MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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In which of the following cases is an instrumental variable not used to obtain a consistent estimator of the unknown coefficients of the population regression function?
A. It is not used when there is an omitted variable bias due to the omission of a variable from the regression equation which is correlated with both the regressor and the regressand.
B. It is not used when there is correlation between the regressors.
C. It is not used when there is measurement errors in the regressors.
D. It is not used when there is simultaneous causality between the regressor and the regressand.
Suppose an instrumental variable regression model with one regressor, X, and one instrument, Z, is of the form:
Y; = Bo +B,X; + Uj,
where
U;
and B, denote the error term which incorporates all the factors affecting the regressand which are not included in the model and the slope coefficient on X, respectively.
Which of the following conditions need to be fulfilled for the instrument to be valid? (Check all that apply.)
A. The instrument must be uncorrelated with the error term, i.e., corr (Z;, u;) = 0.
B. The instrument must be correlated with the regressor, i.e., corr (Z;, X;) # 0.
C. The instrument must be uncorrelated with the regressand, i.e., corr (Z;, Y;) = 0.
D. The instrument must be uncorrelated with the regressor, i.e., corr (Z;, X;) = 0.
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Transcribed Image Text:In which of the following cases is an instrumental variable not used to obtain a consistent estimator of the unknown coefficients of the population regression function? A. It is not used when there is an omitted variable bias due to the omission of a variable from the regression equation which is correlated with both the regressor and the regressand. B. It is not used when there is correlation between the regressors. C. It is not used when there is measurement errors in the regressors. D. It is not used when there is simultaneous causality between the regressor and the regressand. Suppose an instrumental variable regression model with one regressor, X, and one instrument, Z, is of the form: Y; = Bo +B,X; + Uj, where U; and B, denote the error term which incorporates all the factors affecting the regressand which are not included in the model and the slope coefficient on X, respectively. Which of the following conditions need to be fulfilled for the instrument to be valid? (Check all that apply.) A. The instrument must be uncorrelated with the error term, i.e., corr (Z;, u;) = 0. B. The instrument must be correlated with the regressor, i.e., corr (Z;, X;) # 0. C. The instrument must be uncorrelated with the regressand, i.e., corr (Z;, Y;) = 0. D. The instrument must be uncorrelated with the regressor, i.e., corr (Z;, X;) = 0.
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