Compare the adjusted R2 and the coefficient on x1 with those you obtained in part (a).
4. (22 pts) Suppose that you wish to examine the impact of education, gender, and experience on the income of individuals by estimating the following specification.
ln income= b + b educ + b female + b exper + b exper2 + u (1)
where the dependent variable lnincome is the natural log of individuals’ income; educ is the years of education; female is a binary variable that indicates whether an individual is a female (i.e. female=1 if female individual, zero otherwise); and exper is the years of the labor market experience.
The results from estimating this equation are given here.
gen exper_sq=exper^2
reg lnincome female educ exper exper_sq
Source | SS df MS Number of obs = 6540
Model | 872.165992 4 218.041498 Prob > F = 0.0000
Residual | 3601.10591 6535 .551049106 R-squared = 0.1950
Adj R-squared =0.1945
Total | 4473.2719 6539 .68409113 Root MSE = .74233
lnincome | Coef. Std. Err. t P>|t| [95% Conf. Interval]
|
a. Interpret the coefficient on educ variable. Is educ variable statistically significant at 0.01 significance level? Specify appropriate hypothesis, show essential components of the test, and interpret your result.
b. Is the relationship between lnincome and exper variables nonlinear? Explain.
c. Draw a graph that shows the relationship between lnincome and exper variables.
d.At what value of exper does additional experience actually decrease/increase the predicted lnincome?
e.Interpret the coefficient on female variable.
f. Calculate and interpret the coefficient of determination. Be specific by using the numerical value.
g. Are the independent variables jointly significant at .01 significance level? Specify appropriate hypothesis, show essential components of the test, and interpret your result.
h. Now, suppose that you wish to estimate the following specification.
ln income= b + b educ + b female + b exper + b exper2 + b (educ * female ) + u (2)
The results from estimating this equation are the following. gen femeduc= female*educ
reg lnincome female educ femeduc exper exper_sq
Source | SS df MS Number of obs = 6540
lnincome | Coef. Std. Err. t P>|t| [95% Conf. Interval]
|
i. Interpret the coefficients on variables female, educ, and femeduc.
j. Explain the difference between model (1) and model (2). Explain why one needs to estimate the second model.
k. Test the hypothesis that the second model is more/less appropriate than the first model using the “Chow Test” or “the test of exclusion restrictions.”
l. Highlight both the economic and statistical significance of the coefficient on variable femeduc. Carefully discuss the implications of your results.
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