Observations on unit roots and the GMM

Hamilton in his textbook "Time Series Analysis" makes two points relevant to my recent comments in this blog.

The first (page 409 of the hardback 1994 edition) is that the GMM does not use all information in a dataset, but only selected moment conditions. The point is salient in observing the failure to identify misspecification in the AR1 models discussed previously, since OLS, instrumental variables, Arellano-Bond, and of course the various GMM estimation methods can all be cast as GMM models.

The second (page 516) is that "the goal of unit root tests is to find a parsimonious representation that gives a reasonable approximation to the true process". The issue is that if the true process has, say, an AR parameter of 0.95, working under the assumption of a unit root (AR=1) can sometimes give more accurate results than under the assumption that there is not a unit root. The point partially responds to the criticism reported in an earlier post that econometrics in pure and applied form has focussed excessively on unit root analysis. My only caveat would be that because unit roots are usually specified as a null and testing is usually conservative in rejecting the null, the unit root hypothesis might be accepted principally because of the advantage that the null has, and so the statistical benefits of acceptance would be diluted.

It is encouraging when a writer anticipates where a reader's logic will pass through, not least because one thinks that one is on the right track if someone else has passed through already.