25) Extension of Mincer Model

An Extension of the Mincer (1958) Model
Allow for tuition, taxes, length of working life that varies by schooling.
Maintain assumption of exogenous post-school earnings profile
(as in the accounting identity model).
w(s, x) is wage income at experience level x for schooling level s
T (s), the last age of earnings
v, private tuition and non-pecuniary costs of schooling
τ, a proportional income tax rate
r, the before-tax interest rate.
Individuals choose s to maximize the present discounted value of
lifetime earnings
[T
Z(s)−s]
Z s
(1 − τ)e −(1−τ)r(x+s) w(s, x)dx − ve −(1−τ)rz dz. (1)
0
0
1

The first order condition for a maximum yields
[T 0 (s) − 1]e −(1−τ)r(T (s)−s) w(s, T (s) − s) − (1 − τ)r
T(s)−s
Z
· e −(1−τ)rx w(s, x)dx (2)
+
0
T (s)−s
Z
0
e
−(1−τ)rx∂w(s, x)
∂s
dx − v/(1 − τ) =0.
Defining ˜r =(1− τ)r (the after-tax interest rate) and re-arranging
terms yields,
[T 0 (s) − 1]e −˜r(T(s)−s) w(s, T (s) − s)
T (s)−s
R
0
e −˜rx w(s, x)dx
(Term 1)
2

+
T (s)−s
R
0
h i
e −˜rx ∂logw(s,x)
∂s
w(s, x)dx
T (s)−s
R
0
e −˜rx w(s, x)dx
(Term 2)
−
T(s)−s
R
0
v/(1 − τ)
e −˜rx w(s, x)dx
(Term 3)
=˜r. (3)
• Term 1 represents a life-earnings effect – the change in the present
value of earnings due to a change in working-life caused by additional
schooling as a fraction of the present value of earnings measured
at age s.
• Term 2 is the weighted effect of schooling on log earnings by age
• Term 3 is the cost of tuition expressed as a fraction of lifetime income
measured at age s.
• The special case in the Mincer model assumes v =0and T 0 (s) =1,
3

which yields
Z
˜r
T (s)−s
0
e −˜rx w(s, x)dx =
Z
T (s)−s
0
e
−˜rx∂w(s, x)
dx
∂s
• also assumes multiplicative separability between the schooling and
experience components of earnings, so w(s, x) =µ(s)ϕ(x) (i.e. parallel
in schooling). In this special case,
˜r = µ0 (s)
µ(s) . (4)
If wage growth is log linear in schooling, so that µ(s) =exp(ρ s s)
and the above assumptions hold, then the coefficient on schooling in
a Mincer equation (ρ s ) estimates the rate of return to schooling, which
should equal the after-tax interest rate.
4