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Macroeconomics and ARCH James D Hamilton Department of Economics University of California San Diego jhamilton ucsd edu September 24 2007 Revised May 27 2008 Prepared for the Festschrift in Honor of Robert F Engle eds Tim Bollerslev Je rey R Russell and Mark Watson Abstract Although ARCH related models have proven quite popular in finance they are less frequently used in macroeconomic applications In part this may be because macroeconomists are usually more concerned about characterizing the conditional mean rather than the conditional variance of a time series This paper argues that even if one s interest is in the conditional mean correctly modeling the conditional variance can still be quite important for two reasons First OLS standard errors can be quite misleading with a spurious regression possibility in which a true null hypothesis is asymptotically rejected with probability one Second the inference about the conditional mean can be inappropriately influenced by outliers and high variance episodes if one has not incorporated the conditional variance directly into the estimation of the mean and infinite relative e ciency gains may be possible The practical relevance of these concerns is illustrated with two empirical examples from the macroeconomics literature the first looking at market expectations of future changes in Federal Reserve policy and the second looking at changes over time in the Fed s adherence to a Taylor Rule 1 1 Introduction One of the most influential econometric papers of the last generation was Engle s 1982a introduction of autoregressive conditional heteroskedasticity ARCH as a tool for describing how the conditional variance of a time series evolves over time The ISI Web of Science lists over 2000 academic studies that have cited this article and simply reciting the acronyms for the various extensions of Engle s theme involves a not insignificant commitment of paper see Table 1 or the more detailed glossary in Bollerslev 2008 The vast

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