by income source. We find that almost all inequality changes are explained by distributional changes in labor earnings. Neither the changes in contributory transfers (pensions) nor the changes and the expansion of non-contributory social transfers (renta dignidad, bono Juancito Pinto, or bono Juana Azurduy, among others), nor the growth of remittances and of property income account for the remarkable decline in income inequality. Furthermore, an extended counterfactual decomposition of labor earnings reveals that changes in the wage distribution are much more important than changes in the utilization of the labor force (i.e. changes in the patters of participation, employment and hours of work). To explore the ultimate determinants of the changes in the wage inequality we also perform a counterfactual á la Machado- Mata decomposition of the distributional changes in wage inequality. We find that reductions in skill premia have made labor market prices the dominant factor in explaining the inequality decline, accounting for over 5 of the changes in inequality. Keywords: Wage inequality, counterfactual density, full distribution accounting. Preprint submitted to IARIW August 27, 23

3 . Introduction Inequality has been a pervasive characteristic of Latin-America in general, and Bolivia in particular. However, after rising through the 99s, income inequality in Latin America has decline steadily in recent years ([5], [6], []). The primary objective of this paper is to unravel the proximate and, if posible, the ultimate determinants of the equalizing changes in urban income inequality, while identifying the role played by government transfers and by other sources of income, specially the labor market. The literature on the declining income inequality in Latin America during the 2s and its determinants is scarce but growing. [4] identify two proximate factors that account for the decline in inequality in Argentina, Brazil, Mexico, and Peru: a decrease in earnings gap between high-skilled and low-skilled workers; and an increase in government transfers to the poor. They atribute the decrease in the earnings gap to the expansion of basic education during the last couple of decades, which has reduced the share of people with only primary and less than primary in the labor force. On the other hand, they atribute the equalizing contribution of government transfers to the implementation or expansions of large-scale conditional cash transfer programs such as Jefes y Jefas de Hogar in Argentina; Bolsa Escola, Bolsa Familia and BPC in Brazil; Progresa/Oportunidades in Mexico, and Juntos in Peru. [9] uses counterfactual analysis to analyze the determinants of the inequality decline in the 2s for 4 Latin-American countries. They find that nearly half of the average decline in inequality was due to changes in labor income. Changes in transfers on average contribute about one-sixth to the decline in inequality for the region, although they were more important in Chile, Colombia, Costa Rica, and the Dominican Republic. Changes in pensions account for one tenth of the overall decline, largely driven by important contributions in the case of Argentina and Brazil. We find that the labor market accounts for the largest share of the decline, and that government transfers played a minor role in this process. Our results indicate that neither intensity of labor nor labor market participation decisions nor shifts in the labor market composition may be associated with the decline, but reductions in the skill premia via labor market prices were the dominant factor behind the evolution of income inequality in urban Bolivia during the 2s. Section 2 analyze the role of the changes in the wage distribution to explain the declining income inequality in Bolivia. Since we are interested not only in proximate determinants but also in ultimate determinants we analyze also the role of the relative supply, technology, international trade and labor market institutions to explain the observed changes in the skill premium. Section 3 analyze other labor market determinants of income inequality changes, i.e. changes in the distribution of hours of work and changes in the distribution of employment opportunities.section 4 analyze the contribution of changes in the household income from government transfers in explaining changes in income inequality. Section 5 analyze the 2

4 contribution of changes in the household income from inter-household transfers and the role of migration and remittances in explaining changes in income inequality. Section 6 summarize the results and concludes analyzing the policy implications of our evidence. 2. Data We use the set of official household surveys for the period harmonized by Fundación ARU. A full description of the harmonization process is beyond the scope of this paper, however it is important to note that the harmonization process address - to the extent that it is possible, three major comparability issues. First, we use raw data, i.e. the data before any cleaning and imputation procedures applied by the National Bureau of Statistics. Second, as usual in most of the harmonization process, we use a uniform definition of the income aggregates and other covariates. Third, and unlike other harmonization process, we adjust the difference in sampling schemes between surveys using post-stratification techniques to adjust the sampling weights. To construct the income dataset, we first drop all households with missing per capita household income. Then we use the Blocked Adaptive Computationally-efficient Outlier Nomination (BACON) algorithm to nominate and drop outliers in the sample. This algorithm looks for unusually large observations in the data using a Mahalanobis distance and then performs a χ 2 test to determine whether an observation is an outlier. We used α =. for said hypothesis test. When constructing the income variable, we are concerned with the identification of various income sources. With this in mind, we constructed household income allows the identification of several sources, and its components are listed on table 2. 2 Per capita household income, (just income from here on) is constructed as total household income divided among household members, with non-members dropped from the sample. Total household income is the sum of household labor earnings, household income from government transfers, household income from inter-household transfers, household rents from properties, household income from contributory social security and household income from other sources. Government transfers were imputed in all years according to the payment scheme observed for that year 3. 2 More information regarding the construction of these variables is available on the web appendix. 3 e.g. Bonosol a non-contributory social security cash tranfer was not paid in 2, but was paid in 2 (so there were two payments in that year), hence we imputed those payments in 2. 3

