Comparative Advantage and Risk Premia in Labor Markets German Cubas 1 Pedro Silos 2 1 Central Bank of Uruguay and FCS-UDELAR (From Fall’13 U. of Houston) 2 Atlanta Fed QSPS, Utah State University, May 2013
Intro • This paper is about the effect of comparative advantage and risk in the career choice of individuals and their role in explaining earnings differentials across industries. • The compensation for risk in the labor market is a classical (old) problem first explored in Friedman and Kuznets (1939). • The problem is more challenging: heterogeneity in abilities and endogenous career choice. • We tackle this old and complex problem by using modern tools.
Main Questions • Is there a relationship between the level of labor earnings and its volatility? Is it positive? Is it different depending on the nature of the risk (transitory or persistent)?
Main Questions • Is there a relationship between the level of labor earnings and its volatility? Is it positive? Is it different depending on the nature of the risk (transitory or persistent)? Need data.
Main Questions • Is there a relationship between the level of labor earnings and its volatility? Is it positive? Is it different depending on the nature of the risk (transitory or persistent)? Need data. • How to interpret the fact? Argue that the career (sectoral) choice of individuals depends on: risk they face and their comparative advantage (unobservable for the econometrician).
Main Questions • Is there a relationship between the level of labor earnings and its volatility? Is it positive? Is it different depending on the nature of the risk (transitory or persistent)? Need data. • How to interpret the fact? Argue that the career (sectoral) choice of individuals depends on: risk they face and their comparative advantage (unobservable for the econometrician). Need model to decompose mean earnings differentials into compensation for ability and risk.
What we do • New Facts: • Quantify labor income risk across 21 sectors of the US economy (permanent and transitory). • Estimate a relationship between risk (or its two components) and earnings (the “risk premium”). • Theory: • Model with sectoral, consumption/savings choices: • Sectoral differences in earnings risk. • Workers differ in their ability levels (sector-specific).
Why we care • For most individuals labor income is the bulk of the total income. • Labor income risk plays a central role in many economic decisions that individuals make (consumption/savings, portfolio choice, etc.). • Implications for income and wealth inequality. • Understand the role of comparative advantage and risk in wage inequality. Implications for policy.
Preview of Main Results • Find strong and positive relationship between the variance of labor income shocks (both transitory and permanent) and mean earnings. • Moving from the safest to the riskiest industry is associated with an increase of 10% in mean earnings.
Preview of Main Results • Find strong and positive relationship between the variance of labor income shocks (both transitory and permanent) and mean earnings. • Moving from the safest to the riskiest industry is associated with an increase of 10% in mean earnings. • The correlation between mean earnings and the variance of the permanent shock is compensation for risk (with risk aversion parameter of 2).
Preview of Main Results • Find strong and positive relationship between the variance of labor income shocks (both transitory and permanent) and mean earnings. • Moving from the safest to the riskiest industry is associated with an increase of 10% in mean earnings. • The correlation between mean earnings and the variance of the permanent shock is compensation for risk (with risk aversion parameter of 2). • The correlation between mean earnings and the variance of the transitory shock is compensation for sector specific skills (comparative advantage).
Outline of the Talk • Part I - The Story in a Static “Toy” General Equilibrium Model. • Part II - Data and Estimation. • Part III - Full General Equilibrium Model. • Part IV - Findings.
Part I “TOY” GE MODEL Risk vs. Ability
Environment • Risk averse individuals that live for 1 period. • Firm produce output according to Y = ( L 1 ) φ ( L 2 ) 1 − φ . • Competitive labor market in which individuals choose type-1 or type-2 labor: • w 1 • w 2 zγ with • z ∼ G ( z ) • γ = 1 with prob. p and γ = γ H > 1 with prob. 1 − p . • Individuals know z but not the realization of γ . • Individuals choose the labor type that renders the highest utility.
Decision Problem • Assume log utility, then there exist a unique z ⋆ s.t. if z > z ⋆ individuals choose type-2 labor and if z ≤ z ⋆ type-1.
Decision Problem • Assume log utility, then there exist a unique z ⋆ s.t. if z > z ⋆ individuals choose type-2 labor and if z ≤ z ⋆ type-1. 2 1 0 −1 −2 V 1 V 2 −3 −4 0 2 4 6 8 10 12 14 16 18 20 z* z
Equilibrium • Firm max profits w 1 = MPL 1 , w 2 = MPL 2 . • Aggregating L 1 = G ( z ⋆ ) � ∞ L 2 = E γ z ⋆ zdG ( z ) . • Mean Earnings e 2 = w 2 � ∞ z ⋆ zdG ( z ) . 1 − G ( z ⋆ ) e 1 = w 1
The Price of Risk • Changes in the variance of earnings for labor-type 2.
