International labor migration and social security: Analysis of the transition path

J Popul Econ (2004) 17:535 551 DOI 10.1007/s00148-004-0202-5 International labor migration and social security: Analysis of the transition path Doris Geide-Stevenson 1, Mun S. Ho 2 1 Weber State University, Department of Economics, Ogden, UT 84408-3807, USA (Fax: +1-801-626-7423; e-mail: DGSTEVEN@Weber.edu) 2 Kennedy School of Government, Harvard University, 79 John F. Kennedy St., Cambridge, MA 02138, USA (Fax: +1-617-495-1635; e-mail: mun ho@harvard.edu) Received: 14 April 2000/Accepted: 20 May 2003 Abstract. This paper numerically simulates a two-country overlappinggenerations model to study international labor migration when the two countries are characterized by different social-security systems. The present analysis extends previous work beyond steady-state considerations. The most striking result is that in all cases considered, dynamically efficient and inefficient economies in autarkic steady-state, migration leads to temporary welfare losses in both countries. In all cases, the transition path is characterized by temporary dynamic inefficiency in one country. JEL classification: F22 Key words: International migration, social security, OLG model 1. Introduction In the face of increasing international migration flows, the recent decade has seen a renewed debate on the economic impact of immigration (e.g., Friedberg and Hunt 1995; Zimmermann 1995). Often this debate focuses on who gains and who loses from migration. In analyzing these welfare effects of migration, the term immigration surplus has been coined, suggesting that residents of a receiving country gain from immigration (Borjas 1995). Generally this type of analysis employs static models, ignoring capital accumulation over time. Also, the welfare effects on the residents in the All correspondence to Doris Geide-Stevenson. We would like to thank an anonymous referee for very helpful comments. We are responsible for any remaining errors. Responsible editor: Christoph M. Schmidt.

536 D. Geide-Stevenson, M. S. Ho sending country are often not explicitly or incompletely modeled. Other recent work on labor migration has used dynamic models, with the most important strand using the overlapping generations (OLG) framework. This work has focused mainly on migration patterns and welfare effects of two countries in the steady-state. This approach has been popular because, as Galor (1992) has noted, compared to the infinite-lived representative agent model, in an overlapping-generations model, restricting attention to a steady-state welfare analysis does not generate logically inconsistent predictions; the steady-state represents the entire economic environment to which infinitely many generations are subjected. However, even in an OLG model the transition period towards steady-state can last many periods, affecting many generations. This transition period warrants a closer analysis. This paper seeks to extend the dynamic analysis beyond the steady-state to discuss international migration patterns and welfare effects during the transition period by numerically simulating a general equilibrium OLG model of a two-country world. We examine the migration flows and welfare effects during the transition when the border is suddenly opened and labor is allowed to move between these two countries that differ only with respect to the social security policies employed. Labor will move to the country that confers higher utility to its residents, in the process equalizing utilities for residents in both countries. These international labor movements will have differential impacts on various generations. For example, the old generation alive in the initial period owns the immobile capital and experiences an unexpected change in the return to capital when international labor mobility is allowed. A key insight of this paper is that it is not only possible, but likely, for utility levels in both countries during the transition period to fall below autarkic steady-state utility levels. Galor (1986) is the first to use a two-country overlapping-generations model to analyze international labor migration and its welfare effects. In his model, individuals born in different countries differ in their rates of time preference. This gives rise to utility differences and provides a motivation for migration in the steady-state. He shows that the direction of labor migration depends on whether countries under or overinvest relative to the Golden Rule and that bilateral migration becomes a theoretical possibility. Kemp and Kondo (1989) also consider international differences in individual time preferences, but endogenize population growth by relating it to earlier and current rates of migration. Galor and Stark (1991) use a two-country OLG model to analyze the pattern of labor migration when the two countries differ in their technologies. They consider Hicks-neutral differences in technology and a constant population. Kondo (1989) endogenizes population growth and models three types of technological differences: capital-saving, neutrally superior, and labor saving. He shows that if the autarkic steady-state in each country is characterized by under-investment relative to the Golden Rule, labor will emigrate to the country with a capital-saving or neutrally-superior technology, lowering the demand for children in that country. Geide- Stevenson (1998) looks at international differences in social-security systems as an incentive for international factor movements. Again the steady-state pattern of labor migration depends on the autarkic steady-state capital-labor ratios compared with the Golden Rule capital-labor ratios. A general feature of all the models where foreign and domestic residents are assumed homogenous is that migration does not vanish in the long-run

