Exchange rates and prices: A continuous wavelet perspective
In this paper we analyze statistics derived from the cross-wavelet transform of inflation differentials and exchange rate changes for a group of countries with Germany as the reference country. An important tool is the wavelet coherency measure from which we can judge the strength of the price-exchange rate nexus at different time scales, and also whether it has changed in time. Complex cross-wavelets provide information about phase relationship, and we can investigate whether there is any consistent pattern in the lead-lag relationship between prices and exchange rates. Also, we calculate a summary measure, based on singular value decomposition, that shows which countries have significantly similar inflation differential - exchange rate change processes. Our results accord, in some ways, with former findings, but suggest an even gloomier view on the possibility of finding statistically reliable relationships between exchange rates and aggregate price indices (CPI or PPI). In line with the literature we haven't found strong co-movement between prices and exchange rates in the short or medium term. There are only weak indications that at least in some countries the price-exchange rate connection strengthened during the crisis, and detectable cycles at business cycle frequencies do not appear at all. Though by and large the lead-lag relationship between prices and exchange rates is the expected one, still this is unstable practically for every country. Results with respect to the PPI are more promising. The three countries that seem to be closest to theoretical expectations are Sweden, Japan and South-Korea. It is possible that the coherence between exchange rates and prices on the macro level may depend more on similarities of export structure than on trading relations, that microeconomic intuition would suggest. Also it is possible that macro price indices are too noisy by their very nature to be amenable for statistical analyses not committed to strong presumptions.
