Skill premium, labor supply and changes in the structure of wages in Latin America

Fernández, Manuel; Messina, Julián Working Paper Skill premium, labor supply and changes in the structure of wages in Latin America IDB Working Paper Series, No. IDB-WP-786 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Fernández, Manuel; Messina, Julián (2017) : Skill premium, labor supply and changes in the structure of wages in Latin America, IDB Working Paper Series, No. IDB-WP-786, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0000654 This Version is available at: https://hdl.handle.net/10419/173856 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode Skill Premium, Labor Supply and Changes in the Structure of Wages in Latin America Manuel Fernández Julián Messina IDB WORKING PAPER SERIES Nº IDB-WP-786 March 2017 Department of Research and Chief Economist Inter-American Development Bank March 2017 Skill Premium, Labor Supply and Changes in the Structure of Wages in Latin America Manuel Fernández* Julián Messina** * University of Oxford ** Inter-American Development Bank and Institute for the Study of Labor (IZA) Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Fernández, Manuel. Skill premium, labor supply and changes in the structure of wages in Latin America / Manuel Fernández, Julián Messina. p. cm. — (IDB Working Paper Series ; 786) Includes bibliographic references. 1. Income distribution-Latin America. 2. Wages-Skilled labor-Latin America. 3. Labor supply-Latin America. I. Messina, Julián, 1971- II. Inter-American Development Bank. Department of Research and Chief Economist. III. Title. IV. Series. IDB-WP-786 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 Attribution- NonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. 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The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2017 Abstract* Earnings inequality declined rapidly in Argentina, Brazil and Chile during the 2000s. A reduction in the experience premium is a fundamental driver of declines in upper-tail (90/50) inequality, while a decline in the education premium is the primary determinant of the evolution of lower-tail (50/10) inequality. Relative labor supply is important for explaining changes in the skill premiums. Relative demand trends favored high-skilled workers during the 1990s, shifting in favor of low-skilled workers during the 2000s. Changes in the minimum wage, and more importantly, commodity-led terms of trade improvements are key factors behind these relative skill demand trends. JEL classifications: J20, J31 Keywords: Earnings inequality, Unconditional quantile regressions, Supply- Demand framework, Human capital * Julián Messina is a Lead Research Economist at the Research Department of the Inter-American Development Bank ([email protected]); Manuel Fernáandez is a Ph.D. student in Economics at the University of Oxford (manuel.ferna[email protected]). Authors would like to thank João Pedro Azevedo, Brian Bell, Climent Quintana-Domeque, Simon Quinn and seminar participants at the World Bank and Oxford University for helpful comments and suggestions. The views expressed in this article are those of the authors and not those of the Inter-American Development Bank. 1 Introduction Inequality declined sharply in Latin American countries after the turn of the century, a contrast with its own history and global trends (Ferreira et al., 2008; Kahhat, 2010; L´opez-Calva and Lustig, 2010; Gasparini and Lustig, 2011; Gasparini et al., 2011; Levy and Schady, 2013; Lustig et al., 2013). Redistribution through progressive fiscal policy, the emergence of conditional cash transfer programs for the poor, and changes in household demographics played a role in this transition. However, a broad conclusion of previous literature is that the key contribution to inequality reduction was the decline in earnings inequality (Lopez-Calva and Lustig, 2010; Azevedo et al., 2013). Earnings inequality declined in 16 of the 17 countries in Latin America for which consistent statistics can be calculated (Messina and Silva, 2016), although the intensity and turning points diverged across countries. For example, after a decade of stagnant or slowly increasing inequality, the 90th/10th interquartile range of the labor earnings distribution declined by 20 percent in Argentina and 28 percent in Chile between 2000 and 2013. In Brazil, where earnings inequality started to fall as early as 1990, the reduction has been a remarkable 46 percent since the year 2000. There is a relatively extensive literature examining the forces behind increasing inequality in Latin American countries during the 1980s and early 1990s. Trade is often mentioned as a driving force for the inequality increase in Argentina, Brazil, Chile and Mexico (Goldberg and Pavcnik, 2007; Galiani and Sanguinetti, 2003; Green et al., 2001; Pavcnik, 2003; Robertson, 2004). The literature examining the forces behind the recent inequality decline is much less extensive, and it concludes that traditional trade channels are unlikely to account for a significant fraction of the observed trends. Adao (2015) focuses on shocks due to commodity prices and finds that they can account for only 5 to 10 percent of the fall of earnings inequality in Brazil. Also for Brazil, Costa et al. (2016) examine the local labor market effects of import penetration of manufacturing goods and increasing demand for commodities from China and find that, if anything, the overall impact on inequality was mildly positive. Similarly, Halliday et al. (2015) show that the fall of earnings inequality in Mexico that started in 1995 is inconsistent with traditional trade models. An often overlooked aspect is that most countries in the region registered a rapid transformation in the age, education and gender composition of their labor forces. Between 1990 and 2013, the share of college-educated workers increased from 16.6 to 26.6 percent in Argentina, virtually doubled in Chile (14.3% to 27.7%) and almost tripled in Brazil (7.5% to 19.5%). The average worker age increased by more than a year in Argentina (37.3 to 39.0), by three years in Brazil (34.1 to 37.4), and by more than four years in Chile (35.8 to 40.4). The share of females in the labor force increased in all countries with Brazil and Chile ahead of the pack: an increase of more than 8 percentage points. 2 Changes in the composition of the labor force can mechanically affect wage inequality because different types of workers have different levels of within-group wage dispersion (Lemieux, 2006). They can also affect inequality by changing between-group differences in pay, as suggested by the seminal paper of Katz and Murphy (1992) and numerous applications of a simple supply-demand framework to account for changes in the education premium in the US. This paper investigates how these changes in the demographic and skill structure of the labor force influenced the evolution of the distribution of earnings in Argentina, Chile and Brazil during the last 25 years using household survey data. Our analysis starts by distinguishing the contribution of pure composition changes from changes in the structure of pay. Following the work of Firpo et al. (2007, 2009) we construct counter-factual wage distributions that decompose the observed changes in inequality measures into price and composition effects. The analysis distinguishes between overall inequality and inequality at the bottom and top of the distribution of earnings. This is important because trends have been different. While most of the reduction in earnings inequality in Brazil was the result of a decline in the 50th/10th interquartile range (-31% since 2000), the reduction in inequality in Argentina was mostly driven by a fall of the 90th/50th interquartile range (-23% since 2000). In Chile, inequality fell symmetrically at the bottom and at the top of earnings distribution (-15% since 2000). We find that falling education and labor market experience premiums are key determinants of the observed changes in inequality. By contrast, the increasing incorporation of women into the labor force had small effects. The declining experience premium had a larger explanatory power in the reduction of inequality in the upper half of the distribution. In contrast, the decline of the returns to schooling explains a larger share of inequality reduction at the bottom. Against these dominating patterns, pure composition changes related to the increase in educational attainment were inequality enhancing, thus contributing to increasing inequality in the early 1990s in Argentina and Chile but working against the recent inequality