Reply to Cosimano and Jansen

Abstract

First impressions to the contrary, the results obtained by Cosimano and Jansen are remarkably similar to those I reported in 1983. We agree that there was little increase in the variance of inflation in the seventies but a very high variance in the late forties and early fifties. And we agree that the level and variance of inflation do not appear to be systematically related. The points of difference are more methodological and it is here that their paper is most misleading. They claim that my model was misspecified in several fashions. There was serial correlation in some residuals the sample period was incorrect, and the lags were not sufficiently long. However, to make such claims, they must take my model as the null hypothesis and test against it. This is the way all diagnostic tests are constructed and is the general thrust of scientific inquiry. In contrast, they only show that in models superficially similar to mine, there is serial correlation. For example, they estimate my model without the ARCH correction and then find serial correlation for one of the three dependent variables. Had they estimated the model with the heteroskedasticity corrected, the residuals divided by their standard errors should no longer have displayed the serial correlation. In effect, by weighting all data points equally, they give too much weight to the volatile period which has little serial correlation, leaving some serial correlation in the OLS residuals. Furthermore, the test for serial correlation, Godfrey's LM test, only has the correct size under the null that the model is correctly specified in both mean and variance. Thus the admission that there is ARCH invalidates the test based on least squares. The solution proposed by the authors is to throw out the troublesome part of the sample period. This is accompanied by an observation that it coincides with one of the improvements in the CPI statistics (even though the problem shows up in the GNP deflator but not the CPI or PPI equations), and some tests for parameter constancy which allow for a constant variance or one which changes at the split point. (The procedure used for the latter test is not described.) In no case however is there evidence presented directly against the ARCH model. For example, dummy variables for the split could be introduced into my ARCH model either additively or multiplicatively and tested with tor F-tests. In fact, the