The State of Econometrics After Pratt, Schlaifer, Skyrms, and Basmann

Thirty-five years ago, J. W. Pratt and Robert Schlaifer published a critique of then ruling econometric techniques. Introducing a distinction between factors and concomitants in regressions, they determined that a “condition for consistent estimation stated in virtually every book on econometrics is meaningless in one common form, impossible to satisfy in another” and that “the relation of predetermined to excluded variables is irrelevant to consistent estimation of the effects of endogenous variables.” This critique was motivated by a common view that the error term in a regression represents the net effect of omitted variables. As this paper demonstrates, this assumption poses a problem whenever the purpose of a model is to explain an economic phenomenon, because the estimated coefficients as well as the error will be wrong in the sense that they are not unique. But a model that is not unique cannot be a causal description of unique events in the real world. For a remedy, this paper presents a methodology based on conditions under which the error term and the coefficients on regressors included in a model do become unique, where the latter represent the sums of direct and indirect effects on the dependent variable, with omitted but relevant regressors having been chosen to define both these effects. The two effects corresponding to any particular omitted relevant regressor can be learned only by converting that regressor into an included regressor. For those cases where omitted relevant regressors are not identified, thereby preventing a meaningful distinction between direct and indirect effects, we introduce so-called coefficient drivers and a feasible method of generalized least squares, permitting a “total-effects” causal interpretation of the coefficients in a model.