decline. This may be due to within-group differences in pay as highlighted by Lemieux (2006) in the US, or may reflect a phenomenon previously labeled as the paradox of progress (Bourguignon et al., 2005a), by which increases in educational attainment can be inequality-increasing due to convexity of the returns to education. Our analysis continues by assessing the role of the aforementioned labor supply changes in the observed education and experience premiums. Have declines in those premiums been driven by increasing educational attainment and aging of the labor force? Following the seminal work of Katz and Murphy (1992), Murphy and Welch (1992) and Card and Lemieux (2001), we build a stylized model of supply and demand for labor in which workers with different skills are imperfect substitutes in production. We then use household-level data from Argentina, Chile and Brazil to estimate the parameters of 3 the model and to derive implications for the role of supply and demand factors in the evolution of experience and education premiums. We show that a combination of imperfect substitutability between skill groups and the observed movements in relative supplies goes a long way towards explaining the changes in relative returns, especially the declines of both the schooling and experience premiums. Most of the fall in the high school/primary schooling premiums, which we find is a significant factor behind the decline in lower-tail inequality in these countries, can be accounted for by the significant increase of workers with at least a high school degree. According to our model, the observed changes in labor supply should have resulted in an even greater reduction of the high school premium than the observed one, especially during the 1990s. This is because the demand for high school-educated workers increased in this period. The picture for college-educated workers is slightly different. We show that the rising supply of college-educated workers has also pushed the college premium downwards over the past 25 years. However, relative demand trends did not increase steadily, as was the case for high school graduates. Relative demand favored college-educated workers during the 1990s but started declining at the start of the new millennium. The implication is that demand-side trends attenuated labor supply forces towards a declining college premium during the 1990s, but accentuated the decline after 2003. In other words, the demand for college-educated workers followed an inverse U-shaped pattern that peaked in 2003. Further, we show that changes in the educational premiums are not the only factors driving the reconfiguration of the wage structure. The experience premiums also declined substantially to contribute to the inequality reduction, especially within groups of workers with similar levels of schooling. We provide novel estimates in the region for the elasticities of substitution between workers with different experience levels. These estimates suggest that aging of the workforce has contributed to changes in the experience premium, and through this channel to changes in inequality. The supply-demand model used in the second part of the paper is closely related to the framework developed by Manacorda et al. (2010) (henceforth MSPS) to analyze changes in the skill premium in Latin America during the 1990s. We depart from MSPS in two significant ways. First, our model allows for imperfect substitutability across experience groups within schooling levels. We show that this distinction is empirically relevant. MSPS finds workers of different age groups to be perfect substitutes in production, a feature rejected by the data in our model. Second, we extend the model to allow for differential demand trends across education and experience groups, which is crucial for rationalizing the data. Our estimates suggest that relative demand favored more educated and experienced workers during the 1990s, but that there was a shift around the 2000s. Beyond these two extensions we reinforce the call in MSPS for differentiating between workers with secondary schooling and those with at most primary education when think- 4 ing about labor market outcomes in Latin America. In line with MSPS, our evidence suggests these two groups are not perfect substitutes in production. The paper concludes by discussing a number of robustness checks and extensions. In particular, we assess what forces may be behind the trend reversal in the demand for high-skilled workers. Real minimum wages increased dramatically during the 2000s in the three countries. This could compress the skill premium by boosting wages of low-skilled workers. Our findings suggest that they had a role in Brazil and Chile, but declining demand for high-skilled workers after 2003 persists after controlling for the evolution of the minimum wage. Other factors including changes in aggregate labor market conditions as represented by changes in the unemployment rate, and above all the rapid terms of trade improvement boosted by rapidly increasing commodity prices had a significant role in the reversal of skills demand. The rest of the paper is organized as follows. Section 2 discusses the data and main stylized facts, reviewing the evolution of inequality and socio-demographic changes in Argentina, Brazil and Chile. Section 3 shows how changes in inequality were affected by compositional changes and changes in the wage structure associated with education, experience and gender. In Section 4 we develop a simple stylized model of supply and demand based on the descriptive trends in the data, and Section 5 provides estimates to the key parameters of the model and discusses its implications for the evolution of the skill premium. We provide several extensions and robustness exercises that aim at understanding the sensitivity of our results to the modeling choices in Section 6. Finally, Section 7 concludes. 2 Data and Stylized Facts Household surveys for Argentina, Brazil and Chile are used for the analysis. All surveys include information about general characteristics of the workers (e.g., gender, age, education) and their jobs (type of contract, labor earnings, hours worked). With the exception of Argentina, where information is restricted to urban areas,1all other surveys are nationally representative. Earnings refer in the three surveys to total monetary payments from labor in a reference period. Labor earnings are divided by actual worked hours during the same period to obtain hourly earnings. The series are converted into real terms using the Consumer Price Index (CPI).2We restrict the sample to individuals between the ages of 16 and 653and only use earnings of full-time workers (individuals that self- 1Urban areas account for almost 90 percent of the total population in the Argentina in 2013. 2The official CPI is used in Brazil and Chile. Due to inconsistencies found in the official series in Argentina (see Cavallo (2013)), we use the information from PriceStats (http://www.statestreet. com/ideas/pricestats.html) instead. Because the paper focuses on inequality, the use of the price deflator does not make a significant difference in the results. 3We show in the robustness section of the paper that our main results are unchanged if we restrict the sample to prime-age workers (between 25 and 55 years of age). 5 Yt=λt(Lρ Ut +αtLρ St)1/ρ , (4.1) where Ytis total output at time t;LUis the total supply of low-skill labor; LSis the total supply of high-skill labor; λtis a scale parameter that is allowed to vary in time to capture skill-neutral technological change; αtis a time-varying parameter that captures both differences in relative productivities between skilled and unskilled labor, and movements in relative demands between this two types; and ρis a function of the elasticity of substitution (σρ) between skilled and unskilled labor: σρ=1 1−ρ. As noted by Katz and Autor (1999), the fact that we model the economy using an aggregate production function means that we have to be careful not to interpret the parameters as if we were dealing with individual firms. For example, the elasticity of substitution σρreflects not only technical substitution possibilities between workers at the firm level, but also outsourcing and substitution across goods and services in consumption. In a similar way, αtcaptures relative productivity changes both at the intensive (workers performing better at the current jobs) and the extensive margins (e.g., a shift in work tasks across workers of different skill groups), changes in relative prices or quantities of non-labor inputs, and shifts in product demands among industries with different skill intensities. Following Manacorda et al. (2010), we further divide the total supply of unskilled labor (LUt) into two sub-groups. The first sub-group is formed by labor from workers that have at least obtained a high school degree, but that have not completed any post-secondary education. The second sub-group comprises labor from workers that have at most obtained a primary education degree.14 The aggregation is done using a productivity-weighted CES combination of the form LUt =Lδ Pt +βtLδ Ht1/δ , (4.2) where LPt is the total supply of labor from workers with at most primary education; LHt is the total supply of labor from workers with at most secondary education; βtis a time-varying parameter that captures both differences in relative productivities between the two sub-groups and changes in relative demands; and δis a function of the elasticity of substitution (σδ) between the two low-skill types. Finally, we divide workers in each of the three schooling categories (primary, high school and college educated) into two potential experience sub-groups. The first sub-group is composed of workers that have less than 20 years of potential experience, henceforth 14Hence, high school dropouts are included in this group. 