Worker Heterogeneity, Wage Inequality, and International Trade: Theory and Evidence from Brazil

Transcription

1 Worker Heterogeneity, Wage Inequality, and International Trade: Theory and Evidence from Brazil Rodrigo Adão Princeton University / University of Chicago rradao@princeton.edu December, 2016

2 World commodity prices and Brazilian wage inequality change relative to change relative to 1981 World Commodity Prices (LHS) Log-Wage Variance (RHS) Log-Wage Variance Decomposition 1 / 38

3 Relative wage in the commodity sector change relative to change relative to 1981 World Commodity Prices (LHS) Commodity Sector Relative Wage (RHS) 2 / 38

4 Relative employment in the commodity sector change relative to change relative to 1981 World Commodity Prices (LHS) Commodity Sector Relative Employment (RHS) 3 / 38

5 This Paper: 4 Parts 4 / 38

6 This Paper: 4 Parts 1. Model: Two-sector small open economy with worker heterogeneity in sector-specific productivity 4 / 38

7 This Paper: 4 Parts 1. Model: Two-sector small open economy with worker heterogeneity in sector-specific productivity Comparative advantage schedule Sectoral employment Absolute advantage schedule Sector average wage Comparative and absolute advantage schedules Change in wage inequality 4 / 38

8 This Paper: 4 Parts 1. Model: Two-sector small open economy with worker heterogeneity in sector-specific productivity Comparative advantage schedule Sectoral employment Absolute advantage schedule Sector average wage Comparative and absolute advantage schedules Change in wage inequality 2. Nonparametric identification: Market shifters of sector labor demand Sectoral employment Comparative advantage schedule Sector average wage Absolute advantage schedule Extensions: K sectors and sector-specific preferences 4 / 38

9 This Paper: 4 Parts 1. Model: Two-sector small open economy with worker heterogeneity in sector-specific productivity Comparative advantage schedule Sectoral employment Absolute advantage schedule Sector average wage Comparative and absolute advantage schedules Change in wage inequality 2. Nonparametric identification: Market shifters of sector labor demand Sectoral employment Comparative advantage schedule Sector average wage Absolute advantage schedule Extensions: K sectors and sector-specific preferences 3. Estimation: Brazilian regional labor markets Model matches cross-regional responses in average and variance of log-wages 4 / 38

10 This Paper: 4 Parts 1. Model: Two-sector small open economy with worker heterogeneity in sector-specific productivity Comparative advantage schedule Sectoral employment Absolute advantage schedule Sector average wage Comparative and absolute advantage schedules Change in wage inequality 2. Nonparametric identification: Market shifters of sector labor demand Sectoral employment Comparative advantage schedule Sector average wage Absolute advantage schedule Extensions: K sectors and sector-specific preferences 3. Estimation: Brazilian regional labor markets Model matches cross-regional responses in average and variance of log-wages 4. Counterfactual: 2000s commodity boom Brazilian wage inequality 4 / 38

11 Related Literature 1. Extensive Literature on Trade and Labor Markets Neoclassical environments: Lawrence & Slaughter, 1993; Berman et al., 1998; Leamer, 2000; Krugman, 2000; Wacziarg & Wallack, 2004; Goldberg & Pavcnik, 2007 Departures from Heckscher-Ohlin: Verhoogen, 2008; Kambourov, 2009; Helpman et al., 2010, 2015; Artuc et al., 2010; Dix-Carneiro, 2014; Burstein & Vogel, Roy Model Labor Economics: Heckman & Sedlacek, 1985; Borjas, 1987; Heckman & Honoré, 1990; Dahl, 2004; handbook chapters of Acemoglu & Autor, 2011 and French & Taber, 2011 International Trade: Mussa, 1982; Grossman, 1983; Matsuyama, 1992; Ohnsorge & Trefler, 2007; Costinot & Vogel, 2010 Recent quantitative applications: Lagakos & Waugh, 2013; Hsieh et al., 2013; Young, 2014; Burstein et al., 2015; Galle et al., 2015; Caliendo et al., Local labor markets: Effects of import competition Topalova, 2010; Kovak, 2013; Autor et al., 2013; Dix-Carneiro & Kovak, 2015a,b 5 / 38

12 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 5 / 38

13 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 5 / 38

14 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) 6 / 38

15 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) q k = Q k ( L k 1,..., L k G, X k) 6 / 38

16 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) q k = Q k ( L k 1,..., L k G, X k) In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 6 / 38

17 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q k = Q k L k 1,..., L k G, X k) where L k g L k g (i) di S k g In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 6 / 38

18 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q k = Q k L k 1,..., L k G, X k) where L k g L k g (i) di In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) S k g 6 / 38

19 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q k = Q k L k 1,..., L k G, X k) where L k g L k g (i) di In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 1 Comparative advantage: s g (i) ln [ L C g (i)/l N g (i) ] F g (.) S k g 6 / 38

20 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q k = Q k L k 1,..., L k G, X k) where L k g L k g (i) di In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 1 Comparative advantage: s g (i) ln [ L C g (i)/l N g (i) ] F g (.) S k g 2 Absolute advantage: a g (i) ln [ L N g (i) ] H g (. s) 6 / 38

