Some Remarks about Relations between Stochastic Variables: A Discussion Document

In this paper the author examines some fundamental problems in the theory of relationships between stochastic variables. Regression essentially involves a character cause-effect relationship, with the independent variables being the causes and the dependent variable being the effect. Regression should not be confused with an associative type relationship, the linear theory of which is outlined in the text. In associative theory there is no need to appeal to the cause-effect hypothesis. In the regression of several variables the individual coefficients are without meaning or importance except only in the special case of uncorrelated independent variables. The sole purpose of multivariate regression is to estimate (for forecasting etc.) the average value of the dependent variable for given values ​​of the independent variables. In econometrics, it is only in the case of simple regression that the coefficient has meaning. As an example, we show that, to estimate the elasticities of prices and wages from time series, it is necessary to calculate each of these variables separately by a simple regression after having eliminated the trend. The author wonders whether the notion of a system of structural equations is useful in econometrics. It is only in the case of the reduced form, where each equation contains a single endogenous variable, that the theory has practical value for forecasting. The author asks the question of the practical usefulness of the hypothesis of auto-regression of errors in time series. He supports the thesis that errors must be assumed to be absolutely random. It shows, using well-known economic examples, that the auto-regression hypothesis leads to incorrect statements concerning relationships. All statements are summarized in the form of questions at the end of the communication, to serve as a basis for discussion.