Testing selection on observables in parametric models with refreshment samples

2026-08-24

AI Summary

本文提出了一种基于再抽样数据的统计检验方法，用于检测面板数据中观测变量选择假设（MAR）的有效性，通过比较两种加权估计分布实现。

Abstract

In panels with sample selection (that may occur due to attrition, nonresponse, etc.), the assumption of selection on observables (missing at random, MAR) is commonly imposed despite often being implausible. However, this assumption becomes testable when a refreshment sample is available. We develop a statistical test of MAR based on a distance between two estimated distributions: one obtained using the standard inverse probability weighting (IPW) that is valid under MAR and the other obtained using an alternative weighting that is valid under a weaker assumption of additive nonignorability of Hirano et al. (2001). This test implicitly compares the distribution of the IPW-weighted sample in the attrition period with the distribution of the refreshment sample, which coincide if the MAR assumption holds. We establish that, when the input distributions are parametric, our test statistic converges to the generalized chi-squared distribution under the null of MAR. This limit distribution can be estimated using the recursive formulas derived by Franguridi et al. (2026). We illustrate the performance of our test in Monte Carlo simulations. Finally, we apply our test to an empirical example using a subsample of the Understanding America Study (UAS) dataset.

Problem

• sample selection
• missing at random
• refreshment sample

Innovation

• Inverse Probability Weighting (IPW)
• Additive Nonignorability
• Generalized Chi-Squared Distribution
• Refreshment Sample