Disagreement and Uncertainty: A Reply to Rich and Butler
回应Rich和Butler的批评，论证Livingston分歧指标作为通胀不确定性代理变量的有效性，通过GMM估计强化了原结论，并指出分歧指标仍具实用价值。
1. The Issues The objective in Bomberger (1996) was an assessment of the common practice of using the Livingston disagreement measure, s, as a proxy for uncertainty about future inflation at the time of the forecasts. For the period 1946-94 and the subperiod 195294 it was found that the subsequent errors, e, seem to be distributed with a variance that is proportional to disagreement: 62 = als2. This finding offers preliminary support for the use of s as a proxy for 6. Let us label this result A. In the absence of other directly measurable candidates for inclusion in the variance, this specification was compared to a modified GARCH. Many error terms exhibit serial correlation in the absolute size of the errors, and, indeed, a significant GARCH term emerged. However, when St was added to the variance relationship, the GARCH term was not only diminished but, surprisingly, eliminated. This is result B. Although they do not emphasize it, RB confirm result A. Result B is reversed. Why do our results differ? RB argue that result B is reversed because the likely serial correlation in e renders the original ML estimates unsuitable and the original GARCH specification is not appropriate. Their GMM estimates based on an ARCH specification yield the true relationship. On this basis they conclude that researchers should de-t sist from using s as a measure of uncertainty. I wish to demonstrate (i) the use of GMM estimates strengthens the main result A, (ii) the reversal of result B is not related to the choice between GMM and ML, and (iii) the conclusion that disagreement is not a useful proxy for uncertainty is unpersuasive.