Question

I. (Stock and Watson #12.3) A classmate is interested in estimating the variance of the error term in Equation (12.1) a. Suppose that she uses the estimator from the second-stage regression of TSLS: , where X, is the fitted value from the first-stage regression. Is this estimator consistent? (For the purposes of this question suppose that the sample is very large and the TSLS estimators are essentially identical to Bo and B1.) b. Is the estimator below consistent?

Answer 1

onsiden the fouousing given ndions second stage segpression ce TsLs; aven to be D인 Independed vayiatle, aad TsLs oPicents The TSLS So1t can be sobstituled as S2 n-2 ヅan be Sob St iluded to dead to Enoc taiHu as shown bebw

As n gmouon to Fofinily the fiosi tom in the Sonnatioo hfoe, his estaions i not nsisteot n-2 Yi -8 botice that dhe. d enence in this estiat ion s the lada TndeRrded values χ?s ersed instead op again, sobstitute fon the coelPica ient TSLS DTSLS 2 n-2

he ^above ease thex canceled. This qs arpooxi r1adeo d .tle diPinalior) ㅇρ foruoak icの "VODI ance, t gives an appscxiMaHon to the Hade 2 Hence the estination is Con sistent