5 Table : Income components SOURCE Labor Interhousehold transfers Properties Social Security Other DESCRIPTION Net income from primary activity Benefits from primary activity Total in kind income from primary activity Net income from secondary activity Total benefits from secondary activity Total in kind income from secondary activity Family assistance Transfers from within the country Foreign transfers Interests Real state properties and houses rental Agricultural Properties Rental Dividends Equipment rental Retirement Income for war veterans Disability Widowhood Other Rents Compensation for leaving a job Insurance Compensation Other Extraordinary Income Source: Fundación ARU s harmonized series of household surveys To construct the wage dataset, we keep workers with positive salary, whose age is between 8 and 65, and work full time -over 36 hours per week, only for the urban area. Hourly wage was constructed as total labor earnings divided by total hours worked, comprising both primary and secondary activities. In a very small percentage of the sample, earnings information was available while data on total hours worked was not. In these cases we imputed full time working hours. 4

6 3. An overview of income and wage inequality 3.. Income inequality trends in Bolivia during the 2s A full description of the evolution of Bolivian inequality in the 2s is beyond this paper and it may be found in []. However, we ll explain the most notorious features of this process. To grasp the magnitude of the fall of inequality in Bolivia, figure compares the evolution of Brazilian and Bolivian income inequality: Figure : Evolution of Bolivian and Brazilian income inequality, Gini index Brazil: the proud outlier* Bolivia: the unknown outlier Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). *Inequality in focus, April 22, The World Bank. Data comes from SEDLAC (CEDLAS and The World Bank) Inequality in urban Bolivia also declined significantly, as shown in figure 2. The evolution of urban inequality behaved very differently before and after 25, year of the start of the decline and of some notorious political changes in the country. During , inequality measured by the Gini index fluctuated erratically between 54 and Nevertheless, in 25-2, the fall began at a fast pace: The Gini index fell points during those 6 years, and to the best of our knowledge, this decline makes Bolivia the most succesful country in Latin America in reducing inequality in the 2s ([]). 5

7 Figure 2: Evolution of Bolivian urban income inequality, Gini index Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). The distributional changes behind the decline show that 25-2 was a period of high growth for the bottom percentiles of the distribution. The left subfigure from figure 3 shows the Pen s parade for 999, 25 and 2. The parade for 999 and 25 practically lie on the same line, while the 2 parade is clearly shifted upwards for the first 94 percentiles. The income for the top percentiles was reduced, notice how the 2 parade lies to the right of the 25 parade at that part of the distribution. This changes in income are better understood with the right subfigure from figure 3, which shows the yearly growth rate of the average income by percentile. The dashed line on said subfigure shows growth rates during very close to zero for percentiles 2 to 8, and positive growth only for the tails of the income distribution. Average income grew approximately 8 per year for the first 3 percentiles, and then the growth rate falls as one moves towards the top percentiles, and it falls as low as -7 for the giants on the top of the income distribution. Figure 3: Urban sample: Pen s parades and average income by percentile growth rate 29 Bolivianos Quantile Quantile Pen s parades Average income growth rate by quantile Source: Fundación ARU series of harmonized household surveys. Note: Zeros and outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). 6

8 This differences in the growth of average income inevitably lead to gains and losses in income shares. Figure 4 shows the 999, 25 and 2 per capita household income Lorenz curves. The 999 and 25 are very close to each other, while the 2 curve dominates the other two. The right subfigure on figure 4 shows the gains in income share by percentile, which are negative for percentiles to 8 until 25, and positive for the remaining quantiles. However, after 25 they fluctuate around 4 for the first 3 deciles, and the top percentiles had their income share reduced by as much as 4. These changes lead to the nearly 2 reduction of the Gini index that motivates the remainder of the paper. Figure 4: Urban sample: Lorenz curves and gains in income share by percentile L(p) Quantile Quantile Lorenz curves Gains in income share by quantile Source: Fundación ARU series of harmonized household surveys. Note: Zeros and outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). 7