21 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q j = Q j L j 1,..., Lj G, X j) where L j S j LC g g (i) di if j J C g Sg j LN g (i) di if j J N and X j is an industry-specific input. In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 1 Comparative advantage: s g (i) ln [ L C g (i)/l N g (i) ] F g (.) 2 Absolute advantage: a g (i) ln [ L N g (i) ] H g (. s) 6 / 38

22 Small open economy with worker heterogeneity Multiple worker groups: g = 1,..., G Two sectors: Commodity (k = C) and Non-commodity (k = N) ( q k = Q k L k 1,..., L k G, X k) where L k g L k g (i) di In each g, continuum of workers with sectoral productivity ( L C g (i), L N g (i) ) 1 Comparative advantage: s g (i) ln [ L C g (i)/l N g (i) ] F g (.) S k g 2 Absolute advantage: a g (i) ln [ L N g (i) ] H g (. s) 6 / 38

23 Competitive Equilibrium Firms maximize profits: w k g = p k Qk L k g where w k g is the wage per efficiency unit in sector k 7 / 38

24 Competitive Equilibrium Firms maximize profits: w k g = p k Qk L k g where w k g is the wage per efficiency unit in sector k Workers maximize labor earnings: S k g { } i : k = argmax{yg N (i); yg C (i)} 7 / 38

25 Competitive Equilibrium Firms maximize profits: w k g = p k Qk L k g where w k g is the wage per efficiency unit in sector k Workers maximize labor earnings: S k g where ω k g ln w k g and y N g (i) ω N g + a g (i) { } i : k = argmax{yg N (i); yg C (i)} 7 / 38

26 Competitive Equilibrium Firms maximize profits: w k g = p k Qk L k g where w k g is the wage per efficiency unit in sector k Workers maximize labor earnings: S k g where ω k g ln w k g and { } i : k = argmax{yg N (i); yg C (i)} y N g (i) ω N g + a g (i) and y C g (i) ω C g + s g (i) + a g (i) 7 / 38

27 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. 8 / 38

28 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. average log-wage q 1 1 q 8 / 38

29 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. average log-wage q 1 1 q 8 / 38

30 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. average log-wage q 1 1 q 8 / 38

31 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. average log-wage 1 q 8 / 38

32 Average log-wage by comparative advantage quantile For each q [0, 1], set of individuals with comparative advantage σ g (q) Fg 1 (q), and average absolute advantage α g (q) E[a g (i) s g (i) = σ g (q)]. average log-wage 1 q 8 / 38

33 Employment and log-wages in equilibrium 1 q 9 / 38

34 Employment and log-wages in equilibrium 1 q Sector employment composition, l N g : indifference of marginal workers. ω N g ω C g = σ g ( l N g ) 9 / 38

35 Employment and log-wages in equilibrium 1 Average log-wage in non-commodity sector: Ȳ N g = ω N g + 1 l N g l N g 0 α g (q) dq 10 / 38

36 Employment and log-wages in equilibrium 1 Average log-wage in commodity sector: Ȳ C g = ω C g + 1 l C g 1 l N g σ g (q) + α g (q) dq 10 / 38

37 Effect of a change in sectoral wage per efficiency unit 11 / 38

38 Effect of a change in sectoral wage per efficiency unit ω C g ω N g increases constant 11 / 38

39 Effect of a change in sectoral wage per efficiency unit ω C g ω N g increases constant 11 / 38

40 Response of sectoral employment Workers switch from non-commodity sector to commodity sector: l N g < 0 12 / 38

41 Response of sectoral employment Workers switch from non-commodity sector to commodity sector: l N g < 0 ω N g ω C g σ g (l N g ) q l N g 12 / 38

42 Response of average log-wage in non-commodity sector Change in employment composition Change in the average sector efficiency [ Ȳ g N ωg N α g (lg N ) 1 ] l N g lg N α g (q) dq ln ( l N ) g 0 13 / 38

43 Response of average log-wage in commodity sector Changes in ωg C and employment composition [ Ȳ g C ωg C σ g (lg N ) + α g (lg N ) 1 lg C 1 l N g ] σ g (q) + α g (q) dq ln ( lg C ) 14 / 38

44 Different patterns of selection into non-commodity sector Case (a): Positive Selection Case (b): Negative Selection 15 / 38

45 Response of wage inequality 16 / 38

46 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 16 / 38

47 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N Direct effect + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 16 / 38

48 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N ] σ g (q) dq ) l N + lg N lg N g + lg N lg N Effect of worker reallocation 16 / 38

49 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 2 Variance of log-wages in group g: [ V g = lg N lg C (Ȳg C Ȳg N ) 2] [ [ + lg N V α g (q) ] [ q < lg N + lg C V σ g (q) + α g (q) ]] q lg N 16 / 38

50 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 2 Variance of log-wages in group g: [ V g = lg N lg C (Ȳg C Ȳg N ) 2] [ [ + lg N V α g (q) ] [ q < lg N + lg C V σ g (q) + α g (q) ]] q lg N Variance of sector average wage 16 / 38

51 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 2 Variance of log-wages in group g: [ V g = lg N lg C (Ȳg C Ȳg N ) 2] [ [ + lg N V α g (q) ] [ q < lg N + lg C V σ g (q) + α g (q) ]] q lg N Average of sector wage variance 16 / 38

