Distributional Effect of International Trade and Comparative
Advantage in Labor Markets∗
Rodrigo Adão
MIT
September 20, 2015
Abstract
This paper investigates the distributional consequences of international trade shocks in the context of the Brazilian labor market. First, I document a new set of facts about how differential exposure to commodity price shocks across educational groups and regions leads to differential outcomes in terms of sectoral employment and wages. Second, I show that such facts are qualitatively
consistent with a two-sector Roy model where worker heterogeneity regarding comparative and absolute advantage in sector-specific tasks determines the structure of employment and wages. Third,
I establish that the schedules of comparative and absolute advantage are nonparametrically identified from cross-regional variation in sectoral responses of employment and wages induced by
sector demand shocks. Lastly, I build on this result to structurally estimate the model in the sample
of Brazilian local labor markets. My structural estimates indicate that a 10% decrease in commodity prices causes counterfactual increases of 1.2% in the skill wage premium and of 5% in wage
dispersion.
∗ Author
contact information: [email protected]. I am extremely grateful to Daron Acemoglu, Arnaud Costinot and Dave
Donaldson for invaluable guidance and support. I also thank Pol Antras, David Autor, Arthur Braganca, Ariel Burstein,
Dejanir Silva as well as seminar participant at the MIT Labor Lunch and the MIT Macro-International Lunch. All errors are
my own.
1
1
Introduction
In an integrated world economy, shocks in a particular country have the potential to exert different
effects across different workers within another country located on the other side of the globe. For
example, if China implements a large-scale plan of infra-structure expansion, what is the effect on
workers employed in the mining industry relative to those in the auto industry within the U.S.? Alternatively, if Saudi Arabia aggressively reduces oil production, what is the effect on workers residing in
oil-rich regions relative to those in oil-poor regions within Brazil? More generally, if such shocks affect
the relative world price of various products, which workers stand to gain or lose within a country?
And how large are these distributional effects?
Such distributional concerns would not be relevant if homogeneous workers were able to perfectly
switch their sector of employment, their region of residence, and their level of skill. However, this is
unlikely to be true. Consider how the negative shock to the world oil supply caused by Saudi Arabia’s
policy affects different workers in Brazil. In order to expand production in response to higher oil
prices, firms compete for the residents of oil-rich coastal regions with the necessary skills to perform
the daily tasks in the offshore drilling industry, pushing their wages upwards. In contrast, workers
without these skills and those unable to move to the oil-rich areas are not directly affected by the
higher labor demand in the Brazilian oil industry. This simple example suggests that heterogeneous
workers are differentially exposed to international trade shocks due to their limited ability to respond
to changes in sectoral labor demand. In this article, I propose a unified empirical and theoretical
framework to investigate how differential exposure to sectoral shocks across educational groups and
regional markets leads to differential outcomes in terms of employment and wages in the context of
the Brazilian labor market.
The first contribution of the paper is to provide a new set of empirical facts that connect changes
in the international price of agriculture and mining commodities to changes in the Brazilian structure
of wages and employment between 1980 and 2010.1 First, I establish that aggregate movements in
Brazilian wage dispersion are negatively related to the evolution of international commodity prices
with the correlation being mainly driven by changes in wage differentials associated with workers’
level of education, sector of employment and region of residence. Second, I explore the variation in
the importance of different commodity-oriented industries in employment across educational groups
and regional markets to establish a causal relation between commodity prices and labor market outcomes. In each region, I measure exposure to international commodity price shocks for two worker
groups: High-School Graduates (HSG) and High-School Dropouts (HSD). The exposure of a groupregion pair is defined as the interaction between the change in commodities’ world prices and the
initial participation of corresponding commodities in the group’s labor payroll in the region. Armed
with this measure, I document that regional economies more exposed to positive price shocks experienced stronger employment expansions in the commodity sector among both HSG and HSD. This
employment expansion is associated with mixed responses in the commodity sector wage differential: it increases for HSG, but remains stable for HSD. Lastly, higher exposure to positive shocks is
1 Production of basic products constitutes an important part of the Brazilian economy. In 2010, agriculture and mining
industries represented 58.5% of total exports and 19.9% of total employment.
2
related to stronger growth in the group’s average wage which, in turn, translates into a reduction in
the HSG-HSD wage premium because of the relatively higher employment share in the commodity
sector among Brazilian HSD.
In order to explain this rich response pattern in labor market outcomes across groups and regions,
I propose a Two-Sector Roy Economy as in Heckman and Honore (1990). Within each group and region, individuals are heterogeneous with respect to a skill bundle that, ultimately, determines their
efficiency in the sector-specific tasks demanded by the commodity and the non-commodity sectors.
Conditional on the price of these sector-specific tasks, the heterogeneity in sector efficiency translates
into heterogeneity in potential sector wages, generating endogenous selection of an individual to the
sector yielding her the highest labor income. To be more precise, the sector employment decision
is intrinsically related to the worker’s comparative advantage defined as the worker’s efficiency in
the commodity sector task relative to her efficiency in the non-commodity sector task. Whenever the
worker’s comparative advantage is higher than the relative task price offered in the non-commodity
sector, the worker decides to be employed in the commodity sector. Alternatively, the worker’s wage,
given her employment decision, depends also on the worker’s absolute advantage defined as her efficiency in the task specific to the non-commodity sector.
In this environment, an individual’s exposure to sectoral demand shocks is centrally dependent on
her level of comparative advantage. To see this, consider a partial equilibrium comparative statics exercise in which a demand shock increases the task price in the commodity sector while not affecting the
task price in the non-commodity sector. The shock increases the wage of all commodity sector employees, but it only affects the wage of those non-commodity sector employees that decide to switch into
the commodity sector. These sector-switchers are the non-commodity sector employees whose level of
comparative advantage is similar to the pre-shock ratio of sector-specific task price. Accordingly, the
magnitude of the change in sector employment is determined by the amount of such workers in the
economy as controlled by the comparative advantage distribution. To the extent that sector-switchers
are distinct from sector-stayers in terms of sector-specific efficiency, the change in employment composition affects the average efficiency in the sector with the potential to attenuate or reinforce the direct
effect of the task price change. The magnitude of this compositional effect is directly related to the
difference between the average absolute advantage of sector-switchers and sector-stayers. In a group
and region, the average wage response combines the gains of workers employed in the two sectors,
depending on both the sector employment composition and the comparative advantage distribution.
In line with this discussion, I show that two functions are sufficient to evaluate the impact of sectoral shocks on the average and variance of the log-wage distribution in a group and region. Specifically, (i) the distribution of comparative advantage; and (ii) the average absolute advantage conditional on the level of comparative advantage. The second contribution of this paper is to provide a
novel result that establishes the nonparametric identification of such functions using cross-regional
variation in sector labor demand. For each worker group, I assume that regions are segmented labor
markets with parallel schedules of comparative and absolute advantage; yet, I allow regions to have
different skill shifters to accommodate regional variation in the level of sector-specific task supply.
Under this assumption, the schedules of comparative and absolute advantage are nonparametrically
identified, respectively, from responses of sector employment and average sector wage to changes in
3
sector-specific task prices induced by exogenous shocks to sector labor demand in the cross-section of
regions. The identification result is valid for an arbitrary number of observable worker groups and it
imposes no parametric restrictions on the skill distribution.
This nonparametric identification result constitutes a mapping between population moments and
the unknown schedules of comparative and absolute advantage. Its main importance relies on informing the source of variation in the data that uncovers the economic relation of interest without
additional restrictions than those implied by the theory.2 In practice, limited availability of exogenous
variation in the data imposes the need of auxiliary functional form assumptions. With this in mind,
the empirical application of the model builds on a parsimonious log-linear system with two structural
parameters that capture separately dispersion in comparative and absolute advantage. The proposed
system represents a strict generalization of the system implied by a skill distribution of the Frechet
family that entails a single parameter to control both comparative and absolute advantage.3
The combination of the nonparametric identification result and the auxiliary functional form assumption leads to an empirical strategy to estimate the structural parameters of comparative and
absolute advantage using Generalized Method of Moments (GMM). As in the reduced-form analysis, I consider HSG and HSD that are differentially exposed to international commodity price shocks
across Brazilian regional labor markets. The implementation of such strategy requires measurement
of sector-specific task prices for all groups and regions.4 An additional contribution of this paper is
to provide a new methodology to estimate task prices based on the Roy model’s predicted relation
between wage growth and initial sector employment across quantiles of the wage distribution for each
triple of group-region-period. This methodology can be easily implemented as a first-step regression
using repeated cross-section data on wage and employment at the individual level.
The structural estimation delivers two main insights. First, between-sector worker mobility is low
with the elasticity of relative sector employment to relative sector task price estimated to be around one
for both HSG and HSD. Second, the pattern of selection is qualitatively different in the two groups.
For HSD, an expansion in sector employment reduces average efficiency in both sectors, generating
the stability in sector wage premium documented in the reduced-form analysis. However, a sector
employment expansion among HSG is associated with a decrease in average efficiency in the commodity sector and an increase in the non-commodity, creating the strong responses in the sector wage
premium obtained in the reduced-form regressions.
I conclude the paper by applying the framework to answer one counterfactual question: “If commodity prices fall by 10%, how would Brazilian wage inequality be affected?" To answer this question,
I combine the estimated schedules of comparative and absolute advantage with the sectoral allocation
of workers across regions and groups in 2010. Since employment in the commodity sector is higher
among HSD residing in poor regions, the model predicts an increase in wage inequality following the
2 As
noted by Matzkin (2007), such identification results represent an important first step in the empirical analysis of almost any model as the credibility of empirical results would be significantly hindered if identification could only be achieved
under restrictive parametric assumptions.
3 The Frechet distribution has been the basis of numerous recent applications of the Roy Model — see e.g., Hsieh, Hurst,
Jones, and Klenow (2013); Burstein, Morales, and Vogel (2015); and Galle, Rodriguez-Clare, and Yi (2015).
4 Sector-specific task prices are not immediately available in survey datasets that only contain information on individual
labor income. In the model, observable labor income corresponds to the product of the unit task price and the individual’s
endowment of efficiency units.
4
shock. Precisely, the fall in commodity prices triggers a 1.2% increase in the HSG-HSD wage premium
that is accompanied by a 5% increase in the between-component of log-wage variance in the country.
The rest of the paper is organized as follows. Section 2 reviews the related literature. Section
3 presents the empirical facts about the adjustment of the Brazilian labor market following shocks
to the international price of agriculture and mining commodities. Section 4 presents the Two-Sector
Roy Economy and its implications for the equilibrium structure of employment and wages. Section
5 establishes the nonparametric identification of comparative and absolute advantage in a sample of
segmented labor markets. Section 6 implements the identification strategy for High-School Graduates
and High-School Dropouts differentially exposed to commodity price shocks across Brazilian regions.
Section 7 presents the counterfactual exercise that quantifies the effect of changes in commodity prices
on changes in Brazilian wage inequality. Section 8 offers some concluding remarks.
2
Related Literature
Research on the distributive effects of international trade has traditionally built upon the stark predictions regarding the changes in relative wages across worker groups provided by neoclassical models
of trade in Stolper and Samuelson (1941) and Jones (1975). Yet, empirical studies have failed to provide support for the predictions of these canonical models. For instance, a number of authors have
documented (i) movements in wage inequality correlated in both developed and developing countries
(Goldberg and Pavcnik, 2007), (ii) movements in the skill wage premium uncorrelated with changes
in the relative price of skill intensive products (Lawrence and Slaughter, 1993) while correlated with
changes in the skill intensity of production within industries (Bekman, Bound, and Machin, 1998), (iii)
and diminished between-sector responses in employment and wages following trade shocks (Wacziarg
and Wallack, 2004; and Goldberg and Pavcnik, 2007). Such evidence gave rise to a consensus that international trade shocks were, at best, secondary drivers of the changes in wage inequality between
the early-1980s and the mid-1990s.
However, the last decade has witnessed a renewed interest in the distributive effects of trade shocks
motivated by, on the one hand, recent changes in the wage distribution within several countries and, on
the other hand, the integration into the world economy of China and other developing countries.5 Due
to the disconnection between empirical evidence and predictions of neoclassical models, this emerging
literature has expanded the scope of analysis by examining broader dimensions of workers’ exposure
to international trade shocks. The literature has evolved on several directions.
More closely related to this paper is the recent reduced-form literature that establishes the impact
on labor market outcomes of heterogeneous exposure to import competition in terms of sector of employment (Autor, Dorn, Hanson, and Song, 2014), level of education (Dix-Carneiro and Kovak, 2015b),
and region of residence (Topalova, 2010; Kovak, 2013, Autor, Dorn, and Hanson, 2013; and Costa,
Garred, and Pessoa, 2014). In this paper, I build on their reduced-form strategy to provide new evi5 Acemoglu and Autor (2011) document a rich transformation pattern in the wage distribution of the U.S. and other OECD
countries. As noted by Hanson (2012), low- and middle-income countries experienced not only an increase in international
trade volumes but also pronounced changes in their profile of traded goods. In fact, emerging countries increased their
participation in world trade from 13.5% in 1990 to 29.6% in 2012.
5
dence regarding the effect of differential exposure to commodity price shocks on sectoral employment
and wages across educational groups and regional labor markets. This reduced-form evidence is then
combined with the structure of the Two-Sector Roy Economy to provide a methodology to quantitatively investigate the impact of trade shocks on the wage distribution.
Following the explosion of firm-level work in the field of international trade, another strand of
the literature has investigated the effect of international trade shocks on workers employed in different firms within-industries. These papers focus on how market integrations affects the within-industry
matching of workers to firms and the subsequent implications for wage inequality (see e.g. Verhoogen,
2008; Helpman, Itskhoki, and Redding, 2010; Frias, Kaplan, and Verhoogen, 2012; Helpman, Itskhoki,
Muendler, and Redding, 2015; and Burstein and Vogel, 2015). Another approach has been to investigate dynamic effects of international trade shocks, paying particular attention to the welfare costs
implied by the transitional dynamics in the reallocation of workers across sectors (Kambourov, 2009;
Artuç, Chaudhuri, and McLaren, 2010; Dix-Carneiro, 2014; and Dix-Carneiro and Kovak, 2015a) and,
more recently, regions (Caliendo, Dvorkin, and Parro, 2015).
This paper is closely related to the growing body of literature connecting changes in the economic
environment to self-selection of heterogeneous workers. On the theory side, recent papers demonstrate
the potential of the Roy model to generate a rich response pattern in wage inequality — see Ohnsorge
and Trefler (2007), Costinot and Vogel (2010), Acemoglu and Autor (2011), and, for a comprehensive
review, see Costinot and Vogel (2014). On the empirical side, the Roy model has been applied to investigate the consequences of selection to aggregate productivity and output (Lagakos and Waugh, 2013;
Hsieh, Hurst, Jones, and Klenow, 2013; and Young, 2014). Closer in spirit, two papers impose a Frechet
distribution of worker skills to quantify the portion of changes in between-group wage inequality associated with technological changes in the USA (Burstein, Morales, and Vogel, 2015) and import competition in Germany (Galle, Rodriguez-Clare, and Yi, 2015). I complement these recent quantitative
applications by providing a characterization of wage inequality responses in a generic Two-Sector Roy
Model where the skill distribution is completely unrestricted. The generality of the model sheds light
on the different roles played by comparative and absolute advantage in determining the evolution of
labor market outcomes both within- and between-groups. This increases the ability of the model to
capture features of the data that are meaningful in the study of distributional effects of trade shocks.6
Lastly, this paper is related to the large literature on selection models in labor markets. Inspired by
the seminal paper of Roy (1951), this literature investigates the consequences of self-selection based on
unobservable characteristics to observable components of labor income. Evidence in favor of selection
driven by multivariate skills is provided by Gibbons and Katz (1992), Neal (1995), Parent (2000), and
Gibbons, Katz, Lemieux, and Parent (2005). In order to establish the Roy model’s identification in a
single market, the most traditional approach was to impose parametric restrictions on the skill distribution as in Heckman and Sedlacek (1985). Yet, this approach relies heavily on the functional form
imposed on the skill distribution since Heckman and Honore (1990) show that the Roy model cannot
6 Although remaining tractable in the multiple sector setting, the Frechet distribution has features that are unappealing in
labor market analysis. Not only it requires a high degree of between-sector mobility but also it is unable to generate responses
in between-sector wage differentials. In contrast, these restrictive properties are not implied by the log-linear system used in
the empirical application of this paper.
6
be nonparametrically identified in a single cross-section of individuals. Following this negative result, they propose two main alternatives. The first assumes observable shifters in the location of the
skill distribution for individuals in the same market; the so called identification at infinity reviewed in
French and Taber (2011). The second relies on the variation of skill prices across markets with an identical skill distribution. In its majority, the selection literature builds on the first approach to identify
hedonic wage regressions (e.g., Mulligan and Rubinstein, 2008); alternatively, this paper builds upon
the second approach to investigate distributional consequences of sectoral labor demand shocks.
To this end, I provide a nonparametric identification result that complements the elegant result of
Heckman and Honore (1990). By allowing for regional skill shifters, I introduce task supply shocks that
affect sector employment and sector wages across markets while endogenously correlated with sectorspecific task prices in equilibrium. For this reason, identification requires an instrumental variable
that generates exogenous variation in sector-specific task prices. Accordingly, the assumption in this
paper is weaker than the existence of a single skill distributions in all market assumed by Heckman
and Honore (1990) to establish their nonparametric identification result. In this sense, I provide a
generalization of Heckman and Honore’s (1990) result when regions are subject to parallel shocks in
the skill distribution.
3
3.1
International Commodity Prices and the Brazilian Labor Market
Data and Background
Brazil, as primarily an exporter of basic commodities, is particularly exposed to shocks in the world
price of agricultural and mining goods. Such exposure pattern is captured by the relative price of
six commodity categories: Grains, Livestock, Soft Agriculture, Metals, Precious Metals, and Energy.
Together, these commodity groups account for a large share of Brazilian exports, representing 53.8%
of total exports in 1980 and 60.4% in 2012. As described in Appendix A, I construct price indices
for each category using data on commodity transactions in the main exchange markets of the United
States between 1980 and 2012. To replicate relative prices faced by producers in Brazil, international
commodity prices are converted to Brazilian currency and deflated by the Brazilian consumer price
index.
The analysis of labor market outcomes rely on wage and employment data from the Brazilian
Census performed by the Brazilian Institute of Geography and Statistics (IBGE) for 1980, 1991, 2000
and 2010. To focus on individuals with strong labor force attachment mainly affected by marketoriented forces, I consider a benchmark sample of full-time white male employed individuals aged
16-64.7 Individuals are divided into two observable groups: High-School Dropouts (HSD) and HighSchool Graduates (HSG). These two groups reflect the relevant margin of education in Brazil; among
male white workers, the high-school graduation rate was 16.0% in 1980 and 51.4% in 2010.
7 I restrict the benchmark sample to include only white and male individuals because of the strong declines in gender and
race wage differential between 1995 and 2010; see e.g. Ferreira, Firpo, and Messina (2014). The model presented below is not
intended to speak directly to the behavior of these components of the wage structure and, therefore, I exclude their behavior
from the analysis in this section. Appendix B provides robustness exercises including female and non-white individuals,
indicating that all results are essentially the same when these additional worker groups are considered.
7
Figure 1: International Commodity Prices and Wage Dispersion in Brazil, 1980-2010
1.2
2.5
1.0
2.0
0.8
Variance of log wages
Log of deflated international commodity prices (BRL)
International Relative Commodity Prices, 1980-2012
3.0
1.5
1.0
0.5
Wage Dispersion in Brazil, 1980-2010
0.6
0.4
0.2
0.0
0.0
1980
1985
1990
1995
2000
Commodity Price Index
Grains (corn, soybeans, wheat)
Soft (coffee, cacoa, sugar, and others)
Livestock (cattle, hogs, and others)
2005
2010
1980
1991
Residual
Energy (crude oil)
Metals (copper, lead, steel, tin, zinc)
Precious Metals (gold and silver)
2000
2010
Between
(education, sector, region, experience)
Note. Left panel: six-month moving average of log international product price converted to Brazilian currency and deflated by the Brazilian
consumer price index (Sept-1994 = 1). Right panel: variance of log wages among male white full-time workers in the Brazilian Census
of 1980, 1991, 2000 and 2010. Wage decomposition implied by the regression of log real wage on a full set of dummies for high school
graduation, employment in the commodity sector, and microregion of residence, and years of experience (0-39yrs). Details in Appendix A.
