The relation between labor productivity and wages in Brazil : a sectoral analysis

Resumo A produtividade do trabalho é um determinante fundamental do salário real. Entretanto, as dinâmicas do salário e produtividade frequentemente divergem na prática em função de uma série de fatores econômicos e institucionais. Este estudo analisa a relação entre as dinâmicas da produtividade do trabalho e do salário no Brasil entre 1996-2014, adotando uma abordagem setorial para considerar divergências entre setores econômicos. As análises baseiam-se em dados do Sistema de Contas Nacionais e da Pesquisa Nacional por Amostra de Domicílios, e em estimativas de modelos hierárquicos para avaliar os impactos de fatores regionais e setoriais nos salários individuais. Os resultados indicam que a produtividade está positivamente associada ao salário em todos os setores econômicos, mas que fatores institucionais, como formalização do trabalho e salário mínimo, infl uenciam de maneira igualmente signifi cativa, sugerindo que o crescimento do salário entre 1996-2014 foi tanto um resultado de mudanças institucionais quanto de transformações da estrutura produtiva.


Introduction
Labor productivity, understood as the value of output produced per unit of labor input, is a crucial long-run determinant of workers' real wages.Ultimately, workers cannot sustainably earn more value than they create.Neoclassical economic theory formalizes this notion in its assertion that a worker's wage is equivalent to the marginal product of her labor, that is, her productivity (Cahuc et al., 2014).Nevertheless, labor productivity and wage dynamics often diverge substantially in practice, due to a range of institutional and market forces, and this divergence can have important implications for a country's economic development.When real wages lag behind productivity growth, the distribution of income between capital and labor shifts in favor of capital, potentially worsening income inequality and depressing aggregate demand.When wage growth exceeds productivity growth, export competitiveness and investment may suffer (Biesebroeck, 2015).
In light of the theoretical importance of labor productivity to wage growth and economic development, this study examines the relation between productivity and wages in Brazil between 1996 and 2014.This time period encompasses two distinct stages in Brazil's recent economic trajectory: the movement towards liberalization and market-oriented reforms that characterized the late 1990s, and the commodity boom and expansion of pro-social reforms of the 2000s.The fi rst stage is characterized by stagnation in productivity and real wages, while the second stage is marked by modest growth in productivity and signifi cant growth of real wages (Maia;Menezes, 2014;IPEA, 2014).
Importantly, these overall trends disguise broad variation in productivity and wage growth at the sectoral level.Some areas of Brazil's economy, such as industry, have seen low growth in productivity, losses in competitiveness, and shrinking representation in national GDP (Jardim;Perin, 2016;Hiratuka;Sarti, 2015).Other areas, such as agriculture, have experienced rapid productivity growth and substantial wage gains (Gasques et al., 2014;Maia;Sakamoto, 2014).These evolving dynamics complicate traditional notions of development via industrialization, and suggest alternative sectoral priorities and strategies (Baiardi, 2016).
Motivated by these changing dynamics, this study adopts a sectoral perspective in order to address the following questions: i) to what degree have gains or losses in wages been the result of gains or losses in productivity?ii) have productivity gains constituted the primary engine of wage growth, or do they pale before institutional or demographic changes?iii) why do different economic sectors present such varying rates of productivity and wage growth?This sectoral perspective complements previous analyses that examine labor productivity and income in Brazil on a national level (Romanatto et al., 2008).
We fi nd a universally positive association between labor productivity and real wages.More specifi cally, our estimates indicate that elasticity between labor productivity and real wages is largest for sectors where earnings are directly based on productivity (such as pay-on-commission in real estate and commerce), or where productivity is easily measured (industry).In turn, elasticities are smaller for those sectors where worker productivity is more diffi cult for fi rms to measure, or where there are high levels of informal labor (agriculture and construction).Furthermore, results indicate that wages in many sectors are also strongly infl uenced by institutional forces, such as worker formalization, labor unions, and minimum wage.
The study is organized as follows.Part 2 explores theoretical explanations of the frequently observed divergence between labor productivity and wages, and situates this debate in the Brazilian context.Part 3 reviews the methodology and data used to compute labor productivity and real wages for eight sectors of the Brazilian economy between 1996 and 2014, and then develops regression models to estimate productivity-wage elasticities for each sector.Part 4 presents data series on sectoral labor productivity and real wages, as well as regression results, and interprets these data and results in light of recent economic developments in Brazil.Finally, Part 5 offers conclusions.

Theoretical interpretations of productivity-wage relationship
According to neoclassical labor economics, a worker's wage equates to that worker's marginal product of labor in equilibrium.Under perfect competition, a market wage below productivity would induce the fi rm to hire workers until their marginal product fell below the wage rate (under the assumption of diminishing marginal returns).A market wage greater than productivity would induce the fi rm to fi re workers until remaining employees' marginal product rose suffi ciently to restore equilibrium.If the fi rm were a price-maker under imperfect competition, the impacts of the fi rm's hiring and fi ring behavior on the market wage would only amplify this equilibrating tendency (Biesebroeck, 2015;Cahuc et al., 2014).
