We validate our estimated migration flows in two ways. First, we compare our estimated flows with female and male flows reported by Eurostat and the DEMIG project. Second, we compare the sum of the estimated female and male flows with flows reported by Eurostat, DEMIG and UN DESA. In the final part of this section, we discuss the discrepancies between the sum of the sex-specific flows and our previously estimated flows (Abel and Cohen 2019) from the same six methods based on the changes in the total bilateral migrant stock data with no disaggregation by sex. Details on the types of reported migration statistics for each country and period in each of collections are provided in the country_period_validation.csv file in the Figshare collection19.
Both comparisons for our validation use annual reported migration statistics of migration flows. However, the estimates presented above cover five-year periods due to the spacing of the bilateral migrant stock data. To compare the annual reported migration statistics to the estimated five-year migration flows, we compute equivalent five-year reported flows, in each bilateral pair and period, by multiplying the average of the annual reported migration flows during the period by five.
We do not expect the equivalent reported migration flows to be the same as the flows estimated here for two reasons. First, the annual reported migration flows use a variety of definitions that directly influence the number of migrants counted. For example, a country that defines migrants as persons who have changed their country of residence and stayed for three months will count more migrants (all else being equal) than a country that uses twelve months to define migration. Differences in definitions of migration used by countries and their impact on the level of reported international migration flows have been discussed by multiple authors5,21,22,23. Second, a five-year migration flow is likely to be less than five times an annual migration flow because of return migrants or deaths during the period. Rees24 discusses in detail differences between reported one- and five-year migration flow statistics.
Due to these expected discrepancies in the migration levels of the reported and estimated migration flows, we use a correlation measure for our validation rather than an accuracy measure such as mean absolute error. We calculate the Pearson’s correlation between our estimated flows and equivalent reported migration flows for six measures of migration: the count of the bilateral migration flow, the logarithm of bilateral migration flow, the proportion of bilateral migration flows into or out of a given country, the immigration and emigration rates and the net migration count. The populations in the origin and destination countries at the start of the period are used to calculate the emigration and immigration rates, respectively. These six measures for validating migration flow estimates were proposed by Abel & Cohen (2019) to cover varying potential uses for the migration flow estimates. For example, economists might use the logarithm of the migration counts in a gravity model analysis. For a population projection model, demographers might use immigration and emigration rates of migration transitions, i.e., counts of the number of persons who reside in country i at time t and country j at time t + 1.
In our first comparison, we calculate the correlation of the estimated female and male migration flows with our construction of the equivalent reported five-year sex-specific migration flows from the DEMIG project and Eurostat. The DEMIG C2C data set25 provides sending and receiving sex-specific bilateral migration flow data by next or previous place of residence reported by 14 countries. We used the data to create 30,738 equivalent five-year reported sex-specific bilateral migration flows for comparison with the estimated flow. In addition, we calculated 114, 118 and 114 five-year reported sex-specific immigration rates, emigration rates and net migration counts respectively. Eurostat receiving and sending migration flow data were downloaded in March 2021 (provided in tables migr_imm5prv and migr_emi3nxt at https://ec.europa.eu/eurostat/en/). Using data from 42 European and Central Asian countries, we constructed 69,383 equivalent five-year reported sex-specific bilateral migration flows for comparison with the estimated flows. In addition, we calculated 308, 304 and 302 immigration, emigration and net migration five-year reported migration totals over the six periods. The constructed equivalent migration statistics based on the DEMIG C2C and Eurostat data were used to calculate the correlations with the estimated migration flows based on the six migration measures discussed above. The correlations are plotted in a heat map in Fig. 4.
Figure 4 shows modest differences between the correlations of female and male flows for most migration measures and estimation methods, regardless of the data source (DEMIG C2C or Eurostat). The correlations of the estimated female migration flows and the DEMIG C2C measures tend to be higher than the corresponding correlations for the male migration flows. These consistent differences suggest that the estimated methods tend to be better at capturing female migration than male migration from changes in bilateral stocks, especially for flows not involving Europe. The differences between the sex-specific correlations are more balanced from the Eurostat data. The demographic accounting methods, especially the Pseudo-Bayesian method, tend to have higher levels of correlation across all migration measures. The highest correlations, across all estimation methods, are found for the net migration counts and immigration rates. Conversely, the estimated emigration rates consistently provide the lowest correlation with the reported flows in each estimation method. The differences between the correlations from the different data sets (the left and right sides of Fig. 4) occur due to the different reported data. Eurostat covers more countries and more recent data. The DEMIG C2C data includes only two non-European countries that use previous or next place of residence when defining reported bilateral migration flows (New Zealand and South Africa).
