Deck 8: Advanced Methods for Establishing Causal Inference

Question 1

Why do you use only some of the variation of your treatment variable (the component predicted in the first stage) when using an instrumental variable approach?

A) To get smaller standard errors.
B) To avoid the heteroscedasticity problem.
C) To have the estimate of the treatment effect be based only on variation that is exogenous variation to the other factors affecting the outcome.
D) To have the estimate of the treatment effect be based only on variation of the treatment that is correlated with the outcome.

Answer 1

C

Question 2

A variable is exogenous if that variable:

A) has no effect on the treatment variable beyond the combined effects of other variables already in the determining function.
B) has no effect on the outcome variable beyond the combined effects of other variables already in the determining function.
C) has a strong correlation with the weather.
D) is uncorrelated with the residuals of a regression estimated by OLS.

Answer 2

B

Question 3

Which object from the first or second stage reports whether an instrument is relevant?

A) Check if the residuals from the first stage regression are uncorrelated with the instrumental variable.
B) Check if the residuals from the second stage regression are uncorrelated with the instrumental variable.
C) Check if the coefficient on the instrumental variable in the first stage is statistically distinct from zero.
D) Check if the coefficient on the instrumental variable in the second stage is statistically distinct from zero.

Answer 3

C

Question 4

In estimating the effect of price on sales (Sales_i = α₀ + α₁Price_i + U_i), you are attempting to find an instrumental variable that will solve the endogeneity problem caused by the confounding factor of number of competitors being within U_i, which is correlated with price. Which of the following statements would suggest that wholesale costs would satisfy the exogenous condition to be a potential instrument variable?

A) Wholesale costs are uncorrelated with price.
B) Wholesale costs are correlated with price.
C) Wholesale costs are uncorrelated with sales.
D) Wholesale costs are uncorrelated with number of competitors.

Question 5

In estimating the effect of price on sales (Sales_i = α₀ + α₁Price_i + U_i), you are attempting to find an instrumental variable that will solve the endogeneity problem caused by the confounding factor of number of competitors being within U_i, which is correlated with price. Which of the following statements would suggest that wholesale costs would satisfy the relevant condition to be a potential instrument variable?

A) Wholesale costs are uncorrelated with price.
B) Wholesale costs are correlated with price.
C) Wholesale costs are uncorrelated with sales.
D) Wholesale costs are uncorrelated with number of competitors.

Question 6

The process of using two regressions to measure the causal effect of a variable while utilizing an instrumental variable is known as:

A) nonlinear least squares.
B) two-stage least squares.
C) difference in difference.
D) probit.

Question 7

In estimating a regression model with an instrumental variable typically one of two methods is used to estimate the mode. The two methods are:

A) two-stage least squares and fixed effects regression.
B) fixed effects regression and panel data methods.
C) two-stage least squares and generalized method of moments.
D) two-stage least squares and within estimator.

Question 8

Two-stage least squares can be executed:

A) only with advanced software.
B) only on small samples.
C) straightforwardly by combining two separate regressions.
D) only with panel data sets.

Question 9

A weak instrument is an instrumental variable:

A) whose distribution is non-normal.
B) whose partial correlation with the outcome is small.
C) whose partial correlation with the (endogenous) treatment variable is small.
D) that suffers from heteroscedasticity.

Question 10

In the context of regression analysis, a variable that allows us to isolate the causal effect of a treatment on an outcome due to its exogenous correlation with the treatment is known as a(n):

A) instrumental variable.
B) control variable.
C) difference in difference estimator.
D) dummy variable.

Question 11

All of the following conditions are necessary for an instrumental variable Z to be a valid instrument for X in the regression: Y_i = β₀ + β₁X_i + U_i except for which condition?

A) Cov(X_i, Z_i) ≠ 0
B) Cov(Z_i, U_i) = 0
C) Cov(X_i, Y_i) ≠ 0
D) None of these choices are correct.

Question 12

An instrumental variable is relevant if that variable is:

A) a dichotomous variable.
B) normally distributed.
C) a consistent estimator of the coefficient on the treatment.
D) correlated with the treatment after controlling for other control variables in the determining function.

Question 13

Generally speaking a consequence of using an instrumental variable approach with a weak instrument will be:

A) imprecise coefficient estimates (e.g., large standard errors).
B) low coefficient estimates.
C) high (in absolute magnitude) coefficient estimates.
D) multicollinearity.

Question 14

What object from the first stage regression (of two-stage least squares) is critical to incorporate in your implementation of the second stage regression?