There are a number of theoretical explanations for why wages rarely equate to productivity levels in practice.Firstly, wages account for only a fraction of total employee compensation, which may include additional benefi ts such as pension or insurance.If the proportion of these additional benefi ts in total compensation grows, then stagnating real wages could actually disguise an increase in overall employee compensation (Feldstein, 2008).In Brazil, where formal employee benefi ts such as a 13th salary, severance pay, and health insurance are prevalent, recent increases in worker formalization could make this factor a signifi cant determinant of productivity-wage divergence (IPEA, 2009).
Secondly, markets are characterized by information asymmetries, in which fi rms fi nd it diffi cult to assess workers' true productivity and effort levels.In this case, fi rms pay workers according to productivity signals, such as education, which may not directly align with those workers' true productivity (Spence, 1975).Firms may also construct compensation and promotion schedules that incentivize high productivity at the outset of an employee's career by promising higher compensation at the end of the career, thus temporally misaligning productivity and wage (Biesebroeck, 2015).
Thirdly, fi rms may systematically discriminate against workers based on race, gender, or other characteristics, imposing wage penalties on discriminated workers who are equally as productive as their non-discriminated colleagues (Blau;Kahn, 2016;Sakamoto;Kim, 2014;Fryer, 2011).Specifi c to Brazil, Bailey, Loveman and Muniz (2013) present evidence on continuing racial discrimination in employment, and Casari, Bastos, and Feltre (2009) measure substantial gender discrimination in employment, suggesting that the racial and gender composition of economic sectors may be an important factor in understanding wage-productivity divergence in Brazil.
Fourthly, as argued in Manning (2010), labor markets are inherently imperfect, and are characterized by both fi rm and employee rents.Both par-ties face high search costs, and may thus be willing to close employment agreements at wage rates divergent from productivity rates.The actual division of rents between workers and fi rms will result from the relative bargaining positions of these groups, as well as the bargaining mechanisms (Pissarides, 1985).Under this interpretation, increasing formalization of the labor force and decreasing unemployment in Brazil could have improved labor's bargaining power throughout the 2000s, thus contributing to rising wages relative to productivity.
Finally, overarching these microeconomic dynamics, technology-biased innovation and investment have been identifi ed by many authors as a cause of declining labor shares of income (in other words, as a cause of divergence between labor productivity and wages) across industries and countries (Hogrefe;Kappler, 2012;Bentolila;Saint Paul, 1999).In this analysis, capital-augmenting technical progress, such as the widespread adoption of computers from the 1990s onwards, may generate factor biases between capital and labor, with the degree of bias determined by activityspecifi c elasticities of substitution between factors (Karabarbounis;Neiman, 2013;Findlay;Jones, 1999;Feenstra;Hanson, 1999).
Changes in total employee compensation, information asymmetries, discrimination, bargaining power, and capital-augmenting technological progress may have widely varying impacts for different sectors of the Brazilian economy, depending on the characteristics of each sector.Employee benefi ts and career-long incentive structures may have large impacts in highly formalized sectors such as public administration or fi nance, and smaller impacts in agriculture or commerce.Shifts in labor bargaining power through mechanisms such as labor organization (unions), formalization, and lower unemployment may have greater heft in sectors dominated by low-skilled workers, such as agriculture and construction, relative to sectors characterized by higher barriers-to-entry.And differential rates of technology-adoption across sectors may distort the transmission of productivity gains into real wages, depending on whether technologies are capital-or labor-augmenting for any specifi c economic activity.One recent development in the Brazilian labor market that has disproportionately impacted low barrier-to-entry sectors is the signifi cant real valorization of the minimum wage since 2000.This valorization has contributed meaningfully to income growth among less-qualifi ed workers (Saboia;Hallak, 2016).
3 Data and methodology

Data sources
Sectoral labor productivity in Brazil is computed as the quotient of Gross Value Added (GVA) to total hours worked for each sector.Annual data on sectoral Gross Value Added (GVA) are drawn from the National Accounts, presented by the Instituto Brasileiro de Geografi a e Estatística (IBGE).IBGE reports GVA for twelve sectors: 1) Agriculture, 2) Extractive Industry, 3) Manufacturing, 4) Electricity, Gas, Water, and Sewage, 5) Construction, 6) Commerce, 7) Transportation, Storage, and Mail, 8) Information Services, 9) Financial Services, 10) Real Estate, 11) Other Services, and 12) Public Administration, Health, Education, and Social Security.We combine sectors 2 and 3, sectors 4 and 5, sectors 8 and 9, and sectors 10 and 11 in order to reduce the infl uence of extreme outliers and to make data trends visually comparable while preserving the conceptual integrity of each sector to the greatest degree possible. 1The resulting eight aggregated sectors employed throughout this study are: 1) Agriculture, 2) Industry (Manufacturing and Extractive), 3) Construction and Utilities, 4) Commerce, 5) Transportation, Storage, and Distribution, 6) Financial and Information Services, 7) Real Estate and Other Services, and 8) Public Administration, Health, Education, and Social Security.
