Closed-form estimation and inference for panels with attrition and refreshment samples
Grigory Franguridi, Lidia Kosenkova
TL;DR
This paper tackles panel attrition by introducing a closed-form estimator that transforms the empirical distribution via a separability-based identification condition, avoiding tuning and optimization. It uses a two-step plug-in to recover the joint distribution $F$ from observed data and refreshment samples, then solves $\mathbb{E}_F m(Z_1,Z_2;\theta)=0$ for $\theta$, with bootstrap inference enabled by the smooth plug-in. The method is shown to be consistent and asymptotically normal, with simulation evidence and an empirical application (Understanding America Study) illustrating substantial effects and improved handling of attrition relative to naive methods. This work lays groundwork for extending to multiple periods, complex missingness patterns, and high-dimensional covariates while maintaining computational simplicity.
Abstract
It has long been established that, if a panel dataset suffers from attrition, auxiliary (refreshment) sampling restores full identification under additional assumptions that still allow for nontrivial attrition mechanisms. Such identification results rely on implausible assumptions about the attrition process or lead to theoretically and computationally challenging estimation procedures. We propose an alternative identifying assumption that, despite its nonparametric nature, suggests a simple estimation algorithm based on a transformation of the empirical cumulative distribution function of the data. This estimation procedure requires neither tuning parameters nor optimization in the first step, i.e., it has a closed form. We prove that our estimator is consistent and asymptotically normal and demonstrate its good performance in simulations. We provide an empirical illustration with income data from the Understanding America Study.