What “Productive Sorting” Can—and Cannot—Mean
The evidence now contains four explanations for the same U-shaped placement pattern, but explanations are not interchangeable and favorable outcomes are not self-interpreting. This chapter compares the mechanisms across firm size and multinational status, then asks what the earnings, retention, and broader labor-market evidence can support about productive matching. The aim is a disciplined judgment: identify where the evidence is strong, where it is merely consistent with an interpretation, and where the data cannot decide.
That discipline matters because “sorting” can sound neutral or negative depending on the listener. If immigrant students are concentrated in large firms and small businesses, one reader may see efficient use of skills and networks. Another may see institutions directing people into separate niches. Both reactions could be reasonable starting hypotheses. The study’s design allows us to distinguish some patterns, but it does not observe every preference, rejected opportunity, or barrier that would settle the normative question.
Different mechanisms, different scales
The comparison is clearest when firm size and MNE status are treated as separate outcomes. Geography and degree specialization are the strongest measured guides to placement in larger firms. Ethnic self-employment specialization has its clearest role among firms with 20 or fewer employees. Visa capability is positive in the overall model and among larger firms, but its contribution is modest after the other mechanisms are included. Multinational enterprises show the sharpest degree relationship, with geography also relevant and the visa-capability estimate not statistically distinguishable from zero in that split.
The paper’s preferred coefficients make the contrast visible. In the overall sector-and-firm-size analysis, the geographic coefficient is 0.2233 and the degree-specialization coefficient is 0.5422. For firms with more than 20 employees, those estimates are 0.4652 and 0.5631. In the small-firm split, the geographic estimate is -0.0571 and is not statistically distinguishable from zero, while the degree estimate is 0.1687 and is also not statistically distinguishable from zero. The ethnic self-employment coefficient rises from 0.0120 in the full model to 0.2061 among small firms. For MNE placements, the degree coefficient is 1.2730 and the geographic coefficient is 0.2763; the visa-capability estimate is -0.0173 and not significant. Outside MNEs, the degree and geographic coefficients are 0.3377 and 0.2544, while the ethnic estimate is 0.0213.
These coefficients are not personal probabilities. The model compares shares of placements across sector-and-firm-size cells and across immigrant groups. A positive coefficient means that the predictor’s expected distribution aligns with the realized distribution in the corresponding cells. A larger coefficient means stronger alignment within that comparison, not that one mechanism has a fixed effect on every worker. The estimates are useful for ranking explanatory relationships by organizational setting, not for calculating an individual’s career odds.
The results also show why the middle of the distribution matters. Immigrant students spend more of their observed working time at the smallest and largest firms and less in mid-sized firms. The adjusted career estimates show 2.4 to 4.5 percentage points fewer quarters in firms with 101 to 10,000 employees and 3.4 to 6.0 percentage points more quarters in multinational enterprises, depending on the immigrant group.