RIF regression via sensitivity curves

Abstract

This paper proposes an empirical method to implement the recentered influence function (RIF) regression of Firpo et al. (Econometrica 77(3):953–973, 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 sensitivity curve (as reported by Tukey in Exploratory Data Analysis. Addison-Wesley, Reading, MA, 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 et al. (Econometrica 72(6):1737–1772, 2004).