Data on total hours worked per sector, as well as a range of additional variables employed in our analysis, are drawn from the Pesquisa Nacional por Amostra de Domicílios (PNAD), sponsored by IBGE.Data are pooled over the years 1996 to 2014.Data from Brazil's Northern region are excluded 1 Specifi cally, labor productivity for extractive industries and real estate is extremely high relative to negligible levels of employment in those sectors.Extractive industries employed just 0.4% of workers in 2014 (and just 3.47% of total industrial workers), but displayed an average labor productivity value of US$116.4 per hour for that year, over four times higher than the next most productive sector.Likewise, real estate employed only 1.1% of workers in 2014, and displayed a labor productivity value of US$116.0 per hour for that year.For comparative purposes, we merged these sectors with manufacturing and other services, respectively.The elevated value-added per labor hour in extractive industry is likely the result of substantial accumulated capital (e.g.mines, drilling platforms) more than of real contributions of labor in that sector.Thus, presenting extractive industry separately could be misleading, especially considering the minimal size of extractive industrial employment in the PNAD sample.Nonetheless, the sector should not be excluded entirely, given its contribution to national GDP and important interlinkages with advanced areas of Brazilian manufacturing.In sum, the most computationally and conceptually consistent approach appears to be merging extractive industry and manufacturing into an aggregated measure of industry.
due to lack of data on rural areas of this region before 2004.2The four-digit economic Activity codes from the PNAD were grouped into the eight sectors described above, and incorporate the methodological changes introduced in the Classifi cação Nacional de Atividades Econômicas (CNAE) after the year 2000 (Dedecca;Rosandiski, 2003).
Income data from the PNAD were defl ated to 2014 constant values using the Índice Nacional de Preços ao Consumidor, provided by IPEA.GVA values were defl ated to 2014 constant values using the World Bank's GDP defl ator.Defl ated values in Brazilian Reals were then converted to Purchasing Power Parity (PPP) constant 2014 US dollars using data from the IMF's 2014 World Economic Outlook report.3Conversion to US dollars was intended to facilitate international comparisons.

Empirical analysis
Sectoral variation in the productivity-wage relationship may be the result of variation in institutional and market forces among different types of economic activities.Alternatively, it may be the result of differences in average worker characteristics across sectors.To distinguish between these alternative dynamics, we fi t a regression model to pooled annual data from the PNAD for years 1996-2012. 4The objective is to measure the impact of sectoral labor productivity on individual hourly wages.We limit our sample to working adults between the ages of 15 and 65.The dependent variable is the natural logarithm of the i-th individual's labor income per hour (w), which is assumed to be a function of the i-th individual's personal characteristics (vector x), j-th economic sector's characteristics (z) in the state where that individual is employed, and national minimum wage (v) in year t: Factor r i captures unobserved regional heterogeneity and is controlled by fi xed effects using 26 binary variables to represent Brazil's 27 federal units (UF).The factor c t represents economic, political and/or institutional cycles affecting wages.These cycles are controlled for by 4 binary variables representing fi ve federal governments over the sample period (1996-1998: fi rst term of Fernando Henrique Cardoso;1999-2002: second term of Fernando Henrique Cardoso;2003-2006: fi rst term of Luiz Inácio Lula da Silva; 2007-2010: second term of Luiz Inácio Lula da Silva; 2011-2014: fi rst term of Dilma Rousseff).ε ijt is an idiosyncratic error term.Coeffi cients β, δ and φ express the net impact of the explanatory variable on the log of hourly wage.Regression estimates are computed by Ordinary Least Squares (OLS) with heteroscedasticity consistent standard errors.This is a hierarchical approach, where the minimum wage v only varies by year (level 1), economic sectors' characteristics vary by sector/state and year (z, level 2) and individuals' characteristics vary for each individual i of the sector/state s and year t (x, level 3).In a comparative model, we replace the variable minimum wage and cycles c t with temporal fi xed effects, using 16 binary variables to represent the 17 years included in the sample.The intention is to estimate the model under alternative speci- (1) fi cations.The set of individuals' and sectors' characteristics used in our analysis is described in Table 1.More detailed descriptive statistics are presented in Appendix A.
The main advantage of this pooled hierarchical strategy is that it allows for wider variability of the independent variables.This is particularly important for structural characteristics, which only vary across sectors (e.g.productivity), and/or years (e.g.minimum wage).In turn, the main disadvantage of the pooled models is that variability may differ across years (heteroscedasticity), resulting in biased estimates for the standard errors.This problem was avoided by estimating standard errors robust to heteroscedasticity (Wooldridge, 2003, p. 258).
