Professor
Allen

ECG 630

Fall 2001

PROBLEMS IN LABOR SUPPLY

1. Derive the
labor supply equation corresponding to

a.
the indirect utility function

w = wage

u^{*} = kw^{1+a}/1+a + v^{1-b}/1-b v
= nonlabor income

b.
the utility function

C
= consumption

u = a log (C‑C_{o}) + b
log (L-L_{o}) L =
leisure

2. Suppose
you estimated a labor supply function and obtained the following results:

H = 1 + 5w ‑ .125v

Assume the mean values of the
variables are w = 8, H = 40, and v = 8.
Calculate the following:

a. uncompensated
wage elasticity

b. compensated
wage elasticity

c. income
elasticity

3. Ashenfelter
and Heckman (1974) estimated the model

H_{m} = a_{o} + a_{1}w_{m}
+ a_{2}w_{f} + a_{3}Y,

where H_{m} = husband's hours,
H_{f} = wife's hours, w_{m} = husband's wage, w_{f} = wife's
wage, Y_{n} = nonlabor income, and Y = w_{m}H_{m} + w_{f}H_{f}
+ y_{n}. In their article they claim the uncompensated (or
"gross") wage effect for husbands is a_{1}, the income effect
is a_{3}, and the compensated wage effect is a_{1} ‑
H_{m}a_{3}. Explain why they are incorrect.

4. True/False:

a. An
increase in the real wage increases the percentage of the population that
works.

b. An
increase in the income tax affects the labor supply of working women, but not
the labor supply of women who are not in the labor force.

c. Since
the labor force participation rate is more responsive to wages for women, the
substitution effect must be greater for women.

d. If
the participation rates of white married women increased more rapidly over time
than those of black married women, black female wages should have risen
relative to those of whites.

e. Workers
will be absent less often if they are paid higher wages.

5. Tom leaves
Nicole, but in their final settlement Tom has to give her $2 million per year
in child support.

a. Using
a labor supply model based on individual utility maximization, show how the
imposition of child support payments will affect Tom’s and Nicole’s labor
supply decisions.

b. A
year later, Tom and Nicole make up. In
the aftermath of the favorable publicity, Tom’s salary increases by 50
percent. What will the high salary do
to Tom and Nicole’s labor supply, assuming that they are now maximizing a
household utility function?

6. Suppose
that persons were required to work 15 hours per week at an unpaid government
job to be eligible for welfare, food stamps, and Medicaid. Graph the labor-leisure budget set and
compare it to the one that currently applies.
What impact is "workfare" likely to have on the labor force
participation rate (at paid jobs) and hours of work?

7. Consider
three different wage shocks: (a) wages increase in 2002 by 10 percent and then
return to their previous level in 2003; (b) wages are expected to increase in
2003 by 10 percent and then are expected to return to their previous level in
2004; and (c) wages increase in 2002 by 10 percent and this increase is
expected to be permanent. Compare the
impact of each of these wage shocks on the lifetime labor supply profile for a
typical individual who was already working in 2001. Which has the largest impact on 2002 hours? Which has the largest impact on 2010 hours?

8. The following
exercise is adapted from exercises in Berndt, The Practice of Econometrics,
ch. 11. It uses the data set Mroz (click here for ASCII
version, click here for Excel version)

inlf =1 if in labor force, 1975

hours hours worked, 1975

kidslt6 # kids < 6 years

kidsge6 # kids 6-18

age woman’s age in years

educ years of schooling

wage estimated wage from earnings, hours

repwage reported wage at interview in 1976

hushrs hours
worked by husband, 1975

husage husband’s
age

huseduc husband’s years of schooling

huswage husband’s hourly wage, 1975

faminc family
income, 1975

mtr federal marginal tax rate facing women

motheduc mother’s years of schooling

fatheduc father’s years of schooling

unem unemployment rate in county of
resident

city =1 if live in SMSA

exper actual labor market experience

nwifeinc (faminc – wage*hours)/1000

lwage log(wage)

expersq exper^2

a) Compare
the values of kidslt6, kidsge6, age, educ, hushrs, huseduc, huswage, mtr,
exper, and nwifeinc for women who are in the labor force to those for women who
are not in the labor force. Also
compare the values of wage. To obtain
an estimate of wage for women not in the labor force, regress lwage on a
constant, age, educ, city, exper, and expersq and use the coefficients you
obtain to generate a predicted wage.
Create a new variable called lww1 equal to wage for women in the labor
force and equal to the predicted wage for women out of the labor force.

b) Regress
hours on lww1, kidslt6, kidsge6, age, educ, and nwifeinc. Use the entire sample to obtain your results. What estimates do you obtain for the
elasticity of labor supply to wages and nonlabor income? What concerns do you have about these
estimates?

c) Regress
hours on lwage, kidslt6, kidsge6, age, educ, and nwifeinc. Use only those with positive values of hours
to obtain your results. What estimates
do you obtain for the elasticity of labor supply to wages and nonlabor
income? What concerns do you have about
these estimates?

d) Now
estimate a probit model for inlf with the following variables: kidslt6, kidsge6,
age, educ, age squared, educ squared, age*educ, age cubed, educ cubed, (age
squared)*educ, age*(educ squared), motheduc, fatheduc, unem, city, and
nwifeinc. Calculate the inverse Mills
ratio for each observation and call this invr1. Restricting your sample to those in the labor force, regress
lwage on kidslt6, kidsge6, age, educ, age squared, educ squared, age*educ, age
cubed, educ cubed, (age squared)*educ, age*(educ squared), motheduc, fatheduc,
unem, city, and nwifeinc. Then estimate
another lwage model where invr1 as added as a right-hand variable. What difference does controlling for invr1
make for the wage coefficients? Is
sample selectivity an important source of bias in the wage equation?

e) Regress
hours on kidslt6, kidsge6, age, educ, nwifeinc, invr1 and predicted lwage using
the coefficients from the first lwage model you estimated in (d), i.e., the one
without invr1. Run another hours
equation but this time using predicted wage from the model containing
invr1. How much do these results vary
from those in models you estimated in (b) and (c) above where you do not
control for selection bias?