Question 1

Estimation of the IV regression model

Accepted Answer

A) requires exact identification. 
B) allows only one endogenous regressor, which is typically correlated with the error term. 
C) requires exact identification or overidentification. 
D) is only possible if the number of instruments is the same as the number of regressors. 
A) requires exact identification. 
B) allows only one endogenous regressor, which is typically correlated with the error term. 
C) requires exact identification or overidentification. 
D) is only possible if the number of instruments is the same as the number of regressors. C

Question 2

The TSLS estimator is

Accepted Answer

A) consistent and has a normal distribution in large samples. 
B) unbiased. 
C) efficient in small samples. 
D) F-distributed. 
A) consistent and has a normal distribution in large samples. 
B) unbiased. 
C) efficient in small samples. 
D) F-distributed. A

Question 3

The following will not cause correlation between X and u in the simple regression model:

Accepted Answer

A) simultaneous causality. 
B) omitted variables. 
C) irrelevance of the regressor. 
D) errors in variables. 
A) simultaneous causality. 
B) omitted variables. 
C) irrelevance of the regressor. 
D) errors in variables. C

Question 4

Weak instruments are a problem because

Accepted Answer

A) the TSLS estimator may not be normally distributed, even in large samples. 
B) they result in the instruments not being exogenous. 
C) the TSLS estimator cannot be computed. 
D) you cannot predict the endogenous variables any longer in the first stage. 
A) the TSLS estimator may not be normally distributed, even in large samples. 
B) they result in the instruments not being exogenous. 
C) the TSLS estimator cannot be computed. 
D) you cannot predict the endogenous variables any longer in the first stage.

Question 5

Instrument relevance

Accepted Answer

A) means that the instrument is one of the determinants of the dependent variable. 
B) is the same as instrument exogeneity. 
C) means that some of the variance in the regressor is related to variation in the instrument. 
D) is not possible since X and u are correlated and Z and u are not correlated. 
A) means that the instrument is one of the determinants of the dependent variable. 
B) is the same as instrument exogeneity. 
C) means that some of the variance in the regressor is related to variation in the instrument. 
D) is not possible since X and u are correlated and Z and u are not correlated.

Question 6

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

Accepted Answer

A) a first stage F must be statistically significant to indicate a strong instrument. B) a first stage F > 1.96 indicates that the instruments are weak. C) the t-statistic on each of the instruments must exceed at least 1.64. D) a first stage F < 10 indicates that the instruments are weak. A) a first stage F must be statistically significant to indicate a strong instrument. B) a first stage F > 1.96 indicates that the instruments are weak. C) the t-statistic on each of the instruments must exceed at least 1.64. D) a first stage F < 10 indicates that the instruments are weak.

Question 7

If the instruments are not exogenous,

Accepted Answer

A) you cannot perform the first stage of TSLS. 
B) then, in order to conduct proper inference, it is essential that you use heteroskedasticity-robust standard errors. 
C) your model becomes overidentified. 
D) then TSLS is inconsistent. 
A) you cannot perform the first stage of TSLS. 
B) then, in order to conduct proper inference, it is essential that you use heteroskedasticity-robust standard errors. 
C) your model becomes overidentified. 
D) then TSLS is inconsistent.

Question 8

In the case of the simple regression model Yi = β0 + β1Xi + ui, i = 1, …, n, when X and u are correlated, then

Accepted Answer

A) the OLS estimator is biased in small samples only. 
B) OLS and TSLS produce the same estimate. 
C) X is exogenous. 
D) the OLS estimator is inconsistent. 
A) the OLS estimator is biased in small samples only. 
B) OLS and TSLS produce the same estimate. 
C) X is exogenous. 
D) the OLS estimator is inconsistent.

Question 9

When calculating the TSLS standard errors

Accepted Answer

A) you do not have to worry about heteroskedasticity, since it was eliminated in the first stage 
B) you can use the standard errors reported by OLS estimation of the second stage regression. 
C) the critical values from the standard normal table should be adjusted for the proper degrees of freedom. 
D) you should use heteroskedasticity-robust standard errors. 
A) you do not have to worry about heteroskedasticity, since it was eliminated in the first stage 
B) you can use the standard errors reported by OLS estimation of the second stage regression. 
C) the critical values from the standard normal table should be adjusted for the proper degrees of freedom. 
D) you should use heteroskedasticity-robust standard errors.

