Heterogeneity in economic relationships: Scale dependence through the multivariate fractal regression

Heterogeneity of effects between economic variables has been a frequently discussed topic for many years now. However, the estimation of such scale-dependent effects has proved challenging. Here, we propose a multivariate multiscale regression approach based on the combination of detrended fluctuation analysis and detrended cross-correlation analysis, but the idea can be easily translated into other time and frequency domain frameworks. As illustrations, we pick two classic economic models – the Taylor’s rule and the money demand function for the USA and Japan – and we uncover evident scale-dependence in the individual effects not visible by the simple regression tools. Importantly, the proposed framework can be used in any discipline where studying the effects at various scales is of interest. Further applications are thus certainly at hand.