Chaired by Jenna Stearns (UC Davis)

Transcription

1 Keynote Lectures on Labor and Health Economics: Amanda Kowalski (Yale): Personalizing health care with economics Lance Lochner (UWO): Wage dynamics and returns to unobserved skills Chaired by Jenna Stearns (UC Davis)

2 Lance Lochner (Univ. of Western Ontario) Youngmin Park (Bank of Canada) Youngki Shin (McMaster University) North American Summer Meeting of the Econometric Society June 2018

3 Rising Wage Inequality in the US 0.5 Total (lnwt) Between-Group (ft(xt)) Within-Group (wt) Year Substantial increase within (education, race, experience) groups rising residual wage inequality

4 Interpretation, JMP & SBTC Interpretation of rising residual inequality important for understanding its causes & welfare consequences rising returns to unobserved skill? increasing inequality in unobserved skill? increased short-term volatility (unrelated to skill)?

5 Interpretation, JMP & SBTC Interpretation of rising residual inequality important for understanding its causes & welfare consequences rising returns to unobserved skill? increasing inequality in unobserved skill? increased short-term volatility (unrelated to skill)? Since Juhn, Murphy & Pierce (1993), many economists have equated rising residual inequality with an increase in the returns to unobserved ability/skill

6 Interpretation, JMP & SBTC Interpretation of rising residual inequality important for understanding its causes & welfare consequences rising returns to unobserved skill? increasing inequality in unobserved skill? increased short-term volatility (unrelated to skill)? Since Juhn, Murphy & Pierce (1993), many economists have equated rising residual inequality with an increase in the returns to unobserved ability/skill This interpretation motivated a huge and still influential literature on SBTC many studies specifically aimed to explain rising residual inequality & returns to unobserved ability/skill (e.g. Galor & Tsiddon 1997, Acemoglu 1999, Caselli 1999, Galor & Moav 2000, Violante 2002)

7 Interpretation, JMP & SBTC Interpretation of rising residual inequality important for understanding its causes & welfare consequences rising returns to unobserved skill? increasing inequality in unobserved skill? increased short-term volatility (unrelated to skill)? Since Juhn, Murphy & Pierce (1993), many economists have equated rising residual inequality with an increase in the returns to unobserved ability/skill This interpretation motivated a huge and still influential literature on SBTC many studies specifically aimed to explain rising residual inequality & returns to unobserved ability/skill (e.g. Galor & Tsiddon 1997, Acemoglu 1999, Caselli 1999, Galor & Moav 2000, Violante 2002) Still the dominant interpretation within labor economics (e.g. Autor, Katz & Kearney 2008)

8 Other Interpretations Lemieux (2006) argues that some of the increase in residual inequality is explained by an increase in the variance of unobserved skills due to composition changes increase in highly educated and older workers who have larger within-group variances

9 Other Interpretations Lemieux (2006) argues that some of the increase in residual inequality is explained by an increase in the variance of unobserved skills due to composition changes increase in highly educated and older workers who have larger within-group variances Measurement error and short-term fluctuations in earnings may also have increased (Lemieux 2006, Gottschalk & Moffitt 2009)

10 Measuring Skills & Tasks Several recent studies use richer data to incorporate... other direct measures of skills/ability Castex & Dechter (2014) estimate a substantial decline in returns to AFQT between NLSY79 & NLSY97 Deming (2017) estimates an increase in returns to social skills across NLSY cohorts

11 Measuring Skills & Tasks Several recent studies use richer data to incorporate... other direct measures of skills/ability Castex & Dechter (2014) estimate a substantial decline in returns to AFQT between NLSY79 & NLSY97 Deming (2017) estimates an increase in returns to social skills across NLSY cohorts measures of occupational tasks Autor, Levy & Murnane (2003) and Autor & Dorn (2013) document decline in demand for middle-skill jobs due to automation: polarization Caines, Hoffmann & Kambourov (2017) document increase in returns to task complexity

