Assumption Lean Regression

TL;DR

This paper proposes an assumption-lean approach to regression that treats models as approximations, ensuring valid inference and broad applicability, even when models are misspecified.

Contribution

It introduces a framework that explicitly considers models as approximations, enabling asymptotically unbiased estimates and valid inference regardless of model correctness.

Findings

Regression models can be valid approximations with desirable properties.

The approach broadens the scope of regression analysis to include various functionals.

Empirical example demonstrates practical applicability.

Abstract

It is well known that models used in conventional regression analysis are commonly misspecified. A standard response is little more than a shrug. Data analysts invoke Box's maxim that all models are wrong and then proceed as if the results are useful nevertheless. In this paper, we provide an alternative. Regression models are treated explicitly as approximations of a true response surface that can have a number of desirable statistical properties, including estimates that are asymptotically unbiased. Valid statistical inference follows. We generalize the formulation to include regression functionals, which broadens substantially the range of potential applications. An empirical application is provided to illustrate the paper's key concepts.