Lecture 2: The Human Capital Model

Transcription

1 Lecture 2: The Human Capital Model Fatih Guvenen University of Minnesota February 7, 2018 Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

2 Why Study Wages? Labor income is 2/3 of GDP. Most individuals outside of top 10% have very little capital income. Labor income is all they have. So it s crucial to understand: Why do wages grow over the life cycle? Why does labor income varies so much across individuals (inequality)? Why has US wage inequality increased so much since the 1970s? What is the nature of income risk faced by workers? Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

3 The Human Capital Model Developed with seminal contributions by Becker, Schultz, Ben-Porath, Mincer, and Rosen. Key Assumptions: Skills are general (No firm-specificity. Can you have industry- or occupation-specific skills? Will discuss this later.) No slavery (i.e, no commitment by worker). Labor markets are competitive. Lack of commitment can be solved by making workers pay for their own training (Becker). Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

4 Ben-Porath (1967) Model Individuals can borrow and lend at a constant interest rate (denoted by r), which implies that markets are complete. Let δ = 1/ (1 + r). Individuals solve max {i t} T t=1 s.t [ T ] δ t 1 Rh t (1 i t ) t=1 h t+1 = h t + A (h t i t ) α, with h 0 > 0 given i t [0, 1] This formulation does not rest on the assumption of risk-neutrality, but instead requires markets to be complete. [Homework: Prove this statement.] Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

5 Ben-Porath (cont d) α : measures the returns to scale in investment. When it is small (large), you want to spread (bunch) investment over time. Technology could be generalized: Ah β s i α s : 1 Estimates of α and β are typically close. (But estimates themselves seem too high maybe should be revisited). 2 Present technology gives closed-form solutions. 3 Can also introduce pecuniary costs of investment (many papers do. See Seshadri and Manuelli (20 Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

6 Analyzing the Individual s Problem Define: C(Q s ) h s i s = ( ) 1/α Qs. A With this transformation, the problem of an individual can be written as [ S ] max δ s 1 R (h s C(Q s )) {Q s} S s=1 subject to s=1 h s+1 = h s + Q s, with h 0 given Now write it as a Bellman equation: V s (h s ) = max [R (h s C(Q s )) + δv s+1 (h s + Q s )] Q s [0,h s] Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

7 Analyzing the Individual s Problem Assuming interior solution, the FOC: RC (Q s ) = δv s+1 (h s + Q s ) Envelope: V s (h s ) = R + δv s+1 (h s + Q s ) Lead by one period: V s+1 (h s+1 ) = R + δ [ R + δv s+2 (h s+2 ) ]..repeatedly substitute for the RHS to get { } RC (Q s ) = δ R + δr δ S s 1 R C (Q s ) }{{} [ = 1 ( ) ] 1 S s 1 r 1 + r }{{} Fatih Guvenen (2018) Marginal cost Lecture 2: Ben Porath February 7, / 16 (1) (2) (3)

8 Analyzing the Individual s Problem Solve the model: RHS does not depend on Q. LHS is proportional to Q 1 α α s. If α > 0.5, this is a concave function. Alternatively convex. How curvature depends on α : Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

9 Implications The solution again: Q s = A 1 1 α [αmb (r, S s)] α 1 α What happened to R? So, R is not the returns-to-skill. Notice that Q s does NOT depend on current human capital level. This is a consequence of the neutrality assumption. Is this realistic? (i s still depends on h s of course). It would imply for example that somebody who has high initial human capital will spend less time investing in human capital.. seems a bit unrealistic. It also implies a convergence in the wage distribution (var(log(w)) if the only heterogeneity is in initial human capital. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

10 Key observations 1 Ben-Porath delivers several key insights: 1 Key insight: reward from work wage reward from work = wage + acquired human capital distinction can matter a lot, e.g., labor supply elasticity discussed later. 2 Investment declines over the lifecycle in a convex fashion. E.g., interpreting i = 1 as college enrollment, we have college attendance early on. 3 Wages grow in a concave fashion. 4 Can generate a hump shaped wage profile by assuming positive depreciation. 5 Investment and wage growth are higher for high ability people. 6 Can generate a rise in wage inequality over the lifecycle without shocks if A differs across people. More on this later. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

