Economics and statistics final examination

Economics and statistics final examination

Exam: Economics and statistics final examination
1. (40 points, 10 each) Height and gender. You have obtained measurements of height in inches
(HEIGHT) of 29 female students and 81 male students at your university. A regression of the height
on a constant and a dummy variable (FEMALE), which takes the value of one for females and is
zero otherwise, yields the following result:
HEIGHT =71 \ − 4.84 × FEMALE, R2 = 0.40, SER = 2.0
(0.3)(0.57)
where the numbers below the coefficients represent standard errors.
(a) (10 points) What is the interpretation of the intercept? What is the interpretation of the slope?
What is the predicted height for a female?
Answer:
(b) (10 points) At a 1% level, test the hypothesis that the height difference between females and
males is zero, against the alternative that females are shorter than males.
Answer:
1
Economics 122A Spring 2014
(c) (10 points) One of your classmates tells you that your regression is wrong because you must
also include a MALE dummy variable (which equals one if the individual is a male and is zero
otherwise). That is, he suggests you use the following regression model:
HEIGHT = β0 + β1FEMALE + β2MALE + u
What do you think about this suggestion? Would you be able to run this regression? If not,
why not?
Answer:
(d) (10 points) If the regression model is
HEIGHT = β1FEMALE + β2MALE + u,
would you be able to obtain βˆ
1 and βˆ
2? If you can (and using the information above), please
write down the values they will take.
Answer:
2. (10 points) A research paper reports, “…in a simple linear regression with 350 observations, the
estimated slope coefficient βˆ = 1.6 is not statistically different from 1.5 at a 5% level, since its Fstatistic (Yes… that is an F as in Frank) is 0.25.” Suppose you want to do a t-test for the null
hypothesis that the true slope coefficient is equal to 1.2 against a two-sided alternative. Obtain the
p-value for this test. Do you reject the null at a 5% level? What about at a 1% level?
Answer:
2
Economics 122A Spring 2014
3. (15 points) Wages and training. To test the effectiveness of the job training program on the
subsequent wages of workers, we specify the model
wage = β0 + β1train + β2educ + β3exper + u,
where train is a dummy variable that equals one if a worker participated in the program (and zero
otherwise).
Think of the error term u as containing unobserved worker ability. If less able workers have a greater
chance of being selected for the program, and you use an OLS analysis, what is the type of bias in
the OLS estimator of β1? Obtain a formal expression for the bias. Is the estimator for β1 upward or
downward biased?
Answer:
3
Economics 122A Spring 2014
4. (40 points) Wages and education once again. To test the effect of education on wages of workers,
we specify the model
wage = β0 + β1female + β2north + β3educ + β4exper + e,
where wage is the hourly wage in U.S. dollars, educ denotes the years of formal education, exper
denotes the years of work experience, and female and north are dummy variables. female equals 1
for females and is zero for males, while north equals 1 if the worker is from the North of the country
and zero if the worker is from the South. You obtain the following regression results:
Variable Estimated coefficient Robust standard error
Constant 0.28 0.10
female -1.2 0.6
north -0.9 0.3
educ 0.7 0.2
exper 0.1 0.04
(a) (10 points) Determine which of the coefficient estimates are (individually) significantly different
from zero at a 1% level.
Answer:
(b) (10 points) Obtain the p-value for the test H0 : β4 = 0.04 against the alternative H1 : β4 > 0.04,
where β4 is the (true) coefficient on exper. Can you reject the null at a 5% level? How about at
a 10% level?
Answer:
4
Economics 122A Spring 2014
(c) (15 points) An economist believes that the effect of an extra year of education on an individual’s
wage is equivalent to 5 times the effect of an extra year of experience plus 15 cents. How would
you modify the regression to test this hypothesis with a t-test against a two sided alternative?
Answer:
(d) (5 extra points!) Test, at a 1% level, the null hypothesis that all coefficients except the intercept
term are zero. The F-statistic for this test is 5.5. Do not forget to write the null hypothesis.
Answer

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