Since explanatory variables in vectors x and z are measured in different scales, we cannot directly compare coeffi cients in β or δ in order to identify variables with the largest impact on w.Consequently, standardized coefficients were estimated which permit measurement of explanatory variable effects on w in standard deviation units, rather than in terms of the original units of x and z (or w).Standard deviation units are the resultant parameters when all variables are standardized to a mean of 0 and a variance of 1, and are estimated by (Wooldridge, 2003): where is the OLS estimator, is the sample standard deviation for the j-th explanatory variable, and is the sample standard deviation for the dependent variable ln w.
First, baseline regressions were estimated on all pooled observations using Equation 1. Baseline regressions establish economy-wide coeffi cient parameters for subsequent comparison with sectoral results.Furthermore, baseline results provide a sensitivity analysis of alternative model specifi cations (progressively controlling for time (or political-economic cycle) fi xed effects and institutional factors).We next estimate Equation 1 for each economic sector individually, drawing upon only those observations that fall into each economic sector, successively.Sectoral results illustrate variations in the productivity-wage relationship between different economic activities. (2) 4 Results Brazil (1996Brazil ( -2014) ) Brazil successfully managed to bring its hyperinfl ationary experience to an end in 1994 with the Plano Real under the presidency of Fernando Cardoso.Nevertheless, the side effect of a series of initiatives to control infl ation and the growing public defi cit (such as privatization, reduction of tariff barriers, and strong valorization of the Real), coupled with simultaneous international crises in Mexico (1994), Asia (1997), and Russia (1998), led to an increase in unemployment, stagnation in productivity, and declines in real wages over this period, as observed in Figure 1 (Dedecca, 2005;Gennari, 2002).Markets balked briefl y again in 2002 over the election of Luiz Inácio Lula da Silva of the Workers Party to the presidency, but growth soon returned in full force with the international commodity boom of the 2000s.Fueled primarily by China's explosive growth, international commodity prices rose sharply for major Brazilian exports such as iron and soybeans, improving Brazil's terms of trade and attracting foreign investment (Giambiagi, 2011).From 2003 onwards, Lula's government capitalized on this commodity boom by facilitating the expansion of consumer credit and fostering income redistribution through signifi cant real increases in the minimum wage and spending programs like Bolsa Familia.Unemployment shrank, the number of formal salaried jobs multiplied, and income inequality and poverty experienced historic declines (IPEA, 2012).This period was accompanied by a rise in real wages that outstripped growth in labor productivity, as illustrated by the notable rise in real wages relative to productivity in Figure 1.This development suggests that, for the Brazilian economy as a whole, rising real wages over the 2003-2013 period may have been more the result of minimum wage increases and formalization of the labor market than of structural development toward more productive employment.This apparent failure to capitalize on the commodity boom of the 2000s to promote structural productivity gains bodes poorly for prospects of further sustained wage growth in Brazil (Maia;Menezes, 2014).

Productivity and wage trends in
Finally, the decline in both productivity and wages after 2013, as observed in Figure 1, marks the onset of Brazil's current economic crisis.The slowing of China's commodity boom and the crash in oil prices in 2014 reversed Brazil's terms of trade, leading to a rising defi cit that in turn provoked pro-cyclical austerity measures.These recent dynamics have corresponded with declines in real wages and productivity levels.Examining the Brazilian economy on a sectoral level, the wide divergence in productivity levels among different economic activities becomes clear (Figure 2). 5 For instance, in 1996 an average hour of labor in the lowestproductivity sector, agriculture, produced US$4.93 in value (in constant 2014 US dollars), while an average hour of labor in the highest productivity sector, fi nancial and information services, produced US$39.67.From 1996 onwards, these sectoral productivity values display a convergent tendency, such that the difference between the lowest productivity sector in 2014 (commerce) and highest (real estate and other services) was only 43% of the difference in 1996.
5 Observing the striking differences in productivity among economic sectors, it is tempting to think that huge production gains could be realized simply by moving workers from low productivity to high productivity activities.While this indeed is the long-term objective of many national development policies, instantaneous productivity gains from activity-switching are limited because, as noted in Biesebroeck (2015), the values in Figure 2 represent average productivities, not marginal productivities.Productive sectors are typically productive because they embody high capital accumulation and complex infrastructures.Thus, adding an additional worker at the margin will not likely boost overall production by a level commensurate with the average productivity rate of that sector.This convergence is the result of two sectoral developments.The fi rst, the surprising decline in productivity for Financial and Information Services, is the combined result of real productivity trends and changing occupa- tional distributions within the sector.In real terms, the fi nancial services subsector suffered a 40% productivity loss between 1998 and 2014.This dynamic could be related to changes in Brazilian banks' "earnings spread" between lending and borrowing rates, which fell sharply with the decline in interest rates over this period, bringing value-added down with it (Freitas;Prates, 2016;Afonso;Köhler;Freitas, 2009). 6Parallel to these real value-added losses in the fi nancial sector, the activity composition of the information services subsector evolved toward lower-productivity activities such as telemarketing and "other business services."Employment in these lower-productivity components of information services grew by 37% over the 1996-2014 period (relative to overall employment growth of 24%), thus coming to occupy an infl ated proportion of total sectoral employment by 2014 (PNAD, 2016).
