WPS4249 In this context, however, there is the possibility of finding instruments that can be considered exogenous and yet be correlated with remittances. In this regard we employ both internal instruments based on lagged levels and first differences of the remittances variable, and two types of external instruments based on the economic conditions of the countries in which most remittances to developing countries originate. The first variable is based on the per capita GDP of each of the top ten migrant receiving countries of the world, weighted by the inverse of the distance to these ten countries from each remittance receiving country in our sample. We will refer to this series as the Distance variable. The second external instrumental variable is based on the real GDP per capita of the five OECD countries that are the top receivers of migrants for each remittance receiving country, weighted by the share of migration from the corresponding country to each of those five OECD destinations. We refer to this series as the Migration series. In each case, we consider as potential instruments the (logged) level of the variables at the beginning of the period and the growth rates over the period under consideration.<sup>11</sup> The consistency of the GMM estimator above depends on the validity of the assumption that the error terms do not exhibit serial correlation as well as on the validity of the instruments. We present two specification tests to address these issues. The first is the Sargan test of overidentifying restrictions. The second test examines whether the error term υ _it_ in (7) is not serially correlated, which in turn would imply that the difference error in (9) does not present second-order serial correlation (SOSC).

# _(d) Control variables_

We turn to the specification of the set of control variables included in _x_ . There is a wide array of potential explanatory variables that can be used in this context.<sup>12</sup> In this paper, rather than adding to the already huge variety of growth models, we opt for considering a set that has already been used in a number of empirical growth studies. This is the one used by Perotti (1996), Forbes (2000), Banerjee and Duflo (2003), and Knowles (2005), and it includes the average years of secondary education of the male population, the average years of secondary education of the female population, and a measure of market distortions: the price of investment

> (see, e.g., Ziliak 1997). To reduce this bias,  in the estimations below we limit the number of over identifying restrictions by building only one instrument from each variable and lag distance, rather than building one separate instrument from each variable, and lag distance in each time period.

11 The basic intuition behind these instruments is that migrants tend to send more money to their home countries when they face improved economic conditions in the countries where they are established. Thus, higher growth in a given migrant-receiving country is likely to lead to increased remittances flows to countries that have a large share of their stock of migrants located in that country. Moreover, since the importance of each developed country as a destination for migrants of a given developing country is inversely correlated with the distance between those countries, the effect of growth in the former on the flows of remittances to the latter is likely to decrease with the distance between them. In other words, remittances will likely be positively related to growth in migrant destination countries, to the existing stock of migrants in those countries, and to the inverse of the distance between them. On the other hand, the proposed instruments are not likely to affect growth or inequality in migrant-sending countries, beyond their effect through changes in remittances flows..

12 As noted by Durlauf and Quah (1999), by 1998 the number of individual regressors that had been considered as potential explanatory variables in growth regressions exceeded the number of countries in the standard growth dataset.

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