Question 10

Having more relevant instruments

Accepted Answer

A) is a problem because instead of being just identified, the regression now becomes overidentified. 
B) is like having a larger sample size in that the more information is available for use in the IV regressions. 
C) typically results in larger standard errors for the TSLS estimator. 
D) is not as important for inference as having the same number of endogenous variables as instruments. 
A) is a problem because instead of being just identified, the regression now becomes overidentified. 
B) is like having a larger sample size in that the more information is available for use in the IV regressions. 
C) typically results in larger standard errors for the TSLS estimator. 
D) is not as important for inference as having the same number of endogenous variables as instruments.

Question 11

Consider a competitive market where the demand and the supply depend on the current price of the good. Then fitting a line through the quantity-price outcomes will

Accepted Answer

A) give you an estimate of the demand curve. 
B) estimate neither a demand curve nor a supply curve. 
C) enable you to calculate the price elasticity of supply. 
D) give you the exogenous part of the demand in the first stage of TSLS. 
A) give you an estimate of the demand curve. 
B) estimate neither a demand curve nor a supply curve. 
C) enable you to calculate the price elasticity of supply. 
D) give you the exogenous part of the demand in the first stage of TSLS.

Question 12

The distinction between endogenous and exogenous variables is

Accepted Answer

A) that exogenous variables are determined inside the model and endogenous variables are determined outside the model. 
B) dependent on the sample size: for n > 100, endogenous variables become exogenous. 
C) depends on the distribution of the variables: when they are normally distributed, they are exogenous, otherwise they are endogenous. 
D) whether or not the variables are correlated with the error term. 
A) that exogenous variables are determined inside the model and endogenous variables are determined outside the model. 
B) dependent on the sample size: for n > 100, endogenous variables become exogenous. 
C) depends on the distribution of the variables: when they are normally distributed, they are exogenous, otherwise they are endogenous. 
D) whether or not the variables are correlated with the error term.

Question 13

When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows:

Accepted Answer

A)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z Y } } { S _ { Z x } }$ 
B)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { X Y } } { S _ { X } ^ { 2 } }$ 
C)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z X } } { S _ { Z Y } }$ 
D)  $\hat { \beta } _ { 1 } ^ { \text {TSLS} } = \frac { S _ { Z Y } } { S _ { Z } ^ { 2 } }$ 
A)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z Y } } { S _ { Z x } }$ 
B)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { X Y } } { S _ { X } ^ { 2 } }$ 
C)  $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z X } } { S _ { Z Y } }$ 
D)  $\hat { \beta } _ { 1 } ^ { \text {TSLS} } = \frac { S _ { Z Y } } { S _ { Z } ^ { 2 } }$

Question 14

The two conditions for a valid instrument are

Accepted Answer

A) corr(Zi, Xi)= 0 and corr(Zi, ui)≠ 0. 
B) corr(Zi, Xi)= 0 and corr(Zi, ui)= 0. 
C) corr(Zi, Xi)≠ 0 and corr(Zi, ui)= 0. 
D) corr(Zi, Xi)≠ 0 and corr(Zi, ui)≠ 0. 
A) corr(Zi, Xi)= 0 and corr(Zi, ui)≠ 0. 
B) corr(Zi, Xi)= 0 and corr(Zi, ui)= 0. 
C) corr(Zi, Xi)≠ 0 and corr(Zi, ui)= 0. 
D) corr(Zi, Xi)≠ 0 and corr(Zi, ui)≠ 0.

Question 15

The conditions for a valid instruments do not include the following:

Accepted Answer

A) each instrument must be uncorrelated with the error term. 
B) each one of the instrumental variables must be normally distributed. 
C) at least one of the instruments must enter the population regression of X on the Zs and the Ws. 
D) perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out. 
A) each instrument must be uncorrelated with the error term. 
B) each one of the instrumental variables must be normally distributed. 
C) at least one of the instruments must enter the population regression of X on the Zs and the Ws. 
D) perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out.

Question 16

The reduced form equation for X

Accepted Answer

A) regresses the endogenous variable X on the smallest possible subset of regressors. 
B) relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest and the instruments. 
C) uses the predicted values of X from the first stage as a regressor in the original equation. 
D) uses smaller standard errors, such as homoskedasticity-only standard errors, for inference. 
A) regresses the endogenous variable X on the smallest possible subset of regressors. 
B) relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest and the instruments. 
C) uses the predicted values of X from the first stage as a regressor in the original equation. 
D) uses smaller standard errors, such as homoskedasticity-only standard errors, for inference.