International labor migration and social security 537 since economies keep converging to their different autarkic steady-states which again opens up utility differentials and induces more migration. Consequently, these models predict an eventual emptying out of one country. The long-term welfare effects are straightforward since countries re-converge to their pre-migration steady-states. This implies that all residents of the receiving, high utility country eventually enjoy the utility level previously found in the autarkic steady-state of this country. Thus, by design, these types of models do not generate an immigration surplus in the long-run since pre-migration and post-migration steady-state capital-labor ratios and factor prices are identical. The strong implication of one country emptying out is sometimes seen as unpalatable, maybe implying that before this were to happen, policies are put in place in order to prevent this emptying-out. However, this only strengthens the case to study the initial periods after two economies are opened up and before one country has completely emptied out. Other papers exploring international migration in the context of an OLG model include Scholten and Thum (1996). They explore the link between the social security system and immigration policy and show that the median voter s choice of immigration policy leads to inefficient levels of immigration. 1 Some further extensions to the OLG models described above, drop the assumption of homogenous labor and introduce human capital accumulation. Galor and Stark (1994) model a small open economy with perfectly mobile capital where human capital formation is financed by borrowing. If migrants have on average a lower level of human capital than domestic workers, then the adjustment of the economy can be reversed to a lower per capita human capital steady-state equilibrium. A one shot erosion of human capital can result in adverse long-run production and welfare consequences. In contrast, Razin and Sadka (1999) construct a small, open OLG economy where in-migration of unskilled workers is Pareto-improving. The unskilled young immigrants help to finance a public pension system, increasing the benefit to the currently old without adverse effects on future generations as long as factor prices are fixed. Within a continuous time version of the neoclassical growth model, van Dalen (1993) numerically simulates the welfare effects of brain drain, migration of skilled workers, on the immigration country. He shows that for a broad set of parameter choices the immigration country is likely to loose from immigration of skilled labor because the negative capital dilution effect, the reduction of the capital-labor ratio due to in-migration, dominates the welfare-improving free rider effect of education when migrants are already schooled. Reichlin and Rustichini (1998) model an endogenous growth overlapping generations economy with heterogeneous agents where a labor exporting country may find itself on a welfare improving path, or on a welfare reducing path. Thus, they accommodate welfare gains and losses within one framework. The purpose of the present paper is to explore the welfare effects of migration on the labor exporting and labor importing countries simultaneously, along with the temporal pattern of migration, based on the class of simple two-country, overlapping generations models with homogeneous agents. In line with previous work, it is assumed that the two countries are closed except for international movements of labor. An incentive for migration exists when utility differences for the residents of the two countries are observed. For two countries that are characterized by identical technology, social security policy and preferences, utility differentials can exist when these

