Deck 15: Instrumental Variables Estimation and Two Stage Least Squares

Question 1

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.

Answer 1

D
Explanation: The additional assumption required for two stage least squares estimation using time-series data is that there is no serial correlation.

Question 2

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

Answer 2

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

Question 3

Consider the following simple regression model y = ₀ + ₁x₁ + 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 .

Answer 3

C
Explanation: The instrumental variables estimator is always biased if Cov(x,u) 0.

Question 4

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

Question 5

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

Question 6

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 7

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

Question 8

​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) _____.

A)​downward bias
B)asymptotic bias
C) ​upward bias
D) substantial bias

Question 9

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 10

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 11

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 12

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

Question 13

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

Question 14

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 is 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 15

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

Question 16

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
C) Cov(z,x)
0
D) Cov(z,x z) = 0

Question 17

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 IV estimator has a(n) _____.​

A)​downward bias
B)​asymptotic bias
C) ​upward bias
D) ​substantial bias

Question 18

Consider the following simple regression model y = ₀ + ₁x₁ + u. Suppose z is an instrument for x. if Cov(z,u) = 0 and Cov(z,x) 0, the value of ₁ in terms of population covariances is _____.

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

Question 19

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:​

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) < Corr(x,u).
D) ​Corr(z,u)/ Corr(z,x) ≠ Corr(x,u).

Question 20

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

A)R² > 1
B)R² < 0
C) R² = 1
D) R² < 1

Question 21

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.

Question 22

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

Question 23

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

Question 24

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

Question 25

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