The U.S. Phillips-curve by time scale using waveletsMarco

Wavelets are a useful analytical tool to study economic decisions on different times scales. Wavelets are particular types of function that are localized both in time and frequency domain and used to decompose a function f(x) (i.e. a signal, a surface, a series, etc..) into more elementary functions which include information about the same f(x). The main advantage of wavelet analysis is its ability to decompose macroeconomic time series, and data in general, into their time scale components. No analysis of labor market decisions have been undertaken with wavelets so far. Yet, the labor market may be seen as a market where firms and workers (unions) interact having different time horizons and operate on several time scales at once. In this way the relationships among labor market variables, i.e. wages, prices and unemployment, may well vary across time scales. In this paper, instead of analyzing the average relationships among wages, price and unemployment, we use wavelets to examine the relationships among wages, prices and unemployment at each time scale separately. The results from cross-correlation analysis and Granger causality test within scales confirm that time scale decomposition matters for analyzing economic relationships as both the strength of the relationship between variables and the degree and direction of causality may vary across time scales.