ECMT2150 INTERMEDIATE ECONOMETRICS
Week 5 Tutorial – Asymptotics, Dummy Variables, LPM
1. Wooldridge Problem 5.3
The data SMOKE contains information on smoking behavior and other variables for a
random sample of single adults from the United States. The variable cigs is the (average)
number of cigarettes smoked per day. Do you think cigs has a normal distribution in the U.S.
adult population? Explain.
2. Wooldridge Computer Exercise 5.C1
Use the data in WAGE1.dta for this exercise:
a) Estimate the equation
= 0 + 1 + 2 + 3 +
Save the residuals and plot a histogram.
b) Repeat part (a), but with log(wage) as the dependent variable.
c) Would you say that Assumption MLR.6 is closer to being satisfied for the level-level
model of the log-level model?
3. Wooldridge Problem 5.2
Suppose that the model
= 0 + 1 + 2 +
Satisfies the first four GM assumptions, where pctstck is the percentage of a worker’s
pension/superannuation invested in the stock market, funds is the number of mutual funds
that the worker can choose from, and risktol is some measure of risk tolerance (larger risktol
means that a person has a higher tolerance for risk). If funds and risktol are positively
correlated, what is the inconsistency in 1�, the slope coefficient in the simple regression of
pctstck on funds?
4. Wooldridge Problem 3.12
The following equation represents the effects of tax revenue mix on subsequent
employment growth for the population of counties in the United States:
ℎ = 0 + 1ℎ + 2ℎ + 3ℎ + ℎ ,
where growth is the percentage change in employment from 1980 to 1990, ℎ is the
share of property taxes in total tax revenue, ℎ is the share of income tax revenues,
and ℎ is the share of sales tax revenues. All of these variables are measured in 1980.
The omitted share, ℎ, includes fees and miscellaneous taxes. By definition the four
shares add up to one. Other factors would include expenditures on education,
infrastructure, and so on (all measured in 1980).
a) Why must we omit one of the tax share variables from the equation?
b) Give a careful interpretation of 1.
5. Wooldridge Question 7.8
Suppose you collect data from a survey on wages, education, experience and gender. In
addition, you ask for information about marijuana usage. The original question is: ‘On how
many separate occasions last month did you smoke marijuana?’
a) Write an equation that would allow you to estimate the effects of marijuana usage on
wage, while controlling for other factors. You should be able to make statements such as:
‘smoking marijuana five more times per month is estimated to change wage by X%’.
b) Write a model that would allow you to test whether drug usage has different effects on
wages for men and women. How would you test that there are no differences in the
effects of drug usage for men and women?
c) Suppose you think it is better to measure marijuana usage by putting people into one of
four categories: non-user, light user (1 to 5 times per month), moderate user (6 to 10
times per month) and heavy user (more than 10 times per month). Now. Write a model
that allows you to estimate the effects of marijuana usage on the wage.
d) Using the model in (c), explain in detail how to test the null hypothesis that marijuana
usage has no effect on wage. Be very specific and include a careful listing of degrees of
freedom.
e) What are some potential problems with drawing causal inference using the survey data
that you collected?
6. Wooldridge Question 7.4
An equation explaining chief executive officer salary is log()� = 4.59 + 0.257 log() + 0.11 + 0.158 (0.30) (0.032) (0.004) (0.089)
+ 0.181 − 0.283 (0.085) (0.099)
= 209,2 = 0.357
The data used are in CEOSAL1.RAW, where finance, consprod, and utility are binary
variables indicating the financial, consumer products and utilities industries. The
omitted industry is transportation.
a) Compute the approximate percentage difference in estimated salary between the utility
and transportation industries, holding sales and roe fixed. Is the difference statistically
significant at the 1% level?
b) Use Equation (7.10) to obtain the exact percentage difference in estimated salary
between the utility and transportation industries and compare this with the answer
obtained in part i.
c) What is the approximate percentage difference in estimated salary between the
consumer products and finance industries? Write an equation that would allow you to
test whether the difference is statistically significant.
7. Wooldridge Computer Exercise 7.C13
Use the data in APPLE to answer this question.
(i) Define a binary variable as = 1 > 0 and = 0 = 0.
In other words, indicates whether, at the prices given, a family would buy
any ecologically friendly apples. What fraction of families claim they would buy eco-
labeled apples?
(ii) Estimate the linear probability model:
= 0 + 1 + 2 + 3 + 4ℎℎ + 5+ 6 +
and report the results in the usual form. Carefully interpret the coefficients on the
price variables, and .
(iii) Are the non-price variables jointly significant in the LPM? (Use the usual F statistic, even
though it is not valid when there is heteroskedasticity. – we will come back to this
issue in Week 9.) Which explanatory variable other than the price variables seems to
have the most important effect on the decision to buy eco-labeled apples? Does this
make sense to you?
(iv) In the model from part (ii), replace faminc with log(faminc). Which model fits the data
better, using faminc or log(faminc)? Interpret the coefficient on log(faminc).
(v) In the estimation in part (iv), how many estimated probabilities are negative? How many
are bigger than one? Should you be concerned?
(vi) For the estimation in part (iv), compute the percent correctly predicted for each
outcome, ecobuy=0 and ecobuy=1. Which outcome is best predicted by the model?