Model selection for estimation of causal parameters
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A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. This may lead to models that exhibit good overall predictive accuracy, but can be suboptimal for estimating causal quantities such as the average treatment effect. We propose a model selection procedure that estimates the mean-squared error of a one-dimensional estimator. The procedure relies on knowing an asymptotically unbiased estimator of the parameter of interest. Under regularity conditions, we show that the proposed criterion has asymptotically equal or lower variance than competing procedures based on sample splitting. In the literature, model selection is often used to choose among models for nuisance parameters but the identification strategy is usually fixed across models. Here, we use model selection to select among estimators that correspond to different estimands. More specifically, we use model selection to shrink between methods such as augmented inverse probability weighting, regression adjustment, the instrumental variables approach, and difference-in-means. The performance of the approach for estimation and inference for average treatment effects is evaluated on simulated data sets, including experimental data, instrumental variables settings, and observational data with selection on observables.
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