Does Immigration Grease the Wheels of the Labor Market?

Borjas, George J., Brookings Papers on Economic Activity

MOST STUDIES OF the economic impact of immigration are motivated by the desire to understand how immigrants affect various dimensions of economic status in the population of the host country. This motivation explains the persistent interest in determining whether immigrants "take jobs away" from native workers, as well as the attention paid to measuring the fiscal impact that immigration inevitably has on host countries that offer generous welfare benefits.(1)

For the most part, the existing literature overlooks the factor that places immigration issues and the study of labor mobility in general at the core of modern labor economics. The analysis of labor flows, whether within or across countries, is a central ingredient in any discussion of labor market equilibrium. Presumably, workers respond to regional differences in economic opportunities by voting with their feet, and these labor flows improve labor market efficiency.

In this paper I emphasize this different perspective to analyzing the economic impact of immigration: immigration as grease on the wheels of the labor market. Labor market efficiency requires that the value of the marginal product of workers be equalized across labor markets, such as U.S. metropolitan areas, states, or regions. Although workers in the United States are quite mobile, particularly when compared with workers in other countries, this mobility is insufficient to eliminate geographic wage differentials quickly. The available evidence suggests that it takes around thirty years for the equilibrating flows to cut interstate income differentials by half.(2)

I argue that immigration greases the wheels of the labor market by injecting into the economy a group of persons who are very responsive to regional differences in economic opportunities.(3) My empirical analysis uses data drawn from the 1950-90 U.S. censuses to analyze the link between interstate wage differences for a particular skill group and the geographic sorting of immigrant and native workers in the United States. The evidence shows that interstate dispersion of economic opportunities generates substantial behavioral differences in the location decisions of immigrant and native workers. New immigrant arrivals are much more likely to be clustered in those states that offer the highest wages for the types of skills that they have to offer. In other words, new immigrants make up a disproportionately large fraction of the "marginal" workers who chase better economic opportunities and help equalize opportunities across areas. The data also suggest that wage convergence across geographic regions is faster during high-immigration periods. As a result, immigrant flows into the United States may play an important role in improving labor market efficiency.

The paper presents a simple theoretical framework for calculating this efficiency gain from immigration. Simulation of this model suggests that the efficiency gain accruing to natives in the United States--between $5 billion and $10 billion annually--is small relative to the overall economy, but not relative to earlier estimates of the gains from immigration (which are typically below $10 billion). It seems, therefore, that the measurable benefits from immigration are significantly magnified when estimated in the context of an economy with regional differences in marginal product, rather than in the context of a one-region aggregate labor market.

Framework

The intuition underlying the hypothesis developed in this paper is easy to explain.(4) There exist sizable wage differences across regions or states in the United States, even for workers with particular skills looking for similar jobs.(5) Persons born and living in the United States often find it difficult (that is, expensive) to move from one state to another. Suppose that migration costs are, for the most part, fixed costs, and that these are relatively high. The existing wage differentials across states may then fail to motivate large numbers of native workers to move, because the migration costs swamp the interstate differences in income opportunities. As a result, native internal migration will not arbitrage interstate wage differentials away.

In contrast, newly arrived immigrants in the United States are a self-selected sample of persons who have chosen to bear the fixed cost of the geographic move. Suppose that once this fixed cost is incurred, it costs little more to choose one state as the destination over another. Income-maximizing immigrants will obviously choose the destination that offers the best income opportunities. Newly arrived immigrants will then tend to live in the "right" states, in the sense that they are clustered in the states that offer them the highest wages.

In short, the location decisions of immigrant workers should be much more responsive to interstate wage differentials than those of natives. As a result, immigrants may play a crucial--and neglected--role in a host country's labor market: they are "marginal" workers whose location decisions arbitrage wage differences across regions. The immigrant population may therefore play a disproportionate role in helping the national labor market attain an efficient allocation of resources.

The Location Decisions of Native Workers and Immigrants

This hypothesis can be formalized as follows. Consider initially the interstate migration decision faced by workers born in the United States. Let [w.sub.jk] be the wage paid in state j to a native worker with skills k (for example, a worker with a high school diploma). The worker currently lives in state b. The sign of the index function determines the worker's internal migration decision:

(1) I = [max.sub.j] {[w.sub.jk]} - [W.sub.bk] - C,

where C gives the migration costs. Although these include both variable and fixed costs, I assume that they are mostly fixed. Perhaps the most important fixed cost is the disutility suffered by the migrant who leaves family and friends behind and begins life in a new and uncertain environment. The native worker migrates if I [is greater than] 0.(6)

What does the index function in equation 1 imply about the equilibrium sorting of native workers across states? Suppose that the fixed costs of moving are very high, so that the wage gap between the current state of residence and the state offering the highest wage cannot cover the migration costs. In this extreme case, the geographic distribution of native workers is determined solely by the random allocation that occurs at birth and has little to do with interstate differences in economic opportunities. Because native workers do not respond to interstate wage differentials, these differences will persist (in the absence of other equilibrating flows).

