On econometric inference and multiple use of the same data

TL;DR

This paper introduces the neoclassical inference theory for econometrics, addressing issues of data reuse and dependence that undermine traditional Bayesian and Neyman-Pearson methods, and provides adjustments for standard errors.

Contribution

It develops a new econometric inference framework that remains valid despite data reuse, unifying and improving upon existing practices.

Findings

Neoclassical inference theory is immune to data dependence issues.

Provides a simple adjustment for standard errors to account for approximation errors.

Most econometric practices can be encompassed within the new framework.

Abstract

In fields that are mainly nonexperimental, such as economics and finance, it is inescapable to compute test statistics and confidence regions that are not probabilistically independent from previously examined data. The Bayesian and Neyman-Pearson inference theories are known to be inadequate for such a practice. We show that these inadequacies also hold m.a.e. (modulo approximation error). We develop a general econometric theory, called the neoclassical inference theory, that is immune to this inadequacy m.a.e. The neoclassical inference theory appears to nest model calibration, and most econometric practices, whether they are labelled Bayesian or \`a la Neyman-Pearson. We derive a general, but simple adjustment to make standard errors account for the approximation error.