Accounting for the Evolution of U.S. Wage Inequality

Transcription

1 Accounting for the Evolution of U.S. Wage Inequality Lutz Hendricks UNC Preliminary May 24, /42

2 Motivation Wage inequality has increased in the U.S. since the 1970s standard deviation of log wages, college wage premium, residual wage inequality,... Avast,mostnon-structuralliteraturehasinvestigateexplanations. Astructuralmodelallowstoinvestigateshocksandtheirindirect effects. 2/42

3 The Questions How far can a standard human capital model go towards accounting for changing wage inequality? What are the (proximate) causes of rising inequality? What happened to lifetime inequality? 3/42

4 Approach Calibrate a stochastic Roy / Ben-Porath model to match CPS wage moments, , men building on Heckman / Lochner / Taber (1998 RED) Discrete school choice Heterogeneity in abilities, human capital endowments, shocks Rising inequality is due to diverging skill prices (demographics + SBTC) rising schooling rising shock variances 4/42

5 Result Preview The model accounts for trends in several inequality statistics Rising overall wage inequality is 50% skill prices / 50% rising shock variances Rising between group inequality is almost 100% skill prices Rising within group inequality is almost 100% shock variances Lifetime earnings inequality rises nearly as much as overall wage inequality 5/42

6 Guvenen and Kuruscu How does it differ from Guvenen and Kuruscu s A Quantitative Analysis of the Evolution of the U.S. Wage Distribution, ? GK argue that single shock (acceleration of SBTC) accounts for everything There is no role for labor supply / demographics IrunwiththeKatzandMurphyviewthatdemographics+SBTC drive the college wage premium Other differences: stochastic model discrete school choice and skill prices 6/42

7 Model

8 Model Outline General equilibrium Overlapping generations Small open economy - no capital, fixed interest rate Individuals draw endowments: ability a, humancapitalh 1 choose schooling s: HSD, HSG, CD, CG (Roy model) work and produce human capital (Ben-Porath) 8/42

9 Demographics, Endowments, Preferences N c :sizeofcohortborninτ = c T: fixedlifetime t: age l s,c,t :timeendowment,usedforworkandstudying Endowments: a,h 1 joint Normal Preferences: maximize expected lifetime earnings 9/42

10 Human Capital Production In school: duration T s h Ts +1 = F(h 1,a,s) On the job: h t+1 =(1 δ s )h t + A(a,s)(h t l t ) α s (1) A(a,s)=e A s+θ a (2) 10 / 42

11 Labor Supply Labor supply in efficiency units e i,s,c,t = q i,s,c,t ζ i,s,c,t h i,s,c,t (l s,c,t l i,s,c,t ) }{{}}{{} shocks Ben-Porath (3) ζ: transitoryshockormeasurementerror Normal distribution q: persistentshock: AR(1) with linear trend in shock variance 11 / 42

12 Aggregate output and skill prices Aggregate production function where Y τ = [ G ρ CG τ +(ω CG,τ L CG,τ ) ρ CG ] 1/ρ CG (4) G τ = [ CD s=hsd Skill prices equal marginal products: L s,τ :laborsupplyinefficiency units Constant SBTC: ω s /ω HSG grows at a constant rate. (ω s,τ L s,τ ) ρ HS] 1/ρHS (5) w s,τ = Y τ / L s,τ (6) 12 / 42

13 Household Problem: Work Maximizes the expected value of lifetime earnings V(h Ts +1,a,s,c)=maxE T t=t s +1 R t w s,τ(c,t) e s,c,t }{{} earnings (7) subject to law of motion for h time constraint 0 l t ll s,c,t. The model has a closed form solution. 13 / 42

14 Solution: Work Human capital investment is chosen before the current transitory shock, ζ t, is realized. Backward induction leads to (h i,s,c,t l i,s,c,t ) 1 α s = αa(a,s) T t (1 δ s ) j=1 X s,c,t,j E(q i,s,c,t+j t) q i,s,c,t (8) where ( ) 1 j δs w s,τ(c,t+j) X s,c,t,j = l s,c,t+j (9) R w s,τ(c,t) Recursive solution: Solve for l t (h t ),computeh t+1,anditerateforward. 14 / 42