Of course, native workers do in fact move from state to state. Some natives will find that the wage differential between the highest-paying state and the current state of residence is sufficient to cover the fixed migration costs. But many others will find that these migration costs act as a wedge, preventing them from taking full advantage of interstate differences in economic opportunities. As a result, the native working population will not be sorted efficiently, and many native workers end up living in states where their marginal product is not maximized.

Capital flows across localities could help to equilibrate the national economy. In the short run, however, moving physical capital--whether plant or equipment--across localities is expensive. As a result, the adjustment of capital stocks will depend largely on new investment, a process that is gradual and can take many years. In what follows I simplify the exposition by assuming that the capital stock is fixed.

Immigrants are born in country 0 and are income maximizers. Their index function is

(2) I = [max.sub.j] {[w.sub.jk]} - [w.sub.0k] - C.

Since the wage differential between the United States and many other countries far exceeds the differences that exist between regions in the United States, it is likely that many residents of other countries will find it optimal to move to the United States.(7) More important, the self-selected sample of foreign-born workers observed in survey data collected in the United States is composed of persons for whom the index I defined in equation 2 is positive. Suppose then that a particular immigrant worker chooses to live in state [Laplace]. For immigrants in the United States, this residential choice must satisfy the condition

(3) [w.sub.[Laplace]k] = [max.sub.j] {[w.sub.jk]}.

Put differently, immigrants in the United States will reside in the state that pays the highest wage for the skills they possess. Note that the condition in equation 3 holds regardless of the level of fixed costs, the magnitude of interstate dispersion in wages, or the size of the wage differential between the United States and the source country. Relatively high fixed costs (or a relatively high wage in the source country) simply imply that there will be fewer immigrants. But the sample of foreign-born workers who choose to move will still end up in the right state.

This hypothesis has a number of interesting implications. First, because many native workers are "stuck" in the state where they were born, and immigrant workers are clustered in the states that offer the best economic opportunities, immigrants and natives will be observed living in different states. Moreover, different types of immigrants--depending on their skills--will also be living in different states. In short, the labor supply of immigrant workers to a particular regional labor market should exhibit greater sensitivity to interstate wage differentials than the labor supply of natives.

Second, the group of immigrants whose location decisions are most responsive to regional differences in economic opportunities should be the sample of newly arrived immigrants. Over time, economic opportunities will probably change differently in different states, and the sample of new immigrants will become like the sample of natives in one very specific way: they all get trapped in the state where they reside. As a result, earlier immigrant waves should be found living in different states than the newest immigrants.

Third, the insight that the location decisions of a particular group of workers--recent movers--are most sensitive to interstate wage differences is not specific to immigrants. It applies to any group of movers, whether foreign-born or native-born. As a result, the location decisions of the self-selected sample of native workers who have chosen to move across states should also be quite sensitive to interstate wage differentials.

Finally, the clustering effect implicit in equation 3 has important implications for studies of labor market equilibrium and for estimates of the benefits from immigration. Native migration flows, perhaps because of relatively high fixed migration costs, cannot fully arbitrage away the regional wage differences. The immigrant flow, in contrast, is self-targeted to those regions of the country where their productivity is highest. As I will show shortly, this clustering effect greases the wheels of the labor market, by speeding up the process of wage convergence, and improves economic efficiency. It is important to emphasize that these gains from immigration differ conceptually from the productivity gains typically stressed in the literature.(8) The productivity gains arise because immigrants and natives complement each other in the production process, and estimates of these gains explicitly assume that the national labor market is in a "single-wage" equilibrium.

Obviously, these strong theoretical implications follow from a framework that uses very restrictive assumptions. In particular, I ignore the many factors other than wage differentials that determine the location decisions of both immigrants and natives. For example, the resurgence of immigrant flows into the United States since 1965 has led to the creation of large ethnic enclaves in many American cities, but in the context of this model it is unclear that these ethnic enclaves arise exogenously. For instance, the first immigrant arriving in the United States from country n may have chosen to live in region j because that region maximized his or her income opportunities.(9) If most workers in a particular national origin group have roughly similar skills, it would not be too surprising if most new immigrants from that source country also settle in region j. But the ethnic networks that link immigrants in the United States with their source countries also help transmit valuable information about income opportunities to potential migrants. These information flows reduce the costs of migration to specific regions for particular ethnic groups and could lead to a different geographic sorting than that predicted by the income maximization model with fixed migration costs. Any empirical analysis of the magnetic effects generated by interstate differences in labor market opportunities, therefore, must incorporate relevant information about these ethnic networks.