12 Some Limitations of Prior Research Much has been learned from new efforts to measure skills & tasks, but...

13 Some Limitations of Prior Research Much has been learned from new efforts to measure skills & tasks, but... Much of the cross-sectional variation in wages remains unexplained

14 Some Limitations of Prior Research Much has been learned from new efforts to measure skills & tasks, but... Much of the cross-sectional variation in wages remains unexplained Difficult measurement problems require strong (often implicit) assumptions on evolution of skills over lifecycle Castex & Dechter (2014) and Deming (2017) use pre-market skill measures: ignores accumulation on the job most task-based studies implicitly assume worker skills & tasks are time invariant within occupations Spitz-Oener (2006) and Autor & Handel (2013) evidence on differences in tasks within occupations raises questions about this assumption

15 Our Approach & General Contribution Previous studies rely on repeated cross-section data hard to sort out changes in returns vs. distribution of skills

16 Our Approach & General Contribution Previous studies rely on repeated cross-section data hard to sort out changes in returns vs. distribution of skills Panel data is naturally more useful since skills are persistent & should drive long-term differences in wages across workers if skill heterogeneity is important, then workers with a high wage today should also have high wages far into the future current wage residual differences should predict long-term future differences predicted future differences should be greater when skill returns are high

17 Our Approach & General Contribution Previous studies rely on repeated cross-section data hard to sort out changes in returns vs. distribution of skills Panel data is naturally more useful since skills are persistent & should drive long-term differences in wages across workers if skill heterogeneity is important, then workers with a high wage today should also have high wages far into the future current wage residual differences should predict long-term future differences predicted future differences should be greater when skill returns are high Long autocovariances identify the evolution of skill returns, motivating a simple IV estimation approach can then identify distributions of skills and transitory shocks no need to observe additional skill measures or anything about what workers do

18 Main Contributions: Empirical Findings Returns to unobserved skill fell substantially from mid-1980s through 1990s reflects a sharp decline in predictability of future wages more dramatic decline for non-college men (consistent with polarization ) fundamentally different from returns estimated under assumption of time-invariant skill distributions (JMP 1993, Gottschalk-Moffitt 2012) broadly consistent with falling returns to AFQT since 1980s (Castex & Dechter 2014)

19 Main Contributions: Empirical Findings Returns to unobserved skill fell substantially from mid-1980s through 1990s reflects a sharp decline in predictability of future wages more dramatic decline for non-college men (consistent with polarization ) fundamentally different from returns estimated under assumption of time-invariant skill distributions (JMP 1993, Gottschalk-Moffitt 2012) broadly consistent with falling returns to AFQT since 1980s (Castex & Dechter 2014) Rising residual inequality is driven by an increase in the variance of unobserved skill

20 Main Contributions: Empirical Findings Returns to unobserved skill fell substantially from mid-1980s through 1990s reflects a sharp decline in predictability of future wages more dramatic decline for non-college men (consistent with polarization ) fundamentally different from returns estimated under assumption of time-invariant skill distributions (JMP 1993, Gottschalk-Moffitt 2012) broadly consistent with falling returns to AFQT since 1980s (Castex & Dechter 2014) Rising residual inequality is driven by an increase in the variance of unobserved skill rising variance of lifecycle skill growth, not initial skill levels systematic skill growth heterogeneity (HIP) skill growth shocks

21 Main Contributions: Empirical Findings Returns to unobserved skill fell substantially from mid-1980s through 1990s reflects a sharp decline in predictability of future wages more dramatic decline for non-college men (consistent with polarization ) fundamentally different from returns estimated under assumption of time-invariant skill distributions (JMP 1993, Gottschalk-Moffitt 2012) broadly consistent with falling returns to AFQT since 1980s (Castex & Dechter 2014) Rising residual inequality is driven by an increase in the variance of unobserved skill rising variance of lifecycle skill growth, not initial skill levels systematic skill growth heterogeneity (HIP) skill growth shocks not accounted for in composition effects of Lemieux (2006)

