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# value of econometrics

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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

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

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
------------------------------------------------------------------------------

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https://brainmass.com/economics/econometric-models/value-of-econometrics-61529

#### 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

## Statistics for Econometrics Course

I. Jane Smith is a student in the MBA 751 Econometrics course and she received an 83.6% on her final exam grade. The mean of exam scores is expected to be a 75% with a standard deviation of 8.5%. Compute a Z-score for Jane.

II. John Doe is looking at an investment in Acme, Inc. bond offering. Acme, Inc.'s bonds have an annual return of 17.2% (i.e., mean gain of 17.2%) with a standard deviation of 21.5%. A return of 0% means the value of the bond doesn't change, a negative return means that the bond loses money, and a positive return means that the bond gains money. What percent of years does this bond lose money? (NOTE: This is similar to Ex. 3.8 from Diez.)

III. Mount Saint Mary's College has conducted a survey of 144 students on the price of textbooks purchased for ACCT201. Prof. Susan Johns wants to determine if her selection of a textbook for next semester has a reasonable cost based on the previous costs for books. The sample mean for the costs of books from the survey was \$123.45. The sample standard deviation was \$48.24.

i. Calculate the Expected Standard Error.

ii. Construct a 95% Confidence Interval for the sample of book costs. (NOTE: Remember that for a 95% confidence interval the Z-score is 1.96.)

iii. Prof. Johns has developed a hypothesis test to determine the book she has selected with a price of \$130.95 is reasonable.

1. H0 is that the book selection is not reasonable because is fall outside of the confidence interval (found in part ii.)
2. Ha is that the book selection is reasonable because is fall within the confidence interval (found in part ii.)

Why hypothesis is correct? Why?

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