12 denominated as inexperienced workers. The second sub-group comprises workers with 20 years of potential experience or more, henceforth denominated as experienced workers. In practice, we aggregate experience and inexperience workers within schooling levels using a productivity-weighted CES combination. In order to reduce the parameter space, we assume that the elasticities of substitution and the relative productivity parameters within the unskilled group (primary and high school educated) are the same. In particular, we have LKt =LθU KIt +φUtLθU KEt1/θUfor K=P, H (4.3) LSt =LθS SIt +φStLθS SEt1/θS, (4.4) where Iand Eindex inexperienced and experienced workers, respectively; φUt and φSt are time-varying parameters that capture both differences in relative productivities and changes in relative demands between the potential experience sub-groups; and θUand θSare both functions of the elasticities of substitution (σθUand σθS) between the two experience sub-groups within the skilled and unskilled labor types.15 We make two final assumptions that are key to our identification strategy. First, we assume that the labor supply of each labor type is exogenously determined. We acknowledge that this is a strong assumption, especially since we observe a sharp movement of women into the labor market during the last 20 years. Our choices for the relative wage and relative supply series discussed in the next section are made to ameliorate problems of selection arising from endogenous responses of women to changes in market conditions and endogenous responses of labor participation across different skill groups. The robustness section discusses alternative specifications to assess the sensitivity of the results. Second, we assume that the economy is operating along the competitive equilibrium demand curve. The implication of these assumptions is that the wage of each labor type is fully determined by its marginal productivity. Given that we have six different labor types in the model (3 schooling levels ×2 potential experience groups), we get six equilibrium conditions. Denoting lower-case variables as the natural logarithms of the respective upper-case variables, the four equilibrium conditions for the low-skill types (PI, PE, HI and HE) are summarized in the following expression 15Even though modeling choices were made trying to mimic the observed data patterns, there is necessarily some degree of arbitrariness. In the robustness section we estimate an alternative specification to assess the importance of some of the modeling assumptions for the results. 13 wKJt = log ζKJt +1 σρ (yt−lUt) + 1 σδ (lUt −lKt) +1 σθU (lKt −lKJt) for K=H, P and J=E, I (4.5) where ζPIt = 1; ζPEt =φUt;ζHIt =βt; and ζHEt =βtφUt. In a similar way, the two equilibrium conditions for the high-skill types (SI and SE) are wSJt = log ζSJt +1 σρ (yt−lSt) + 1 σθS (lSt −lSJt) for J=E, I (4.6) where ζSIt =αt; and ζSEt =αtφSt. The model has two types of relevant parameters that we wish to estimate: four parameters that are functions of the elasticities of substitution across types (ρ,δ,θU and θS), and a set of time varying relative productivities/demand shifters parameters (αt,βt,φUt and φSt). As shown by Johnson and Keane (2013), we could fit the trends in relative wages perfectly if we did not impose any restrictions on the evolution of the relative demand parameters, but this would mean that we would not be able to identify the parameters capturing the elasticities of substitution. We then restrict these relative productivities to follow a cubic trend in their natural logarithm.16 For example, the parameter αtis allowed to change according to log αt=α0+α1×t+α2×t2+α3×t3. (4.7) 5 Results 5.1 Step I The parameters of the model are estimated sequentially in three stages. In each stage we recover a subset of the parameters, and use them to construct the unobserved productivity weighted CES labor aggregates which are then used as inputs in the next step. For the first stage, we use the equilibrium conditions from equations (4.5) to find the expression that characterizes the evolution of relative earnings between experienced and inexperienced labor within the unskilled labor types. In particular, we have 16We also tried quartic time trends without significant changes to our main results (results are available upon request). The estimated parameters associated with the fourth order of the quartic specification were no longer statistically significant. In the robustness section of the paper we also present the results from an exercise in which we allow for more flexibility in the specification of the time trends. 14 wKEt −wKIt =φUt −1 σθU (lKEt −lKIt) for K=P, H. (5.1) The two equations in (5.1) show that changes in log relative wages between unskilled experienced labor and unskilled inexperienced labor depend on i) the evolution of the log relative supplies, scaled by the inverse of the elasticity of substitution; and ii) the evolution of relative demand (φUt), which will be captured by a year-trend polynomial of order three. Note that the relative earnings and relative labor supply series can be constructed directly from the data in each country. In all cases we limit our sample to population between ages 16 and 65. The labor supply of each labor type is drawn from the entire working age population, irrespective of employment status or hours worked. Using working age population to construct labor supply is more appropriate in our context than using the employed population, considering the assumption that labor supply is exogenous in the model.17 The labor earnings series only uses full-time workers (reported working 35 hours or more) when estimating the average earnings of the labor types.18 Moreover, we further restrict the sample to include only male workers when constructing the relative earnings series. This is done to address the concern of sample selection problems regarding female participation in the labor market, especially in a period of rapid movement of women into the workforce. We estimate the two equations in (5.1) by OLS pooling the data from the three countries. We allow the demand trends to be country-specific but restrict the elasticities of substitutions to be common across countries. Both equations in (5.1) are estimated in a single regression that includes a skill dummy indicator (P/H). Results of the first step estimates are shown in column 1 of Table 4. High and low experience workers within the unskilled group are not perfect substitutes, with the point estimate of the elasticity of substitution around 3.2.19 Based on the observed changes in relative supplies in each country, the estimated elasticity of substitution implies a predicted fall in the experience premium, absent any demand changes, of -6.6 percent in Argentina, -17 percent in Brazil, and -26 percent in Chile. This relative supply channel, by itself, closely matches the observed change in the experience premium within low-skilled types in Chile (-25.6%), but underestimates the observed fall in Argentina (-12.3%), and slightly overestimates the observed decline in Brazil (-12.6%). Figure 3 (Panel A) shows the negative co-movement 17In the robustness section of the paper we show that using total employment or total hours worked has little effect on our estimates. 18We report the results when using both full-time and part-time workers in the robustness section of the paper. 