The Allocation of Talent and U.S. Economic Growth Chang-Tai Hsieh Erik Hurst Chad Jones Pete Klenow April 2014
Big changes in the occupational distribution White Men in 1960: 94% of Doctors, 96% of Lawyers, and 86% of Managers White Men in 2008: 63% of doctors, 61% of lawyers, and 57% of managers
Share of Each Group in High Skill Occupations High-skill occupations are lawyers, doctors, engineers, scientists, architects, mathematicians and executives/managers.
Our question Suppose distribution of talent for each occupation is identical for whites, blacks, men and women. Then: • Misallocation of talent in both 1960 and 2008. • But less misallocation in 2008 than in 1960. How much of productivity growth between 1960 and 2008 was due to the better allocation of talent?
Outline 1. Model 2. Evidence 3. Counterfactuals
Model N occupations, one of which is “home”. Individuals draw talent in each occupation { ǫ i } . Individuals then choose occupation ( i ) and human capital ( s , e ). U = c β ( 1 − s ) Preferences h = s φ i e η ǫ Human capital c = ( 1 − τ w ) wh − ( 1 + τ h ) e Consumption
What varies across occupations and/or groups w i = the wage per unit of human capital in occupation i (endogenous) φ i = the elasticity of human capital wrt time invested for occupation i τ w ig = labor market barrier facing group g in occupation i τ h ig = barrier to building human capital facing group g for i
Timing Individuals draw and observe an ǫ i for each occupation. They also see φ i , τ w ig , and τ h ig . They anticipate w i . Based on these, they choose their occupation, their s , and their e . w i will be determined in GE (production details later).
Some Possible Barriers Acting like τ w • Discrimination in the labor market. Acting like τ h • Family background. • Quality of public schools. • Discrimination in school admissions.
Identification Problem (currently) Empirically, we will be able to identify: ig ) η ( 1 + τ h τ ig ≡ 1 − τ w ig But not τ w ig and τ h ig separately. For now we analyze the composite τ ig or one of two polar cases: • All differences are from τ h ig barriers to human capital accumulation ( τ w ig = 0) • Or all differences are due to τ w ig labor market barriers ( τ h ig = 0).
Individual Consumption and Schooling The solution to an individual’s utility maximization problem, given an occupational choice: s ∗ 1 i = 1 + 1 − η βφ i 1 � � η w i s φ i 1 − η i ǫ e ∗ ig ( ǫ ) = τ ig 1 � � w i s φ i 1 − η i ǫ c ∗ ig ( ǫ ) = ¯ η τ ig β � � 1 − η 1 − η w i s φ i β ǫ i i ( 1 − s i ) η β U ( τ ig , w i , ǫ i ) = ¯ τ ig
The Distribution of Talent We assume Fr´ echet for analytical convenience: F i ( ǫ ) = exp ( − T ig ǫ − θ ) • McFadden (1974), Eaton and Kortum (2002) • θ governs the dispersion of skills • T ig scales the supply of talent for an occupation Benchmark case: T ig = T i — identical talent distributions T i will be observationally equivalent to production technology parameters, so we normalize T i = 1.
Result 1: Occupational Choice β 1 − η � w i s φ i � 1 − η β ǫ i i ( 1 − s i ) η β U ( τ ig , w i , ǫ i ) = ¯ τ ig Extreme value theory: U ( · ) is Fr´ echet ⇒ so is max i U ( · ) Let p ig denote the fraction of people in group g that work in occupation i : 1 − η T 1 /θ ig w i s φ i w θ ˜ i ( 1 − s i ) β ig p ig = w ig ≡ ˜ . where � N τ ig s = 1 ˜ w θ sg Note: ˜ w ig is the reward to working in an occupation for a person with average talent
Result 2: Wages and Wage Gaps Let wage ig denote the average earnings in occupation i by group g : � N � 1 1 θ · ( 1 − τ w 1 − η ig ) w i H ig = ( 1 − s i ) − 1 /β γ ¯ � w θ wage ig ≡ η ˜ sg q g p ig s = 1 The wage gap between groups is the same across occupations: � 1 1 θ · �� w − θ s ˜ 1 − η wage i , women s , women = w − θ wage i , men � s ˜ s , men • Selection exactly offsets τ ig differences across occupations because of the Fr´ echet assumption • Higher τ ig barriers in one occupation reduce a group’s wages proportionately in all occupations.
Occupational Choice Therefore: � τ ig � − θ � wage g � − θ ( 1 − η ) p ig T ig = p i , wm T i , wm τ i , wm wage wm Misallocation of talent comes from dispersion of τ ’s across occupation-groups.
Inferring Barriers � T ig θ � p ig θ � wage g � 1 � − 1 � − ( 1 − η ) τ ig = τ i , wm T i , wm p i , wm wage wm We infer high τ barriers for a group with low average wages. We infer particularly high barriers when a group is underrepresented in an occupation. We pin down the levels by assuming τ i , wm = 1. The results are similar if we instead impose a zero average τ in each occupation.