Throughout the analysis, I classify individuals into a sector and a regional labor market. According
to their self-reported industry of employment, I map workers either to the commodity sector or to the
non-commodity sector. Industries specialized in the production of agricultural and mining products
are included in the commodity sector, covering 13.9% of the national labor income in 1980 and 12.9% in
2010. All manufacturing and service industries are included in the non-commodity sector. In addition,
I allocate individuals to a regional labor market based on their microregion of residence. Between
1991 and 2010, the Census contains a balanced panel of 558 microregions where each microregion
corresponds to a set of economically integrated municipalities. In the 1980 Census, only a subset of
these microregions can be constructed due to changes in administrative boundaries of municipalities
and states between 1980 and 1991. Appendix A discusses details on the construction and measurement
of labor market outcomes.8
Let us now turn to the aggregate trends in international commodity prices and Brazilian wage
dispersion presented respectively on the left and right panels of Figure 1. Between 1980 and 2012, the
evolution of relative commodity prices is U-shaped: the strong price decline of the 1980s was followed
by a recovery of equivalent magnitude from the late 1990s until 2012. Notice that, while the price
drop was homogeneous across commodity categories, the price recovery exhibited great betweencategory heterogeneity. In opposite direction, wage dispersion, after increasing in the 1980s, began
a compression process in the 1990s that accelerated in the 2000s. This movement in wage dispersion
can be decomposed into observable and residual components by regressing log wages on a full set
of dummies for years of experience, level of education, sector of employment and microregion of
residence. The decomposition indicates that observable worker attributes account for a sizeable part
of the wage dispersion movement — i.e., 44.5% of the change in 1980-1991 and 78.1% in 1991-2010.
8 Table A1 presents the allocation of industries to sectors in each year of the Census. Also, Appendix A describes both the
construction of microregions in the 1980 Census and the consequences of the changing municipality boundaries to the panel
of microregions across years.
8
Figure 2: Components of Wage Dispersion in Brazil, 1980-2010
Return to Observable Worker Characteristics
1.2
0.4
1.0
Wage Differentials
Variance of log wages
Decomposition of Between-Component of Wage Dispersion
0.5
0.3
0.2
0.8
0.6
0.4
0.1
0.2
0.0
1980
HSG Wage Premium
1991
Region Wage Premium
2000
Sector Wage Premium
1980
2010
HSG Wage Premium
Covariance
1991
2000
P90/P10 Region Wage Premium
2010
Sector Wage Premium
Note. Left panel: decomposition of the between-component of the log-wage variance associated with the set of dummies for high school
graduation, employment in the commodity sector, and microregion of residence. Right panel: estimated return to observable worker attributes implied by the log-wage regression. The dispersion in the 558 regional wage differentials is represented by the difference between
90th and 10th percentiles of the estimated regional fixed effects.
To investigate further the negative aggregate correlation between commodity prices and the betweencomponent of wage dispersion, Figure 2 presents the full decomposition of the portion of log-wage
variance associated with worker’s affiliation in terms of education-sector-region. The left panel indicates that the substantial contribution of this component to the 1991-2010 decline in wage dispersion is
distributed across all its terms: 34.0% is related to the education dummy, 10.7% to the sector dummy,
23.9% to regional dummies, and 31.4% to the covariance of these terms. Importantly, the right panel
shows that this fall in log-wage variance was driven by strong reductions in the differential return to
observable worker attributes.
This discussion can be summarized as follows.
Fact 1. Between 1980 and 2010, international commodity prices and Brazilian wage dispersion are negatively
correlated. A large fraction of the change in wage dispersion in the period is related to observable worker attributes with substantial movements in wage differentials associated with the worker’s level of education, sector
of employment and region of residence.
3.2
Exposure to Commodity Price Shocks and Labor Market Outcomes
The similarity between the aggregate trends in wage dispersion and commodity prices is suggestive
of their interconnection. Yet, this correlation is potentially driven by confounding shocks afflicting
the Brazilian economy in the period. This section addresses the causal effect of commodity prices on
labor outcomes separately for High-School Dropouts and High-School Graduates. To this extent, I
treat microregions as local subeconomies subject to differential price shocks according to their initial
profiles of industry specialization. By comparing worker groups in regions differentially exposed to
commodity price shocks, the reduced-form exercise sheds light on the adjustment pattern of wages
and employment following sectoral labor demand shifts. In the exercise, I consider a balanced panel
9
of 518 microregions in the years of 1991, 2000 and 2010.9
3.2.1
Heterogeneity in Exposure to Commodity Price Shocks
To capture heterogeneous exposure to fluctuations in international commodity prices, I construct a
Bartik-Instrument for each microregion and group. Specifically, the shock exposure corresponds to the
interaction between the commodity participation in the group-microregion wage bill on the initial year
and the change in the international commodity price on the period. Precisely, the exposure of group g
in microregion r to the commodity price shock is given by
∆Zg,r,t =
∑
φg,r ( j) · ∆ ln pt ( j)
(1)
j∈J C
where ∆ ln pt ( j) is the log-change in the international price of product j between years t − 1 and t; and
φg,r ( j) is the share of industry j in total labor payments of the commodity sector to individuals of group
g in microregion r on the initial year of 1991.
Intuitively, expression (1) entails a stronger response in the regional demand for worker groups
specialized in the production of commodities experiencing stronger international price gains.10 Consequently, ∆Zg,r,t embeds two dimensions of exposure heterogeneity. First, cross-regional variation
in initial industry composition creates exposure heterogeneity for individuals of the same group that
reside in different microregions. Second, cross-industry variation in skill intensity generates exposure
heterogeneity between groups in the same region. As shown in Table A4, these two variation sources
are important in Brazil, giving rise to great exposure heterogeneity across both regions and groups.
Figure 3 exhibits the pattern of spatial exposure to the commodity price shock among microregions for
HSG (left panel) and HSD (right panel). Notice that shock exposure differs significantly for the two
groups with a cross-region correlation of only .493. Moreover, Figure 3 indicates that HSG tend to have
lower shock exposure than HSD — specifically, the median exposure is 4.7 log-points for HSG and 6.3
log-points for HSD.
9I
restrict the sample to only include those microregions with positive employment in the commodity sector for all years
and groups. As a result, the final sample contains 518 microregions that represented 98.4% of the country’s population on
1991. As discussed in Appendix A, there are two reasons to exclude the 1980-1991 period from the baseline sample. First,
changing municipality borders only allows the construction of a subset of the microregions included in the 1991-2010 Censuses. Second, the 1980-1991 period was marked by severe economic turbulences in Brazil that have the potential to hinder
the connection between international and domestic relative commodity prices — these events include hyperinflationary
sprouts, suspension of foreign currency convertibility, and the adoption of restrictive internal controls on prices and wages.
Nevertheless, Appendix B attests that similar results are obtained with a restricted sample of microregions spanning the
entire 1980-2010 period.
10 The initial industry composition is indicative, as in Costinot (2009), of the region’s comparative advantage in production,
reflecting local availability of natural resources like soil fertility and oil reserves. Accordingly, the intuition behind the labor
demand response in expression (1) follows directly from the comparative static exercises in Costinot and Vogel (2010, 2014).
Alternatively, Kovak (2013) connects production specialization to comparative advantage implied by the local endowment
of industry-specific factors, deriving an expression similar to (1) for the response of regional labor demand to small price
shocks. Recently, reduced-form strategies based on related measures of local exposure to trade shocks have become popular
in the literature; see e.g. Topalova (2010), Kovak (2013), and Autor, Dorn, and Hanson (2013).
10
Figure 3: Heterogeneity in Exposure to Commodity Price Shock, 1991-2010
3.2.2
Reduced-Form Evidence
In order to investigate the effect of exposure to the commodity price shock on labor market outcomes,
I consider the following reduced-form specification:
∆Yg,r,t = β g · ∆Zg,r,t + Xg,r,t γg + v g,r,t
(2)
where ∆Yg,r,t is the change in a labor market outcome for individuals of group g in microregion r
between years t − 1 and t; and Xg,r,t is a control vector of group-microregion characteristics potentially correlated with the exposure measure. In the baseline specification, the control vector includes
macroregion-period dummies, the initial share of group labor income in the commodity sector, and the
initial share of workers earnings at most the federal minimum wage. Also, microregions are weighted
by their share in the national population of 1991 and standard errors are clustered by microregion to
account for serially correlated errors.
Conditional on the initial share of group labor income in the commodity sector, specification (2)
relies exclusively on the variation in relative product prices within the commodity sector. Accordingly,
the causal interpretation of model (2) requires that shocks in Brazilian regions are not large enough
to affect the world price of basic commodities. A requirement especially plausible given the strong
growth in Chinese imports of agriculture and mining products during the period; arguably, an exoge-
11
nous demand shock to relative prices of raw materials.11
Sectoral Wages and Employment. Columns (1)-(3) of Table 1 estimate equation (2) with the dependent
variable being the commodity sector employment share of HSG in Panel A and HSD in Panel B. The
positive significant coefficients in column (1) indicate that, for both HSG and HSD, higher commodity
prices induce workers to reallocate from the non-commodity to the commodity sector. However, estimates suggest very limited between-sector mobility: a 10% increase in commodity prices cause the
commodity sector employment share to increase by .31 p.p. for HSG and .77 p.p. for HSD. Compared
to a region in the 10th percentile of shock exposure, these estimates imply that a region in the 90th
percentile had a differential commodity sector expansion of 0.6 p.p. for HSG and 1.0 p.p. for HSD.
To test robustness and potentially eliminate confounding effects, I augment the model with period
dummies interacted with a set of initial labor market conditions in column (2) and a quadratic polynomial of the initial commodity sector size in column (3). These controls represent period-specific effects
projected on initial region characteristics, capturing for example effects related to the introduction of
cash transfer programs and secular differences in sector productivity growth. Although these additional controls absorb a large part of the cross-section variation in sector employment change, they
only strengthen estimated coefficients.
Turning to the impact of commodity prices on sectoral wages, columns (4)-(6) estimate model (2)
with the commodity sector average wage premium as dependent variable. In column (4), the two
groups exhibit different qualitative responses. The price shock triggers a significant positive response
Table 1: Exposure to Commodity Price Shocks and Sector Employment and Wages
Dependent Variable:
Change in Commodity Sector
Employment Share
Change in Commodity Sector
Average Log Wage Premium
(1)
(2)
(3)
(4)
(5)
(6)
0.031**
(0.009)
0.038**
(0.010)
0.038**
(0.010)
0.298**
(0.083)
0.437**
(0.095)
0.416**
(0.098)
0.283
0.343
0.405
0.143
0.198
0.220
Commodity price shock
0.077*
(0.031)
0.101**
(0.029)
0.099**
(0.029)
-0.110
(0.144)
0.061
(0.161)
0.059
(0.161)
R2
0.508
1036
0.557
1036
0.559
1036
0.160
1036
0.218
1036
0.218
1036
Initial labor market conditions x period dummies
No
Yes
Yes
No
Yes
Yes
Initial commodity sector size controls x period dummies
No
No
Yes
No
No
Yes
A. High-School Graduates
Commodity price shock
R2
B. High-School Dropouts
Baseline Controls
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991. All models include
ten macroregion-period dummies and the following baseline controls on 1991: share of group labor income in the commodity sector and share of workers earnings at most the
federal minimum wage. Labor market conditions: cubic of per-capita income, quadratic of share of white individuals, share of employed individuals, share of individuals in urban
areas, share of workers earnings at most the federal minimum wage, share of social security dependents (only HSD). Commodity sector size controls: quadratic polynomial of
commodity sector share in group labor income. Standard Errors clustered by microregion. ** p<0.01, * p<0.05
11 Between 1992 and 2010, the average annual growth rate of Chinese imports was 17.2% for all products, 16.2% for
Agriculture, and 28.3% for Mining. Over the period, Hanson (2012) provides a careful discussion of the transformation in
the profile of international trade of emerging economies and, in special, China. To the extent that this transformation was
mainly driven by internal changes in the production structure of China, this large demand shock represented an exogenous
impulse to world commodity prices in the period. In Table B4 of Appendix B, I investigate the sensitivity of results when the
exposure to commodity price shocks is instrumented with the exposure to Chinese commodity imports growth.
12
of the commodity sector wage differential for HSG; in contrast, there is a nonsignificant response for
HSD. These conclusions are robust to the inclusion of additional controls in columns (5) and (6).
In light of the results in Table 1, I state the following conclusion.
Fact 2. Exposure to commodity price shocks is positively related to the commodity sector employment of both
HSG and HSD. In addition, shock exposure is ambiguously related to the commodity sector wage premium, exhibiting a positive relation for HSG and a nonsignificant relation for HSD.
Group Wages. Table 2 investigates the consequences of the commodity price shock to the average
log wage of HSG in Panel A and HSD in Panel B. Columns (1)-(3) indicate that exposure to higher
commodity prices is associated with higher average wages for the two worker groups. In columns
(4)-(6), I access the robustness of this relation to the use of an alternative exposure measure based on
the interaction of ∆Zg,r,t with the initial commodity sector size. As in Autor, Dorn, and Hanson (2013),
this alternative measure explicitly incorporates differences in the overall sectoral allocation of workers
across microregions and groups.12 Again, estimates indicate a positive response of average wages to
higher commodity prices. This result suggests that, despite the mixed wage response at the sector
level, the commodity price shock has a positive impact on the microregion’s labor demand, putting
upward pressure on wages of HSG and HSD.
Results in Table 2 imply a sizeable effect of the commodity price shock on the behavior of region
Table 2: Exposure to Commodity Price Shocks and Group Wages
Change in Average Log Wage
Dependent Variable:
(1)
(2)
(3)
0.296**
(0.069)
0.283**
(0.066)
0.288**
(0.064)
(4)
(5)
(6)
0.694*
(0.342)
0.510*
(0.260)
0.636*
(0.292)
0.374
0.415
0.422
0.628**
(0.204)
0.557**
(0.208)
0.558*
(0.221)
A. High-School Graduates
Commodity price shock
Commodity sector size x Commodity price shock
R2
0.399
0.433
0.440
0.271**
(0.103)
0.280**
(0.097)
0.268**
(0.099)
B. High-School Dropouts
Commodity price shock
Commodity sector size x Commodity price shock
R2
0.555
0.624
0.636
0.552
1036
0.621
1036
0.634
1036
Initial labor market conditions x period dummies
No
Yes
Yes
No
Yes
Yes
Initial commodity sector size controls x period dummies
No
No
Yes
No
No
Yes
Baseline Controls
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991 and include ten
macroregion-period dummies. Baseline controls as in Table 1. Standard Errors clustered by microregion. ** p<0.01, * p<0.05
12 In this case, exposure to the price shock of each commodity is proportional to its overall participation in the regional
wage bill of the worker group. In the model presented below, the response of group average wage is proportional to the
overall sector allocation of group workers, being more closely related to the alternative exposure measure. In contrast, the
model predicts that sectoral wages and employment within each group respond to sectoral demand shocks, being more
closely related to ∆Zg,r,t . In Table B6, I attest that qualitative conclusions of the sector-level analysis remain valid if the
alternative exposure measure is considered.
13
and education wage gaps in Brazil. To see this, consider the differential wage growth of a microregion
in the 90th percentile of shock exposure relative to another in the 10th percentile. Estimates in column
(4) predict that this differential growth is 1.9 p.p. for HSG and 4.2 p.p. for HSD. Higher relative wage
gains for HSD follow from their higher exposure to commodity price shocks and, in this case, translate
into a 2.2 p.p. reduction in the high-school wage premium.
Fact 3. Exposure to commodity price shocks is positively related to the average wage of both HSG and HSD. Estimated coefficients suggest a sizeable impact of commodity prices on educational and regional wage differentials.
Sensitivity Analysis. Having established Facts 2 and 3, Appendix B turns to an empirical investigation
of the robustness of these results. In particular, I obtain similar conclusions if the baseline specification is extended to include additional sector composition controls, microregion-specific time trends,
additional periods and additional worker groups (Tables B1-B3). To address concerns regarding the
effect of supply conditions in Brazil on world commodity prices, I also attest that similar results are
obtained when the exposure to commodity price shocks is instrumented with the exposure to Chinese
commodity imports growth in 1991-2010 (Table B4). Lastly, I show that exposure to commodity price
shocks is not related to the change in the labor supply of both native and migrant workers (Table B5).
Following an increase in the world price of commodities, Facts 2 and 3 indicate that the adjustment
pattern of wages and employment depends on the shock exposure across regions and groups. To be
more precise, regional economies more exposed to the price shock experience a stronger employment
expansion in the commodity sector for both HSG and HSD. Although shock exposure is related an
increase in the average wage at the group level, there are mixed within-group responses in sector average wages. In the next section, I propose a Two-Sector Roy Economy that, following commodity
price shocks, generates such adjustment pattern through the self-selection of heterogeneous individuals to sectors. This structural framework delivers a methodology to evaluate the impact of commodity
price shocks on the wage distribution, allowing a quantitative investigation of the aggregate relation
between the Brazilian wage structure and the international commodity prices emphasized in Fact 1.
4
4.1
Two-Sector Roy Economy
Environment
Consider a segmented labor market populated by workers of multiple groups, g, that self-select into
either the commodity sector (k = C) or the non-commodity sector (k = N). In sector k, production
depends on the sum of sector-specific tasks performed by all sector employees of a particular worker
group. Following a long tradition in Roy-like models, assume that workers can only be employed in
a single sector. Employees in each sector are paid a salary in exchange for each completed unit of the
sector-specific task assigned to their group. Denote wkg as the unit price in sector k of the task performed
by workers of group g. This notation allows, but does not require, sector-specific task prices to differ
14
across groups.13
Within each group, there is a continuum of heterogeneous individuals indexed by i ∈ I g . Individual i is endowed with a bivariate skill vector, ( TgC (i ), TgN (i )), that determines her effective supply of
sector-specific tasks. Specifically, individual i if employed in sector k performs Tgk (i ) units of the task
specific to sector k and earns a wage of wkg Tgk (i ). The analysis is simplified by working with a log-linear
transformation of earnings so that the potential log-wage of individual i of group g in sector k is given
by ω gk + ln Tgk (i ) where ω gk ≡ ln wkg .
Assume that individuals choose to be employed in the sector that gives them the highest wage.14
Accordingly, individual i self-selects into sector K g (i ) where
n
K g (i ) = arg max ω gC + ln TgC (i );
o
ω gN + ln TgN (i ) .
(3)
To characterize the structure of employment and wages in the Two-Sector Roy Economy, let us
define individual i’s comparative advantage as s g (i ) ≡ ln( TgC (i )/TgN (i )), and absolute advantage as
a g (i ) ≡ ln TgN (i ). In a given group, suppose individuals independently draw their skill vector from a
common bivariate distribution such that
s g (i ) ∼ Fg (s)
and
{ a g (i )|s g (i ) = s} ∼ Hg ( a|s)
(4)
where α g (q) ≡ ( Fg )−1 (q) is the quantile function of comparative advantage.
The skill distribution in (4) implies that, in a particular quantile q ∈ [0, 1], there is a set of individuals in group g whose level of comparative advantage is α g (q). Among these individuals, there is a
conditional distribution of absolute advantage, Hg a|α g (q) , with average and variance respectively
denoted by A g (q) ≡ E a g (i )|s g (i ) = α g (q) and Vg (q) ≡ Var a g (i )|s g (i ) = α g (q) .