The second trend leading to sectoral productivity convergence is the dramatic rise in agricultural productivity since 1996.Labor productivity in agriculture (historically Brazil's lowest productivity sector) grew by 121.7% over the 1996-2014 period, with an annual growth rate of 4.8%.This rapid growth was the result of a number of interrelated dynamics.Rural labor shortages incentivized investments in labor-augmenting technologies, rural workers' average education levels increased, new transgenic seeds boosted yields, and domestic and international research and extension improved innovation and technology adoption.Overarching these trends, agribusiness assumed an expanded role in capital-intensive, monoculture production for export, especially on the newly opened Cerrado frontier (Buainain, 2014;Guanziroli, 2014;Maia;Sakamoto, 2012;Gasques et al, 2014).
Two additional trends should be noted in Figure 2. Firstly, Real Estate and Other Services' high levels of "productivity" are misleading, since much of real estate's value derives from accumulated capital (past labor embodied in property).Thus, when dividing the large value gains enjoyed by real estate during Brazil's sustained property appreciation by the small number of hours worked in this sector, the resulting labor productivity values appear surprisingly high.These values should be treated with due caution.
6 Value-added in the fi nancial services sector is imputed directly from the spread between lending rates and interest rates.Thus, when annual interest rates declined from 34.2% at the beginning of 1998 to 17.7% at the end of 2004, fi nancial spreads declined in parallel, reducing fi nancial sector "productivity" (Banco do Brasil, Histórico das taxas de juros, 2016: https://www.bcb.gov.br/Pec/Copom/Port/taxaSelic.asp).income gains (37.1% total increase), and fi nancial and information services exhibit the greatest losses (9.3% total decrease) (Figure 3). 7ages for most sectors roughly follow productivity trends for the corresponding sector, with three noteworthy exceptions.Firstly, despite monotonic declines in productivity in the fi nancial and information services sector, wages for this sector nevertheless pick up after 2003, suggesting a rise in the relative wage (an increasing share of average value-added going to wages).This divergence may be the result of the information asymmetries and bargaining power dynamics described above.Financial and information services jobs are more likely to be career-track, and thus subject to the type of seniority-biased incentive structuring identifi ed as a potential source of wage-productivity divergence by Biesebroeck (2015).Furthermore, jobs in this sector require higher education levels, potentially allowing educated workers (still relatively scarce in the Brazilian labor market) to exert greater bargaining power over employers.8Finally, despite the erosion of union power in the fi nancial sector throughout the 1990s and early 2000s, labor organization in this sector remains high relative to other areas, further improving workers' bargaining power and driving up relative wage (PNAD, 2016).
In the second incidence of productivity-wage divergence, public employees' wages realize a total increase of 30.1% between 1996 and 2014, despite total productivity growth of only 6.9% over this period.It is important to note that productivity in the public sector must be interpreted carefully.Because output in the government sector is measured as equal to the total value of inputs, the appreciation of relative wages in the public sector indicates only that salaries constitute a higher share of total costs in the sector, not that public workers are necessarily retaining a greater proportion of their value-added (Boyle, 2006).Alternatively, this apprecia-tion of the relative wage may indeed be a consequence of the signifi cant bargaining power imparted on public employees by institutional protections and benefi ts, high levels of labor organization, and the relatively high education levels of these workers.
In the third notable instance of productivity-wage divergence, the low wage-levels of workers in the real estate and other services sector illustrates the extent to which value added per hour in this sector, as displayed in Figure 2, is in fact constituted by property rents rather than true labor productivity.
In sum, sectoral labor productivity and real wages both evolved in signifi cant ways over the 1996 to 2014 period.To what degree were these developments related?Did gains in productivity drive gains in wages, as neoclassical labor economics would predict, or were institutional and/or personal worker characteristics more determinative of earnings levels?In order to disentangle these alternative scenarios, estimates of micro-level wage equations are presented in the following section.

Impacts of sectoral productivity on wages
We fi rst estimate alternative baseline specifi cations (Equation 1), and report results in Table 2.All model specifi cations fi t relatively well to the PNAD pooled sample, with coeffi cients of determination above 46%.Standard errors are robust to heteroscedasticity and estimates are stable and signifi cant over multiple specifi cations.