11 Implications 1 Shortcoming: No well-defined concept of returns to skill as mentioned before. 2 Why do wages grow over the lifecycle? 1 w s = hs C (Qs ) and w s+1 = hs+1 C ( ) Qs+1 w s+1 w s = hs+1 hs + C (Qs ) C ( Qs+1 ) = Qs + [ C (Qs ) C ( Qs+1 )] So it is partly because (i) the stock of human capital grows, and also (ii) simply because individuals reduce investment. 2 Kuruscu (2006, AER): if α is large the second effect is the main reason for the rise in wages. He estimates α to be about If true, the benefit of training is rather low, less than 1%. 4 Some are skeptical. One reason is that an α that high implies: Q s = A 1 α 1 α [αmb (r, S s)] 1 α 1 extreme sensitivity of investment to ability differences. (Does this make sense?) 2 extreme sensitivity to changes in MB (interest rates, returns, etc.) Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

12 Open Questions 1 If you can say something useful about the value of α you can grab many people s attention. Move beyond the average wage growth over the lifecycle and look at other moments to identify α. 2 One difficulty of human capital model is that OJT is very difficult to measure. Homework: Take the Ben-Porath model. Assume two periods. Introduce endogenous leisure: u (c, l) = log c + log l. Allow for savings between periods 1 and 2. Solve for the value function in period 2 and plug into period 1 problem. Can you solve for (h 1, c 1, l 1 ) using the first order conditions? Why or why not? Modify the problem to make it well-behaved and easily solved through the FOCs. Play with preferences if necessary. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

13 Discussion Missing from Ben-Porath model: 1 No Returns to skill: one cannot easily study what happens to human capital accumulation, etc, when the return to education, etc goes up. We will return to this point. 2 No Jobs, Occupations, etc: A bit too simple in its treatment of jobs, occupations.. none of them exist here. They do in real life. So how to combine the two? 3 There is only one type of skill. And it s fully transferable across jobs. A lot of subsequent work generalizing this. See Acemoglu-Pischke papers in the reading list as well as several papers by Kambourov-Manovski and followers. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

14 Recent Applications 1 Frisch labor supply elasticity: ε f dloght dlogw t λ where λ is marginal utility of wealth, h t is labor hours and w t is hourly wage. Long-running debate with micro estimates ( h = a + e w + resid) finding values of e close to zero. Macro work inferring a high value (>2-3). Imai and Keane (2004): w is not correct measure of return to work. Should include human capital. Finds much higher values of e. 2 Wealth of nations: What determines world income distribution? 1 (Hall and Jones, QJE, 1999): Differences in capital stock or educatin explains little. 8X gap from TFP. 2 Manuelli and Seshadri (AER, 201X): Education is not human capital. Build Ben-Porath model. Finds much smaller gap. 3 We will discuss more applications in later weeks. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

15 Active Research Areas 1 Multi-dimensional skills. 1 A lot of empirical evidence backing this up: e.g.: ASVAB test scores show at least 3 broad class of skills (cognitive, physical, motor/coordination) Importance of soft skills : interpersonal skills, emotional maturity, etc. These are measured through surveys and turn out to be surprisingly informative for wage and employment outcomes. O*NET: classification of occupations/jobs into many skill and ability categories. 2 Raises the question of mismatch: a worker might have high skills on average but poor match to portfolio of requirements at job. 3 Quite a bit of recent work on incorporating it into human capital models (Heckman et al, Lise-Postel-Vinay-2016, Guvenen et al 2016, Papageorgiu and de Melo 2017) 2 Ben-Porath with pecuniary costs: models of (esp. higher) education. Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16

16 Fun Reading Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, / 16