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

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.

💡 Research Summary

The paper tackles the pervasive problem of attrition in panel surveys by exploiting auxiliary refreshment samples, which are random draws from the target population collected at later waves. While earlier work (e.g., Hirano et al., 2001) showed that identification can be restored under additive non‑ignorability, those approaches either impose implausibly strong restrictions on the attrition mechanism or require computationally intensive procedures such as non‑linear optimization or iterative raking.

The authors propose a new, non‑parametric identifying assumption—called quasi‑separability—stating that the probability of staying in the panel, conditional on the cumulative distribution of the first‑wave variables Z₁ and second‑wave variables Z₂, can be written as
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