I am currently estimating a cointegrating regression (DOLS), where my residuals have autocorrelation. Sometimes it is just in one or two lags, but sometimes it is more. My question is: Can I apply HAC and carry on with my estimation? I.e. would HAC standard errors compensate for the autocorrelation?
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1$\begingroup$ I edited the title in the hope of making it more informative. I hope I did not misrepresent your point. It is an interesting question, but looks like a tough one, too... $\endgroup$– Richard HardyCommented Jun 7, 2015 at 21:52
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$\begingroup$ In DOLS, leads and lags compensate for autocorrelation. Why would you want to use HAC s.e.s on top? $\endgroup$– Christoph HanckCommented Jun 8, 2015 at 3:25
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$\begingroup$ Richard Hardy, thanks! @ChristophHanck, because I have tried every possible combination of leads and lags and some autocorrelation still remains. $\endgroup$– econstudentCommented Jun 8, 2015 at 6:00
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1 Answer
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The motivation for including leads/lags within a DOLS is to control for bias in small samples. Actually, to be more specific the lags\leads are included to ensure that the OLS estimates are normally distributed. More importantly, lag/leads are not related to correcting for autocorrelation. These issue are first discussed in Banerjee 1986 et al, who shows that bias in introduced as a results of the strict exogeneity assumption not holding. Saikkonen 1991 is the first to suggest using lag/lead difference to control for bias.
More importantly for your application is that it is actually essential you use HAC variance. As a matter of fact the seminal paper on DOLS, Stock and Watson (1993), discusses this in-depth. Read these Zivot Notes, since they contain the essential information. For a application with Newey-West errors read this.
