Business cycles in open economies: A reply

Abstract

thank Hahn for pointing out our mistake concerning the reversed lead-lag order in Tables 3 and 5. The qualitative conclusions reached in the text with respect to the Austrian and German output has to be changed accordingly, recognizing that the lead and the lag of order one are both significant. Besides this, Hahn makes two fundamental criticisms. First, he questions the validity of the HP-filter as an accurate method to extract the trend component from economic time series; and second, he claims that the relative volatility of consumption and output has to be reversed. The first criticism is not new and has been reported elsewhere [Singleton, 1988; Canova, 1991; Harvey and Jaeger, 1993]. In our view, it is misdirected because there is no intention to estimate and model the stochastic characteristics of the data at this stage of the analysis. If this had been our primary object, we would have applied multivariate time series analysis instead. Second, even if one is willing to follow Hahn's advice and estimate structural time series models along the lines of Harvey [1989], the qualitative conclusion regarding the relative consumption volatility remains unaltered. In searching for stylized facts, it has become customary to characterize the business cycle by movements and co-movements of time series at the business cycle frequencies which, following Hodrick and Prescott [1980], are defined as cycles shorter than 8 years. Given the non-stationary nature of most macroeconomic time series, some prefiltering (trend extraction) of the raw data is necessary. Given these goals and the definition of what constitutes a business cycle, the HPfilter has several desirable properties. First, it practically annihilates the long-run frequencies leaving unaltered the short ones and has a small transition width compared to first differences or exponential smoothing (see the corresponding gains in our working paper). Second, the filter is invertible so that the spectrum of the original series can be easily reconstructed. Finally, it allows an automatic trend extraction which treats all series alike. Thus the HP-filter can be considered as a sophisticated "first difference filter" which acts like a magnifying glass focused on the business cycle.