9 3.2. Wage inequality Figure 5 depicts the evolution of wage inequality during the 2s. The 9- log wage differential fluctuated around its 999 level until 25, initial year of the declining trend that went on until 2. As shown on panel A of table 2, the 9- wage ratio fell 48 between 999 and 2, but almost all of the decline happened between 25 and 2, when the ratio fell 46. Until 25, the 9- only fell 2 log points. Figure 5: Evolution of wage inequality, Log wage differential Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Inequality did not vary the same way above or below the median. Between 999 and 25 upper and lower tail inequality displayed opposing trends, as inequality below the median fell.7 log points, while upper tail inequality rose by 9.22 log points. However, after 25 the 9-5 and 5- ratios behaved similarly, but the decline was concentrated almost exclusively in the upper tail: a sharp decline in the 9-5 differential was observed, as it fell almost 37 points, while the 5- ratio showed a more modest fall, of a little over 9 log points. Falling upper tail inequality accounts for nearly 8 of the decline after 25. Figure 6 shows the evolution of wage inequality by gender, and the remaining panels on table 2 show its changes by subperiod, as well. For males, inequality behaved very similarly as full sample inequality: the 9- ratio did not rise or fall significantly between 999 and 25, and a clear falling trend is observed in the latter years of the period of analysis. The 9- ratio fell 37.5 log points between 999 and 2, nevertheless, it rose slightly, 2.9 points, until 25, and fell over 4 points between 25 and 2. Offsetting trends in lower and upper tail inequality were present before and after 25. Upper tail male inequality grew by 7.5 log points while the 5- ratio fell 4.5. After 25, the decline in upper tail inequality is remarkable, as the 9-5 ratio fell 42.8 log points while the 5- ratio rose slightly 2.5 log points. Wage inequality in the female sample shows a different behavior that the male and full sample inequality. Wage inequality among females fell almost twice as much as male wage 8

10 Table 2: Log wage differentials changes by subperiod ( log change) Differential Percent variation Annualized percent change A. Full sample B. Males C. Females Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). inequality, and the reduction in lower tail inequality was higher than the reduction of above the median inequality. There is a declining trend for the 9- ratio throught out the 2s, but still, inequality fell more after 25. The total inequality reduction was of 68.6 log points between 999 and 2, and 53 out of those 68 happened after 25. Upper tail inequality behaves in similar fashion as upper tail male inequality, the rise before 25 is not as pronounced, only 2.6 log points. After 25, upper tail inequality falls 33.9 log points. The 5- ratio falls all throughout the 2s in almost equal proportions before and after 25, so the decline in inequality among females certainly accelerates after 25, but cannot be atributed solely to declining upper tail inequality. 9

11 Figure 6: Evolution of wage inequality by sex, Males 3 Females Log wage differential 2.5 Log wage differential Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). To start analyzing the distributional changes behind the decline in wage inequality, let us turn to figure 7. The leftmost subfigure on figure 7 shows the evolution of the log average wage for our full sample. Log average wage grew throughout the 2s, but at a much faster rate after 25. Between 999 and 25, it grew at a rate of 7 per year, but between 25 and 2, it did so at.68 per year, as seen on table. Splitting the sample by sex leads to the same conclusion: faster growth after 25, however, growth was almost two times faster for females. Male average wage grew at a yeraly rate of.37 between 999 and 25, and at.37 per year after 25. Average wage for females grew at.74 per year until 25, but this rate is 2.32 from 25 on. This translates into a total percent change in average wage for females of 8 from 999 to 2, with over three quarters of that change happening between 25 and 2. Similarly, nearly 8 of the total percent variation in male average wage occurred after 25. Splitting the sample by educational attainment in four categories: incomplete high school, complete high school, college dropouts and college graduates leads to insights necessary to understand the evolution of wage inequality. The rightmost subfigure on figure 7 shows the evolution of the log average wage by educational attainment. The average wage for high school dropouts grew and astounding 33.2 in the 3 years analyzed. It fell 3 in , but grew 36.2 in 25-2, at a yearly rate of 6 in such period. The average wage for high school graduates fell 22.7 until 25, and then it grew 8.8. Workers with college education saw their average income vary at negative rates. For college dropouts it fell 9. in , and an extra 2. after 25. The average wage for college graduates fell almost 33 in After a slight.6 growth between 999 and 25, it fell at a yearly rate of in 25-2, leading to a -34 percent variation in said period.

