Human Capital: Theory

Lent Term Lecture 2 Dr. Radha Iyengar

What is Human Capital?

• Part of original conception of inputs in production. Adam Smith said that there were 4 inputs in which we might invest: 1. Machines or mechanical inputs 2. Building/infrastructure 3. land 4. human capital

Education and “General” Human Capital We’re going to study first education (schooling including college/graduate education) This is important because it is: • Expandable and maybe doesn’t depreciate (like physical capital) • Transportable and shareable (not true with “specific capital”)

What are we going to study?

• Theory – Static Model (Card) – Dynamic Model (Heckman) The goal of theory is to motivate the large body of empirical work • Empirics – Some talk of methods (identification, diff-in diff, IV) – Reconciling different estimates – Economics of Education (briefly!)

A Static Model of Human Capital Acquisition

(for details see: David Card, “Causal Effect of Education on Earnings”

Handbook of Labor Economics)

A Static Model of Education and Earnings • Because of its tractability, Card uses a static model that abstracts away from the relationship between completed schooling and earnings over the lifecycle. (we’ll do a dynamic model next). • Two assumptions: – that most people finish schooling and only then enter the labor force (smooth transition).

– the effect of schooling independent of experience (Separability above)

The basics

• Simple Linear regression first introduced by Mincer • Takes the general form of linearity in Schooling, quadratic in experience.

log(

y

) 

a



bS



cX



dX

2 

e

(1) Assumptions: 1. separability of experience and education. 2. log-earnings are linear in education. – correct measure of schooling is years of education – each year of schooling is the same. (more on this later)

Wages or earnings?

• Earnings conflates hours and wages • Card reports that about two-thirds of the returns to education are due to the effect of education on earnings —the rest attibutable to the effects on hours/week and week/year.

• The specification in (1) explains about 20 30 percent of the variation in earnings data.

Why use Semi-Log Specification?

• log earnings are approximately normally distributed.

• Heckman and Polachek show that the semi-log form is the best in the the Box Cox class of transformations. (we can talk about this more later in the empirical part)

Defining some Terms

• Let our utility function U(S, y) = log(y) – h(s) where y is earnings, S is years of schooling, and h(s) is an increasing, convex function. Then, define our discounted present value (DPV) function: 

y

(

S

) exp(

rt

)

dt



y

(

S

) exp( 

rs

) /

r

Simple relationship between returns and costs • So that we have h(S) = rS • more generally we could have a convex h(.) function if the marginal cost of each year of schooling increases faster than the foregone earnings for that year —maybe because of credit constraints)

Results

Optimal schooling is implicitly defined by

h

' (

S

) 

y

'

y

( (

S S

) ) (2) That is there are two sources of heterogeneity: 1. Differences in costs (represented by h(S)) 2. Difference in marginal returns (represented by y’(S)/y(S))

Optimal Schooling

• a simple specification of these two components

y

' (

S

)

h

' (

S

)

y

 (

r i S

)  

k

2

b i S



k

1

S

(3a) (3b)

(define E(b) = b and E(r)= r and k 1 , k 2 > 0)

• This gives us the optimal schooling expression:

S i

*  (

b i



r i

) /(

k

1 

k

2 ) (4)