Question

Consider the following two estimated models (1) and (2), with all the variables already described below

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Dependent variable:

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log(wage)

   (1)    (2)

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educ    0.057*** 0.061***

   (0.006) (0.006)

tenure    0.018** 0.023***

(0.009) (0.009)

black    0.070 (0.276)

tenuresq -0.0003 -0.0004

   (0.0005) (0.001)

educ:black -0.031

(0.021)

tenure:black 0.018**

(0.008)

Constant 5.924*** 5.829***

   (0.088) (0.083)

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Observations    935 935

R2 0.170 0.137

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Note: *p<0.1; **p<0.05; ***p<0.01

a. From model (1), what is the estimated return to education for: i) black workers; ii) non-black workers?

b. Based on the estimated model (1) and with a 5% significance level, how significant is the impact of the variable tenure 2 on workers’ wages. (State clearly your null and alternative hypotheses, the statistics to be used, and your conclusion).

c. Provide a possible rationale for the presence of the variable tenure 2 in the models estimated above.

d. Holding everything else constant, what is the estimated effect of an additional tenure year on the wage of: i) a black worker? ii) a non-black worker?

e. From model (1), at what estimated number of tenure years does an additional year actually lower the predicted log(wage) for: i) a black worker? ii) a non-black worker?

f. From model (1), calculate the estimated effect of the 25th tenure year on the wage of: i) a black worker; ii) a non-black worker.

g. From the estimated equation (1), provide an appropriate interpretation for each of the coefficients associated to the variables black, educ, and educ*black.

h. What is the estimated percentage wage difference between black and non-black workers?

i. Based on estimated models (1) and (2), and with a 5% significance level, test whether being black has a statistically significant impact on worker’s earnings (state clearly your null and alternative hypotheses, the statistics to be used, and your conclusion).

Answer 1

a. i). Coefficient of educ = 0.057 which means for 100% unit increase in Education, there will be 5.7% increase in wages.

ii). coefficient of educ:black = -0.031 which means for 100% unit increase in Education, there will be 3.1% decrease in wages for black.

b). Ho: The tenure2 is not significant in the model,

H1: The tenure2 is not significant in the model

or

Test statistics : where 1,0 = 0.

Since, for tenure2 the absense of * shows it is not significant at 10%, 5% or 1%.

Hence, variable is not significant.

c). For both the models (1) and (2),

For tenure2 the absense of * shows it is not significant at 10%, 5% or 1%.

Hence, variable is not significant.

d).

i). Coefficient of tenure = 0.018 which means for 100% unit increase in Education, there will be 1.8% increase in wages.

ii). coefficient of educ:black = 0.018 which means for 100% unit increase in Education, there will be 1.8% increase in wages for black.

Same contribution

e). 100 years will actually bring a notifiable change.

f).

i). Coefficient of tenure = 0.018 which means for 100% unit increase in Education, there will be 1.8% increase in wages and 25*0.018 = 0.45 units of difference in wage.

ii). coefficient of educ:black = 0.018 which means for 100% unit increase in Education, there will be 1.8% increase in wages for black and 25*0.018 = 0.45 units of difference in wage.

Same contribution

g).

i). Coefficient of educ = 0.057 which means for 100% unit increase in Education, there will be 5.7% increase in wages.

ii). Coefficient of educ = 0.070 which means for 100% unit increase in Education, there will be 7% increase in wages.

iii). coefficient of educ:black = -0.031 which means for 100% unit increase in Education, there will be 3.1% decrease in wages for black.