Welfare Implications

Why does the greater sensitivity of immigrants than natives to regional wage differentials generate economic gains? How large are those gains? And do they accrue to immigrants or to the native population?

Before addressing these questions, it is instructive to review how the benefits from immigration arise in the traditional, one-sector model. Suppose the production technology in the host country can be described by a linear homogeneous aggregate production function with two inputs, capital and labor (L), the price of the output being the numeraire. Suppose further that all workers, whether native or foreign-born, are perfect substitutes in production. Finally, assume that natives own the entire capital stock in the host country and that the supply of all factors of production is perfectly inelastic.

In a competitive equilibrium, the price of each factor equals its marginal product. Figure 1 illustrates the initial preimmigration equilibrium, with N native workers employed at a wage of w. Because the supply of capital is fixed, the area under the curve representing the marginal product of labor ([f.sub.L]) gives the economy's total output. National income, all of it accruing to natives, is then given by the trapezoid ABN0.

[ILLUSTRATION OMITTED]

The entry of M immigrants shifts the supply curve to S' and lowers the market wage to w'. The area in the trapezoid ACL0 now gives national income. Part of the increase in national income is distributed directly to immigrants (who get w'M in labor earnings). The area in the triangle BCD is the increase in national income that accrues to natives, or the "immigration surplus." Note that the immigration surplus arises because natives own all of the capital, and the additional labor raises the return to this fixed capital stock. The immigration surplus, as a fraction of GDP, is(10)

(4) surplus = 1/2 s[Delta][m.sup.2],

where s is labor's share of national income, [Delta] is the absolute value of the factor price elasticity (or -d ln w/d ln L), and m is the fraction of the work force that is foreign-born. To illustrate, suppose that labor's share of income is 0.7, that the factor price elasticity is 0.3 (so that a 10 percent increase in labor supply lowers wages by 3 percent), and that immigrants make up 10 percent of the work force (as in the United States today). Equation 4 then implies that the immigration surplus is on the order of 0.1 percent of GDP, or roughly $10 billion annually.

Now consider the nature of the gains from immigration in a multi-region economy where there are wage differences across regions in the initial equilibrium.(11) Suppose the United States has two regions and that the same linear marginal product schedule, [f.sub.L], gives the labor demand curve in each. The total (and fixed) number of natives in the economy is N, with a fraction [Lambda] of the natives living in region 1. For concreteness, assume that [Lambda] [is less than] 0.5. Further suppose that labor is supplied inelastically in each region, with supply curves [S.sub.1] and [S.sub.2], respectively. As before, natives own the entire capital stock, which is fixed within each region. Figure 2 illustrates the initial equilibrium. The supply imbalance between the two regions implies that [w.sub.1], the wage in region 1, exceeds [w.sub.2], the wage in region 2.

[ILLUSTRATIONS OMITTED]

Since capital is fixed in each region, one can write the quadratic production function in region j (j = 1, 2) as

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [L.sub.j] gives the number of workers in region j, and [Beta] [is greater than] 0. This quadratic production function generates the linear marginal product curves in figure 2. The initial wage of workers in region 1 equals [w.sub.1] = [Alpha] - 2[Beta][Lambda]N, and the wage in region 2 is [w.sub.2] = [Alpha] - 2[Beta](1 - [Lambda])N. These wages are assumed to be positive over the relevant range of employment. I assume initially that natives are immobile, so that the regional wage differential is not arbitraged away by internal migration.

Suppose the United States decides to admit M immigrants. It is useful to write M in terms of the number and geographic distribution of natives in the labor markets. In particular, the difference in the number of natives residing in the two regions is [N.sub.2] - [N.sub.1] = (1 - 2[Lambda])N. The number of immigrants can then be written as

(6) M = k(1 - 2[Lambda]) N.

The parameter k = 1 when the number of immigrants exactly equals the supply imbalance between the two regions. If all of these immigrants were to enter region 1 (as income-maximizing behavior on the part of immigrants would imply), immigration would completely equalize wages between the two regions. In terms of figure 2, this case of "complete immigration" would shift the supply curve in region 1 to [[bar]S.sub.1], and the single wage in the national economy would be [w.sub.2]. For simplicity, I will assume that 0 [is less than or equal to ] k [is less than or equal to] 1 throughout the analysis.

Let [Theta] be the fraction of immigrants who choose to live in region 1. The total number of workers in each region can then be written as

(7) [L.sub.1] = [Lambda]N + k[Theta](1 - 2[Lambda])N

(8) [L.sub.2] = (1 - [Lambda])N + k(1 - [Theta])(1 - 2[Lambda]) N,

and GDP in this two-region economy with immobile native workers is given by

(9) Q = [Alpha][N + k(1 - 2[Lambda])N] - + k[[Theta](1 - 2[Lambda])N].sup.2] -[Beta][[(1 - [Lambda]N + k(1 - [Theta])(1 - 2[Lambda]N].sup.2].

