Transcription of CHAPTER 4. INSTRUMENTAL VARIABLES
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1 Econ. 240B D. McFadden, 1999 CHAPTER 4. INSTRUMENTAL VARIABLES1. INTRODUCTIONC onsider the linear model y = X + , where y is n 1, X is n k, is k 1, and is n that contamination of X, where some of the X VARIABLES are correlated with , is can occur, for example, if contains omitted VARIABLES that are correlated with the includedvariables, if X contains measurement errors, or if X contains endogenous VARIABLES that aredetermined jointly with Revisited: Premultiply the regression equation by X to get (1) X y = X X + X.
IV estimator (7) when E = σ2Ω can be reinterpreted as a conve ntional 2SLS estimator applied to the transformed regression Ly = LX β + η using the instruments (L )-1W, where L is a Cholesky array that satisfies LΩL = I. When Ω depends on unknown parameters, it is often possible to use a
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