4.2
Sectoral Wages and Employment: Comparative and Absolute Advantage
The most direct implication of the preference structure in (3) is the endogenous sorting of workers to
sectors. Due to the heterogeneity in sector-specific task efficiency of workers, this endogenous sorting
decision has strong implications for the pattern of employment and wages in the two sectors of the
economy. To analyze such pattern, I consider a graphical representation of the economy in terms of
quantiles of the comparative advantage distribution.
Figure 4 exhibits the average potential log wage in each sector for individuals distributed across different comparative advantage quantiles. If employed in the non-commodity sector, workers in quantile
q perform, on average, A g (q) units of the sector-specific task, receiving in return an average potential
13 This particular formulation follows closely the environment in the extensive literature inspired by the seminal work of
Roy (1951); see e.g. Heckman and Sedlacek (1985), Heckman and Honore (1990), and, more recently, Ohnsorge and Trefler
(2007), Lagakos and Waugh (2013) and Young (2014). In Appendix C, I provide a detailed description of the production and
market structures that generate such sector-specific task prices in general equilibrium.
14 Equivalently, one could assume that individuals derive utility solely from the optimal consumption bundle acquired
with their labor income. By introducing within-group heterogeneity entirely on sector-specific labor efficiency, the distributive impact of a trade shock is completely captured by the behavior of observable labor income. In this environment, identical
homothetic preferences imply that changes in the welfare distribution are directly related to changes in the wage distribution. Notice that this preference structure abstracts from private employment benefits and mobility costs. In Appendix D.3,
I explore an extension that incorporates such features into the model.
15
log wage of ȲgN (q) = ω gN + A g (q). Alternatively, if employed in the commodity sector, they perform
an average of α g (q) + A g (q) units of the sector-specific task and earn an average potential log wage
of ȲgC (q) = ω gC + α g (q) + A g (q). In a particular quantile, the unique source of dispersion in potential
sector wages is the dispersion of absolute advantage, Vg (q) — illustrated by the hump-shaped curves
in quantile q1 .15
In Figure 4, A g (q) is strictly decreasing in q, implying that individuals in high quantiles of comparative advantage have, on average, lower levels of absolute advantage. However, the skill distribution
in (4) does not impose any restriction on the relation between comparative and absolute advantage.
Consequently, the behavior of A g (q) is free to change in an arbitrary way across comparative advantage quantiles. Figure 5 illustrates the other extreme case in which A g (q) is strictly increasing in q. As
discussed below, these two cases have very distinct implications for the adjustment of sector average
wages following sectoral demand shocks.
q1
q
q
1
1
Figure 4: Case I - A g (q) decreasing.
Figure 5: Case II - A g (q) increasing.
Sector Employment and Comparative Advantage. The preference structure in (3) implies that individuals self-select into the sector yielding the highest wage. For all individuals in a given quantile
of comparative advantage, the sectoral employment choice can be determined from the comparison
between the two sectoral curves of average potential wage in Figures 4-5.16 In high quantiles of comparative advantage, the relatively higher efficiency in the commodity sector task yields a relatively
higher wage in that sector, implying self-selection into the commodity sector. In contrast, individuals
15 The
two potential wage curves exhibit the single-crossing property because, by construction, α g (q) is increasing in q.
Hence, they cross at most once. To simplify the analysis, I assume that task prices are such that these curves cross at least
once. This is the case if Fg (.) has full support on R so that limq→0 α g (q) = −∞ and limq→1 α g (q) = ∞. In general equilibrium,
this is also implied by restrictions on the production technology guaranteeing that, in both sectors, the marginal product of
a task unit goes to infinity as the total task quantity goes to zero.
16 To formalize this claim, consider individual i with comparative advantage s (i ) = α ( q ). This worker has a potential
g
g
log wage of ω gN + a g (i ) in the non-commodity sector and ω gC + α g (q) + a g,m (i ) in the commodity sector. For this individual,
potential sector wages correspond to vertical shifts of those of a worker with the same level of comparative advantage but a
different level of absolute advantage. Consequently, the sectoral choice of individual i with s g (i ) = α g (q) is identical to that
of a hypothetical individual i0 with s g (i0 ) = α g (q) and a g (i0 ) = A g (q).
16
in low quantiles of comparative advantage obtain a relatively lower wage in the commodity sector,
finding it optimal to self-select into the non-commodity sector. In equilibrium, the sector employment
composition is determined by marginal individuals with comparative advantage equal to the relative
task price, ω gN − ω gC . These marginal workers have exactly the same potential wage in the two sectors,
being indifferent between them.
Formally, individuals in quantiles of comparative advantage Q gN ≡ {q : q < l gN } are employed in
the non-commodity sector and those in quantiles QCg ≡ {q : q ≥ l gN } are employed in the commodity
sector where the employment share in the non-commodity sector, l gN , is determined by the unique
intersection of the sectoral schedules of average potential wage,
ω gN − ω gC = α g l gN .
(5)
This discussion highlights the central feature of the Two-Sector Roy Economy: workers are not readily
substitutable between sectors. Because of the efficiency differential in sector-specific tasks, workers do
not switch sectors to arbitrage the differential in sector-specific task prices in equilibrium. The sector
employment composition in (5) reflects this heterogeneity in sector efficiency, depending on the shape
of the schedule of comparative advantage, α g (.).
Sector Average Wage and Average Sector-Specific Efficiency. The endogenous selection of individuals
to sectors implies that the sector average wage embodies only the average labor income of individuals
employed in the sector: Ȳgk = E[Ȳgk (q)|q ∈ Qkg ]. As a result, the average log wage in the non-commodity
sector is given by
ȲgN = ω gN + Ā gN (l gN )
s.t.
Ā gN (l ) ≡
1
l
ˆ
l
A g (q) dq ;
(6)
0
and the average log wage in the commodity sector is
ȲgC
=
ω gC
+
ĀCg (l gN )
s.t.
ĀCg (l )
1
≡
1−l
ˆ
1
[α g (q) + A g (q)] dq.
(7)
l
In expressions (6)-(7), there are two determinants of the average wage in each sector. First, the
sector-specific task price, ω gk , that directly affects the wage of sector employees. Second, the sector
employment composition, l gN , that affects the average efficiency in the sector-specific task through the
term Ākg l gN . Because of the heterogeneity in average sector-specific efficiency illustrated in Figures
4-5, the range of quantiles allocated to each sector has a direct effect over that sector’s average wage.
In other words, the pattern of variation in average sector-specific task efficiency across comparative
advantage quantiles —A g (.) in the non-commodity sector and α g (.) + A g (.) in the commodity sector—
determines the average efficiency of sector employees summarized in the shape of Ākg (.).
4.3
Average and Variance of Group Log Wages
In the Two-Sector Roy Economy, average and variance of the log-wage distribution of workers in group
g are determined by their sectoral allocation decision, Qkg , as well as their schedules of comparative
and absolute advantage, α g (q) and A g (q). By construction, the average wage in group g is Ȳg =
17
l gN · ȲgN + l gC · ȲgC and, therefore, expressions (6)-(7) imply
ˆ
Ȳg =
where e g ≡
´1
0
ω gC
· l gC
+ ω gN
· l gN
1
+
l gN
α g (q)dq + e g
(8)
A g (q)dq.
Since individuals are not readily substitutable between sectors, they are solely exposed to the task
price in their sector of employment. As a result, the average wage in (8) depends on the sector employment composition as captured by ω gC · l gC + ω gN · l gN . The other two terms reflect the average efficiency
of workers in the two sector-specific tasks. While the term e g captures the average absolute advantage
´1
that affects efficiency in both sectors, the term l N α g (q)dq captures the comparative advantage that
g
affects only the efficiency of commodity sector employees.
Among individuals of group g, there are two sources of wage dispersion: the between-sector average wage differential and within-sector wage dispersion. To be more precise, the law of total variance
implies that
2
Vg = l gN l gC · ȲgC − ȲgN + l gN · VgN + l gC · VgC
(9)
where Vgk corresponds to the log-wage variance of individuals employed in sector k. As indicated in
Figures 4-5, this within-sector wage variance combines the variation in average wage of individuals
distributed across comparative advantage quantiles employed in the sector, Yg (q), and the variation in
absolute advantage in any particular comparative advantage quantile, Vg (q). Consequently, the logwage variance in sector k is Vgk = E[Vg (q)|q ∈ Qkg ] + Var [Ȳgk (q)|q ∈ Qkg ]. By applying this expression
into (9), the log-wage variance in group g can be written as
i
i
h
2
h
Vg = l gN l gC · ȲgC − ȲgN + l gN · Var A g (q)q < l gN + l gC · Var α g (q) + A g (q)q ≥ l gN + νg
(10)
where the variance is taken in the conditional uniform distribution of quantiles allocated to each sec´1
tor. In equation (10), the term νg ≡ 0 Vg (q) dq captures the portion of wage dispersion related to
the absolute advantage dispersion within comparative advantage quantiles, being independent of the
endogenous worker sorting for its symmetric effects on potential wages in the two sectors.
4.4
Comparative Statics: Sector Demand Shocks
To better understand the mechanics of the Two-Sector Roy Economy, let us analyze the adjustment of
labor market outcomes following a positive shock to task demand in the commodity sector. To simplify
the analysis, I consider a demand-driven increase in ω gC while holding constant both ω gN and the skill
distribution. With this exercise, I show how the model is capable of rationalizing the response of the
Brazilian labor market to the commodity price shock (i.e., Facts 1-3 in Section 3).
As illustrated in Figures 6-7, the increase in the commodity sector task price implies an upward shift
in the commodity sector curve of potential average wage. Following the shock, individuals initially
indifferent between the two sectors find it optimal to be employed in the commodity sector, reducing
the employment share in the non-commodity sector by ∆l gN < 0. The magnitude of the between18
sector employment flow is directly related to the slope of the comparative advantage schedule: for the
same variation in the relative task price, the sector employment response is smaller if the slope of the
comparative advantage schedule, α g (.), is higher. This is immediately implied by equation (5):
∆
h
ω gN
− ω gC
i
ˆ
l gN +∆l gN
=
l gN
∂α g (u)
du.
∂q
(11)
q
q
1
1
Figure 6: Positive selection into non-commodity Figure 7: Negative selection into non-commodity
sector.
sector.
Although the non-commodity sector task price is constant, the implied outflow of non-commodity
sector employees affects the sector’s employment composition and, consequently, the sector’s average
wage. To the extent that the absolute advantage of sector-switchers differs from that of sector-stayers,
the change in sector employment affects the sector average efficiency. If A g (q) is decreasing as illustrated in Figure 6, then sector-stayers have a higher level of absolute advantage than sector-switchers
(i.e., blue area). In this case, the outflow of workers leaves the non-commodity sector with employees
whose average absolute advantage is relatively higher, raising the average wage in the sector. However, this is not the only possibility. In Figure 7, A g (q) is increasing so that the outflow of workers
lowers the average wage in the non-commodity sector. To formalize this discussion, notice that expression (6) yields
ˆ
∆ȲgN − ∆ω gN =
l gN +∆l gN
l gN
∂ Ā gN (u)
∂q
ˆ
l gN +∆l gN
du =
l gN
1
A g (u) − Ā gN (u) du.
u
(12)
By expression (12), the implied response in the non-commodity sector average efficiency, ∆ȲgN −
∆ω gN , depends on the slope of Ā gN (.) that is directly related to the difference between the absolute
advantage of sector-switchers, A g (l gN ), and sector-stayers, Ā gN (l gN ). Following the reduction in noncommodity sector employment, this compositional effect has an ambiguous sign; for example, it is
positive if A g (.) is decreasing (i.e., Figure 6) or negative if A g (.) is increasing (i.e., Figure 7).
19
In the commodity sector, the shock has two effects on the average wage. There is an increase in
the log-wage of commodity sector employees implied by the growth of the the commodity sector task
price. The magnitude of this increase is represented by the vertical shift of the curve of potential average wage in the commodity sector. In addition, there is a compositional effect driven by the inflow
of new employees whose sector-specific efficiency differs from that of original employees in the commodity sector. As discussed above for the non-commodity sector, the sign of this effect is ambiguous,
being controlled by the slope of ĀCg (.).17
As a consequence of the shock, the upper-envelope of the two curves of potential sector wage shifts
upwards and, therefore, the average group wage increases. Formally, expression (8) yields
"
∆Ȳg =
∆ω gC
· l gC
+ ∆ω gN
· l gN
+ αg
l gN
+ ∆l gN
ˆ
· ∆l gN
−
l gN +∆l gN
l gN
#
α g (q) dq .
(13)
The first two terms correspond to the positive wage gain implied by the shock if workers were to
remain in their initial sector of employment. Yet, the change in sector composition associated with the
shock introduces an additional source of average wage variation: the compositional effect captured by
the term in brackets. For the positive shock considered, the compositional effect is also positive because
individuals only move into the commodity sector to take advantage of its higher wage growth.18 At
last, notice that this compositional effect is second-order: for small price shocks, sector-switchers are
the marginal individuals with the same potential wage in the two sectors so their reallocation does not
affect the log-wage distribution of the group.
Proposition 1 summarizes the predictions of the model following an exogenous increase in the
commodity sector task price.
Proposition 1. Suppose an increase in the commodity sector task demand such that ∆ω gC > ∆ω gN ≥ 0. Then,
i. There is an increase in the employment share of the commodity sector whose magnitude is controlled by
the slope of the schedule of comparative advantage, α g (.).
ii. There is an ambiguous change in the average wage of both sectors due to the existence of compositional
effects controlled by the slope of the schedule of sector average efficiency, Ākg (.).
iii. There is an increase in the average group wage whose magnitude depends on the initial sector allocation of
workers in the group.
17 In
the commodity sector, the average efficiency in the sector-specific task combines the schedules of comparative and
absolute advantage. From expression (7),
ˆ
∆ȲgC − ∆ω gC =
l gN +∆l gN
l gN
∂ ĀCg (u)
∂q
ˆ
du = −
l gN +∆l gN
l gN
1 α g (u) + A g (u) − ĀCg (u) du.
1−u
According to this expression, changes in the employment composition have ambiguous consequences to the commodity
sector average efficiency. The magnitude of this compositional effect is related to the difference between the sector-specific
efficiency of sector-switchers, α g (l gN ) + A g (l gN ), and sector-stayers, ĀCg (l gN ). In Figures 6 and 7, the average efficiency in
the commodity sector is increasing in q. Thus, an employment expansion triggers the absorption of individuals with lower
sector-specific efficiency, reducing the average wage in the commodity sector.
18 This follows immediately from ∆l N < 0 and the fact that α (.) is increasing.
g
g
20
Taking the commodity price increase as a demand-driven shock to sector-specific task prices such
that ∆ω gC > ∆ω gN ≥ 0, Proposition 1 can be readily used to interpret Facts 2 and 3 in Section 3.19 Consistent with Fact 2, the model predicts a positive response in the commodity sector employment share
and an ambiguous response of the commodity sector wage premium. Through the lens of the TwoSector Roy Model, this pattern of adjustment is related to the existence of compositional effects implied
by the between-sector worker reallocation. This compositional effect may reinforce or diminish the direct effect of the task price change. If there is positive selection into the non-commodity sector (Figure
6), then the compositional effect increases the average wage in the non-commodity sector — as, for example, in the weak response of the commodity sector wage premium for HSD. However, to the extent
that workers are negatively selected into the non-commodity sector (Figure 7), the compositional effect reinforces the direct price effect — as, for example, in the strong response of the commodity sector
wage premium for HSG.
Despite these mixed wage responses at the sector level, the model also predicts, as in Fact 3, a gain
in the average wage of all worker groups. At the group level, the change in the average wage combines
the changes in sector-specific task prices using the sectoral allocation of workers. This creates a link
between the magnitude of the average wage response and the sector employment composition.
In order to move from this qualitative analysis to a quantitative examination of the impact of the
commodity price shock on the Brazilian wage structure, it is necessary to recover the schedules of
comparative advantage, α g (.), and absolute advantage, A g (.). To be more precise, the knowledge of
these schedules allows the counterfactual decomposition of the log-wage variance based on equation
(10), permitting the quantification of the commodity price shock contribution to the wage dispersion
behavior in Brazil (Fact 1).
5
Identification of Comparative and Absolute Advantage
This section investigates the nonparametric identification of the schedules of comparative and absolute
advantage in the Two-Sector Roy Economy. This result establishes a mapping between population data
and the unknown functions α g (.) and A g (.) without additional restrictions than those implied by the
theory. In this sense, such result represents an important first step in the empirical analysis of the
model. It indicates the source of variation in the data that uncovers the main economic relation of
interest, focusing on robust predictions of the model. Alternatively, as noted by Matzkin (2007), the
credibility of empirical results would be significantly hindered if identification could only be achieved
under restrictive parametric assumptions.
5.1
Assumptions
In order to establish identification of comparative and absolute advantage in the Two-Sector Roy Economy of Section 4, it is necessary to make additional assumption regarding observable labor market
19 For a particular worker group g in microregion r, assume that changes in sector-specific task prices are proportional to
k
the exposure to the commodity price shock: ∆ω g,r,t
= βkg · ∆Zg,r,t such that βCg > β N
g ≥ 0. If the commodity price shock
affects sector task demand, then this assumption can be interpreted as the linear projection of the change in sector-specific
k , on the shock exposure, ∆Z
task prices, ∆ω g,r,t
g,r,t .
21
outcomes as well as their relation to unobservable variables.
Panel of Segmented Labor Markets. Consider a country constituted of regions, r, in different years,
t. Each region-year pair is a segmented labor market equivalent to the Two-Sector Roy Economy of
C , ω N ).20
Section 4. Assume that sector-specific task prices are observable variables denoted by (ω g,r,t
g,r,t
In equilibrium, these prices are jointly determined by supply and demand for sector-specific tasks. Let
D g,r,t denote a vector of task demand conditions in the market, including, among other variables, final
product prices, and shifters of production technology and trade costs. In addition, assume that task
supply is determined by a skill distribution satisfying the following regularity conditions.
Assumption 1. [Skill Distribution] Suppose individual i of group g in region r at year t, i ∈ I g,r,t , indepen
dently draws s g (i ), a g (i ) from a bivariate distribution such that the following decomposition holds.
i. Comparative Advantage:
s g (i ) = s̃ g (i ) + ũ g,r,t
and
{s̃ g (i )} ∼ Fg (s)
where ũ g,r,t, is a group-region-time shifter of comparative advantage.
ii. Absolute Advantage:
e
{ a g (i )|s̃ g (i ) = s} ∼ Hg,r,t ( a|s) = µHga ( a|s) + (1 − µ) Hg,r,t
( a)
e ( a ) ≡ H e ( a | ũ
where Hg,r,t
g,r,t , θg,r,t ) is a group-region-time mixing distribution of absolute advantage
´
e ( a ).
such that ṽ g,r,t ≡ (1 − µ) a dHg,r,t
The regularity conditions in Assumption 1 guarantee that the pattern of sector selection is identical
in every market. Intuitively, they impose parallel curves of potential sector wage across both regions
and years; leaving nevertheless the shape of these curves completely unrestricted. In terms of the
notation introduced in Section 4, Assumption 1 implies that the schedules of comparative and absolute
advantage are respectively given by
α g,r,t (q) = α g (q) + ũ g,r,t
(14)
A g,r,t (q) = A g (q) + ṽ g,r,t
(15)
where α g (q) ≡ ( Fg )−1 (q) and A g (q) ≡ µ
´
a dHga a|α g (q) .
Equations (14)-(15) attest the importance of Assumption 1 for its dimensionality reduction implication: cross-market heterogeneity in labor market outcomes is generated by shocks to sector task
supply in ũ g,r,t , ṽ g,r,t and sector task demand in Z g,r,t . In this context, ũ g,r,t is a shifter of comparative
advantage, representing in the model a supply-driven shock to sector employment across markets.
e ( a ).
