Econometrics final project using Stata.

1. Mia Attruia
Econometrics
STATA Project
1. The model below is used to test the rationality of assessments of
housing prices. Specifically, consider the simple regression model price =
β0 + β1assess + u, where price is the house price in thousands of dollars,
and assess is the assessed value in thousands of dollars. The assessment is
rational if β1 = 1 and β0 = 0.
(i) After estimating the model by OLS, we obtain: n = 85, SSR =
159, 147.71, R
2
= 0.8164. Test H0 : β1 = 1 against a two-
sided alternative. Perform the test at the 10% significance
level. What do you conclude?
(ii) Now,testH0 :β2 =β3 =β4 =β5 =0(atthe10%level)inthemodel
price = β0 + β1assess + β2lotsize + β3sqrft + β4bdrms +
β5colonial + u, where colonial is a dummy equal to one if the
house is in the colonial style. The SSR from estimating this
model using the same 85 houses is 147,381.38.
Answer
1. (i) The t statistic for H0: b1 = 1 is (0.97 – 1)/0.051 » - 0.588, and the p-value is
0.2776*2 = 0.5552, which is much larger than 0.1. Therefore, we fail to reject b1
= 1 at the 10% significance level.
(ii) We use the SSR form of the F statistic. We are testing q = 4 restrictions and the df
in the unrestricted model is 85 – 5 – 1 = 79. We are given SSRr = 216,264.24 and
SSRur = 164,857.03. Therefore,
F =
(159,147.71-147,381.38)/2
»1.58
147,381.38 / 79
From Table G.3a, the 10% critical value with 4 numerator and 90 denominator
degrees of freedom is 2.01. Because the test statistic is less than the critical value,
we fail to reject H0.

2. Mia Attruia
Econometrics
STATA Project
2. An equation explaining chief executive officer salary is ︎ where roe is
return on equity (in percentage form), and finance, consprod, and
utility are dummy variables indicating the financial, consumer
products, and utilities industries. The omitted industry is
transportation.
price = −11.66 + 0.97assess (16.6) (0.051)
log(salary) = 6.84 + 0.006roe + 0.138finance + 0.179consprod −
0.392utility (0.11) (0.005) (0.102) (0.097) (0.113)
n = 209, R
2
= 0.153,
(i) By what percentage is salary predicted to increase if roe increases by
10 points? Does roe have a practically large effect on salary?
(ii) Interpret the coefficient on consprod using the approximation (be
specific).
(iii) Use the formula that we discussed in class to obtain the exact
estimated effect of consprod. Compare it with the answer obtained
in part (ii).
(iv) Is the difference in salaries between the consumer products and
transportation industries statistically significant at the 5% level?
Explain.
(v) What is the approximate percentage difference in estimated salary
between the utilities and finance industries? Explain.
Answer
2. (i) A 10 point ceteris paribus increase in roe is predicted to increase salary by
about 6%, which is a reasonably sizable effect.
(ii) Holding other things fixed, the executive officer salary is about 17.9% higher in

3. Mia Attruia
Econometrics
STATA Project
the consumer products industry than in transportation industry.
(iii) Using the formula, the exact estimated effect is [exp(0.179)-1]*100 = 19.6%,
which is somewhat higher than in part (ii).
(iv) The t statistic is 0.179/0.097 » 1.84, p-value = 0.067, which is not statistically
insignificant at the 5% level.
(v) The difference is – 0.392 - 0.138 = - 0.53. That is, the salary is estimated to be
about 53% lower in the utilities than in the finance industry.

4. Mia Attruia
Econometrics
STATA Project
3. Use the data in WAGE2 for this exercise.
(i) Estimate the model log(wage) = β0 + β1educ + β2exper + β3married +
β4black + u and report the results in a usual equation form (similar to how
we do it in class). Interpret the coefficient on married using the
approximation (be specific).
(ii) Holding other factors fixed, what is the approximate difference in
monthly earnings between blacks and nonblacks? Is this difference
statistically significant? Justify your answer.
(iii) Create an interaction term, marrblack = married ∗ black. Add this
variable in the model and estimate the extended model (it is not necessary
to report the estimated equation). What is the estimated wage differential
between married blacks and married nonblacks? Explain.
Answer
3. (i) The estimated equation is
log(wage) = 5.46 + 0.0719 educ + 0.018 exper + 0.195 married – 0.211 black (0.12)
(0.006) (0.003) (0.041) (0.038)
n = 935, R
2
= 0.1812.
The coefficient on married implies that, holding other factors fixed, married men earn
about 19.5% more than nonmarried men.
(ii) The coefficient on black implies that, holding other factors fixed, black men earn
about 21.1% less than nonblack men. The p-value is 0.000, and so it is very statistically
significant.
(iii) The estimated monthly earnings for the two groups are: ˆˆˆˆˆˆ
Marriedblacks: waˆge=b0 +b1educ+b2 exper+b3 +b4 +b5 ˆˆˆˆ
Marriednonblacks: waˆge=b0 +b1educ+b2 exper+b3 ˆˆ

5. Mia Attruia
Econometrics
STATA Project
So, the difference is b4 + b5 » -0.242 + 0.036 = -0.206 . That is, married blacks are
predicted to earn about 20.6% less than married nonblacks.