52 Response of wage inequality 1 Average of log-wages in group g: ( Ȳ g = ωg C lg C + ωg N lg N + [σ g lg N + l N g ) l N lg N g + lg N lg N ] σ g (q) dq 2 Variance of log-wages in group g: [ V g = lg N lg C (Ȳg C Ȳg N ) 2] [ [ + lg N V α g (q) ] [ q < lg N + lg C V σ g (q) + α g (q) ]] q lg N 16 / 38

53 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 16 / 38

54 Set of segmented labor markets, m Assume that wage per efficiency unit is observable: (ω C g,m, ω N g,m) 17 / 38

55 Set of segmented labor markets, m Assume that wage per efficiency unit is observable: (ω C g,m, ω N g,m) Assumption A1. 1 Comparative Advantage: s g (i) F g (s) 2 Absolute Advantage: {a g (i) s g (i) = s} H a g (a s) 17 / 38

56 Set of segmented labor markets, m Assume that wage per efficiency unit is observable: (ω C g,m, ω N g,m) Assumption A1. 1 Comparative Advantage: s g (i) F g (s) and s g (i) = s g (i) + ũ g,m 2 Absolute Advantage: {a g (i) s g (i) = s} H a g (a s) 17 / 38

57 Set of segmented labor markets, m Assume that wage per efficiency unit is observable: (ω C g,m, ω N g,m) Assumption A1. 1 Comparative Advantage: s g (i) F g (s) and s g (i) = s g (i) + ũ g,m 2 Absolute Advantage: {a g (i) s g (i) = s} µh a g (a s) + (1 µ)h e g,m(a) 17 / 38

58 Set of segmented labor markets, m Assume that wage per efficiency unit is observable: (ω C g,m, ω N g,m) Assumption A1. 1 Comparative Advantage: s g (i) F g (s) and s g (i) = s g (i) + ũ g,m 2 Absolute Advantage: {a g (i) s g (i) = s} µh a g (a s) + (1 µ)h e g,m(a) 17 / 38

59 Shocks to comparative and absolute advantage ω N g,m ω C g,m = σ g ( l N g,m ) + ũg,m Ȳg,m k ωg,m k = ᾱg k ( ) l N g,m + ṽ k g,m 1 18 / 38

60 Shocks to comparative and absolute advantage ω N g,m ω C g,m = σ g ( l N g,m ) + ũg,m Ȳg,m k ωg,m k = ᾱg k ( ) l N g,m + ṽ k g,m 1 18 / 38

61 Identification of Comparative and Absolute Advantage NPIV: Newey and Powell (2003) ω N g,m ω C g,m = σ g (l N g,m Ȳ k g,m ω k g,m = ᾱ k g ) + ũ g,m ( ) lg,m N + ṽg,m k 19 / 38

62 Identification of Comparative and Absolute Advantage NPIV: Newey and Powell (2003) ω N g,m ω C g,m = σ g (l N g,m Ȳ k g,m ω k g,m = ᾱ k g ) + ũ g,m ( ) lg,m N + ṽg,m k A2 E [ũ g,m Z g,m ] = E [ṽ g,m Z g,m ] = 0 19 / 38

63 Identification of Comparative and Absolute Advantage NPIV: Newey and Powell (2003) ω N g,m ω C g,m = σ g (l N g,m Ȳ k g,m ω k g,m = ᾱ k g ) + ũ g,m ( ) lg,m N + ṽg,m k A2 E [ũ g,m Z g,m ] = E [ṽ g,m Z g,m ] = 0 A3 For f (.) with finite expectation, E [ f (l N g,m) Z g,m ] = 0 f (l N g,m ) = 0 19 / 38

64 Identification of Comparative and Absolute Advantage NPIV: Newey and Powell (2003) ω N g,m ω C g,m = σ g (l N g,m Ȳ k g,m ω k g,m = ᾱ k g ) + ũ g,m ( ) lg,m N + ṽg,m k A2 E [ũ g,m Z g,m ] = E [ṽ g,m Z g,m ] = 0 A3 For f (.) with finite expectation, E [ f (l N g,m) Z g,m ] = 0 f (l N g,m ) = 0 Theorem Suppose that A1-A3 hold. Then, the schedules of comparative advantage, σ g (.), and absolute advantage, α g (.), are nonparametrically identified. 19 / 38

65 Extensions 1 Multiple Sectors: Multiple Sectors 2 Non-Monetary Employment Benefit: Non-Monetary 20 / 38

66 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 20 / 38

67 Empirical Application: sample of Brazilian regions Employment and wages Brazilian Census (1991, 2000, 2010): male, white, full-time, years Two groups: High School Graduates (HSG) and High School Dropouts (HSD) Two sectors: commodity (agriculture and mining) and non-commodity (manufacturing and service) Regional labor markets: 518 microregions World price of agriculture and mining commodities Six groups in CRB index: Grains, Soft, Livestock, Precious Metals, Metals, Oil Prices in U.S. exchange markets converted to Brazilian currency Worker Sample Commodity Prices 21 / 38

68 Exposure to commodity price shocks: groups and regions Z g,r,t = { } φ j g,r ln pt j j J C φ j g,r : Share of product j in earning of group g in region r at 1991 [within commodity sector] ln p j t: Log-change in the world price of product j, and / 38

69 Exposure to commodity price shocks: groups and regions Z g,r,t = { } φ j g,r ln pt j j J C φ j g,r : Share of product j in earning of group g in region r at 1991 [within commodity sector] Sector Composition ln p j t: Log-change in the world price of product j, and / 38

