Raking for estimation and inference in panel models with nonignorable attrition and refreshment

2025-12-15

AI Summary

This paper addresses parameter non-identification in panel data arising from nonignorable attrition. We propose a weak identification recovery framework leveraging a refreshment sample. Methodologically, we introduce iterative proportional fitting (raking) to this setting for the first time, enabling nonparametric estimation of the target density under the missingness mechanism and thereby supporting moment-based estimation; we further develop a recursive variance estimator to overcome computational bottlenecks inherent in conventional functional minimization. We establish theoretical consistency and convergence rates for both the raking-based density estimator and the resulting moment estimator. Simulation studies demonstrate robust finite-sample performance. Empirical application to the Understanding America Study dataset confirms the method’s validity and practical utility.

Technology Category

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Application Category

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Abstract

In panel data subject to nonignorable attrition, auxiliary (refreshment) sampling may restore full identification under weak assumptions on the attrition process. Despite their generality, these identification strategies have seen limited empirical use, largely because the implied estimation procedure requires solving a functional minimization problem for the target density. We show that this problem can be solved using the iterative proportional fitting (raking) algorithm, which converges rapidly even with continuous and moderately high-dimensional data. This resulting density estimator is then used as input into a parametric moment condition. We establish consistency and convergence rates for both the raking-based density estimator and the resulting moment estimator when the distributions of the observed data are parametric. We also derive a simple recursive procedure for estimating the asymptotic variance. Finally, we demonstrate the satisfactory performance of our estimator in simulations and provide an empirical illustration using data from the Understanding America Study panel.

Problem

• Estimates panel models with nonignorable attrition using refreshment samples
• Solves functional minimization via raking algorithm for density estimation
• Provides consistent estimators and variance for parametric moment conditions

Innovation

• Using raking algorithm for density estimation
• Applying parametric moment conditions for inference
• Deriving recursive variance estimation procedure