19Using a different model specification for the United States, Card and Lemieux (2001) provide estimates of this elasticity between 4 and 6, while Johnson and Keane (2013) report estimates of around 10, which are not statistically significant. 15 of relative prices of experience and relative quantities, once the demand trends in Equation (5.1) are accounted for.20 We can also use the equilibrium conditions from Equations (4.6) to arrive at a similar expression for the evolution of relative earnings between experienced and inexperienced workers within the high-skilled types. This expression takes the form wSEt −wSIt =φSt −1 σθS (lSEt −lSIt). (5.2) We proceed symmetrically with the estimation of equation (5.2), as we did for the unskilled group. We cannot reject the null hypothesis that experienced and inexperienced workers are perfect substitutes within the high-skilled group, but the precision of the estimation is low, which can be partly explained by the small number of observations available for the regression (Table 4). Panel (b) of Figure (3) shows a scatter plot of log relative earnings and log relative supplies between experience groups among collegeeducated workers once the demand trends in equation (5.2) are accounted for. In contrast with the unskilled worker case, the regression line is virtually flat. Figure 4 shows the evolution of the cubic demand trends captured by log φUt and log φSt.21 The results are heterogeneous across countries. In Argentina and Chile, relative demand for higher experience tended to increase during the 1990s, but has been either stagnant or in the decline since the beginning of the 2000s for both skilled and unskilled workers. The trend-reversal is also observed in Brazil, but the shift takes place later, by the middle of the 2000s. Thus, the fall in the experience premiums where driven in part by ageing in the three countries. The supply effects were attenuated by a rise in relative demand for more experienced workers during the 1990s, and accentuated by a decline in relative demand during the 2000s. 5.2 Step II The second step is aimed at recovering parameter estimates for the elasticity of substitution between the two low-skilled labor types (σδ), and for the time trends capturing the evolution of their relative demands (log βt). We use the equilibrium conditions from equations (4.5) to derive two equations characterizing the evolution of relative wages between workers with secondary education and those with at most primary education: 20The log relative earnings series correspond to the residuals of a regression of the observed log relative earnings on country-specific cubic time trends and a skill dummy indicator. Correspondingly, the log relative supply series are obtained as the residuals of a regression of observed log relative supplies on country-specific cubic time trends and a skill dummy indicator. 21Each series is scaled so that it takes a value of zero at the first year in which data for the country is available. 16 wHJt −wPJt =βt−1 σδ (lHt −lP t)... −1 σθU [(lHJt −lHt)−(lP Jt −lPt)] for J=E, I, (5.3) where both lHt and lPt are productivity-weighted CES labor aggregates. Although neither of the two labor aggregates is observed in the data, we can use the two equations in (4.3) and the estimated parameters from step I to calculate them. The second term in equation (5.3) is capturing overall (aggregated across experience groups) relative supplies between workers with at most primary education and workers with at most a high school degree. The last term represents relative changes in the potential experience composition between the two low skill groups. Note that the coefficient associated with this last term is the inverse elasticity of substitution between experience subgroups among unskilled workers, which was already estimated in step I. The estimated results in this second step serve as an internal consistency check. We estimate both equations in (5.3) in a single regression, adding an experience group dummy indicator (E/I). As before, demand trends are allowed to be country-specific and approximated by a cubic trend, but the elasticities of substitution are assumed to be the same across countries. Results of the second step estimates are shown in column 3 of Table 4. The estimated elasticity of substitution between workers with at most primary education and workers with at most secondary education is 2.2. This number is in line with the 2.8 estimate found by Manacorda et al. (2010) for a different set of countries in the region during the 1990s, and reinforces the message that within the context of Latin America, there is a meaningful difference in the way the labor market treats the skills supplied by workers with secondary education and workers with at most primary completed. The estimate of σθUis very similar to that obtained in step I. Panel (a) of Figure 5 shows the tight connection between changes in the high school premium vis-´a-vis primary education and relative supply. The figure shows the evolution in the three countries of a log earnings and relative supply series that have been purged from country-specific demand trends and changes in the potential experience composition of the labor force. The negative co-movement between changes in labor supply and earnings is apparent, and confirmed by Panel (b) of Figure 5, which shows the estimated demand trends as captured by log βt. Relative demand for high school graduates was very stable in Brazil, increased weakly in Argentina, and only increased strongly in Chile during the 1990s. Thus, the observed sharp declines in the high school/primary schooling premiums were fundamentally driven by the educational upgrading of the workforce. Relative demand trends, if anything, favored high school graduates. This is further illustrated in Figure 6, which shows the fit of the model including or excluding demand 17 trends. The exclusion of demand trends does not alter the model fit for Brazil, which is remarkably close to the observed relative wages. Over the whole period the decline of the high-school premium would have been larger in both Argentina and Chile had demand forces not favored high school graduates over those with basic education. 5.3 Step III As a last step we obtain an estimate of the elasticity of substitution between skilled and unskilled labor (σρ) to assess the role of relative skill labor supply on the observed changes in the skill premium. After some manipulation of Equations (4.5) and (4.6) we can derive the following four expressions, log ∼ WSJt WKJt != log αt−1 σρ log LSt LUt −1 σδ log LUt LKt −1 σθS log LSIt LSt ... −1 σθU log LKt LKJt for K=H, P and J=E, I, . (5.4) where the terms log ∼ WSJt WKJt !are the log relative earnings of skilled and unskilled workers of a given experience group that has been “demand-detrended” using the time trend estimates from the previous steps.22 With the exception of LUt and LSt, all of the productivity-weighted CES labor aggregates have been previously used in the estimation. Constructing LUt and LSt is straightforward using the parameters previously estimated and equations (4.2) and (4.4). The set of equations in (5.4) incorporate all the parameters of the production function. Hence, the estimation of these set of equations provides a third estimate for the elasticity of substitution σθU; a second estimate for both elasticities of substitution σθSand σδ; and a first estimate of the elasticity of substitution between skilled and unskilled workers σρ. We estimate the four equations in a single regression, using a country-specific cubic demand trend for log αt, and including skill-experience dummy variables as covariates. Results of the third step estimates are shown in column 4 of Table 4. The estimated elasticity of substitution between skilled and unskilled labor is 2.1, very close to the elasticity of substitution between the two unskilled sub-groups. Our point estimate for 22In particular, log   ∼ WSEt WHEt  = log WSEt WHEt −log ˆ φst ˆ βtˆ φUt ; log   ∼ WSEt WP Et  = log WSEt WP Et − log ˆ φSt ˆ φUt ; log   ∼ WSIt WHIt  = log WSIt WHIt −log 1 ˆ βt; and log   ∼ WSIt WP It  = log WSIt WP It . 