Functional reciprocity of the macroeconomic variables

This paper’s objective is to evaluate the intensity of the connection between two economic time series – x and y - by the degree in which they are representing a linear interdependent pair. This intensity is measured by the product of the slope coefficients of separate regressions y=f(x) and x=f(y), and will be called hereafter “the functional reciprocity” (recxy) of the respective variables. The closer to unity is recxy, the higher will be the intensity of the said functional reciprocity i, and vice versa. A high functional reciprocity is a solid argument for utilizing the orthogonal regression, however the converse reasoning is not valid: there is not certain that the estimator obtained by this econometric technique would reflect the actual intensity of the connected variables. The bundle of macroeconomic indicators involved into monetary processes is a good empirical platform for testing the proposed methodology. The USA experience during the junction of the last two centuries (1960-2022) was chosen as study case, with the focus on relationships among the global output, inflation, broad money M3, money velocity, and interest rate. Quarterly frequency was preferred, the statistical series thus obtained being not only reliable enough, but also able to provide consistent econometric estimations. The main problem identified by this paper was a pronounced instability of the functional reciprocities resulted from statistical data. By itself, the randomly resampling procedure did not allow surpassing this inconvenience. The VAR technique proved to be a more proper tool to transform volatile series into more stable ones; it was applied on both statistical and resampled series. Comparison of the results of the post-sample simulations to the averages of initial database has brought up two remarks: i) it seems reasonable to assign more credibility to the steady state approximations, since they yield from a considerably longer series of iterations; ii) whenever there are cases when the steady state estimations themselves are contradictory, they dictate the necessity to improve the proposed algorithm, for example by involving a great number of resampled series - a question requiring further research.