70 Effect of shock exposure on sectoral labor outcomes lg,r,t C = β g φ j g,r ln p j t + X g,r,tγ g + v g,r,t j J C Dependent Variable: Change in A. High School Graduates Commodity Sector Employment Share Commodity price shock 0.031*** (0.010) R 2 B. High School Dropouts Commodity Sector Average Log Wage Premium Average of Log Wage Variance of Log Wage (1) (2) (3) (4) Commodity price shock 0.072** (0.028) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Initial labor market conditions Yes Yes Pre-trends Other groups Labor Supply Industry-level responses 23 / 38

71 Effect of shock exposure on sectoral labor outcomes ) C (Ȳ g,r,t Ȳg,r,t N = β g φ j g,r ln p j t + X g,r,tγ g + v g,r,t j J C Dependent Variable: Change in A. High School Graduates Commodity Sector Employment Share Commodity Sector Average Log Wage Premium Commodity price shock 0.031*** 0.407*** (0.010) (0.111) R 2 B. High School Dropouts Average of Log Wage Variance of Log Wage (1) (2) (3) (4) Commodity price shock 0.072** (0.028) (0.177) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Yes Yes Initial labor market conditions Yes Yes Pre-trends Other groups Labor Supply Industry-level responses 23 / 38

72 Effect of shock exposure on sectoral labor outcomes Ȳ g,r,t = β g φ j g,r ln p j t + X g,r,tγ g + v g,r,t j J C Dependent Variable: Change in A. High School Graduates Commodity Sector Employment Share Commodity Sector Average Log Wage Premium Average of Log Wage Variance of Log Wage (1) (2) (3) (4) Commodity price shock 0.031*** 0.407*** 0.141*** (0.010) (0.111) (0.051) R 2 B. High School Dropouts Commodity price shock 0.072** ** (0.028) (0.177) (0.073) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Yes Yes Yes Initial labor market conditions Yes Yes Yes Pre-trends Other groups Labor Supply Industry-level responses 23 / 38

73 Effect of shock exposure on sectoral labor outcomes V g,r,t = β g φ j g,r ln p j t + X g,r,tγ g + v g,r,t j J C Dependent Variable: Change in A. High School Graduates Commodity Sector Employment Share Commodity Sector Average Log Wage Premium Average of Log Wage Variance of Log Wage (1) (2) (3) (4) Commodity price shock 0.031*** 0.407*** 0.141*** ** (0.010) (0.111) (0.051) (0.057) R 2 B. High School Dropouts Commodity price shock 0.072** ** (0.028) (0.177) (0.073) (0.086) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Yes Yes Yes Yes Initial labor market conditions Yes Yes Yes Yes Pre-trends Other groups Labor Supply Industry-level responses 23 / 38

74 Measuring changes in wage per efficiency unit 24 / 38

75 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth 24 / 38

76 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth Let Y g (π) be the wage growth in quantile π of the log-wage distribution. 24 / 38

77 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth Let Y g (π) be the wage growth in quantile π of the log-wage distribution. Y g (π) = ω C g + 24 / 38

78 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth Let Y g (π) be the wage growth in quantile π of the log-wage distribution. Y g (π) = ω C g + [ ] ωg N ωg C lg N (π) where, at quantile π of the log-wage distribution, l N g (π) is the initial employment share in non-commodity sector 24 / 38

79 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth Let Y g (π) be the wage growth in quantile π of the log-wage distribution. Y g (π) = ω C g + [ ] ωg N ωg C lg N (π) + v g (π) where, at quantile π of the log-wage distribution, l N g (π) is the initial employment share in non-commodity sector v g (π) is an idiosyncratic efficiency shock 24 / 38

80 Measuring changes in wage per efficiency unit Exposure to changes in wage per efficiency unit of own sector of employment Variation in pre-shock sector allocation Variation in wage growth Let Y g (π) be the wage growth in quantile π of the log-wage distribution. Y g (π) = ω C g + [ ] ωg N ωg C lg N (π) + v g (π) where, at quantile π of the log-wage distribution, lg N (π) is the initial employment share in non-commodity sector v g (π) is an idiosyncratic efficiency shock For each of the 2,072 group-region-period, estimate this equation by OLS. Details 24 / 38

81 Effect of shock exposure on wage per efficiency unit ωg,r,t k = β g φ j g,r ln p j t + X g,r,tγ g + e g,r,t j J C Dependent Variable: change in wage per efficiency unit A. High School Graduates Commodity sector Non-commodity sector (1) (2) Commodity price shock 0.974*** 0.276*** (0.372) (0.066) R 2 B. High School Dropouts Commodity price shock 1.436** (0.638) (0.088) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Yes Yes Initial labor market conditions Yes Yes 25 / 38

82 Parametric Restrictions: Log-Linear System For σ g > 0 and α g R, σ g (q) = σ g [ln (q) ln (1 q)] and α g (q) = α g ln (q) Fréchet, σ g = α g : sector wage premium and log-wage variance are constant 26 / 38

