Question

III-(15pts) You are given the following estimated equation: log(wage)- 0.18+0.093edu +0.044exp+0.043 female-0.016edu female-0.010exp female-0.00068 exp (0.0001) 0.014) 0.4160 0.003 Std errors (0.132) (0.009) (0.005) (0.196) n-526 R-square With all the variables described as follows: logiwage)-log of average hourly wage: female is a dummy variable equal to 1 if the observed person is a female, and 0 if male; edu female is an interaction variable equal to education 'female; edu is the number of years of schooling exp is the number of years of experience exp female is an interaction variable equal to experience 'female exp experience experience. a. Is the parameter associated to exp. statistically significant at 5%? (1pt) b. Provide a possible rationale for the presence of the variable exp in estimated equation above (1pt) What is the estimated return to an additional year of experience for a female worker? For d. What is the estimated optimal number of experience years for a female worker? For a male e. Calculate the estimated effect of the St year of experience i) on a female's wage, and i) f. From the estimated equation above, provide an appropriate interpretation for each of the g Is education more valuable for male or for female workers? What about experience? (1 pt) c. a male worker? (2pts) worker? (2pts) on a male's wage. (2pts). parameters associated with the following variables: female, education, and female.edu? (3pts) h. Ifa male and a female have 2 years of experience each, how many years of education would it take for their wages to be the same? (Ipt) In order to test whether gender does significantly affect the wage earned by workers, the following restricted model has been estimated

Answer 1

since lengthy answer for better understanding, i am typing it instead of writing

Solution:

(a).is parameter associated to exp2 statistically significant at 5%:

H0: The coefficient of exp² is 0.

Ha: The coefficient of exp² is not 0.

The estimated coefficient of exp² is -0.00068

The standard error of estimated coefficient of exp² is 0.0001

t =  estimated coefficient / standard error = -0.00068 / 0.0001 = -6.8

Degree of freedom = n - k - 1 where k is number of independent variables in the model.

= 526 - 7 = 519

Critical value of t at 5% significance level and df = 519 is 1.96

As, observed absolute t value (6.8) is greater than the critical value, we reject the null hypothesis and conclude that there is significant evidence that the coefficient of exp² is not 0 and the variable exp² is statistically significant in the model.

(b). possible rationale for the presence of the variable exp2:

A possible reason for the presence of variable exp² can be that the relation between log(wage) and experience is not linear and inclusion of the squared experience term in the model captures more variation of the log(wage) variable.

(c) estimated return to an additional year of experience for female worker:

The estimated model is,

log(wage) = 0.18 + 0.093 edu + 0.044 exp + 0.043 female - 0.016 educ*female - 0.010 exp*female - 0.00068 exp²

For female worker, female = 1

log(wage) = 0.18 + 0.093 edu + 0.044 exp + 0.043 * 1 - 0.016 educ*1 - 0.010 exp*1 - 0.00068 exp²

log(wage) = 0.223 + 0.077 edu + 0.034 exp - 0.00068 exp²

When exp = exp + 1

log(wage) for additional year of experience = 0.223 + 0.077 edu + 0.034 (exp + 1) - 0.00068 (exp + 1)²

= 0.223 + 0.077 edu + 0.034exp + 0.034 - 0.00068 exp² - 0.00068 - 2 * 0.00068 exp

= (0.223 + 0.077 edu + 0.034 exp - 0.00068 exp² ) + 0.034 - 0.00068 - 2 * 0.00068 exp

= log(wage) for previous year + 0.03332 - 0.00136 exp

log(wage) for additional year of experience - log(wage) for previous year = 0.03332 - 0.00136 exp

So, for female, the estimated return for additional year of experience is 0.03332 - 0.00136 exp.

For male worker, female = 0

log(wage) = 0.18 + 0.093 edu + 0.044 exp + 0.043 * 0 - 0.016 educ*0 - 0.010 exp *0 - 0.00068 exp²

log(wage) = 0.18 + 0.093 edu + 0.044 exp - 0.00068 exp²

When exp = exp + 1

log(wage) for additional year of experience = 0.18 + 0.093 edu + 0.044 (exp + 1) - 0.00068 (exp + 1)²

= 0.18 + 0.093 edu + 0.044 exp + 0.044 - 0.00068 exp² - 0.00068 - 2 * 0.00068 exp

= (0.18 + 0.093 edu + 0.044 exp - 0.00068 exp² ) + 0.044 - 0.00068 - 2 * 0.00068 exp

= log(wage) for previous year + 0.04332 - 0.00136 exp

log(wage) for additional year of experience - log(wage) for previous year = 0.04332 - 0.00136 exp

So, for male, the estimated return for additional year of experience is 0.04332 - 0.00136 exp.

(d) estimated optimal number of experience years for a female worker:

For female worker,

log(wage) = 0.223 + 0.077 edu + 0.034 exp - 0.00068 exp²

Differentiating wrt exp, we get

d/d(exp) log(wage) = 0.034 - 2 * 0.00068 exp = 0

=> exp = 0.034 / (2 * 0.00068) = 25

Differentiating again, wrt exp, we get

d/d(exp) log(wage) = - 2 * 0.00068 which is less than 0.

Hence log(wage) is maximum at exp = 25.

So, the optimal number of experience years for a female worker is 25.

For male worker,

log(wage) = 0.18 + 0.093 edu + 0.044 exp - 0.00068 exp²

Differentiating wrt exp, we get

d/d(exp) log(wage) = 0.044 - 2 * 0.00068 exp = 0

=> exp = 0.044 / (2 * 0.00068) = 32.35

Differentiating again, wrt exp, we get

d/d(exp) log(wage) = - 2 * 0.00068 which is less than 0.

Hence log(wage) is maximum at exp = 32.35.

So, the optimal number of experience years for a male worker is 32.35.

(e) estimated effect of the 5th year of experience on male and female:

i) effect on female's wages=0.044*5+ -0.01*5-0.00068*25-0.044*4+0.01*4+0.00068*16=-0.02788

ii) effect on male's wages= 0.044*5-0.00068*25-0.044*4+0.00068*16=-0.02972

(f) appropriate interpretation :

edu- higher years of schooling leads to higher average hourly wage.

female- female workers have higher average hourly wage compared to males

edu.female-females with higher education have a lower average hourly wage compared to males with the same level of education

(g) education more valuable for females or males:

Both education and experience are more valuable for male workers.

(h) no of years of education male and female take for their wages to be same:

0.18+0.093*edu+0.088+0.043-0.016*edu-0.02-0.00272=0.18+0.093*edu+0.088-0.00272

edu=1.4375

(i) significant or not at 5% :

Null Hypothesis: $eta=0$

Alternate Hypothesis:

0

t-value = β/S.E 0.043/0.196 0.219

Since observed t statistic is less than the critical value at 5% i.e t=1.645,

we fail to reject the null hypothesis.

Hence,

gender is not a statistically significant factor in explaining workers' wages.