EUROPEAN ECONOMIC REVIEW ELSEVIER

European Economic Review 40 (1996) 1737-1743

On the political economy of immigration Jess Benhabib New York Unioersity, Department

of Economics,

269 Mercer

Street, 7th Floor, New York, NY 10003,

USA

Received 15 March 1993; revised IS April 1995

Abstract We study how immigration policies that impose capital and skill requirements would be determined under majority voting when native agents differ in their wealth holdings and vote to maximize their income. JEL classijication:

F22; J 18

Ke?;~~ordstImmigration policy

1. Introduction How does immigration affect the economic welfare of the native population? An early answer to this question has been given by Berry and Soligo (1969). In the context of a representative agent economy, they found that irrespective of how much capital the immigrants bring with them into the country, the welfare of the natives, as measured by the welfare of the representative agent, must (except for singular cases> necessarily improve. (For further elaborations and generalizations see Quirba (1988) and Meier and Wenig (19921.) With a native population that is heterogeneous in terms of wealth distribution, however, it is intuitively clear that free immigration will not benefit everyone. In this paper we will study how immigration policies that impose capital and skill (human capital) requirements on heterogeneous immigrants would be determined under majority voting when natives vote for policies that will improve their economic well-being. Of course the preferences of natives concerning immigration policies will also be influenced by non-economic considerations. A desire to maintain cultural and ethnic homogeneity is surely at work in some societies. On the other hand, naturalized 0014.2921/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved SSDZ 0014-2921(95)00122-O

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European Economic Review 40 (1996) 1737-1743

immigrant groups may want their relatives, friends and ex-compatriots to join them, irrespective of how an unrestrictive immigration policy would affect their welfare. Here we focus only on the purely economic considerations and try to isolate their impact on immigration policy. Our goal is to provide a simple model which may be used to address issues in the political economy of migration. In Section 2 we consider the case of one-shot immigration with heterogeneous native and immigrant populations. We show that the native population will be polarized between those who would like an immigration policy to maximize the domestic capital-labor ratio and those who would like an immigration policy that would minimize it. We study the determinants of political outcomes when policies are set according to preferences of the majority. ’ Section 3 suggests some possible extensions to the case of continuous immigration.

2. The model Individuals are indexed by the units of capital that they own, k. The density of individuals is given by the continuous density function N(k), defined on [0, m>. The initial capital stock, K(O) = K,, is given by K, =

=N( k)kdk /0

and the initial population L, =

size, L(0) = L,, is

mN(k)dk. /0

(2)

The median type, k,, is the solution to the equation

lOk”N( k) dk = o 5 L,

.’

The density function of potential (one-shot) immigrants is Z(k), defined over [O, m) and continuous. An immigration policy PCs, 9) restricts the types of potential immigrants to those with s I k I q, so that the total immigration flow is /,4Z(k)dk. Of course, s, q E [O, a>. The post-immigration capital-labor ratio is given by R(s,q)

=R$=

K,+

j,“Z(k)kdk

L, + fZ( k) dk

’

(4)

We denote the pre-immigration capital-labor ratio by R, = R(s, s). We assume a constant-returns neoclassical production function F( K, L) = Lf< K/L). The competitive wage rate, as usual, is w =f( K/L) -f’( K/L)K/L

’ For an excellent historical study of how pro-immigration and anti-immigration forces got polarized as immigration depressed wage rates in the period from 1890 to 1920, see Goldin (1993).

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and the interest rate is r = f’( K/L). Let ki be the type indifferent to immigration policy P(s, q), so that her pre-immigration and post-immigration incomes are identical. Then f( R,) -f’(

R,) R, +f’(

‘,)ki

-f(

‘:)

-f’(

‘f)

+f’(

‘,4)ki.

