Question 1

Consider the following simple regression model y=β₀ + β₁x₁ + u.The variable z is a poor instrument for x if _____.

Accepted Answer

A poor instrument for x is one that has a low correlation with x. If z has a high correlation with x, it is a strong instrument. If z has a high correlation with u, it may lead to biased estimates due to the presence of endogeneity.

Question 2

The test for overidentifying restrictions is valid if _____.

Accepted Answer

The test for overidentifying restrictions is valid under the assumption of homoskedasticity. This condition ensures that the standard errors of the estimates are correctly specified, allowing for the proper functioning of the test.

Question 3

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

Accepted Answer

The order condition for identification states that for an equation in a structural model to be identified, there must be at least as many excluded exogenous variables as there are included endogenous variables. This ensures that there are enough restrictions to uniquely estimate the coefficients of the included endogenous variables.

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?

Accepted Answer

Two-stage least squares estimation with time series data requires the assumption that the error terms are not serially correlated, as time series data are often characterized by autocorrelation in the error terms. This assumption is not required for cross sectional data, as the observations are assumed to be independent. The other assumptions listed (A, B, and C) are needed for both time series and cross sectional data.

Question 5

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

Accepted Answer

The two-stage least squares estimation method assumes that the error term has zero mean, ensuring that the instruments are uncorrelated with the error term, which is crucial for obtaining unbiased estimators.

Question 6

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

Accepted Answer

The bias direction of the ordinary least squares (OLS) estimator does not necessarily oppose that of the instrumental variable (IV) estimator. The bias in each estimator depends on the specific nature of the endogeneity or external factors affecting the variables, not on a fixed relationship between the biases of the two estimators.

Question 7

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

Accepted Answer

Instrumental variables can still be used to estimate a regression equation even if the regression model suffers from the measurement error problem, as long as the instrumental variable is correctly chosen to be correlated with the endogenous explanatory variable but uncorrelated with the error term, including the measurement error.

Question 8

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

Accepted Answer

Two stage least squares estimation can be applied to a panel data set. However, it requires instrumental variables that are time-varying and exogenous, and their validity needs to be checked carefully.

Question 9

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

Accepted Answer

Comparing different instrumental variables estimates is used to test for overidentifying restrictions, which arise when the number of instruments used in the analysis exceeds the number of endogenous explanatory variables. This test helps to ensure that the instrumental variable estimates are consistent and reliable. The other options listed (B, C, and D) are related to different types of statistical issues that can arise in econometric analysis, but are not directly applicable to the task of comparing instrumental variable estimates.

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?

Accepted Answer

The instrumental variables estimator is used to address the bias that arises when Cov(x,u)≠0, making it a suitable method in such cases.

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?

Accepted Answer

Instrument relevance requires that z is correlated with the endogenous variable x. Therefore, the correct condition is Cov(z,x)≠ 0. The other options (A and B) refer to the correlation between z and the error term u, which is not relevant for assessing instrument relevance. Option D (Cov(z,x)=0) implies that z is uncorrelated with x, which means that it cannot be a valid instrument.

Question 12

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

Accepted Answer

The answer of The necessary condition for identification of an...

Question 13

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

Accepted Answer

The sampling variance for the IV estimator is larger than the variance for the OLS estimator because the IV estimator uses additional variables (instruments) that introduce additional noise and make the estimates less precise. This is reflected in the formula for the variance of the IV estimator, which includes a term R²/S, where R² is the R-squared from the first stage regression of the instruments on the endogenous variables, and S is the covariance matrix of the instruments. This term is always greater than or equal to 1, so the IV estimator always has a larger variance than the OLS estimator. Therefore, the correct choice is D.

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?

Accepted Answer

Instrument exogeneity requires that the instrument, z, is uncorrelated with the error term, u. Therefore, Cov(z,u)= 0.

Question 15

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

Accepted Answer

The answer of Which of the following is true of...

Question 16

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

Accepted Answer

Increasing the number of overidentifying restrictions can result in overfitting, leading to biased estimates in two stage least squares estimators. This is known as the overidentification problem.

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 _____.

Accepted Answer

The answer of Consider the following simple regression model y=β₀...

Question 18

Which of the following assumptions is known as exclusion restrictions?

Accepted Answer

The answer of Which of the following assumptions is known...

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.

Accepted Answer

The variable z introduced in this situation is called an instrumental variable. An instrumental variable is a variable that is correlated with the endogenous variable of interest (in this case, x), but is uncorrelated with the error term (in this case, u). By using an instrumental variable, we can address the issue of endogeneity and obtain consistent estimators of the coefficients of interest. Dummy variables are frequently used in regression models to represent categorical variables, lagged dependent variables are used to model autoregressive processes, and random variables do not have a specific meaning in this context.

Question 20

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

Accepted Answer

The two-stage least squares (2SLS) estimator is designed for situations where there are endogenous explanatory variables, using instrumental variables to address the endogeneity. When the explanatory variables are exogenous, the ordinary least squares (OLS) estimator is more efficient (i.e., it has a smaller variance) than the 2SLS estimator, because OLS does not suffer from the inefficiencies introduced by the use of instrumental variables, which are necessary in 2SLS to correct for endogeneity.

Quiz 15: Instrumental Variables Estimation and Two Stage Least Squares

Consider the following simple regression model y=β₀ + β₁x₁ + u.The variable z is a poor instrument for x if _____.

The test for overidentifying restrictions is valid if _____.

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

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?

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

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

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

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

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

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

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?

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

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

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?

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

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

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 _____.

Which of the following assumptions is known as exclusion restrictions?

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

Quiz 15: Instrumental Variables Estimation and Two Stage Least Squares

Consider the following simple regression model y=β0 + β1x1 + u.The variable z is a poor instrument for x if _____.

The test for overidentifying restrictions is valid if _____.

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

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?

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

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

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

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

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

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

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?

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

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

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?

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

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

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 _____.

Which of the following assumptions is known as exclusion restrictions?

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

Consider the following simple regression model y=β₀ + β₁x₁ + u.The variable z is a poor instrument for x if _____.

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

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?

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?

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 _____.