RIF Regression via Sensitivity Curves

TL;DR

This paper introduces a practical method for RIF regression using sensitivity curves as an alternative to influence functions, employing cubic splines for computational efficiency, and demonstrates its effectiveness through simulations and an application to polarization measurement.

Contribution

It proposes a novel empirical approach to RIF regression using sensitivity curves and cubic splines to handle large samples efficiently.

Findings

Sensitivity curves converge to influence functions under general conditions.

The cubic spline method provides accurate interpolation for large datasets.

Monte Carlo simulations confirm good finite sample properties.

Abstract

This paper proposes an empirical method to implement the recentered influence function (RIF) regression of Firpo, Fortin and Lemieux (2009), a relevant method to study the effect of covariates on many statistics beyond the mean. In empirically relevant situations where the influence function is not available or difficult to compute, we suggest to use the \emph{sensitivity curve} (Tukey, 1977) as a feasible alternative. This may be computationally cumbersome when the sample size is large. The relevance of the proposed strategy derives from the fact that, under general conditions, the sensitivity curve converges in probability to the influence function. In order to save computational time we propose to use a cubic splines non-parametric method for a random subsample and then to interpolate to the rest of the cases where it was not computed. Monte Carlo simulations show good finite sample properties. We illustrate the proposed estimator with an application to the polarization index of Duclos, Esteban and Ray (2004).