Chapter 15
1. Consider the following simple regression model: y = β0 + β1x1 + u. In order to obtain consistent
estimators of β0 and 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
2. 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
3. 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
4. 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.
5. 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 β1 in terms of population covariances is _____.
a.Cov(z,y)
Cov(z,x)
b. Cov(z,u)
Cov(z,x)
c. Cov(z,u)
d. Cov(z,x)
6. 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
7. 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
8. 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
9. 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.
10. 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.
11. 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.
12. 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
13. 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
14. 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.
15. 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.
16. If the instrumental variable estimator has an upward bias, the ordinary least square estimator
always has a downward bias.
17. Instrumental variables cannot be used for estimating a regression equation if the regression model
suffers from the measurement error problem.
18. The two stage least squares estimator is less efficient than the ordinary least squares estimator
when the explanatory variables are exogenous.
19. Increasing the number of overidentifying restrictions can cause severe biases in two stage least
squares estimators.
20. Two stage least squares estimation cannot be applied to a panel data set.