Time scale regression analysis of the wage Phillips curve in the US

Wavelet analysis, although used extensively in many areas of applied sciences, has not yet fully entered the economics discipline, even if many economic processes are the result of the actions of several agents who simultaneously operate at different horizons and/or have different term objectives. Wavelets provide a unique decomposition of time series observations that enable one to decompose the data in ways that are potentially revealing of relationships that are at best problematical using standard methods and aggregated data. In this paper we apply wavelet analysis to one of the most studied empirical relationship in economics: the wage Phillips curve. Thus, after decomposing labor productivity, unemployment rate, wage inflation and price inflation into their time-scale components using the maximum overlap discrete wavelet transform (MODWT), we estimate the wage Phillips curve specification on a scale-by-scale basis. The results show that the nature of the relationship between variables is not the same through all timescales since the significance and the estimated size effect of the regression variables of the wage Phillips relationships differ widely by time scale. In particular, the results at the longest scales, where the variables have large coefficient values, are very highly significant and explain Preprint submitted to Elsevier 15 October 2008 a substantial proportion of the total variation of nominal wage changes, indicate that the medium-run may be an appropriate perspective for the wage Philips curve relationship.