The parameter [Theta] equals 1 when the geographic sorting of immigrants in the United States is the sorting that maximizes immigrant income. Not surprisingly, this type of immigrant behavior also maximizes GDP for the entire U.S. population (which now includes both natives and immigrants). Put differently, Q is maximized at [Theta] = 1 for a given volume of immigration. Figure 2 illustrates the nature of this result for the special case where k = 1. The increase in GDP to the entire country if all immigrants were to migrate to region 1 equals the area under the demand curve between points B and C. In contrast, the increase in GDP if all immigrants were to migrate to region 2 equals only the area under the demand curve between the points B' and C'. Comparing these two polar cases makes it clear that the net increase in GDP attributable to optimizing behavior on the part of immigrants is given by the shaded triangle BCE.

In an important sense, this result summarizes the economic content of the statement that immigration greases the wheels of the labor market: income-maximizing behavior leads to a more efficient allocation of resources and maximizes GDP per capita in the host country. This type of immigrant behavior speeds up the process of adjustment to long-run equilibrium, and the larger national output may impart benefits to some sectors of the economy. In the absence of any redistribution mechanism, however, it turns out that the immigrants get to keep much of the increase in GDP that can be attributed to their locating in the high-wage region. As a result, it is important to examine to what extent natives benefit from the fact that income-maximizing immigrants cluster in high-wage regions and thereby improve market efficiency. Consider again the case where natives are immobile. The income accruing to natives is then given by

(10) [Q.sub.N] = Q - [w.sub.1][M.sub.1] - [w.sub.2][M.sub.2].

The maximization of equation 10 with respect to [Theta] indicates that the relation between [Q.sub.N] and [Theta] is U-shaped. In fact, the value of [Q.sub.N] is the same at the two polar extremes of [Theta] = 0 and [Theta] = 1, and the income accruing to natives is minimized when [Theta] = 0.5, regardless of the value of k. Put differently, natives gain the most when immigrants cluster in one region, regardless of where they cluster, and natives gain the least when immigrants allocate themselves randomly across regions.

Figure 2 also illustrates the intuition behind this result for the special case where k = 1. Suppose that all immigrants cluster in the high-wage region ([Theta] = 1). The net gain to natives is then given by the triangle BCD. In contrast, suppose that all of the immigrants end up in the low-wage region ([Theta] = 0). The net gain to natives then equals the triangle B'C'D', which is obviously equal in area to triangle BCD. The assumption of identical and linear demand curves in the two regions effectively builds in the result that the net gain to natives is the same whenever there is complete clustering, regardless of where immigrants cluster.(12)

This conclusion also depends crucially on the assumption that the native work force is immobile. It is easy to show that natives benefit more when immigrants cluster in high-wage regions as long as natives can move across regions and it is costly to make that internal move. After all, the initial regional wage gap would have eventually motivated some native workers to move across regions. The clustering of income-maximizing immigrants in the high-wage region reduces the number of natives who need to engage in internal migration and hence reduces the migration costs that natives have to incur.

To illustrate this point in a simple framework, suppose that immigrants enter the country first, and that natives then base their internal migration decisions on the postimmigration regional wage gap. Suppose further that, although costly, the internal migration of natives is instantaneous and complete, in the sense that all natives who need to move to equalize wages across regions do so immediately. The number of natives who need to move across regions is then given by

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Define the "net" income accruing to natives as

(12) [Q.sub.N] = Q - [wM.sub.1] - [wM.sub.2] - C(R),

where w = [w.sub.1] = [w.sub.2], and C(R) gives the migration costs associated with R native workers moving across regions, with C'(R) [is greater than] 0. Because natives "fill in" to arbitrage the regional wage gap regardless of where immigrants choose to cluster, it should be evident that the quantity Q - [wM.sub.1] - [wM.sub.2] in equation 12 is independent of [Theta]. In the end, half of the labor force end up in region 1 and half in region 2, and wages are equalized. The relationship between [Q.sub.N] and [Theta], therefore, depends entirely on how the geographic sorting of immigrants affects migration costs. Inspection of equations 11 and 12 shows that the larger the fraction of immigrants who cluster in the high-wage region (that is, the greater is [Theta]), the fewer natives need to move across regions, the lower is the level of migration costs, and the larger is the net income that accrues to the native population.(13)

In fact, the increase in migration costs that natives must incur …

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Publication information: Article title: Does Immigration Grease the Wheels of the Labor Market?. Contributors: Borjas, George J. - Author. Journal title: Brookings Papers on Economic Activity. Publication date: Spring 2001. Page number: 69. © 2008 Brookings Institution. COPYRIGHT 2001 Gale Group.

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