18 this elasticity is higher than the 1.4 and 1.6 values reported by Katz and Murphy (1992) and Johnson and Keane (2013) respectively for the United States; it is in line with the 2-2.5 range estimated by Card and Lemieux (2001) also in the United States; and is somewhat lower than the 2.5-5 range reported by Manacorda et al. (2010) for the Latin American region. Estimates of the other elasticities of substitution are very similar to those obtained in columns 1-3. The results show that the large influx of college graduates into the labor market of the last 20 years depressed the college premium significantly. To see this more clearly, Panel (a) of Figure 7 shows a scatter plot of log relative earnings and log relative supplies once country-specific demand trends, changes in relative potential experience composition, and changes in schooling composition within the unskilled group are taken into account.23 The negative co-movement between relative supplies and relative earnings is evident. Panel (b) of Figure 7 shows the estimated relative demand trends between skilled and unskilled workers, as captured by log αtin Equation (5.4). In the three countries we observe a similar pattern, albeit with different magnitudes. Relative demand tended to favor college-educated workers during the 1990s, but this trend started to reverse around 2002. By the end of the period relative demand is back to the 1990s level in Argentina and Brazil, but remained higher in Chile. Figure 8 shows the evolution of the observed skill premium and the predictions of the model in the three countries. The skill premium follows an inverted U-shaped pattern in Argentina and Chile, increasing up to the early 2000s and declining thereafter. This is very much in line with the observed evolution of inequality documented in Figure 1. Also in line with the evolution of inequality, the skill premium in Brazil declines slowly during the 1990s but more quickly during the 2000s. Relative labor supply had a strong impact on the evolution of relative earnings by pulling the skill premium down. The dashed line in Figure 8 shows the predictions of the model where relative demand trends (log αt) have been shut down. Labor supply changes alone actually over-predict the fall of the skill premium during the past two decades. However, they also completely miss the inverted U-shaped dynamics observed in Argentina and Chile, and in Brazil they strongly over-predict the inequality reduction. It is a strong demand for skills in the 1990s that slowly reverses in the 2000s that explains the inverted U shape of the skill premium. Thus, we conclude that while relative supply changes tended to pull the college premium downwards over the past 20 years, relative demand changes ameliorated this effect during the 1990s and magnified the relative supply channel after 2000. 23The log earning series is constructed as the residuals of an estimation of Equation (5.4) that omits the aggregate relative supply term (log(LSt/LUt)). The log relative supply series corresponds to the residuals of an estimation of Equation (5.4) in which the aggregate relative supplies (log(LSt/LUt)) are used as the dependent variable. 19 5.4 The Role of the Minimum Wage, Unemployment and the Commodity Price Boom The simple supply and demand framework presented above is silent about the role of institutional and cyclical conditions in the labor market in explaining changes in the wage structure. This is a limitation that may by relevant in our context because these economies have experienced sharp changes in labor market institutions such as the minimum wage and external conditions. The commodity price boom that started in the early 2000s brought about sharp improvements in terms of trade and a period of unprecedented growth in the three countries (Erten and Ocampo, 2013; The World Bank, 2016). We follow Autor et al. (2008) and extend the empirical implementation of the model to examine the sensitivity of our estimates to including controls for changes in the minimum wage, unemployment, and terms of trade. Figure 9 shows the evolution of minimum wages, unemployment and terms of trade in Argentina, Brazil and Chile over the period of analysis. Unemployment rose in the three countries during the late 1990s and early 2000s and then declined steadily after 2002 (Panel a). The pattern is particularly marked in Argentina, which suffered a major economic and financial crisis between the end of 2001 and 2003. The cyclical conditions in these economies, as captured by the unemployment rates, broadly coincide with the movements in the college premium previously documented. Between 1990 and 2012 the real hourly minimum wage increased by 120 percent in Brazil and by 138 percent in Chile. In Argentina it only increased after the 2001 crisis but at a fast pace, more than doubling in the decade that followed. Sharp increases in the minimum wage may result in substantial real wage gains for low-skilled workers, possibly contributing to the reduction of the skill premium. The commodity super cycle that started in 2002 (Panel c) benefited these three net commodity exporter countries, resulting in a rapid improvement in terms of trade (Panel d). The changes in relative skill demand at the start of the 2000s could be a result of a favorable product demand shift in the commodity sector, which tends to be intensive in low-skilled labor. The extension of the empirical model is done by including the log of the real hourly minimum wage, the unemployment rate, and the log terms of trade index as covariates in the third step of the estimation of the model, which corresponds to Equation (5.4). We take advantage of the similar evolution across the three countries in the relative demand for skilled workers and restrict log αtto be common across countries. This allows us to simultaneously identify demand trends and the three additional covariates. To allow for greater flexibility in the evolution of demand we replace in this specification the third order polynomial time trend with a full set of year dummies. Changing the specification of residual demand or including additional covariates does not alter the main message of previous sections: relative skill supply had an important 20 role in the determination of the skill premium. Column I of Table 5 shows the baseline model estimates when we replace country-specific cubic time trends with a set of common year dummies. Results are very similar to our baseline mode except for a small reduction in the elasticity of substitution between skilled and unskilled workers, which declines from 2.1 to 1.5. If anything, relative supply trends become more important. Columns II-IV show the results when we include the three additional set of covariates one at a time and column V includes all the covariates in the same specification. The estimated elasticities of subsitution are very stable across specifications, and we cannot reject equality of the coefficients. The estimated coefficients associated to the minimum wage have a negative sign and are statistically significant for Brazil and Chile in column V, with elasticities of -0.38 -0.50, respectively. Changes in the unemployment rate present different signs in Chile and Brazil. Improvements in the labor market appear to be associated with a decline (increase) of the college premium in Chile (Brazil). Terms of trade improvements during the 2000s appear to have contributed to the fall of the skill premium in Argentina and Brazil, while they are not significant in the case of Chile (Column V). This suggests that the commodity price boom of the last decade could be behind the shift in relative demand against skilled workers. These alternative specifications provide some insights into what factors might be behind the residual demand trend reversal observed in the early 2000s. Panel (a) of Figure 10 shows the evolution of common demand trends as measured by the year specific fixed effects corresponding to Column I of Table 5. The trend reversal around the year 2002 in this baseline model is clearly depicted in the figure. In Panel (b) of Figure 10 we show the same demand trends for a model that includes controls for the log minimum wage and the unemployment rate. The inverted U-shaped pattern of residual demand is preserved, although the fall in relative demand for high-skill workers after 2002 is slightly attenuated. A different story emerges when we include controls for the change in the terms of trade in each country (see Panel (c)). In this case we observe a deceleration of the relative demand for high-skill workers around 2002, but it is significantly smaller than the one estimated in the baseline model. Moreover, if we include the full set of controls the estimated relative skill demand remain flat after 2002. These results are suggestive that cyclical and institutional conditions of the labor market, especially regarding the improvements in external conditions of the economies following the commodity boom, were important determinants of the fall of the skill premium during the 2000s. In the absence of these changes, demand trends favoring high-skill workers would have attenuated the fall in earnings inequality brought about by the educational upgrading of the workforce. 