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2. PRODUCTION, COMPLEMENTARITIES AND GAINS FROM MIGRATION

Both U.S. natives and foreign born workers can be differentiated into several imperfectly substitutable skill groups (classified by education and experience). Following Borjas (2003), we choose a nested constant elasticity of substitution (CES) production function, in which physical capital and different types of labor are combined to produce output. We impose lower substitutability between groups of different schooling levels than between groups of different experience levels but with the same schooling. U.S.-born and foreign-born laborers are allowed a further degree of imperfect substitutability even when they have the same education and experience.

Calculated Effects of Immigration on Wages

Table 2 shows the calculated effects of an increase in foreign-born workers on the wages of U.S.-born workers. The elasticities are obtained from data on wages and employment shares relative to 1990, together with changes in the supply of skills from immigration during 1990-2000, are from the IPUMS of Ruggles et al. (2005).

Column (a) reports the calculated partial elasticity of the wages of U.S.-born workers to an immigrant inflow of the same education-experience group, while column (b) reports the partial elasticity of U.S.-born wages to immigrants only in the same education group. The total effect of immigration on the wages of U.S.-born workers of each skill group is shown in column (c), while the elasticity of the average wage of U.S.-born workers to total immigration is reported in column (d). The final column (e) reports the calculated percentage change in the average wages of U.S.-born workers as a consequence of the 1990-2000 inflow of immigrants. The table only reports the average by education groups (across experience groups). The first three rows of Table 2 show the calculated impact (for different parameter values) of the actual immigration increase in the 1990s. This increase, expressed as the change of foreign-born in each skill-group relative to total initial employment (1990) was 1.5% and 3% as the consensus values for the parameters and 0% respectively. By way of contrast, the last three rows of the table present the
effects of some counterfactual immigration flows.

In the following, parameters Sub(…), which capture the imperfect substitutability between the U.S. and foreign born in the same skill group, have never before been estimated. We group educational achievements into four categories: High School Dropouts (HSD), High School Graduates (HSG), College Dropouts (CD), College Graduates (CG). Es(…) refers to the actual elasticities of wages to changes in inflows of specific categories of labour, i.e. a net 1% increase in the inflow of high school dropouts will be associated with Es(HSD)% increase in wages of the resident native-born high school dropouts.

Table 1. Elasticity of Substitution between US-Born and Foreign-Born Workers within the Same Education-Experience Group.

** Statistically significant at 1% level.

Table 2. Calculated Effects of Immigration (1990-2000) on Wages of US-born.

Let us describe the results in Table 2.

Specification 1, reported strictly as a benchmark for comparison, assumes that U.S.- and foreign-born workers of the same skill group are perfect substitutes. Our estimates contradict this assumption that is used as the standard one in the literature. Under this assumption the overall effect on average U.S. wages from the 1990-2000 migratory inflow is very small (elasticity of 0.09) but positive. This result is in contrast with Borjas (2003) who finds a strong negative effect of total immigration on average U.S. wages (elasticity -0.3). Borjas’ effect is entirely due to his assumption of a fixed capital stock (rather than an endogenously accumulated one, as in our model) which seems extreme for a ten-year span. The small effect on average wages is accompanied by a strong redistributive effect. “Own” elasticities are negative and large, average around -0.3 for an increased relative supply of foreign-workers in the same education-experience group, and -0.62 for an increased relative supply in the same education group. Therefore the relative size of immigrant groups across skills heavily affects the relative wage effects. The first row of Table 2 implies that the real wages of high-school dropouts decreased by 4.5%, the wages of workers with a high-school degree increased by 2%, and the wages of college graduates did not change. These differences stem from the fact that immigrants are over represented among the low-skilled, under-represented among the intermediately-skilled, and proportionally represented among the highly-skilled.

Specification 2 calculates the effects of immigration when we use the values estimated in Table 2. We use values of seven and four (very close to our point estimates) as the elasticities of substitution within the lowest and highest education groups, respectively, and a value of ten for the two intermediate groups. Both the effects on the average wage of U.S.-born workers and the effects on the distribution change quite dramatically. First of all, the elasticity of average wages to immigration becomes large and positive. The 8% increase in foreign-born workers increases the average U.S. wage by 2.2%. Moreover the three top education groups all gain by significant amounts (around a 2.4% real wage increase for each in response to this immigration) while only the low-skill group looses (around a 2.4% wage decrease). A critical thing to note is that while the gains for the intermediately-educated are still driven by the relative supplies of the foreign-born (who are scarce in these groups), the gains for the college educated stem from the lower degree of substitutability between U.S. and foreign-born laborers in this group.

Specification 3 assumes an elasticity of substitution somewhat lower than our point estimate from Table 1. This is done in order to account for a potential upward bias that may arise from any endogeneity in the skill composition of immigrants. The chosen values are, however, within two standard deviations from the estimates of Table 1. As we can see, the effect of immigration on average wages here is even more dramatic. Converting elasticities into actual changes, the average wage of U.S. born workers increases by 2.7%, and the most dramatically affected group is that of U.S.-born college graduates, whose wage increases by 3.5%! We label this specification as our “preferred” one for reasons that will become clear in the next section, when we compare the calculated elasticities to those empirically estimated from the data.

The last three specifications in Table 2 use our preferred parameter combination to evaluate the effects of some “counterfactual” migratory flows.

Specification 4: If the U.S. were to stop the immigration of low skilled workers and replace them with immigrants among the intermediately skilled, so that total migration remains unchanged, the overall beneficial effects of immigration on the average U.S. wage would decline slightly (it would increase by 2.6% rather than by 2.7%). This results from the relative scarcity of U.S.-born high school dropouts and the higher substitutability between natives and foreigners in the intermediate education groups.

Conversely, Specification 5 eliminates the inflow of high school graduates in favor of an equal increase in high school dropouts (making even more extreme the over representation of foreign-born among the group of low educated workers). This move slightly increases the average marginal benefit accrued to U.S. workers via their wages (to 2.75%). Of course these two policies would generate large effects on relative wages, with the second move exasperating the negative impact on the wages of lowly-skilled U.S. natives (a decrease by over 8% as result of immigration).

The most harmful scenario for average U.S. wages, however, is the one reported in Specification 6, in which the inflow of college graduates is eliminated in favor of an equal increase in college dropouts. In this case the effect of immigration descends from large and positive to essentially 0. Clearly the high complementarities of foreign-born workers in high-skill professions is a key element of the overall gains from migration generated by our model.