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

37 Pages Posted: 1 Jun 2019

See all articles by P.A.V.B. Swamy

P.A.V.B. Swamy

Federal Reserve Board

Peter von zur Muehlen

Federal Reserve Board

J.S. Mehta

Temple University - Mathematics Department

I-Lok Chang

American University - Department of Mathematics & Statistics

Date Written: May 6, 2019

Abstract

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.

Keywords: unique time-varying coefficient and unique error term; direct effect; indirect effect; and total effect of a regressor; omitted relevant regressor; coefficient driver; measurement-error bias

JEL Classification: C16; C21; C22

Suggested Citation

Swamy, P.A.V.B. and von zur Muehlen, Peter and Mehta, J.S. and Chang, I-Lok, The State of Econometrics After Pratt, Schlaifer, Skyrms, and Basmann (May 6, 2019). Available at SSRN: https://ssrn.com/abstract=3383763 or http://dx.doi.org/10.2139/ssrn.3383763

P.A.V.B. Swamy (Contact Author)

Federal Reserve Board ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Peter Von zur Muehlen

Federal Reserve Board ( email )

10435 Hunter View Road
Vienna, VA VA 22181
United States
5713281783 (Phone)

J.S. Mehta

Temple University - Mathematics Department ( email )

Wachman Hall
1805 North Broad Street
Philadelphia, PA 19122
United States

I-Lok Chang

American University - Department of Mathematics & Statistics ( email )

Washington, DC
United States

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