538 D. Geide-Stevenson, M. S. Ho economies are on different points along their adjustment paths towards the steady-state. More fundamentally, countries are assumed to differ in their social security policies. The major results of this paper are as follows. For identical countries on different points on their transition paths, migration will only take place in the first period. In cases where there are fundamental differences between countries there are prolonged patterns of migration. The levels of migration are typically monotonically declining over time, with even small differences in utility resulting in relatively large initial levels of migration after the two economies are opened up. In all cases studied, utility levels in both countries fall below the steady-state utility level of the labor exporting, i.e., low-utility country. Thus, unrestricted migration will result in making everybody, other than the initial old generation in the high-utility country, worse off during a transition period. Section 2 of the paper describes the basic overlapping generations economy used as basis for the simulations. In Sect. 3 the various cases are analyzed. Section 4 concludes. 2. The basic model The basic model used for the analysis is first described for a closed economy and then for an open economy, i.e., an economy where international labor mobility between the two countries is allowed. 2.1. Closed economy Time is discrete and indexed by the subscript t, t = 0,1,2,3,.... At date t, a generation of size N t of identical two-period lived individuals is born. In the first period of their lives each individual inelastically supplies one unit of labor. Labor income w t is taxed at a rate z (social security tax), z 0, and the net income (1)z)w t is then split into first-period consumption c 1t and savings s t. Old age consumption c 2t+1 is financed by the returns on private savings r t+1 s t and a social security transfer (when z > 0) from the young generation born at t+1. The gross rate of return on savings is denoted by r t+1. The size of generation t is N t and the size of generation t+1 is N t+1 where N tþ1 =N t ¼ n ð1þ with n being the gross rate of population growth. The decision problem for a representative member of generation t is: max uðc 1t Þþhuðc 2tþ1 Þ; c 1t 0; c 2tþ1 0; 0 z < 1 ð2þ s. t. c 1t þ s t ¼ w t ð1 zþ; c 2tþ1 ¼ r tþ1 s t þ nzw tþ1 The discount factor is h =1/(1 + d) where d is the pure rate of time preference. The specific utility function used in the simulations is of the CES-type V ðc 1t ; c 2tþ1 Þ¼2c 0:5 1t þ h2c 0:5 2tþ1 ð3þ

International labor migration and social security 539 This utility function is strictly monotonic, with strictly convex indifference curves that do not intersect the axes. u 0 ð0þ ¼1; u 0 ð1þ ¼ 0: The first-order condition for the individual s decision-making process is: u 0 ðc 1t Þ u 0 ðc 2tþ1 Þ ¼ c0:5 2tþ1 c 0:5 ¼ hr tþ1 ð4þ 1t Together with the intertemporal budget constraint w t ð1 zþþ nzw tþ1 r tþ1 ¼ c 1t þ c 2tþ1 r tþ1 one can solve for the individual s savings function s ¼ sðw t ; w tþ1 ; r tþ1 ; zþ: ð6þ The parameter z is the social security tax rate on labor income and determines the type of social-security system that a country relies on. For z ¼ 0, old-age consumption is financed exclusively by private savings and the savings function can be written as s ¼ s (w t, r t+1 ). For any z > 0, the country operates a pay-as-you-go social security system. In this basic model, output Y t is produced following a neoclassical, constant returns to scale technology Y t = F(K t,n t ) where K t denotes the capital stock. This production function can be rewritten in per-capita form y t = f(k t ) where k t is the capital-labor ratio and y t per-capita output. The specific functional form used for the simulations is of the Cobb-Douglas type y t ¼ kt a ð7þ where the technological parameter 0 < a < 1. This function f is twice continuously differentiable, positive, and strictly concave f ðk t Þ > 0; f 0 ðk t Þ > 0 and f 00 ðk t Þ < 0 for k t > 0, and f 0 ð1þ ¼ 0; f 0 ð0þ ¼1. Under perfect competition, the first-order conditions for a profit-maximizing firm are: f 0 ðk t Þ¼akt a 1 ¼ r t f ðk t Þ k t f 0 ðk t Þ¼ð1 aþkt a ð8þ ¼ w t Labor input is exogenously given, determined by the number of young individuals in the economy. Capital represents last period s output, which was not consumed. As each generation dissaves completely in the second period of their lives the existing capital stock is fully used for old-age consumption. Therefore, the capital stock fully depreciates in each period and the gross interest rate r t contains the 100% depreciation rate. Conditions (8) represent the factor market equilibrium where firms fully employ the fixed supply of inputs at period t. In autarky, steady-state equilibrium in the home country, i.e., k t ¼ k t+1, is fully described by Eqs. (4), (5), (8) and the goods-market clearing condition (9) representing the equality of net savings and net investment. K tþ1 K t ¼ N t sðw t ; w tþ1 ; r tþ1 ; zþ K t ð9þ nk tþ1 ¼ sðw t ; w tþ1 ; r tþ1 ; zþ ¼w t ð1 zþ c 1t Equations (9) describe the relationship between k t and k t+1 and capture the dynamic properties of the economy. Additional restrictions on preferences ð5þ