Signs and magnitudes of control variables are as expected from the literature.The coeffi cient of 0.089 for schooling in Model 3 indicates that a one-year increase in an employed individual's years of schooling, all else equal, is associated with a 9.3% (e 0.089 -1 = 0.092) increase in hourly earnings.The coeffi cient of -0.274 for female indicates that, all else equal, women's average hourly wages are 24.0%(e -0.274 -1 = -0.240)lower than men's, indicating extensive gender inequalities in the Brazilian labor market.The coeffi cient of -0.114 for non-white indicates that, all else equal, black and indigenous workers present an average hourly wage that is 10.8% (e -0.114 -1 = -0.108)lower than white and Asian workers, indicating the presence of strong racial inequalities in employment.The positive coeffi cient estimates for age and negative estimates for age 2 indicates an invert-ed-U relation between wages and working experience 9 .
The coeffi cient estimates of productivity, 0.123 in Models 1 and 2, indicate that a 1% increase in each observed worker's state-and activity-specifi c labor productivity is associated with a 0.123% increase in real hourly wages for the average worker.This impact increases only slightly when we control for unionization and formal employment in Model 3 (0.166%).While positive and signifi cant, this elasticity appears to be low by international standards (Peeters;Den Reijer, 2011).Institutional factors also play a signifi cant role in determining wage levels.
The coeffi cient value of minimum wage, 0.251 in Model 2 (0.238 in Model 3), indicates that a 1% increase in the national real minimum wage is associated with a 0.251% increase in real wages (0.238% in Model 3).The coeffi cient value of 1.019 for union in Model 3 indicates that a 1 percentage point increase in the proportion of organized workers in an observed worker's state is associated with a 1.019% increase in real wages for that worker, all else equal.Finally, the coeffi cient of 0.394 for formal indicates that a 1 percentage point increase in the proportion of formalized workers in an observed worker's state is associated with a 0.394% increase in real wages for that worker.
Estimates for the standardized coeffi cients allow us to understand to what extent relative change (one standard deviation) in an explanatory variable affects relative variation in the dependent variable.The similar estimates for log of productivity (0.122), unionized (0.098), and formal (0.089) suggest that real wages were equally affected by both relative variations in labor productivity and institutional factors.This fi nding suggests that remuneration in the Brazilian labor market (both absolutely and relatively between sectors) is not merely determined by market-driven forces such as labor productivity, but also by structural characteristics, many of which are activity-specifi c.The association between relative changes in the minimum wage and in the hourly wage is slightly lower (0.066), but this result may hide important differences between labor-and capital-intensive sectors.Thus, we next estimate sectoral regressions in order to assess the activity-specifi c nature of wage-determinants.
Table 3 reports sectoral regression results, generated by fi tting the wage-regression model developed above to seven pooled datasets, each of which include only individuals employed in the respective economic sector. 10 Standard errors are robust to heteroscedasticity, and estimates, with some exceptions, are signifi cant at the 1% level.Estimates for the standardized coeffi cients are presented in Appendix C.
Signs and magnitudes of social control variables are again as expected, though there is notable sectoral variation.Results indicate that returns to schooling are higher than the baseline average in fi nancial and information services (e 0.131 -1 = 14,0% per year of education), and public administration and services (e 0.119 -1 = 12.7%).Returns to formal education are lowest in agriculture (e 0.043 -1 = 4.4%) and real estate and other services (e 0.054 -1 = 5.5%). 11 These results indicate that returns to education are higher in more skillintensive sectors, suggesting the presence of skill-biased technological change and job polarization (increasing separation between high-and low-paying activities) as potential generators of both wage differentiation and persistent inequality among sectors (Berman et al., 1997;Autor, 2010).The gender wage-penalty varies signifi cantly by sector.The negative wage impact of being female is greatest in industry (e -0.351 -1 = -29.6%)and real estate and other services (e -0.324 -1 = -27.6%),and smallest in construction (e -0.019 -1 = -1.9%)and agriculture (e -0.201 -1 = -18.2%).The effects of race on wages appear to be more robust and consistent over economic sectors.Race-related wage penalties range from a minimum impact of -5.8% for non-whites in agriculture, to a maximum impact of -15.5% for nonwhites in Financial & Information Services.The variable of focus in this study, log of productivity, exhibits signifi cant variation over economic sectors, though its impact is universally positive.All else equal, a 1% increase in the level of labor productivity in an observed worker's state and economic sector has the largest positive impact on real wages in real estate and other services (+0.34%), commerce (+0.20%), public services (+0.19%), and industry (+0.15%).Productivity has lower impact on wages in fi nancial and information services (+0.10%), construction and utilities (+0.09%), and agriculture (insignifi cant).The relatively large positive impacts measured in real estate and commerce may be due to the prevalence of work-on-commission in these sectors.Many workers earn according to their sales performance, and should thus exhibit high levels of association between labor productivity and earnings.The relatively large impact of labor productivity on wages in the public sector is likely the result of labor productivity accounting methods.As noted before, public sector workers' value-added is calculated directly from inputs, thus eliciting a positive association between productivity and wages.The labor productivity-wage relationship is potentially relatively low in the fi nancial and information services sector due to information asymmetries inherent to these activities.In banking, marketing, research, and other activities in this sector, fi rms fi nd it diffi cult to assess employees' true productivity levels.In contrast, productivity impacts on wages in industry are relatively high due, presumably, to the facility with which fi rms can measure employees' productivity and by the degree to which employers regulate employees through employment contracts (Rose;O'Reilly, 1998).Finally, the impacts of labor productivity on wages are smallest in construction and agriculture.This may be due in part to the generally low levels of worker qualifi cation and the substantial infl uence of institutional variables such as minimum wage in these sectors.It is important to note that agriculture exhibits especially high levels of heterogeneity in fi rm and worker productivity, causing low sector-level elasticity to obscure noteworthy real productivity and wage gains among modern agricultural practices (Maia;Sakamoto, 2014).