In addition, ṽ g,r,t is a shifter of the overall task efficiency implied by the mixing distribution Hg,r,t
20 In this Section, I treat sector-specific task prices as, for all purposes, observable variables determined in the equilibrium
of the Two-Sector Roy Economy. Section 6.1 provides a methodology to estimate task prices based on the model’s predicted
relation between wage growth and initial sector employment across quantiles of the wage distribution.
22
Notice that this market-specific component of the absolute advantage distribution is independent of
comparative advantage, capturing supply shocks to labor efficiency not directly related to sector employment.21
To move towards an empirical application of the model in Section 4, I make an additional assump
tion regarding the structure of the supply shocks ũ g,r,t , ṽ g,r,t . In particular, I assume that they combine
observable and unobservable components as follows.
Assumption 2. [Error Structure] Assume that the shifters of comparative and absolute advantage, ũ g,r,t , ṽ g,r,t ,
can be written as
ũ g,r,t = X g,r,t γug + u g,r,t ,
ṽ g,r,t = X g,r,t γvg + v g,r,t
where X g,r,t is an observable vector of group-region-year variables; and u g,r,t , v g,r,t is an unobservable vector of
and
group-region-year supply shocks. Also, normalize the shifters so that E[ũ g,r,t ] = E[ṽ g,r,t ] = 0
Instrument: Sector Demand Shifter. As discussed above, labor market outcomes in equilibrium are
determined by both supply and demand conditions in each region-year pair. Accordingly, in order to
recover the task supply structure represented by the schedules of comparative and absolute advantage
in α g (.) and A g (.), it is necessary an observable shifter of sector task demand that varies across regions
and years. Hence, I assume the existence of an observable subvector Z g,r,t in the vector of sector
demand shifters, D g,r,t , that satisfies the following exogeneity restriction.
Assumption 3. [Exogeneity] E u g,r,t |Z g,r,t , X g,r,t = E v g,r,t |Z g,r,t , X g,r,t = 0.
Assumption 3 is the usual exogeneity restriction of an instrument: conditional on X g,r,t , Z g,r,t is
mean independent from unobservable shocks to sector task supply, (u g,r,t , v g,r,t ). In this case, the instrument must be a regional shock to sector demand that is uncorrelated with regional shifters of
comparative and absolute advantage. Following the intuition of the comparative statics exercise in
Section 4, Z g,r,t generates exogenous variation in sector-specific task prices whose quantitative implications for sector employment and wages are directly connected to the schedules of comparative and
absolute advantage.
As standard in the nonparametric identification literature, I impose an additional completeness
condition on the instrument vector, Z g,r,t .
h
i
N ,X
Assumption 4. [Completeness] For any f (.) with finite expectation, E f (l g,r,t
)
Z
,
X
g,r,t
g,r,t
g,r,t = 0 imN ,X
plies that f (l g,r,t
g,r,t ) = 0 almost surely.
Assumption 4 is the equivalent of a rank requirement in the context of nonparametric models.
Newey and Powell (2003) show that it is necessary and sufficient for identification of nonparametric
21 For
group g, the heterogeneity in the skill distribution across markets is controlled by ũ g,r,t and θg,r,t . The term ũ g,r,t affects market-specific components of both comparative and absolute advantage, allowing for correlated supply-driven movements in sector employment and overall labor efficiency. The vector θg,r,t allows for a rich pattern of variation in labor
efficiency across markets, capturing differences in the mass of workers at various ranges of absolute advantage through
e ( a ). Hence, at a particular part of the income distribution, variation in θ
the distribution Hg,r,t
g,r,t introduces supply-driven
shocks to income growth across markets.
23
instrumental variable models of the class considered in this paper. Intuitively, this condition guaranN to
tees that the instrument Z g,r,t induces enough variation in the endogenous sector composition l g,r,t
uniquely discriminate the function consistent with the underlying data generating process.
5.2
Identification of Comparative and Absolute Advantage
Under Assumptions 1 and 2, the conditions determining the employment share and the average wage
in the non-commodity sector — i.e., equations (5)-(6) — immediately imply that
h
i
N
C
N
ω g,r,t
− ω g,r,t
= α g l g,r,t
+ X g,r,t γug + u g,r,t
h
i
N
N
N
Ȳg,r,t
− ω g,r,t
= Ā gN l g,r,t
+ X g,r,t γvg + v g,r,t
where, by construction, A g (q) =
∂
∂q
h
(16)
(17)
i
q · Ā gN (q) .
The variation in the instrument vector Z g,r,t creates variation in the sector employment composition
that is orthogonal to variation in the shifters of the skill distribution across markets. As in the labor
market adjustment to demand shocks described by Proposition 1 of Section 4, this exogenous demand
variation gives rise to responses in sector employment and sector average wage that are quantitatively
connected to the economy’s skill distribution. To be more precise, the schedule of comparative advantage, α g (.) in equation (16), controls the magnitude of the change in the relative task price associated
with the change in sector employment implied by the exogenous demand shock. The subsequent
change in the composition of workers employed in the non-commodity sector triggers a change in the
N − ω N ]. In equation (17), this compositional effect is
sector’s average efficiency as measured by [Ȳg,r,t
g,r,t
controlled by the function Ā gN (.) which is directly related to the schedule of absolute advantage, A g (.).
In line with this discussion, an instrument satisfying Assumptions 3-4 identifies α g (.) and A g (.)
respectively from equations (16) and (17).
Proposition 2. Consider a panel of segmented labor markets such that Assumptions 1-2 hold. If there is an
instrument vector Z g,r,t satisfying Assumptions 3-4, then the schedules of comparative advantage, α g (.), and
absolute advantage, A g (.), are nonparametrically identified respectively from equations (16) and (17).
Proof. As a direct application of Lemma 1 in Appendix D.1, the functions α g (.) and Ā gN (.) are identified
from equations (16) and (17) with the instrument Z g,r,t . Using the definition of Ā gN (.), we immediately
h
i
∂
q · Ā gN (q) . identify A g (.) such that A g (q) = ∂q
In the Two-Sector Roy Economy, comparative and absolute advantage immediately determine efficiency in the task specific to the commodity sector and, consequently, the average efficiency in that
sector. As a result, there is one overidentification restriction in the model. To see this, notice that, under
Assumptions 1 and 2, equation (7) yields
h
i
C
C
N
Ȳg,r,t
− ω g,r,t
= ĀCg l g,r,t
+ X g,r,t (γug + γvg ) + (v g,r,t + u g,r,t )
24
(18)
i
h
∂
where, by definition, α g (q) + A g (q) = − ∂q
(1 − q) · ĀCg (q) .
From equation (18), the instrument Zg,r,t satisfying 3-4 identifies ĀCg (.) which is directly related to
the sum of the schedules of comparative and absolute advantage, α g (.) + A g (.).
Proposition 3. Consider a panel of segmented labor markets such that Assumptions 1-2 hold. If there is an
instrument vector Z g,r,t satisfying Assumptions 3-4, then the sum of the schedules of comparative and absolute
advantage, α g (.) + A g (.), is nonparametrically identified from equation (18).
Proof. As a direct application of Lemma 1 in Appendix D.1, the function ĀCg (.) is identified from
equations (18) with the instrument Z g,r,t . Using the definition of ĀCg (.), we immediately identify
i
h
∂
A g (.) + α g (.) such that α g (q) + A g (q) = − ∂q
(1 − q) · ĀCg (q) . 6
Empirical Application
The above results establish identification of the schedules of comparative and absolute advantage using cross-market variation in sectoral labor demand. Armed with these theoretical results, I now turn
to the estimation of comparative and absolute advantage from the adjustment of labor market outcomes in Brazilian microregions differentially exposed to international commodity price shocks between 1991 and 2010. The empirical application builds directly upon the reduced-form results of Section 3: precisely, the impact of the commodity price shock on between-sector responses of employment
and wages. A detailed description of the data used in this section is given in Appendix A.
6.1
Sector-Specific Task Prices
In order to apply the results of Section 5, it is first necessary to measure sector-specific task prices in
each region and year. In this section, I propose a methodology to estimate task prices using promptly
available information on labor income and employment at the individual level.
In the Two-Sector Roy Economy, individuals are not readily substitutable between sectors, implying that their wages are only exposed to changes in the task price of their own sector of employment.
Following task price shocks, this observation implies that, across different parts of the wage distribution, variation in the pre-shock sector employment composition translates into variation in the growth
of wages. Intuitively, if all individuals at the bottom of the distribution are employed in the commodity sector, then the wage gain at the bottom is entirely attributed to the change in the task price of
the commodity sector. In such case, an increase in the task price of the non-commodity sector has no
impact on the wage of individuals at the bottom of the wage distribution.
To formalize this intuition, let Yg,r,t (π ) denote the π-quantile of the log-wage distribution of group
g in region r at year t. For small shocks, I show in Appendix D.2 that the wage growth between periods
t0 and t in quantile π of the log-wage distribution is given by
h
i
C
N
C
N
∆Yg,r,t (π ) = ∆ω g,r,t
+ ∆ω g,r,t
− ∆ω g,r,t
· l g,r,t
(π ) + µ g,r,t · X̃ g,r,t (π ) + ∆v g,r,t (π )
0
25
(19)
N ( π ) is the initial employment share of the nonwhere, at quantile π of the log-wage distribution, l g,r,t
0
commodity sector, X̃ g,r,t (π ) is a set of observable controls, and ∆v g,r,t (π ) is a productivity shock.22
For each triple of group-region-period, equation (19) implies that changes in task prices can be
consistently estimated from the relation across wage distribution quantiles between the initial sector
N ( π ), and the wage growth, ∆Y
composition, l g,r,t
g,r,t ( π ). In this context, an estimator based on equa0
tion (19) relies on the assumption that, conditional on the set of controls X̃ g,r,t (π ), pre-shock variation
in sector employment composition is uncorrelated with variation in labor efficiency shocks among
individuals with different levels of labor income in a particular group-region-period. Additionally,
such estimator hinges on a central feature of the Roy Model embedded in equation (19): the indifference of marginal individuals between the two sectors. For small price shocks, sector-switchers are
the marginal individuals with the same potential wage in the two sectors so their reallocation has no
first-order impact on the group’s log-wage distribution.23
Armed with the model’s prediction in equation (19), I proceed to estimate task price changes by
regressing wage growth between two years on the initial year’s sector employment composition in a
set of wage distribution quantiles for each group-region-period. Towards this end, I use Census data
N ( π ) and ∆Y
to construct l g,r,t
g,r,t ( π ) in various quantiles of the log-wage distribution. In the baseline
0
specification, I divide workers into bins of 1 p.p. width computed from the log-wage distribution
quantiles for a group-region-period.24
The implementation of expression (19) allows for a vector of observables variables that vary with
the position in the wage distribution. Accordingly, the baseline specification includes the following
dummy variables as nonparametric controls: (i) indicator that wage percentile is at the bottom, middle
or top of the log-wage distribution; (ii) indicator that wage percentile is below the federal minimum
wage (pre-year and post-year). These dummies capture, for example, differential efficiency gains for
workers in distant parts of the wage distribution, and income gains generated by bunching around
the minimum wage. In this specification, sector-specific task prices are identified from the variation
in pre-shock sector employment in small neighbourhoods of the log-wage distribution of workers in
the same group-region-period. As in Section 3, I focus on the sample of male white full-time worker
22 In Appendix D.2, I show that equation (19) is generated by a first-order expansion of the implicit equation defining
Yg,r,t (π ). In this context, ∆v g,r,t (π ) is a shock to the absolute advantage of individuals spread across quantiles of the logwage distribution. It is introduced by shocks to (ũ g,r,t , θg,r,t ) that affect the market-specific mixing distribution of absolute
e ( a ) ≡ H e ( a | ũ
advantage, Hg,r,t
g,r,t , θg,r,t ) in Assumption 1. The change in the mixing distribution of absolute advantage has
consequences for the labor efficiency of individuals at different income levels. As a result, the process generating innovations
in (ũ g,r,t , θg,r,t ) creates, through ∆v g,r,t (π ), idiosyncratic shocks to wage growth across quantiles of the wage distribution.
23 Expression (19) is modified whenever there exists a wedge in sector potential wage of sector-switchers. This is the
case in the presence of non-monetary benefits of employment. To the extent that sector-switchers are spread over the wage
distribution, the wedge affects wage gains across quantiles. Consistent with this intuition, there is a new term in equation
(19) that is proportional to the fraction of sector-switchers among individuals at the π-quantile of the log-wage distribution.
For a detailed analysis of this case, see Appendix D.3.
24 In principle, equation (19) can be implemented with any division of individuals into quantiles; in practice, however,
this choice entails a tradeoff. On the one hand, a coarse discretization yields a low number of quantiles with potentially
little variation in initial sector employment to precisely estimate task prices. On the other hand, a refined discretization
exacerbates measurement error of sector employment in each quantile because of the low number of sampled individuals
in each sector. Also, extreme values of income could be generated by measurement error, affecting wage growth in the tails
of the wage distribution. With these considerations in mind, the estimation is implemented with 88 percentile bins of 1 p.p.
width between the 6th and the 94th percentiles. Below, I show that similar results are obtained if bins of 2 p.p. width are
used. See Appendix A for more details on data construction.
26
divided in two educational groups, High-School Graduates (HSG) and High-School Dropouts (HSD).
Table 3: Summary Statistics: Estimated Sector-Specific Task Prices, 1991-2010
Log change in commodity
sector task price
Log change in non-commodity
sector relative task price
R2
Mean
SD
Mean
SD
Mean
(1)
(2)
(3)
(4)
(5)
1991 - 2000
0.320
0.370
-0.151
0.347
55.5%
2000 - 2010
0.150
0.645
-0.306
0.609
75.8%
1991 - 2000
0.524
0.579
-0.364
0.619
71.5%
2000 - 2010
0.440
0.579
-0.360
0.634
83.0%
A. High-School Graduates
B. High-School Dropouts
Note. Sample of 518 microregions in 1991-2000 and 2000-2010. Statistics are weighted by the microregion share in national population on
1991. Worker sample of male white individuals distributed in 1 p.p. percentile bins of hourly wage (N = 88). Baseline specification includes the
following dummies: (i) indicator that income percentile is below the federal minimum wage (pre and post years); (ii) indicator that income
percentile belongs to range P6-P30 and P30-P75.
Table 3 presents the summary statistics of estimated task prices implied by the baseline specification in 2,072 group-region-period triples. Columns (1)-(2) display statistics of the estimated task price
C , and columns (3)-(4) of the estimated relative task price of the nonin the commodity sector, ∆ω g,r,t
N − ∆ω C . The commodity sector task price presented robust growth in both
commodity sector, ∆ω g,r,t
g,r,t
periods. Between 1991 and 2010, the average increase was 47.0 log-points for HSG and 96.4 log-points
for HSD. Simultaneously, the relative task price in the non-commodity sector decreased sharply. Lastly,
column (5) reports the average R2 of the estimation in the sample of microregions. A large fraction of
the variation in wage growth across quantiles of the earnings distribution is captured by equation (19);
in the two periods, the average R2 is above 55% for HSG and 71% for HSD.
To address robustness to implementation choices, Table 4 presents the correlation between task
price estimates implied by different specifications of equation (19) and those implied by the baseline
specification. Columns (1)-(3) and (5)-(7) indicate a high correlation between estimates obtained with
different control sets. Notice that, when minimum wage controls are omitted, estimated task prices
are extremely similar to those of the baseline specification. This suggests that quantile range controls
absorb much of the variation captured in the minimum wage dummies. Columns (4) and (8) attest that
the particular choice of bin width has little impact on estimates: the correlation is above .88 between
baseline estimates and those obtained with a coarser discretization of 2 p.p. bins.
6.2
Parametric Restrictions: Log-Linear System
The nonparametric identification in Section 5 is an asymptotic result. In practice, limitations in the
availability of exogenous variation in the data may prevent the implementation of a fully flexible estimator capable of nonparametrically recovering the functions of interest. In such cases, auxiliary
27
Table 4: Estimated Sector-Specific Task Prices, Correlation with Benchmark Specification
Commodity sector task price
Non-commodity sector relative task price
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.776
0.855
0.973
0.926
0.807
0.874
0.969
0.916
0.802
0.914
0.960
0.886
0.812
0.912
0.960
0.893
No
No
Yes
No
No
Yes
Yes
Yes
No
No
Yes
No
No
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
No
Yes
Yes
No
Yes
No
Yes
No
No
Yes
A. High-School Graduates
Correlation with baseline estimates
B. High-School Dropouts
Correlation with baseline estimates
Baseline Controls
Percentile below federal minimum wage
Percentile in bottom, middle or top of wage distribution
Discretization of wage distribution
Bins of 1 p.p. (N = 88)
Bins of 2 p.p. (N = 44)
Note. Sample of 518 microregions in 1991-2000 and 2000-2010. Statistics are weighted by the microregion share in national population on 1991. Baseline estimates based on the discretization of the wage
distribution in 88 bins of 1 p.p. width, including indicator dummies of percentile bins below the federal minimum wage (pre and post years) and percentile bins in bottom, middle or top of the wage distribution
(P6-P30 and P30-P75).
functional form assumptions on α g (.) and A g (.) are particularly useful to increase estimation precision. It is important however that these parametric assumptions do not impose artificial restrictions
on the model. In the Two-Sector Roy Model, it is particularly relevant that functional forms allow for
separate roles for comparative and absolute advantage since they are related to distinct predictions of
the model.
Accordingly, the benchmark specification in the empirical application below is based on the following log-linear version of system (16)-(17).
Assumption 5. [Log-Linear System] Suppose schedules of comparative and absolute advantage in system
(16)-(17) are given by
α g (q) = α g · [ln (q) − ln (1 − q)]
and
A g (q) = Ã g + A g · ln (q)
where α g ≥ 0 and A g ∈ R.
Assumption 5 commands constant-elasticity schedules of comparative and absolute advantage.
Following the discussion in Section 4, the positive parameter α g controls the dispersion of comparative
advantage; alternatively, the parameter A g controls the pattern of variation in average absolute advantage of individuals distributed across quantiles of comparative advantage. In the empirical application,
these parametric restrictions are useful for two main reasons. First, they simplify the instrument’s rank
requirement since, as discussed below, they allow the use of standard instrumental variable estimators.
Second, parameters α g and A g can be interpreted as the average elasticity of the comparative and absolute advantage schedules. In other words, these parameters correspond to the local treatment effect
induced by the labor demand instrument in the cross-section of markets.25
25 In the spirit of the series estimator proposed by Newey and Powell (2003), the log-linear system could be augmented to
include higher-order polynomials. In the limit, such expansion would recover nonparametrically functions α g (.) and A g (.).
Yet, the implementation of this estimator is not feasible in most applications. As pointed out by Newey (2013), the estimation of nonlinearities tend to be accompanied by sharp increases in standard errors, requiring multiple strong instruments.
The application in this paper is no exception and, for this reason, the constant-elasticity specification in Assumption 5 is
particularly attractive.
28
It is important to notice that the system in Assumption 5 is a strict generalization of the system
obtained under a Frechet distribution of skills that form the basis of numerous recent empirical applications of the Roy Model — see e.g., Hsieh, Hurst, Jones, and Klenow (2013); Burstein, Morales, and
Vogel (2015); and Galle, Rodriguez-Clare, and Yi (2015). As discussed in Appendix D.4, the Frechet
distribution leads to a similar log-linear system, but it entails a single parameter to control both comparative and absolute advantage. In terms of the system above, the Frechet distribution requires that
α g = − A g where α g < 1. These restrictions have strong consequences to the model’s predictions
regarding the responses of employment and wages following sector demand shocks. Namely, they
impose constraints not only on the magnitude of the between-sector reallocation but also on the pattern of selection into both sectors. In fact, α g = − A g rules out responses in sector wage differentials,
being unable to replicate the positive impact of commodity prices on the the commodity sector wage
premium documented in Section 3. In contrast, the more general log-linear system in Assumption 5
contains parameters that separately control comparative and absolute advantage. Specifically, α g is
positive to reflect a positively sloped comparative advantage schedule and A g is free to capture both
positive and negative selection in the absolute advantage schedule.26
6.3
Estimation Procedure
Now we are ready to propose an estimator for the schedules of comparative and absolute advantage
directly related to the identification result in Proposition 2. To this extent, I take advantage of the parametric restrictions in Assumption 5 to construct a consistent GMM procedure with moment conditions
that use the differential exposure of Brazilian microregions to the variation in international commodity
prices in the two period windows of 1991-2000 and 2000-2010.
