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?

Accepted Answer

The instrumental variable approach is used to address endogeneity in the treatment variable by finding an instrument that is correlated with the treatment but not with unobserved factors affecting the outcome. By using only the variation of the treatment variable that is explained by the instrument, we ensure that the estimate of the treatment effect is based only on exogenous variation to the other factors affecting the outcome. Therefore, choice C is the correct answer.

Question 2

A variable is exogenous if that variable:

Accepted Answer

B

Question 3

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

Accepted Answer

The first-stage regression is used to determine whether the instrumental variable is relevant. If the coefficient on the instrumental variable is statistically significant, then it can be used in the second-stage regression. Thus, option C is the best choice as it checks whether the coefficient on the instrumental variable in the first stage is statistically different from zero.

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?

Accepted Answer

Wholesale costs being uncorrelated with the number of competitors suggests that they do not share the same confounding factor, satisfying the exogeneity condition for an instrumental variable.

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?

Accepted Answer

Wholesale costs need to be correlated with price to serve as a valid instrument, as they must affect the endogenous variable (price) to help identify its causal effect on sales.

Question 6

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

Accepted Answer

Two-stage least squares involves running two regressions to account for potential endogeneity and measure the causal effect of a variable. It uses an instrumental variable to address the endogeneity issue by first regressing the endogenous variable on the instrumental variable, then using the predicted values from that regression as the independent variable in a second regression to estimate the causal effect. Nonlinear least squares, difference in difference, and probit are not methods specifically designed for addressing endogeneity in causal inference.

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:

Accepted Answer

Two-stage least squares (2SLS) and generalized method of moments (GMM) are the two methods typically used in estimating a regression model with an instrumental variable. While fixed effects regression and within estimator are also commonly used in econometrics, they are not specific to instrumental variable estimation. Panel data methods may include instrumental variable techniques, but are not a broader category that includes other methods as well. Therefore, the best choice is C, which includes the two methods specific to instrumental variable estimation.

Question 8

Two-stage least squares can be executed:

Accepted Answer

Two-stage least squares involves first regressing the endogenous variable(s) on the exogenous variables and instruments, and then using the predicted values from this regression as the new "exogenous" variable(s) in a second regression of the endogenous variable on these predicted values and the remaining exogenous variables. This can be done by simply running two separate regressions and using the predicted values from the first as inputs in the second, so it can be done straightforwardly without advanced software or panel data sets.

Question 9

A weak instrument is an instrumental variable:

Accepted Answer

A weak instrument is one whose partial correlation with the endogenous treatment variable is small, meaning that it explains very little of the variation in the treatment variable. This makes it difficult to use the instrument to identify the causal effect of the treatment on the outcome. The other choices are not necessarily indicative of a weak instrument.

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):

Accepted Answer

An instrumental variable is a variable that is correlated with the treatment variable but is not directly related to the outcome. It allows us to isolate the causal effect of the treatment on the outcome by acting as a control for unobserved confounding variables. Control variables, difference in difference estimators, and dummy variables are not specifically designed to isolate causal effects in this way.

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?

Accepted Answer

Condition C, Cov(X, Y) ≠ 0, is not necessary for Z to be a valid instrument for X. The validity of an instrumental variable requires it to be correlated with the independent variable X (A) and not correlated with the error term U (B), but it does not require X and Y to be correlated once we control for the instrument.

Question 12

An instrumental variable is relevant if that variable is:

Accepted Answer

An instrumental variable is relevant if it is correlated with the treatment after controlling for other control variables in the determining function. Option A and B are not correct because a dichotomous variable and normal distribution are not the only qualifications for an instrumental variable. Option C is also not correct because a consistent estimator of the coefficient on the treatment is necessary, but not sufficient for an instrumental variable to be relevant.

Question 13

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

Accepted Answer

A weak instrument can lead to imprecise coefficient estimates, with large standard errors. This is because a weak instrument has little ability to explain the variation in the endogenous variable, making it difficult to properly identify the causal effect of the independent variable on the dependent variable. As a result, the estimated coefficients may be less reliable and less precise.

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?

Accepted Answer

The critical object from the first stage of two-stage least squares (2SLS) regression to incorporate in the second stage is the estimated predictions for the endogenous variable. This is because the second stage uses these predictions as a proxy for the actual values of the endogenous variable to address potential endogeneity issues.

Question 15

Suppose you are trying to estimate the following regression: Y_i = β₀ + β₁X₁_i + β₂X₂_i + β₃X₃_i + U_i, with an instrument for Z_i for X₂_i. 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?

Accepted Answer

The first stage of the two-stage least squares involves regressing the endogenous variable (Y_i) on the instrument (X₂_i) and all other exogenous variables (X₁_i, X₂_i, X₃_i, and Z_i). Therefore, Y_i is not included in the first stage.

Question 16

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

Accepted Answer

An instrumental variable is used to address endogeneity in a determining function, where the variable of interest may be affected by unobservable factors. An instrumental variable is not found directly in the determining function because it is chosen to be correlated with the endogenous variable but not directly related to the outcome variable. This allows the effect of the endogenous variable on the outcome variable to be estimated without bias.

Question 17

Suppose you are trying to estimate the following regression: Y_i = β₀ + β₁X₁_i + β₂X₂_i + β₃X₃_i + U_i, with an instrument for Z_i for X₂_i. 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?

Accepted Answer

In the second stage of two-stage least squares (2SLS), the instrumented variable (in this case, $X_{2i}$) is replaced by its predicted values from the first stage. Therefore, the original variable $X_{2i}$ will not be included directly in the second stage regression; instead, its predicted values from the first stage are used.

Question 18

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

Accepted Answer

An instrumental variable must be relevant, meaning it is correlated with the endogenous explanatory variable, and exogenous, meaning it is not correlated with the error term in the regression model.

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?

Accepted Answer

The standard errors reported in the second stage of a two-stage least squares estimation are not accurate because the procedure does not account for the fact that the fitted values used as regressors in the second stage are estimated, not observed, quantities. This can lead to underestimation of the true standard errors.

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?

Accepted Answer

Instrumental variables allow for the identification of causal effects by using variation in the treatment that is not correlated with unobserved variables that could confound the relationship between the treatment and the outcome. This helps in isolating the direct effect of the treatment from other factors.

Quiz 8: Advanced Methods for Establishing Causal Inference

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 variable is exogenous if that variable:

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

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

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

Two-stage least squares can be executed:

A weak instrument is an instrumental variable:

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) :

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?

An instrumental variable is relevant if that variable is:

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

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

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

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

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?

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

Quiz 8: Advanced Methods for Establishing Causal Inference

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 variable is exogenous if that variable:

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

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

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

Two-stage least squares can be executed:

A weak instrument is an instrumental variable:

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) :

All of the following conditions are necessary for an instrumental variable Z to be a valid instrument for X in the regression: Yi = β0 + β1Xi + Ui except for which condition?

An instrumental variable is relevant if that variable is:

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

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

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

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

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?

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

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?