(5)

Adding and subtracting f’(R:)R, to the right of (5) and rearranging, we obtain (6a); adding and subtracting f’(R,)R% to the right of (5) and rearranging, we obtain (6b): f(&)

-f(C)

-f’@%)(&-R:)

We can now immediately

=[.f’(V)

derive the following

-.f’vh)l(ki-~“)~ (64

Proposition:

Proposition 1. (a) Th e average person of type k = R, obtains a higher income than his pre-immigration income under any immigration policy P(s, q) if R, # Rf; (b) If Re ki have a higher post-immigration income under policy P( s, q); (c) if R, < Re then R, < ki < R% and all natives of type k < ki haue a higher post-immigration income under policy P( s, q); (d) If we assume that natives vote against an immigration policy that reduces their income, then a policy P(s,q) will be defeated in a referendum if 1. k, s ki when R% R,; (e) Any immigration policy P(s, q) such that Rf # R, will be approved if the median wealth, k,, is sufficiently close to the average wealth, R,. Proof (b) and (c) follow since the left-hand side of (6a) left-hand side of (6b) is positive under the strict concavity of (5) if we replace ki with R, and note that the strict concavity left-hand side is smaller than the right-hand side. (d) is obvious is obvious from inspecting (d.i), (d.ii) in conjunction with (b)

is negative and the f. (a) follows from off implies that the and immediate. (e) and (c). 0

We note that (a) above corresponds to the graphical result of Berry and Soligo (1969) if all individuals have the same wealth, that is if there is a representative agent. Next we would like to investigate which immigration policy would defeat any other policy in a pairwise contest under majority voting. For this purpose we first characterize the policies for which the highest and the lowest post-immigration capital-labor ratios are obtained. Some elementary algebra shows that the maximum R( s, q) is attained by R(s,_ m> where s is the highest s such that R(s, m) = s.

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That is we can start by permitting the immigration from the highest end of the distribution Z(k) and reduce s until the average capital-labor ratio R(s, m) attained is equal to the marginal capital-labor ratio s. Any s > s obviously raises the capital-labor ratio and must be allowed to immigrate m order to attain the maximum R(s, q). Similarly to minimize the capital-labor ratio we must start at the bottom to allow the immigration of all types [0,41, where 4 is the lowest 4 such that R(0, q> = q. 2 Of course if R, = 0, 4 = 0. We define the maximum attainable R as R = R(s, x) and the minimum attainable R as R = R(0, ?>. Consider now the preferred immigration policy of an arbitrary type k,. The preferred capital-labor ratio R of type k, is the solution to Max f(R)

(7)

-f’(R)R+f’(R)k,.

RE[R,Rl

The objective function is convex with a minimum at k, = R. Thus type k, either prefers R or R: The population will be polarized between those who prefer R and therefore immigration policy P(s, m) to all other policies, and those who prefer R, and therefore immigration policy P(0, 4) to all other policies. To sort out what the majority prefers consider the type k, who is indifferent between i? and R. We have f(R)

-f’(

R)R +f’( @k,

=f(l?)

-f’(R)R_-

+f’(&)k,.

(8)

Constructing the analogues of Eqs. (6a) and (6b) with R and E replacing R, and R,Y, it is easy to show that R < K, < i?. It follows that all types k < k, prefer P(s, m) and types k < k, prefer P(0, 4). We can summarize these points in Proposition 2: Proposition 2. If k, < k,(k, > k,), and uoters care only about their income, PCs, m> (P(0, 4)) defeats all other immigration policies under majority voting with pa&vise alternatiues. While minimal capital requirements or skills may be required of immigrants, it may not be legally feasible to restrict immigration to [0,41: Once in the country immigrants may not be prevented from bringing in their wealth or they may pretend to be unskilled when they are not. If 4 must be ~0, the alternative feasible policy that minimizes R is free immigration, that is P(0, a>. Thus in Proposition 2 we may replace P(0, 4) with P(0, ~1. The contest would then be between free immigration and restricted immigration with minimum skill or capital requirements. We must be careful to define wealth appropriately so that skills and human capital are included as part of wealth. As the German and Swiss experiences of the

* There may of course be comer solutions if the support of I(k) is bounded. Modifying for those cases is straightforward and therefore omitted.

the analysis

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last few decades indicate, a highly skilled population may well favor the immigration of a large number of unskilled workers rather than allow the unskilled wage rate to increase, at least for a limited amount of time. 3 There are a number of considerations that the model fails to address and which may be taken up in future work. An important and interesting one has to do with the multisectoral nature of the economy and the nonhomogeneity of the labor force. We typically find that immigrants are concentrated in particular sectors and that they do not always directly compete with many segments of the labor force. No doubt incorporating this point into the model would alter the analysis and the results to some extent. More importantly, a realistic description of immigration policy may involve not only minimum or maximum skill and wealth requirements, but also a bound on the total number of immigrants. This would be important if the size of potential immigrants was large and uncertain. Voting on the volume of immigration may be as important as voting on the quality of migrants, and rationing immigrants of a given skill at borders is common practice. Modifying the analysis to incorporate these considerations which would also require the modelling of a rationing mechanism would no doubt enrich the analysis. Finally the model pays no attention to immigration that may be temporary and to the possibility of return migration. These consideration certainly have an important bearing on the labor market and on the political attitudes toward immigration.

