Deck 7: Basic Methods for Establishing Causal Inference

Question 1

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

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

Answer 1

A

Question 2

It is often times necessary to make reference to a base group in regression analysis, which denotes what?

A) The preferred selection of control variables to have in the regression equation.
B) The set of homoscedastic errors.
C) The excluded dummy variable among a set of dummy variables representing a categorical, ordinal or interval variable.
D) The control group in a randomized control trial.

Answer 2

C

Question 3

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

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.

Answer 3

D

Question 4

What condition best describes the endogeneity problem?

A) The variance of the errors (U_i) depends on X_i.
B) Some variables within X_i are perfectly correlated with other variables in X_i.
C) The distribution of the errors (U_i) is non-normal.
D) One of the X_i variables is correlated with the error term (U_i).

Question 5

In determining the causal effect of Price on Sales, if advertising spend is a good control variable, how will the correlation of the error terms from the regression, Sales_i = β₀ + β₁Price_i + U_i, and Sales_i = α₀ + α₁Price_i + α₂Advertising_i + V_i and price be related?

A) Cor(U_i, V_i) = 0
B) Cor(U_i, Price_i) = 0, Cor(Price_i, V_i) = 0
C) Cor(U_i, Price_i) ≠ 0, Cor(Price_i, V_i) = 0
D) Cor(U_i, Price_i) = 0, Cor(Price_i, V_i) ≠ 0

Question 6

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

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 7

A selected sample is one that is:

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

Question 8

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, StoreProfits_i = β₀ + β₁West Coast_i + β₂Avg.Tenure_i + U_i), 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?

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 9

A dummy variable is:

A) a variable with a low t-stat and high p-value.
B) a placeholder for a variable to be gathered later.
C) a dichotomous variable that is used to indicate the presence or absence of a characteristic.
D) an unbiased estimate of the true variable.

Question 10

In attempting to estimate the causal effect of employee hours worked on total units produced, you include the age of the production equipment as a control variable. Which of the following conditions would not be a good reason to include this control variable?

A) Older production equipment often requires more employees to work on them.
B) Older production equipment often is less productive (i.e., produce fewer units on average).
C) The age distribution of the plants is highly non-normal.
D) The semi-partial correlation of total units produced on age of the machine holding number of employees fixed is positive and statistically significant.

Question 11

Suppose you are estimating the following model: Y_i = β₀ + β₁X_i + U_i. 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?

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 12

A representative sample is one whose:

A) distribution is approximately normal as it gets larger.
B) sample is drawn randomly.
C) distribution approximately matches that of the population, for a subset of observed, independent variables.
D) distribution exactly matches the population distribution for the outcome variable.

Question 13

An ordinal variable is one that contains categories that:

A) have an obvious order, but the difference in values is not meaningful.
B) do not have an obvious ordering.
C) have an obvious ordering, and the difference in values is meaningful.
D) None of the answers is correct.

Question 14

Suppose you know the determining function for what drives restaurant sales is of the following form WeeklySales_i = β₀ + β₁WeeklyPromoSpend_i + β₂HolidayWeek_i + U_i. 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?

A) If summer weeks are contained in U_i (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.

Question 15

Irrelevant variables are ones that:

A) do not affect the outcome.
B) affect the outcome but only in the population.
C) affect the outcome in the sample.
D) have variables with low p-values.

Question 16

Which step is not involved with constructing a representative sample?

A) Choose the independent variables you want to match.
B) Collect the sample by randomly sampling from each stratum (defined by your pre-chosen independent variables).
C) Use information about the population to stratify (categorize) each of the chosen variables.
D) Run a t-test to check if the outcomes are different across stratums.

Question 17

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?

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 18

Assuming that you are trying to determine the true effect of how years of education affect career earnings (Earnings_i = β₀ + β₁Education_i + U_i), and that this effect is positive . What would be the likely induced correlation between Education and U_i of receiving a sample that only had individuals that made over $85,000?

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

Question 19

Suppose you are estimating the following model: Y_i = β₀ + β₁X_i + U_i. You believe the variance of the unobserved factors (U) varies with X. If this is true, what is the consequence?

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 20

Suppose you have estimated the following regression: Refrigerator Sales_i = β₀ + β₁Price_i + U_i. However, when presenting your results, someone in the audience claims your estimate is biased because your sample only contains sales figures for refrigerators that are priced over $300. Their point is:

A) correct. You have a selected sample on the Y variable, so your estimate is biased.
B) correct. You have a selected sample on the X variable, so your estimate is biased.
C) incorrect. You have a selected sample on Y variable, but this does not bias your estimate.
D) incorrect. You have a selected sample on X variable, but this does not bias your estimate.

Question 21

Does the interpretation on the estimated coefficient on the treatment change if you use a proxy variable to control for a confounding factor?

A) No, the estimated coefficient is a consistent estimate of the causal effect.
B) No, but instead of getting causal estimate you're only estimating partial correlations.
C) Yes, the coefficient on the treatment is biased.
D) Yes, the coefficient on the treatment suffers from the simultaneity bias.