A) The estimated coefficient for the treatment variable from the first stage.
B) The estimated residuals for the treatment variable from the first stage.
C) The estimated predictions for the endogenous variable from the first stage.
D) The estimated residuals for the endogenous variable from the first stage.

Question 15

Suppose you are trying to estimate the following regression: Y_i = β₀ + β₁X_1i + β₂X_2i + β₃X_3i + U_i, with an instrument for Z_i for X_2i. All of the following variables will be included (on the right- and left-hand side of this regression) in the first stage of two-stage least squares except for which one?

A) X_1i
B) X_2i
C) X_3i
D) Y_i

Question 16

Why is it the case that an instrumental variable is not found directly in the determining function?

A) If an instrument is exogenous, then it has no effect on the outcome beyond those already in the determining function.
B) If an instrument is relevant, then it has no effect on the outcome beyond those already in the determining function.
C) If an instrument is exogenous, then it has an effect on the outcome just not a statistically significant one.
D) If an instrument is relevant, then it has an effect on the outcome just not a statistically significant one.

Question 17

Suppose you are trying to estimate the following regression: Y_i = β₀ + β₁X_1i + β₂X_2i + β₃X_3i + U_i, with an instrument for Z_i for X_2i. All of the following variables will be included (on the right- and left-hand side of this regression) in the second stage of two-stage least squares except for which one?

A) X_1i
B) X_2i
C) X_3i
D) Y_i

Question 18

In order for a variable to be a valid instrumental variable it needs to satisfy which two conditions?

A) Exogenous and consistent
B) Efficient and uncorrelated
C) Relevant and exogenous
D) Relevant and efficient

Question 19

If you conduct your estimation using two-stage least squares by separately estimating each regression (say in Excel), what condition should you be aware of when interpreting your second stage results?

A) The coefficients will be too low.
B) The coefficients will be too high.
C) The standard errors reported in the second stage are not accurate.
D) The residuals do not sum to zero as they due in the first stage.

Question 20

In words, why can utilizing an instrumental variable be an effective means toward identifying the causal effect of a treatment on an outcome?

A) It allows you to identify the causal effect of the treatment by controlling for unobservables that may crucially affect the outcome.
B) It allows you to identify the causal effect of the treatment by using only variation in the treatment that is correlated with unobservables that affect the outcome.
C) It allows you to identify the causal effect of the treatment by using only variation in the treatment that isn't correlated with unobservables that affect the outcome.
D) None of the answers is correct.

Question 21

All standard regression software should be able to help you in determining if your instrument is:

A) exogenous.
B) relevant.
C) consistent.
D) measured with error.

Question 22

Suppose you are estimating demand relationships, where you are attempting to identify the effect of price on quantity sold (i.e., Q_i = α₀ + α₁Price_i + U_i). It will often be the case that the use of an instrumental variable for price will likely yield a coefficient (for α₁) that relates to the use of multiple regression in what way?

A) Is lower, because price and U_i are likely positively correlated.
B) Is lower, because price and U_i are likely negatively correlated.
C) Is higher, because price and U_i are likely negatively correlated.
D) Is higher, because price and U_i are likely positively correlated.

Question 23

Fortunately, the difference-in-differences estimate of a treatment effect also can be reported/interpreted as:

A) a simple difference in mean outcomes.
B) the coefficient on an interaction term.
C) the ratio of t-stats.
D) the second stage estimates of two-stage least squares.

Question 24

A fixed effects model is one in which the data generating process includes:

A) controls for cross-sectional groups.
B) controls for heteroscedasticity.
C) some control variables (e.g., Income) that vary over time.
D) a selected sample of cross-sectional units.

Question 25

Suppose you've regressed profits across stores (i) in Indiana and Michigan over two years (t) on an Indiana dummy variable as well as on an interaction between an Indiana dummy variable and Year 2 dummy variable. Thus, your regression equation is: Profits_it = β₀ + β₁Indiana_it + β₂Year2_it Indiana_it + U_i. What is the marginal effect of a store being in Indiana based off this regression equation?

A) β₀ + β₁ + β₂
B) β₁ + β₂ × Year2_it
C) β₀ + β₁
D) β₂

Question 26

Suppose you have two departments and have daily data on complaints and number of products they oversee for the departments over two years. In the second year, you increased the number of products under the scope of department #2 by 10. To estimate the effect of this increase in the number of products, you estimate the following regression: Complaints_it = α + β₁ × Department #2_it + β₂ × Year2_it + β₃ × Department #2_it × Year2_it + U_it. In this regression, what is the "diff-in-diff"?