15 Household Problem: Schooling Choose schooling to maximize W s (p s,h 1,a,s,c)=lnV(F[h 1,a,s],a,s,c) + µ }{{} s,c + πp s + π a (T s T 1 )a }{{} lifetime earnings "psychic cost" The household values: lifetime earnings V school costs µ s,c :common;allowthemodeltomatchcohort schooling psychic costs generate imperfect ability sorting With Type I Extreme Value shocks p s :schoolchoicehasaclosedform solution. 15 / 42

16 Cognitive Test Scores IQ as a proxy for unobserved ability. Helps with identification of ability dispersion (θ) and school choice IQ = a + σ IQ ε IQ (10) ε IQ N(0,1) (11) 16 / 42

17 Calibration

18 Data Moments Mean and standard deviation of log wage by (s,c,t): March CPS, Men born between 1935 and Test scores (IQ): mean scores of high school and college students selected cohorts Taubman and Wales (1972) and NLSY79 Shocks: PSID: covariance matrix of log wages 18 / 42

19 Assumptions schooling technology = job training technology for aggregation: cohorts born before 1935 look like 1935 cohort cohorts born after 1968 look like 1968 cohort 19 / 42

20 Fixed Parameters Parameter Description Value T Lifespan 65 τ Birth cohorts 1935, 1938, 1941,..., 1962, 1965, 1968 T s School duration 2, 3, 5, 7 l t,s,τ Market hours CPS data n/a Nodes of skill price spline 1950, 1957, 1964,..., 2010, 2021, 2032 R Gross interest rate / 42

21 Calibration Approach Simulate 1, 000 individuals in each cohort. Choose school costs µ s,c to match the fraction of persons choosing each school level in each cohort. Choose variance of transitory shocks to best fit variance of wages across ages (for each s,τ) Minimize sum of squared deviations from calibration targets. 21 / 42

22 Calibrated Parameters 36 calibrated parameters governing endowments, technologies, shocks 36 parameters governing skill prices unrestricted skill weight on HSG labor by year for all other school groups: skill weight in 1964 and rate of SBTC Of note: Ben-Porath curvature parameters α s near much lower than most previous estimates (> 0.8) 22 / 42

23 Calibrated Parameters Parameter Description Value On-the-job training A s Productivity 0.14, 0.12, 0.15, 0.23 α s Curvature 9, 0, 0.38, 6 δ s Depreciation rate 0.050, 0.040, 0.048, Endowments σ h1 Dispersion of h θ Ability scale factor π 1 Psychic cost scale factor γ ap Ability weight in psychic cost γ ah Governs correlation of lnh 1 and a σ IQ Noise in IQ 10 Shocks σ(q 1 ) Std dev of first shock 0.03, 0.01, 0.29, 0.29 ρ s Shock persistence 0.98, 0.97, 0.99, 0.98 σ(ζ), 1964 Stddeviationofshocks 0.12,0.11,0.08,0.08 σ(ζ), 2010 Stddeviationofshocks 0.12,0.16,0.11,0.14 Other w s Skill price growth rate, [pct] -1.27, -9, -1, (1 + ρ HS ) 1, (1 + ρ CG ) 1 Substitution elasticities 6.03, / 42

24 Model Fit: Mean Log Wages (HSG) Mean log wage D: 1935 M: Age Mean log wage D: 1938 M: Age Mean log wage D: 1941 M: Age Mean log wage D: 1944 M: Age Mean log wage D: 1947 M: Age Mean log wage D: 1950 M: Age Mean log wage D: 1953 M: Age Mean log wage D: 1956 M: Age 24 / 42

25 Model Fit: Mean Log Wages (CG) Mean log wage Mean log wage Mean log wage Mean log wage D: 1935 M: Age 0 D: 1941 M: Age M: 2 D: Age 0.79 D: 1953 M: Age Mean log wage Mean log wage Mean log wage Mean log wage D: 1938 M: Age 8 D: 1944 M: Age 0.70 D: 1950 M: Age 0.84 D: 1956 M: Age 25 / 42

