Question 1

Consider the following simple regression model y = 0 +   1x1 + u. The variable z is a poor instrument for x if _____. A) there is a high correlation between z and x B) there is a low correlation between z and x C) there is a high correlation between z and u D) there is a low correlation between z and u" class="answers-bank-image d-inline" rel="preload" > 0 + 0 +   1x1 + u. The variable z is a poor instrument for x if _____. A) there is a high correlation between z and x B) there is a low correlation between z and x C) there is a high correlation between z and u D) there is a low correlation between z and u" class="answers-bank-image d-inline" rel="preload" > 1x1 + u. The variable z is a poor instrument for x if _____.

Accepted Answer

A)  there is a high correlation between z and x
B)  there is a low correlation between z and x
C)  there is a high correlation between z and u
D)  there is a low correlation between z and uE) C) and D)
F) All of the above

Question 2

​A standard linear model which is supposed to measure a causal relationship is called a structural equation.

Accepted Answer

A) True 
 B)False

Question 3

Consider the following simple regression model: y = 0 +   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity? A) Cov(z,u)  > 0 B) Cov(z,x)  > 0 C) Cov(z,u)  = 0 D) Cov(z,x)  = 0" class="answers-bank-image d-inline" rel="preload" > 0 + 0 +   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity? A) Cov(z,u)  > 0 B) Cov(z,x)  > 0 C) Cov(z,u)  = 0 D) Cov(z,x)  = 0" class="answers-bank-image d-inline" rel="preload" > 1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity?

Accepted Answer

A)  Cov(z,u)  > 0
B)  Cov(z,x)  > 0
C)  Cov(z,u)  = 0
D)  Cov(z,x)  = 0E) All of the above
F) C) and D)

Question 4

Which of the following assumptions is required for two stages least squares estimation with time series data but not required for two-stage least squares estimation with cross sectional data?

Accepted Answer

A)  The conditional mean of the error term is zero.
B)  The error term has constant conditional variance.
C)  The model includes at least one dummy variable.
D)  The error terms are not serially correlated.E) A) and B)
F) A) and C) D

Question 5

What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous.

Accepted Answer

A)  The explanatory variable is not endogenous and therefore using 2SLS is ill-advised.
B)  The explanatory variable is not endogenous and therefore OLS should not be used.
C)  The explanatory variable is endogenous and therefore using 2SLS should be considered.
D)  The explanatory variable is endogenous and therefore OLS should be used.E) A) and B)
F) B) and D)

Question 6

The order condition for identification of an equation requires that there should be _____.

Accepted Answer

A)  at least one exogenous explanatory variable in a structural equation
B)  at least as many excluded exogenous explanatory variables as there are included endogenous explanatory variables
C)  at least as many dummy variables in an equation as there are exogenous explanatory variables
D)  as many lagged independent variables in an equation as there are exogenous explanatory variablesE) A) and C)
F) A) and D)

Question 7

If the instrumental variable estimator has an upward bias, the ordinary least square estimator always has a downward bias.

Accepted Answer

A) True 
 B)False  False

Question 8

Which of the following assumptions is required for two-stage least squares estimation method?

Accepted Answer

A)  There are perfect linear relationships among the instrumental variables.
B)  There is strong correlation between each instrumental variable and the error term.
C)  The conditional variance of the error term depends on an exogenous explanatory variable.
D)  The error term has zero mean.E) None of the above
F) A) and B)

Question 9

Which does an intention-to-treat parameter measure in a program evaluation study?

Accepted Answer

A)  The effect of participation in the program.
B)  The effect of the program on those who were eligible but did not participate.
C)  The effect of being eligible to participate in the program.
D)  The effect on the probability of participation due to being eligible to participate.E) A) and C)
F) All of the above

Question 10

Identification fails when there are more included endogenous variables than excluded exogenous variables in the structural equation.

Accepted Answer

A) True 
 B)False

Question 11

If we focus only on consistency, it is necessarily better to use IV than OLS if the correlation between z and u is smaller than that between x and u.

Accepted Answer

A) True 
 B)False

Question 12

The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing _____.

Accepted Answer

A)  overidentifying restrictions
B)  endogeneity
C)  heteroskedasticity
D)  serial correlationE) A) and D)
F) B) and D)

Question 13

​Consider the following simple regression model y = β0 + β1x1 + u. Suppose Corr(x,u)  > 0, Corr(z,x)  > 0, and Corr(z,u)  < 0. Then, the OLS estimator has a(n)  _____.

Accepted Answer

A)  ​downward bias
B)  asymptotic bias
C)  ​upward bias
D)  substantial biasE) C) and D)
F) All of the above

Question 14

The sampling variance for the instrumental variables (IV)  estimator is larger than the variance for the ordinary least square estimators (OLS)  because _____.

