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IL. (15pts) You are given the following three estimated models, with all the variables described as in question II Dependent variable: log (wage) educ 0.056** 0.062* 0.049* 0.022) (0.006) (0.022) feduc 0.027 C0.027) 0.021 0.028) married 1.000 0.606 (0.518) (0.466) age 0.032 C0.114) (0.103) (0.116) 0.034 feduc. educ -0.001 (0.002) -0.0003 (0.002) married.age 0.037 0.025 C0.016) (0.014) 0.001 0.001 -0.00000 C0.002) C0.002) C0.002) agesq Constant 5.306**5.218* 5.090*** (1.923) C1.723) C1.932) observations 741 R2 741 0.151 741 0.142 0.170 Note: *p<0.1; *pc0.05; pc.01 a. What is the estimated return to education? Does it depend positively or negatively on father's education? Explain. (2pts) b. Based on the estimated models (1) and (2) and with a 5% significance level, test the hypothesis that father's education has a significant impact on workers' wages. (State clearly your null and alternative hypotheses, the statistics to be used, and your conchusion) (2 pts). c. Provide a possible rationale for the presence of the variable age* in the model estimated above. (lpt) d. Holding everything else constant, what is the estimated effect of getting one year older on the wage of i) a married worker? ii) a non-married worker? (2pts) e. At what value of age does an additional year actually lower the predicted log(wage) for i) a married worker? ii) a non-married worker? (2 pts) f. Calculate the estimated effect of the 35th year of age on the wage of i) a married worker, i) a non- married worker. (2pts). g. From the estimated equation above, provide an appropriate interpretation for each coefficient associated to the variables married, and married.age. (2pts) h. Based on estimated models ( 1) and (3), and with a 5% significance level, test whether the marital status has a statistically significant impact on the worker's earnings (state clearly your mull and alternative hypotheses, the statistics to be used, and your conclusion). (2 pts)

Answer 1

1. The estimated return of years of education is statistically significant and positive with log of wage, as the coefficient  
61
is positive in all the models.

The years of education depends negatively on father's years of education as the coefficient $\beta _{5}$ is negative where coefficient of years of education (
61
) and fathers years of education ($\beta _{2}$) both are positive

2. The Null hypothesis for father's education have any effect is

Но . 32=0

and alternate hypothesis is $H^{_{1}} : \beta _{2} \neq 0$

so null means the fathers education has no significant effect in the model

the Z values for model 1 and model 3 are (.027/0.027) = 1 and (.021/0.028) = .75 respectively

so we are not able to reject the null hypothesis. so father's education has no effect.  

3. The variable age^2 also has no significant effect in the model. parallaly  we are using age and age^2 in the same model. So it is advisable to drop the age^2 from the model

4. For a non married worker:

the final effect in log(wages ) = $\beta _{4} + \beta _{7}$

for a married worker :

the final effect in log(wages) = $\beta _{4} + \beta _{7} + \beta _{3} + \beta _{6}$ (coeff of age + age^2 + married + married*age)

5. continuing from above:

for a non married worker 1 year extra age correspond to ( $\beta _{4} + \beta _{7}$ ) = 0.031% increase in wage (model 1)

for a married worker 1 extra year age corresponds to $\beta _{4} + \beta _{7} + \beta _{3} + \beta _{6}$ = 0.932% decrease in wage (model 1)

6. at the age of 35th,

the married worker has wage (-1 + 35*.017) = 0.297% is more than an unmarried worker (model 1)

7. taking from model 1

marriage is a binary variable. the coeff only impact the wage when the person is married. and the value is statistically significant

the marriage*wage is also applicable when the person is marriage, 0 otherwise

8.Model 3 don't have marriage variable. so the required cann't be determined

for model 1:

the Z score = (-1/.518) = - 1.93

which is statistically significant,

so marriage has significant impact on employee's wage