1.) Which of the following is not an assumption of the CLRM?
a.) The model is correctly specified
b.) The independent variables are exogenous
c.) The errors are normally distributed
d.) The errors have mean zero
e.) The errors have constant variance
2.) For a model to be correctly specified under the CLRM, it must:
a.) be linear in the coefficients
c.) include all relevant independent variables and their associated transformations
c.) have an additive error term
d.) all of the above
e.) none of the above
3.) In order for our independent variables to be labelled “exogenous” which of the following must be true:
a.) E(εi) = 0
b.) Cov(Xi,εi) = 0
c.) Cov(εi,εj) = 0
d.) Var(εi) = σ2
e.) none of the above
4.) The OLS estimator is said to be BLUE when:
a.) Assumptions 1 through 2 are satisfied
b.) Assumptions 1 through 3 are satisfied
c.) Assumptions 1 through 4 are satisfied
d.) Assumptions 1 through 5 are satisfied
e.) Assumptions 1 through 6 are satisfied
5.) The Gauss-Markov Theorem says that when the 6 classical assumptions are satisfied:
a.) The least squares estimator is unbiased
b.) The least squares estimator has the smallest variance of all linear unbiased estimators
c.) The least squares estimator has an approximately normal sampling distribution
d.) The least squares estimator is consistent
e.) None of the above
6.) The central limit theorem tells us that the sampling distribution of least squares regression coefficients:
a.) is always normal
b.) is always normal in large samples
c.) approaches normality as the sample size increases
d.) is normal in Monte Carlo simulations
e.) none of the above
7.) The sampling variance of the slope coefficient in the regression model with one independent variable:
a.) will be smaller when there is more variation in ε
b.) will be larger when there is less variation in ε
c.) will be smaller when there is more variation in X
d.) will be larger when there is more co-variation in ε and X
e.) none of the above
8.) Suppose you want to test the following hypothesis at the 5% level of significance:
H0: μ = μ0
H1: μ ≠ μ0
Which of the following statements is/are true?
a.) the probability of a Type I error is 0.025
b.) the probability of a Type I error is 0.05
c.) the probability of a Type II error is 0.95
d.) the probability of a Type II error is 0.05
e.) none of the above
9.) The F test of overall significance
a.) is based on a test statistic that has an F distribution with k and n-k-1 degrees of
freedom
b.) is based on a test statistic that has an F distribution with n-k-1and k degrees of freedom
c.) helps to detect whether relevant variables have been omitted from the model
d.) a and c
e.) b and c
10.) Given the equation for the F statistic, we can say that it is
a.) decreasing in R2, decreasing in n, and decreasing in k
b.) increasing in R2, increasing in n, and increasing in k
c.) decreasing in R2, increasing in n, and decreasing in k
d.) increasing in R2, increasing in n, and decreasing in k
e.) none of the above
11.) The F test of overall significance is valid if:
a.) Assumptions 1 through 6 of the CLRM are true
b.) the Central Limit Theorem can be invoked
c.) the Gauss-Markov Theorem is true
d.) the errors of the regression are normally distributed
e.) none of the above
12.) From a gravity model of trade, you estimate that Pr[0.9828  distance  0.7982]  95% , this
allows you to state that:
a.) there is a 95% chance that all potential estimates of the coefficient on distance are in this range
b.) you can reject the null hypothesis that the true coefficient on distance is equal to zero at the
5% level of significance
c.) there is a 5% chance that some of the potential estimate of the coefficient on distance fall
outside of this range
d.) all of the above
e.) none of the above
13.) Omitting a relevant explanatory variable that is correlated with the other independent variables
causes:
a.) no bias and no change in variance
b.) no bias and an increase in variance
c.) no bias and a decrease in variance
d.) bias
e.) none of the above
14.) Adding an irrelevant explanatory variable that is uncorrelated with the other independent variables
causes:
a.) bias and no change in variance
b.) bias and an increase in variance
c.) no bias and no change in variance
d.) no bias and an increase in variance
e.) none of the above
15.) The RESET test is designed to detect problems associated with:
a.) specification error of a known form
b.) heteroskedasticity
c.) multicollinearity
d.) serial correlation
e.) none of the above
16.) Omitting a constant term from our regression will likely lead to:
a.) a lower R2, a lower F statistic, and biased estimates of the independent variables when β0 = 0
b.) a higher R2, a lower F statistic, and biased estimates of the independent variables when β0 = 0
c.) a higher R2, a lower F statistic, and biased estimates of the independent variables when β0 = 0
d.) a higher R2, a higher F statistic, and biased estimates of the independent variables when β0 = 0
e.) none of the above
17.) In the regression model ln Yi  0  1 ln X i   i ,
a.) β1 measures the elasticity of Y with respect to X
b.) β1 measures the elasticity of X with respect to Y
c.) β1 measures the percentage change in Y for a one unit change in X
d.) the marginal effect of X on Y is constant
e.) none of the above
18.) Suppose we estimate the linear regression Yˆi  10  2 X i  5Fi where Yi is person i’s hourly wage, Xi
is years of employment experience, and Fi equals one for women and zero for men. If we redefined the
variable Di to equal one for men and zero for women instead, the least squares estimates would be:
a.) Yˆi  5  2 X i  5Di
b.) Yˆi  5  2 X i  5Di
c.) Yˆi  10  2 X i  5Di
d.) Yˆi  10  2 X i  5Di
e.) none of the above
19.) The consequences of multicollinearity are that the OLS estimates:
a.) will be biased while the standard errors will remain unaffected
b.) will be biased while the standard errors will be smaller
c.) will be unbiased while the standard errors will remain unaffected
d.) will be unbiased while the standard errors will be smaller
e.) none of the above
20.) Which of the following pairs of independent variables would violate Assumption VI?