Institutional variables also exert strong and signifi cant effects on real wages at the sectoral level.Results indicate that a 1 percentage point increase in union participation in an observed worker's state is signifi cantly negatively associated with real wages in agriculture (-0.30%) and commerce (-0.34%), and signifi cantly positively associated with real wages in public services (+0.63%), construction & utilities services (+0.38%) and fi nancial and information services (+0.29%).This divergent behavior may refl ect divergent levels of labor organization across sectors.For example, agriculture and commerce are characterized by low levels of labor organization (14% and 15% respectively in 2014), while fi nancial and information services and public services are characterized by high levels of labor organization (25% and 27%, respectively). 12Furthermore, fi nancial and information services and public services are characterized by higher barriers to entry, high-skilled (diffi cult to replace) jobs, and institutional protections that facilitate labor organization and action (IPEA, 2009).
As a result, an increase in labor organization in unorganized sectors (agriculture and commerce) may have the effect of pulling resources away from the large majority of non-organized workers, thus resulting in the negative coeffi cient reported in Table 3.In organized sectors (fi nancial and information services and public services), an increase in labor organization benefi ts a large enough proportion of workers to pull up sectoral wages as a whole, resulting in the positive coeffi cient measured for these sectors.
The impacts of formal (measuring the proportion of formalized workers in each state) are signifi cant and positive across all sectors. 13Since worker formalization primarily impacts labor markets by requiring fi rms to pay minimum wage, this variable should exhibit the largest impact on sectors characterized by high proportions of minimum-wage employment, i.e. sectors with low average wages.Indeed, results in Table 3 indicate that a 1 percentage point increase in state-level formalization is associated with the largest wage gains (+0.64%) in agriculture, which presents the lowest wage levels of any economic sector, and the smallest wage gains (+0.21%) in real estate and other services and fi nancial and information services, the latter of which presents the highest wage levels of any economic sector.Despite low average wages in real estate and other services, the net impact of formalization on wages in this sector is likely low due to high withinsector heterogeneity-ranging from extremely high wage activities, such as real estate, to low wage activities, such as cleaning and security services.
The substantial increases of the minimum wage over the sample period primarily favored low-wage sectors: agriculture and real estate and other services.For each 1% variation in the minimum wage, average wages in these sectors increased by 0.50% and 0.46%, respectively.In turn, the impact of minimum wage on high-skill jobs, such as in fi nancial and informafi nancial and information services, the true contrast in levels of labor organization between the former and latter sectors is even larger than the quoted statistics suggest.Furthermore, to avoid overgeneralization, it should be noted that some specifi c subsectors in construction and utilities are also characterized by high levels of unionization, namely, production and provision of electric energy and water (41%).13 Formally employed public sector workers do not possess a "carteira assinada" (formal employment registration) certifying their formal employment status.They thus appear among informal workers in the PNAD sample.To avoid misestimation based on this misleading classifi cation, the variable formal was dropped from the public services sectoral regression model.tion services, are negligible.
Overall, the standardized coeffi cients in Appendix C highlight that labor productivity has played an important role in increasing hourly wages.Relative changes in labor productivity exerted larger effects on average wages in sectors characterized by productivity-based pay, i.e. commerce and real estate and other services.Nevertheless, institutional factors such as minimum wage also signifi cantly explain the dynamics of average wages in Brazil, especially in low-paying sectors.Relative variation in the minimum wage exerted the largest impact on hourly wages in agriculture, real estate and other services, commerce, and construction and other utilities.

Conclusions
Real wages may diverge from labor productivity due to a range of economic and institutional factors.Economic factors include changes in nonpay compensation, information asymmetries between workers and fi rms, the emergence of worker or fi rm rents as the result of labor market disequilibrium and search costs, and technology-biased innovation and investment that distorts factor income shares.Institutional factors include labor market formalization, labor organization, and minimum wages.The degree to which these factors cause wage growth to diverge from productivity growth has signifi cant implications for economic competitiveness, investment, and the distribution of income among factors of production.
