Rethinking the gains from immigration: theory and evidence from the US
Open Republic: April/ May/ June 2006

An earlier version of this paper was published by the Centre for Economic Policy Research (CEPR), London, Discussion Paper No. 5226 September 2005

1. INTRODUCTION

The United States has experienced a surge of immigration for the last three decades. As Figure 1 illustrates, the percentage of foreign-born residents in the United States has been steadily growing since 1970, and reached a proportion of over 13% of the population by 2005. Economists, demographers and social scientists have used both theoretical models and empirical analysis to gauge the impact of these immigrants on the U.S. economy, and on its native residents. The National Research Council (1997) produced a 430-page volume analyzing the characteristics and effects of immigration on American society. Since then, a number of other studies have re-examined the issue.

Our paper wishes to take a fresh look at the overall issue, emphasize important connections between economic theory and empirical findings, and provide a coherent framework to measure the impact of immigration on the average productivity of U.S. natives.

The question we tackle is: what is the impact of immigration on the productivity and income of workers born in the United States? The question really has two parts. First: does the inflow of foreign-born workers have a positive or negative net effect on the average production and income of U.S.-born residents? This question supposes that we aggregate the wages and incomes of quite heterogeneous U.S. workers. Second: how are the gains and losses from immigration distributed across U.S. born workers with different skills, and between labor and physical capital?

The consensus emerging from the recent literature is that the effects of immigration on the average (aggregate) income accruing to U.S. natives is rather small. Quantifications of this effect (Borjas, 1995) imply that the sum total of foreign-born workers accounts for a mere 0.1% increase in the average income of U.S.-born residents. Therefore, the argument goes, one can neglect this minuscule average effect and concentrate on the second question dealing with the distributional effects of immigration. Moreover, as immigrants are normally endowed with little physical capital most of the literature (Borjas 1995, 2003) represents immigration as an increase in the labor supply with a constant capital stock, and so finds a negative impact of immigration on average wages and a positive impact on the return to capital.

The “macro” aspects of the issue (average income and average wages) have been analyzed more superficially then the “micro” aspects. Most of the recent debate has focused on the effects of immigration on the relative wages of more and less educated U.S.-born workers. Some economists argue in favor of a large relative impact (Borjas, 1994, 1999, 2003; Borjas, Freeman and Katz, 1997) while others favor a smaller, barely significant effect (Butcher and Card, 1991; Card, 2001; Lewis, 2003).

While the size and significance of these relative wage effects from immigration remain controversial, this paper intends to combine this analysis with the analysis of average wage effects, which have rashly and facilely been considered settled (or unapproachable, or irrelevant) in the literature. As such we nest the “macro” (average) and the “micro” (distributional) aspects of the problem within the same framework.

The effects of immigration on the average wage of U.S.-born individuals are extremely difficult to estimate directly with aggregate U.S. data. Time series of aggregate U.S. wage and immigration numbers after World War II contain few observations, and the issues of omitted variable bias and endogeneity make the inference of causality a daunting task. The reported effects of migration on average wages found in the literature have been calculated (rather than estimated) while imposing crucial restrictions on the substitutability of skills and the supply of factors (labor and capital).

We will argue that these assumptions, which produce estimates implying that immigration has negligible effects on the total income of U.S. born residents and negative effects on the average wages of U.S. born workers, may not be the most appropriate. Treating the issues of skill complementarities and physical capital accumulation more carefully, we uncover positive effects of immigration on the average wages and incomes of natives. We analyze this crucial point by employing estimation and simulation exercises on both aggregate data and data from metropolitan areas.

The modern analysis of the effects of immigrant inflows on the wages of natives began with studies (Grossman 1982; Altonji and Card 1991) that treated the foreign-born simply as a single homogeneous group of workers, imperfectly substitutable with U.S.-born workers. A number of studies on the relative supply of skills and relative wages of U.S.-born workers (Katz and Murphy 1992; Card and Lemieux 2001) make clear, however, that workers with different levels of schooling and experience are better considered as imperfectly substitutable factors. As a consequence, more recent analysis of the impact of immigration on the wages of U.S.-born workers has been carried out partitioning workers among imperfectly substitutable groups by education and experience, while assuming perfect substitution within each group (e.g. Card 2001 and Borjas 2003).

Our paper combines the first and second approaches – both cases can be seen as special examples nested in our general framework. We assume the existence of an aggregate production function that combines workers and physical capital, while using education, experience and place of origin (U.S. versus elsewhere) to categorize imperfectly substitutable groups. Following Borjas (2003) we nest two groups (U.S. born and foreign born workers) within eight experience groups, and these in turn into four educational attainment groups. This allows for the imperfect substitutability of workers both of different country origins and of different education-experience levels.

This imperfect substitutability may arise from different training, occupational choices and various unobserved characteristics of workers. While intuition suggests that a Chinese-born cook is not a perfect substitute for an American cook, and that an Italian tailor and a French architect differ from their U.S. counterparts, the degree of substitutability between the foreign and U.S. born must ultimately be determined empirically.

