literature contains many theoretical and applied papers arguing how households can use migration to respond to shocks, and so relying on fixed effects requires having a compelling story as to why one household suddenly changed migration status at the time that it did, and why this is not otherwise related to the outcome of interest.

Fixed effects may potentially raise fewer concerns when migration or migrant outcomes like employment and wages are the dependent variable, and the fixed effects are being used to help ensure that impacts are being identified from shocks in an independent variable. A first example is Mckenzie et al. (2014). Their analysis involves panel data on migration from Philippines to various countries. The unit of observation is the destination country of migrants, and outcomes of interest are counts and wages of migrants going to those countries. Fixed effects for destination country account for time-invariant omitted variables at the destination level. The focus is on the impact of changes in destination log GDP on migrant flows and migrant wages. Reverse causation is plausibly ruled out because Philippine migrants are a small share of destination labor forces. Omitted variable concerns that remain are about whether changes in GDP _per se_ are the causing factor, as opposed to changes that happen to coincide with GDP changes (such as changes in public policies). Changes in public policies (such as immigration policies) are not necessarily identification concerns, however, if they are mechanisms through which GDP shocks lead to changes in migration. A second example of a fixed effects approach is Mahajan and Yang (2020), who examine the effect of hurricanes on international migration to the U.S. The unit of observation is combinations of origin-country and year from 1980 to 2002, and the outcome of interest is immigration to the U.S. (expressed as a share of origin country population). The analysis regresses immigration on an origin country’s hurricane index (a measure of the origin country’s hurricane exposure) in a given year, including origin-country fixed effects, year fixed effects, and differential origin-country-specific linear time trends. Fixed effects for origin country in a panel data setting are crucial here, to account for an important time-invariant omitted variable: a country’s _propensity_ to be struck by hurricanes. If this analysis was done with cross-sectional data, or if country fixed effects were not included in the regression, interpretation of the coefficient on hurricanes would be confounded by the effect of the country’s general exposure to hurricanes – a geographic characteristic of a country that could itself predict the outcome of interest. For example, hurricane exposure is highly correlated with location in the tropics, which itself could have effects on many outcomes of interest, including migration.<sup>9</sup> omitted variable bias to remain. Third, these remittances could themselves be endogenous, responding to shocks to education.

> 9Another example is Abarcar (2017), who examines how return migration by Australian immigrants is affected by exchange rate shocks in immigrants’ home countries, taking advantage of exchange rate variation over time while controlling for household fixed effects. The analysis actually looks at return migration in first-differences, which is equivalent to inclusion of household fixed effects when there are only two time periods.

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