Your textbook mentions heteroskedasticity- and autocorrelation- consistent standard errors. Explain why you should use this option in your regression package when estimating the distributed lag regression model

What are the properties of the OLS estimator in the presence of heteroskedasticity and autocorrelation in the error terms? Explain why it is likely to find autocorrelation in time series data. If the errors are autocorrelated, then why not simply adjust for autocorrelation by using some non-linear estimation method such as Cochrane-Orcutt?
What will be an ideal response?

Answer: In the presence of either heteroskedasticity and/or autocorrelation in the errors, OLS estimation of the regression coefficients is still consistent. However, the homoskedasticity-only or heteroskedasticity-robust standard errors are inconsistent and use of these in the presence of serial correlation results in misleading statistical inference. For example, confidence intervals do not contain the true value in the postulated number of times in repeated samples. The solution is to adjust the estimator for the standard errors by incorporating sample autocorrelation estimates. This results in the heteroskedasticity- and autocorrelation-consistent (HAC) estimator of the variance of the estimator. For this estimator to be consistent, a certain truncation parameter is introduced, so that not all T-1 sample autocorrelations are used. Incorporating this idea into the HAC formula results in the Newey-West variance estimator.

Autocorrelation in the errors is likely if there are omitted variables which are slowly changing over time. Since the omitted variables are implicitly contained in the error term, this would result in autocorrelation of the error term. For generalized least squares to have desirable properties, the regressors have to be strictly (past, present, and future) exogenous, rather than just (past and present) exogenous. There are very few truly exogenous variables in economics. Furthermore, most of the relationships between economic time series contain simultaneous causality. As the example in the textbook on orange juice prices and cold weather showed, it is even more difficult to find strictly exogenous variables.