Closed-form estimation and inference for panels with attrition and refreshment samples

2024-10-15

AI Summary

This paper addresses the challenge of causal identification in panel data compromised by sample attrition and augmented with refreshment samples. We propose a closed-form estimator grounded in nonparametric identification assumptions—requiring no tuning parameters or numerical optimization—and construct it directly via empirical cumulative distribution function transformations. Under mild regularity conditions, we establish its consistency and asymptotic normality. Monte Carlo simulations and an empirical application to income data from the Understanding America Study demonstrate its robustness and superior performance relative to existing approaches. The key contribution is the first analytically tractable, optimization-free, and theoretically justified causal inference framework for attrition–refreshment panel designs—uniquely reconciling statistical rigor with computational efficiency.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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. 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.

Problem

• Addressing panel data attrition with refreshment samples
• Simplifying estimation under nonparametric identification assumptions
• Providing closed-form, tuning-free estimation algorithm

Innovation

• Nonparametric assumption enables simple estimation
• Closed-form algorithm using empirical CDF transformation
• No tuning parameters or optimization required