Question 22

The successful use of a proxy variable to control for a confounding factor will allow you to accomplish all of the following except:

A) consistently estimate the treatment effect of interest.
B) limit the endogeneity problem associated with the confounding factor.
C) uncover the size of the semi-partial correlation of the confounding factor and the outcome.
D) conduct appropriate hypothesis testing for the treatment effect of interest.

Question 23

In estimating the effect of price on sales, what is likely to be a confounding factor that one would at best have only a proxy variable for?

A) Price
B) Sales
C) Month
D) Brand awareness

Question 24

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

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 25

Which of the following variables might be a proxy variable for the confounding factor of cognitive ability in a sample of workers and their ability to generate sales?

A) Test scores
B) Past sales records
C) Tenure at the company
D) Age

Question 26

The determining function that drives movie ticket sales is given by the following equation: Sales_it = α₀ + α₁ HolidaySeason_it + α₂CastAwareness_it + U_it, where the unit of observation is a particular movie (i) in month (t). Suppose one wanted to use cumulative past movie appearances of the entire cast of a movie as a proxy for CastAwareness. Which of the following conditions would not be one required for this to be an adequate proxy variable?

A) CumulativePastMovieAppearances to be correlated with CastAwareness.
B) HolidaySeason, CastAwareness, and CumulativePastMovieAppearances to be uncorrelated with "other factors" (U_it).
C) CastAwareness to be uncorrelated with HolidaySeason.
D) HolidaySeason and CumulativePastMovieAppearances to be uncorrelated with "other factors" affecting CastAwareness.

Question 27

The use of a proxy variable changes how you must interpret which of the following statistics?

A) R-squared
B) P-value of coefficient on treatment
C) Standard errors on treatment
D) None of the answers is correct.

Question 28

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: Price_i = 10.2 (3.2) + 2.3 (0.8) Agent + -2.9 (0.3) Distance to Downtown_i, 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?

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 29

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

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 30

Suppose you have the following regression results from a regression of home prices on house attributes for a random sample of house transactions: $$\begin{array} { | l | r | r | } \hline & \text { Coefficierts } & \text { Stardard Error } \\\hline \text { Iratercept } & 16310.0 & 4114.5 \\\hline \text { Nurrber of Bedroorrs } & 7295.3 & 1399 . \\\hline \text { Number of Bathroorrs } & 23473.0 & 4032.0 \\\hline\end{array}$$ r-squared = 0.302 Adjusted r-squared = 0.299 If we assume that the proper model to predict the market value of houses is given by this regression, and we also happen to know that number of bathrooms and number of bedrooms is uncorrelated both in the sample and in the target population of house sales, why might we still want to include number of bathrooms in a regression to identify the causal effect of number of bedrooms on home prices?

A) It lowers the adjusted r-squared.
B) It increases the r-squared value.
C) It provides a sanity check on our regression.
D) It also leads to more consistent estimates of the treatment effect.

Question 31

The determining function that drives share of accepted job offers for a company is given by the following equation: AcceptedOffers_t = α₀ + α₁StartingSalary_t + α₂EconomicClimate_t + U_t, where the unit of observation is particular month (t). Suppose one wanted to use the national unemployment rate (unemployment_t) as a proxy for EconomicClimate. Which of the following describes a condition required to hold for this to be an adequate proxy variable?

A) α₂ < 0
B) StartingSalary, EconomicClimate, and Unemployment rate to be uncorrelated with "other factors" (U_t)
C) α₂ > 0
D) EconomicClimate is correlated with StartingSalary

Question 32

Your first candidate for a regression to identify the effect of X₁ on Y is: Y_i = β₀ + β₁X_1i + β₂X_2i + U_i, where X₂ is a control variable. Suppose a member of your consulting team suggests to you that another variable R_i 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 R_i as a control in your regression?

A) R_i has no effect per se on Y_i.
B) R_i has a strong correlation with X₂.
C) R_i is exogenous.
D) spcorr(R_i, Y_i (X_i1, X_i2)) ≠ 0

Question 33

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:

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

Question 34

The determining function that drives share of accepted job offers for a company is given by the following equation: AcceptedOffers_t = α₀ + α₁StartingSalary_t + α₂EconomicClimate_t + U_t, where the unit of observation is particular month (t). Suppose one wanted to use the national unemployment rate (unemployment_t) 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)?

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 35

A proxy variable is a variable used in a regression equation in order to:

A) report the r-squared value appropriately.
B) make the adjustment for the adjusted r-squared.
C) proxy for a confounding factor in an attempt to alleviate the endogeneity problem.
D) improve the standard errors on the treatment effect.

Question 36

In estimating the effect of a difference in earnings for ivy league graduates, non-ivy league college graduates, and non-college graduates the following regression is run: Earnings_i = β₀ + β₁IvyLeague_i + β₂NonIvyCollegeGraduate_i + U_i. What does the coefficient β₁ represent?