To this end, let us combine equations (16)-(17) with the functional forms in Assumption 5 to write
the following first-difference system:
.
C
N
C
N
l g,r,t
∆ω g,r,t
− ∆ω g,r,t
= α g · ∆ ln l g,r,t
+∆X g,r,t γug + ∆u g,r,t
(20)
N
N
N
∆Ȳg,r,t
− ∆ω g,r,t
= A g · ∆ ln l g,r,t
+∆X g,r,t γvg + ∆v g,r,t
(21)
where X g,r,t is a control vector of group-microregion-period variables that include group-microregion
k
fixed effects; and ∆ω g,r,t
is the changes in the task price of sector k estimated with the procedure de-
scribed in Section 6.1.
Also, the overidentification restriction in Proposition 3 delivers an additional equation to the sys-
26 Appendix D.4 provides a detailed discussion on the pattern of sector selection implied by the Frechet distribution.
While
the restriction of α g = − A g is a direct implication of assuming a Frechet distribution, the restriction of α g < 1 is necessary
to guarantee a finite supply of tasks in each sector. In Appendix D.4, I propose an alternative skill distribution that delivers
the log-linear model in Assumption 5 with the sole restriction of a positively sloped comparative advantage schedule (i.e.,
α g positive). Appendix D.4 also discusses the system implied by normally distributed skills — as in Roy (1951), Heckman
and Sedlacek (1985), and Ohnsorge and Trefler (2007). Although the normal distribution leads to distinct functional forms,
the implied system also entails two parameters that parametrize the slopes of the schedules of comparative and absolute
advantage, allowing for a flexible selection pattern.
29
tem. Specifically, equation (18) under Assumption 5 implies that
"
C
C
∆Ȳg,r,t
− ∆ω g,r,t
= − αg + Ag · ∆
N
l g,r,t
C
l g,r,t
#
N
C
ln l g,r,t
− α g · ∆ ln l g,r,t
+ ∆X g,r,t γeg + ∆e g,r,t
(22)
where X g,r,t is the same control vector as above.
Conditional on the parameter vector Θ g ≡ (α g , A g , γug , γvg , γeg ), equations (20)-(22) immediately al low the computation of the vector of structural errors: e g Θ g ≡ ∆u g,r,t , ∆v g,r,t , ∆e g,r,t r,t . Combined
with a matrix of instruments W g ≡ ∆Z g,r,t , ∆X g,r,t r,t satisfying Assumption 3, the error vector e g (Θ g )
provides moment conditions for the consistent estimation of Θ g with the following GMM estimator:
Θ̂ g = arg min e g (Θ g )0 W g ΦW0g e g (Θ g )
Θg
(23)
where Φ is a matrix of moment weights.27 As in Section 3, microregions are weighted by their share in
the national population of 1991 and standard errors are clustered by microregion to account for serially
correlated errors.
To build instruments for the estimation of the parameter vector, I rely on a generalization of the
regional exposure to commodity price shocks of Section 3. Precisely, I consider the following set of
instruments:
∆Z g,r,t = ∆F φg,r ( j) · ln pt ( j) j∈J C
(24)
where F(.) is a quadratic polynomial function. Similarly to Section 3, ln pt ( j) is the international logprice of commodity category j at year t; and φg,r ( j) is the share of industry j in total labor payments of
the commodity sector to individuals of group g in microregion r on the initial year of 1991.
In the empirical application, the instrument vector contains five major commodity groups: Grains,
Soft Agriculture, Livestock, Mining (Metals and Precious Metals), and Energy.28 As in Section 3, the
control vector ∆X g,r,t contains ten macroregion-period dummies, initial commodity sector size controls,
and initial labor market conditions interacted with period dummies.29
6.4
Results
Table 5 presents the structural estimates obtained with the procedure described in Section 6.3. Column (1) reports the structural parameters implied by the estimation of equations (20)-(21) under the
27 In
the main specification, I use the two-step optimal GMM weights. The sensitivity analysis in Appendix E shows that
similar results are obtained with other matrices of moment weights.
28 In principle, one could use any non-linear function of the six commodity categories. Yet, the inclusion of too many
instruments may lead to the well known weak instrument problem. To maintain a parsimonious number of instruments, I
adopt two simplifications. First, I aggregate the two categories with lowest employment participation, Metals and Precious
Metals, into a single category, Mining. Second, I consider a quadratic polynomial function, yielding two instruments per
commodity category. In Appendix E, I show that similar results are obtained with alternative specifications for the instrument
vector.
29 Labor market conditions: quadratic polynomial of per-capita income, share of white individuals, share of employed
individuals, share of formal sector employees, share of individuals earnings less than the federal minimum wage, and share
of social security earners (only HSD). Commodity sector size controls: quadratic polynomial of commodity sector share in
group labor income and dummy for commodity sector share in group labor income in the bottom and top deciles of national
distribution.
30
parameter restriction imposed by a skill distribution of the Frechet family (i.e., α g = − A g ). For both
groups, estimated parameters indicate a steep schedule of comparative advantage that is associated
with a low degree of between-sector employment reallocation.30 Evaluated at the national sector employment composition of 2010, estimates imply that, following a 10% increase in the relative task price
in the commodity sector, the share of workers employed in the commodity sector increases from 5.14%
to 5.63% for HSG and from 19.94% to 21.65% for HSD.
Table 5: Structural Parameters: Log-Linear System
Frechet model
𝛼𝑔 = −𝐴𝑔
Log-linear model
(1)
(2)
Log-linear model
with
overidentification
(3)
𝛼𝐻𝑆𝐺
1.040**
(0.195)
1.051**
(0.192)
0.835**
(0.212)
𝐴𝐻𝑆𝐺
-1.040**
(0.195)
2.483*
(0.976)
1.966*
(0.935)
-
0.000
0.005
𝛼𝐻𝑆𝐷
0.963**
(0.151)
1.873*
(0.773)
0.916*
(0.399)
𝐴𝐻𝑆𝐷
-0.963**
(0.151)
-0.888**
(0.146)
-0.727**
(0.142)
-
0.208
0.644
A. High-School Graduates
Test of Frechet restriction (p-value)
B. High-School Dropouts
Test of Frechet restriction (p-value)
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. Two-Step GMM estimator with microregions
weighted by their share in the 1991 national population. Excluded instruments: quadratic polynomial of local exposure to
international product prices. Control vector includes macroregion-period dummies, initial commodity sector size controls, and
initial labor market conditions interacted with period dummies (full description in Section 6.3). Standard Errors clustered by
microregion. ** p<0.01, * p<0.05
As discussed above, the Frechet distribution entails a very particular pattern of selection that rules
out responses in sector wage differentials. Such feature is inconsistent with the reduced-form evidence
for HSG presented in Section 3. To allow for a more flexible behavior of sector average wages, column
(2) presents the estimation of the log-linear model in equations (20)-(21). Indeed, this additional degree
of freedom is important for HSG as the estimated parameter has the inverse sign and the Frechet
restriction is rejected at usual significance levels. Among HSG, the estimated parameters indicate
negative selection into the non-commodity sector with curves of potential sector wages similar to those
in Figure 5. In contrast, the estimated parameters for HSD imply similar qualitative predictions of
those of the Frechet model, yielding positive selection into both sectors with curves of potential sector
wages similar to those in Figure 4. In this case, the Frechet restrictions cannot be rejected at usual
significance levels.
Lastly, column (3) presents the implementation of the full estimation procedure that includes the
overidentifying equation (22). The overidentification equation yields more precise estimates for HSD
30 In fact, it is not possible to reject the hypothesis that α = 1 at the usual significance levels. Thus, estimated parameters
g
suggest higher dispersion of comparative advantage than that allowed by the Roy model with a Frechet distribution of skills.
31
and has little effect on estimates for HSG. In this case, comparative advantage parameters indicate
between-sector employment reallocation whose magnitude is similar to that of the Frechet model in
column (1). Nevertheless, the slope of the absolute advantage schedule is similar to that reported in
column (2), indicating a response in the sector wage premium that is positive for HSG and almost zero
for HSD.
7
Counterfactual Exercise: Effect of International Commodtiy Prices on
the Wage Distribution
To conclude, I use the estimated schedules of comparative and absolute advantage to investigate the
consequences to the Brazilian wage distribution of shocks in international commodity prices. Precisely,
I ask: “In 2010, how the wage structure would change if commodity prices fall by 10%?" The counterfactual exercise takes into account the variation in shock exposure across microregions and groups to
compute the implied change in the national dispersion of wages.
7.1
First-Step: From Changes in Sector-Specific Task Prices to Changes in the Log-Wage
Distribution
As a first step to answer this question, I consider responses in the average and the variance of the
log-wage distribution among workers of group g in region r following a change in sector-specific task
C , ∆ω N ), triggered by a sector demand shock — in this case, the change in international
prices, (∆ω g,r
g,r
commodity prices. To this extent, I consider the estimated schedules of comparative and absolute
advantage, obtained in Section 6, while holding constant the structure of task supply (i.e. ∆ṽ g,r =
∆ũ g,r = 0).
In this environment, equations (20)-(22) immediately deliver the changes in sector employment,
k , and sector average wages, ∆Ȳ k , implied by the counterfactual change in sector-specific task
∆l g,r
g,r
prices. Together with equation (8) in Section 4, we obtain the counterfactual change in the average
log-wage:
ˆ
N
N
C
N
∆Ȳg,r = ∆ω gC + ∆ω g,r · l g,r
)∆l g,r
− αg
+ α g log(l g,r
/l g,r
|
{z
}
|
Direct Effect
N + ∆l N
l g,r
g,r
N
l g,r
N
[log(q) − log(1 − q)] dq + ∆ω g,r ∆l g,r
{z
Compositional Effect
(25)
}
N − ∆ω C is the counterfactual change in relative task prices; and l N is the observed
where ∆ω g,r ≡ ∆ω g,r
g,r
g,r
employment share of the non-commodity sector among workers of group g in region r.
In equation (25), the first term is the direct effect on the wage of sector employees if they are unable
to reallocate between sectors. Notice that this direct effect depends solely on the pre-shock employment composition, being independent from estimated parameters. The second term is the compositional effect generated by the reallocation of workers in response to the shock which, intuitively, depends on the slope of the comparative advantage schedule. As noted in Section 4, this compositional
effect is negligible for small price shock since, in such cases, only workers with very similar potential
wages in the two sectors choose to switch their sector of employment.
32
To compute the change in log-wage variance among workers of group g in region r, we rely on the
model’s predicted response obtained from equation (10) in Section 4:
2
2
N
N
C
C
C
N
C
N
N C
C
N
∆Vg,r = l g,r
+ ∆l g,r
l g,r
+ ∆l g,r
· Ȳg,r
− Ȳg,r
+ ∆Ȳg,r
− ∆Ȳg,r
− l g,r
l g,r · Ȳg,r
− Ȳg,r
ˆ lg,r
N
h
i2
h
i2 2
2 k
k
N
N
k
N
+
(l g,r
+ ∆l g,r
) Ākg (l g,r
+ ∆l g,r
) − l g,r
Ākg (l g,r
)
(α g + A g ) log(q) − α g log(1 − q) − A g log(q) dq − ∑
N + ∆l N
l g,r
g,r
k =C,N
(26)
C − Ȳ N is the commodity sector wage premium that is observed among workers of group g
where Ȳg,r
g,r
in region r; and Ākg (.) is the schedules of average efficiency in sector k estimated in Section 6 (i.e., the
right hand side of equations (21)-(22)).
The log-wage variance has a between-sector component that responds to the change in sector wage
premium as captured by the term in the first row of equation (26). The term in the second row captures the variance in log-wages within the two sectors of the economy. This is directly related to the
estimated schedules of comparative and absolute advantage that govern the dispersion of average
sector-specific efficiency across the comparative advantage quantiles allocated to each sector.
7.2
Second-Step: Pass-Through from Changes in Commodity Prices to Changes in SectorSpecific Task Prices
In order to implement equations (25)-(26), it is necessary to evaluate how the change in commodity
prices translates into changes in sector-specific task prices for each group and microregion. In this
section, I focus on the reduced-form pass-through of the shock exposure to sector-specific task prices
as captured by the following equation:
k
∆ω g,r,t
= βkg · ∆Zg,r,t + ∆X g,r,t γkg + ∆e g,r,t
(27)
where X g,r,t is the control vector of group-microregion-period variables described in Section 6.3. As
above, microregions are weighted by their share in the national population of 1991 and standard errors
are clustered by microregion.
Table 6 reports the estimation of equation (27) in the sample of Brazilian microregions in 1991-2000
and 2000-2010. Estimates in columns (1)-(4) indicate that exposure to the commodity price shock is
associated with a higher task price in the commodity sector. With the full control vector used in the
structural estimation, the estimated pass-through is 0.9-1.2 for HSD and 1.2-1.3 for HSG. In addition,
columns (5)-(8) investigate the relation between shock exposure and non-commodity sector task prices,
implying a pass-through of .25-.35 for HSG and 0-.10 for HSD. In response to higher commodity prices,
these estimates suggest stronger gains in the commodity sector task price which, in turn, imply an
increase in the relative task price of the commodity sector. Combined with the commodity sector
employment expansion, this change in sector-specific task prices yield the structural estimation above.
In the counterfactual analysis, I calibrate the pass-through from commodity prices to sector-specific
task prices using the estimates in Table 6. To focus on supply-driven movements in inequality, I assume
that the pass-though is identical for HSG and HSD. Taking an intermediate value of the estimates for
the two groups, the pass-though from international commodity prices to task prices is set to be 1.10 in
33
the commodity sector and 0.25 in the non-commodity sector.
Table 6: Exposure to Commodity Price Shocks and Sector-Specific Task Prices
Change in task price of commodity sector
Dependent Variable:
Change in task price of non-commodity sector
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
1.407**
(0.394)
1.120**
(0.390)
1.096**
(0.392)
0.962**
(0.359)
0.354**
(0.071)
0.323**
(0.069)
0.324**
(0.069)
0.282**
(0.062)
0.524
0.570
0.585
0.598
0.558
0.585
0.586
0.592
Commodity price shock
1.599*
(0.730)
1.292*
(0.571)
1.268*
(0.574)
1.274*
(0.571)
-0.056
(0.112)
0.028
(0.092)
0.008
(0.091)
-0.014
(0.089)
R2
0.644
0.689
0.690
0.690
0.461
0.555
0.576
0.576
Initial commodity sector size controls
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Initial labor market conditions x period dummies
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Initial commodity sector size controls x period dummies
No
No
Yes
Yes
No
No
Yes
Yes
Initial size of manufacturing sector x period dummies
No
No
No
Yes
No
No
No
Yes
A. High-School Graduates
Commodity price shock
R2
B. High-School Dropouts
Structural Estimation Controls
Additional Controls
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991 and include ten macroregion-period dummies. Structural
estimation controls described in Section 6.3. Standard Errors clustered by microregion ** p<0.01, * p<0.05
7.3
Counterfactual Predictions
In any microregion r on 2010, we are interested in the counterfactual change of the wage distribution
implied by a 10% decrease in international commodity prices. Using the pass-through obtained in
Section 7.2, I compute the change in sector-specific task prices triggered by the price shock:
k
= βkg · 0.10
∆ω g,r
where βCg = 1.10 and β N
g = 0.25.
For every group g and region r, equations (25)-(26) yield the counterfactual change in the average
and the variance of log-wages conditional on estimated parameter of comparative and absolute adC , ∆ω N ). Table 7
vantage, (α g , A g ), and the counterfactual changes in sector-specific task prices, (∆ω g,r
g,r
report these counterfactual responses at the national level where the aggregate log-wage variance is
computed with the total variance formula and the microregion’s employment share in 2010. Table 7
also reports the bootstrapped 90% confidence intervals associated with such changes.31
As shown in column (1), the fall in commodity prices causes average wage losses for the two worker
groups. Yet, the wage loss is more pronounced among HSD due to their higher employment share in
the commodity sector — the 2010 national employment share of the commodity sector was 5.1% for
HSG and 19.9% for HSD. Consequently, the 10% decrease in commodity prices leads to an increase in
31 To compute confidence intervals, I take
R draws from the asymptotic normal distribution of the GMM estimator implied
by the estimates in Table 5. With each parameter draw, I compute counterfactual changes in the average and the variance
of the log-wage distribution using equations (25)-(26). The confidence interval bounds correspond to the 5th and the 95th
percentiles of the counterfactual changes obtained from the R parameter draws. In Table 7, I set R = 300.
34
Table 7: Effect of 10% decrease in commodity prices, benchmark estimates
Change in group
average wage
Percentual change in the between component of log-wage
variance
national average
between-region
within-group
between sector
within region-group
Total
(1)
(2)
(3)
(4)
1.09
[1.09; 1.09]
11.09
[-2.35; 48.31]
12.18
[-1.26; 49.40]
-4.13
[-4.15; -4.02]
3.26
[3.10; 3.34]
-3.72
[-12.88; 13.65]
-0.47
[-9.54; 16.45]
-3.52
[-3.52; -3.51]
2.76
[2.57; 2.80]
1.71
[-2.14; 12.22]
4.48
[0.62; 14.91]
Panel A. High-School Graduates
-2.94
[-2.94; -2.92]
Panel B. High-School Dropouts
Panel C. All Workers
Note. Initial labor market outcomes in 518 microregions on 2010. Estimated parameters of the Log-linear model in column (3) of Table 5.
For each worker group, columns (2)-(4) report the percentual change in the between-component of log-wage variance implied by the
decomposition presented in Figure 1. Pass-through of commodity prices to task prices equal to 1.1 in the commodity sector and 0.25 in
non-commodity sector. Each response is accompanained by its 90% confidence interval computed with the bootstrap procedure
described in the main text.
the HSG wage premium of approximately 1.2%. Notice that confidence intervals are extremely tight,
reflecting the quantitative dominance of the parameter-free direct effect in equation (25).
Columns (2)-(4) present the percentage change in the between component of the log-wage variance
implied by the shock.32 Column (2) shows the increase in wage dispersion associated with the change
in average regional wages. Because areas specialized in commodity production had lower wages on
2010, the negative shock triggers an increase in the log-wage dispersion within both groups. At the
national level, this effect is reinforced by the higher shock exposure of low-wage workers in the group
of HSD. Column (3) shows the shock effect on the log-wage variance within groups and regions computed with equation (26). For HSG, the negative impact of the shock on the commodity sector wage
differential leads to an increase in the log-wage variance. In contrast, the weaker response for HSD
leads to a decrease in the log-wage variance. Lastly, column (5) combines these components to obtain
the counterfactual change in total wage dispersion: a 10% decrease in commodity prices implies a 4.5%
increase in the Brazilian log-wage variance.
8
Conclusion
This paper contributes to our understanding of the role of comparative advantage in labor markets in
the response of within- and between-wage inequality following international trade shocks. This paper
establishes a reduced-form relation between exposure to international price shocks and labor market
outcomes that asks for differential effects depending on the worker’s affiliation to groups, regions
and sectors. Such structure is provided by a Two-Sector Roy Model where the distribution of worker
32 The between component of the log-wage variance is obtained form the log-wage decomposition presented in Figure 2
of Section 3.
