Transcription of CHAPTER 4. INSTRUMENTAL VARIABLES
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CHAPTER 4. INSTRUMENTAL VARIABLES
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 . One can interpret the OLS estimate bOLS as the solution obtained from (1) by first approximating X by zero, and then solving the resulting k equations in k unknowns,(2) X y = X XbOLS, for the unknown coefficients.
In truth, the conditional expectation of ν given W X is not necessarily zero, but clean instruments will have the property that (W X) /n p 0 because W and are uncorrelated in the population. This is enough to make the ... moments. Their appeal relies on their behavior in large samples, although an important question is ...
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