locations, and then employing different bounding approaches and reweighting approaches to examine how sensitive the results might be to different assumptions about individuals who are not found. McKenzie (2015) provides more details on data collection for migration experiments.

_Measurement of beliefs can be crucial._ Equation 3 makes clear that migration decisions depend not just on the actual wages and amenities in different locations, but also on what individuals believe these to be. Haaland et al. (2022) offer a nice recent guide to conducting information experiments, which offers several lessons for things to measure in migration experiments. First, the expected directional response to an information treatment depends on what people believe in the first place, and we should expect heterogeneity in the responses. For example, individuals who under-estimate wages at the destination may increase their migration likelihood when given the correct information, whereas individuals who overestimate wages may decrease this likelihood. Looking only at the average effect without measuring baseline beliefs would miss this important heterogeneity. Second, there are a lot of design issues in how to provide information, and it is important to think carefully about whether the information provided is credible, and whether potential migrants will trust the information. Third, you want to then measure how beliefs are updated, so that we can distinguish between a treatment not working because the information did not change beliefs, versus it not working because other constraints were more important.

_Measuring welfare improvements can be difficult when people change locations._ Migration can deliver large gains in incomes. For example, Gibson et al. (2017) use a visa lottery to show that migrating from Tonga to New Zealand leads to a 263 percent gain in income in the first year, with these benefits persisting over time for a lifetime benefit of US$237,000. However, the change in location also means migrants face different costs of living, different amenities (e.g. different quality schools, differences in opportunities for their children, differences in access to nature, differences in access to cultural opportunities, etc.). The logic of equation 3 and revealed preference would suggest that migrating (at least in expectation) should make people better off. But, as we have discussed, these expectations may be based on incorrect information in some cases, or migrants may have correct expectations but still be unlucky and not earn as much as expected.

A partial solution to this problem is to attempt to measure a broader range of outcomes, including direct measurement of amenities and survey measures that may better capture well-being than income or expenditure. Examples include subjective happiness, or mental health. But these subjective well-being measures also face difficulties when people change locations, since their reference groups may change. Stillman et al. (2015) find that impacts on subjective well-being differ depending on whether migrants use their previous life as a reference or compare themselves to their contemporaneous surroundings. Likewise, tastes and preferences may change over time as migrants assimilate into a new culture and form 10