35
heterogeneity in terms of sector-specific efficiency governs the sectoral allocation in various groups
and regions. Using robust predictions of the model, I show that this distribution is nonparametrically
identified from cross-regional variation in employment and wages induced by exogenous variation in
sector labor demand. The application of this novel strategy to Brazilian regions suggest a rich estimated pattern of worker selection that cannot be captured by traditional models. In the counterfactual
analysis, the estimates of comparative and absolute advantage attest the importance of selection forces
in the behavior of wage differentials associated with educational groups, regions and sectors.
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38
A
Data Construction and Measurement
Commodity Price Data. To capture Brazil’s exposure to world prices of basic products, I build price indices for six commodity categories. The first source of international commodity prices is the Commodity Research Bureau that publishes price indices by commodity group based on product spot prices in
the main exchange markets in the United States. In the paper, I use those groups with sizeable employment participation in Brazil: Grains (corn, soybeans, and wheat), Soft Agriculture (cocoa, coffee, sugar,
orange juice and others), Livestock (hides, hogs, lard, steers, tallow), Metals (copper scrap, lead scrap,
steel scrap, tin, zinc). In addition, I build price indices for two commodity groups using future prices
in the New York Mercantile Exchange: Precious Metals (gold and silver) and Energy (crude oil). These
series of international nominal prices were converted into local currency using the nominal exchange
rate and deflated by the Brazilian consumer price index (IPCA).33 To avoid short-term price volatility,
the reduced-form analysis relies on the average price in the six months preceding the process of data
collection of the Census. Specifically, I use the average price between March and August of each year.
Labor Market Data. Data on labor market outcomes come from publicly available long versions of the
Brazilian Census performed by the Brazilian Institute of Geography and Statistics (IBGE) for the years
of 1980, 1991, 2000, and 2010. From the Census, I extract a sample of full-time workers aged between 16
and 64. Full-time workers are defined as those reporting more than 35 weekly worked hours. I restrict
the sample to workers with calculated experience between 0 and 39 years. Experience is defined as
the individual’s age minus a predicted initial working age that equals 23 for college graduates, 18 for
high-school graduates and 15 for those with only primary education. The benchmark sample is further
restricted to include only white male workers. This restriction allows us to focus on individuals with
strong labor force attachment that are not directly subject to changes in employer prejudice attitudes
towards female and non-white individuals. In fact, Ferreira, Firpo, and Messina (2014) show that
gender and race wage differentials were important drivers of recent changes in the Brazilian wage
inequality. In robustness exercises, I extend the benchmark sample to also include female and nonwhite workers.
Individuals in the sample are allocated to sectors according to their self-reported industry of employment. Table A1 shows the industry classification used in this paper together with corresponding
industry codes in each year of the Census. I use crosswalk tables publicly provided by the IBGE to link
the different activity codes in the Censuses of 1980-1991, 2000 and 2010. The division of industries in
the commodity sector accommodates available information on international prices as described above.
Regional Labor Markets. As a regional labor market unit, I use the microregion concept created by the
IBGE in the 1991 Census. Each of the 558 microregions corresponds to a set of economically integrated
municipalities with interconnected labor markets. This definition of regional labor markets in Brazil is
similar to Commuting Zones in the United States, being recently used in a series of papers analyzing
the response of local labor markets to aggregate trade shocks (e.g. Kovak, 2013, and Dix-Carneiro and
33 All commodity price series were downloaded from the Global Financial Database. In the end of 2008, the soft and grains
indices were unified under the foodstuff index. Thus, I build these series for 2009-2010 using each index description. Series
of nominal exchange rate and IPCA were downloaded from the IPEADATA.
39
Table A1: Industry Classification and Census Activity Codes
Industry
1980-1991 Census (Atividades)
2000 Census (CNEA-Dom)
2010 Census (CNEA-Dom 2.0)
Commodity Sector
Grains (corn, soybeans, wheat)
Soft (coffee, cocoa, sugar, and others)
20; 21; 22
11; 12; 14-17; 23; 24
1102; 1103; 1107
1104; 1105; 1110-1116; 2001; 2002;
15022; 15042
1201-1205; 1208; 1209; 1300; 1402; 5001;
5002; 15010; 15030
1102; 1103; 1107
1104; 1105; 1110-1116; 10022; 10093
Livestock (cattle, hogs, and others)
26; 27; 41; 42
Metals (copper, lead, steel, tin, and zinc)
Precious Metals (gold and silver)
Energy (crude oil)
Other agriculture and mining
58
55
51
13; 18-19; 25; 28; 29; 31-37; 50; 52-54; 56;
57; 59; 581
13002
13001
11000
1101; 1106; 1108; 1109; 1117; 1118; 1206;
1207; 1401; 10000; 12000; 14001-14004
7002
7001
6000
1101; 1106; 1108; 1109; 1117-1119; 1206;
1207; 1401; 5000; 8001-9000
Manufacturing
100-300
15021; 15041; 15043; 15050; 16000-37000 10021; 10091; 10092; 10099-32999; 38000
Non-Tradable Goods and Services
340-901
1500; 40010-99000
1201-1205; 1208; 1209; 1402; 1999; 3001;
3002; 10010; 10030
Non-Commodity Sector
1500; 33001-37000; 39000-99000
Kovak, 2015a,b). Despite the sharp increase in the number of municipalities between 1991 and 2010,
the IBGE maintained the same microregion definition in the Censuses of 1991, 2000 and 2010.34 In the
1980 Census, the microregion variable does not exist so I create it from existing municipalities in 1980.
Because of the change in municipality borders between 1980 and 1991, it is only possible to replicate
a subset of the microregions using historical administrative borders. To be more precise, I recover 540
microregions in the 1980 Census compared to the 558 microregions in the 1991 Census.35
Wage Distribution. As a measure of individual wage, I use the self-reported monthly labor income
in the main job. Table A2 presents the trends in log wage inequality among male white full-time
workers. As discussed in the main text, the variance of log wage has an inverted U-shape in the
period: it increased in the 1980s and decreased in the 1990s and 2000s. To attest that the behavior
of log wage variance is not entirely related to individuals with extreme wage values, I consider the
change in the differential between percentiles of the wage distribution. Specifically, the P90-P10 wage
gap increased by 40 log-points in 1980-1991 and decreased by 66.3 log-points in 1991-2010. In terms of
observable worker characteristics, the wage premium associated with two attributes were particularly
important in the wage compression process of 1991-2010: educational and sectoral wage differentials
fell respectively by 32.1 and 19.0 log-points in the period.
To further investigate the movement in wage inequality, I perform a wage variance decomposition
with a regression of log wages on a full set of dummies for years of experience, level of education, sector of employment and microregion of residence. Table A3 presents the result of this decomposition
34 There
were 4,491 municipalities in 1991 and 5,565 in 2010. Out of the 1074 municipalities created in the period, 998
municipalities had parent municipalities in a single microregion and, therefore, they were allocated to this microregion. The
other 76 municipalities had parent municipalities in more than one microregion. These municipalities, that represented .33%
of employment in 2000, were allocated to the microregion of the parent municipality that ceded the highest population share
to the new municipality. This procedure adopted by the IBGE minimizes any measurement error implied by the border
change. In fact, all results in the paper are robust to using a sample of 491 microregions built by aggregating microregions
such as to keep borders unchanged in the period.
35 Out of the 3,991 municipalities in the 1980 Census, I am able to link 3,938 municipalities to at least one of the 4,491
municipalities in the 1991 Census. With these linked municipalities, I construct microregions in 1980 using the microregion
assigned to corresponding municipalities in 1991. The main problem of this method is the existence of new municipalities
in 1991 that belonged to a different microregion than their parent municipalities in 1980. This is the case for 85 of the 500
municipalities created between 1980 and 1991, accounting for .67% of total employment in 2000.
40
Table A2: Trends in Brazilian Log Wage Inequality, 1980-2010
1980
1991
2000
2010
Variance
0.893
1.095
1.017
0.781
P90th - P50th
P50th - P10th
P90th - P10th
1.378
0.944
2.322
1.476
1.247
2.722
1.492
1.092
2.584
1.386
0.673
2.060
High-school wage differential
1.161
1.046
0.965
0.725
Non-commodity sector wage differential
0.388
0.422
0.358
0.231
Note. Sample of male white full-time workers extracted from the Brazilian Census of 1980, 1991, 2000 and 2010. Education and sector
wage differentials implied by a regression of log real wage on a full set of dummies for high-school degree, employment in the
commodity sector, microregion of residence, and experience (0-39yrs).
between 1980 and 2010. The education-sector-region component is the main driver of wage dispersion, accounting for 49.8% of the 1980-1991 growth and 69.1% of the 1991-2010 decline. Notice that
this component’s contribution is distributed across all its three terms. Conclusions in Table A3 are
related to results reported elsewhere in the literature. In particular, Ferreira, Firpo, and Messina (2014)
highlight the importance of falling educational and state wage gaps for the 1995-2012 decrease in wage
inequality observed among workers in the PNAD survey. Using administrative data for formal sector employees, Helpman, Itskhoki, Muendler, and Redding (2015) conclude that observable worker
attributes account for roughly half of the increase in log wage variance between 1986 and 1995.
Table A3: Decomposition of the Variance of Log Wages, 1980-2010
1980
1991
2000
2010
Overall
Residual
Between
Education-Region-Sector
Education
Region
Sector
Covariance (education, region, sector)
Experience
Covariance (experience, education-region-sector)
0.893
1.095
1.017
0.781
0.481
0.412
0.593
0.502
0.581
0.436
0.524
0.257
0.356
0.457
0.387
0.240
0.181
0.059
0.027
0.089
0.205
0.107
0.029
0.117
0.209
0.073
0.017
0.088
0.131
0.055
0.006
0.049
0.095
-0.040
0.077
-0.033
0.099
-0.050
0.059
-0.042
Note. Sample of male white full-time workers extracted from the Brazilian Census of 1980, 1991, 2000 and 2010. Wage
decomposition implied by a regression of log real wage on a full set of dummies for high-school degree, employment in the
commodity sector, microregion of residence, and experience (0-39yrs).
Sample of Microregions in the Reduced-Form Exercise. In the reduced-form exercise, I select a baseline sample of 518 microregions with positive employment in the commodity sector for all groups in
the 1991-2010 period, covering 98.4% of the country’s population on 1991. The 1980-1991 period is
excluded from the baseline sample mainly because of the turbulent economic environment in Brazil
during the 1980s. The decade was marked by hyperinflationary episodes, suspension of foreign currency convertibility, and the adoption of restrictive internal controls on prices and wages. In this environment, it is not clear that relative international prices were very informative about relative prices
faced by domestic producers when deciding resource allocation. More normal economic conditions
41
returned after the series of structural reforms implemented in 1993-1994 that brought monetary stabilization, eliminated price controls, and restored full currency convertibility. In any case, robustness
exercises attest that similar results hold in the extended sample spanning the entire 1980-2010 period.
Bartik-Instrument Weights. To build the group-region exposure to international commodity prices, I
compute total labor income by industry as the weighted sum of monthly wages of individuals reportk ( j ) as the total
ing to have their main job in the industry using Census sampling weights. Denote Yg,r,t
labor payments of industry j for workers of group g in microregion r on year t. The initial industry
participation in sector labor payments to group g in microregion r is
k
φg,r ( j) ≡ Yg,r,1991
( j)/
∑
k
Yg,r,1991
( j)
j∈J k
where J k is the set of industries in sector k.
Table A4 reports summary statistics of industry composition in the sample of 518 microregions on
1991. Columns (1) and (3) indicate that regions, on average, have a large fraction of their work force
allocated to the commodity sector with agriculture accounting for the bulk of the sector’s labor expenditure. Importantly, columns (2) and (4) document great heterogeneity in industry composition across
microregions. Comparing columns (1) and (3), it is possible to identify different exposure patterns
for the two groups. While HSD are more likely to be employed in the production of grains and soft
agricultural items, HSG are more likely to be employed in the production of livestock and crude oil.
Table A4: Summary Statistics: Labor Income Share by Industry in Brazil, 1991
High-School Graduates
Industry
High-School Dropouts
Mean
(1)
SD
(2)
Mean
(3)
SD
(4)
9.0%
9.6%
21.6%
19.7%
4.7%
13.0%
35.5%
3.0%
1.0%
8.4%
34.3%
11.6%
16.1%
21.1%
7.2%
4.0%
17.1%
20.7%
10.1%
19.5%
26.8%
1.6%
1.8%
2.3%
37.9%
16.3%
18.0%
15.6%
4.2%
4.7%
6.2%
19.8%
2. Manufacturing
16.1%
10.7%
18.1%
11.3%
3. Non-Tradable Goods and Services
74.9%
10.8%
60.4%
14.8%
1. Commodity Sector
Grains (corn, soybeans, wheat)
Soft (coffee, cocoa, sugar and other)
Livestock (cattle, hogs, and others)
Metals (copper, lead, steel, tin, and zinc)
Precious Metals (gold and silver)
Energy (crude oil)
Other agriculture and mining
Note. Sample of male white full-time workers extracted from the Brazilian Census of 1991. Statistics are weighted by the microregion share
in national population on 1991.
Regional Labor Market Outcomes. For each triple of group-region-year, I compute labor market outcomes used in the reduced-form exercise: sector employment, sector average log wage and average
log wage.
To calculate wage outcomes, I estimate wage regressions separately for each year using the entire
sample of workers in the country. Specifically, I regress the log monthly wage on a full set of experi42
ence dummies (0-39yrs) interacted with dummies for female and white workers. The residual of this
regression corresponds to a wage measure adjusted for variation in these demographic characteristics
across groups and microregions. For each triple of group-region-year, the sector average log wage is
the weighted average of the adjusted wage among individuals reporting to have their main job in the
sector. Lastly, the average log wage is the weighted average of the adjusted wage among all individuals
in the triple of group-region-year. In both cases, the computation uses Census sampling weights.
Sector employment corresponds to the sum of efficiency-adjusted hours supplied by sector employees in a group-region-year. First, the efficiency adjustment is performed by multiplying individual weekly hours by a time-invariant measure of relative wage for each cell of sex-race-educationk , is the weighted sum of efficiency-adjusted
experience.36 Second, the total sector employment, Hg,r,t
hours of individuals reporting to have their main job in the sector computed with Census sampling
k
k / ( H C + H N ).
weights. Thus, sector employment share is defined as l g,r,t
≡ Hg,r,t
g,r,t
g,r,t
To obtain total labor supply, I use the aggregate amount of efficiency-adjusted hours in a groupC + H N . Lastly, the labor supply of immigrants is computed exactly as above
region-year: H̄g,r,t ≡ Hg,r,t
g,r,t
in a restricted sample of individuals identified as non-native residents of each microregion.37
Task Price Estimation Data. In the structural exercise, the estimation of sector-specific task prices requires initial sector employment and wage growth across percentiles of the wage distribution for each
triple of group-region-period. To this extent, I compute percentiles of log hourly wage from the sample
of individuals in a group-region-period using Census sampling weights. Individuals are distributed
across percentile bins according to their log hourly wage — in the benchmark specification, I consider
bins with width of 1pp. The sector employment share in each percentile bin corresponds to the fraction of efficiency-adjusted hours reported by sector employees in that percentile bin. Additionally, the
wage growth in each percentile corresponds to the difference in the average hourly wage of individuals in that percentile bin between two consecutive years. Since extreme wage values are more likely to
be generated by measurement error, I ignore the wage distribution tails by restricting the estimation to
bins between the 6th and the 94th percentiles. Thus, the task price estimation is based on 88 percentile
bins for each of the 2,072 group-region-period triples.
Chinese Imports Data. The series of Chinese imports by industry used in the robustness exercise
below is constructed from imports information at the 2-digit SITC (rev3) industry level in the Comtrade
database. I use China imports from the rest of the world in Food & live animals, Crude material,
Mineral fuel, and Animal/Veg Oil. I map the 26 industries in these groups to the six commodity
categories on Table A1 (crosswalk available upon request).
36 I consider 48 cells based on two sex groups, two race groups (white and non-white), three educational groups (highschool dropouts, high-school graduates and college graduates) and four experience groups (0-9, 10-19, 20-29 and 30-39 years).
For each cell, the relative wage is the average hourly wage divided by the average wage of female non-white high-school
dropouts with 0-9 years of experience. The cell weight is the average relative wage across regions and years (1991, 2000,
2010). In the 1980 Census, weekly hours are only reported in ranges. To compute efficiency-adjusted hours, I assign 45 and
54 weekly hours to individuals reporting respectively 40-48 and 49+ hours.
37 Given the information in the Census, I can only identify as microregion natives those individuals satisfying one out
of two conditions. First, they were born in the same municipality that they current live in. Second, if they were born in a
different municipality, then I also consider microregion natives those that moved into the current municipality from another
municipality in the same microregion during the previous ten years.
43
B
Reduced-Form Evidence: Sensitivity Analysis
Having established the main results in Section 3, I turn to an empirical investigation of the robustness
of these results taking as starting point the detailed specification with period dummies interacted with
macroregion dummies, initial labor market conditions and initial commodity sector size controls.
Additional Controls. Table B1 extends the baseline model with additional demographic controls in
the initial period. In columns (2), (6) and (10), I investigate the effect of the increase in employment
formalization in Brazil in 1991-2010 — for the share of formalized employees increased from 72.3%
in 1991 to 82.3% in 2010. To the extent that formalization was lower in rural areas, this increase is
potentially correlated with regional exposure to commodity price shocks. I address this concern with
the inclusion of the initial share of formal sector employees in the microregion.38 Yet, these controls
have almost no impact on estimated coefficients.
The other two variables refine the set of initial sector composition controls, capturing more flexibly
confounding effects related to heterogeneity in regional exposure to sectoral shocks. I introduce the
initial share of group labor income in manufacturing industries (columns 3, 7 and 11) and in agriculture
and mining products without international prices (columns 4, 8 and 12). By interacting these variables
with period dummies, I allow for an arbitrary change in the price of these products relative to the price
of internationally traded commodities. In both cases, coefficients are essentially the same for HSG, but
they are slightly lower for the wage and sector employment responses of HSD remaining nevertheless
statistically significant at 5%.
Additional Period. Table B2 estimates the model in the extended sample spanning the entire period of
1980-2010. As argued above, the peculiar economic conditions in Brazil could potentially weaken the
connection between domestic and international commodity prices during the 1980s. Yet, columns (2)
and (5) indicate very similar responses in terms of group wages and commodity sector employment.
Differences arise for the response of the commodity sector wage differential in column (8). In this
case, the coefficient for HSG falls by 40%, moving towards the lower bound of the baseline confidence
interval. For HSD, we obtain a higher and more precise coefficient compared to the nonsignificant
coefficient implied by the baseline specification.
Compared to the period of 1991-2010, the 1980s exhibit another important difference: commodity
prices experienced strong losses in the decade. Taking advantage of this qualitatively different price
behavior, columns (3), (6) and (9) estimate the model using only within-microregion variation across
time — that is, I include microregion-specific time trends in the model. This specification addresses
concerns that shock exposure is picking up secular trends in microregions specialized in the commodities with larger price gains in 1991-2010. Although the microregion fixed effects absorb much of the
cross-section variation in labor market outcomes, they have little effect on estimated coefficients.39
38 Restricting the sample to formal sector employees creates a selection problem because low-wage individuals are more
likely to drop out of the sample which attenuates wage gains in the period. To avoid this issue, I control for the pre-sample
formal sector size which captures any correlation between production specialization and employment formalization.
39 In omitted exercises, I have estimated the model with micreoregion fixed effects in the baseline sample of 1991-2010. In
this case, standard errors become five to ten times higher. This increase is related to the high correlation in shock exposure
between 1991-2000 and 2000-2010 — the autocorrelation of shock exposure is 0.734. Consequently, there is little within-
44
Additional Worker Groups. In Table B3, I extend the sample to include female and non-white individuals. With this exercise, I evaluate whether these additional worker groups exhibit similar behaviors in
the labor market. This possibility is specially relevant given the large changes in gender and race wage
gaps in the period (Ferreira, Firpo, and Messina, 2014). In columns (2), (6) and (10), I include female
white individuals without significant changes in estimated coefficients. The inclusion of non-white
male individuals entails a more intricate change in estimated coefficients as shown in columns (3), (7)
and (11). Responses of sector employment and wages became weaker for HSG in Panel A, but the opposite is true for HSD in Panel B. These different estimated responses are likely related to differences
between white and non-white individuals in terms of unobservable characteristics driving their sectoral allocation. This is particularly important among HSG because of the extremely low high-school
graduation rate among non-white individuals in Brazil.
