Lecture 2: The Human Capital Model - WordPress.com€¦ · models(Heckmanetal,Lise-Postel-Vinay-2016,Guvenenetal2016, PapageorgiuanddeMelo2017) 2 Ben-Porathwithpecuniarycosts: modelsof(esp

Lecture 2: The Human Capital Model

Fatih Guvenen

University of Minnesota

February 7, 2018

Fatih Guvenen (2018) Lecture 2: Ben Porath February 7, 2018 1 / 16

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:

I Why do wages grow over the life cycle?

I Why does labor income varies so much across individuals (inequality)?

I Why has US wage inequality increased so much since the 1970s?

I What is the nature of income risk faced by workers?


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- oroccupation-specific skills? Will discuss this later.)

I No slavery (i.e, no commitment by worker).

I Labor markets are competitive.

I Lack of commitment can be solved by making workers pay for theirown training (Becker).


Ben-Porath (1967) Model

Individuals can borrow and lend at a constant interest rate (denotedby r), which implies that markets are complete. Let δ = 1/ (1 + r) .

Individuals solve

max{it}Tt=1

[T∑t=1

δt−1Rht(1− it)

]s.t

ht+1 = ht + A (ht it)α , with h0 > 0 given

it ∈ [0, 1]

This formulation does not rest on the assumption of risk-neutrality,but instead requires markets to be complete. [Homework: Prove thisstatement.]


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: Ahβs iαs :

1 Estimates of α and β are typically close. (But estimates themselvesseem too high—maybe should be revisited).

2 Present technology gives closed-form solutions.

3 Can also introduce pecuniary costs of investment (many papers do. SeeSeshadri and Manuelli (20


Analyzing the Individual’s ProblemDefine:

C (Qs) ≡ hs is =

(Qs

A

)1/α

.

With this transformation, the problem of an individual can be writtenas

max{Qs}Ss=1

[S∑

s=1

δs−1R × (hs − C (Qs))

]subject to

hs+1 = hs + Qs , with h0 given

Now write it as a Bellman equation:

Vs (hs) = maxQs∈[0,hs ]

[R (hs − C (Qs)) + δVs+1 (hs + Qs)]


Analyzing the Individual’s ProblemAssuming interior solution, the FOC:

RC ′(Qs) = δV ′s+1 (hs + Qs)

Envelope:V ′s (hs) = R + δV ′s+1 (hs + Qs)

Lead by one period:

V ′s+1 (hs+1) = R + δ[R + δV ′s+2 (hs+2)

]..repeatedly substitute for the RHS to get

RC ′(Qs) = δ{R + δR + ...+ δS−s−1R

}(1)

(2)

C ′(Qs)︸︷︷︸Marginal cost

=1r

[1−

(1

1 + r

)S−s]

︸︷︷︸Marginal benefit

(3)


Analyzing the Individual’s ProblemSolve the model:

RHS does not depend on Q.

LHS is proportional to Q1−αα

s . If α > 0.5, this is a concave function.Alternatively convex.

How curvature depends on α :


Implications

The solution again:

Q∗s = A1

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? (is still depends on hs of course).

It would imply for example that somebody who has high initial humancapital will spend less time investing in human capital.. seems a bitunrealistic.

It also implies a convergence in the wage distribution (var(log(w)) ifthe only heterogeneity is in initial human capital.


Key observations

1 Ben-Porath delivers several key insights:

1 Key insight: reward from work 6= wage reward from work = wage +acquired human capital

F 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 attendanceearly on.

3 Wages grow in a concave fashion.

4 Can generate a hump shaped wage profile by assuming positivedepreciation.

5 Investment and wage growth are higher for high ability people.

6 Can generate a rise in wage inequality over the lifecycle without shocksif A differs across people. More on this later.


Implications1 Shortcoming: No well-defined concept of returns to skill as

mentioned before.2 Why do wages grow over the lifecycle?

1 ws = h∗s − C (Q∗s ) and ws+1 = h∗s+1 − C

(Q∗

s+1)

ws+1 − ws = h∗s+1 − h∗s + C (Q∗s )− C

(Q∗

s+1)

= Q∗s +

[C (Q∗

s )− C(Q∗

s+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 reasonfor the rise in wages. He estimates α to be about 0.95.

3 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:

Qs = A1

1−α [αMB (r ,S − s)]α

1−α

1 extreme sensitivity of investment to ability differences. (Does this makesense?)

2 extreme sensitivity to changes in MB (interest rates, returns, etc.)


Open Questions1 If you can say something useful about the value of α you can grab

many people’s attention.I 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 tomeasure.

Homework:I Take the Ben-Porath model. Assume two periods.I Introduce endogenous leisure: u (c , l) = log c + log l . Allow for savings

between periods 1 and 2.I Solve for the value function in period 2 and plug into period 1 problem.

Can you solve for (h1, c1, l1) using the first order conditions? Why orwhy not?

I Modify the problem to make it well-behaved and easily solved throughthe FOCs. Play with preferences if necessary.


Discussion

Missing from Ben-Porath model:

1 No Returns to skill: one cannot easily study what happens to humancapital 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 tocombine the two?

3 There is only one type of skill. And it’s fully transferable across jobs.F A lot of subsequent work generalizing this. See Acemoglu-Pischke

papers in the reading list as well as several papers byKambourov-Manovski and followers.


Recent Applications

1 Frisch labor supply elasticity: εf ≡ d loghtd logwt

|λ where λ is marginal utilityof wealth, ht is labor hours and wt is hourly wage.

I 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).

I 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 educatinexplains 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.


Active Research Areas1 Multi-dimensional skills.

1 A lot of empirical evidence backing this up:

F e.g.: ASVAB test scores show at least 3 broad class of skills (cognitive,physical, motor/coordination)

F Importance of “soft skills”: interpersonal skills, emotional maturity, etc.These are measured through surveys and turn out to be surprisinglyinformative for wage and employment outcomes.

F O*NET: classification of occupations/jobs into many skill and abilitycategories.

2 Raises the question of mismatch: a worker might have high skills onaverage but poor match to portfolio of requirements at job.

3 Quite a bit of recent work on incorporating it into human capitalmodels (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.


Fun Reading


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Lecture 2: The Human Capital Model - WordPress.com€¦ · models(Heckmanetal,Lise-Postel-Vinay-2016,Guvenenetal2016, PapageorgiuanddeMelo2017) 2 Ben-Porathwithpecuniarycosts: modelsof(esp