Question

Analyze the selection of migrants using the Roy model. Show using diagram when migrants will be positively selected, and when they will be negatively selected. Can both positive and negative selection occur at the same time? Explain.

Answer 1

Model of self-selection
In 1951 Roy analyzes the impact of self-selection in occupational choice on the income distribution. Roy motivates his analysis by saying that his contemporaries implicitly assumed that the distribution of incomes is arbitrary “developed by the process of historical accident.” In contrast, the core of Roy’s model is to ask how the distribution of earnings is affected if individuals purposefully  select their occupation. Roy’s paper is definitely worth reading, but the key characteristics of the model are somewhat difficult to wade through given the verbal style of the text. It doesn't have a mathematical notation.
Roy’s original model was based on two occupations – (rabbit) hunting and fishing. The goal was to understand self-selection: will the individuals best suited for fishing choose to fish? Will the individuals best suited for hunting choose to hunt? The core idea of the model is to take seriously the idea that - in a market economy - individuals will not randomly sort themselves across the two occupations. In markets where non-random sorting is important, comparing the wage gap between hunters and fishermen will reflect not only a “real” difference in potential earnings but will also be a function of which individuals select into hunting and fishing. This type of self-selection comes up as an issue in nearly every sub-field of economics.

The United States is the most important destinations of high-skilled migrants from Germany. In the United States, earnings inequality among university graduates is much higher than in Germany. As predicted by the Roy/Borjas model, high-skilled individuals who migrate from Germany to the United States are positively selected, compared to non-migrants in Germany. Migrants to the United States are positively selected across almost all characteristics, but the most important factors are university subjects, university grades, university quality, and gender. Migrants from Germany to the United States are particularly concentrated in high-paying STEM fields.

The Roy/Borjas model predicts that mean earnings should affect the number of migrants to each country but not the direction of selection. Nonetheless, differences in mean earnings will affect migration choices and may be correlated with differences in the 75/25 ratios. Migration decisions, especially those of lower-skilled migrants (among the high-skilled), may also be affected by expected unemployment spells that could be correlated with earnings inequality. In this specification, the coefficient on the 75/25 ratio is equal to 0.174. Migration decisions, especially of high-skilled women, may also be affected by differences in child care provision that may be correlated with earnings inequality. To address this concern, control for public expenditures on family benefits. As migration decisions may also be affected by expectations about general well-being that may be correlated with earnings inequality, we control for a measure of life satisfaction in each country. The previous checks confirm a robust effect of earnings inequality on mean selection levels. The selection pattern to locations with more extreme levels of equality or inequality is robust to controlling for country-level confounding factors. The selection pattern to locations with more similar levels of inequality remains broadly consistent with the predictions of the model. The most important deviation from the model prediction occurs for selection to somewhat unequal countries, in particular if we control for mean earnings.

Are migrants positively or negatively self-selected from within their populations of origin? The largest flows of free migration ever—that of Italians to the United States between 1907 and 1925. Relying on the well-established relationship between population average stature and living standards, it quantifies migrant self-selection by comparing the heights of migrants to the height distributions of their respective birth cohorts in their provinces of origin. The analysis reveals opposite patterns of self-selection across and within Italian provinces. Italian migrants were shorter, on average, than all Italians of the same birth cohort, suggesting negative self-selection on the national level. However, when compared only to the distribution of stature in their own provinces of origin, find that Italian passengers were, on average, taller, indicating positive self-selection on the local level. Moreover, find that the degree of self-selection from a province and birth cohort was decreasing in its average stature, suggesting that less-developed province-cohorts, where liquidity constraints to migration were more likely to bind, provided relatively higher quality migrants. The findings demonstrate the importance of distinguishing between self-selection from country as a whole and self-selection from within a particular sub-national region. Comparisons of migrants to their national-level origins, which are the norm in the literature on migrant self-selection, may fail to capture a significant portion of the self-selection occurring within a group of potential migrants.

Economists of migration have long sought to determine whether and why migrants are positively or negatively self-selected from their populations of origin, but a variety of data constraints have limited the conclusions that could be drawn. Alternatively, data on migrants may be collected after some time is spent in the receiving country, and may no longer represent their position in the sending population. Stature data solve both of these problems, allowing migrant self-selection to be easily characterized. Furthermore, a number of previous studies have relied on modern data on migration in order to determine whether the most or least productive members of a particular economy will choose to migrate.

In the modern context, however, observed migrants are not simply those who wish to migrate; they must also be deemed acceptable by the receiving country. Simply comparing migrants to non-migrants thus does not directly reveal the underlying process of self-selection into migration. Few legal restrictions to migration to the United States from Europe, effectively eliminates this issue; comparing migrants to non-migrants thus effectively identifies which portion of the population found migration to be optimal. So it contributes to understanding the effects of migration on the sending and receiving economies, which are widely believed to be strongly affected by the quality of migrants.