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Unformatted text preview: University of California D. Steigerwald Department of Economics Economics 140A Exercise 7 1. Consider the population model (in deviation-from-means form) , * t t t U X Y in which * t X is latent. The observed regressor is , * t t t V X X in which t V is independent of t U . Further, we know that t V and t U are symmetrically distributed about 0. a. Detail why, in the presence of measurement error, is not identified. b. Let med(X) be the median of n X X , , 1 and define 1 t Z if X med X t 1 t Z if X med X t . In certain texts, t Z has been advanced as a valid instrument. Is t Z a valid instrument? c. Can the assumption that t V is symmetrically distributed about 0 restore identification? If so, construct the corresponding estimator of . 2. Consider the simple model in deviation-from-means form (1) Y t = X t + U t . Inspection of the distribution of the residuals reveals that V(U t ) = 2 2 t Z , where Z t is known, so that you know the error variance up to a multiplicative constant....
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08