26 Model Fit: Standard Deviation (HSG) Std log wage Model Data Std log wage Age cohort Age cohort 1938 Std log wage Std log wage Age cohort Age cohort 1944 Std log wage Std log wage Age cohort Age cohort 1950 Std log wage Std log wage Age cohort Age cohort / 42

27 Model Fit: Standard Deviation (HSG) Std log wage 0.8 Model Data Std log wage Age cohort Age cohort 1938 Std log wage Std log wage Age cohort Age cohort 1944 Std log wage Std log wage Age cohort Age cohort 1950 Std log wage Std log wage Age cohort Age cohort / 42

28 Results

29 Questions 1 How far can a simple human capital model go towards accounting for wage distribution facts? 2 What is the contribution of various shocks to changing wage inequality? 3 Limetime earnings inequality? 29 / 42

30 Approach Use counterfactual experiments to shut down one shock at a time 1 fixed wages: w s,τ = w s, fixed schooling at level of 1935 cohort 3 fixed shock variances: σ ξ,s,τ = σ ξ,s,1964 Two cases: 1 Direct effect: holding human capital investments and school choices constant 2 Total effect: allowing human capital investments to adjust All inequality statistics hold population composition constant at cross-year average. 30 / 42

31 Overall Wage Dispersion Std log wage Model Data Year Roughly 50% due to diverging skill prices, 50% due to rising shock variances 31 / 42

32 Fanning Out of the Wage Distribution 0.3 Change in log wage Model Data Wage percentile 32 / 42

33 Residual Wage Inequality Std dev of residual wage 5 Mostly due to rising shock variances Year 33 / 42

34 Wage Dispersion and Schooling 5 5 Std log wage 5 Std log wage 5 Model Data Model Data Year Year 5 5 Std log wage 5 Std log wage 5 Model Model Data Data Year Year 34 / 42

35 College Premium 5 College wage premium Almost entirely due to diverging skill prices 0.25 Model Data Year 35 / 42

36 College Premium: Young and Old College wage premium Model Data Year College wage premium Model Data Year Ages Ages Early decline in the young college premium is due to falling human capital investment of high school graduates in the 1970s. 36 / 42

37 Returns to Experience 0.35 Model Data 5 Model Data Wage growth, ages Wage growth, ages Birth year Birth year High school graduates College graduates Changes are 50% skill prices / 50% human capital investment. 37 / 42

38 Summary 1 Overall wage inequality: 50% due to diverging skill prices / 50% due to rising shock variances 2 Within group inequality: due to rising shock variances 3 College wage premium: due to diverging skill prices Human capital investment plays a role for the divergent behavior of young / old. 4 Returns to experience: 50% skill prices; 50% human capital investment. 5 Rising education matters only for skill prices. 6 Secondary effects are generally small. 38 / 42

39 Why Are Indirect Effects Small? Optimal human capital investment: (h i,s,c,t l i,s,c,t ) 1 α s = αa(a,s) T t (1 δ s ) j=1 X s,c,t,j E(q i,s,c,t+j t) q i,s,c,t Changing skill prices affect X s,c,t,j. Investment response is the same for all individuals in a [school, age] cell (except for interaction with expected shock growth term) Small effect on within group inequality Rising shock variances affect E(q i,s,c,t+j t)/q i,s,c,t Investment response is the same for all individuals in a [school, age] cell Small amplification of within group inequality Since Var(q) rises by similar amounts for CG and HSG: small effect on college premium. 39 / 42

40 Lifetime Earnings Inequality Std of lifetime earnings Increase similar to standard deviation of log wages. 50% diverging skill prices. 50% rising shock variances (accounts for within school group rise in lifetime earnings inequality) Birth year 40 / 42

41 Predictability of Lifetime Earnings Predictability = [var of lifetime earnings without shocks] /[varof lifetime earnings] Huggett / Ventura / Yaron (2011 AER): This model: for college educated workers 0.25 for high school educated workers Why so much smaller than HVY? 41 / 42

42 The End