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There is a long-standing debate in the statistical, epidemiological andeconometric fields as to whether nonparametric estimation that usesdata-adaptive methods, like machine learning algorithms in model fitting,confer any meaningful advantage over simpler, parametric approaches inreal-world, finite sample estimation of causal effects. We address thequestion: when trying to estimate the effect of a treatment on an outcome,across a universe of reasonable data distributions, how much does the choice ofnonparametric vs.~parametric estimation matter? Instead of answering thisquestion with simulations that reflect a few chosen data scenarios, we proposea novel approach evaluating performance across thousands of data-generatingmechanisms drawn from non-parametric models with semi-informative priors. Wecall this approach a Universal Monte-Carlo Simulation. We compare performanceof estimating the average treatment effect across two parametric estimators (ag-computation estimator that uses a parametric outcome model and an inverseprobability of treatment weighted estimator) and two nonparametric estimators(Bayesian additive regression trees and a targeted minimum loss-based estimatorthat uses an ensemble of machine learning algorithms in model fitting). Wesummarize estimator performance in terms of bias, confidence interval coverage,and mean squared error. We find that the nonparametric estimators nearly alwaysoutperform the parametric estimators with the exception of having similarperformance in terms of bias and similar-to-slightly-worse performance in termsof coverage under the smallest sample size of N=100.

All models are wrong, but which are useful? Comparing parametric and nonparametric estimation of causal effects in finite samples