THE STATE OF ECONOMETRICS AFTER JOHN W. PRATT, ROBERT SCHLAIFER, BRIAN SKYRMS, AND ROBERT L. BASMANN

Swamy Paravastu (), Peter von zur Muehlen (), Jatinder Singh Mehta () and I-Lok Chang ()
Additional contact information
Swamy Paravastu: Federal Reserve Board (Retired)
Jatinder Singh Mehta: Temple University
I-Lok Chang: American University

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 8, 627-654

Abstract: SUMMARY Thirty-six years ago, introducing a distinction between factors and concomitants in regressions, John W. Pratt and Robert Schlaifer determined that the error term in a regression represents the net effect of omitted relevant regressors. 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-effect” causal interpretation of the coefficient on each regressor included 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; C16; C21; C22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-021-00273-y

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