cities where unemployment is expected to be continue to be high or rise further. Our view is the common trends assumption is likely to be more plausible when the units being compared are more similar to one another to begin with, which is where combining matching with DiD can be of use (e.g. Gibson and McKenzie (2014)). Newer, “doubly-robust” approaches to DiD build on this idea to yield valid estimates when either the selection on observables needed for propensity scores or the parallel trends modelling assumption used in DiD holds.

A second common form of difference-in-differences estimation in migration studies is to examine the impact of staggered policies introduced into different states or different countries at different points in time. For example, Otsu (2021) uses panel data from 1999 to 2020 to examine the impact of sanctuary cities (cities that do not share data on immigrants with the Federal government) on crime, with cities adopting this policy over time. At the country level, Kahanec et al. (2016) examine the impact of different countries joining the European Union’s free movement of workers on bilateral migration flows. In cases like these, where treatments are staggered over time, recent literature has shown that in the presence of treatment effect heterogeneity or dynamic treatment effects, the standard twoway fixed effects difference-in-differences estimator is a weighted average of many different comparisons, and it is possible that some of these weights may even be negative, making it hard to interpret the estimate (Goodman-Bacon, 2021). Different estimators have been developed to deal with this problem, which involve making sure that treated units are only ever compared to ‘clean controls’ and not to earlier treated units (see de Chaisemartin and D’Haultfoeuille (2022) and Roth et al. (2022) for a survey). A key point to note here is that with treatment heterogeneity, researchers need to clearly specify precisely which weighted average they are interested in estimating.

A third type of difference-in-differences commonly used in the migration literature involves situations in which there is different exposure to some policy change across different regions, sometimes due to some pre-existing migration networks. In these cases the treatment is no longer binary, but can be continuous or have multiple discrete values. For example, Abarcar and Theoharides (2022) examine the impact of changes in U.S. working visas (H-1B visas) for medical professionals, which affected some parts of the Philippines more than others based on their prior participation in medical worker migration to the U.S. Theoharides (2020) considers a natural experiment that occurred in the Philippines in 2006, in the form of a nearly-complete shutdown of a large specific migration channel – that of Filipino female “overseas performance artists” (OPAs) going to Japan. The identification strategy exploits the fact that OPA migration was unevenly distributed across provinces prior to 2006, so pre-2006 province shares of OPA migration are associated with greater declines in migration from pre- to post-2006. Dinkelman and Mariotti (2016) provide a third example, examining the impact of migrant work opportunities (male outmigration to the South African mines) on education in Malawian origin areas. She compares cohorts of 22