Given the data on women who worked in the previous year and those who have not, several models have been estimated

 1. The labor supply of married women has been a subject of a great deal of economic research. Given the data on women who worked in the previous year and those who have not, several models have been estimated. The variable indicating whether a woman worked is LFP=Labor Force Participation, which takes the value 1 if a woman worked and 0 if she did not.

(a)   Consider the following supply equation specification:

HOURS = β1+β2ln(wage)+β2educ+β4age+β5kidsl6+β6kids618+β7nwifeinc+µ What sign do you expect each of the coefficients to have, and why?

(b)  The variable nwifeinc=non-wife income is defined as nwifeinc = faminc − wage ∗ hours 

The summary statistics for the variables: wife’s age, number of children less than 6 years old in the household, and the family income for the women who worked (LFP=1) and those who did not work (LFP=0) are provided in the table. Comment on any differences you observe. 

 (c) NWIFEINC and ln(WAGE) variables in part (a) are endogenous. Can the HOURS equation be estimated satisfactory using the

(d)  Table 1 provides the results of the least squares regression on only the women who worked (LFP=1). Did things come out as expected? If not, why?

TABLE 1

Dependent variable: HOURS Included observations: 428                                                                

Dependent variable: LNWAGE

(f)  Is the supply equation in part (a) identified? Name the instrumental variable if any. 

(g)  Two-stage least squares estimation of the supply equation is provided in Table

3. Discuss the sign and significance of the estimated parameters.

TABLE 3

Dependent variable: HOURS Included observations: 428                                                      

 2.      It is common for companies to spend money and time on employee training pro- grams to improve productivity in the workplace. A company is interested in an- alyzing the effect of a training program on employees’ productivity. Data from a random sample of 10,000 workers ages 18 and older were collected and a regression

PRODUCT IV IT Y = Xβ + αT RAINING + µ 

was estimated, where X is a matrix of socio-demographic characteristics, and TRAINING is a dummy variable that is equal to 1 if the person participated in the training program and is equal to zero otherwise. TRAINING can depend on many factors and one of them could be whether a company received a job training grant to help subsidize the cost of the training, therefore

 T RANING = Zγ + θGRANT + . 

Here Z is a matrix of firm related factors and GRANT=1 if company received a training grant and =0 otherwise.

(a)       In estimating the PRODUCTIVITY equation the variable TRAINING can potentially be endogenous. Why using OLS can fail in estimating this regres- sion model? Explain.

(b)       Propose an estimation method that will help resolve this endogeneity problem. Describe the estimation method in detail.

(c)       Is the PRODUCTIVITY equation identified? If so why? Is it exact, under or over-identified?