Consider the linear regression model y = X3 + e, e~ IID(0, oIn), where y and...
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Consider the linear regression model y = X3 + e, e~ IID(0, o²In), where y and are n x 1, X is n x k and non-random, and 3 is k x 1. Let W be an n x l non-random matrix of instruments with 1> k. The test of overidentifying restrictions in this model can be derived from the test regression Wb + error term, where ê=y-X3₁y are the IV residuals, as n times the uncentered R² from the test regression. Show that this test statistic is equal to the Sargan test statistic, that is, the minimized IV criterion function for the model divided by the IV estimate of the error variance for the model. Consider the linear regression model y = X3 + e, e~ IID(0, o²In), where y and are n x 1, X is n x k and non-random, and 3 is k x 1. Let W be an n x l non-random matrix of instruments with 1> k. The test of overidentifying restrictions in this model can be derived from the test regression Wb + error term, where ê=y-X3₁y are the IV residuals, as n times the uncentered R² from the test regression. Show that this test statistic is equal to the Sargan test statistic, that is, the minimized IV criterion function for the model divided by the IV estimate of the error variance for the model.
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Related Book For
Statistics Principles and Methods
ISBN: 978-0470904114
7th edition
Authors: Richard A. Johnson, Gouri K. Bhattacharyya
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