Annex A. Methodology to estimate patterns of return migration

Estimating immigrant exits using destination countries’ data

United States

To estimate the exit rate from the United States, the following approach is used. First, the American community survey is used to determine an initial cohort (immigrants) that entered the United States in year t. Then, the number of immigrants remaining after five years is determined (remainings_t,t+5) using the same survey. Third, age- and sex-specific mortality rate data is extracted from the Human Mortality Database to estimate the number of deaths in the cohort during the period of interest (deaths_t,t+5). Finally, the number of exits (exits_t,t+5) is derived as follows:

Equation11

${\mathit{e}\mathit{x}\mathit{i}\mathit{t}\mathit{s}}_{\mathit{t},\mathit{t}+5}$ =${\mathrm{ }\mathit{i}\mathit{m}\mathit{m}\mathit{i}\mathit{g}\mathit{r}\mathit{a}\mathit{n}\mathit{t}\mathit{s}}_{\mathit{t}\mathrm{ }}-\mathrm{ }{\mathit{r}\mathit{e}\mathit{m}\mathit{a}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\mathit{s}}_{\mathit{t},\mathit{t}+5}\mathrm{ }-{\mathrm{ }\mathit{d}\mathit{e}\mathit{a}\mathit{t}\mathit{h}\mathit{s}}_{\mathit{t},\mathit{t}+5}$

The 5-year exit rate (exit_rate_{t, t+5)} is obtained by dividing the number of exits by the initial cohort:

Equation 2

${\mathit{e}\mathit{x}\mathit{i}\mathit{t}\_\mathit{r}\mathit{a}\mathit{t}\mathit{e}}_{\mathit{t},\mathrm{ }\mathit{t}+5}=\frac{{\mathit{e}\mathit{x}\mathit{i}\mathit{t}\mathit{s}}_{\mathit{t},\mathrm{ }\mathit{t}+5}}{{\mathit{i}\mathit{m}\mathit{m}\mathit{i}\mathit{g}\mathit{r}\mathit{a}\mathit{n}\mathit{t}\mathit{s}}_{\mathit{t},}}$

The entry periods considered are 2010, 2011, 2012, 2013 and 2014. It should be noted, however, that the number of cohorts in a given year t is determined using the t+1 survey data. This avoids the problem of partial coverage. The main limitation of this approach is that immigrants who returned before one year are not captured in the initial cohort. In addition, for the periods considered, there are no observations with missing information on the year of entry. Therefore, the treatment of missing values is not applicable.

Canada

For Canada, the same approach as the United States is used to determine the exit rate. The main difference is that, in the case of Canada, the 2011 and 2016 national censuses are used. Specifically, the 2011 census is used to estimate the number of immigrants who arrived in 2010. Next, the Human Mortality Database is used to estimate the number of deaths by sex and age between 2011 and 2015. Third, the 2016 Census is used to determine the number of immigrants who entered in 2010 and were still in the country in 2015. Lastly, Equation 1 and Equation 2 above determine the number of leavers and the exit rate. Note that observations for which entry year information is not available are assigned proportionally to the weights of the different entry years available to keep them in the sample.

European OECD countries

Exit rates for European OECD countries are estimated from the International Migration Database and the Labour Force Surveys (LFS). Specifically, the international migration database is used to estimate the initial cohort flows to overcome the partial coverage issue inherent in LFS. Next, we use the LFS to estimate the size of the initial cohort in year t + k. Estimates based on LFS data, however, raise issues of non-response bias and sample instability, which must be accounted for in the analysis. To address these concerns, the same approach as (OECD, 2008[1]) is followed. First, non-response is reallocated proportionally to the weights of the different length-of-stay responses to maintain the total number of immigrants. To account for sample size volatility, the data is smoothed by constructing an envelope around the initial cohort so that the number of immigrants retained for a given length of stay is the average between the maximum and minimum values in the envelope. Figure A A.1 shows the adjustments made for the 2010 cohort of immigrants who entered the United Kingdom.

Figure A A.1. Evolution of the number of immigrants entering the United Kingdom in 2010

By length of stay

Source: Own estimates based on Labour Force Surveys and International Migration Database.

Estimating return migration using origin countries’ data

For the analysis of return migration to origin countries, census or survey data is used to identify return migrants at date t in the origin country based on residence information at date t-5. Then, censuses and surveys in the receiving country can be used to determine the number of emigrants who arrived in the destination country before t-5. Once the number of returning migrants (return migrants_t-5,t) and the number of immigrants in t-5 in the destination country (immigrants_t−5) are determined, the return rate (return_rate_{t−5, t)} to the origin country can be calculated as follows:

Equation 3

${\mathit{r}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\_\mathit{r}\mathit{a}\mathit{t}\mathit{e}}_{\mathit{t}-5,\mathrm{ }\mathit{t}}=\frac{{\mathit{r}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathit{e}\mathit{e}\mathit{s}}_{\mathit{t}-5,\mathit{t}}}{{\mathit{i}\mathit{m}\mathit{m}\mathit{i}\mathit{g}\mathit{r}\mathit{a}\mathit{n}\mathit{t}\mathit{s}}_{\mathit{t}-5}}$

It should be noted that the mortality of immigrants between the two periods must be considered, but the methodological difficulties in measuring the mortality of this very mobile population may call the estimates into question. In most major host countries, the literature has shown that the mortality of foreign-born people seems to be lower than that of the host country. Therefore, and given the low mortality rate in OECD countries, deaths are negligible.