540 D. Geide-Stevenson, M. S. Ho and technology are needed to ensure the existence, uniqueness, and stability of a steady-state equilibrium (Galor and Ryder 1989). Provided that the sufficient conditions for a unique, non-trivial steady-state equilibrium hold, global stability of the equilibrium prevails with 0 <dk t+1 /dk t < 1 evaluated around the steady-state equilibrium. For a given initial capital stock K 0, initial level of population N 0, and parameter values for h, a, n, and z, the transition to steady state for the variables N, K, k, c 1,c 2, w, r over t time periods is fully described by the set of t-1 equations of the type (1), (4), (5), (8), (9), the definition of k t as K t /N t,an equation determining c 2 (0) consumption of the old generation alive in t ¼ 0 and a steady-state equation of the type k(t) = k(t-1) where T denotes the terminal period. These equations fully describe the transition to steady-state from an initial capital labor ratio k 0 when the stability condition is met. 2.2. Open economy For the two-country, open-economy case, all variables pertaining to the foreign country will be denoted with an *. While residents of both countries are assumed to have identical utility functions, their level of utility will differ because of different consumption levels while young and old. Different levels of consumption are implied because the countries may differ in their endowment of initial capital, K o 6¼ Ko, or more fundamentally in their social security policies, z o 6¼ z o. Apart from differences in their social security policies, the two countries are assumed to be identical so that the same set of equations describing the home country transition to a steady-state also describes the foreign country s transition to steady-state. When the borders are opened, people migrate at each period t until utility levels are equalized: V ðc 1t ; c 2tþ1 Þ¼Vðc 1t ; c 2tþ1 Þ: ð10þ If the foreign country relies on private savings to provide for old age consumption while the home country operates a pay-as-you-go social security system, so that z>0 and z*=0, Geide-Stevenson (1998) shows that the steady-state pattern of migration depends on the steady-state capital labor ratios as compared to the Golden Rule capital-labor ratios. When the socialsecurity system provides higher returns than can be obtained from private savings, i.e., n>r, it is advantageous for young individuals to move to the social security country and vice versa. With labor migration taking place, it is shown that in the long-run all young individuals of the low-utility country might move to the high-utility country since incentives to migrate do not vanish in the long-run. As long as residents of both countries have identical preferences, the domestic economies in both countries will always replicate themselves in per-capita terms after migration takes place. In the overlappinggenerations model with production, capital stocks are not fixed, but are created via savings. Eventually, after a gain or a loss of workers and given stability conditions, the economy will converge to the same steady-state capital-labor ratio that existed before migration took place. Thus, both economies will converge to a situation where the old utility differentials reemerge, triggering another wave of migration. In this analysis the transitional or temporal pattern of migration is not explicitly considered.