IV: Exposure to Chinese Imports Growth. Now I address concerns regarding endogeneity of relative
commodity prices introduced if Brazilian regions are large enough to affect the world price of basic
commodities. For example, a negative shock to a region’s commodity sector labor supply would simultaneously imply a decrease in sector employment and an increase in world prices, introducing a
negative bias in the OLS estimates. Motivated by the strategy in Autor, Dorn, and Hanson (2013), I propose an instrument based on the regional exposure to Chinese imports growth. That is, I instrument
∆Zg,r,t with the following variable:
∆Mg,r,t =
∑
φg,r ( j) · ∆ ln Mt ( j)
j∈J C
where Mt ( j) is the total value of Chinese imports of product j in year t.
Table B4 presents the estimation of this model by 2SLS. Estimated coefficients for HSG are essentially the same albeit more imprecise. For HSD, there is an increase in point estimates, but this change
is not significant given the even stronger increase in standard errors.
Shock Exposure and Labor Supply. The labor demand shock captured in the exposure variable has
the potential to affect the total quantity of hours supplied by workers in a microregion. Such response
can be related to changes in the labor supply of native workers and/or changes in the flow of immigrant workers. To investigate the labor supply response to commodity price shocks, Table B5 estimates
model (2) for the log change in total hours supplied by all workers in columns (1)-(2) and immigrant
workers in columns (3)-(4). Among HSD, shock exposure is not related to the labor supply of both
native and non-native workers. For HSG, columns (1) and (3) indicate a weak negative relation between their labor supply and the commodity price shock. Yet, this negative relation disappears once
the initial educational composition of the labor force is included in columns (2) and (4). These controls
capture the educational achievement convergence across Brazilian microregions in the period, eliminating the relation between labor supply growth and shock exposure.40 Overall, Table B5 suggests
limited responses in regional labor supply following commodity price shocks.
microregion exposure variation to precisely estimate the coefficient of interest. When the 1980-1991 period is included, there
is a significant increase in exposure variation within microregions, leading to the more precise results in Table B2.
40 In omitted exercises, I attest that educational compositional controls do not affect the results in Tables 1 and 2.
45
Alternative Measure of Shock Exposure. Table B6 investigates the robustness of sector-level responses
to the use of the alternative exposure measure computed with the overall industry participation in
the group-region wage bill. Columns (1)-(3) indicate that employment in the commodity sector is
positively related to this alternative measure of price shock exposure. Also, predicted elasticities are
similar to those in the baseline specification: using the average commodity sector size for each group,
estimated coefficients in column (1) imply that a 1% increase in commodity prices cause the commodity
sector employment share to increase by .029 p.p. for HSG and .069 p.p. for HSD. Column (4)-(6)
perform the same exercise for the change in the commodity sector wage premium. Similar to the
baseline specification, there is a significant response in sector wage differential for HSG. However, the
alternative measure also predicts a significant positive response in the sector wage premium for HSD
— notwithstanding the coefficient remains lower than its counterpart for HSG.
46
47
0.636
R2
Yes
Initial commodity sector size controls x period dummies
No
No
No
Initial size of manufacturing sector x period dummies
Initial size of other agriculture and mining in the
commodity sector x period dummies
No
Yes
No
Yes
Yes
0.645
0.201*
(0.086)
0.443
0.277**
(0.060)
(3)
Yes
No
No
Yes
Yes
0.639
0.217*
(0.101)
0.440
0.283**
(0.067)
(4)
No
No
No
Yes
Yes
0.559
1036
0.099**
(0.029)
0.405
0.038**
(0.010)
(5)
No
No
Yes
Yes
Yes
0.565
1036
0.097**
(0.029)
0.406
0.039**
(0.010)
(6)
No
Yes
No
Yes
Yes
0.560
1036
0.089**
(0.029)
0.407
0.039**
(0.010)
(7)
Yes
No
No
Yes
Yes
0.566
0.067*
(0.030)
0.406
0.036**
(0.010)
(8)
Change in Commodity Sector Employment
Share
No
No
No
Yes
Yes
0.218
1036
0.059
(0.161)
0.220
0.416**
(0.098)
(9)
No
No
Yes
Yes
Yes
0.221
1036
0.062
(0.162)
0.223
0.420**
(0.098)
(10)
No
Yes
No
Yes
Yes
0.221
1036
0.080
(0.163)
0.220
0.410**
(0.100)
(11)
Yes
No
No
Yes
Yes
0.221
0.000
(0.171)
0.221
0.414**
(0.100)
(12)
Change in Commodity Sector Average Log
Wage Premium
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991 and include ten macroregion-period dummies. Baseline controls as in Table 1. Standard Errors clustered by microregion. **
p<0.01, * p<0.05
No
Yes
No
Yes
Yes
0.637
Initial size of formal sector x period dummies
Additional Controls
Yes
Initial labor market conditions x period dummies
Baseline Controls
0.268**
(0.098)
0.441
0.440
0.268**
(0.099)
0.286**
(0.064)
(2)
0.288**
(0.064)
(1)
Change in Average Log Wage
Commodity price shock
B. High-School Dropouts
R2
Commodity price shock
A. High-School Graduates
Dependent Variable:
Table B1: Exposure to Commodity Price Shocks and Labor Market Outcomes, Additional Controls
48
No
Extended sample: including 1980-1991
Yes
Yes
No
Yes
Yes
0.624
0.235**
(0.054)
0.500
0.214**
(0.049)
(2)
Yes
Yes
Yes
Yes
Yes
0.706
0.285**
(0.079)
0.597
0.231**
(0.069)
(3)
No
Yes
No
Yes
Yes
0.559
1036
0.099**
(0.029)
0.405
0.038**
(0.010)
(4)
Yes
Yes
No
Yes
Yes
0.490
1036
0.071**
(0.021)
0.319
0.051**
(0.013)
(5)
Yes
Yes
Yes
Yes
Yes
0.603
1036
0.068*
(0.028)
0.417
0.062**
(0.018)
(6)
Change in Commodity Sector
Employment Share
No
Yes
No
Yes
Yes
0.218
1036
0.059
(0.161)
0.220
0.416**
(0.098)
(7)
Yes
Yes
No
Yes
Yes
0.259
1036
0.339**
(0.095)
0.223
0.234*
(0.099)
(8)
Yes
Yes
Yes
Yes
Yes
0.426
1036
0.417**
(0.125)
0.322
0.218+
(0.132)
(9)
Change in Commodity Sector
Average Log Wage Premium
Note. Stacked sample of 518 microregions in baseline sample and 503 microregions in extended sample. All regressions are weighted by the microregion share in national population on 1991 and include macroregion-period
dummies and initial share of group labor income in the commodity sector. Labor market conditions as in Table 1. Industry composition measured in the initial period of 1991 for baseline sample and of 1980 for extended sample.
Commodity sector size controls in extended sample: share in group labor income of other agriculture and mining industries in the commodity sector, and quadratic polynomial of the share in group labor income of the commodity
sector (columns 2-3). Standard Errors clustered by microregion. ** p<0.01, * p<0.05, + p<0.1
Yes
Baseline sample: 1991-2000 and 2000-2010
Sample Period
Microregion-specific linear time trend
No
Yes
Additional Controls
Yes
Initial commodity sector size controls x period dummies
0.636
Initial labor market conditions x period dummies
Baseline Controls
R2
Commodity price shock
0.268**
(0.099)
0.440
R2
B. High-School Dropouts
0.288**
(0.064)
(1)
Change in Average Log Wage
Commodity price shock
A. High-School Graduates
Dependent Variable:
Table B2: Exposure to Commodity Price Shocks and Labor Market Outcomes, Additional Period, 1980-2010
49
Yes
No
No
Including female
Including non-white
No
Yes
Yes
Yes
Yes
0.650
0.295**
(0.099)
0.539
0.240**
(0.064)
(2)
Yes
No
Yes
Yes
Yes
0.653
0.317**
(0.110)
0.561
0.303**
(0.062)
(3)
Yes
Yes
Yes
Yes
Yes
0.664
0.338**
(0.108)
0.617
0.260**
(0.063)
(4)
No
No
Yes
Yes
Yes
0.559
1036
0.099**
(0.029)
0.405
0.038**
(0.010)
(5)
No
Yes
Yes
Yes
Yes
0.591
1036
0.113**
(0.031)
0.420
0.032**
(0.008)
(6)
Yes
No
Yes
Yes
Yes
0.620
0.113**
(0.031)
0.410
0.028**
(0.009)
(7)
Yes
Yes
Yes
Yes
Yes
0.652
1036
0.121**
(0.034)
0.441
0.022**
(0.008)
(8)
Change in Commodity Sector Employment
Share
No
No
Yes
Yes
Yes
0.218
1036
0.059
(0.161)
0.220
0.416**
(0.098)
(9)
No
Yes
Yes
Yes
Yes
0.254
1036
0.091
(0.149)
0.280
0.469**
(0.100)
(10)
Yes
No
Yes
Yes
Yes
0.258
0.234*
(0.099)
0.276
0.359**
(0.099)
(11)
Yes
Yes
Yes
Yes
Yes
0.285
1036
0.227*
(0.090)
0.359
0.431**
(0.101)
(12)
Change in Commodity Sector Average Log
Wage Premium
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regression are weighted by the microregion share in national population on 1991 and include ten macroregion-period dummies. Baseline controls as in Table 1. Standard Errors clustered by microregion. **
p<0.01, * p<0.05
Yes
Baseline sample: male / white
Additional worker groups
Yes
Initial commodity sector size controls x period dummies
0.636
Initial labor market conditions x period dummies
Baseline Controls
R2
Commodity price shock
0.268**
(0.099)
0.440
R2
B. High-School Dropouts
0.288**
(0.064)
(1)
Change in Average Log Wage
Commodity price shock
A. High-School Graduates
Dependent Variable:
Table B3: Exposure to Commodity Price Shocks and Labor Market Outcomes, Additional Worker Groups
Table B4: Exposure to Commodity Price Shocks and Labor Market Outcomes, 2SLS using Exposure
to Chinese Imports Growth
Change in Average Log Wage
Dependent Variable:
Change in Commodity Sector
Employment Share
Change in Commodity Sector
Average Log Wage Premium
(1)
(2)
(3)
(4)
(5)
(6)
0.286**
(0.064)
0.262**
(0.095)
0.039**
(0.010)
0.035+
(0.020)
0.420**
(0.098)
0.398+
(0.205)
A. High-School Graduates
Commodity price shock
F-stat of excluded variable
36.1
36.1
36.1
B. High-School Dropouts
Commodity price shock
0.268**
(0.098)
0.746**
(0.271)
F-stat of excluded variable
0.097**
(0.029)
0.261*
(0.109)
28.6
0.062
(0.162)
0.575
(0.364)
28.6
28.6
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. 2SLS estimator where the instrument is the microregion's exposure to growth in Chinese imports. All regressions are weighted by
the microregion share in national population on 1991. Regressions include period dummies interacted with macroregion dummies, initial formal sector size and baseline controls described on Table 1.
Standard Errors clustered by microregion. ** p<0.01, * p<0.05, + p<0.1
Table B5: Exposure to Commodity Price Shocks and Labor Supply
Change in Log of Total
Labor Supply
Dependent Variable:
Change in Log of
Immigrants' Labor Supply
(1)
(2)
(3)
(4)
-0.529+
(0.271)
0.051
(0.114)
-0.535+
(0.279)
0.055
(0.131)
0.686
0.811
0.649
0.753
Commodity price shock
0.006
(0.173)
0.209
(0.156)
0.005
(0.221)
0.226
(0.202)
R2
0.847
1036
0.877
1036
0.845
1036
0.869
1036
Initial labor market conditions x period dummies
Yes
Yes
Yes
Yes
Initial commodity sector size controls x period dummies
Yes
Yes
Yes
Yes
Initial educational composition of labor force x period dummies
No
Yes
No
Yes
A. High-School Graduates
Commodity price shock
R2
B. High-School Dropouts
Baseline Controls
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991 and
include ten macroregion-period dummies. Baseline controls as in Table 1. Educational composition of labor force: share of colloge graduates and share of high-school
graduates and some college. Standard Errors clustered by microregion. + p<0.1
50
Table B6: Exposure to Commodity Price Shocks and Sector Labor Outcomes, Alternative Measure
Dependent Variable:
Change in Commodity Sector
Employment Share
Change in Commodity Sector
Average Log Wage Premium
(1)
(2)
(3)
(4)
(5)
(6)
Commodity sector size x Commodity price shock
0.193*
(0.094)
0.196*
(0.089)
0.158+
(0.087)
1.971*
(0.858)
2.032*
(0.870)
1.365+
(0.703)
R2
0.282
0.341
0.402
0.143
0.195
0.215
Commodity sector size x Commodity price shock
0.183*
(0.088)
0.175+
(0.092)
0.161+
(0.092)
0.683**
(0.227)
1.075**
(0.244)
1.068**
(0.241)
R2
0.507
1036
0.555
1036
0.557
1036
0.164
1036
0.227
1036
0.228
1036
Initial labor market conditions x period dummies
No
Yes
Yes
No
Yes
Yes
Initial commodity sector size controls x period dummies
No
No
Yes
No
No
Yes
A. High-School Graduates
B. High-School Dropouts
Baseline Controls
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. All regressions are weighted by the microregion share in national population on 1991 and include ten
macroregion-period dummies. Baseline controls as in Table 1. Standard Errors clustered by microregion. ** p<0.01, * p<0.05, + p<0.1
51
C
Two-Sector Roy Economy: Competitive Equilibrium
In this section, I describe the production and market structures that generate generate the demand for
sector-specific tasks with log-prices given by (ω gk , ω gN ). To this extent, I assume that each market is a
small open economy with a segmented competitive labor market. Specifically, goods are freely traded
in the world market but factors of production are not. Therefore, product prices are exogenously
determined internationally and factor prices are endogenously determined locally.
C.1
Demand of Sector-Specific Tasks
Suppose sector k is constituted of multiple competitive industries, j ∈ J k . In each industry j of sector k, the production technology requires workers of group g to perform a sector-specific task. The
production function combines the sum of the sector-specific task produced by all industry employees,
k,j
{ Tg } g , and other industry-specific inputs, Xk,j . Formally, the production function is
q
k,j
=Q
k,j
k,j
{T }g , X
k,j
k,j
|Bm
ˆ
Tgk
s.t.
k,j
=
i ∈I g
Tgk (i ) · L g (i ) di
(28)
k,j
where L g (i ) is an indicator function that equals one if individual i is employed in industry j of sector
k; and Xk,j is the vector of industry-specific inputs.
In equation (28), the central restriction is that production in every industry j of sector k requires
the same sector-specific task. Thus, individuals are perfect substitutes across industries within the
sector. Notice that the production function allows, but does not require, tasks of different groups to be
imperfect substitutes.
Firms take as given the unit log-price of the sector-specific task, ω gk . Hence, the demand for the
k,j
k,j
sector-specific task of group g in industry j of sector k is Tg ({wkg } g |Zk,j ) = Tg such that
ω gk = ln pk,j + ln
k,j
∂Qk { Tg } g , X̄k,j Bk,j
∂Tgk
for all g
where Dk,j ≡ ln pk,j , Bk,j , X̄k,j is the vector of industry-sector demand shifters with X̄k,j denoting the
endowment of the industry-specific factor.
Lastly, the sector-specific task demand combines the task demand of all industries in the sector:
Tgk {ω gk } g Dk =
∑
k,j
Tg
{ω gk } g Dk,j
(29)
j∈J k
where Dk ≡ Dk,j j∈J k is the vector of sector demand shifters.41
41 The simplicity of this production structure sheds light on the distributive channel implied by worker heterogeneity in
the Two-Sector Roy Economy. Accordingly, one could consider alternative environments with a generic demand for sectorspecific tasks as in the case of non-competitive product markets and additional mobile factors of production.
52
C.2
Supply of Sector-Specific Tasks
In the analysis of Section 4, I have focused on the structure of employment and wages in the TwoSector Roy Economy. Here, I describe the consequences of this structure to the supply of sector-specific
tasks. Recall that preferences in (3) imply individuals with comparative advantage below α g (l gN ) are
employed in the non-commodity sector. As a result, the total supply of tasks in the non-commodity
sector is
T̄gN
l gN
ˆ
≡ Īg ·
l gN
E exp( a g (i ))|s g (i ) = α g (q) dq
(30)
0
where Īg is the mass of individuals of group g; and E exp( a g (i ))|s g (i ) = α g (q) is determined by the
conditional distribution of absolute advantage in (4).
Analogously, individuals with comparative advantage above α g (l gN ) are employed in the commodity sector. Thus,
T̄gC
l gN
ˆ
≡ Īg ·
1
l gN
exp(α g (q)) · E exp( a g (i ))|s g (i ) = α g (q) dq.
(31)
The supply of sector-specific tasks depends on both the skill distribution and the endogenous sector employment composition. As discussed in Section 4, the sector employment composition, l gN , is
determined by the free mobility condition (5) which I repeat here to facilitate exposition:
ω gN − ω gC = α g l gN .
C.3
(32)
Competitive Equilibrium
Market Clearing. The competitive equilibrium requires the equalization of supply and demand for
tasks in each sector. For group g in sector k, this is equivalent to
Tgk
{ω gk } g Dk
=
T̄gk
l gN
(33)
where Tgk {ω gk } g Zk is the task demand in (29), and T̄gk l gN is the task supply in (30)-(31).
The following definition outlines the competitive equilibrium of the Two-Sector Roy Economy.
Definition 1. [Competitive Equilibrium] The competitive equilibrium in the Two-Sector Roy Economy is
determined by the vector of sector-specific task prices, {(ω gC , ω gN )} g , such that, for all g and k, (i) sector-specific
task demand, Tgk {ω gk } g Dk , is given by (29); (ii) sector-specific task supply, T̄gk l gN , is given by (30)-(31);
(iii) sector employment composition, l gN , is given by (32); and (iv) market clearing is given by (33).
53
D
Theory: Auxiliary Results and Model Extensions
D.1
Lemma 1
Lemma 1. Consider a model of the form:
em = ym − Φ (lm ) − Xm γ.
Assume there is an instrumental variable Zm satisfying Assumption 4. If E[em | Zm , Xm ] = 0, then the function
Φ(.) is identified up to a constant. With the normalization E[Xm γ] = 0, the constant in Φ(.) is also identified.
Proof. First, E[em | Zm , Xm ] = 0 implies that E [Φ (lm ) + Xm γ| Zr,t , Xr ] = E [ym | Zm , Xm ]. Now let us
proceed by contradiction. Suppose there exist Φ̃ (lm ) and γ̃ such that E Φ̃ (lm ) + Xm γ̃| Zm , Xm =
E [ym | Zm , Xm ]. By Assumption 4,
Φ (lm ) − Φ̃ (lm ) = Xm (γ − γ̃) almost surely.
Take m and m0 such that Xm = Xm0 . The condition above implies that, for all lm and lm0 , we must
have Φ (lm ) − Φ̃ (lm ) = Φ (lm0 ) − Φ̃ (lm0 ). Thus, Φ(.) is identified up to a constant. To determine this
constant, we can use the normalizations E[em ] = E[Xm γ] = 0 which imply that E[Φ̃ (lm )] = E[ym ]. D.2
Derivation of Equation (19)
The analysis in this section considers a shock to endogenous and exogenous variables in an arbitrary
region and year; accordingly, I drop indices r and t to simplify the notation. Define individual i’s
log-wage as y g (i ) such that
y g (i ) = max{ω gC + s g (i ) + a g (i ); ω gN + a g (i )}.