22 Main Contributions: Supply vs. Demand Decomp. To see whether the rising variance of unobserved skills drove the decline in returns, we develop an assignment model of the labor market workers with heterogeneous skills matched to firms/jobs with heterogeneous productivity decompose changes in returns into changes due to technology shifts (demand) vs. changes in the skill distribution (supply)

23 Main Contributions: Supply vs. Demand Decomp. To see whether the rising variance of unobserved skills drove the decline in returns, we develop an assignment model of the labor market workers with heterogeneous skills matched to firms/jobs with heterogeneous productivity decompose changes in returns into changes due to technology shifts (demand) vs. changes in the skill distribution (supply) Model implies equilibrium wage functions like those we estimate

24 Main Contributions: Supply vs. Demand Decomp. To see whether the rising variance of unobserved skills drove the decline in returns, we develop an assignment model of the labor market workers with heterogeneous skills matched to firms/jobs with heterogeneous productivity decompose changes in returns into changes due to technology shifts (demand) vs. changes in the skill distribution (supply) Model implies equilibrium wage functions like those we estimate Results suggest that both supply and demand factors played important roles decline in skill demand was more important than supply shifts for non-college workers (consistent with automation)

25 Outline Identification issues PSID data Estimating the evolution of skill prices, skill distributions, and shock distributions Assignment model supply vs. demand shifts Conclusions & New Efforts

26 Log Wage Specification We consider the following log wage equation: ln W i,t = f t (x i,t ) + µ t θ i,t + ε i,t }{{} w i,t x i,t reflects observed characteristics (education, race, experience) residual w i,t combines skills, skill returns, and other shocks

27 Log Wage Residuals We focus primarily on log wage residuals: w i,t = µ t θ i,t + ε i,t θ i,t = θ i,t 1 + ν i,t µ t reflects the labor market returns to unobserved skills non-linear skill pricing (as in assignment model) θ i,t reflects time-varying unobserved skills idiosyncratic skill growth shocks systematic skill growth heterogeneity (HIP) ε i,t reflects measurement error or idiosyncratic transitory non-skill shocks (e.g. temporary illness, family disruption, temporary firm-productivity shocks)

28 Normalizations and Assumptions (Baseline) w i,t = µ t θ i,t + ε i,t θ i,t = θ i,t 1 + ν i,t Normalizations: all components are mean zero set µ t = 1 for some t Cov(θ t, ε t ) = Cov(ν t, ε t ) = 0, t, t Cov(ε t, ε t ) = 0 for t t k (transitory non-skill shocks) Cov(w t, w t ) = µ t µ t Cov(θ t, θ t ) Cov(θ t, ν t ) = 0 for t > t (ignore HIP now but relax later) Cov(θ t, θ t ) = V ar(θ t ) Distribution for initial skills may vary across cohorts Distributions for ν t and ε t may vary by experience and time

29 Identifying & Estimating Skill Returns Over Time Since ν t is uncorrelated with past skill levels and serial correlation in ε t dies out after k periods, we have Cov(w t, w t ) Cov(w t 1, w t ) = µ t µ t 1 for t t 1 k Suggests using past residuals as valid instruments for w t 1 Can use 2SLS to estimate µt µ t 1 for all but first k + 1 periods

30 Identifying & Estimating Skill Returns Over Time Since ν t is uncorrelated with past skill levels and serial correlation in ε t dies out after k periods, we have Cov(w t, w t ) Cov(w t 1, w t ) = µ t µ t 1 for t t 1 k Suggests using past residuals as valid instruments for w t 1 Can use 2SLS to estimate µt µ t 1 for all but first k + 1 periods Using future residuals as instruments will generally lead to µ upward biased estimates of t µ t 1 under reasonable conditions, can difference this bias away to obtain estimates of early returns can be used to estimate V ar(νt) V ar(θ t 1)

31 Identifying the Rest Once skill returns have been identified, the rest is easy: Can identify V ar(θ t c) (and then V ar(ν t c)) from V ar(θ t c) = Cov(w i,t, w i,t c) µ t µ t for t t + k Next, identify V ar(ε t c) = V ar(w i,t c) µ 2 t V ar(θ t c) Given everything else, correlation structure for ε i,t is identified from Cov(w i,t, w i,t ) for t t k Cannot identify these features for the last k periods, since it is impossible to distinguish between skill growth shocks and non-skill shocks without future observations