International labor migration and social security 541 The following section explores the transition to steady-state via numerical simulations of various cases. 3. Migration patterns and welfare effects In this section we explore four scenarios when two economies are opened up to international movements of labor. We simulate the open-economy model to obtain migration flows, utility levels, factor prices, population growth rates and the time path of public pension payments during the transition period 2. Since the steady-state analysis of international migration indicates different results depending on whether countries under- or overinvest relative to the Golden Rule capital-labor ratio, i.e., whether countries are dynamically efficient or inefficient in autarky, the simulations cover both situations. The four cases are tabulated in Table 1. In cases 1 and 4, parameter values are chosen such that one country is dynamically inefficient in the time period just before migration is allowed (n* > r*), while the second country is dynamically efficient (n r). In case 2 both countries have a social security tax, while in cases 1 and 3 z* = 0. In case 4 instead of setting fixed tax rates, the benefit ratio q is chosen as the policy variable 3. These fundamental differences in the social security policies of the two countries in the four cases imply convergence to different steady-states. These differences generate the steady-state utility differentials between the two countries and generate incentives for ongoing migration. If countries are identical in all respects, but merely at a different stage in their transition to a common steady-state capital-labor ratio, migration will take place only in the first period after opening the two economies. After this initial period, the two countries have identical capital labor ratios and utility levels and migration ceases. In all cases we consider the following parameter values: N t ¼ N t * ¼ 100 for all t ¼ 0, 1, 2..., i.e., in autarky both countries are characterized by constant population so that n = n*. Also, the technology parameter a = a*. In the open economy model only migration will change the size and growth rate of the population. 3.1. Case 1 Dynamic inefficiency in autarky In numerically implementing the transition path of an open economy the following parameter values are chosen for the first case. Home and foreign country are identical with respect to their technology used with a = a* = 0.3. The foreign country is assumed to rely entirely on private savings for old-age Table 1. Summary of parameter values h = h* z z* q Autarky Case 1 dynamic inefficiency 0.9 0.05 0 N/A n < r, n* > r* Case 2 dynamic efficiency with tax 0.9 0.05 0.02 N/A n < r, n* r* Case 3 dynamic efficiency without tax 0.8 0.05 0 N/A n < r, n* < r* Case 4 fixed benefit ratio 0.9 N/A N/A 0.02 n r, n* > r*

542 D. Geide-Stevenson, M. S. Ho consumption, z* = 0, while the home county operates a pay-as-you-go social security scheme with the social security tax z = 0.05. These parameter values result in r>n>r*in autarkic steady-state. Due to the social security system, residents in the home country save less which results in a lower capital-labor ratio and a higher marginal product of capital and rental rate r. The foreign country could gain from the introduction of a social-security scheme because the population growth rate n* exceeds the private return on savings r*. The autarkic steady-state in the foreign country is characterized by dynamic inefficiency. This implies that the foreign country has accumulated too much capital and welfare could be improved by reducing the capital-labor ratio. The home country has chosen a social security tax z that exceeds the optimal social-security tax z opt which would result in the Golden Rule capital labor ratio. 4 Given the present parameter values, numerical analysis reveals that the foreign country is the high-utility country in steady-state so that the foreign country will be the receiving country. To start the simulation, the initial capital stocks are naturally chosen to be at the respective autarkic, steady-state values, K 0 * = 18.633 and K 0 =16.797 (with the fixed population size N = N* = 100). Figure 1 shows the resulting pattern of migration in this case. The number of migrants declines monotonically over time until the low utility country empties out. Figure 2 plots the utility level of the world population after the borders are opened. For comparison, the utility levels of the two countries autarkic steady-state are also marked as the two horizontal lines V(home) ¼ 1.73834 and V(foreign) ¼ 1.73892. Clearly, at t ¼ 0, the young in the home country have an incentive to move to the foreign country. However, the simulation results show that during the initial time periods after migration is allowed, the utility levels of the young in both countries are lowered below the autarkic 12 10 Migration 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10111213141516171819202122232425 Time Fig. 1. Case 1 (dynamically inefficient country, excessive tax home) Migration from home to foreign

