About

Max H. Farrell is an Associate Professor of Economics at the University of California, Santa Barbara, holding the Mellichamp Chair of Mind and Machine Intelligence. His research focuses on econometrics, particularly in the areas of regression discontinuity designs, nonparametric inference, and the application of deep learning in economics.

Research topics

• Political Science
• Mathematics
• Applied mathematics
• Statistics

Selected publications

• rdhte: Heterogeneous Treatment Effects in Regression Discontinuity Designs

  2025-03-25 · 1 citations

  datasetOpen access

  Understanding heterogeneous causal effects based on pretreatment covariates is a crucial step in modern empirical work in data science. Building on the recent developments in Calonico et al (2025) &lt;<a href="https://rdpackages.github.io/references/Calonico-Cattaneo-Farrell-Palomba-Titiunik_2025_HTERD.pdf" target="_top">https://rdpackages.github.io/references/Calonico-Cattaneo-Farrell-Palomba-Titiunik_2025_HTERD.pdf</a>&gt;, this package provides tools for estimation and inference of heterogeneous treatment effects in Regression Discontinuity (RD) Designs. The package includes two main commands: 'rdhte' to conduct estimation and robust bias-corrected inference for conditional RD treatment effects (given choice of bandwidth parameter); and 'rdbwhte', which implements automatic bandwidth selection methods.

  PublisherOA PDFDOI

• Treatment Effect Heterogeneity in Regression Discontinuity Designs

  ArXiv.org · 2025-03-17

  preprintOpen access

  Empirical studies using Regression Discontinuity (RD) designs often explore heterogeneous treatment effects based on pretreatment covariates. However, the lack of formal statistical methods has led to the widespread use of ad hoc approaches in applications. Motivated by common empirical practice, we develop a unified, theoretically grounded framework for RD heterogeneity analysis. We show that a fully interacted local linear (in functional parameters) model effectively captures heterogeneity while still being tractable and interpretable in applications. The model structure holds without loss of generality for discrete covariates, while for continuous covariates our proposed (local functional linear-in-parameters) model can be potentially restrictive, but it nonetheless naturally matches standard empirical practice and offers a causal interpretation for RD applications. We establish principled bandwidth selection and robust bias-corrected inference methods to analyze heterogeneous treatment effects and test group differences. We provide companion software to facilitate implementation of our results. An empirical application illustrates the practical relevance of our methods.

  PublisherOA PDFDOI

• rdhte: Conditional Average Treatment Effects in RD Designs

  ArXiv.org · 2025-07-01

  preprintOpen access

  Understanding causal heterogeneous treatment effects based on pretreatment covariates is a crucial aspect of empirical work. Building on Calonico, Cattaneo, Farrell, Palomba, and Titiunik (2025), this article discusses the software package rdhte for estimation and inference of heterogeneous treatment effects in sharp regression discontinuity (RD) designs. The package includes three main commands: rdhte conducts estimation and robust bias-corrected inference for heterogeneous RD treatment effects, for a given choice of the bandwidth parameter; rdbwhte implements automatic bandwidth selection methods; and rdhte lincom computes point estimates and robust bias-corrected confidence intervals for linear combinations, a post-estimation command specifically tailored to rdhte. We also provide an overview of heterogeneous effects for sharp RD designs, give basic details on the methodology, and illustrate using an empirical application. Finally, we discuss how the package rdhte complements, and in specific cases recovers, the canonical RD package rdrobust (Calonico, Cattaneo, Farrell, and Titiunik 2017).

  PublisherOA PDFDOI

• Binscatter regressions

  The Stata Journal Promoting communications on statistics and Stata · 2025-03-01 · 8 citations

  articleCorresponding

  In this article, we introduce the package binsreg , which implements the binscatter methods developed by Cattaneo et al. (2024a, arXiv:2407.15276 [stat.EM]; 2024b, American Economic Review 114: 1488–1514). The package comprises seven commands: binsreg, binslogit, binsprobit, binsqreg, binstest binspwc , and binsregselect . The first four commands implement binscatter plotting, point estimation, and uncertainty quantification (confidence intervals and confidence bands) for least-squares linear binscatter regression ( binsreg ) and for nonlinear binscatter regression ( binslogit for logit regression, binsprobit for. probit regression, and binsqreg for quantile regression). The next two commands focus on pointwise and uniform inference: binstest implements hypothesis testing procedures for parametric specifications and for nonparametric shape restrictions of the unknown regression function, while binspwc implements multigroup pairwise statistical comparisons. The last command, binsregselect , implements. data-driven number-of-bins selectors. The commands offer binned scatterplots and allow for covariate adjustment, weighting, clustering, and multisample analysis, which is useful when studying treatment-effect heterogeneity in randomizec and observational studies, among many other features.

