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

arXiv: https://arxiv.org/abs/2508.13076 · HTML: https://mlsanity.com/paper/2508.13076/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions](https://mlsanity.com/paper/2604.24660/) (2026)

## Abstract (arXiv)

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.