International labor migration and social security 543 1.74 1.739 1.738 Utility 1.737 1.736 V(open) V(Home) V(Foreign) 1.735 1.734 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Time Fig. 2. Case 1 (dynamically inefficient country, excessive tax home) Utility Levels during transition compared to autarkic levels steady-state utility level of the sending (low-utility) country. In this example, it takes 11 periods (generations) to reach a utility level that is above the initial steady-state autarkic level for the low-utility country. During this substantial transition period, migration makes everybody, other than the initially old in the foreign country, worse off. In the long-run, since incentives to migrate do not vanish and the low-utility country eventually empties out, the world will be characterized by the higher steady-state utility. Thus, in the long-run migration is Pareto-improving. However, the explicit analysis of the transition period provides the surprising result that even though incentives for migration exist, migration will temporarily make everyone born during the initial few periods worse off than compared to the respective autarkic steady-states, even the young in the home country. Thus, during transition to steady-state where everyone lives in the high-utility country, there exists no immigration surplus, rather an immigration deficit that extends to both countries. This result is partly due to the perfectly competitive nature of the economy. When the economy first opens, all the young in the home country see an incentive to move and a high percentage (about 10%) actually moves. The foreign country also remains dynamically inefficient when migration is first allowed. In fact, calculations reveal that the dynamic inefficiency is aggravated with migration in the sense that the difference between n* and r* increases. As Table 2 shows, compared to autarkic steady-state (in the row labeled ss), migration temporarily increases both n* and r*, but widens the difference between the two variables. This provides an intuitive explanation of why utility falls below the utility level of the foreign country without migration and possibly also below the utility level of the home country in autarky. While this result seems surprising, numerical results for all other variables are as expected. These results make clear why transitional utility can be lower for both countries. With an open economy, the foreign country capital labor

544 D. Geide-Stevenson, M. S. Ho Table 2. Transitional dynamics of population growth rates and rental rates of capital Case 1 Time n n* r r* ss 1 1 1.04581 0.97259 0 0.895997 1.104003 0.968442 1.042323 1 0.889055 1.090042 0.970216 1.031191 2 0.890595 1.07242 0.971428 1.020335 3 0.893982 1.05828 0.973517 1.011186 4 0.89882 1.046985 0.976576 1.00376 5 0.90472 1.037984 0.980409 0.997801 6 0.911333 1.030809 0.984785 0.993037 7 0.918361 1.025079 0.989492 0.989226 8 0.925562 1.020487 0.994354 0.98617 9 0.932743 1.016788 0.999231 0.983711 ratio falls below the autarky level as population increases. This reduces the wage and increases the rental rate of capital. The lower wage reduces first period consumption, but second period consumption increases with the rental rate of capital. Welfare levels are pulled in opposite directions by these two effects. For the parameters chosen, our simulations show that the net effect is a reduction in utility. Conversely, in the open economy, the home country capital labor ratio increases along with the wage and first period consumption compared to autarkic steady-state. On the other hand, the rental rate of capital and the social security payments received fall, lowering second period consumption. Social security payments are lower because the population growth rate falls by more than the wage increases. Simulation then reveals that the opposing welfare effects on first and second period consumption also result in a net reduction of utility. For the old generation in t ¼ 0 a different story emerges. As expected, the old in the foreign country benefit from in-migration since they own the fixed * capital stock that now earns a higher rental rate. Old age consumption c 20 increases from 0.18122 to 0.19422. Conversely, the old in the home country lose from out-migration since rental rates on capital and social security payments are adversely affected. Their old age consumption c 20 decreases from 0.19616 to 0.18165. 3.2. Case 2 Dynamic efficiency with tax in autarky In order to explore how robust the results from Case 1 are, we examine a case where both countries are initially in an autarkic steady-state that is characterized by dynamic efficiency. This is achieved by retaining the structure of the example simulated in Case 1, except for the introduction of a pay-as-you go social security scheme in the foreign country also. Now, we assume z* = 0.02. Compared to case 1 this leads to a lower capital-labor ratio in autarkic steady-state in the foreign country which eliminates the dynamic inefficiency and approximates the golden rule capital-labor ratio (n*» r*). 5 In autarky, the foreign country is again the high utility country with V* = 1.73929 versus V = 1.73834 in the home country. Once the countries are opened, migration flows go from the home to the foreign country. Figure 3 shows how migration is monotonically declining over time, at a rate faster than in Case 1.