Finally, we include physical capital in production, and treat its accumulation as driven by market forces that equalize real returns to capital in the long run. This is also a departure from the literature, which mostly assumes a fixed capital stock when evaluating the distributional effects of immigration.

In summary then, our production function can be used to calculate the relative, absolute and average wage effects from the recent inflow of immigrants, as well as simulate the effects of counter-factual scenarios.

In the first part of the paper we estimate the elasticity of substitution between foreign and U.S.-born workers within education-experience cells using data from U.S. censuses from 1970 to 2000. Adopting an empirical methodology similar to Borjas (2003) we find that the data support imperfect substitutability between the two groups. In particular, among the college educated the elasticity of substitution between U.S. and foreign born is around four, while among high-school dropouts it is around seven. This elasticity grows larger (around 10) for intermediately educated groups.

Using both these estimates, and previous estimates of the elasticity of substitution between experience groups (Card and Lemieux 2001) and educational groups (Katz and Murphy 1992) we can calculate the effects of immigration during the 1990s on relative wages, or on absolute wages by education group, or on the average wages of U.S.-born workers. We calculate that the average wage of U.S. born workers experienced an increase between 2% and 2.5% in response to the inflow of foreign-born workers in the 1990-2000 period. At the same time, the inflow lowered the real wage of native workers without a high school degree by 1%, but increased the real wage of native workers with at least a high-school degree as much as 3-4%.

The remainder of the paper is organized as follows. In section 2 we use aggregate CES production function in order to estimate the elasticities of substitution between U.S. and foreign-born workers within each education group. We calculate the impact of immigration in the 1990s on the relative, absolute and average wages of U.S.-born workers. This section also presents direct estimates of the impact of the relative skills of immigrants on relative U.S. wages using national data, and compares them with the values obtained from the production function. Section 3 concentrates on the effect immigrants have on average U.S. wages, using the variation of immigrant inflows and wage changes across US cities from 1970 to 2000. All estimates find positive and significant effects of immigration on the average wages and value of houses for the U.S.-born. These effects are entirely consistent with the positive aggregate effects of immigration on the wages of U.S.-born workers calculated in Section 2.

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.

3. AVERAGE EFFECTS OF IMMIGRATION ACROSS CITIES: WAGES, VALUE OF HOUSING AND
EMPLOYMENT

The most striking and potentially controversial finding of Table 2 is, however, the large positive overall gains for U.S.-born labor. Since this aggregate effect is impossible to detect from national aggregate data, we aim to measure it by using cross-city variations. We intend to provide not only empirical evidence in favor of this positive aggregate effect, but also a detailed account of how such an effect can be produced and maintained in a long-run equilibrium. Hence we accompany wage regressions with regressions of cross-city values of housing and changes in employment.

In prior work (Ottaviano and Peri 2005; Ottaviano and Peri, forthcoming) we have detected a positive and very robust relationship between the average wages of U.S.-born workers and the share of foreigners across U.S. cities. These articles separately analyze the wage-rent equilibrium (Ottaviano and Peri 2005) and the wage-employment equilibrium (Ottaviano and Peri, forthcoming), concluding that the simultaneous positive effects of immigration on all the variables analyzed (concerning U.S.-born workers) can only be reconciled with the idea that immigrants tend to provide a positive influence on the productivity of native workers.

We have illustrated in section 2 how the overall positive effects on the U.S.-born emerge from the various complementarities of the foreign-born across skills. Here we reproduce some of the wage-employment-rent estimates across cities which confirm these positive effects from immigration on each variable, while in the next section we quantitatively match these estimates with a simple general equilibrium open-city model.

Data across the 86 largest metropolitan areas in the United States for the 1970-2000 period suggests a strong positive correlation between the share of foreign-born and each of the three variables. Metropolitan areas where foreign-born workers abound exhibit faster growth in the average wages, employment, and property values of U.S.-born workers. The described statistics show that more immigrants are associated with all the characteristics of a booming metropolitan economy.

For the remainder of this section we analyze more formally these positive correlations in order to understand whether they are likely to be spurious or due to omitted variables. Using the Integrated Public Use Microdata of the U.S. censuses of 1970, 80, 90 and 2000 for individuals in 86 metropolitan areas, we estimate regressions which consider as an explanatory variable “The Percentage Increase of the total employment of city i in decade t; due to immigration”, defined as the percentage change in employment due to an influx of foreign-born workers.

The coefficient C1 captures the elasticity of U.S.-born employment to an increase of foreign-born workers. The coefficient C2 quantifies the percentage increase in the average real wage (in 2000 constant dollars) of U.S.-born workers in city i and decade
t from an increase in foreign-born workers.12 Finally coefficient C3 quantifies the percentage increase in the real average house value (in 2000 constant dollars) for U.S.-born workers in city i and decade t in response to an increase in foreign-born workers relative to total employment. Table 3 reports the estimates of the coefficients C1, C2 and C3. Column I reports those obtained with the panel of 86 cities over 4 census years and column II reports those based on 117 cities over 3 census years.

Table 3. Estimates of the Total Effects of Immigration on Average Wages, Housing Values and In/Outflows of US-born Residents: US Metropolitan Areas.

