entire families, while in others only some members emigrate.<sup>5</sup> A third form of selection which also occurs in many contexts is selection into which migrants return. Since we are examining the short-run impacts of migration, this source of selectivity is not an issue here.<sup>6</sup> We are not aware of any study of the impact of migration on sending households which explicitly deals with the second form of selection, since almost all developing country migrant datasets lack information on entire households that move. The literature has used a variety of approaches to address the first form of selection. Examples include assuming selection on observables (e.g. Adams, 1998; Cox-Edwards and Ureta, 2003), parametric selection correction models (e.g. Barham and Boucher, 1998; Acosta, Fajnzylber and Lopez, 2007), propensity-score matching (Esquivel and Huerta-Pineda, 2006), instrumental variables methods, predominantly using current migration networks (e.g. Mansuri, 2006, Brown and Leeves, 2007) or historic networks as instruments (e.g. Woodruff and Zenteno, 2007; McKenzie and Rapoport 2007)7 and work by Yang (2008) which uses a natural experiment provided by exchange rate shocks in destination countries to look at impacts within the group of households with migrants abroad.

However, one may question the identification assumptions underlying these nonexperimental approaches to constructing no-migration counterfactuals. There is evidence that migrants self-select both in terms of observables and unobservables (McKenzie, Gibson and Stillman, 2009, Akee, 2009), so methods that assume selection on observables (which include OLS and matching) are likely to be biased. Selection correction methods rely on parametric structure and dubious excludability assumptions. For example, Acosta et al. (2007) and Barham and Boucher (1998) assume that household asset holdings predict selection into migration but do not directly affect earnings or labor force participation, when these assets could be used to help finance own businesses, or could be the result of labor earnings. The use of current migration networks as an instrument is subject to concerns about other variables at the community level which also affect migration and outcomes of interest. For example, a recent community weather shock such as a drought may have led to both increased migration and a reduction in agricultural income in the community. Historic

> 5 A further issue faced by some of the literature is the attempt to distinguish the impact of remittances from the overall impact of migration. See McKenzie (2005) for a critique of this approach. 6 None of the PAC migrants had returned to live in Tonga during the period of our study.

> 7 Other instrumental variables have been also been used, but the exclusion restriction underlying these are perhaps less convincing than the historic network variables. For example, Amuedo-Dorantes and Pozo (2006a) assume that the number of Western Union branches in a state in Mexico affects labor supply only through current migration, when these branches are likely to have been established as the result of factors which have driven migration historically, including the level of development in a state, which likely also impact on labor supply.

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