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

Rudolph Kara E. (), Williams Nicholas T., Miles Caleb H., Antonelli Joseph and Diaz Ivan
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Rudolph Kara E.: Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, USA
Williams Nicholas T.: Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, USA
Miles Caleb H.: Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, USA
Antonelli Joseph: Department of Statistics, University of Florida, Gainesville, USA
Diaz Ivan: Division of Biostatistics, Department of Population Health, New York University Grossman School of Medicine, New York, USA

Journal of Causal Inference, 2023, vol. 11, issue 1, 15

Abstract: There is a long-standing debate in the statistical, epidemiological, and econometric fields as to whether nonparametric estimation that uses machine learning in model fitting confers any meaningful advantage over simpler, parametric approaches in finite sample estimation of causal effects. We address the question: when estimating the effect of a treatment on an outcome, how much does the choice of nonparametric vs parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach to compare estimators across a large number of data-generating mechanisms drawn from nonparametric models with semi-informative priors. We apply this proposed approach and compare the performance of two nonparametric estimators (Bayesian adaptive regression tree and a targeted minimum loss-based estimator) to two parametric estimators (a logistic regression-based plug-in estimator and a propensity score estimator) in terms of estimating the average treatment effect across thousands of data-generating mechanisms. We summarize performance in terms of bias, confidence interval coverage, and mean squared error. We find that the two nonparametric estimators can substantially reduce bias as compared to the two parametric estimators in large-sample settings characterized by interactions and nonlinearities while compromising very little in terms of performance even in simple, small-sample settings.

Keywords: parametric; nonparametric; causal inference (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:11:y:2023:i:1:p:15:n:1028

DOI: 10.1515/jci-2023-0022

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