The purpose of an estimator is what it does: Misspecification, estimands, and over-identification

TL;DR

This paper examines how misspecification in over-identified models affects estimators and their estimands, emphasizing the importance of transparent reporting and robust practices in empirical research.

Contribution

It reviews recent findings on estimation under misspecification, introduces a new theoretical insight on Hansen's J-statistic, and offers guidelines for more transparent empirical analysis.

Findings

Misspecification alters what estimators estimate in over-identified models.

Widespread use of inefficient estimators and limited specification testing.

Hansen's J-statistic asymptotically measures the range of estimates at a given standard error.

Abstract

In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review of recent applications of generalized method of moments in the American Economic Review suggests widespread acceptance of this fact: There is little formal specification testing and widespread use of estimators that would be inefficient were the model correct, including the use of "hand-selected" moments and weighting matrices. Motivated by these observations, we review and synthesize recent results on estimation under model misspecification, providing guidelines for transparent and robust empirical research. We also provide a new theoretical result, showing that Hansen's J-statistic measures, asymptotically, the range of estimates achievable at a given standard error. Given the widespread use of inefficient estimators and the resulting researcher degrees of freedom, we thus particularly recommend the broader reporting of J-statistics.