2024/03/12 by Śılvia Gonçalves, Goncalves, Silvia, Serena Ng +1
Computer Science · Mathematics · #Advanced Causal Inference Techniques #Bayesian Modeling and Causal Inference #Econometrics (econ.EM) #FOS: Economics and business #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2403.08130
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information not captured by the model. While the literature has focused on sampling uncertainty, it vanishes with the sample size. Often overlooked is the possibility that the out-of-sample error can be informative about the missing counterfactual outcome if it is mutually or serially correlated. Motivated by the best linear unbiased predictor (\blup) of \citetgoldberger:62 in a time series setting, we propose an improved predictor of potential outcome when the errors are correlated. The proposed \pup is practical as it is not restricted to linear models, can be used with consistent estimators already developed, and improves mean-squared error for a large class of strong mixing error processes. Ignoring predictability in the errors can distort conditional inference. However, the precise impact will depend on the choice of estimator as well as the realized values of the residuals.