12 Figure 7: Evolution of log average wages, Full sample 3.5 By gender 3.5 By educational attainment Log mean wage 2.5 Log mean wage Log mean wage Males Females High school dropout College dropout High school graduate College graduate Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Figure 8: Evolution of the th, 5th and 9th percentiles of the log wage distribution by gender, Full sample Males Females Log wage percentile 2.5 Log wage percentile 2.5 Log wage percentile th 5th 9th th 5th 9th th 5th 9th Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.).

13 Table 3: Log average wage changes by subperiod ( log change) Percent variation Annualized percent change Sample Full Males Females High school dropout High school graduate College dropout College graduate Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Analyzing the percentiles of the wage distribution shows that inequality declined mostly because of the steady growth of the 5th and th percentiles, while the 9th percentile fluctuated around its 999 level throught the 2s, as seen on figure 8 and table 4. The 9th percentile of the wage distribution grew 2.8 in only to fall 2.9 in the subsequent subperiod. The total percent variation observed for the 5th wage percentile is 27.5, as it fell 6 between 999 and 25 to rise The largest growth was observed for the th percentile, which grew constantly between 999 and 2, although its growth rate spiked after 25. During , it grew at a yearly rate of.89, but its yearly growth after 25 was 7.2 per year, leading to a total percent variation of 43 between 25 and 2, and of 48 between the start and end years of our analysis. The growth of below the median and median income accounted for the vast majority in the total wage inequality decline in the 2s. These selected percentiles behave in a similar fashion in the male sample. Even though the 9th percentile has a small positive total percent variation between 999 and 2, it grew 8.2 until 25, but afterwards it falls 6.9 during The 5th percentile also fell and rose during the 2s: fell 9.37 in , but grew 36 in The th percentile grew throught the 2s, but after 25, it did so at a yearly rate over 6 times higher that its pre 25 rate. This lead to a total percent variation of 38.8 between 999 and 2, and 33 out those 38, occurred due to changes during In the female sample, changes in inequality occurred to larger differences in growth rates among the selected percentiles. Whereas in the male sample the 9th percentile suffered very little changes during the entire period, in the female sample it grew.5 between 999 and 2. Before 25, it had grown.6, but in the latter period it fell slightly,.. In The 5th and th percentiles grew 4.7 and 79 respectively, with nearly three quarters of said growth happening after 25. 2

14 Table 4: Log wage percentile changes by subperiod ( log change) Percent variation Annualized percent change Percentile A. Full sample B. Males B2. Females C. High school dropouts C2. High school graduates C3. College dropouts C4. College graduates Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Figure 9 shows the evolution of the selected percentiles by educational attainment, which show different trends among them. The trends for all selected percentiles in the incomplete high school category show growing tendencies during 999-2: high school dropouts 9th wage percentile fell 9.6 until 25, but grew 33.5 in The 5th percentile also grew notoriously after 25, 4.7, after a small decline of 2.7 during The th 3

15 percentile achieved a percent variation four times higher after 25 than its pre 25 growth: 5.5 post 25 against 3.7 in the previous subperiod. This was the percentile with the largest percent variation during 999-2, and during Among those workers with complete high school, all three selected percentiles show similar growth patters, a decline in followed by a strong recovery after 25, however, their full period results are different. The th and 5th percentiles had very similar growth percentages after 25, both being very close to 3, but the 5th percentile fell 6 percent points more than the th in , hence the difference in their net full period change. I the case of the 9th percentile, the 25-2 rise was not even half the nearly 3 fall pre 25. The th, 5th and 9th wage percentiles for workers with at least some college education varyied negatively in 999-2, altohugh their fluctuating patterns differ between those two categories. The th and 5th percentile in the college dropout category fell until 25 but recovered afterwards. The 9th percentile rose in , but fell in Regarding college graduates, these percentiles fell throughout the entire period, with the exception of the 9th, with grew 9.9 pre 25, but registered the lowest growth rate of all, -43.5, post 25. As it is evident from figure, which shows how the vast majority of workers in the top wage percentiles have a college degree, changes in the wage distribution that affect negatively workers with such educational attainment, will reduce inequality by moving top wages downwards, thus closing the wage gap between the more educated and the rest of the labor force. When turning to the evolution of the composition of the labor force in figure, there are no abrupt changes in the composition by sex nor the composition by educational attainment. Male participation in full time employment remained constant around 65, but there were some changes in the composition by educational attainment. From 999 to 22, work force composition by educational attainment remained relatively unchanged, but then it started to become more educated. The share of full time workers with incomplete high school fell from 58 in 999 to 43 in 2, high school graduate share grew from 9 to 25, the proportion of workers with some tertiaty education remained constant around 5, but the employment of workers with a college degree rose substatially, from 9 to 6. 4

