Question 1

Suppose you know the determining function for what drives restaurant sales is of the following form WeeklySalesi = β0 + β1WeeklyPromoSpendi + β2HolidayWeeki + Ui. Suppose further that your client told you that she is spending $1,000 per week on weekly promotions, except during the summer where she doubles it. Which statement best describes the role of "summer weeks" in estimating the causal effect of weekly promotion spent using the determining function above?

Accepted Answer

A)   If summer weeks are contained in Ui (i.e., they affect Sales) , then there is an endogeneity problem.
B)   If summer weeks leads to more promotion and doesn't affect sales, then there is an endogeneity problem.
C)   There is no potential endogeneity problem with the determining function above.
D)   Because weekly promotions are unrelated to whether or not it's a holiday week, there is no endogeneity problem. A

Question 2

Can we estimate the following equation using standard linear regression techniques: Yi = β0 + β1Xi + β2Xi2 + Ui?

Accepted Answer

A)   No, this is not linear in X.
B)   No, we cannot isolate the treatment.
C)   Yes, this is linear in X.
D)   Yes, this is linear in our parameters. D

Question 3

A selected sample is one that is:

Accepted Answer

A)   non-normal.
B)   nonrandom.
C)   distributed according to the Student t distribution.
D)   efficient. B

Question 4

A control variable is a variable included in a regression equation whose purpose is to:

Accepted Answer

A)   alleviate an endogeneity problem.
B)   improve the fit of the model.
C)   provide a placebo test.
D)   ensure the sample is representative.

Question 5

Your first candidate for a regression to identify the effect of X1 on Y is: Yi = β0 + β1X1i + β2X2i + Ui, where X2 is a control variable. Suppose a member of your consulting team suggests to you that another variable Ri should be a control that is also included in your regression, in order for you not to be worried about the endogeneity problem. What condition could you credibly test using data on Y, X1, X2, and R which could justify the inclusion of Ri as a control in your regression?

Accepted Answer

A)   Ri has no effect per se on Yi.
B)   Ri has a strong correlation with X2.
C)   Ri is exogenous.
D)   spcorr(Ri, Yi (Xi1, Xi2) )  ≠ 0

Question 6

Suppose in an attempt to estimate the effect of how listing with a real estate agent impacts a house's selling price you estimate the following regression: Pricei = 10.2 (3.2) + 2.3 (0.8) Agent + -2.9 (0.3) Distance to Downtowni, where Distance to Downtown is a proxy variable, which can be used to control for the desirability of the location, and the standard errors for each coefficient are reported in parenthesis. How should we interpret the regression results for the coefficient on Agent?

Accepted Answer

A)   The unconditional correlation between housing prices and house sales with a listing agent are positive.
B)   The unconditional correlation between whether a listing is listed with an agent and how far it is from downtown is negative.
C)   Listings with an agent sell for higher prices holding fixed the desirability of the location of the listing.
D)   None of the answers is correct.

Question 7

Suppose you are estimating the following model: Yi = β0 + β1Xi + Ui. You believe the variance of the unobserved factors (U) varies with X. If this is true, what is the consequence?

Accepted Answer

A)   Your estimate for β1 will be biased.
B)   Your estimate of β0 will be biased.
C)   Your estimate for β0 and β1 will be biased.
D)   None of the above answers is correct

Question 8

Using a proxy variable can be appropriate in all of the following settings except estimating a:

Accepted Answer

A)   multiple linear regression.
B)   regression with both treatment and control variables.
C)   regression where the outcome is measured with error.
D)   regression where the proxy is uncorrelated with confounding factor causing the endogeneity problem.

Question 9

If you are using number of competitors as a control variable and the local unemployment rate as a proxy for economic climate in a regression to estimate the effect of price on sales, all the following variables will show up in the regression except for:

Accepted Answer

A)   the number of competitors.
B)   price.
C)   economic climate.
D)   sales.

Question 10

Sometimes including independent variables in a regression serve as a "data sanity check," in so much as they facilitate a:

Accepted Answer

A)   more efficient estimate of the treatment effect in question.
B)   more unbiased estimate of the treatment effect
C)   comparison between the estimated coefficient for that variable and the value for that coefficient as predicted by theory.
D)   secondary measure of the standard error of the treatment effect of interest.

Question 11

The presence of a confounding factor will lead to failure of which of the critical assumptions used to justify claiming your estimates consistently estimate a causal effect?

Accepted Answer

A)   The determining function is linear in parameters.
B)   The sample is a random sample from the population.
C)   The errors will be homoscedastic.
D)   The model's error terms and the treatments will all be uncorrelated.