* Statistically significant at 5% confidence level.

The first row of Table 3 shows the estimated impact of immigration on the employment of native workers. This effect is positive but quite imprecisely estimated. No evidence exists that increasing aggregate emigration of U.S.-born workers from cites attracts larger number of immigrants. The impact of immigration on wages (rows 2 and 3) and on the value of housing (rows 4 and 5) of U.S.-born residents is significantly positive.

Alternatively we use yearly or hourly wages of U.S.-born workers (rows 2 and 3) and control for individual characteristics. The estimates in row 2 and 3 imply that a 1% increase in the share of foreign-born workers in total employment raises average wage of U.S. workers by between 0.35 to 0.46 percentage points.

The last two rows calculate the impact of foreign-born workers on the value of housing for U.S.-born residents. We use gross rents and values of housing as alternative measures of the value of housing. The estimated coefficients imply that an increase of foreign workers by 1% of the initial employment causes an increase in the value/price of housing for the U.S.-born by 1.1 to 1.6 percentage points.

These estimates imply a strong positive impact from foreign-born workers on city economies, which put upward pressures on wages and housing prices, and attract native workers. Remarkably the average effect from immigrants on U.S. wages (mostly between 0.35 and 0.38) is very close to the effect of immigration on the average wages calculated in Table 2, row 3, equal to 0.34.

Table 4. Simulation of the Long-Run Impact of Immigration Shock on Wages, Housing Values and In/Outflows of US-born residents, from the City-Model.

Table 4 considers the following scenario: total immigration inflow: 8%, increase in High-School dropouts inflow of 1.9%, increase in High-School graduates of 1.5%, increase in College dropouts of 1.5% and increase in College graduates of 3%. Maintaining the common average shock that mirrors the actual increase in foreign-born workers during the 1990s, the columns correspond to simulations for different combinations of parameter values. The first two rows report the short-run effects from immigration on the average wages and housing values for U.S.-born workers. The following three rows report the effects on the average variables for U.S.-born individuals (i.e., the percentage change in average wage, the percentage change in the value of housing, and in- or out-migration), all calculated in the new ‘long-run’ equilibrium, after internal migration takes place and the new equilibrium is reached.

The first column of Table 4 (specification I) shows results from the main simulation that uses the baseline choices for the parameters. Specification II employs the parameter values that are closer to the point estimates of Table 1. The remarkable feature of these two specifications is that they generate long-run elasticities of average wages and rents that match very closely the estimated range of elasticities in Table 3. Specification III is shown purely for reference as it assumes very high values for the elasticity of substitution between U.S. and foreign born (not supported by the evidence).

It is clear that the large positive effect on average wages and rents depends heavily on the imperfect substitutability between the U.S. and foreign born. If, as in this specification, natives and foreigners are close to perfect substitutes, then the effect on wages and rents is smaller, and is accompanied by a net out-migration of U.S.-born workers.

Specifications IV to VII show the robustness of the simulated elasticities to changes in other parameters. Specification IV increases the elasticity of substitution between local services (produced by U.S. and foreign born workers) to 7; specification V increases the share of total expenditures on housing services to 25%; specification VI reduces the share of spending on food-entertainment to 15%; and specification VII increases the elasticity of substitution between schooling groups to 2.

Each specification produces the results that are either positive or very close to 0, confirming that there seem to be no strong tendencies for U.S.-born residents to leave cities that experience migration. Thus, for plausible parameter values, our simple (and quite standard) model finds significant positive effects of immigration on the average wages and rents of U.S.-born workers. Quite remarkably, the magnitude of this effect is equal to what our IV estimates produce across U.S. cities.

4. CONCLUSION

Along with goods and capital, the increased movement of people across countries has been a prominent feature of the last few decades. While in general economists are among the staunchest supporters of freer trade and capital movement, they have primarily argued that migration hurts U.S. native workers, in particular those with low skills.

It turns out both empirically and theoretically that immigration, as we have known it during the nineties, had a sizeable beneficial effect on the wages of U.S.-born workers. For a flow of migrants that increases total employment by 10% and a skill distribution that mirrors the one observed in the nineties, U.S.-born workers experience a 3-4 percentage points increase in their wages. This results because U.S. and foreign-born workers are not perfectly substitutable, even when they have similar observable skills. Workers born, raised and partly educated in foreign environments are not identical to workers born and raised in the U.S. This set of differences that we might label ‘diversity’ is the basis for the gains from immigration that accrue to U.S.-born workers. Even a small degree of difference, captured by a relatively high elasticity of substitution between U.S. and foreign-born workers (between 4 and 7), is enough to generate the average wage gains that we estimate from U.S. metropolitan data.

We believe that sharpening our understanding of the complementarities and substitutability between the U.S. and Foreign born in different sectors and skills, along with using an aggregate production function approach, are crucial steps in quantifying the benefits of immigration to the U.S. economy. We hope that this article may encourage a line of research into such “gains” from immigration, rooted in production complementarities (between workers and with physical capital) that may account for these important and thus far neglected effects from immigration.

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