Misspecified Z-estimation and OLS with mixed (random+fixed) regressors yield conservative robust SEs and identify causal ATEs under randomization, with corrections for fully-interacted specs and clustered data.
Model-free Study of Ordinary Least Squares Linear Regression
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abstract
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the case where the covariates are fixed, errors are mean zero Gaussians with variance independent of the (fixed) covariates. Even though OLS has been studied under misspecification from as early as the 1960's, the implications have not yet caught up with the main stream literature and applied sciences. The present article is an attempt at a unified viewpoint that makes the various implications of misspecification stand out.
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Misspecified regressions with mixed regressors: robust inference and causal interpretation
Misspecified Z-estimation and OLS with mixed (random+fixed) regressors yield conservative robust SEs and identify causal ATEs under randomization, with corrections for fully-interacted specs and clustered data.