# 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

Do you have a similar assignment that you would wish our expert writers to handle for you? Place an order with us on https://assignmentsproficient.com/ and expect the best grades and help from qualified writers

Economics and statistics final examination Economics and statistics final examination