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I am facing some difficulties understanding this question. It hasn't been long since I started with econometrics, so I'm new to all of this.

Suppose we have a function $$E[c_t|y_t,c_{t-1},y_{t-1},c_{t-2},...]=\alpha +\gamma y_t +\delta c_{t-2}$$ that is estimated using OLS. Assume that $c_t$ and $y_t$ are stationary and ergodic. Is it neccessary using HAC variance estimation to construct standard errors?

I understand that HAC is used when the error term is serially correlated, but I don't know what steps are needed to start this problem?

One of my friend's solution

But apparently, the suggested answer is: The regressors $y_t$ and $c_{t-2}$ are inside the conditional set. Therefore, it is a proper time series regression and OLS is consistent. The immediate past of left side variable $y_t$ is inside the conditional set. Therefore, there is no serial correlation in the error term and HAC is not needed

Maybeline Lee
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  • Not enough info. You've given the mean model, but what can be said of the residual error? If it's heteroscedastic, then you need some form of sandwich variance estimate to get consistent estimates of standard errors. – AdamO Mar 16 '21 at 21:52
  • @AdamO I just edited the question – Maybeline Lee Mar 16 '21 at 21:54

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