83 Parametric Restrictions: Log-Linear System For σ g > 0 and α g R, σ g (q) = σ g [ln (q) ln (1 q)] and α g (q) = α g ln (q) Fréchet, σ g = α g : sector wage premium and log-wage variance are constant Case (a): Fréchet α g = σ g and σ g (0,1) Case (b): α g > 0 and α g + σ g > 0 Case (c): α g < 0 and α g + σ g < 0 26 / 38

84 GMM Estimator of structural parameters Under Assumption A5, estimate Θ g (σ g, α g ) using ωg,r,t N ωg,r,t C ( ) = σ g l N g,r,t + X g,r,t γg u + u g,r,t Ȳg,r,t k ωg,r,t k = ᾱg k ( ) l N g,r,t + X g,r,t γg k + vg,r,t k With W g [ Z C g,r,t, X g,r,t ], ˆΘ g = arg min Θ g e g (Θ g ) W g ΦW g e g (Θ g ) where Φ is the optimal weight matrix. 27 / 38

85 Estimates of structural parameters Fréchet model Log-linear model σ g = α g (1) (2) A. High School Graduates σ HSG 0.711*** 0.860*** (0.261) (0.263) α HSG *** 1.864* (0.261) (0.995) Test of Fréchet restriction (p-value) J-test of overidentification (p-value) B. High School Dropouts σ HSD 0.967*** 0.960* (0.167) (0.529) α HSD *** *** (0.167) (0.196) Test of Fréchet restriction (p-value) J-test of overidentification (p-value) SLS Specification Other groups 28 / 38

86 Average log-wage by comparative advantage quantile Main estimates High School Graduates High School Dropouts q q Non-commodity sector Commodity sector 29 / 38

87 Model fit Ȳ g,r,t = β g φ j g,r ln p j t + X g,r,tγ g + e g,r,t j J C A. High School Graduates Regression Analysis Predicted change with Log-linear model Predicted change with Fréchet model (1) (2) (3) Change in log-wage average 0.141*** [0.06, 0.22] [0.22, 0.45] [0.22, 0.46] Change in log-wage variance B. High School Dropouts Change in log-wage average 0.144** [0.02, 0.26] [-0.01, 0.52] [-0.02, 0.38] Change in log-wage variance 30 / 38

88 Model fit V g,r,t = β g φ j g,r ln p j t + X g,r,tγ g + e g,r,t j J C A. High School Graduates Regression Analysis Predicted change with Log-linear model Predicted change with Fréchet model (1) (2) (3) Change in log-wage average 0.141*** [0.06, 0.22] [0.22, 0.45] [0.22, 0.46] Change in log-wage variance ** [-0.22, -0.03] [-0.71, 0.07] - B. High School Dropouts Change in log-wage average 0.144** [0.02, 0.26] [-0.01, 0.52] [-0.02, 0.38] Change in log-wage variance [-0.28, 0.01] [-0.44, 0.33] - 30 / 38

89 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 30 / 38

90 In 1991, how would wage inequality change if commodity prices were equal to those of 2010? 31 / 38

91 In 1991, how would wage inequality change if commodity prices were equal to those of 2010? Sectoral shock: change in world price of basic commodities (1 st step) Change in wage per efficiency unit: ω C g,r,t and ω N g,r,t (2 nd step) Change in wage inequality using estimates of comparative and absolute advantage parameters 31 / 38

92 In 1991, how would wage inequality change if commodity prices were equal to those of 2010? Sectoral shock: change in world price of basic commodities (1 st step) Change in wage per efficiency unit: ω C g,r,t and ω N g,r,t (2 nd step) Change in wage inequality using estimates of comparative and absolute advantage parameters Two alternative procedures for 1 st step: 1 Reduced-form pass-through: Use estimates from regression of wage per efficiency unit on shock exposure across Brazilian regions 31 / 38

93 In 1991, how would wage inequality change if commodity prices were equal to those of 2010? Sectoral shock: change in world price of basic commodities (1 st step) Change in wage per efficiency unit: ω C g,r,t and ω N g,r,t (2 nd step) Change in wage inequality using estimates of comparative and absolute advantage parameters Two alternative procedures for 1 st step: 1 Reduced-form pass-through: Use estimates from regression of wage per efficiency unit on shock exposure across Brazilian regions 2 General equilibrium model: Calibrate labor demand structure and compute counterfactual changes in wage per efficiency unit (Dekle-Eaton-Kortum, 2007) 31 / 38

94 commodity price rise High School Graduates High School Dropouts q q Non-commodity sector Commodity sector 32 / 38

95 commodity price rise: Effect on sectoral wage 33 / 38

96 commodity price rise: Effect on average wage 34 / 38

97 commodity price rise: Effect on Brazilian log-wage variance Panel A. High School Graduates Panel B. High School Dropouts Panel C. All Workers Log-linear model Fréchet model (1) (2) % % % Note. Counterfactual change in Brazilian log-wage variance, along with the percentage of the actual change in log-wage vairance between 1991 and / 38

98 commodity price rise: Effect on Brazilian log-wage variance Panel A. High School Graduates Panel B. High School Dropouts Panel C. All Workers Log-linear model Fréchet model (1) (2) % 1.33% % 8.09% % 8.38% Note. Counterfactual change in Brazilian log-wage variance, along with the percentage of the actual change in log-wage vairance between 1991 and / 38