In Brazil, real wages grew signifi cantly more than did labor productivity between 1996 and 2014.However, this general trend disguises significant sectoral variations, which can be grouped into four conceptual trends.Firstly, in the agriculture and commerce sectors, large gains in labor productivity were accompanied by real wage increases and improvements in the quality of employment.This dynamic was likely due to a positive interplay between productivity-enhancing market developments (incorporation of new technologies, high levels of investment, exploitation of new consumer markets/agricultural frontiers) and income-enhancing institutional developments (formalization and minimum wage valorization).In conjunction, these forces resulted in productivity gains that outpaced wage growth, leading to declining relative wages in agriculture and commerce (see Appendix A for data on relative wages).
In a second sectoral trend, the construction and real estate and other services sectors enjoyed real wage gains over the 1996-2014 period, despite stagnation in labor productivity.Both sectors offer little natural room for drastic productivity growth through the incorporation of new technologies, investments, or practices.And both were major benefi ciaries of institutional interventions such as formalization and valorization of the minimum wage. 14Together, these forces resulted in a sharp rise in relative wage for construction and real estate and other services.
In a third variation of the productivity-wage relationship, both labor productivity and real wages largely stagnated or declined slightly in the industry and transportation sectors.In the case of industry, international competition likely held down wages, while productivity suffered from ongoing processes of deindustrialization.By its nature, the transportation sector offers little room for major productivity gains, while the average wage may have fallen as a result of changing forms of employment relations (i.e., increasing levels of self-employment) and increasing relative costs of transport (Chahad;Cacciamali, 2005).These dynamics explain the moderate decline in relative wages for industry and transportation.
In a fourth and fi nal trend, the fi nancial and information services and public services sectors saw stable or declining levels of labor productivity, accompanied by increasing or stable real wages.Productivity declines in financial and information services were due largely to changes in the Brazilian banking system over the 1998-2004 period.Earnings increases in both sectors may have resulted from persistently high returns to education, growing demand for qualifi ed workers, and high levels of labor organization.As a result, the relative wage rose sharply for these sectors between 1996 and 2014.
It is important to note that all analyses above should be interpreted with caution, due to the diffi culty inherent in estimating absolute values of labor productivity for some sectors, particularly public services and real estate.Nevertheless, the values serve to elucidate temporal dynamics of labor productivity within (if not necessarily across) sectors, revealing essential patterns in the productivity-wage relationship.
Estimation of hierarchical wage models using pooled data assessed the main structural and individual determinants of real wages over the sample period.Growth in sector-and state-level labor productivity was signifi -cantly positively associated with growth in real wages for all economic sectors from 1996 to 2012.Elasticity between labor productivity and real wages was greatest for sectors where workers' earnings are often based directly on productivity (real estate, commerce), or where fi rms can easily measure employees' productivity (industry).Elasticities appear smaller in sectors where productivity is more diffi cult for fi rms to measure, or where there are high levels of minimum wage employment (agriculture, construction) or labor organization (fi nancial and information services).
In general, productivity's impact on wages was comparable to the impacts of institutional factors, particularly worker formalization and minimum wage.Formalization, which primarily impacts labor markets through the enforcement of a minimum wage-fl oor, exhibited the largest impacts on sectors with high proportions of minimum wage employment.Labor organization had varied effects on wage levels.In sectors with high levels of organization, increases in union-participation exhibited a signifi cantly positive association with wages.In contrast, increases in union-participation in less-organized sectors were negatively associated with wages, perhaps because union activity served to draw earnings away from the larger share of non-unionized workers.Nonetheless, unionization changed little over the sample period and exerted a relatively small impact on hourly wages.
Wage growth in line with the fi rst sectoral trend (observed in the agriculture and commerce sectors) may be the most sustainable in the long term, in the sense that increased earnings over the 1996 to 2014 period accompanied real gains in labor productivity.In contrast, rising relative wages in the fi nancial and information services and public services sectors highlight the capacity of labor organization, institutional protections, and skill-biased job polarization to decouple wages from productivity levels.In sum, institutional mechanisms display the capacity to substantially reallocate factor incomes toward workers, but these mechanisms face natural limitations if not accompanied by growth in labor productivity.Thus, sustainable future wage growth in Brazil will likely depend on positive interplays between market-driven productivity gains and continued institutional interventions.

APPENDIX C
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Table 2
Baseline regression estimates for the dependent variable ln of hourly wage 9 Age is employed throughout this analysis as a proxy for working experience.(continues on next page)

Table 3
Sectoral regression estimates for the dependent variable log of hourly wage 11 It is noteworthy that many skilled workers in sectors such as agriculture and construction gain qualifi cations through on-the-job training and apprenticeships rather than formal education.Thus, low estimates of returns to schooling in these sectors should not be interpreted as non-responsiveness of wages to skills or qualifi cations.(continues on next page) + = Signifi cant at 10%; * = Signifi cant at 5%; ** Signifi cant at 1%; *** Signifi ca at 0.1%.FE Indicates Control of Fixed Effects Related to Year or State Dummy Variables.