3. An extension When an immigration policy is in place, immigrants will continue to arrive into a country period after period, and if eventually they are accorded voting rights, they will influence subsequent immigration policies. We may denote the wealth density of the potential immigrants by cZ(k, t) where c is a parameter, and t denotes the time period, and may assume that the fraction of immigrants that acquire voting rights is given by a function p( t - T) where T is the arrival time of immigrants. At time t the immigration policy implemented will be the most preferred policy of the majority of the voting population. There is an element of myopia in this, since the voting population does not consider the effect of current policies on the composition of future populations, and their impact on the future immigration flows and policies. This may not be unrealistic if periods under consideration are sufficiently long (not years but decades) and if people discount the future sufficiently. Alternatively, a population with limited foresight may restrict immigration when the proportion of new immigrants gets too large, or 3

Some of the recent events in Germany

suggest that the time for a policy reversal may have arrived.

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European Economic Reciew 40 (19961 1737-1743

when a myopic policy will swing the median voter in the subsequent period and initiate a major policy revision, for example from P(s, m> to P(0, S). Examples of such cases with a Cobb-Douglas production function and exponential as well as Pareto densities for the domestic and the potential immigrant populations are constructed in Benhabib (1992). Simulations indicate that a common pattern is an initially increasing capital-labor ratio associated with restrictive capital or skill requirements on immigrants. Here the restrictive policies are the result of the exponential, or any other wealth distributions whose medians are lower than their means: the capital-poor are in the majority. In time however immigration flows can alter the initial distribution, with the skilled and the capital rich eventually becoming the majority. An abrupt switch of immigration policy takes place to allow poor and unskilled workers into the country. Because the potential population of immigrants is skewed towards the poor and the unskilled, large numbers of immigrants can arrive very quickly, changing the population density and lowering the capital-labor ratio in a short time. Consequently, a restrictive immigration policy is reinstituted before long, and the capital-labor ratio starts to rise again. In many cases we observe a long and damped asymmetric cycle. If there is domestic capital growth that is equivalent to a rightward shift in the distribution of wealth however, there may be no policy reversals. The reason is that relative to the domestic wealth distribution, the wealth of even the richer potential immigrants becomes insignificant, and immigration alone cannot swing the majority to become capital-rich: k, remains below k,. These results are invariant to adding multiplicative shocks to the production function, with or without technical progress, as long as the distribution of wealth is not essentially affected. Stochastic shocks to factor shares that change income distribution and therefore the median voter, or growth that changes the wealth of the domestic the population relative to the wealth of the potential immigrant populations however can affect immigration policies that are implemented.

Acknowledgements This paper was written after a stimulating conversation with A. Wenig. I am, however, responsible for errors and misconceptions. I would like to thank the C.V. Starr Center for Applied Economics at New York University for technical assistance and the referees of this journal and the editor, F. Bourguignon, for helpful comments and suggestions that improved the paper.

References Berry, R.A. and R. Soligo, 1969, Some welfare aspects of international Economy 71, 778-794.

migration,

Journal of Political

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Benhabib, Jess, 1992, A note on the political economy of immigration, Working paper RR #92-42 (C.V. Starr Center, New York University, New York). Goldin, C., 1993, The political economy of immigration restriction in the United States, 1890-1921, Working paper no. 4345 (National Bureau of Economic Research, Cambridge, MA). Meier, V. and A. Wenig, 1992, Welfare implications of international labor migration, Working paper (University of Bielefeld, Bielefeld). Quirba, M.G., 1988, On generalizing the economic analysis of international migration: A note, Canadian Journal of Economics 21, 874-876.