Question 17

Two Stage Least Squares is calculated as follows; in the first stage:

Accepted Answer

A) Y is regressed on the exogenous variables only. The predicted value of Y is then regressed on the instrumental variables. 
B) the unknown coefficients in the reduced form equation are estimated by OLS, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables. 
C) the exogenous variables are regressed on the instruments. The predicted value of the exogenous variables is then used in the second stage, together with the instruments, to predict the dependent variable. 
D) the unknown coefficients in the reduced form equation are estimated by weighted least squares, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables. 
A) Y is regressed on the exogenous variables only. The predicted value of Y is then regressed on the instrumental variables. 
B) the unknown coefficients in the reduced form equation are estimated by OLS, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables. 
C) the exogenous variables are regressed on the instruments. The predicted value of the exogenous variables is then used in the second stage, together with the instruments, to predict the dependent variable. 
D) the unknown coefficients in the reduced form equation are estimated by weighted least squares, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables.

Question 18

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

Accepted Answer

A)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$ 
B)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$ 
C)  $\left( \hat { \beta } _ { 1 } ^ { T SLS } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z }) ^ { 2 } \right. }$ 
D)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right)u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$ 
A)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$ 
B)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$ 
C)  $\left( \hat { \beta } _ { 1 } ^ { T SLS } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z }) ^ { 2 } \right. }$ 
D)  $\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right)u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }$

Question 19

The J-statistic

Accepted Answer

A) tells you if the instruments are exogenous. 
B) provides you with a test of the hypothesis that the instruments are exogenous for the case of exact identification. 
C) is distributed $\chi _ { m - k } ^ { 2 }$ where m-k is the degree of overidentification. 
D) is distributed $\chi _ { m - k } ^ { 2 }$ where m-k is the number of instruments minus the number of regressors. 
A) tells you if the instruments are exogenous. 
B) provides you with a test of the hypothesis that the instruments are exogenous for the case of exact identification. 
C) is distributed $\chi _ { m - k } ^ { 2 }$ where m-k is the degree of overidentification. 
D) is distributed $\chi _ { m - k } ^ { 2 }$ where m-k is the number of instruments minus the number of regressors.

Question 20

The IV regression assumptions include all of the following with the exception of

Accepted Answer

A) the error terms must be normally distributed. 
B) E(ui | W1i,…, Wri)= 0. 
C) Large outliers are unlikely: the X's, W's, Z's, and Y's all have nonzero, finite fourth moments. 
D) (X1i,…, Xki, W1i,…,Wri, Z1i, … Zmi, Yi)are i.i.d. draws from their joint distribution. 
A) the error terms must be normally distributed. 
B) E(ui | W1i,…, Wri)= 0. 
C) Large outliers are unlikely: the X's, W's, Z's, and Y's all have nonzero, finite fourth moments. 
D) (X1i,…, Xki, W1i,…,Wri, Z1i, … Zmi, Yi)are i.i.d. draws from their joint distribution.

Estimation of the IV regression model

The TSLS estimator is

The following will not cause correlation between X and u in the simple regression model:

Weak instruments are a problem because

Instrument relevance

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

If the instruments are not exogenous,

In the case of the simple regression model Y_i = β₀ + β₁X_i + u_i, i = 1, …, n, when X and u are correlated, then

When calculating the TSLS standard errors

Having more relevant instruments

Consider a competitive market where the demand and the supply depend on the current price of the good. Then fitting a line through the quantity-price outcomes will

The distinction between endogenous and exogenous variables is

When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows:

The two conditions for a valid instrument are

The conditions for a valid instruments do not include the following:

The reduced form equation for X

Two Stage Least Squares is calculated as follows; in the first stage:

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

The J-statistic

The IV regression assumptions include all of the following with the exception of

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 12: Instrumental Variables Regression

Estimation of the IV regression model

The TSLS estimator is

The following will not cause correlation between X and u in the simple regression model:

Weak instruments are a problem because

Instrument relevance

The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,

If the instruments are not exogenous,

In the case of the simple regression model Yi = β0 + β1Xi + ui, i = 1, …, n, when X and u are correlated, then

When calculating the TSLS standard errors

Having more relevant instruments

Consider a competitive market where the demand and the supply depend on the current price of the good. Then fitting a line through the quantity-price outcomes will

The distinction between endogenous and exogenous variables is

When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows:

The two conditions for a valid instrument are

The conditions for a valid instruments do not include the following:

The reduced form equation for X

Two Stage Least Squares is calculated as follows; in the first stage:

(Requires Appendix material)The relationship between the TSLS slope and the corresponding population parameter is:

The J-statistic

The IV regression assumptions include all of the following with the exception of

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

Additional Topics in Time Series Regression

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

In the case of the simple regression model Y_i = β₀ + β₁X_i + u_i, i = 1, …, n, when X and u are correlated, then