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Nonlinear Budget Set Regressions for the Random Utility Model
This paper is about the nonparametric regression of a choice variable on a nonlinear budget set when there is general heterogeneity, i.e., in the random utility model (RUM). We show that utility maximization makes this a three-dimensional regression with piecewise linear, convex budget sets with a more parsimonious specification than previously derived. We show that the regression allows for measurement and/or optimization errors in the outcome variable. We characterize all of the restrictions of utility maximization on the budget set regression and show how to check these restrictions. We ...
Beta-sorted portfolios—portfolios comprised of assets with similar covariation to 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 statistical 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 portfolios construction. Our framework rationalizes the well-known ...
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 standard choices of five or ten. To ...