Aggregates H i = � G � Human Capital h jgi dj g = 1 i = 1 ( A i H i ) ρ � 1 /ρ �� I Production Y = Y = � I � G � Expenditure ( c jgi + e jgi ) dj i = 1 g = 1
Competitive Equilibrium 1. Given occupations, individuals choose c , e , s to maximize utility. 2. Each individual chooses the utility-maximizing occupation. 3. A representative firm chooses H i to maximize profits: � I � 1 /ρ I � ( A i H i ) ρ � max − w i H i { H i } i = 1 i = 1 4. The occupational wage w i clears each labor market: G � � H i = h jgi dj g = 1 5. Aggregate output is given by the production function.
Solution in a Special Case • ρ = 1 so that w i = A i • 2 groups, men and women • φ i = 0 (no schooling time), τ h = 0 • A and τ w are joint lognormal Then: � N � 1 1 θ · 1 − η � A θ wage m = i i = 1 � � ln wage w 1 τ w ) − 1 2 ( θ − 1 ) Var ( ln ( 1 − τ w = ln ( 1 − ¯ i )) . 1 − η wage m
Outline 1. Model 2. Evidence 3. Counterfactuals
Data • U.S. Census for 1960, 1970, 1980, 1990, and 2000 • American Community Survey for 2006-2008 • 67 consistent occupations, one of which is the “home” sector. • Look at full-time and part-time workers, hourly wages. • Prime-age workers (age 25-55).
Examples of Baseline Occupations Health Diagnosing Occupations • Physicians • Dentists • Veterinarians • Optometrists • Podiatrists • Health diagnosing practitioners, n.e.c. Health Assessment and Treating Occupations • Registered nurses • Pharmacists • Dietitians
Occupational Wage Gaps for White Women in 1980 Occupational wage gap (logs) 0.6 Doctors 0.5 Farm Mgrs Managers Supervisor(P) Sales Computer Tech Lawyers Textile Mach. 0.4 Prod. Inspectors Mgmt Related Info. Clerks Other Vehicle Metal Work Misc. Repairer Food Financial Clerk Engineers Other Techs Insurance Misc. Admin Secretaries Architects Fabricators 0.3 Eng. Techs Science Techs Plant Operator Records Clerks Science Construction Arts/Athletes Private Hshld Wood Work Math/CompSci Police Nurses Freight Mail Health Service Textiles Motor Vehicle Professors 0.2 Firefighting Cleaning Health Techs Mechanics Wood Mach. Agriculture Print Mach. Extractive Elec. Repairer Guards Librarians Food Prep Therapists 0.1 Forest Teachers 0 Farm Work Social Work −0.1 1/64 1/16 1/4 1 4 16 64 Relative propensity, p(ww)/p(wm)
Change in Wage Gaps for White Women, 1960–2008 Change in log wage gap, 1960−2008 0.6 Firefighting 0.4 Farm Mgrs Farm Work Wood Mach. 0.2 Metal Proc. Agriculture Personal Service 0 Cleaning Teachers Social Work Freight Computer Tech Office Machine Fabricators Health Service Eng. Techs Mail Prod. Inspectors Insurance Textiles Science Food Prep Professors Math/CompSci Doctors −0.2 Arts/Athletes Guards Librarians Construction Secretaries Engineers Elec. Repairer Sales Other Supervisor(P) Health Techs Managers Nurses Plant Operator −0.4 Records Lawyers Architects −0.6 −0.8 −3 −2 −1 0 1 2 3 4 Change in log p(ww)/p(wm), 1960−2008
Test of Model Implications: Changes by Schooling Occupational Similarity to White Men 1960 2008 1960–2008 High-Educated White Women 0.38 0.59 0.21 Low-Educated White Women 0.40 0.46 0.06 Wage Gap vs. White Men 1960 2008 1960–2008 High-Educated White Women -0.50 -0.24 -0.26 Low-Educated White Women -0.56 -0.27 -0.29
Estimating θ ( 1 − η ) � T ig θ � p ig θ � wage g � 1 � − 1 � − ( 1 − η ) τ ig = τ i , wm T i , wm p i , wm wage wm Under Fr´ echet, wages within an occupation-group satisfy 2 Γ( 1 − θ ( 1 − η ) ) Variance = � 2 − 1 . Mean 2 � 1 Γ( 1 − θ ( 1 − η ) ) • Assume η = 1 / 4 for baseline (midway between 0 and 1/2). • Then use this equation to estimate θ . • Attempt to control for “absolute advantage” as well (next slide).
Estimating θ ( 1 − η ) (continued) Estimates of θ ( 1 − η ) Adjustments to Wages Base controls 3.11 Base controls + Adjustments 3.44 Wage variation due to absolute advantage: 3.44 25% 50% 4.16 75% 5.61 90% 8.41 Base controls = potential experience, hours worked, occupation-group dummies Adjustments = transitory wages, AFQT score, education
Estimated Barriers ( τ ig ) for White Women Barrier measure, τ 5 4 Construction Lawyers 3 Doctors 2 Teachers Home 1 Secretaries 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year
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