16 Figure 9: Evolution of the th, 5th and 9th percentiles of the log wage distribution by educational attainment, High school dropout High school graduate College dropout College graduate Log wage percentile 2 Log wage percentile 2 Log wage percentile 2 Log wage percentile th 5th 9th th 5th 9th th 5th 9th th 5th 9th Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Figure : Labor force composition by educational attainment in the wage distribution, 999, 25 and High school dropouts College dropouts High school graduates College graduates High school dropouts College dropouts High school graduates College graduates High school dropouts College dropouts High school graduates College graduates Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.).

17 Figure : Evolution of the labor force composition by gender and educational attainment, Males Females High school dropouts Complete high school Incomplete college Complete college Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old, full time (>36 hours) workers. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). 4. Proximate determinants of income inequality 4.. Methods Let y be a random variable that may be written as the sum of n variables y i, i =,...,n. We seek to construct a counterfactual scenario ỹ j that shows how the inequality of y would have evolved if some components of y, y i, i j would have remained constant and other component y j would have been allowed to vary in time, i.e. y = n i y i ỹ j = y j + n y i i j where y i is some constant value for the i-th component y i. We have a time series of t periods for y and each of its components. Paes de Barros, et. al (26), propose the following decomposition to simulate changes in the inequality of y generated by the i-th component y i :. Calculate the percentiles for the distribution of y for every period t. 2. Estimate the components averages for each percentile c, y c i, for every period t 3. Simulate a distribution for y, y c in which y c i is imputed to every observation in percentile c, for every period t. 6

18 Based on the simulated distribution y c, we construct the following counterfactual scenario:. We estimate each component s intertemporal average, y c i 2. We construct the counterfactual scenario given by: n ỹ j t = y j c + i y c i j (4.) one component is allowed to vary according to its percentile average y j c, but all the others are left constant at their intertemporal average. Our starting point for the analysis of the proximate determinants of the change in inequality is the analysis of the ability of each income component to track changes in per capita household income inequality. Let y h denote the total household income for the h-th household in the sample, and let y h be defined as the sum of household labor earnings y LM h, household government transfers y G h, inter-household transfers y H, household rents from prperties h y P, household income from contributory social security yss and household income from h h other sources y O h. If there are N h members in household h, it s per capita household income, y h, is given by : y h = [ Y LM h + Y GT h + Y HT h N h + Y P h + Y SS h + Y O ] h Equation 4.2 makes explicit the contribution of our six proximate determinants of income inequality: ) the labor market, where individuals offer hours of work to firms for exchange of a wage, or with other households to produce self-employment 2) The generosity and reach of redistributive policy, whether it s in cash or in kind, 3) off-market insurance mechanisms via inter-household transfers, usually through foreign remittances and 4) the coverage of contributory social security. (4.2) Thus, a simulated distribution would be given by ỹ ct = [ Yct LM + Yct GT + Yct HT + Y P N ht ct + Y ct SS ] + Yct O (4.3) where Yct LM denotes the average per capita labor earnings for percentile c in year t. Hence, the counterfactual distribution for per capita household labor earnings would be: ỹct LM = [ Yct LM + Yc GT + Yc HT + Yc P N ht ] + Yc SS + Yc O during for percentile c. We re- where Yc peat this procedure for every income component we are able to identify. represents the average of component Y c (4) Labor earnings is probably the most difficult component to model, as it is more complex in terms of its configuration, which depends on three factors:. Labor market participation decisions 7

