arXiv subjects

Richard K. Crump

Publications and source records attributed to Richard K. Crump.

5 recordsLinked to original sources

arXiv2026

Beta-Sorted Portfolios

Beta-sorted portfolios---portfolios comprised of assets with similar covariation with selected risk factors---are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their econometric properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric estimator with a nonparametric first step and a beta-adaptive portfolio construction. Our framework rationalizes the well-known estimation algorithm with precise economic and statistical assumptions on the general data-generating process. We provide conditions which ensure valid estimation and inference allowing for a range of hypotheses of interest in financial applications. We show that the rate of convergence of the estimator changes depending on the value of beta. We demonstrate that valid inference depends critically on the object of interest and discuss drawbacks of the widely used Fama-MacBeth variance estimator. To address these limitations, we propose a new variance estimator. We demonstrate the usefulness of our theoretical results in two empirical applications, including one in which we introduce a novel risk factor that captures the business credit cycle and show that it predicts both the cross-sectional and time-series behavior of U.S. stock returns.

econ.EM↗

arXiv2026

Nonlinear Binscatter Methods

Binscatters are a powerful tool for empirical work in the social, behavioral, and biomedical sciences. Available tools rely on least squares estimation of the conditional mean. We introduce novel binscatter methods based on nonlinear, possibly nonsmooth M-estimation, covering generalized linear, robust, and quantile regression models. We provide theoretical results and practical tools, including optimal bin selection, confidence bands, and statistical tests regarding functional form or shape restrictions. We demonstrate our methods by studying the relationship of income and (lack of) health insurance. We provide software for Python, R, and Stata. Our technical results may be of independent interest.

stat.ME↗

arXiv2024

Binscatter Regressions

We introduce the package Binsreg, which implements the binscatter methods developed by Cattaneo, Crump, Farrell, and Feng (2024b,a). The package includes 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 multi-group pairwise statistical comparisons. Finally, the command binsregselect implements data-driven number of bins selectors. The commands offer binned scatter plots, and allow for covariate adjustment, weighting, clustering, and multi-sample analysis, which is useful when studying treatment effect heterogeneity in randomized and observational studies, among many other features.

econ.EM↗

arXiv2024

On Binscatter

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.

econ.EM↗

arXiv2019

Characteristic-Sorted Portfolios: Estimation and Inference

Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We develop a general framework for portfolio sorting by casting it as a nonparametric estimator. We present valid asymptotic inference methods and a valid mean square error expansion of the estimator leading to an optimal choice for the number of portfolios. In practical settings, the optimal choice may be much larger than the standard choices of 5 or 10. To illustrate the relevance of our results, we revisit the size and momentum anomalies.

econ.EM↗