21 Halliday, T., Lederman, D. and Robertson, R. (2015). Tracking wage inequality trends with prices and different trade models : evidence from Mexico. Policy Research Working Paper Series 7471, The World Bank. Johnson, M. and Keane, M. (2013). A Dynamic Equilibrium Model of the US Wage Structure, 1969-1996. Journal of Labour Economics 31(1): pp. 1–49. Kahhat, J. (2010). Labor earnings inequality: The demand for and supply of skills. In L´opez-Calva, L. F. and Lustig, N. (eds), Declining Inequality in Latin America: A Decade of Progress?. Brookings Institution Press, chap. 2. Katz, L. and Autor, D. (1999). Changes in the wage structure and earnings inequality. In Ashenfelter, O. and Card, D. (eds), Handbook of Labor Economics. Amsterdam: North-Holland, vol. 3A, chap. 26. Katz, L. and Murphy, K. (1992). Changes in relative wages, 1963-1987: Supply and demand factors. The Quarterly Journal of Economics 107(1): pp. 35–78. Lemieux, T. (2006). Increasing Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill? The American Economic Review 96(3): pp. 461–498. Lemieux, T., MacLeod, B. and Parent, D. (2009). Performance Pay and Wage Inequality. Quarterly Journal of Economics 124(1): pp. 1–49. Levy, S. and Schady, N. (2013). Latin america’s social policy challenge: Education, social insurance, redistribution. Journal of Economic Perspectives 27: 193–218. Londo˜no, J. L. and Szekely, M. (2000). Persistent Poverty and Excess Inequality: Latin America, 1970-1995. Journal of Applied Economics 3(1): pp. 93–134. Lopez-Calva, L. F. and Lustig, N. (2010). Declining Inequality in Latin America: A Decade of Progress?. Brookings Institution Press. L´opez-Calva, L. F. and Lustig, N. (2010). Explaining the decline in inequality in Latin America: Technological change, educational upgrading, and democracy. In L´opez- Calva, L. F. and Lustig, N. (eds), Declining Inequality in Latin America: A Decade of Progress?. Brookings Institution Press, chap. 1. Lustig, N., Lopez-Calva, L. and Ortiz-Juarez, E. (2013). Deconstructing the Decline in Inequality in Latin America. Tulane Economic Working Paper Series. Manacorda, M., S´anchez-Paramo, C. and Schady, N. (2010). Changes in Returns to Education in Latin America: The Role of Demand and Supply of Skills. Industrial and Labor Relations Review 63(2): pp. 307–326. 28 Messina, J. and Silva, J. (2016). Wage Inequality in Latin America. Understanding the Past to Prepare the Future. World Bank Unpublished Manuscript. Murphy, K. and Welch, F. (1992). The Structure of Wages. The Quarterly Journal of Economis 107(1): pp. 285–326. Murphy, K. M. and Welch, F. (1990). Empirical Age-Earnings Profiles. Journal of Labor Economics 8: 202–229. Pavcnik, N. (2003). What explains skill upgrading in less developed countries? Journal of Development Economics 71: 311 – 328. Robertson, R. (2004). Relative prices and wage inequality: evidence from mexico. Journal of International Economics 64: 387 – 409. Sanchez-Paramo, C. and Schady, N. (2003). Off and Running? Technology, Trade, and the Rising Demand for Skilled Workers in Latin America. The World Bank. Policy Research Working Paper 3015. The World Bank (2016). The Commodity Cycle in Latin America: Mirages and Dilemas. Semiannual Report, Office of the Regional Chief Economist. 29 A Appendix A.1 Tables and Figures Figure 1: Interquantile Log Earnings Ratio by Country Notes: Sample consists of full-time workers (reported working 35 hours or more) between ages 16 and 65. 30 Figure 2: Composition-Adjusted College/High School and High School/Primary Earnings Gap Notes: Sample consists of full-time workers (reported working 35 hours or more) between ages 16 and 65. See Appendix A for details on the construction of the compositionally adjusted series. Figure 3: Adjusted Relative Earnings and Relative Supplies by Experience Level (a) Unskilled Workers (b) Skilled Workers Notes: Log relative earnings correspond to the residuals from a regression of observed relative earnings on country-specific cubic time trends and a skill dummy. Log relative supplies correspond to the residuals from a regression of observed relative supplies on country-specific cubic time trends and a skill dummy. 31 Figure 4: Experienced/Inexperienced Demand Index by Skill Level (a) Unskilled Workers (log ˆ φUt) (b) Skilled Workers (log ˆ φSt) Notes: Relative demand trends between experienced and inexperienced workers are countryspecific cubic time trends estimated following Equations (5.1) and (5.2). Each series is scaled so that it takes a value of zero at the first year in which data for the country are available. Figure 5: Supply and Demand Factors Behind the Fall in the High-School/Primary Earnings Gap (a) Relative Earnings and Supplies (b) HS/Primary Demand Index (log ˆ βt) Notes: Panel A depicts log relative earnings and log relative supplies of workers with at most a high school degree with respect to those with only primary education, once the countryspecific demand trends and changes in the relative potential experience composition are taken into account. The log earning series is constructed as the residuals of an estimation of Equation (5.3) that omits the aggregate relative supply term (lHt −lPt). The log relative supply series corresponds to the residuals of an estimation of Equation (5.3) in which the aggregate relative supplies (lHt −lP t) are used as the dependent variable. Panel (b) depicts the estimated relative demand trends between workers with at most a high school degree and those with only primary schooling as captured by the country-specific cubic time trends in Equation (5.3). Each series is scaled so that it takes a value of zero at the first year in which data for the country are available. 32 Figure 6: High School/Primary Observed and Predicted Relative Earnings Notes: “Observed” refers to the Log (HS/Primary) Earnings Ratio observed in the data. “Predicted” refers to the model prediction derived from the estimation of Equation (5.3). “Predicted (no demand trend)” is the prediction of a modified version the model in Equation (5.3) that omits the country-specific time trends. 33 Figure 7: Supply and Demand Factors Behind the Fall in the Skilled/Unskilled Earnings Gap (a) Relative Earnings and Supplies (b) Skilled/Unskilled Demand Index (log ˆαt) Notes: Panel A depicts log relative earnings and log relative supplies of skilled with respect to unskilled workers once the country-specific demand trends, changes in relative potential experience composition, and changes in schooling composition within the unskilled group are taken into account. The log earning series is constructed as the residuals of an estimation of Equation (5.4) that omits the aggregate relative supply term (lSt −lUt). The log relative supply series corresponds to the residuals of an estimation of Equation (5.4) in which the aggregate relative supplies (lSt −lUt) are used as the dependent variable. Panel (b) depicts the estimated relative demand trends between skilled and unskilled workers as captured by the country-specific cubic time trend in Equation (5.4). Each series is scaled so that it takes a value of zero at the first year in which data for the country are available. 34 Figure 8: High School/Primary Observed and Predicted Relative Earnings Notes: “Observed” refers to the Log (Skilled/Unskilled) Earnings Ratio observed in the data. “Predicted” refers to the model prediction derived from the estimation of Equation (5.4). The observed and predicted unskilled earnings series is constructed as a weighted average between the two low-skill sub-groups, where the weights correspond to the respective labor share. “Predicted (no demand trend)” is the prediction of a modified version the model in Equation (5.4) that omits the country-specific time trends. 35 Figure 9: Relative Skill Demand. Conditioning Factors (a) Unemployment Rate (b) Minimum Wage (c) Commodity Price Index (d) Terms of Trade Notes: The unemployment rate series in Panel (a) is taken from the World Economic Outlook (WEO) database. The Minimum wage series in Panel (b) is taken from the annual indicators of the International Labour Organization (ILO). The source of the series in Panel (c) is The IMF’s Primary Commodity Price System. The Food and Beverage series includes cereal, vegetable oils, meat, seafood, sugar, bananas, oranges, coffee, tea, and cocoa. The Fuel series includes crude oil (petroleum), natural gas, and coal. The Raw Agricultural and Metals series includes timber, cotton, wool, rubber, hides, copper, aluminum, iron ore, tin, nickel, zinc, lead, and uranium. See http://www.imf.org/external/np/res/commod/index.aspx for a description of the construction of the indices. The series in Panel (d) are taken from the United Nations Conference on Trade and Development (UNCTAD). Unit value indexes are based on data reported by countries, supplemented by UNCTAD’s estimates using the previous year’s trade values at the Standard International Trade Classification three-digit level as weights. 