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Miss Junting Duan
Ph.D. Candidate in Management Science and Engineering
Department of Management Science and Engineering
Stanford University

A prevalent problem in empirical research is missing covariate data when conducting model estimation. This paper develops a novel framework for adaptively incorporating partially observed covariates with imputed values into downstream estimation and inference. Commonly used approaches, either discarding all partially observed samples or naively treating imputed values as observed data, are generally inefficient or biased. Our approach combines bias correction with an adaptive weighting scheme for imputed values, using optimal weights that balance the efficiency trade-off between imputation error and effective sample size. Our method ensures valid inference while improving statistical efficiency by leveraging all available data. We establish the asymptotic normality of the proposed estimator under general missing data patterns and a broad class of imputation methods. Through simulations, we demonstrate the superior performance of our method over naive approaches, as it achieves both lower bias and variance while being robust to imputation quality. In an empirical study of carbon emissions and stock returns, we show that properly accounting for missing emissions data yields no evidence of correlation between stock returns and emissions directly produced by the company but a negative correlation with value chain emissions.