99 General equilibrium model 36 / 38

100 General equilibrium model Additional parametric assumptions Industry j of in the aggregate sector k: Nested-CES production function q j = B j (L j ) ηj (X j ) 1 ηj where L j ρ 1 [β jhsg (LjHSG ) ρ ] + β j HSD (Lj HSD ) ρ 1 ρ ρ 1 ρ Sectoral supply of effective labor units are given by L N g = κ g l N g 0 1 e αg (q) dq and L C g = κ g e σg (q)+αg (q) dq l N g 36 / 38

101 General equilibrium model Additional parametric assumptions Industry j of in the aggregate sector k: Nested-CES production function q j = B j (L j ) ηj (X j ) 1 ηj where L j ρ 1 [β jhsg (LjHSG ) ρ ] + β j HSD (Lj HSD ) ρ 1 ρ ρ 1 ρ Sectoral supply of effective labor units are given by L N g = κ g l N g 0 1 e αg (q) dq and L C g = κ g e σg (q)+αg (q) dq l N g Computation: {ˆω HSD C, ˆωN HSD, ˆωC HSG, ˆωN HSG } from labor market clearing with η j : Labor share in production of industry j ρ = 1.63: Match aggregate elasticity between skilled and unskilled workers of / 38

102 commodity price rise: effect on Brazilian log-wage variance Panel A. High School Graduates Panel B. High School Dropouts Panel C. All Workers Calibrated General Equilibrium Model Reduced-Form Pass- Through (1) (2) % 8.13% % 2.46% % 5.12% Note. Counterfactual change in Brazilian log-wage variance, along with the percentage of the actual change in log-wage vairance between 1991 and / 38

103 Outline 1 Introduction 2 Model 3 Identification 4 Estimation 5 Counterfactuals 6 Conclusion 37 / 38

104 Concluding Remarks Neoclassical economy with worker heterogeneity in sectoral productivity Sector demand shifter triggers sectoral responses in employment and wages that uncovers comparative and absolute advantage schedules Structural estimation in a sample of regional labor markets in Brazil 1 Model matches cross-regional responses in wage inequality 2 Importance of allowing for comparative and absolute advantage 3 World commodity prices Wage inequality in producer countries 38 / 38

105 Graphical representation: Change in wage inequality q 1 1 Change in Wage Inequality 38 / 38

106 Trends in World Commodity Prices Commodity Price Index Precious Metals (gold and silver) Energy (crude oil) Soft (coffee, cacoa, sugar, and others) Livestock (cattle, hogs, and others) Metals (copper, lead, steel, tin, zinc) Grains (corn, soybeans, wheat) Data 38 / 38

107 Summary Statistics: Benchmark Sample Commodity sector Non-commodity sector Average Age Share of high school dropouts 93.8% 76.8% 70.2% 44.7% Share in urban areas 30.4% 46.4% 94.2% 95.5% Share in formal sector 33.8% 65.2% 80.0% 84.0% Share earning below minimum wage 59.1% 41.2% 19.5% 14.2% Data 38 / 38

108 Trends in Brazilian Wage Inequality Change in Log Hourly Real Wage, Change in Log Hourly Real Wage by Percentile Brazilian male workers, Hourly Wage Percentile Data Introduction 38 / 38

109 Trends in Brazilian Wage Inequality Log of world commodity price index change relative to Log-wage variance change relative to 1981 World Commodity Prices Log-Wage Variance: Overall Between Between component: predicted values of the regression of log wage on a full set of dummies for years of experience (0 39 years), years of education (0 16 years), state of residence (27 states), race (white dummy), and sector of employment (commodity sector). Data Introduction 38 / 38

110 Decomposition of the Variance of Log-Wages, Overall Residual Between Sector Education State Race Experience Covariance Data 38 / 38

111 Labor Income Share by Industry in Brazil, 1991 Industry High School Graduates High School Dropouts Mean SD Mean SD (1) (2) (3) (4) 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 Manufacturing Non-Tradable Goods and Services Note. Sample of male white full-time workers extracted from the Brazilian Census of Statistics are weighted by the microregion share in national population on Shock Exposure 38 / 38

112 Estimation of wage per efficiency unit Implementation details Discretization of log-wage distribution: 1 p.p. bins, 6 th 94 th percentiles (N = 88) X g,r,t(π): dummies for distribution range (bottom, middle, top) and minimum wage proximity (pre and post periods) A. High School Graduates Mean SD Mean SD Mean (1) (2) (3) (4) (5) % % B. High School Dropouts Log change in commodity sector wage per efficiency unit Log change in non-commodity sector relative wage per efficiency unit % % R 2 Main Results 38 / 38

113 Estimation of wage per efficiency unit Alternative specification Change in wage per efficiency unit A. High School Graduates (1) (2) (3) (4) (5) (6) Correlation with baseline estimates B. High School Dropouts Correlation with baseline estimates Baseline Controls Commodity sector Non-commodity sector Percentile below federal minimum wage Yes No Yes Yes No Yes Percentile in bottom, middle or top of wage distribution No Yes Yes No Yes Yes Discretization of wage distribution Bins of 1 p.p. (N = 88) Yes Yes No Yes Yes No Bins of 2 p.p. (N = 44) No No Yes No No Yes Main Results 38 / 38