32 Incorporating Systematic Skill Growth Heterogeneity Skill growth innovations may be correlated over time as in HIP model (e.g. Haider 2001, Guvenen 2009) Allow for heterogeneity in systematic lifecycle growth rates: ν i,t = τ t (c i )δ i + ν i,t Assume: E[δ] = 0 (residuals already purged of avg. wage growth) δ may be correlated with initial skill θ c ν t uncorrelated with (θ c, δ, ν t ), t t ε t uncorrelated with (θ c, δ, ν t ), t, t

33 Incorporating Systematic Skill Growth Heterogeneity Skill growth innovations may be correlated over time as in HIP model (e.g. Haider 2001, Guvenen 2009) Allow for heterogeneity in systematic lifecycle growth rates: ν i,t = τ t (c i )δ i + ν i,t Assume: E[δ] = 0 (residuals already purged of avg. wage growth) δ may be correlated with initial skill θ c ν t uncorrelated with (θ c, δ, ν t ), t t ε t uncorrelated with (θ c, δ, ν t ), t, t τ t (c) allows for variation in systematic skill growth across time and cohort/experience (at younger ages) assume τ t (c) = 0 for all t, e = t c ē skill innovations are serially uncorrelated for experienced workers can identify µ t as earlier from experienced workers

34 PSID Data: Overview PSID Data Estimation Results We use panel data from PSID on annual earnings and hours worked for American men for calendar years annually observed up to 1996, biennially thereafter Earnings: household head s total wages and salaries (excluding farm and business income) Wages = earnings / hours worked Similar results for weekly wages and annual earnings

35 Sample Restrictions PSID Data Estimation Results Exclude non-random oversamples (SEO, Latino) Male heads of households Ages: Potential experience: 1-40 years Non-students Positive annual earnings and hours worked Trim top and bottom 1% of earnings within each experience-education category-year cell education categories: non-college (48%) or college (52%) 10-year experience groups Resulting data set has 3,766 men and 44,547 person-year observations Descriptive Statistics

36 Obtaining Residuals PSID Data Estimation Results Residuals from cross-section regressions for log wages run separately for each year and by education category (non-college vs. college): experience dummies race dummies (black, white, hispanic) education dummies (7 subcategories) race dummies cubic polynomial in experience education dummies cubic polynomial in experience

37 PSID Data Estimation Results Variance of Log Wages by Education Total Variance Residual Variance 0.5 Non-College College 0.5 Non-College College Year Year

38 PSID Data Estimation Results Predicted Residuals by Baseline Residual Quartile ( ) E[wb ε Ignoring HIP, E[w t w b Q j ] = µ b w b Q j ] t µ b for t b Quartile 1 Quartile 2 Quartile Quartile Year indicates declining skill returns in late 1980s and 1990s

39 Long Residual Autocovariances PSID Data Estimation Results Ignoring HIP, Cov(w t, w b ) = µ t µ b V ar(θ b ) for t b Year Negative slopes in late 1980s and 1990s suggest declining skill returns Upward shifting lines suggests that variance of unobserved skill is increasing over time Similar patterns for experienced workers More

40 PSID Data Estimation Results Long Residual Autocovariances by Education 0.22 Non-College 0.22 College Year Year Cov(w t, w b ) = µ t µ b V ar(θ b ) for t b + 6

41 PSID Data Estimation Results 2SLS Estimation of Skill Price Changes Assuming k = 6 (e.g. ε t MA(5)), we estimate µt µ t 2 for 3-4 year periods from : Regress w i,t on w i,t 2 using the following instruments: (w i,t 8, w i,t 9 ) for (w i,t 8, w i,t 10 ) for Requires no assumptions on experience or time effects on variances of skills or shocks In all cases, over-identification tests fail to reject validity of our instruments

