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Difference-in-Differences Estimates under Selective Migration

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  • Valli, Roberto

    (ETH Zürich)

Abstract

Difference-in-differences designs often study place-based treatments that can trigger migration in and out of treated areas. When treatment changes who is observed, aggregate and within-individual DiD no longer retrieve the average treatment effect on the treated. This paper uses principal stratification to characterize three estimands under treatment-induced migration: a locality-level treatment effect, a stayer average treatment effect, and an individual ATT for the pre-treatment population. Aggregate DiD identifies the locality-level effect under aggregate parallel trends, while within-individual DiD identifies the stayer effect under stayer parallel trends. Together, the two assumptions imply parallel trends for escapees, a non-trivial restriction on the group whose departure drives compositional change. With panel data, the stayer effect and the compositional term are point-identified, and the ATT lies in a one-parameter sensitivity region. With repeated cross-sections, Lee-type bounds apply in the one-sided exit case. An appendix extends these results to natural turnover and treated-control interference.

Suggested Citation

  • Valli, Roberto, 2026. "Difference-in-Differences Estimates under Selective Migration," SocArXiv s7pw3_v1, Center for Open Science.
    • Handle: RePEc:osf:socarx:s7pw3_v1
    DOI: 10.31219/osf.io/s7pw3_v1
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    References listed on IDEAS

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    1. Ghanem, Dalia & Hirshleifer, Sarojini & Kédagni, Désiré & Ortiz-Becerra, Karen, 2024. "Correcting attrition bias using changes-in-changes," Journal of Econometrics, Elsevier, vol. 241(2).
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