affected by migration, and so one ideally needs to control for pre-migration household wealth. Alternatively, one can try to approximate it by certain household assets that are less likely to be affected by current remittance flows and more likely to reflect long term wealth, such as housing amenities (see e.g. Acosta, 2006). When done well, propensity score matching can lead to a significant improvement over the OLS estimates.

# _3.5.5. Going around the problem: working in differences and instrumental variables_

A major advantage of panel data or data with retrospective variables is that it allows control for issues of time-invariant unobservable characteristics. When only a migrant sample is available a single difference estimator can compare post-migration income to pre-migration income and take the average difference as a mean impact of migration. This estimator could be corrected by a mean change in the home country income. When a panel includes both migrants and non-migrants, a double difference (difference-indifferences) estimator directly estimates gains from migration (if the model is correct), for example in the following regression: Δoutcomei = αi + β*migrationi + γ*Xi + εi.

Use of instrumental variables is prevalent in the research on the impact of migration. A powerful instrument can eliminate problems of endogeneity, omitted variables and measurement error. Yet the technique can be deceptive. Below we will discuss its application to migration in greater detail.

<u>How does the instrument work?</u> The direct source of bias in the OLS estimator is a violation of the independence of explanatory variable (say, migration) from the error term in the equation. Suppose that ability influences both migration and an outcome of interest (say, income). However, since ability is unobserved it ends up in the error term, which now becomes correlated with migration. By finding a variable (an “instrument”) that is correlated with migration but uncorrelated with ability (or, equivalently, it is uncorrelated with income for reasons beyond its effect on migration) one can “split” the variation in migration and “use” only the part uncorrelated with the error term.

<u>How to find a good instrument?</u> Technically speaking an instrument must be relevant (correlated with the explanatory variable) and exogenous (not correlated with the dependent variable other than through the explanatory variable). Instrument relevance is testable (by regressing the outcome on the instrument), while instrument exogeneity, in principle, needs to be “argued”. The instrument should not be “weak” (i.e. weakly correlated with the explanatory variable), so an F-statistic below 10 may be a cause for concern (Staiger and Stock, 1997). One instrument is often preferable to a set of them (Angrist and Krueger, 2001).

In reality, as Angrist and Krueger (2001) argue, good instruments often come from detailed knowledge of the economic mechanism and institutions determining variables of interest. A very popular method is to look for “natural experiments”, where a force majeure (natural shocks or a blunt government intervention) causes an exogenous change in an otherwise endogenous explanatory variable. In the context of migration we need to think of reasons why one household may have a migrant and another “identical” 9