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Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the xt equals zero (x=0) :
Consider the variance of the OLS slope estimator in the following simple regression model, where the sample average of the xt equals zero (x=0) : yt=0+1xt+ut The OLS estimator 1 of 1 can be written as follows, where SSTx=t=1nxt2 only if x=0 : 1=1+SSTx1i=1nxtut The variance of 1 (conditional on x ), accounts for the serial correlation in ut, where 2=Var(ut) and E(utut+j)=Cov(utut+j)=j2 : Var(1)=SSTXX2+2SSTX22t=1n1j=1ntjxtxxtj Suppose the errors in a regression model have AR(1) serial correlation, meaning j=0. Suppose j>0 for all j. Which of the following can explain the conditions under which OLS standard errors will overstate the true sampling variation? Check all that apply. The independent variables in regression models are often positively correlated over time. The term xtxt+j>0 for most pairs t and t+j. The independent variables in regression models are negatively correlated over time. The term xtxt+j
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