Deck 15: Instrumental Variables Estimation and Two Stage Least Squares

Question 1

Consider the following simple regression model y=β₀ + β₁x₁ + 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

Answer 1

B

Question 2

The test for overidentifying restrictions is valid if _____.

A)the regression model exhibits heteroskedasticity
B)the regression model exhibits homoskedasticity
C)the number of instrumental variables are less than the number of endogenous explanatory variables
D)the number of instrumental variables are just enough for obtaining consistent estimators.

Answer 2

B

Question 3

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

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 variables

Answer 3

B

Question 4

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

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.

Question 5

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

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.

Question 6

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

Question 7

Instrumental variables cannot be used for estimating a regression equation if the regression model suffers from the measurement error problem.

Question 8

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

Question 9

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

A)overidentifying restrictions
B)endogeneity
C)heteroskedasticity
D)serial correlation

Question 10

Consider the following simple regression model y=β₀+ β₁x₁+ u.Suppose z is an instrument for x. Which of the following statements is true?

A)The condition Cov(z,u)= 0 can be tested statistically.
B)The condition Cov(z,x)≠ 0 cannot be tested statistically.
C)The instrumental variables estimator is always biased if Cov(x,u)≠0.
D)The ordinary least squares estimator is unbiased if Cov(x,u)≠0.

Question 11

Consider the following simple regression model y=β₀+ β₁x₁+ 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
C)Cov(z,x)≠ 0
D)Cov(z,x)=0

Question 12

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

A)order condition
B)rank condition
C)condition of instrumental exogeneity
D)the condition of instrumental relevance.

Question 13

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

A)R?² >1
B)R?² <0
C)R?² =1
D)R?² <1

Question 14

Consider the following simple regression model: y = β₀+ β₁x₁+ 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

Question 15

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

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.

Question 16

Increasing the number of overidentifying restrictions can cause severe biases in two stage least squares estimators.

Question 17

Consider the following simple regression model y=β₀ + β₁x₁ + u.Suppose z is an instrument for x.if Cov(z,u)= 0 and Cov(z,x)≠ 0,the value of β₁in terms of population covariances is _____.

A)
B)
C)Cov(z,u)
D)Cov(z,x)

Question 18

Which of the following assumptions is known as exclusion restrictions?

A)The assumption that an instrumental variable is excluded from a regression model and is correlated with the error term
B)The assumption that an instrumental variable is excluded from a regression model and correlated with an exogenous explanatory variable
C)The assumption that an exogenous explanatory variable is excluded from a regression model and is uncorrelated with the error term
D)The assumption that an endogenous explanatory variable excluded from a regression model and is uncorrelated with the error term

Question 19

Consider the following simple regression model: y = β₀+ β₁x₁+ u.In order to obtain consistent estimators of β₀and β₁,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 variable
D)random

Question 20

The two stage least squares estimator is less efficient than the ordinary least squares estimator when the explanatory variables are exogenous.