42 Implied 2SLS µ t Patterns 1.5 PSID Data Estimation Results All Non-College College All, Experience Year Tables

43 PSID Data Estimation Results Leads as Instruments & the Variance of Skill Growth Using leads (rather than lags) as instruments should produce upward biased estimates of growth in returns if skill growth shocks are important Adding the first two available leads out of w t+6,..., w t+9 as instruments produces larger estimated µ t growth rates reject equality of estimates for all periods from (5% sig.) Differences between estimates using leads vs. lags as instruments imply substantial variation in skill growth rates V ar(ν t 1+ν t) V ar(θ t 2) range from 0.16 to 0.29 over time

44 Minimum Distance Estimation PSID Data Estimation Results We now use full w i,t covariance matrix to estimate skill returns, variance of unobserved skills & shock variances Assume ε i,t MA(q) (benchmark assumes q = 5): ε i,t = ξ i,t + β 1 ξ i,t 1 + β 2 ξ i,t β q ξ i,t q Assume V ar(ξ t c) = ω(t)κ(e) where e = t c is experience Assume ν t serially uncorrelated, V ar(ν t c) = π(t)φ(e) Assume κ(e) and φ(e) are quadratic in experience (normalize φ(20) = κ(20) = 1) ω(t) is unrestricted, but π(t) is a cubic function of time Assume V ar(θ c c) is a cubic function of cohort year Normalize µ 1985 = 1

45 Minimum Distance µ t Patterns PSID Data Estimation Results Year Ignoring time variation in V ar(ν t ) (as in prior literature) results in very different patterns Figure

46 PSID Data Estimation Results µ t Estimated Separately by Education 1.5 Non-college 1.5 College Year Year Stronger decline in skill returns for non-college men

47 PSID Data Estimation Results Residual Variance Decomposition by Education Non-College Total (Data) Total (Fitted) Unobserved Skill (µtθt) Transitory (εt) Total (Data) Total (Fitted) Unobserved Skill (µtθt) Transitory (εt) College Year Year Trends in residual variance largely driven by unobserved skills (despite falling returns), not increased short-run volatility

48 PSID Data Estimation Results Skill Variance Decomposition by Education Non-College Total Unobserved Skill (θt) Initial Skill (ψ) Accumulated Skill Shocks College Total Unobserved Skill (θt) Initial Skill (ψ) Accumulated Skill Shocks Year Year Rising skill variance driven by increasing variance of accumulated skill growth innovations

49 PSID Data Estimation Results Time Trends in the Variances of Skill Growth Shocks, π(t), by Education 0.03 Non-College 0.03 College Year Year Rising variance of unobserved skills not purely a composition effect (as in Lemieux (2006)) Other Results

50 PSID Data Estimation Results Incorporating Systematic Skill Growth Heterogeneity Incorporate heterogeneity in unobserved skill growth: ν i,t = τ t (c i )δ i + ν i,t For practical reasons, we combine college/non-college groups and assume the following in estimation: Separability in experience and time: τ t (c) = χ t η(e) χ t is a cubic polynomial in time linearly declining differences in skill growth over the lifecycle: η(e) = max{1 e/ē, 0} with ē = 30 normalize χ 1985 = 1 and η(0) = 1 V ar(δ c) & Cov(δ, θ c c) are cohort-invariant Cohort trends in V ar(θ c c) as earlier (i.e. cubic in time)

51 PSID Data Estimation Results Estimated χ t and Skill Variance Decomposition χ t V ar(θ t ) Decomposition Total Unobserved Skill (θt) Initial Skill (ψ) Accumulated Skill Shocks Heterogenous Growth Year Year

52 PSID Data Estimation Results Estimated Skill Returns µ t Year

53 Supply vs. Demand To what extend is the fall in skill returns driven by the rising variance of skills? requires a framework in which skill pricing functions are non-linear We develop an assignment model of the labor market to study the changing roles of supply and demand (e.g. Sattinger 1979)