A) The additional increase (decrease) in earnings from going from graduating college to graduating from an Ivy league school.
B) The average earnings of an Ivy league graduate.
C) The additional increase (decrease) in earnings from going from no college degree to an Ivy league degree.
D) The average earnings of an ivy league graduate conditional on graduating from any college.

Question 37

Which of the following correlations would be an acceptable way to show that the variable (P_i) is a suitable proxy for A_i in the regression Y_i = β₀ + β₁T_i + β₂A_i + U_i?

A) Corr(Y_i, T_i) ≠ 0
B) spCorr(Y_i, T_i (P_i)) ≠ 0
C) pCorr(Y_i, P_i; T_i) ≠ 0
D) None of the answers is correct.

Question 38

Suppose you have the following regression results from a regression of home prices on house attributes for a random sample of house transactions: $$\begin{array} { | l | r | r | } \hline & \text { Coefficierts } & \text { Stardard Error } \\\hline \text { Iratercept } & 16310.0 & 4114.5 \\\hline \text { Nurrber of Bedroorrs } & 7295.3 & 1399 . \\\hline \text { Number of Bathroorrs } & 23473.0 & 4032.0 \\\hline\end{array}$$ r-squared = 0.302 Adjusted r-squared = 0.299 If we assume that the proper model to predict the market value of houses is given by this regression, and thus we are getting unbiased estimates of the true relationships between number of bedrooms/bathrooms and sales price, what is the effect on sales price of increasing the number of bathrooms in a house by one, holding number of bedrooms fixed?

A) Approximately, $16,310 dollars.
B) Approximately, $ 7,295 + 23,473 = $30,768.
C) Approximately, $23,473.
D) Approximately, an increase of 30%.

Question 39

The determining function that drives share of accepted job offers for a company is given by the following equation: AcceptedOffers_t = α₀ + α₁StartingSalary_t + α₂EconomicClimate_t + U_t, where the unit of observation is particular month (t). Suppose one wanted to use the national unemployment rate (unemployment_t) as a proxy for EconomicClimate. Which of the following would be a condition that would rule out the unemployment rate being a good proxy for economic climate?

A) α₂ < 0
B) Unemployment rate to be correlated with "other factors" (U_t)
C) α₂ > 0
D) EconomicClimate is correlated with StartingSalary

Question 40

Suppose you have the following regression results from a regression of home prices on house attributes for a random sample of house transactions: $$\begin{array} { | l | r | r | } \hline & \text { Coefficierts } & \text { Stardard Error } \\\hline \text { Iratercept } & 16310.0 & 4114.5 \\\hline \text { Nurrber of Bedroorrs } & 7295.3 & 1399 . \\\hline \text { Number of Bathroorrs } & 23473.0 & 4032.0 \\\hline\end{array}$$ Given these results which additional condition would be sufficient to ensure number of bathrooms satisfies the "primary criteria" for a good control variable in attempting to identify the causal effect of number of bedrooms on house prices?

A) The number of bathrooms is correlated with house prices.
B) The number of bedrooms is correlated with house prices.
C) The number of bathrooms is correlated with the number of bedrooms.
D) The p-value for the number of bedrooms.

Question 41

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

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.

Question 42

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?

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 43

Suppose you've regressed profits on price, assuming a quadratic functional form. Your regression equation is: Profits_i = β₀ + β₁Price_i + β₂Price_i² + U_i. What is the marginal effect of price in this equation?

A) β₀ + β₁ + β₂
B) β₁ + β₂ × Price_i
C) β₀ + β₁ + 2β₂
D) β₁ + 2β₂ × Price_i

Question 44

Suppose the fitted (assumed causal) regression line for your data is as follows: Log(Output) = 6.2 + 0.4 × Log(Labor) + 0.5 × Log(Capital)
Interpret the coefficient on Log(Labor).

A) Holding capital fixed, when labor goes up by 1, output goes up by 0.4
B) Holding capital fixed, when labor goes up by 1, output goes up by 6.6
C) Holding capital fixed, when labor goes up by 1%, output goes up by 0.4%
D) Holding capital fixed, when labor goes up by 1%, output goes up by 40 units

Question 45

Which of the following regressions would yield a coefficient estimate that would be directly interpreted as the price elasticity of demand?

A) Quantity_i = α₀ + α₁log(Price_i)
B) log(Quantity_i) = α₀ + α₁log(Price_i)
C) Quantity_i = α₀ + α₁Price_i
D) Quantity_i = α₀ - α₁log(Price_i)

Question 46

The percentage change in one variable with a percentage change in another is known as a(n):

A) percentage point change.
B) log-level change.
C) elasticity.
D) linear effect.

Question 47

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 Consumption_t = α₀ + α₁Price_t + α₂Temperature_t + U_t?

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 48

Which of the following cannot be estimated using traditional linear regression techniques?

A) log(Y) = β₀ + β₁log(X) + U_i
B) log(Y) = β₀ + β₁X + U_i
C) Y = β₀ + β₁log(X) + U_i
D) None of the answers is correct.

Question 49

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

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.