Accepted Answer

A)  R2 > 1
B)  R2 
C)  R2 = 1
D)  R2 < 1E) B) and C)
F) All of the above

Question 15

Two stage least squares estimation cannot be applied to a panel data set.​

Accepted Answer

A) True 
 B)False  False

Question 16

Consider the following simple regression model: y = 0 +   1x1 + u. In order to obtain consistent estimators of   0 and   1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)    0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable. A) dummy B) instrumental C) lagged dependent D) random" class="answers-bank-image d-inline" rel="preload" > 0 + 0 +   1x1 + u. In order to obtain consistent estimators of   0 and   1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)    0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable. A) dummy B) instrumental C) lagged dependent D) random" class="answers-bank-image d-inline" rel="preload" > 1x1 + u. In order to obtain consistent estimators of 0 +   1x1 + u. In order to obtain consistent estimators of   0 and   1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)    0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable. A) dummy B) instrumental C) lagged dependent D) random" class="answers-bank-image d-inline" rel="preload" > 0 and 0 +   1x1 + u. In order to obtain consistent estimators of   0 and   1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)    0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable. A) dummy B) instrumental C) lagged dependent D) random" class="answers-bank-image d-inline" rel="preload" > 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)  0 +   1x1 + u. In order to obtain consistent estimators of   0 and   1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x)    0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable. A) dummy B) instrumental C) lagged dependent D) random" class="answers-bank-image d-inline" rel="preload" > 0 and Cov (z,u)  = 0. The variable z is called a(n)  _____ variable.

Accepted Answer

A)  dummy
B)  instrumental
C)  lagged dependent
D)  randomE) B) and C)
F) A) and C)

Question 17

Which of the following is true of two stage least squares estimators?

Accepted Answer

A)  The two stage least squares estimator is equal to the instrumental variable estimator if R2 is equal to 1.
B)  The two stage least squares estimators are biased if the regression model exhibits multicollinearity.
C)  The two stage least squares estimators have lower variance than the ordinary least squares estimators.
D)  The two stage least squares estimators have large standard errors when R2 lies close to 0.E) B) and D)
F) A) and B)

Question 18

The necessary condition for identification of an equation is called the _____.

Accepted Answer

A)  order condition
B)  rank condition
C)  condition of instrumental exogeneity
D)  the condition of instrumental relevanceE) A) and D)
F) A) and C)

Question 19

Consider the following simple regression model y = 0 +   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance? A) Cov(z,u)  > 0 B) Cov(z,u)   0 + 0 +   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance? A) Cov(z,u)  > 0 B) Cov(z,u)   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance?

Accepted Answer

A)  Cov(z,u)  > 0
B)  Cov(z,u)  
C)  Cov(z,x)  0 +   1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance? 
A)  Cov(z,u)  > 0 
B)  Cov(z,u)   0
D)  Cov(z,x z)  = 0E) A) and C)
F) None of the above

Question 20

Consider the following simple regression model y = β0 + β1x1 + u and z is an instrument for x. Suppose x and z are both positively correlated with u and Corr(z,x)  > 0. Then, the asymptotic bias in the IV estimator is less than that for OLS only if:​

Accepted Answer

A)  ​Corr(z,u) / Corr(z,x)  = Corr(x,u) .
B)  ​Corr(z,u) / Corr(z,x)  > Corr(x,u) .
C)  ​Corr(z,u) / Corr(z,x)  
D)  ​Corr(z,u) / Corr(z,x)  ≠ Corr(x,u) .E) A) and B)
F) A) and C)

Exam 15: Instrumental Variables Estimation and Two Strage Least Squares

Consider the following simple regression model y = ₀ + ₁x₁ + u. The variable z is a poor instrument for x if _____.

Correct Answer
verified

A standard linear model which is supposed to measure a causal relationship is called a structural equation.

Correct Answer
verified

Consider the following simple regression model: y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity?

Correct Answer
verified

Which of the following assumptions is required for two stages least squares estimation with time series data but not required for two-stage least squares estimation with cross sectional data?

Correct Answer
verified
D

What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous.

Correct Answer
verified

The order condition for identification of an equation requires that there should be _____.

Correct Answer
verified

If the instrumental variable estimator has an upward bias, the ordinary least square estimator always has a downward bias.

Correct Answer
verified
False

Which of the following assumptions is required for two-stage least squares estimation method?

Correct Answer
verified

Which does an intention-to-treat parameter measure in a program evaluation study?

