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Exercise 5 - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 140A Exercise 5 1. (A difficult question. Answer for extra credit.) We will investigate the following claim (which appears in nearly this form in Studenmund's undergraduate econometrics text) If an equation that contains a lagged dependent variable as a regressor has a serially correlated error term, then OLS estimates of the coefficients will be inconsistent. To investigate, we define a regression model in a slightly different way. Let t Y be a strictly stationary and ergodic random variable that is observed into the infinite past. Assume that 0 t EY and 2 t EY . Define t t t Y Var Y Y Cov , 1 and 1 t t t Y Y U so that we can write t t t U Y Y 1 for t=1,…,n . a. Show that 0 t EU and 0 , 1 t t U Y Cov . b. Show that the OLS estimator B from a regression of t Y on 1 t Y , for t=1,…,n , is consistent for β .
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