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Suppose, we wish to predict future observations, e.g., by estimating the following simple AR(1) model with OLS: $Y_t=\beta_0 + \beta_1 \cdot Y_{t-1} + u_t$. Further assume that $E[u_t|Y_{t-1}]\neq 0$. Because our only goal is forecasting, we do not care about this endogeneity. My question: can we consistently and unbiasedly estimate the standard error of $\widehat{\beta}_1$? Put differently, can we calculate a valid $t$-statistic?

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  • $\begingroup$ You do care for endogeneity in forecasting. Then again you contradict yourself: if you're forecasting, why do you care for t-statistics, that's inference thing? $\endgroup$ – Aksakal Dec 6 '16 at 18:27
  • $\begingroup$ Under certain assumptions you can estimate the standard error consistently (this requires an instrument variable), but without having strictly exogenous regressors you will never get anything unbiased... Also Aksakal comments are right on point, the question is one big contradiction $\endgroup$ – Repmat Dec 6 '16 at 18:40
  • $\begingroup$ Thanks for your replies. @Aksakal: I don't quite get your answer. Why should I care about endogeneity? @ Repmat: Okay, I get that I will not get an unbiased estimator of the population parameter. Maybe, I should put my question differently. If my only goal is forecasting, does it make sense to look at the $t$-statistic? For example, if I include an additional variable, can I judge whether I should include this variable by looking at the $t$-statistic? $\endgroup$ – bachelor Dec 6 '16 at 18:42

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