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A Practical Guide to Estimating Conditional Marginal Effects: Modern Approaches
\title{\Large\bf A Practical Guide to Estimating Conditional Marginal Effects: Modern Approaches
\thanks{Jiehan Liu, PhD student, Department of Political Science, Stanford University. Email: \url{[email removed]}. Ziyi Liu, PhD student, Haas School of Business, University of California, Berkeley. Email: \url{[email removed]}. Yiqing Xu, Assistant Professor, Department of Political Science, Stanford University. Email: \url{[email removed]}. We are grateful to Justin Grimmer, Jens Hainmüller, and Jonathan Mummolo for helpful comments and suggestions. We thank the Series Editor, R. Michael Alvarez, for his guidance. We thank Ziyi Chen, Rivka Lipkovitz, Tianzhu Qin, Jinwen Wu, and Zehao Wang for excellent research assistance. Zehao and Tianzhu both contributed significantly to the implementation of the DML methods and the refinement of \texttt{interflex}. All errors are our own. We also thank the authors of the replicated studies for generously sharing their code and data. }
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\author{Jiehan Liu\\(Stanford)\and Ziyi Liu\\(Berkeley)\and Yiqing Xu\\(Stanford)}
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\begin{abstract}
\noindent This Element offers a practical guide to estimating conditional marginal effects—how treatment effects vary with a moderating variable—using modern statistical methods. Commonly used approaches, such as linear interaction models, often suffer from unclarified estimands, limited overlap, and restrictive functional forms. This guide begins by clearly defining the estimand and presenting the main identification results. It then reviews and improves upon existing solutions, such as the semiparametric kernel estimator, and introduces robust estimation strategies, including augmented inverse propensity score weighting with Lasso selection (AIPW-Lasso) and double machine learning (DML) with modern algorithms. Each method is evaluated through simulations and empirical examples, with practical recommendations tailored to sample size and research context. All tools are implemented in the accompanying \texttt{interflex} package for \texttt{R}.
\bigskip\noindent\textbf{Keywords:} causal inference, conditional marginal effects, double machine learning
\end{abstract}
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\section{Introduction}
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\section{The Classic Approaches}
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\section{AIPW and Extensions}
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\section{Double Machine Learning}
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\section{Monte Carlo Evidence}
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\section{Conclusion}
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