19 2. Decisions on the amount of hours to work 3. Hourly wage To analyze these component, notice that per capita labor earnings may be written as y LM h = n ei w i h i (4.5) where n is the number of household members, e i is a dummy variable that is for employed household members, w i is the hourly wage and h i is the amount of total hours worked by the i -th individual in the household. The term e i n may be further decomposed into e i n = n p e i (4.6) n n p with n p n is the labor market participation rate, and e i n p is the employment rate. We perform the Paes de Barros decomposition to equation 4.5 to identify which labor market factor within the household labor earnings component is better able to track observed inequality Results for the Paes de Barros decomposition Figure 2 displays the results for the Paes de Barros decomposition by income source. The top leftmost subfigure from figure 2 shows the result for the labor earnings component, and the subfigure next to it, the results for the government transfers component. It is clear that the government transfers component is unable to reproduce the evolution of the Gini index, whereas the labor earnings component tracks inequality very closely: It moves almost perfectly throughout the pre 25 fluctuations, and follows the post 25 decline very closely. No other component is able to accompany the observed inequality path, and most resemble straight lines below to base inequality -the inequality one would observe if all components were left constant at their intertemporal average values. After establishing that labor earnings is the main household income component, we need to determine whether it s relevance comes from changes in participation decisions, employment opportunities, labor intensity or due to wages. Figure 3 shows the result of the labor earnings component decomposition into these factors, and they are also conclusive as to which labor market factor is more important in explaining the evolution of observed inequality, which is hourly wage. Household members of various ages may decide to participate in the labor market and become employed, however, we only consider workers aged 8-65 in our analysis, as they account for over 87 of total household labor earnings, in over 86 of the households in the sample. Bearing this sample restriction in mind, which evidently prevents a better fit of our simulation, the wage component approximates better the decline from 25 on -particularly from 28 on, and the fluctuations, than any other components. Thus, the relevance of the labor earnings component comes from labor market prices, and not from changes in participation decisions, employment opportunities or workers deciding to change their total hours of work. 8

20 Figure 2: Urban sample: Counterfactual simulations by income source Gini index 9 6 Gini index 9 6 Gini index Observed inequality Base inequality Labor earnings counterfactual Observed inequality Base inequality Government transfers counterfactual Observed inequality Base inequality Other household transfers counterfactual Labor earnings Government transfers Inter-household transfers Gini index 9 6 Gini index Observed inequality Base inequality Rents from properties counterfactual Observed inequality Base inequality Social security counterfactual Rents from properties Social security Source: Fundación ARU series of harmonized household surveys. Note: Zeros and outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.).

21 4.3. Paes de Barros decomposition for labor earnings components Figure 3: Urban sample: Counterfactual simulations by labor earnings source Gini index 9 6 Gini index Observed inequality Base inequality Hourly wage counterfactual Observed inequality Base inequality Total hours worked counterfactual Hourly wage Total hours worked Gini index 9 6 Gini index Observed inequality Base inequality Participation rate counterfactual Observed inequality Base inequality Employment rate counterfactual Participation rate Employment rate Source: Fundación ARU series of harmonized household surveys. Note: Zeros and outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.).

22 5. Ultimate determinants of wage inequality 5.. Methods To analyze what we call ultimate determinants of wage inequality, we use two versions of a widely used decomposition method: The Juhn, Murphy and Pierce decomposition. First we use the original decomposition ([2]), and then we use a quantile version of [2], featured in [7] and [2] The Juhn, Murphy and Pierce (JMP) decomposition In [2], these authors developed a tool that allowed them to describe the components of wage density changes that could be attributed to observable prices, observable quantities and residuals: unobserved prices and quantities. Their method, the full distribution accounting, is described next. Let the wage equation for time t be and let u i t be Y i t = X i t β i t + u i t (5.) u i t = F (θ i t X i t ) (5.2) where F ( X i t ) is the inverse cumulative distribution of wage residuals conditional on X i t, and θ i t is i s percentile rank in the residual distribution. In this framework, changes in inequality over time come from. Changes in the distribution of observable individual characteristics, X 2. Changes in the returns to such characteristics, β 3. Changes in the distribution of residuals, (θ X ) Define β to be the average price of observables over some lapse and F ( X i t ) as the average cumulative distribution of residuals. Then, the difference in inequality between a given period and the period s average may be written as Y i t = X i t β + X i t (β t β) + F (θ i t X i t ) + [F (θ i t X i t ) F (θ i t X i t )] (5.3) and this difference allows the estimation of counterfactual distributions. To calculate the counterfactual distribution of wages holding constant observable prices and residuals at their average, and varying only the distribution of observable characteristics, we estimate Y i t () = X i t β + F (θ i t X i t ) (5) To allow observable prices and quantities to vary over time, we calculate Y i t (2) = X i t β i t + F (θ i t X i t ) (5.5) 2

