†† PROBLEMS IN LABOR SUPPLY
1. Derive the labor supply equation corresponding to
††† a.† the indirect utility function†††††††††
††††††††††††††††††††††††† ††††††††††††††††††††† ††††††††††††††††††† w = wage
†††††††† u* = kw1+a/1+a† +† v1-b/1-b††††††† ††††††††† v = nonlabor income
††† b.† the utility function
††††††††††††††††††††††††††††††††††††††††††††† † ††††††††††††††††††† C = consumption
†††††††† u = a log (C‑Co) + b log (L-Lo)†††††††††† 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
††††††††† Hm = ao + a1wm + a2wf + a3Y,
††††††††† where Hm = husband's hours, Hf = wife's hours, wm = husband's wage, wf = wife's wage, Yn = nonlabor income, and Y = wmHm + wfHf + yn. In their article they claim the uncompensated (or "gross") wage effect for husbands is a1, the income effect is a3, and the compensated wage effect is a1 ‑ Hma3. Explain why they are incorrect.
††††††††† 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 Tomís and Nicoleís labor supply decisions.
††††††††† b.†††††† A year later, Tom and Nicole make up.† In the aftermath of the favorable publicity, Tomís salary increases by 50 percent.† What will the high salary do to Tom and Nicoleís 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?
††††††††† inlf††††† ††††††††† =1 if in labor force, 1975
††††††††† hours ††††††††† hours worked, 1975
††††††††† kidslt6††††††††† # kids < 6 years
††††††††† kidsge6††††††††† # kids 6-18
††††††††† age††† ††††††††† womanís 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††††††††† husbandís age
††††††††† huseduc††††††††† husbandís years of schooling
††††††††† huswage††††††††† husbandís hourly wage, 1975
††††††††† faminc††††††††† family income, 1975
††††††††† mtr†††† ††††††††† federal marginal tax rate facing women
††††††††† motheduc††††††††† motherís years of schooling
††††††††† fatheduc††††††††† fatherís years of schooling
††††††††† unem ††††††††† unemployment rate in county of resident
††††††††† city†††† ††††††††† =1 if live in SMSA
††††††††† exper ††††††††† actual labor market experience
††††††††† nwifeinc††††††††† (faminc Ė 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?