The Price of Risk • Changes in the variance of earnings for labor-type 2. 2 1.98 1.96 1.94 1.92 e 2 1.9 1.88 1.86 1.84 1.82 0 0.5 1 1.5 2 2.5 3 3.5 4 σ 2 γ mechs
Risk vs Ability: Example • We increase the mean ability levels, E ( z ) (affects earnings of type-2 labor). Curves shift upwards.
Risk vs Ability: Example • We increase the mean ability levels, E ( z ) (affects earnings of type-2 labor). Curves shift upwards. 2.15 2.1 E(z) 4 E(z) 2.05 3 E(z) 2 2 e2 E(z) 1 1.95 1.9 1.85 1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 σ 2 γ
Risk vs Ability: Example • Suppose there is a set of islands (sectors or industries). • Each island is characterized by a different pair of volatility of earnings ( σ 2 γ ) and mean ability level ( E ( z )). • What would we be the observed relationship between volatility and earnings? • What would we be the observed relationship between volatility and mean ability?
Risk vs Ability: Case 1 (as in the data) 2.15 2.1 e2 4 2.05 e2 3 2 e2 2 e2 1.95 e2 1 1.9 1.85 1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 σ 2 γ ,3 γ ,4 γ ,1 γ ,2 γ • Earnings and Risk are positively correlated.
Risk vs Ability: Case 1 (as in the data) 2.15 E(z) 4 2.1 e2 4 E(z) 3 2.05 E(z) 2 e2 3 2 E(z) 1 e2 2 e2 1.95 e2 1 1.9 1.85 1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 σ 2 γ ,2 γ ,3 γ ,4 γ ,1 γ
Risk vs Ability: Case 1 (as in the data) 2.15 E(z) 4 2.1 e2 4 E(z) 3 2.05 E(z) 2 e2 3 2 E(z) 1 e2 2 e2 1.95 e2 1 1.9 1.85 1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 σ 2 γ ,2 γ ,3 γ ,4 γ ,1 γ • Earnings and Risk are positively correlated.
Risk vs Ability: Case 1 (as in the data) 2.15 E(z) 4 2.1 e2 4 E(z) 3 2.05 E(z) 2 e2 3 2 E(z) 1 e2 2 e2 1.95 e2 1 1.9 1.85 1.8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 σ 2 γ ,2 γ ,3 γ ,4 γ ,1 γ • Earnings and Risk are positively correlated. Risk ( σ 2 γ ) and Ability ( E ( z ) ) are positively correlated.
Risk vs Ability in GE: Case 2 2.15 E(z) 4 2.1 E(z) 3 e2 4 2.05 E(z) 2 e2 3 2 e2 2 E(z) 1 e2 e2 1 1.95 1.9 1.85 1.8 0 0.5 1 1.5 2 σ 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 γ ,1 γ ,4 γ ,3 γ ,2 γ
Risk vs Ability in GE: Case 2 2.15 E(z) 4 2.1 E(z) 3 e2 4 2.05 E(z) 2 e2 3 2 e2 2 E(z) 1 e2 e2 1 1.95 1.9 1.85 1.8 0 0.5 1 1.5 2 σ 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 γ ,1 γ ,4 γ ,3 γ ,2 γ • Earnings ( e 2 ) and Risk ( σ 2 γ ) are negatively correlated.
Risk vs Ability in GE: Case 2 2.15 E(z) 4 2.1 E(z) 3 e2 4 2.05 E(z) 2 e2 3 2 e2 2 E(z) 1 e2 e2 1 1.95 1.9 1.85 1.8 0 0.5 1 1.5 2 σ 2 2.5 3 3.5 4 4.5 σ 2 σ 2 σ 2 σ 2 γ ,1 γ ,4 γ ,3 γ ,2 γ • Earnings ( e 2 ) and Risk ( σ 2 γ ) are negatively correlated. Risk ( σ 2 γ ) and Ability ( E ( z ) ) are negatively correlated.
Part II DATA Earnings and Risk in Labor Markets
Data • Survey of Income and Program Participation (SIPP). • Use 3 surveys: • 1996-1999. • 2001-2003. • 2004-2007. • Construct a panel of individuals (of length T ) for each of the three. • Obtain quarterly measures of labor earnings, unemployment insurance, employment status, age, education level, industry, occupation, gender. clean
Estimating Risk • Estimate (for each panel): log ( Y ijt ) = y ijt = α ij + β j X ijt + u ijt . • Predictable component. • Unpredictable component: our notion of risk.
Estimating Risk • Estimate (for each panel): log ( Y ijt ) = y ijt = α ij + β j X ijt + u ijt . • Predictable component. • Unpredictable component: our notion of risk. • Not all risks are created equal. • Transitory shocks to income are easy to smooth with a buffer stock of savings. • Permanent (or very persistent) shocks are more serious.
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