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e2-245a

# e2-245a - X ∗ t other than X t − V t In e f ect we need...

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Economics 245A Exercise 2 Consider the errors-in-variables model (that is, measurement error in the re- gressor) Y t = X t β + U t , in which the regressor is latent. We observe X t = X t + V t . We assume that X t , U t and V t are independent Gaussian random variables with zero mean. a) For the ordinary least squares estimator P n t =1 X t Y t P n t =1 X 2 t , discuss why replacement of X t with X t V t results in an expression that we cannot easily use to calculate the exact ° nite sample bias. b) To evaluate the exact ° nite sample bias, we use an expression for
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Unformatted text preview: X ∗ t other than X t − V t . In e f ect, we need to & nd the part of V t that is uncorrelated with X t . To do so, we construct W t = aV t − bX ∗ t , for values of a and b to be determined. The values of a and b must be such that E ( X t W t ) = 0 and also satisfy X ∗ t = cX t − W t . Find the values of ( a,b, c ) and use the resultant W t to derive the exact & nite sample bias of the OLS estimator....
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