Question 12

Suppose the relationship between temperature and demand for electricity is non-linear, due to the high demand for electricity when it is both very cold and very hot outside. What is the risk of estimating the effect of price on demand for electricity by the regression equation: Electricity Consumptiont = α0 + α1Pricet + α2Temperaturet + Ut?

Accepted Answer

A)   The estimate of α1 will be biased.
B)   The sample will not be representative.
C)   Electricity consumption will be censored from above.
D)   None of the answers is correct.

Question 13

Suppose you've run a regression relating log(Output) to log(Worker Hours) in Excel. You are willing to make the necessary assumptions to deduce causality and run hypothesis tests. Your results are as follows: $$\begin{array} { l c c c c } 
& \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } \
\hline \text { Irtercept } & 17.4583044 & 28.47075584 & 0.613201297 & 0.541240031 \
\text { Log(Worker Hours) } & 2.699483287 & 0.711729096 & 3.792852225 & 0.000264681
\end{array}$$ How should you interpret the coefficient on Log(Worker Hours) of 2.69?

Accepted Answer

A)   A 1% increase in Worker Hours leads to a 2.69% increase in Output.
B)   A 1 unit increase in Worker Hours leads to a 2.69% increase in Output.
C)   A 1% increase in Worker Hours leads to a .0269% increase in Output.
D)   A 2.69% increase in Worker Hours leads to a 1% increase in Output.

Question 14

The determining function that drives share of accepted job offers for a company is given by the following equation: AcceptedOfferst = α0 + α1StartingSalaryt + α2EconomicClimatet + Ut, where the unit of observation is particular month (t). Suppose one wanted to use the national unemployment rate (unemploymentt) as a proxy for EconomicClimate (i.e., ran the above regression replacing the UnemploymentRate with EconomicClimate). How should we interpret the estimated coefficient on the UnemploymentRate (i.e., the proxy variable)?

Accepted Answer

A)   A good estimate for α2 in the above determining function.
B)   A good estimate for α1 in the above determining function.
C)   A good estimate for α1 + α2 in the above determining function.
D)   None of the answers is correct.

Question 15

If the decision to include average tenure at the company as a control variable in an attempt to estimate if West coast store locations are outperforming store locations in the rest of the country (i.e., the regression, StoreProfitsi = β0 + β1West Coasti + β2Avg.Tenurei + Ui), which of the following conditions need to be true in order for the estimate of β1 to be the same regardless of whether Avg. Tenure is used as a control or not?

Accepted Answer

A)   The p-value on average tenure is low.
B)   The p-value on average tenure is above 0.10
C)   Average tenure and West Coast are uncorrelated.
D)   The semi-partial correlation of Store Profits on West Coast holding Avg. Tenure fixed is zero.

Question 16

Dropping irrelevant variables from a regression equation might provide a better regression in what sense?

Accepted Answer

A)   Only when the irrelevant variables are uncorrelated with the treatment(s) .
B)   Might facilitate more efficient/precise estimates of the treatment effect (smaller standard errors) .
C)   Only if the irrelevant variables have low p-values.
D)   Only if the irrelevant variables have many outliers.

Question 17

Assuming that you are trying to determine the true effect of how years of education affect career earnings (Earningsi = β0 + β1Educationi + Ui), and that this effect is positive . What would be the likely induced correlation between Education and Ui of receiving a sample that only had individuals that made over $85,000?

Accepted Answer

A)   Negative
B)   Positive
C)   There is not enough information.
D)   None of the answers is correct.

Question 18

Suppose you are estimating the following model: Yi = β0 + β1Xi + Ui. Suppose also that you only observe values of Y that are above 50. What is the consequence of this selection on the values of Y?

Accepted Answer

A)   Your estimate for β1 will be biased.
B)   Your model will suffer from the heteroscedasticity problem.
C)   Your estimate for β1 will be biased and your model will suffer from the heteroscedasticity problem.
D)   None of the answers is correct.

Question 19

What are the two primary criteria for identifying "good" controls?

Accepted Answer

A)   They are likely correlated with the treatment and they do not influence the outcome per se.
B)   They are likely uncorrelated with the treatment and they influence the outcome.
C)   They are likely correlated with the treatment and do not influence the outcome.
D)   They are likely correlated with treatment and they influence the outcome.

Question 20

Why is the use of polynomial functional forms typical in trying to estimate non-linear functional forms?

Accepted Answer

A)   They yield more efficient estimates than other non-linear functional forms.
B)   They offer a high degree of flexibility.
C)   They provide coefficients that have elasticities as interpretations.
D)   They have standard errors that are easier to interpret.

Exam 7: Basic Methods for Establishing Causal Inference

Can we estimate the following equation using standard linear regression techniques: Y_i = β₀ + β₁X_i + β₂X_i² + U_i?