That is, which pairs of variables are perfect linear functions of each other?
a.) Right shoe size and left shoe size of students enrolled in BUEC 333
b.) Consumption and disposable income in Canada over the last 30 years
c.) Xi and 2Xi
d.) Xi and Xi2
e.) none of the above
21.) Which of the following is not an appropriate remedy for serial correlation?
a) Generalized least squares
b) Ordinary least squares and Newey-West standard errors
c) Drop a redundant variable
d) Add an omitted variable
e) None of the above
22.) The Durbin-Watson test:
a) is pretty useless
b) tests for positive serial correlation
c) tests for first-order autocorrelation
d) tests for multicollinearity
e) none of the above
23.) Impure serial correlation:
a) is the same as pure serial correlation
b) can be detected with residual plots
c) is caused by mis-specification of the regression model
d) b and c
e) none of the above
24.) If regression errors are serially correlated, then:
a) least squares coefficient estimates are biased
b) GLS coefficient estimates are biased
c) least squares standard errors are wrong, but we can get consistent estimates of them
using the Newey-West formula
d) the BLUE is weighted least squares
e) none of the above
1.) Economists have long tried to understand the determinant of stock market performance. One
possibility is that the stock market is affected by the weather on Wall Street. Using daily data for 28
years, one researcher estimated an equation with the following variables (standard errors in parentheses):
D̂J t  ˆ0  0.10 DJ t 1  0.0010 J t  0.017 M t  0.0005Ct
(0.01)
(0.0006) (0.004)
(0.0002)
N = 6,911
R 2  0.02
Where: DJt = the percentage change in the Dow Jones Industrial Average on day t
Jt = a dummy variable equal to 1 if the t-th day was in January and 0 if otherwise
Mt = a dummy variable equal to 1 if the t-th day was a Monday and 0 if otherwise
Ct = a variable equal to 1 if the cloud cover from sunrise to sunset on the t-th day was 20% or
less, equal to -1 of the cloud cover was 100% and 0 if otherwise
a) The researcher did not include an estimate of the constant term in the published regression
results. Which of the Classical Assumptions supports the conclusion that you should
not spend too much time analysing estimates of the constant term? Explain.
b) Which of the Classical Assumptions would be violated if you decided to add a dummy
variable to the equation that was equal to 1 if the t-th day was a Tuesday, Wednesday,
Thursday, or Friday and equal to 0 if otherwise?
c) Carefully state the meaning of the coefficients on DJt-1 and Mt.
d) The variable C reflects the fact that approximately 85% of all New York City’s rain falls
on days with 100% cloud cover. In this case, is C a dummy variable? What
assumptions did the author have to make to use this variable?
e) The researcher concludes that these findings cast doubt on what is known as the “efficient
markets hypothesis”. Do some quick research on this topic (hello, Wikipedia). Based
on the results above, would you agree? Why or why not?
2.) Prescription drug prices vastly differ across countries, leading to charges of international price
discrimination on the part of drug companies. Researchers have estimated a model of prices of
pharmaceuticals in a cross section of 32 countries. Their estimates are given below (standard errors in
parentheses).