114 Commodity Price Shocks and Commodity Sector Employment Share Dependent Variable: A. High School Graduates (1) (2) (3) (4) (5) (6) (7) (8) Commodity price shock 0.031*** 0.042*** 0.039*** 0.039*** 0.039*** 0.049*** 0.019** 0.014* (0.010) (0.010) (0.012) (0.011) (0.012) (0.017) (0.009) (0.007) R 2 B. High School Dropouts Commodity price shock 0.072** 0.177*** 0.086*** 0.062** 0.063*** 0.058** 0.092*** 0.100*** (0.028) (0.066) (0.029) (0.029) (0.020) (0.027) (0.029) (0.032) R 2 Baseline Controls Initial sector composition controls Yes No Yes Yes Yes Yes Yes Yes Initial labor market conditions Yes No Yes Yes Yes Yes Yes Yes Baseline controls x period dummies Yes No No Yes Yes Yes Yes Yes dependent variable x period dummies No No No Yes No No No No Extended Sample Change in Commodity Sector Employment Share Including No No No No Yes Yes No No with microregion-specific linear time trend No No No No No Yes No No Additional worker groups Including nonwhite No No No No No No Yes Yes Including female No No No No No No No Yes Reduced-Form Evidence 38 / 38

115 Commodity Price Shocks and Commodity Sector Wage Premium Dependent Variable: A. High School Graduates (1) (2) (3) (4) (5) (6) (7) (8) Commodity price shock 0.407*** 0.347*** 0.426*** 0.492*** 0.192* *** 0.387*** (0.111) (0.095) (0.114) (0.119) (0.109) (0.144) (0.099) (0.100) R 2 B. High School Dropouts Commodity price shock *** 0.352*** (0.177) (0.163) (0.189) (0.200) (0.090) (0.122) (0.112) (0.100) R 2 Baseline Controls Initial sector composition controls Yes No Yes Yes Yes Yes Yes Yes Initial labor market conditions Yes No Yes Yes Yes Yes Yes Yes Baseline controls x period dummies Yes No No Yes Yes Yes Yes Yes dependent variable x period dummies No No No Yes No No No No Extended Sample Commodity Sector Average Log Wage Premium Including No No No No Yes Yes No No with microregion-specific linear time trend No No No No No Yes No No Additional worker groups Including nonwhite No No No No No No Yes Yes Including female No No No No No No No Yes Reduced-Form Evidence 38 / 38

116 Commodity Price Shocks and Group Wage Average Dependent Variable: A. High School Graduates (1) (2) (3) (4) (5) (6) (7) (8) Commodity price shock 0.141*** 0.322*** 0.139*** 0.111*** 0.096** 0.102* 0.164*** 0.151*** (0.051) (0.120) (0.052) (0.043) (0.041) (0.054) (0.042) (0.050) R 2 B. High School Dropouts Commodity price shock 0.144** 0.379** 0.201** ** 0.148** 0.149* 0.163** (0.073) (0.158) (0.087) (0.074) (0.044) (0.061) (0.080) (0.077) R 2 Baseline Controls Initial sector composition controls Yes No Yes Yes Yes Yes Yes Yes Initial labor market conditions Yes No Yes Yes Yes Yes Yes Yes Baseline controls x period dummies Yes No No Yes Yes Yes Yes Yes dependent variable x period dummies No No No Yes No No No No Extended Sample Average of Log Wage Including No No No No Yes Yes No No with microregion-specific linear time trend No No No No No Yes No No Additional worker groups Including nonwhite No No No No No No Yes Yes Including female No No No No No No No Yes Reduced-Form Evidence 38 / 38

117 Commodity Price Shocks and Group Wage Variance Dependent Variable: A. High School Graduates (1) (2) (3) (4) (5) (6) (7) (8) Commodity price shock ** *** * ** *** ** * * (0.057) (0.092) (0.062) (0.058) (0.041) (0.055) (0.050) (0.044) R 2 B. High School Dropouts Commodity price shock ** * *** *** (0.086) (0.089) (0.104) (0.085) (0.032) (0.041) (0.076) (0.068) R 2 Baseline Controls Initial sector composition controls Yes No Yes Yes Yes Yes Yes Yes Initial labor market conditions Yes No Yes Yes Yes Yes Yes Yes Baseline controls x period dummies Yes No No Yes Yes Yes Yes Yes dependent variable x period dummies No No No Yes No No No No Extended Sample Variance of Log Wage Including No No No No Yes Yes No No with microregion-specific linear time trend No No No No No Yes No No Additional worker groups Including nonwhite No No No No No No Yes Yes Including female No No No No No No No Yes Reduced-Form Evidence 38 / 38

118 Commodity Price Shocks and Regional Labor Supply Dependent Variable: A. High School Graduates Change in Log of Total Labor Supply Change in Log of Immigrants' Labor Supply Change in formal sector size (1) (2) (3) Commodity price shock (0.139) (0.036) R 2 B. High School Dropouts Commodity price shock * (0.150) (0.185) (0.041) R 2 Baseline Controls Controls in Table 1 Yes Yes Yes Reduced-Form Evidence 38 / 38

119 Commodity Price Shocks and Industry Relative Average Log Wage Dependent Variable: Change in A. High School Graduates Relative Industry Log Relative Industry Average Employment Log Wage (1) (2) Commodity price shock 3.241*** (1.089) (0.351) R 2 B. High School Dropouts Commodity price shock (3.338) (0.483) R 2 Baseline Controls (interacted with period dummies) Initial sector composition controls Yes Yes Initial labor market conditions Yes Yes Reduced-Form Evidence 38 / 38