Under Assumption 1, this implies that the log-wage distribution of group g is given by
Pr [y g (i ) ≤ y] = Pr [y g (i ) ≤ y; s g (i ) ≤ ω gN − ω gC ] + Pr [y g (i ) ≤ y; s g (i ) > ω gN − ω gC ]
ˆ lgN
ˆ 1 h
i
h
i
N
Pr a g (i ) ≤ y − ω gC − α g (q) − ũ g α g (q) dq
=
Pr a g (i ) ≤ y − ω g α g (q) dq +
(34)
l gN
0
where Pr [ a g (i ) ≤ a|s̃ g (i ) = s] ≡ µHga ( a|s) + (1 − µ) H e ( a|u g , θg ).
Recall that, by construction, Yg (π ) is implicitly defined as the solution of Pr y g (i ) ≤ Yg (π ) = π.
Taking a first-order expansion of this equation,
f gN
Yg (π ) +
where f gN (y) ≡
f gC
Yg (π )
∂Pr [y g (i )≤y; s g (i )≤ω g ]
,
∂y
∆Yg (π ) = f gN Yg (π ) · ∆ω gN + f gC Yg (π ) · ∆ω gC − ∆v0g (π )
f gC (y) ≡
∂Pr [y g (i )≤y; s g (i )>ω g ]
,
∂y
and ω g ≡ ω gN − ω gC .
In this expression, the first-order impact of the endogenous change in l gN is eliminated by the employment condition (5), reflecting the fact that marginal workers are indifferent between the two sec54
tors. The term ṽ˜ g (π ) incorporates changes to other exogenous parameters of the skill distribution:
"ˆ
∆v0g (π )
≡ (1 − µ )
l gN
0
∇θ H
ˆ
"
+ f gC Yg (π ) + (1 − µ)
0
l gN
e
Yg (π ) − ω gN ũ g , θg
∇u H e
ˆ
dq +
1
l gN
∇θ H
ˆ
N
Yg (π ) − ω g ũ g , θg dq +
e
1
l gN
Yg (π ) − ω gC
∇u H e
#
− α g (q) − ũ g ũ g , θg dq · ∆θg
Yg (π ) − ω gC − α g (q) − ũ g ũ g , θg dq
!#
i
h
To obtain equation (19), notice that, by definition, l gN (π ) ≡ P s g (i ) ≤ ω gN − ω gC y g (i ) = Yg (π )
which is equivalent to
i
h
P y g (i ) = Yg (π ); s g (i ) ≤ ω gN − ω gC
f gN Yg (π )
N
l g (π ) =
= N
P y g (i ) = Yg (π )
f g Yg (π ) + f gC Yg (π )
Thus,
∆Yg (π ) = ∆ω gC · l gC (π ) + ∆ω gN · l gN (π ) + ∆v00g (π )
i
h
where ∆v00g (π ) ≡ −∆v0g (π ) f gN Yg (π ) + f gC Yg (π ) .
Finally, equation (19) is obtained by assuming a particular structure of observable and unboservable components of ṽ g (π ):
∆v00g (π ) ≡ µ g · X̃ g (π ) + ∆v g (π ).
D.3
Model Extensions: Non-monetary Employment Benefits
This section extends the Two-Sector Roy Economy of Section 4 by incorporating non-monetary employment benefits — a reduced-form for work conditions and switching cost. The environment of
Section 4 remains the same except that now I allow workers to derive utility from both consumption
and employment. In particular, assume that, if employed in sector k, a consumption bundle c yields
utility τgk · u(c) where u(.) is homogeneous of degree one. Thus, individual i’s payoff of employment
in sector k is given by
Ugk (i ) = τgk ·
wkg Tgk (i )
P
(35)
where τgk is the private benefit of being employed in sector k for workers of group g; and P is the price
index (i.e., the cost of achieving one utility unit).
Without loss of generality, normalize τgC ≡ 1 and denote τg ≡ ln τgN . Assuming that workers
maximize their total utility, individual i chooses to be employed in sector K g (i ) such that
n
K g (i ) = arg max ω gC + ln TgC (i );
o
τg + ω gN + ln TgN (i ) .
Following the same steps of Section 4, the employment share in the non-commodity sector is determined by the following condition:
ω gN − ω gC = α g l gN − τg .
55
(36)
∆ũ g .
Intuitively, the choice of employment balances potential earnings against amenities of the sector.
These amenities are captured by the wedge τg . Those individuals with strong comparative advantage
in the commodity sector (i.e., high s g (i )) obtain higher income in the commodity sector compared to
the non-commodity sector. To the extent that the higher income compensates for any non-monetary
benefit, these individuals choose to be employed in the commodity sector. Hence, every individual
with s g (i ) above the threshold ω gN − ω gC + τg,m self-selects into the commodity sector.
The private benefit only affects the allocation of individuals to sectors. Conditional on the sector
allocation, workers have the same sector-specific task efficiency. Hence, the remaining equilibrium
conditions are not modified with the average sector wage is still given by (6)-(7).
The main modification implied by private employment benefits is the introduction of compositional effects in the aggregate wage distribution. To see this, notice that expression (34) still determines
Yg (π ), but its first-order approximation contains one extra term:
f gN Yg (π ) + f gC Yg (π ) ∆Yg (π ) = f gN Yg (π ) · ∆ω gN + f gC Yg (π ) · ∆ω gC − ṽ˜ g (π )+
i
h + Hga Yg (π ) − ω gN − τg α g (l gN ) − Hga Yg (π ) − ω gN α g (l gN ) ∆l gN .
The extra term in this equation is directly implied by equation (36). It is zero if τg = 0; however
it cannot be ignored if τg 6= 0. To obtain a clear interpretation for this term, consider the fraction of
marginal workers with a wage of Yg (π ): ψg (π ) ≡ P[s̃ g (i ) = α g (l gN )y g (i ) = Yg (π )]. These marginal
workers are the sector-switchers for small shocks. Using Bayes’ rule,
P y g (i ) = Yg (π )s̃ g (i ) = α g (l g )
P y g (i ) = Yg (π )s̃ g (i ) = α g (l g )
ψg ( π ) = ´ 1 =
f gN Yg (π ) + f gC Yg (π )
0 P y g (i ) = Yg ( π ) α g ( q ) dq
where the numerator is the wage density conditional on a comparative advantage equal to α g (l gN ).
h
i
Notice that P y g (i ) = Yg (π )s̃ g (i ) = α g (l gN ) = h g Yg (π ) − ω gN α g (l gN ) because the wage distri bution among marginal workers is Hg y − ω gN α g l gN .42 Thus,
h g Yg (π )|α g (l gN )
.
ψg ( π ) = N
f g Yg (π ) + f gC Yg (π )
Using this expression, we have that
Hg Yg (π ) − ω gN − τg α g (l gN ) − Hg Yg (π ) − ω gN α g (l gN )
≈ −τg · ψg (π ).
f gN Yg (π ) + f gC Yg (π )
42 This
expressions relies on the assumption that marginal workers are allocated to the non-commodity sector since
they are indifferent between
the two sectors. If instead they are allocated to the commodity sector, we would have
Hg y − ω gN − τg α g l gN
and the same steps lead to an identical final expression.
56
Hence, the wage gain at quantile π is, up to a first-order approximation, given by:
∆Yg (π ) = ∆ω gC · l gC (π ) + ∆ω gN · l gN (π ) − ∆l g · [τg ψg (π )] + ṽ g (π )
(37)
where ψg (π ) is the share of sector-switchers among workers at the π-percentile of the earnings distribution.
The additional term in (37) captures the compositional effect introduced by the difference in sector
potential wage of marginal workers in the presence of non-monetary employment benefits. Accordingly, the compositional effect is proportional to the fraction of sector-switchers among individuals at
wage quantile π, ψg (π ), and their between-sector wage wedge, τg .
D.4
Parametric Restrictions on the Distribution of Comparative and Absolute Advantage
This section discusses prominent distributional assumptions that determine the form of α g (.) and
Ākg (.). To simplify notation, we omit subscripts for groups, regions and years.
D.4.1
Normal Distribution
Particularly important in the selection literature is the case of log-normally distributed sector-specific
skill (Roy, 1951; Heckman and Sedlacek, 1985; Borjas, 1987; Ohnsorge and Trefler, 2007; and Mulligan
and Rubinstein, 2008). That is, assume that sector-specific skill is independently drawn from a bivariate
normal distribution:
C
N
"
ln T (i ), ln T (i ) ∼ N
µC
µN
# "
;
σC2
σCN
σCN
2
σN
#!
.
Because the comparative advantage of individual i is defined as s(i ) = ln T C (i ) − ln T N (i ), it is
2 − 2σ
straight forward to conclude that s(i ) ∼ N (µ, σ2 ) where µ ≡ µC − µ N and σ2 ≡ σC2 + σN
CN . As a
2 . Thus, the distribution
result (s(i ), a(i )) is jointly normal with covariance of Cov(s(i ), a(i )) = σCN − σN
of a(i ) conditional on s(i ) = s is normal with conditional mean given by
E [ a(i )|s(i ) = s] = µ̃ + ρ · s
s.t.
µ̃ ≡ (1 + ρ)µ N − ρµC ,
and the variance is
V [ a(i )|s(i ) = s] =
By definition, F (s) ≡ Φ
s−µ
σ
σ22
≡
2
σN
ρ≡
2
σCN − σN
;
2 − 2σ
σC2 + σN
CN
2 2
σCN − σN
− 2
.
2 − 2σ
σC + σN
CN
where Φ(.) is the CDF of the standard normal distribution. Thus,
α ( q ) ≡ F −1 ( q ) = µ + σ · Φ −1 ( q ).
57
(38)
Also, notice that
Ā N (l N ) ≡
Because
1
lN
´ lN
0
ˆ
0
l
ρ
E a(i )|s(i ) = α g (q) dq = µ̄ + N
l
ˆ
lN
α(q)dq = (µ̃ + ρµ) +
0
ρσ
lN
ˆ
lN
Φ−1 (q)dq.
0
Φ−1 (q)dq = φ Φ−1 (l N ) ,
φ Φ −1 ( l N )
Ā (l ) = µ̄ − (ρσ) ·
lN
N
(39)
where µ̄ ≡ (µ̃ + ρµ) = µ N .
For completeness, consider the average task efficiency in the commodity sector:
1
ĀC (l N ) ≡
1−l
ˆ
1
l
φ Φ −1 ( l N )
.
α(q) + E [ a(i )|s(i ) = α(q)] dq = (µ + µ̄) + σ(1 + ρ) ·
1 − lN
Equations (38)-(39) illustrate the connection between the parameters governing the skill distribution and the schedules of comparative and absolute advantage. First, the dispersion of comparative
advantage, σ, controls the magnitude of the between-sector reallocation of individuals in response
to changes in the relative task price. Second, the sensitivity of the mean absolute advantage to the
comparative advantage, ρ, controls the compositional effect of employment on sector average wage.
D.4.2
Extreme Value Distribution
Recent papers have adopted a skill distribution of the Frechet family (Hsieh, Hurst, Jones, and Klenow,
2013; Burstein, Morales, and Vogel, 2015; Galle, Rodriguez-Clare, and Yi, 2015). The main advantage
of this distribution is its tractability in the multi-dimensional problem of sectoral choice, allowing for
an analytical characterization of the equilibrium with an arbitrary number of sectors. As discussed
below, this tractability comes at a price: it imposes a restrictive pattern of selection across sectors.
Specifically, assume that skill in each sector is independently draw from a Frechet distribution:
"
T C (i ), T N (i ) ∼ exp −
∑
Tk
−κ
#
k =C,N
where I assume that κ > 1 to guarantee finiteness of first-order moments.
First, consider the distribution of comparative advantage:
ˆ
F (s) ≡ Pr [s(i ) < s] =
∞
−∞
e
− e −κ ( a + s )
κe
−κa −e−κa
e
ˆ
da =
∞
−∞
κe−κa e−(1+e
Define x ≡ (1 + e−κs )e−κa such that dx = −κ (1 + e−κs )e−κa da. Thus, F (s) =
α(q) ≡ F
−1
1
(q) = ln
κ
58
q
1−q
−κs ) e−κa
1
1+e−κs
da.
and, therefore,
.
(40)
Second, consider the joint distribution of absolute and comparative advantage:
ˆ
Pr [ a(i ) < ā; s(i ) < s] =
ā
−∞
κe−κa e−(1+e
−κs ) e−κa
da =
−κs −κ ā
1
e−(1+e )e .
−
κs
1+e
To obtain the average task efficiency, notice that the skill distribution in the non-commodity sector
is
h
Pr a(i ) < a|s(i ) < α l N
i
=e
−κα l N
− 1+e ( ) e−κa
1
= e− l N e
−κa
= e−e
−κ a+ κ1 ln l N
(
)
where the second equality follows from the definition of α(.).
Since this is a Gumbel distribution with parameters β ≡ 1/κ and µ ≡ − κ1 ln l N , the average task
efficiency in the non-commodity sector is
Ā N (l ) =
γ 1
− ln l N
κ
κ
where γ is the Euler-Mascheroni constant. From this expression, we can recover
A(q) =
γ−1 1
− ln l N .
κ
κ
(41)
Analogously, the skill distribution in the commodity sector is
h
i
−κ ( aC + κ1 ln(1−l N ))
Pr ln T C (i ) < aC |s(i ) > α l N = e−e
⇒
γ 1 ĀC l N = − ln 1 − l N .
κ
κ
The schedules of comparative and absolute advantage in equations (40)-(41) are fully characterized
by the skill dispersion parameter, κ. If skill dispersion is low (i.e., κ is high), then a small variation
in the relative task price is associated with a large response of sector employment. In addition, a
sector employment expansion causes a decrease in the average sector efficiency whose magnitude is
also controlled by the skill dispersion. In other words, the extreme value distribution only allows
for positive selection in both sectors. This very particular pattern of selection has strong implications
for the wage distribution, implying that both sectors exhibit the same distribution of labor earnings.
Specifically, the log-wage distribution in sector k is
G N ( y ) = e−e
−κ y−ω N + κ1 ln l N
(
)
= e−e
−κ y−ω C + κ1 ln(1−l N )
(
)
= GC (y)
where the second equality follows from the employment equation in (5).
D.4.3
Log-Linear System: A Skill Distribution Example
In this section, I describe a distribution that delivers the log-linear functional forms in Assumption 5.
To avoid infinite moments, assume that comparative advantage has a modified logistic distribution
59
with an upper bound. In particular,
(
s (i ) ∼ F ( s ) =
1
1
1+ e − α s
if s < S̄
1
if s ≥ S̄
where α > 0 and s ∈ (−∞, S̄] such that S̄ ≡ −α ln[ε/(1 − ε)] and ε ≥ 0.
Immediately,
(
α(q) =
α ln [q/(1 − q)] if q < 1 − ε
α ln [(1 − ε)/ε]
if q ≥ 1 − ε
.
where ε ≥ 0.
Although the comparative advantage distribution has finite moments for every ε ≥ 0 and α > 0,
this is not necessarily true for its moment generating function. Accordingly, the upper bound in the
support implies a well defined moment generating function for all ε > 0 and, therefore, a finite supply
N < 1 − ε and,
of sector-specific tasks. Notice that positive employment in both sectors implies that l g,r
therefore, the empirically relevant portion of the quantile function is that in Assumption 5.
Also, assume that the conditional distribution of absolute advantage is normal with a linear conditional mean:
{ a(i )|s̃(i ) = α(q)} ∼ N A g (q), σ2
Thus,
1
Ā (l ) ≡ N
l
N
ˆ
N
lN
s.t. A(q) ≡ Ā + A · ln q.
A(q) dq = A N + A · ln l N
0
where A N = ( Ā − A).
N < 1 − ε and
With positive employment in both sectors, l g,r,t
1
Ā (l ) ≡
1 − lN
C
N
ˆ
1
α(q) + A(q) dq = AC − (α N + A) ·
lN
lN
ln l N − αC · ln(1 − l N ).
1 − lN
where AC ≡ ( Ā − A) + αe · ln [(1 − ε)/ε].
E
Structural Estimation: Sensitivity Analysis
In Table E1, I evaluate the robustness of the structural results of Section 6 to specific choices of the estimation procedure regarding the moment weighting matrix and the set of instruments. In this investigation, I focus on the log-linear model with the overidentification restriction. Column (1) replicates
the baseline specification with the Two-Step GMM estimator and the vector of instruments built from
the quadratic polynomial of the exposure to international prices in Grains, Soft Agriculture, Livestock,
Mining and Energy.
Columns (2)-(3) estimate the model with alternative moment weighting matrices. Specifically, column (2) imposes that structural errors in the three equations are independent and, in addition, column
(3) imposes that structural errors are homoskedastic (i.e., 2SLS weights). In both cases, point estimates
are similar albeit, as expected, more imprecise.
60
Table E1: Structural Parameters, Specification Robustness
Baseline
Choice of Moment Weight
Matrix
Choice of Instrument Vector
(1)
(2)
(3)
(4)
(5)
(6)
0.835**
(0.212)
0.879**
(0.185)
0.997**
(0.237)
0.924**
(0.359)
0.698**
(0.219)
0.933**
(0.110)
1.966*
(0.935)
1.759*
(0.834)
2.032*
(0.978)
1.501+
(0.873)
1.605+
(0.897)
2.595*
(0.904)
0.916*
(0.399)
1.302*
(0.701)
1.475+
(0.879)
0.394
(0.536)
0.823
(0.568)
1.030*
(0.460)
-0.727**
(0.142)
-0.640**
(0.134)
-0.795**
(0.147)
-0.811**
(0.190)
-0.552**
(0.212)
-0.617**
(0.146)
A. High-School Graduates
𝛼𝐻𝑆𝐺
𝐴𝐻𝑆𝐺
B. High-School Dropouts
𝛼𝐻𝑆𝐷
𝐴𝐻𝑆𝐷
Matrix of Moment Weights
Optimal GMM weights
Yes
No
No
Yes
Yes
Yes
Optimal weights under independent equations
No
Yes
No
No
No
No
2SLS weights under independent equations
No
No
Yes
No
No
No
Exposure to international prices in Grains, Soft, Livestock,
Mining and Energy
Yes
Yes
Yes
Yes
Yes
Yes
Squared exposure to international prices in Grains, Soft,
Livestock, Mining and Energy
Yes
Yes
Yes
No
No
Yes
Sum of squared exposure to international prices in Grains,
Soft, Livestock, Mining and Energy
No
No
No
No
Yes
No
Sum of cubic and quartic of exposure to international
prices in Grains, Soft, Livestock, Mining and Energy
No
No
No
No
No
Yes
Vector of instruments
Note. Stacked sample of 518 microregions in 1991-2000 and 2000-2010. GMM estimator with microregions weighted by their share in the 1991 national population. All columns correspond to the log-linear
model with the overidentification equation. Control vector includes macroregion-period dummies, initial commodity sector size controls, and initial labor market conditions interacted with period dummies (full
description in Section 6.3). Standard Errors clustered by microregion.** p<0.01, * p<0.05, + p<0.1
In columns (4)-(6), I estimate the model with different instrument sets. The instrument vector in
column (3) is restricted to contain only the exposure to commodity price shocks by category. In this
case, estimates are similar for HSG, but the comparative advantage parameter for HSD is lower and
more imprecise. Similar conclusions are obtained with the inclusion of the sum of the squared exposure
to commodity price shocks in column (5). Thus, the disaggregated squared exposure is the main source
of identification of the comparative advantage parameter for HSD. Lastly, column (6) augments the
instrument vector to also include the cubic and quartic of the microregion’s total exposure to the price
shock. In this case, results are very similar, indicating that there is little additional gain from the use of
higher order polynomials in (24).
61