54 Model of the Labor Market Workers supply skill Θ t earning wage W t (Θ t ) Jobs differ by productivity Z t e.g., task, hierarchy, capital Output is produced by assigning workers of each skill level to a job production function Y t (Θ t, Z t ) is increasing and supermodular in (Θ t, Z t ) Everything assumed to be education sector-specific To simplify, we abstract from non-skill shocks could reflect unanticipated shocks to quantity of labor services, job match productivity, or measurement error estimates suggest little secular change

55 Firm s Problem & Equilibrium Taking market wages W t (Θ t ) as given, employer with productivity Z t chooses what skill to hire Θ t (Z t ) arg max Θ t {Y t (Θ t, Z t ) W t (Θ t )}

56 Firm s Problem & Equilibrium Taking market wages W t (Θ t ) as given, employer with productivity Z t chooses what skill to hire Θ t (Z t ) arg max Θ t {Y t (Θ t, Z t ) W t (Θ t )} Equilibrium: positive assortative matching due to supermodularity (Becker, 1973) Workers with higher Θ t earn more because they are more productive at any given job (direct return) they work at more productive jobs (sorting effect)

57 Equilibrium Skill Pricing & Wages Generally, equilibrium wages will be non-linear in skills Log wages are linear in (log) skills if: Θ t and Z t are normally distributed Cobb-Douglas production: Y t (Θ t, Z t ) = exp(λ t Θ t + γ t Z t ) log wages are given by ln W t = ζ t + µ t Θ t where σ Zt µ t = λ }{{} t + γ t σ Θt direct return }{{} sorting Note: Returns to skill returns to job, d ln W t /dz t

58 Corresponding Empirical Specification Within college vs. non-college workers, Θ i,t = g t (x i,t ) }{{} + θ i,t }{{} observed skill unobserved skill with E[θ t x t ] = 0, so log wages are ln W i,t = ζ t + µ t g t (x i,t ) + µ t θ i,t + ε i,t }{{}}{{} f t(x i,t ) w i,t Already estimated µ t and distributions of θ i,t using residuals w i,t

59 Observed vs. Unobserved Skill Variance Decomposition Total Skill (Θt) Observed Skill (gt(xt)) Unobserved Skill (θt) Non-College Total Skill (Θt) Observed Skill (gt(xt)) Unobserved Skill (θt) College Year Year

60 Recovering Supply and Demand Factors We can decompose changes in skill prices µ t = λ t + γ tσ Zt σ Θt into Demand effects due to changes in technology and the distribution of firm productivity: λ t and γ t σ Zt and changes in the Supply of skills: σ Θt

61 Recovering Supply and Demand Factors We can decompose changes in skill prices µ t = λ t + γ tσ Zt σ Θt into Demand effects due to changes in technology and the distribution of firm productivity: λ t and γ t σ Zt and changes in the Supply of skills: σ Θt How? We show that the labor share = λt µ t, so we can recover λ t given estimates of µ t and measures of the labor share We can then plug our estimates of µ t, λ t, and σ Θt into the expression above for µ t to recover γ t σ Zt

62 Education Sector-Specific Labor Shares Requires non-college- and college-specific labor shares We use industry-specific labor shares weighted by fraction of workers by education type KLEMS data for US, (Jorgenson, et al. 2012) Non-College College Year

63 Demand Factors Production: Y t (Θ t, Z t ) = exp(λ t Θ t + γ t Z t ) Non-College College λ t Non-College College γ t σ Zt Year Year

64 Decomposing Supply and Demand Effects on µ t 1.5 Non-College Actual Holding Supply Factor Constant Holding Demand Factors Constant 1.5 College Actual Holding Supply Factor Constant Holding Demand Factors Constant Year Year Falling skill returns driven mostly by demand factors for non-college workers Both supply & demand forces driving (smaller) decline for college workers

65 Summary We use panel data to separately identify changes in skill returns from changes in the distributions of skill no measures of ability or job tasks are needed simple IV strategy can identify changes in skill returns critical to account for changes in the dispersion of skill growth when estimating evolution of returns