P̂i  38.22  1.43GDPNi  0.60CVNi  7.31PPi  15.63DPCi  11.38IPCi
(0.21)
(0.32)
(6.52)
(3.96)
(7.16)
N = 32
R 2  0.78
Where: Pi = the level of pharmaceutical prices in the i-th country divided by that of the US
GDPNi = per capita domestic product in the i-th country divided by that of the US
CVNi = per capita consumption of pharmaceuticals divided by that of the US
PPi = a dummy variable equal to 1 if patents for pharmaceutical products are recognized in
the i-th country and 0 if otherwise
DPCi = a dummy variable equal to 1 if the i-th country applied strict price controls and 0 if
otherwise
IPCi = a dummy variable equal to 1 if the i-th encourage price competition and 0 if otherwise
a) Explain what your expectations are for the sign of each of the independent variables.
b) Formulate and test appropriate hypotheses concerning the regression coefficients using the
t-test at the 5% level of significance.
c) Set up and interpret 90% confidence intervals for the coefficients on GDPN and PP.
d) Do you think the researchers should conclude that international price discrimination exists?
Why or why not?
e) How would the estimated results have differed if the authors had not divided each
country’s prices, per capita income, and per capita consumption by that of the US?
Explain your answer.
3.) There are at least two different possible approaches to the problem of building a model of the costs of
production of electric power. Model I hypothesizes that per-unit costs (C) as a function of the number of
kilowatt-hours produced (Q) continually and smoothly falls as production is increased, but it falls at a
decreasing rate. Model II hypothesizes that per-unit costs (C) decrease fairly steadily as production (Q)
increases across plant type, but costs start at a higher level for hydroelectric plants than for other kinds of
facilities.
a) Referring to Lecture 11b, what functional form would you recommend for estimating
Model I? Be sure to write out a specific equation.
b) Referring to Lecture 11b, what functional form would you recommend for estimating Model
II? Be sure to write out a specific equation.
c) Would R2 be a reasonable way to compare the overall fits of the two equations? Why or
why not?
4.) The Director of Admissions has contracted you to review the annual numbers for the number of
applications that SFU received from high school seniors. Evaluate the following regression results
(standard errors in parentheses):
N̂ t  15000  18000A t  150ln Tt  3000Pt
(9000)
(150)
(6000)
N  22
R 2  0.50
where: Nt the number of high school seniors who apply for admission in year t
At the number of people on the admission staff who visit high schools full time
spreading information about the school in year t
Tt dollars of tuition in year t
Pt the percent of the faculty that had PhDs in year t
a) Discuss the expected signs of the coefficients.
b) Compare these expectations with the estimated coefficients using the appropriate tests,
assuming a 5% level of significance.
c) Evaluate the possible econometric problems that could have caused any observed
differences between the estimated coefficients and what you expected.
d) Determine whether the semilog function for T makes theoretical sense.
e) How would you improve this specification
5.) Given your good work on the contract work above, now the undergraduate dean hires you to figure out
how to reduce damage done to SFU dorms by rowdy students. Your first step is to build a model of last
term’s damage to each dorm as a function of the attributes of that dorm (standard errors in parentheses):
D̂i  210  733Fi  0.805Si  74.0A i
(253)
(0.752) (12.4)
N  33
R 2  0.84
where: Di the amount of damage in dollars done to the i-th dorm last term
Fi the percentage of the i-th dorm residents who are freshmen
Si the number of students who live in the i-th dorm
Ai the number of incidents involving alcohol that were reported to Ancillary Services from the
i-th dorm last terms (where such incidents involving alcohol may or may not involve damage
to the dorm)
a) Hypothesize signs, calculate t-scores, and test hypotheses for these results at the 5% level.
b) What problems appear to exist in this equation? Omitted variables, irrelevant variables, or
multicollinearity? Why?
c) Suppose you were now told that the simple correlation coefficient between S and A was 0.94.
Would that change your answer? How?
d) Is it possible that the unexpected signs in your regression could have been caused by
multicollinearity? Why?
6.) In your role as a market analyst, you decide to investigate the relationship between stock market
returns in Canada and oil prices. You estimate the following regression on annual data for the period 1965
to 2005 (standard errors in parentheses):
Yˆt  7.05  0.11Pt  3.2 Rt  1.5Gt
(1.25) (0.02) (0.1) (0.3)
R 2  0.55 n  40 F  14.7 DW  0.9
where: Yt is the percentage return of the Toronto Stock Exchange in year t,
Pt is the average price of oil (in Dollars per barrel) in year t,
Rt is the average Canadian interest rate (in percent) in year t,
Gt is the percentage change in Canadian GDP in year t.
a) Test the null hypothesis that, all else equal, oil prices have no effect on stock market
returns, at the 5% level of significance.
b) What is the marginal effect of GDP growth on stock market returns?
c) What proportion of variation in stock market returns growth is explained by variation in oil
prices, the interest rate, and GDP growth over this period?
d) Does anything appear to be wrong with your regression specification? Do you think any
assumptions of the CLRM are violated? If yes, what do you think the cause is? If not,
explain why not. Does this affect your answer to part a) in any way?