A) α + β₁
B) β₁ + β₃
C) α + β₃
D) β₃

Question 27

To estimate a difference-in-differences it requires that one has a:

A) panel data set.
B) cross-sectional data set.
C) time series.
D) selected sample.

Question 28

When might it be the case that a difference-in-differences estimator still does not identify a consistent estimate of the causal treatment effect?

A) If the treatment is non-normally distributed.
B) If there are non-time varying effects that generate differences between treated and non-treated groups.
C) If there are time varying effects that generate amongst both treated and non-treated groups symmetrically.
D) If there are time-varying trends that are different amongst treated and non-treated groups.

Question 29

Which object from the first or second stage reports whether an instrument is exogenous?

A) Check if the residuals from the first stage regression are uncorrelated with the instrumental variable.
B) Check if the residuals from the second stage regression are uncorrelated with the instrumental variable.
C) Check if the instrumental variable is uncorrelated with the outcome variable.
D) None of the answers is correct.

Question 30

The following regression results are from the first stage regression of Price on income and wholesale costs-which is serving as the instrument for a particular grocery product across different markets: Price_i = 3.2(1.0) + 4.3(0.8)WholesaleCosts_i + 5.5(2.7)Income_i, where standard errors are reported in parenthesis. What conclusion can be drawn about the instrumental variable?

A) It's unbiased.
B) With a t-stat over 2.5 (4.3/0.8), the instrument is relevant.
C) With a t-stat over 2.5 (4.3/0.8), the instrument is exogenous.
D) It's under reporting the effect of income on price.

Question 31

The hardest part of implementing the instrumental variables approach is:

A) deciding between using two-stage least squares or generalized method of moments.
B) reporting the appropriate standard errors.
C) finding and defending the exogeneity condition of your instrumental variable.
D) determining which of your instrumental variables are relevant.

Question 32

Typically, the justification for an instrumental variable will come from:

A) some sound theoretical argument and some empirically testable conditions.
B) empirically testable conditions only.
C) "big data" application data sets.
D) panel data sets.

Question 33

In the regression model Unemployment Rate_it = α + γ₁ × Alabama_it + γ₂ × South Carolina_it + γ₃ × North Carolina_it + β₁Income_it+ φYear_it + ε_it, the coefficients for the fixed effects of the model will be given by:

A) φ.
B) α.
C) U_it.
D) γ₁, γ₂, γ₃.

Question 34

Suppose you have two departments and have daily data on complaints and number of products they oversee for the departments over two years. In the second year, you increased the number of products under the scope of department #2 by 10. To estimate the effect of this increase in the number of products, you estimate the following regression: Complaints_it = α + β₁ × Department #2_it + β₂ × Year2_it + β₃ × Department #2_it × Year2_it + U_it. Which coefficient controls for non-time varying effects that make department #1 have more complaints than department #2?

A) β₁
B) β₂
C) α + β₃
D) β₃

Question 35

In lieu of including a separate dummy variable for each different time period of a panel, often times the use of a simple time trend is chosen. This choice will lead to a(n):

A) increase in the r-squared.
B) increase in the adjusted r-squared.
C) increase in the number of parameters to be estimated.
D) decrease in the number of parameters to be estimated.

Question 36

Generally speaking, the difference-in-differences is defined to be the:

A) difference in outcomes from random assignment.
B) difference in outcomes from different treatment levels.
C) difference in the temporal change for the outcome between treated and untreated groups.
D) None of the answers is correct.

Question 37

Which of the following scenarios might allow you to try and test the exogeneity condition of an instrumental variable empirically?

A) When you know your instrument is relevant beforehand.
B) When you can estimate the model using generalized method of moments.
C) When you have two instrument variables and two endogenous variables.
D) When you have two instrument variables and one endogenous variable.

Question 38

The controls for cross-sectional groups in the data generating process are known as:

A) treatment effects.
B) fixed effects.
C) instrumental variables.
D) difference-in-differences.

Question 39

The difference-in-differences approach relaxes some of the required assumptions for establishing causality by leveraging what dimension of the empirical setting?

A) Observing repeated observations of the same cross-sectional units over time.
B) Observing multiple cross-sectional units receiving the treatment.
C) Observing a time series for one series.
D) Being able to construct an instrument from the first stage difference.

Question 40

Suppose the U.S. Federal Reserve raised its interest rate by 1 percentage point between 2014 and 2015, but the Bank of Canada made no change in its interest rate. You estimate the following model in an attempt to assess the effect of the change in interest rate on the unemployment rate: Unemployment_it = β₀ + β₁U.S._it + β₂Y2015_it + β₃U.S._it × Y2015_it + U_it
Here, U.S._it is a dummy variable equaling one if the observation is in the U.S. and Y2015_it is a dummy variable equaling one if the observation is in 2015. Which of the following variables may generate an endogeneity problem when attempting to use the estimate for the diff-in-diff (β₃) as the effect of the interest rate change?