  PublisherDOI

• On Binscatter

  American Economic Review · 2024 · 115 citations

  • Political Science
  • Political Science

  Binscatter is a popular method for visualizing bivariate relationships and conducting informal specification testing. We study the properties of this method formally and develop enhanced visualization and econometric binscatter tools. These include estimating conditional means with optimal binning and quantifying uncertainty. We also highlight a methodological problem related to covariate adjustment that can yield incorrect conclusions. We revisit two applications using our methodology and find substantially different results relative to those obtained using prior informal binscatter methods. General purpose software in Python, R, and Stata is provided. Our technical work is of independent interest for the nonparametric partition-based estimation literature. (JEL C13, C14, C18, C51, O31, R32)

  PublisherDOI

• Nonlinear Binscatter Methods

  arXiv (Cornell University) · 2024-07-21 · 1 citations

  preprintOpen access

  Binned scatter plots are a powerful statistical tool for empirical work in the social, behavioral, and biomedical sciences. Available methods rely on a quantile-based partitioning estimator of the conditional mean regression function to primarily construct flexible yet interpretable visualization methods, but they can also be used to estimate treatment effects, assess uncertainty, and test substantive domain-specific hypotheses. This paper introduces novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation methods, covering generalized linear, robust, and quantile regression models. We provide a host of theoretical results and practical tools for local constant estimation along with piecewise polynomial and spline approximations, including (i) optimal tuning parameter (number of bins) selection, (ii) confidence bands, and (iii) formal statistical tests regarding functional form or shape restrictions. Our main results rely on novel strong approximations for general partitioning-based estimators covering random, data-driven partitions, which may be of independent interest. We demonstrate our methods with an empirical application studying the relation between the percentage of individuals without health insurance and per capita income at the zip-code level. We provide general-purpose software packages implementing our methods in Python, R, and Stata.

  PublisherOA PDFDOI

• Nonlinear Binscatter Methods

  Staff reports · 2024-08-01 · 7 citations

  reportOpen access

  Binned scatter plots are a powerful statistical tool for empirical work in the social, behavioral, and biomedical sciences. Available methods rely on a quantile-based partitioning estimator of the conditional mean regression function to primarily construct flexible yet interpretable visualization methods, but they can also be used to estimate treatment effects, assess uncertainty, and test substantive domain-specific hypotheses. This paper introduces novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation methods, covering generalized linear, robust, and quantile regression models. We provide a host of theoretical results and practical tools for local constant estimation along with piecewise polynomial and spline approximations, including (i) optimal tuning parameter (number of bins) selection, (ii) confidence bands, and (iii) formal statistical tests regarding functional form or shape restrictions. Our main results rely on novel strong approximations for general partitioning-based estimators covering random, data-driven partitions, which may be of independent interest. We demonstrate our methods with an empirical application studying the relation between the percentage of individuals without health insurance and per capita income at the zip-code level. We provide general-purpose software packages implementing our methods in Python, R, and Stata.

  PublisherDOI

• Higher-order refinements of small bandwidth asymptotics for density-weighted average derivative estimators

  Journal of Econometrics · 2024-09-21 · 2 citations

  article
  PublisherDOI

• Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators

  arXiv (Cornell University) · 2022-12-31

  preprintOpen access

  The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter restrictions and model assumptions that imply an asymptotic linear representation of the point estimator. These conditions can be restrictive, and the resulting distributional approximation may not be representative of the actual sampling distribution of the statistic of interest. In particular, the approximation is not robust to bandwidth choice. Small bandwidth asymptotics offers an alternative, more general distributional approximation for kernel-based DWAD estimators that allows for, but does not require, asymptotic linearity. The resulting inference procedures based on small bandwidth asymptotics were found to exhibit superior finite sample performance in simulations, but no formal theory justifying that empirical success is available in the literature. Employing Edgeworth expansions, this paper shows that small bandwidth asymptotic approximations lead to inference procedures with higher-order distributional properties that are demonstrably superior to those of procedures based on asymptotic linear approximations.

  PublisherOA PDFDOI

• Coverage error optimal confidence intervals for local polynomial regression

  Bernoulli · 2022-08-29 · 30 citations

  preprintOpen accessSenior author

  This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for t statistics and coverage error expansions for interval estimators that (i) hold uniformly in the data generating process, (ii) allow for the uniform kernel, and (iii) cover estimation of derivatives of the regression function. The terms of the higher-order expansions, and their associated rates as a function of the sample size and bandwidth sequence, depend on the smoothness of the population regression function, the smoothness exploited by the inference procedure, and on whether the evaluation point is in the interior or on the boundary of the support. We prove that robust bias corrected confidence intervals have the fastest coverage error decay rates in all cases, and we use our results to deliver novel, inference-optimal bandwidth selectors. The main methodological results are implemented in companion R and Stata software packages.

  PublisherOA PDFDOI

Frequent coauthors

• Matias D. Cattaneo

  47 shared

• Sebastián Calónico

  Columbia University

  24 shared

• Yingjie Feng

  11 shared

• Richard K. Crump

  Federal Reserve Bank of New York

  8 shared

• Rocío Titiunik

  7 shared

• Tengyuan Liang

  6 shared

• Sanjog Misra

  University of Chicago

  6 shared

• Ernst Schaumburg

  Indian School of Business

  5 shared