Econometrics
Spring 2011
Final Exam
Statement of Academic Honesty:
This exam entirely reflects my own work. I have not given assistance to anyone, nor have I received assistance from anyone. I am not aware that any other students have done so.
Signature: __________________________________________________
Name: __________________________________________________
State whether each of the following assertions is true or false, and give a brief explanation of your answer.
a. Pre-testing is more important in quasi-experimental research designs than it is in experimental research designs.
In this problem, you will match each of the 10 research topics below to the most appropriate method of econometric analysis. There are 10 research topics and 10 econometric techniques. Each answer is used once, and only once, so pick the best option for each topic.
a. OLS with log specification b. OLS with interaction terms c. Two-stage least squares d. Panel regression
e. Probit model f. Poisson regression g. Truncated data model h. Censored data model i. Ordered probit j. Multinomial probit
1. A study on wages and productivity across many different industries in the United States for each of the last 25 years.
2. A study on marital status and asset holdings – the data set records the value of people’s assets if positive, but records $0 for people with negative net assets (i.e. net debtors).
3. A study on how police presence affects crime rates.
4. A study on whether the existence of a union has a different impact on workplace satisfaction for men than for women.
5. A study conducted by McDonalds on what determines the size of soda that customers order – small, medium, large or extra large.
6. A study that estimates the advertising elasticity of demand for the airline industry.
7. A study on the determinants of a child’s IQ – the government has removed children with an IQ below 80 from the data set.
8. A study of the determinants of whether households have an Internet connection in their house.
9. A study on customers’ preferred brand of digital camera among the top three brands – Sony, Canon or Kodak.
a. Let and be any nonzero constants. Prove that Correl
X,Y
Correl X Y
,
.Let Y designate wage. F and M designate female and male respectively. C and N designate college degree, and no college degree respectively. Then E Y F C
| ,
denotes the expected wage for a female college graduate, with other expectations defined similarly. Consider the model:
0 1 2 3 *
Y F C F C u
a. Solve for the parameters of the model
0, 1, 2, 3
in terms of E Y F C
| ,
,
| ,
E Y M C , E Y F N
| ,
and E Y M N
| ,
.ANSWERS: 0 ________________________________
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2
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3
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You run a regression of wages (y) on 25 different factors that have no effect on wages; all the true coefficients are equal to 0. Consider the estimated regression line:
0 1 1 2 2 25 25
ˆ ˆ ˆ ˆ
ˆ
y x x x
a. What is the probability that at least one of the estimated coefficients
ˆ ˆ1, 2, ,ˆ25
willtest as significantly different from zero at the 5% level?
You have data on consumption spending and income for a large number of households. You are interested in estimating the household consumption function – that is, the way in which
consumption spending C depends on income Y.
a. A common assertion is that marginal propensity to consume falls as income rises.1 Write down the specification that you would use to test this hypothesis and state the relevant null and alternative hypotheses explicitly.
b. Suppose that instead of household-level data, you had country-level data on total income (GDP) and total consumption expenditures across many countries. Explain the
endogeneity problem that arises in this case.
1 Recall that the marginal propensity to consume is the increase in consumption spending that results from an
This question refers to the handout that was distributed along with the exam. The research question concerns the determinants of a student’s cumulative GPA at AUS.2
a. Explain the reason for the omitted groups throughout (a few words is sufficient).
b. Referring to model 1 – Confirm that the coefficient on male is significant at the 1% level. Show your calculations and how you came to your result.
c. Referring to model 1 – Comment on the sign and relative magnitude of the enrollment year dummies. Describe the pattern and give a plausible explanation.
d. Referring to model 2 – All else equal, what is the expected difference in GPA between a student from a British-curriculum high school and a UAE-curriculum high school? Which is higher?
e. Referring to model 2 – The coefficient for the need-based tuition reduction dummy is positive and significant. Provide a plausible causal reason and also a plausible
endogenous reason for this association.
f. Referring to model 2 – The coefficient on UAE high-school curriculum is close to zero and not significant. But if we eliminate the TOEFL score dummies from the regression, the coefficient becomes negative and significant. Provide an interpretation.4
3 This dummy is equal to 1 if the student receives a scholarship from the university and equal to 0 otherwise. 4 Note that the UAE curriculum is taught mostly in Arabic, while the British and American high school curricula are
This question uses the dataset smoke.wf1, which consists of a random sample of 807 individuals. A researcher is interested in whether smoking reduces annual income, perhaps through days lost to work due to illness or reduced productivity. The following are the variables used for this problem.
Variable Description
income Annual income in US dollars
cigs Number of cigarettes smoked per day
educ Years of schooling
age Age, in years
cigpric Price of a pack of cigarettes, in cents
restaurn Dummy, =1 if restaurant smoking ban
where the individual lives
The equation of interest is:
2
0 1 2 3 4
ln(income) cigs educ age age u
a. Explain the reverse causation between income and cigs.
b. Estimate the model with TSLS using ln
cigpric
and restarun as instruments for cigs. Enter the estimated coefficients and White standard errors below.Coefficient Estimate Standard Error
c. Interpret the coefficient ˆ1 precisely.
d. Conduct a test for instrument relevance. Explain exactly what you did and how you came to your conclusion.