Correct Answer
verified

Identification fails when there are more included endogenous variables than excluded exogenous variables in the structural equation.

Correct Answer
verified

If we focus only on consistency, it is necessarily better to use IV than OLS if the correlation between z and u is smaller than that between x and u.

Correct Answer
verified

The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing _____.

Correct Answer
verified

Consider the following simple regression model y = β₀ + β₁x₁ + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the OLS estimator has a(n) _____.

Correct Answer
verified

The sampling variance for the instrumental variables (IV) estimator is larger than the variance for the ordinary least square estimators (OLS) because _____.

Correct Answer
verified

Two stage least squares estimation cannot be applied to a panel data set.

Correct Answer
verified
False

Correct Answer
verified

Which of the following is true of two stage least squares estimators?

Correct Answer
verified

The necessary condition for identification of an equation is called the _____.

Correct Answer
verified

Consider the following simple regression model y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance?

Correct Answer
verified

Consider the following simple regression model y = β₀ + β₁x₁ + u and z is an instrument for x. Suppose x and z are both positively correlated with u and Corr(z,x) > 0. Then, the asymptotic bias in the IV estimator is less than that for OLS only if:

Correct Answer
verified

Exam 15: Instrumental Variables Estimation and Two Strage Least Squares

Consider the following simple regression model y = 0 + 1x1 + u. The variable z is a poor instrument for x if _____.

Correct AnswerverifiedShow Answer

​A standard linear model which is supposed to measure a causal relationship is called a structural equation.

Correct AnswerverifiedShow Answer

Consider the following simple regression model: y = 0 + 1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity?

Correct AnswerverifiedShow Answer

Which of the following assumptions is required for two stages least squares estimation with time series data but not required for two-stage least squares estimation with cross sectional data?

Correct AnswerverifiedD

What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous.

Correct AnswerverifiedShow Answer

The order condition for identification of an equation requires that there should be _____.

Correct AnswerverifiedShow Answer

If the instrumental variable estimator has an upward bias, the ordinary least square estimator always has a downward bias.

Correct AnswerverifiedFalse

Which of the following assumptions is required for two-stage least squares estimation method?

Correct AnswerverifiedShow Answer

Which does an intention-to-treat parameter measure in a program evaluation study?

Correct AnswerverifiedShow Answer

Identification fails when there are more included endogenous variables than excluded exogenous variables in the structural equation.

Correct AnswerverifiedShow Answer

If we focus only on consistency, it is necessarily better to use IV than OLS if the correlation between z and u is smaller than that between x and u.

Correct AnswerverifiedShow Answer

The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing _____.

Correct AnswerverifiedShow Answer

​Consider the following simple regression model y = β0 + β1x1 + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the OLS estimator has a(n) _____.

Correct AnswerverifiedShow Answer

The sampling variance for the instrumental variables (IV) estimator is larger than the variance for the ordinary least square estimators (OLS) because _____.

Correct AnswerverifiedShow Answer

Two stage least squares estimation cannot be applied to a panel data set.​

Correct AnswerverifiedFalse

Correct AnswerverifiedShow Answer

Which of the following is true of two stage least squares estimators?

Correct AnswerverifiedShow Answer

The necessary condition for identification of an equation is called the _____.

Correct AnswerverifiedShow Answer

Consider the following simple regression model y = 0 + 1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance?

Correct AnswerverifiedShow Answer

Consider the following simple regression model y = β0 + β1x1 + u and z is an instrument for x. Suppose x and z are both positively correlated with u and Corr(z,x) > 0. Then, the asymptotic bias in the IV estimator is less than that for OLS only if:​

Correct AnswerverifiedShow Answer

Consider the following simple regression model y = ₀ + ₁x₁ + u. The variable z is a poor instrument for x if _____.

Correct Answer
verified

A standard linear model which is supposed to measure a causal relationship is called a structural equation.

Correct Answer
verified

Consider the following simple regression model: y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity?

Correct Answer
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Correct Answer
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D

Correct Answer
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Correct Answer
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Correct Answer
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False

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Consider the following simple regression model y = β₀ + β₁x₁ + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the OLS estimator has a(n) _____.

Correct Answer
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Correct Answer
verified

Two stage least squares estimation cannot be applied to a panel data set.

Correct Answer
verified
False

Correct Answer
verified

Correct Answer
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Correct Answer
verified

Consider the following simple regression model y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance?

Correct Answer
verified

Consider the following simple regression model y = β₀ + β₁x₁ + u and z is an instrument for x. Suppose x and z are both positively correlated with u and Corr(z,x) > 0. Then, the asymptotic bias in the IV estimator is less than that for OLS only if:

Correct Answer
verified