36 Figure 10: Skilled/Unskilled Demand Index. The Role of Unemployment, Minimum Wages and Commodity Prices (a) Skilled/Unskilled Demand. Baseline (b) Skilled/Unskilled Demand After Controlling for Minimum Wage and Unemployment Rate (c) Skilled/Unskilled Demand After Controlling for Terms of Trade (d) Skilled/Unskilled Demand After Controlling for Minimum Wage, Unemployment Rate and Terms of Trade Notes: Each panel depicts the estimated relative demand trends between skilled and unskilled workers (log ˆαt) using different specifications of the last stage of the baseline model. Panel (a) corresponds to the estimates of the year fixed effects of column I in Table 5. Panel (b) corresponds to the estimates of the year fixed effects of a model that includes controls for the unemployment rate and the natural logarithm of the minimum wage. Panel (c) corresponds to the estimates of the year fixed effects of column IV in Table 5, which includes controls for the log of the terms of trade index. Panel (d) corresponds to the estimates of the year fixed effects of column V in Table 5, which includes controls for the log real minimum wage, the unemployment rate of each country, and the log of the terms of trade index. The demand trends are scaled so that they take a value of zero in 1990. 37 Table 7: Model Estimation Results. Prime Age Workers (25-55) STEP IA IB II III Elasticities −1/σθU-0.345*** -0.398*** -0.426*** (0.049) (0.042) (0.044) −1/σθS-0.182 -0.195** (0.148) (0.068) −1/σδ-0.439*** -0.462*** (0.023) (0.019) −1/σρ-0.562*** (0.101) Demand Argentina Time 0.038** 0.055** 0.027 0.069*** (0.018) (0.022) (0.018) (0.016) Time2/100 -0.595** -0.815** -0.346 -0.916*** (0.265) (0.288) (0.262) (0.191) Time3/1000 0.206* 0.265** 0.140 0.293*** (0.109) (0.101) (0.109) (0.067) Demand Brazil Time -0.027** 0.009 -0.014 0.042** (0.010) (0.015) (0.009) (0.017) Time2/100 0.351*** 0.087 0.194* -0.233 (0.100) (0.199) (0.104) (0.178) Time3/1000 -0.098*** -0.057 -0.055* 0.031 (0.028) (0.066) (0.030) (0.048) Demand Chile Time 0.007 0.044** 0.081*** 0.099*** (0.012) (0.015) (0.013) (0.014) Time2/100 0.030 -0.392** -0.614*** -0.661*** (0.151) (0.178) (0.161) (0.126) Time3/1000 -0.020 0.082 0.139** 0.130*** (0.046) (0.052) (0.049) (0.035) N96 48 96 192 R20.801 0.642 0.936 0.960 *** 1 percent ** 5 percent * 10 percent. Robust standard errors in parenthesis. Notes: Each column presents the results of the estimation of the different stages of the model, restricting the sample to workers between the ages of 25 and 55. Column IA shows the OLS estimates of the inverse of the elasticity of substitution between experience and inexperience workers within the low-skilled group (σθU ) (see Equation (5.1)); column IB corresponds to the OLS estimates of the inverse of the elasticity of substitution between experience and inexperience workers within the skilled group (σθS) (see Equation (5.2)); column II shows the OLS estimates of the inverse of the elasticity of substitution between the two low-skill groups (σδ), and a second estimate of the inverse of the elasticity of substitution σθU (see Equation (5.3)); finally, column III shows the OLS estimates of the inverse of the elasticity of substitution between skilled and unskilled workers (σρ), as well as additional estimates from the other elasticities in the model. 44 Table 8: Model Estimation Results: Part-Time and Full-Time Workers. Supply Measure Working Age Pop. Occupied Pop. Total Hours Worked Elasticities −1/σθU-0.389*** -0.373*** -0.359*** (0.044) (0.043) (0.043) −1/σθS-0.171* -0.171* -0.125 (0.094) (0.092) (0.090) −1/σδ-0.478*** -0.466*** -0.462*** (0.020) (0.020) (0.019) −1/σρ-0.432** -0.467*** -0.372** (0.136) (0.130) (0.112) Demand Argentina Time 0.040** 0.049** 0.049** (0.015) (0.015) (0.016) Time2/100 -0.414** -0.544** -0.501** (0.206) (0.204) (0.213) Time3/1000 0.125 0.165** 0.145* (0.080) (0.078) (0.080) Time3/10000 Demand Brazil Time 0.049** 0.051** 0.058** (0.017) (0.017) (0.018) Time2/100 -0.301 -0.331* -0.338* (0.197) (0.192) (0.193) Time3/1000 0.049 0.055 0.052 (0.057) (0.055) (0.054) Time3/10000 Demand Chile Time 0.103*** 0.096*** 0.110*** (0.021) (0.019) (0.017) Time2/100 -0.702*** -0.691*** -0.736*** (0.184) (0.167) (0.168) Time3/1000 0.150** 0.156*** 0.155** (0.050) (0.046) (0.047) Time3/10000 Observations 192 192 192 R20.942 0.943 0.943 *** 1 percent ** 5 percent * 10 percent. Robust standard errors in parenthesis. Notes: The table reports the third stage estimates of the parameters of the model when we include part-time workers in the construction of the wage series. Each column presents the results using alternative measures of the total labor supply by each group. The first column corresponds to our baseline results; the second column limits the sample to include only employed population; and the final column uses total hours worked. 45 Table 9: Model Estimation Results: Alternative Production Function STEP I II III Elasticities −1/σδ-0.372*** -0.264*** -0.341*** (0.026) (0.011) (0.014) −1/σθ-0.138** -0.171*** (0.045) (0.043) −1/σρ-0.762*** (0.047) Demand Argentina Time 0.027* 0.108*** (0.014) (0.012) Time2/100 -0.002 -0.011*** (0.002) (0.002) Time3/1000 0.000 0.000*** (0.000) (0.000) Demand Brazil Time -0.003 0.007 (0.012) (0.010) Time2/100 0.001 0.001 (0.001) (0.001) Time3/1000 -0.000 -0.000 (0.000) (0.000) Demand Chile Time 0.062*** 0.084*** (0.010) (0.009) Time2/100 -0.005*** -0.005*** (0.001) (0.001) Time3/1000 0.000** 0.000** (0.000) (0.000) N336 672 672 R20.973 0.934 0.886 *** 1 percent ** 5 percent * 10 percent. Robust standard errors in parenthesis. Notes: Each column presents the results of the estimation of the different steps in the alternative model described in the Appendix A.4. 46 A.2 Data and Variable Construction The household surveys used in Argentina for the period between 1995 and 2003 are waves of the Encuesta Permanente de Hogares (EPH), collected by the Instituto Nacional de Estad´ıstica (INDEC). This survey was replaced by the Encuesta Permanente de Hogares Continiua (EPH-C) after 2003, breaking the series. The transition between the EPH and the EPH-C included changes in the questionnaires and the frequency in which the surveys were collected. The geographical coverage in EPH-C was extended to include additional agglomerates. In order to maintain consistency over the period of study we only use the agglomerates that are present in both surveys. The EPH and the EPH-C are representative for urban areas, but close to 90 percent of the population in Argentina live in urban centers. The survey used in Brazil is the Pesquisa Nacional por Amostra de Domicilios (PNAD), collected by the Instituto Brasilero de Geograf´ıa y Estad´ısticas (IBGE). The PNAD is a nationally representative survey that has been carried out on a yearly basis since 1967. We use the different waves starting from the year 1990. Due to exceptional circumstances the survey was not collected in 1994 and 2000. The household survey used for Chile is the Encuesta de Caracterizaci´on Socioecon´omica Nacional (CASEN). The CASEN is a nationally representative household survey collected by the Ministry of Planning through the Department of Economics at Universidad de Chile. The survey was first implemented in 1987 and was carried out every two years from 1990 to 2000, and every three years thereafter. We use all the waves from 1990 to 2013. We constructed variables capturing the educational attainment and potential experience of all individuals in the sample. Although the countries we analyze differ in the structure of their educational systems, the SEDLAC project has attempted to homogenize the information from the different countries to make it comparable.25 We use SEDLAC’s coding in the construction of the educational attainment series. In particular, we define five possible levels of educational attainment: i) primary education completed or less; ii) high school incomplete; iii) high school completed; iv) college incomplete; and v) college completed or more. Potential experience is defined as the result of subtracting the total number of years of education completed (plus 6) from the age of the individual. Although we define five possible levels of educational attainment, we mostly work with three categories: primary or less, high school completed and college