Measuring Mutual Causality in Macroeconomy

The interdependence (mutual causality) between some macroeconomic time series remains obscure because of several circumstances, three of which have special implications: (i) inadequacy of adopted measuring tools, where algorithms suited for other types of causality than mutual causality are used; (ii) insufficient dimension of the database in use (in acceptance of the law of large numbers); and (iii) the compared variables are expressed numerically by series, making them highly sensitive to stochastic noises or/and cyclicity (regular or irregular). The present study discusses these circumstances, using modern U.S. statistics for numerical illustration. Usually, macroeconomic interdependences are studied using the popular Granger test, which assimilates causality by the potentiality of a linear model to forecast future values of a time series, calling to prior values of another time series; it thus measures “sequential causality” (Hicks, 1980). However, quantifying the connection between series $$x$$ x and $$y$$ y by the degree in which they represent a linear interdependent couple may be a more appropriate approach for mutual causality. It is expressed by the product of slope coefficients on separate regressions $$y=f(x)$$ y = f ( x ) and $$x=f(y)$$ x = f ( y ) ,, named functional reciprocity ( $${rec}_{xy}$$ rec xy ). The closer to unity that $${rec}_{xy}$$ rec xy is, the higher the intensity of interaction between the analyzed time series. According to Hicksian interpretation, such an approach belongs, instead, to “contemporaneous (mutual) causality.” The present study’s research methodology is built on two pillars: on the one hand, the resampling statistical series is adopted as an artificially expanding-sample procedure, and, on the other hand, the steady-state estimations of macroeconomic variables is based on an extensive interpretation of the vector autoregression technique. Our empirical research attests the plausibility of such a methodology, which provides more credible information for calculating the functional reciprocities among macroeconomic variables. Unlike current statistics, the steady-state estimations obtained by this algorithm reveal an important interdependence between the global output and main monetary indicators.