66 Summary We use panel data to separately identify changes in skill returns from changes in the distributions of skill no measures of ability or job tasks are needed simple IV strategy can identify changes in skill returns critical to account for changes in the dispersion of skill growth when estimating evolution of returns Using the PSID, we show that skill returns declined substantially since the mid-1980s reflects large declines in long-run residual autocovariances stronger declines for non-college men variance of unobserved skills increased markedly driven by increases in variances of both wage growth shocks and heterogeneity in lifecycle growth rates

67 Summary We use panel data to separately identify changes in skill returns from changes in the distributions of skill no measures of ability or job tasks are needed simple IV strategy can identify changes in skill returns critical to account for changes in the dispersion of skill growth when estimating evolution of returns Using the PSID, we show that skill returns declined substantially since the mid-1980s reflects large declines in long-run residual autocovariances stronger declines for non-college men variance of unobserved skills increased markedly driven by increases in variances of both wage growth shocks and heterogeneity in lifecycle growth rates Suggests a shift in focus from theories of rising skill returns to theories of growing inequality in lifecycle skill accumulation

68 Summary Develop an assignment model of the labor market yields equilibrium wage functions like those commonly assumed in the empirical literature estimates suggest that fall in demand explains most of the declining skill returns for non-college workers, while both supply & demand shifts are important for college workers

69 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar

70 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar (Log) skills are a random walk for older workers What if θ i,t = ρ t θ i,t 1 + ε i,t?

71 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar (Log) skills are a random walk for older workers What if θ i,t = ρ t θ i,t 1 + ε i,t? In this case, we estimate ρ t µ t /µ t 1

72 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar (Log) skills are a random walk for older workers What if θ i,t = ρ t θ i,t 1 + ε i,t? In this case, we estimate ρ t µ t /µ t 1 ρ t = ρ < 1 vs. declining skill returns ρ < 1 implies greater depreciation rate D i for more-skilled older workers: E[D i θ i,t 1] (1 ρ)θ i,t 1 These depreciation differences would need to be fairly large for skill returns to be increasing in late 1980s and 1990s

73 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar (Log) skills are a random walk for older workers What if θ i,t = ρ t θ i,t 1 + ε i,t? In this case, we estimate ρ t µ t /µ t 1 ρ t = ρ < 1 vs. declining skill returns ρ < 1 implies greater depreciation rate D i for more-skilled older workers: E[D i θ i,t 1] (1 ρ)θ i,t 1 These depreciation differences would need to be fairly large for skill returns to be increasing in late 1980s and 1990s Strong decline in ρ t in late 1980s & 1990s would imply that skills depreciated more rapidly for skilled workers during that period skill differences became less meaningful for future

74 Unconvinced that Returns to Unobs. Skill have Fallen? Two key assumptions: Non-skill shocks die out can allow for ε t AR(1) still identified & results are very similar (Log) skills are a random walk for older workers What if θ i,t = ρ t θ i,t 1 + ε i,t? In this case, we estimate ρ t µ t /µ t 1 ρ t = ρ < 1 vs. declining skill returns ρ < 1 implies greater depreciation rate D i for more-skilled older workers: E[D i θ i,t 1] (1 ρ)θ i,t 1 These depreciation differences would need to be fairly large for skill returns to be increasing in late 1980s and 1990s Strong decline in ρ t in late 1980s & 1990s would imply that skills depreciated more rapidly for skilled workers during that period skill differences became less meaningful for future distinction unimportant from individual s view (either way, value of current skills erodes more quickly over time)

75 Priors Not Necessarily Based on Strong Foundations Several strong assumptions needed when using repeated cross-sectional data (as most of the literature)

76 Priors Not Necessarily Based on Strong Foundations Several strong assumptions needed when using repeated cross-sectional data (as most of the literature) Regressing log wages on measures of initial skills for different cohorts (e.g. Castex & Dechter 2014) also requires many strong assumptions: 1. Cohort stationarity in quality of skill measurements 2. Cohort stationarity in the variance of initial skills 3. Cohort stationarity in the covariance between initial skills and early skill growth 4. Time/cohort stationarity in importance of lifecycle skill growth heterogeneity for young workers 5. ρ t = ρ for all t Our estimates suggest that 2 and (especially) 4 are not true! With 5 only, our results at least imply weaker growth in skill returns over late 1980s and 1990s

