e3-245a - Y t y t = X t E V t v t If Ý V t v t Þ have...

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Economics 245A Exercise 3 Consider the regression model with a jointly endogeneous regressor Y t = y t K + X t L + U t , in which y t = Y t J + X t N + u t . Let X t be a scalar regressor and assume that a valid scalar instrument Z t exists. a) Is K identified within this framework? Show that the IV estimator can be expressed as B = > c t Y t > c t y t . b) Let > c t Y t = M 1 and let > c t y t = M 2 .I f Ý M 1 , M 2 Þ has a uniform distribution over the rectangle Ý ? a , a Þ × Ý ? a , a Þ , show that the probability density of B is pdf Ý b Þ = 1 4 ? 1 ² b ² 1 1 4 b 2 | b | > 1 .
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Unformatted text preview: Y t y t = X t E + V t v t . If Ý V t , v t Þ have independent uniform distributions over the rectangle Ý ? a , a Þ × Ý ? a , a Þ , show that the limiting distribution of B is Cauchy. Does this result hold under more general conditions? d) Suppose that Z t is causal for y t , that is, it enters on the right side of the equation for y t . How does this change your answers to a) and c)?...
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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