120 Estimates of structural parameters Alternative sample A. High School Graduates σ HSG α HSG B. High School Dropouts σ HSD α HSD Additional worker groups (1) (2) (3) 0.860*** 0.818*** 0.639*** (0.263) (0.243) (0.184) 1.864* 3.633* 4.923** (0.995) (1.914) (2.032) 0.960* 1.175*** 1.163*** (0.529) (0.417) (0.363) *** *** *** (0.196) (0.203) (0.165) Baseline sample: male / white Yes Yes Yes Including non-white No Yes Yes Including female No No Yes Structural Estimation 38 / 38

121 Estimates of structural parameters Alternative estimator Estimator Baseline: GMM OLS 2SLS 2SLS A. High School Graduates (1) (2) (3) (4) σ HSG 0.860*** *** 1.336*** (0.263) (0.081) (0.274) (0.456) CLR Confidence Interval - - [0.503, 2.007] [0.036, 3.303] F of excluded instruments α HSG 1.864* ** 1.651* (0.995) (0.142) (0.950) (0.916) CLR Confidence Interval - - [0.480, 5.861] [-0.355, 5.602] F of excluded instruments B. High School Dropouts σ HSD 0.960* *** (0.529) (0.061) (0.653) (3.164) CLR Confidence Interval - - [0.455, 5.255] [0.097, 7.081] F of excluded instruments α HSD *** *** *** *** (0.196) (0.032) (0.163) (0.214) CLR Confidence Interval - - [-1.401,-0.560] [-1.778,-0.433] F of excluded instruments Vector of Excluded Instruments Disaggregated exposure to price shocks Yes No Yes No Aggregate exposure to price shocks No No No Yes Structural Estimation 38 / 38

122 Estimates of structural parameters Alternative estimates of wage per efficiency unit A. High School Graduates σ HSG α HSG B. High School Dropouts σ HSD α HSD Baseline Alternative measure of wage per efficiency unit (1) (2) (3) (4) 0.860*** 0.976* 0.644** (0.263) (0.557) (0.255) (0.958) 1.864* * (0.995) (0.877) (1.020) (0.570) 0.960* ** (0.529) (0.630) (0.667) (0.647) *** *** * * (0.196) (0.200) (0.261) (0.223) Baseline controls Percentile below federal minimum wage Yes Yes No Yes Percentile in bottom, middle or top of wage distribution Yes Yes Yes No Discretization of wage distribution Bins of 1 p.p. (N = 88) Yes No Yes Yes Bins of 2 p.p. (N = 44) No Yes No No Structural Estimation 38 / 38

123 Extensions: Multiple Sectors, k = 0,..., K 1 Comparative advantage: s k g (i) + ũ k g,m ln [ L k g (i)/l 0 g (i) ] with sg (i) F g (s) 2 Absolute advantage: a g (i) ln [ L 0 g (i) ] µh g (a s) + (1 µ)h e g,m(a) Identify comparative advantage schedule: F g (s) Identify absolute advantage schedule: α g (s) µ a dh g (a s) Sufficient to compute changes in the average and the variance of log-wage distribution 38 / 38

124 Extensions: Multiple Sectors, k = 0,..., K Identification of F g (.) Employment share in sector k: lg,m k = χ k g ( ω g,m ) s S k ( ω g,m) df g (s), I show that χ g (.) is invertible: ω 0 g,m ω k g,m = σ k g (l 1 g,m,..., l K g,m) + ũ k g,m where l k = χ k g (σ g (l 1,..., l K )) for all k. Thus, K F g (s) = 1 χ k g ( s). k=1 38 / 38

125 Extensions: Multiple Sectors, k = 0,..., K Identification of α g (.) Average wage in sector k = 0: Ȳ 0 g,m = ω 0 g,m + ᾱ 0 g (l 1 g,m,..., l K g,m) + ṽ g,m where ᾱ 0 g (l) 1 l 0 σ 1 g (l)... σ K g (l) α g (s) f g (s) d s Thus, α g (s) = 1 f g (s) K [ l 0 ᾱg 0 (χ g ( ω)) ] ω 1... ω K ω=s. Extensions 38 / 38

126 Extensions: Non-Monetary Benefit U k g (i) = τ k g (i) w k g,ml k g (i) 1 Comparative advantage: s g (i) + ũ g,m ln[τ C g (i)l C g (i)/τ N g (i)l N g (i)] F g (.) 2 Absolute advantage in sector k: a k g (i) + ṽ k g,m ln [ L k g (i) ] H g (a s) 38 / 38

127 Extensions: Non-Monetary Benefit U k g (i) = τ k g (i) w k g,ml k g (i) 1 Comparative advantage: s g (i) + ũ g,m ln[τ C g (i)l C g (i)/τ N g (i)l N g (i)] F g (.) 2 Absolute advantage in sector k: a k g (i) + ṽ k g,m ln [ L k g (i) ] H g (a s) ω N g,m ω C g,m = σ g (l N g,m ) + ũ g,m Ȳg,m k = ωg,m k + ᾱg k (lg,m) N + ṽg,m k where ᾱg k (l) 1 l l 0 αn g (q) dq 1 1 l 1 l αg C (q)dq Extensions 38 / 38