A) Changes in the U.S. fiscal policy between 2014 and 2015
B) Changes in overall level of trade in North American between 2014 and 2015
C) The difference in average labor force participation between U.S. and Canada
D) Changes in international immigration laws between 2014 and 2015

Question 41

Given the regression results Unemployment Rate_it = α + 0.8 (0.3) × Alabama_it - 0.4 (0.2) × South Carolina_it + 0.2 (0.3) × North Carolina_it + 0.4 (0.12)MinimumWage_it - 0.1 (0.1)Year_t, where the coefficients are reported with their standard errors in parenthesis, how should we interpret the coefficient for minimum wage?

A) An increase in minimum wage will increase the unemployment rate.
B) An increase in minimum wage will increase the unemployment rate, holding fixed (time constant) differences across states.
C) An increase in minimum wage will increase the unemployment rate, holding fixed the downward trend in unemployment rates occurring across all of these three states.
D) An increase in minimum wage will increase the unemployment rate, holding fixed (time constant) differences across states, and the downward trend in unemployment rates occurring across all of these three states.

Question 42

A potential downside of using within estimation is:

A) r-squared is less meaningful.
B) the coefficients will be biased.
C) the estimator will not yield estimates of the fixed effects themselves.
D) the standard errors will be larger.

Question 43

Generally speaking, what are the methods available to the econometrician who wants to estimate a linear model with a fixed effects model design (i.e., dummy variable for individual units observed over multiple periods)?

A) Within Estimator and Fixed Effects regression
B) Diff-in-diff and Two-stage least squares
C) Two-stage least squares and Fixed Effects regression
D) Within estimator and instrumental variable regression

Question 44

Interpreting the coefficients on fixed effects will always be based on what?

A) If the regression was run using STATA or Excel.
B) The sign of the coefficient on the instrumental variable in the first stage regression.
C) The base group omitted from the regression.
D) The standard error on the treatment variable.

Question 45

Given the role of cross sectional fixed effects in the empirical strategy for identifying causal effects, instead of conducting hypothesis tests of any one coefficient on a fixed effect being zero, it is typical to conduct what sort of hypothesis test?

A) A hypothesis test for a fixed effect coefficient being equal to 1 instead of zero.
B) A hypothesis test for a fixed effect coefficient being equal to -1 instead of zero.
C) A joint hypothesis test for all of the fixed effect coefficients being equal to zero.
D) A joint hypothesis test that the fixed effect coefficients are all equal to the treatment effect.

Question 46

When one uses within-group differences in variables to estimate parameters in the data generating process, you are using what approach?

A) Two-stage least squares
B) Nonlinear least squares
C) Within estimation
D) Time trends

Question 47

All of the following coefficients/statistics will be the same across the dummy variable and within estimator approaches for estimating a fixed effects model except:

A) coefficient on treatment variable.
B) coefficient on time trend.
C) coefficient on additional control variables.
D) R-squared

Question 48

Given the regression results Unemployment Rate_it = α + 0.8 (0.3) × Alabama_it - 0.4 (0.2) × South Carolina_it + 0.2 (0.3) × North Carolina_it + 0.4 (0.12)MinimumWage_it - 0.1 (0.1)Year_t, where the coefficients are reported with their standard errors in parenthesis, what might be a fact that would make you concerned about the interpretation of the coefficient on minimum wage as being causal?

A) North Carolina has consistently had a higher share of college educated in the population relative to other states in the analysis.
B) National policies have led to stricter conditions to apply for unemployment insurance.
C) The minimum wage rate is different across many states in the southern region of the U.S.
D) In most instances, when a state raises the minimum wage it is also accompanied by state legislation that changes fiscal policy towards economic activity.

Question 49

In estimating a fixed effects model using panel data, which of the following variables will not be effective controls if you use a full set of (cross sectional) fixed effects for individuals?

A) Year to year changes in income for individuals
B) Yearly (cumulative) education attainment for individuals
C) Income taxes paid
D) Birthplace of the individual

Question 50

A potential upside of using within estimation besides the reduction in the number of parameters to be estimated is:

A) r-squared is more meaningful.
B) the coefficients will be biased.
C) the estimator will yield estimates of the fixed effects themselves.
D) the standard errors will be larger.