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Unformatted text preview: Econ 104  Problem Set 5 Lorenzo Braccini * December 7, 2011 Question 1 a) First note the following: Q s i = Q d i 1 P i =  + u d i u s i Now consider this fact: Cov( 1 P i ,u s i ) = Cov(  + u d i u s i ,u s i ) = Var( u s i ) = 1 Cov( P i ,u s i ) Hence for 1 6 = 0 (in particular we expect 1 > 0) we have that: Cov( P i ,u s i ) = Var( u s i ) 1 Therefore we can conclude that there is (negative) correlation be tween P i and u s i . b) No, the OLS estimator is not consistent in this case. In fact: b 1 = 1 + ( 1 n n i =1 P i u s i ) P u s 1 n n i =1 ( P i P ) 2 * blorenzo@sas.upenn.edu 1 Now note that: 1 n n X i =1 P i u s i p E [ P i u s i ] = Cov( P i ,u s i ) P u s p E [ P i ] E [ u s i ] = 0 and that: 1 n n X i =1 ( P i P ) 2 p Var( P i ) Finally, the last three facts imply that: b 1 p 1 + Cov( P i ,u s i ) Var( P i ) = 1 + ( P,u s ) u s P c) Suppose it exists an observable random variable Z i such that: Cov( Z i ,u s i ) = 0 Cov( P i ,Z i ) 6 = 0 i.e. a valid instrument. I would then estimate and 1 by 2SLS using Z i as instrument for P i . I would then estimate using the sample average of Q d i ....
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This note was uploaded on 02/29/2012 for the course GG 101 taught by Professor Gg during the Spring '12 term at UPenn.
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