Working Paper: NBER ID: w14151
Authors: James D. Hamilton
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 efficiency 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.
Keywords: No keywords provided
JEL Codes: E52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| misspecifying the conditional variance in a model (C32) | invalid hypothesis tests regarding the conditional mean (C12) |
| OLS estimates will systematically reject the null hypothesis even when it is true (C51) | high kurtosis in the data (C46) |
| incorrect specification of the variance (C20) | spurious rejections of the null hypothesis (C12) |
| correct specification of conditional variance (C29) | significantly more efficient estimates of the conditional mean (C51) |
| failing to account for heteroskedasticity in the regression model (C21) | biased estimates of the coefficients describing the Federal Reserve's response to inflation and output (C51) |
| GARCH model (C58) | more accurate picture of the dynamics involved (C69) |
| traditional OLS approach (C51) | misleading inferences regarding expected future interest rates (E43) |