23 Finally, to let all components vary simultaneously, we have [2] propose the following decomposition: Y i t (3) = X i t β i t + F (θ i t X i t ) = Y i t (5.6). Y i t () Y is the component of the difference in inequality between t and the average period due to changing quantities 2. Y i t (2) (Y i t () Y ) is the marginal contribution of changing prices 3. Y i t (3) (Y i t (2) is the marginal contribution of changing residuals. This is the original decomposition procedure. We use a slightly modidified version to make the results of this procedure comparable to the results of the other procedure: instead of relating changes to period average prices, quantities or unobservables, we use observed and unobserved prices and quantities from 999. This alteration would cause equation 5 to be Y i t () = X i t β F 999 (θ i,999 X i,999 ) (5.7) and similarly for equations 5.5 and 5.6. We refer to this procedure as the OLS version of the JMP decomposition Quantile implementation of the Juhn, Murphy and Pierce decomposition Despite being a widely used tool, the original JMP decomposition is not conceptually appealing because it uses OLS regressions, a model for the conditional mean, to analyze changes throughout the entire distribution. This drawback has been overcome with the methodology proposed by Machado and Mata (MM) 25, using quantile regressions. And later, Autor, Katz and Kearney (AKK) extended the original MM decomposition to allow for a richer decomposition of log wage differentials. We now detail this approach. Let Q θ (w X ) denote the θ th quantile of the distribution of log wages, conditional on the vector of covariates. These conditional quantiles can be modeled as Q θ (w X ) = X β(θ) (5.8) If equation (5.8) is correctly specified, Q θ (w X ) as a function of θ (,) provides a full characterization of the distribution of wages conditional on X. Realizations of w i given X i may be viewed as independent draws from the distribution X β(θ), where the random variable θ is distributed uniformly on (,). After fitting the conditional quantile function, it is i possible to use the estimated parameters ˆβ(θ) to simulate the conditional distribution of w given X. By the Probability Integral Transformation, if θ, θ 2,...,θ j are drawn from a uniform (,) distribution, the corresponding j estimates of the conditional quantiles of wages at X, ŵ = {X β(θ i )} j, constitute a random sample from the estimated conditional distribution of i= wages, given the set of covariates. 22

24 To generate a random sample from the marginal density of w, we can draw rows of data X i from g (X ), and for each row, draw a random θ j from the uniform (,) distribution. We then form ŵ i = X ˆβ(θ i j ) which is a draw from the wage density implied by the model. By repeating this procedure, we can draw an arbitrarily large sample from the desired distribution which is equivalent to numerically integrating the estimated conditional quantile function ˆQ θ (w X ) over the distribution of X and θ to form f (ŵ) = ˆQ θ (w X )d X dθ X,θ By applying the labor force composition data g τ (X ) from time τ to the price matrix ˆβ t (X ) on time t, we can simulate the counterfactual distribution that would prevail if composition was that of period τ and prices were those of time t. Because the ˆβ τ (X ) matrix describes the conditional distribution of wages for given values of X, this simulation captures the effects of composition on both between and within group inequality Extension to residual inequality Melly 25 and AKK 24 extend the original MM approach to residual inequality in the following way. Defini the vector ˆβ(5) as a measure of between-group inequality, and denote it by ˆβ b = ˆβ(5). Now define a measure of within group inequality as the difference between the estimated coefficient vector ˆβ(θ) and the median coefficient vector ˆβ b ˆβ w (θ) = [ ˆβ(θ) ˆβ b ], θ (,) (5.9) By applying the coefficient matrix ˆβ w (θ) to the distribution of covariates, one can calculate the estimated dispersion of w that is exclusively attributable to residual inequality. The conditional quantile model provides a complete characterization of the distribution of wages as a function of three components: the distribution of covariates, g (X ), and the vectors of between-group prices and the matrix of within (residual) prices: f t (ŵ t ) = f ( g t (X ), ˆβ b t, ˆβ w t Now we estimate quantile coefficient vectors for each time period. These QR coefficients ˆβ provide the prices for the simulation exercise. Then, we calculate the residual price vector ˆβ w using equation (5.9), and then draw simulated data from the distribution f t (ŵ t ) = f ( g t (X ), ˆβ b t, ˆβ w ) t by applying the matrices ˆβb t, ˆβ w t to the rows of g t (X ). The observed change in inequality between any two periods, t and τ, can be decomposed into three components using the following sequential decomposition. Let Q θ = Q θ (f τ (w)) Q θ (f t (w)) equal the observed change in the θ th wage quantile between periods t and τ. Define Q X θ = Q θ (f (g t (X ), ˆβ b t, ˆβ ) w t ) Q θ (f (g τ (X ), ˆβ b t, ˆβ ) w t ) ) 23

