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value of econometrics

An Economics department at a large university keeps track of its majors'
starting salaries. We address the question of the value of taking
econometrics, based on last year's crop of 50 majors. Let SAL=$ salary,
GPA = grade point average on a 4.0 scale, METRICS=1 if student took
econometrics, METRICS = 0 otherwise, SEX=1 if student is a female,
otherwise =0.

Consider the following regression
SAL = B1 + B2GPA + B3METRICS + B4METRICS * GPA + et

(a) Based on table 1, what is the marginal effect (benefit) of taking
econometrics?

(b) What is the predicted wage difference between a student who took
econometrics and one who did not, given that their GPA =3.0?
Consider another regression

SAL = B1+B2GPA+B3METRICS+B4SEX+B5METRICS*SEX+et

(c) Based on table 2, what is the reference group in this model? What
is the estimated salary of them?

(d) Does the model suggest salary difference among gender? Justify
your answer

(e) Is the value of econometrics the same for men and women? Justify
your answer.

Source | SS df MS Number of obs = 50
-------------+------------------------------ F( 3, 46) = 45.59
Model | 275083851 3 91694616.9 Prob > F = 0.0000
Residual | 92520533 46 2011315.94 R-squared = 0.7483
-------------+------------------------------ Adj R-squared = 0.7319
Total | 367604384 49 7502130.28 Root MSE = 1418.2

------------------------------------------------------------------------------
salary | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gpa | 1918.108 396.7813 4.83 0.000 1119.428 2716.787
metrics | 8440.214 2399.488 3.52 0.001 3610.296 13270.13
metricsgpa | -1197.261 828.1421 -1.45 0.155 -2864.224 469.7027
_cons | 23379.25 1207.748 19.36 0.000 20948.18 25810.32
------------------------------------------------------------------------------

Solution Preview

(a) Based on table 1, what is the marginal effect (benefit) of taking
econometrics?
The coefficient of metrics is 8440.214, and that of interacted term METRICS * GPA is

-1197.261. Then d(Sal) / d (Metrics) = 8440.214 - 1197.261 GPA.
This means that the marginal benefit of taking econometrics is ($8440.214 -1197.261 GPA)

more in annual earning. Obviously, it depends on the student's GPA score.

(b) What is the predicted wage difference between a ...

Solution Summary

What is the marginal effect (benefit) of taking econometrics?

$2.19