In our second comparison, we calculate the correlation of the sum of the estimated male and female bilateral flows with the constructed equivalent reported five-year migration flows with no sex-disaggregation from five collections of reported migration data. First, the DEMIG C2C data set25 allowed the calculation of 17,434 five-year bilateral flows and 66, 68 and 66 immigration, emigration and net migration totals, respectively. Second, the DEMIG TOTAL data set26 yielded constructed equivalent five-year reported immigration, emigration and net migration totals for 63, 65 and 50 country-periods, respectively. Third, Eurostat provided 35,189 constructed five-year bilateral flows and 157, 155 and 154 immigration, emigration and net migration five-year totals, respectively. Fourth, the International Migration Flows to and from Selected Countries: The 2015 Revision (IMFSC2015) of UN DESA27 reported migration by place of residence to, from and between 39 countries, allowing us to construct 32,375 five-year bilateral flows and 172, 155 and 155 immigration, emigration and net migration totals, respectively. Fifth, the five-year net migration counts published in WPP201916 were available for all 1,188 = 197 × 4 + 200 × 2 country-period combinations.
We correlate the equivalent migration statistics from the five data sources with the sum of the male and female estimated migration flows from each method in the top panels of Fig. 5. The correlations of the sum of the male and female migration flows are of similar strengths to those from the sex-specific correlations for each estimation method and migration measure. Demographic accounting methods have higher correlations. The strongest correlations are in the net migration counts and immigration rates. The correlations from comparisons with the Eurostat and UN DESA IMFSC2105 are similar, as might be expected because the reported statistics come from many of the same countries. The correlations for the counts of net migration from WPP2019 are higher than the correlations from the net migration counts from the other data sets as they are based on five-year intervals, where no additional calculations were required to construct an equivalent five-year flow from annual migration statistics. There is a perfect positive correlation in all country-period combinations between the net migration counts from WPP2019 and the two methods that used the closed demographic accounting framework. These two methods use the scaling technique of Abel and Sander9 that constrains the estimated bilateral migration flows to sum to net migration by adjusting migrant stock totals so that difference in the total populations follow the demographic accounting equation.
For comparison, the bottom panels of Fig. 5 provide the correlations between the five data sources for the total migration flows with the estimated bilateral migration flows obtained from applying the six estimation methods to the changes in the total bilateral migrant stocks – an updated version of the estimates carried out by Abel & Cohen6 to the same sources of input data used in this paper. There are some minor changes in the correlations as the estimated flows from the changes in the total bilateral stock data are not constrained to match the sum of the estimated flows from changes in the female and male bilateral stock data, leading to some discrepancies between the set of estimates. Table 2 provides some summary statistics for these discrepancies between the estimated flows based on the change in the total bilateral stock data and the sum of the estimated flows of female and male flows presented in this paper.
The vast majority of the discrepancies between the two sets of estimates are very close to zero. In Table 2, all the mean discrepancies, for all 6 methods, are negative. For example, for the stock difference drop negative method, the flow estimates based on changes in total migrant stocks minus the sum of male and female flow estimates is on average −6.4 persons. That is, the sums of the sex-specific estimates are on average larger than the updated aggregate estimates for all methods. The median discrepancy is zero, the interquartile ranges of the discrepancies are all less than 0.1 migrants, the inter-decile ranges of the discrepancies are less than six migrants and 99th inter-percentile ranges of all the discrepancies are less than 2,000 migrants.
However, a few large differences that form long tails for the distribution of the discrepancies occur where there are simultaneously large increases in the female bilateral stock and large decreases in the male bilateral stock, or vice versa. For example, according to the UN DESA stock data, the number of Puerto Rican born migrants residing in the USA dropped by 15,028 between 2010 and 2015, leading to a migration flow estimate of zero for the period for both the stock differencing approaches. For the same period, the number of female Puerto Rican born migrants residing in the USA declined by 119,357 whereas the number of males increased by 104,329, leading to an estimated female flow of zero and male flow of 104,329. The sum of these male and female flows creates the maximum discrepancy of the stock differencing approaches shown in Table 2.
This validation provides some guidance to the relative strengths of each estimation method in relation to the migration measure of concern to the end user. There are some broad consistencies in the relative levels of correlations of each method over different data sources. The Pseudo-Bayesian demographic accounting approach tends to provide the highest levels of correlations with reported migration flow statistics. The similarities in the relative rankings of the methods over the different data sources might be due to a common set of European countries where international migration flow data are more readily available. Different levels of correlations might have been obtained if data were available from more countries and periods. In the estimated migration flows, there are 470,472 origin-destination-period combinations that could potentially form the basis of the first three (bilateral) migration measures and 1,188 origin-period or destination-period totals for the last three migration measures. In the validation exercises, equivalent reported flows from each data collection were available for less than 15 percent of the bilateral flow measures and under 28 percent of the total migration flow measures, with the exception of the total net migration from WPP2019, where all 1,188 of the corresponding reported values were available.