completed. Individuals with incomplete levels of education are distributed equally between the previous and next completed level. For example, mean real hourly earnings of workers with college education are calculated as a weighted average between the observed mean wages of this group and the observed mean wages of workers with college incomplete. The weight of 25See CEDLAS and The World Bank (2014) for a detailed description of the SEDLAC database 47 the latter group is equal to half of their actual number. This also implies that in the labor supplies used in the model, the supply of workers with primary education completed or less includes half of the total supply of workers of the high school incomplete category. The supply of workers with high school education completed includes both half of the supply of workers with high school incomplete and half of the supply of workers with college incomplete. Finally, the supply of workers with college education completed includes half of the total supply of workers with college incomplete. Each survey includes a question asking workers for the total monetary income from labor in a reference period. This is the variable that we use throughout the paper to capture labor earnings. The variable is divided by the total number of hours worked to obtain hourly earnings. The series are converted into real terms using the consumer price index of the respective countries.26 In the main specification we restrict the sample to individuals between the ages of 16 and 65, and only use earnings of full-time workers (individuals working 35 hours or more in the reference week). The composition adjusted earnings of aggregate groups are constructed using a fixed-weighted average of the different sex-education-experience sub-groups. We first run a regression of log hourly earnings on the full set of covariates that include indicators for the five education categories, seven dummies for potential experience in five-year intervals, and all possible interactions. The regression is estimated separately for males and females in each available country-year. The predicted log wages from these regressions are evaluated for the 70 sub-groups, and a weighted average is estimated when aggregating to broader groups. The weights are equal to the mean employment share of each sub-group across all years. A.3 Using RIF to Decompose Changes in Distributional Statistics beyond the Mean Firpo et al. (2007, 2009) allow extending the traditional Oaxaca-Blinder decomposition to distributional statistics beyond the mean. This is achieved through the use of influence functions (IF). Influence functions measure the effect that an infinitesimal amount of “errors” have on a given estimator (Cowell and Victoria-Feser, 1996), but they also have properties that allows us to model the sensitivity of a given unconditional wage quantile to a change in a set of covariates. To see this, let qτ(FW) be τth quantile of the distribution of wages, expressed in terms of the cumulative distribution FW(w). Define the following mixture distribution: GW, = (1 −)FW+HWfor 0≤≤1 (A.1) 26Due to inconsistencies found in the official Consumer Price Index in Argentina (see Cavallo (2013)), we use the information from PriceStats (http://www.statestreet.com/ideas/pricestats.html) to deflate nominal wages in this country. 48 where HWis some perturbation distribution that only puts mass at the value w. In that case, GW, is a distribution where, with probability (1−), the observation is generated by FW, and with probability , the observation takes the arbitrary value of the perturbation distribution. By definition, the influence function corresponds to: IF(w;qτ, FW) = lim→0 qτ(GW,)−qτ(FW) (A.2) where the expression is analogous to the directional derivative of qτin the direction of HW. Analytical expressions for influence functions have been derived for many distributional statistics.27 The influence function in the case of the τth quantile takes the form: IF(w;qτ, FW) = τ− 1 [w≤qτ] fW(qτ)(A.3) where 1 [·] is an indicator function and fWis the PDF.28 Using some of the properties of influence functions, a direct link with the traditional Oaxaca-Blinder approach can be established. In particular, a property that is shared by influence functions is that, by definition, the expectation is equal to zero. Z+∞ −∞ IF(w;qτ, FW)dF(w) = 0 (A.4) Firpo et al. (2009) propose a simple modification in which the quantile is added back to the influence function, resulting in what the authors call the Recentered Influence Function (RIF). RIF(w;qτ, FW) = qτ+IF(w;qτ, FW) (A.5) The importance of this transformation lies in the fact that the expectation of the RIF is precisely the quantile qτ. With this result, Firpo et al. (2009) show that we can model the conditional expectation of the RIF as a linear function of the explanatory variables. E[RIF(wt;qτ, FW,t|Xt)] = X0 tγt(A.6) Moreover, if we apply the law of iterated expectations to Equation A.6, the end result is an expression that directly relates the impact of changes in the expected values of the covariates on the unconditional quantile qτ. Note that this result is all that is required to extend the Oaxaca-Blinder decomposition to quantiles, since the basic components of 27Essama-Nssah and Lambert (2011) provides a comprehensive list of influence functions for different distributional statistics. 28Note that the influence function in this case depends on the density. In order to obtain the empirical density the authors propose non-parametric kernel density estimation. 49 the method are all present in Equation (A.6). Estimation of Equation (A.6) can be done by OLS, and only requires replacing the dependent variable, log wtin the original wage setting model with the RIF of the quantile qτ. The interpretation of the estimates bγtcan be thought of as the effect of a small change in the distribution of Xon qτ, or as linear approximation of the effect of large changes of Xon qτ(Firpo et al., 2007). A.4 Alternative Model Specification In this section we present an alternative specification of the production function of the model in Section 4.1. We mostly follow the work of Manacorda et al. (2010), with some small modifications to allow for comparability with our baseline results. Production in the economy is also modeled using a nested constant elasticity of substitution (CES) function with three levels. The first level is identical to the one we use Yt=λt(Lρ Ut +αtLρ St)1/ρ (A.7) with the parameters having the same interpretation. In the second level, labor from skilled and unskilled workers is divided into seven potential experience sub-groups, aggregating them with a productivity-weighted CES combination of the form LMt = 7 X A=1 φMALθ MAt!1/θ for M=S, U (A.8) where Aindexes the potential experience groups; φMA is a time-invariant parameter capturing differences in relative productivities between potential experience groups; and θis a function of the elasticity of substitution: σθ=1 1−θ. Two key differences with our baseline model are worth pointing out. First, the second level of the production function aggregates labor by experience, not by skill sub-groups. The ordering between the second and third levels is then shifted. Second, the model assumes that there are no relative demand/productivity changes between workers with different levels of potential experience. This follows from the assumption that the respective parameters (φMA) are time-invariant, which largely simplifies the estimation. Finally, the supply of labor from workers with a given potential experience within the unskilled group is composed of a CES combination of labor from the two lower schooling levels 50 LUAt =Lδ PAt +βtLδ HAt1/δ (A.9) where Pand Hdenote workers with primary education or less and high school completed, respectively; βtis a time-variant measure of the relative productivity between the two low education levels; and δis a function of the elasticity of substitution between the two groups: σδ=1 1−δ. Note that βtis constant across potential experience groups, so relative demand shifts are common in this dimension. Finally, the natural logarithm of the two time-variant parameters (αtand βt) are estimated using cubic time trends. Two differentiating factors between this specification and the work of Manacorda et al. (2010) are worth pointing out. First, we allow for differential demand trends within low skilled workers, which they assume to be constant. Second, we allow for a more flexible specification of the demand trends by fitting a cubic polynomial instead of a linear time trend. This allows us to fit the trend reversals in the skill premiums that we observe in the data. 51