77 Related Work in Progress Allow for nonparametric skill return functions µ t (θ it ) and skill/shock distributions better investigate issues related to polarization requires larger sample using SIPP waves linked to W-2 earnings records from over 45,000 observations per year observe earnings not wages (except SIPP survey years) integrating analysis with labor supply model

78 Related Work in Progress Preliminary µ t estimated from SIPP/W-2 earnings look very similar to our PSID-based estimates using wages 1.5 2SLS estimates (IV: w i,t 8 ) All Non-College College 1.5 GMM estimates (HIP model) Non-College College Year Year

79 Related Work in Progress Intergenerational relationships use data from Canada s Intergenerational Income Database earnings data (from tax records) on children & their parents from explore evolution of intergenerational relationships (conditional on age or time) for skills initial levels & growth rates transitory shocks directly account for changing skill returns

80 Thanks

81 Sample Statistics Race: 92% White, 6% black, 1% hispanic Educational Attainment Education (years) Percent Less than High School (1-11) 13 Completed High School (12) 35 Some College (13-15) 21 Completed College (16) 21 Advanced Degrees (17+) 10 Back

82 Autocovariances for Log Wages Balanced Sample Year Back

83 Autocovariances for Log Wages Years of Experience Year Back

84 Autocovariances for Log Wages 1-15 Years of Experience Year Back

85 2SLS estimates of skill return growth rates, A. All men (µ t µ t 2 )/µ t (0.0446) (0.0375) (0.0379) (0.0338) (0.0349) (0.0354) N st stage F -Stat B. Non-college men (µ t µ t 2 )/µ t (0.0605) (0.0561) (0.0601) (0.0496) (0.0577) (0.0544) N st stage F -Stat C. College men (µ t µ t 2 )/µ t (0.0609) (0.0481) (0.0489) (0.0472) (0.0467) (0.0457) N st stage F -Stat Back

86 2SLS estimates of skill return growth rates, A. All men (µ t µ t 2 )/µ t (0.0251) (0.0275) (0.0274) N st stage F -Stat B. Non-college men (µ t µ t 2 )/µ t (0.0430) (0.0472) (0.0752) N st stage F -Stat C. College men (µ t µ t 2 )/µ t (0.0309) (0.0343) (0.0291) N st stage F -Stat Back

87 Importance of Time-Varying Skill Growth Shocks for µ t 1.5 Baseline Version A Version B Version C A: ε i,t ARMA(1, 1) Year B: ε i,t ARMA(1, 1), time-invariant skill growth shock dist. C: ε i,t ARMA(1, 1), time-invariant skill growth shock dist., identical initial skill distributions across cohorts like Haider (2001), Moffitt & Gottschalk (2012) Back

88 Variance of Initial Skill, θ c, by Education 0.8 Non-College 0.8 College Cohort Cohort Back

89 Experience Patterns for the Variances of Skill Shocks, φ(e), by Education 10 Non-College 10 College Experience Experience Back

90 Time Trends in the Variances of Transitory Non-Skill Shocks, ω(t), by Education 0.35 Non-College 0.35 College Year Year Back

91 Experience Patterns for the Variances of Transitory Non-Skill Shocks, κ(e), by Education 1.1 Non-College 1.1 College Experience Experience Back

92 Increasing Variance of Skill Growth Strong increases in the variances of all skill growth components over late 1980s and 1990s Heterogeneity Between-Group Skill Growth Shocks χ t g(x it ) π(t) Year Year

93 Other Potential Factors Increase in minimum wage would reduce d ln W t /dθ t 1.5 Real Federal Minimum Wage (1985=1) Real Average Minimum Wage (1985=1) µt Implied by 2SLS µt Estimated by MD Year For more general CES production functions, changes in average skill levels can also affect d ln W t /dθ t falling return could be due to increase in average skill levels or disappearance of good jobs (e.g. due to trade)