25 As the contribution of changing quantities to Q θ. Let Q b θ = Q θ (f (g τ (X ), ˆβ b t, ˆβ w t ) ) Q θ (f (g τ (X ), ˆβ b τ, ˆβ w t ) ) be the marginal contribution of changing between-group prices to Q θ. And finally define Q w θ = Q θ (f (g τ (X ), ˆβ b τ, ˆβ w t ) ) Q θ (f (g τ (X ), ˆβ b τ, ˆβ w τ ) ) to be the marginal contribution of changing within-group prices to Q θ. In our estimations, τ denotes the earlier year Results for the OLS version of the Juhn, Murphy and Pierce decomposition Figure 4 shows the results of the OLS JMP decomposition for the 9- ratio. The percent variation taking 999 as the initial year is shown on the y axis, and the end year is on the x axis. The leftmost subfigure on figure 4 shows the evolution of the change in the 9- differential, for the full sample. Until 25, the maximum total variation in the 9- ratio was -3. (year 24), as seen on panel A of table 5. From 25 on, the declining trend speeds up, to reach its minimum value in 2, falling almost 52. The contribution of observable quantities remained stable, never going over, and positive, offsetting the trend in 999-2, hence observable prices and unobservable prices and quantities account for the decline. Unobservables never fluctuated below -26, and do not have a clear falling tendency, as the one observable prices had, which after remaining close to in , began to be the main driver for the decline, and from 28 on, they become more important in magnitude than unobservables. To determine if it was above or below the median inequality, let us turn to figure 5, which shows the results of this decomposition to the 9-5 and 5- differentials. It is clear from the leftmost subfigure on figure 5 that both ratios fell during 999-2, but it was the 9-5 ratio the one with the most clear and intense declining trend. Observable quantities did not play a significant role in the explanation of the change in below the median inequality, as it offset the effect of prices and unobservables, and it never went over 3. Observable prices played a secondary role as the effect they had on the change in inequality follows the observed falling trend, but the magnitude of their contribution fails to reach half the magnitude of unobservables, which account for the vast majority of the decline in lower tail inequality. The main driver behind the declining inequality trend is the effect of observable prices in above the median inequality. Observable quantities also have a positive, offsetting effect on the change of the 9-5 ratio that never surpassed the mark. The effect of unobservables is negative and fluctuates around -, so it practically vanishes when considering the effect of quantities. So we left with the effect of prices, which was not meaningful until 25, but from that year on, its declining trend accelerates to becoming the most meaningful factor when accounting for the declining trend: After 25, its contribution fluctuates from half to two thirds of the total reduction. 24

26 Splitting the sample by sex yields the same qualitative results. Results for the male sample, depicted in figure 6, make a conclusive statement regarding the role of workforce composition and prices in the inequality decline: When looking at the results for 2, the year with lowest inequality, the contribution of prices is close to null, while observable prices account for half the inequality variation. When looking at lower and upper tail inequality in the male sample, the role of prices becomes even more important. From figure 7, it is evident than above the median inequality follows more closely the trend of the 9- differential, and the role of prices is even more important, as it explains the slight inequality growth, and the even more important subsequent decline, as it contributes to three quarters of the total price effect. The results for the female sample, place greater importance on the role of prices. In the year with lowest inequality, 2, out of the nearly 7 percent points reduction, 5 may be attributed to the effect of observable prices. The contribution of falling upper tail inequality is also higher in the female sample: Out of the 5 percent points due to the effect of prices, 4 come from falling above the median inequality in 2. 25

27 Figure 4: Full sample: Contribution of observable and unobservable prices and quantities to the evolution of the change in inequality (9- percentile log wage differential, OLS JMP decomposition) 2 Total change 2 Prices 2 Quantities 2 Unobservables Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old workers with positive salary. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Note: The covariates include 4 education groups (incomplete high school, high school graduate, some college and college graduate), experience groups and all the interactions among them. Figure 5: Full sample: Contribution of observable and unobservable prices and quantities to the evolution of the change in inequality (9-5 and 5- percentile log wage differentials, OLS JMP decomposition) Total change Prices Quantities Unobservables Source: Fundación ARU series of harmonized household surveys. Sample: 8-65 years old workers with positive salary. Outliers were dropped from the sample. Outliers were nominated using the BACON algorithm (α =.). Note: The covariates include 4 education groups (incomplete high school, high school graduate, some college and college graduate), experience groups and all the interactions among them.