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Solutions Manual

Econometric Analysis
Fifth Edition

William H. Greene
New York University

Prentice Hall, Upper Saddle River, New Jersey 07458

Contents and Notation
Chapter 1 Introduction 1 Chapter 2 The Classical Multiple Linear Regression Model 2 Chapter 3 Least Squares 3 Chapter 4 Finite-Sample Properties of the Least Squares Estimator 7 Chapter 5 Large-Sample Properties of the Least Squares and Instrumental Variables Estimators 14 Chapter 6 Inference and Prediction 19 Chapter 7 Functional Form and Structural Change 23 Chapter 8 Specification Analysis and Model Selection 30 Chapter 9 Nonlinear Regression Models 32 Chapter 10 Nonspherical Disturbances - The Generalized Regression Model 37 Chapter 11 Heteroscedasticity 41
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The residual vector in the regression of y on X is MXy = [I - X(X′X)-1X′]y. The residual vector in the regression of y on Z is = [I - Z(Z′Z)-1Z′]y MZy = [I - XP((XP)′(XP))-1(XP)′)y = [I - XPP-1(X′X)-1(P′)-1P′X′)y = MXy Since the residual vectors are identical, the fits must be as well. Changing the units of measurement of the regressors is equivalent to postmultiplying by a diagonal P matrix whose kth diagonal element is the scale factor to be applied to the kth variable (1 if it is to be unchanged). It follows from the result above that this will not change the fit of the regression. 4. In the least squares regression of y on a constant and X, in order to compute the regression coefficients on X, we can first transform y to deviations from the mean, y , and, likewise, transform each column of X to deviations from the respective column means; second, regress the transformed y on the transformed X without a constant. Do we get the same result if we only transform y? What if we only transform X?


In the regression of y on i and X, the coefficients on X are b = (X′M0X)-1X′M0y. M0 = I - i(i′i)-1i′ is the matrix which transforms observations into deviations from their column means. Since M0 is idempotent and symmetric we may also write the preceding as [(X′M0′)(M0X)]-1(X′M0′M0y) which implies that the regression of M0y on M0X produces the least squares

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