In this exercise, we examine the hours of market work by married women as a function of their education and number of children. Use data file cps5mw_small for this exercise. The data file cps5mw contains more observations.

a. Estimate the linear regression model

Interpret the coefficient of NCHILD. Estimate the expected hours worked by a married woman whose wage is \(\$ 20\) per hour, who has 16 years of education, and who has no children. Do the same calculation for a woman with one child, two children, and three children. How much does the expected number of hours change with each additional child?

b. Define the indicator variables POSTGRAD \(=1\) if \(E D U C>16,0\) otherwise; \(C O L L E G E=1\) if \(E D U C=16,0\) otherwise; and SOMECOLLEGE if \(12

c. Define indicator variables \(O N E K I D=1\) if \(N C H I L D=1,0\) otherwise; \(T W O K I D S=1\) if \(N C H I L D=2,0\) otherwise; and MOREKIDS \(=1\) if \(N C H I L D>2,0\) otherwise. Estimate the HRSWORK equation (XR7.16.1) but replace NCHILD by these three indicator variables. Interpret the estimated coefficients of the three indicator variables. Estimate the expected hours worked by a married woman with 16 years of education, whose wage is \(\$ 20\) per hour with no children, one child, two children, and more than two children. Compare and contrast these estimates to those in (a).

d. Estimate the model (XR7.16.1) replacing \(E D U C\) with the three indicator variables in (b) and replacing NCHILD with the three indicator variables in (c). Compare and contrast this model to the models in (a)-(c).

e. Define the indicator variable \(E D U C 12=1\) if \(E D U C=12,0\) otherwise. Define indicator variables EDUC12, EDUC13, EDUC14, EDUC16 similarly. In this sample, there are no women with 15 years of education. Define \(E D U C 18=1\) if \(E D U C>16,0\) otherwise. Estimate the HRSWORK equation (XR7.16.1) replacing NCHILD by the three indicator variables and \(E D U C\) by the five new indicator variables. Have any essential conclusions changed by using this specification?

f. Which of the specifications in (a)- (e) has the highest \(R^{2}\) ? The highest adjusted- \(R^{2}\), the smallest SCHWARZ criterion (SC or BIC) value? Which model do you prefer taking into account economic, econometric, and fit aspects?

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HRSWORK, +WAGE + B3EDUC + BNCHILD + e (XR7.16.1)