capture the (short or medium-run) network effects. Interestingly, when colonial links are included in such a stock-flow model, they turn out to be insignificant since their effect is absorbed by the existing network. From an economic point of view, the implications of those results is that recent migrants tend to come because they can rely on a network at destination, not because of past colonial links that offer current advantages.

The measurement of migration flows in destination countries is also a tricky issue. In most countries, we can rely on census data to provide the stock of migrants in a given year. For most national census rounds, a ten-year frequency is the rule. Therefore, the only way to measure migration flows over a ten-year period is to take the difference between stocks in two successive census rounds. This in turn raises several additional complications. First, the net migration flows are affected by the mortality rate of migrants present in the initial census. Second, there can be significant return migration which varies across origin and destination countries. For instance, using US data, Rosenzweig (2008) shows that the level of skill premia in the origin country is an important factor for the return migration rate of skilled migrants and students. Third issue arises due to regularization (legalization) programs implemented for undocumented migrants who are not recorded in many censuses (such as in most European countries). If regularization programs are implemented between the two censuses, the stocks of migrants in the second census and hence the size of the migration flows will increase in the data without actual movement of people. Another theoretical argument developed by Br ̈ucker (2006) suggests that using net migration flows instead of stocks might be misleading in the case of heterogeneous agents. This is especially important when it comes to estimating the impact of wage differentials on migration. In models like ours, we do not explicitly include the wage differentials for several reasons. One reason is the absence of reliable wage indices by skill level in most origin countries. A second reason is that wages are captured by country fixed effects in most of our estimations. To sum up, there are obviously negative and positive biases in measuring migrations flows through the changes in migrant stocks from census data. Whether this tends to underestimate or overestimate the true values is obviously difficult to know in advance.

# 3.4 Defining a network

The investigation of the network effect relies on a specific definition of diaspora which is the stock of nationals from country o living in destination d at a given time. This is a natural definition of the people who are supposed to provide assistance and help to the new arrivals. On the one hand, restricting the diaspora to people with the same nationality might be restrictive. Ethnic networks are also known to be efficient and do not necessarily correspond to national borders. Migrants speaking the same language can be also very useful for the assimilation of new migrants. On the other hand, defining the network at the national level might overestimate the number of people able to provide help. Obviously, people located in large countries such as the US can provide assistance mainly 10