International labor migration and social security 545 30 25 Migration 20 15 10 5 Migration 0 0 5 10 15 20 25 30 35 Time Fig. 3. Case 2 (Golden rule foreign, excessive tax home country) Migration from home to foreign 1.74 1.738 Utility 1.736 1.734 1.732 1.73 V(open) V(Home) V(Foreign) 1.728 1.726 0 5 10 15 20 25 30 35 Time Fig. 4. Case 2 (Golden rule foreign, excessive tax home country) Utility levels during transition compared to autarkic levels The utility levels plotted in Fig. 4 reveal that welfare in the open economy falls below the autarky utility level achieved in the sending (low-utility) country for the first six periods. The numerical simulation also shows that even though the foreign country was initially in a dynamically efficient steadystate, migration temporarily induces dynamic inefficiency by pushing the population growth rate n* above r* during the first nine periods after opening the economy. This example suggests that it may not be the initial autarkic steady-state which matters for the welfare results, but rather the characterization of the transition path itself as dynamically efficient or inefficient. 3.3. Case 3 Dynamic efficiency without tax in autarky To further check for the robustness of the results obtained in simulating Cases 1 and 2, we construct another case where both countries are initially in a

546 D. Geide-Stevenson, M. S. Ho Table 3. Transitional dynamics of population growth rates and rental rates of capital Case 2 Time n n* r r* ss 1 1 1.04581 1.00154 0 0.746299 1.253701 0.852115 1.173286 1 0.704156 1.176109 0.842035 1.125094 2 0.68918 1.110777 0.831186 1.082951 3 0.685632 1.069516 0.826858 1.053642 4 0.690435 1.043883 0.82877 1.034665 5 0.700944 1.02804 0.835296 1.022705 6 0.715198 1.018207 0.856513 1.015224 7 0.731821 1.012042 0.856513 1.010529 8 0.749854 1.008122 0.869256 1.007554 9 0.768616 1.005588 0.882584 1.005643 steady-state characterized by dynamic efficiency. For this third case, the discount factor, captured by the parameter h is changed from 0.9 to 0.8 for both countries. 6 As indicated in Table 1, all other parameter values are identical to case 1. Assuming a lower discount factor leads to lower capitallabor ratios in both countries since both the domestic and the foreign young have less of an incentive to save for the more heavily discounted second period. Thus the rental rate is higher in autarkic steady states. This lead to a situation where both countries are dynamically efficient with n<rand n* < r*. It is no surprise that the existence of a social security scheme in the home country (z = 0.05) leads to lower steady-state utility in the home country with V = 1.64803 and V* = 1.65408. Again, the incentives are such that the young move from the home to the foreign country. The migration pattern for this case is shown in Fig. 5. Again, migration levels are highest in the initial period after international labor mobility is allowed and then decline monotonically. The time path of utility in the open economy is shown in Fig. 6. Here again, welfare for all the young drops below the utility levels achieved in autarkic steady-state in the sending country. 25 20 Migration 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Time Fig. 5. Case 3 (Both dynamically efficient, no tax foreign) Migration pattern from home to foreign

International labor migration and social security 547 Utility 1.656 1.654 1.652 1.65 1.648 1.646 1.644 1.642 1.64 1.638 1.636 1 2 3 4 5 6 7 8 9 101112131415161718192021 Time V(Open) V(Home) V(Foreign) Fig. 6. Case 3 (Both dynamically efficient, no tax foreign) Utility levels during transition compared to autarkic levels Even though both countries started out in their respective dynamically efficient steady-states, opening the countries to migration results in an adjustment path that shows temporary dynamic inefficiency for the foreign country. The analysis shows that during the initial period t 0, n 0 *>r 0 *, the population growth rate exceeds the rental rate of capital. While migration increases both the rental rate of capital (from 1.06019 to 1.215167) and the population growth rate (from 1 to 1.215209), the impact on the population growth rate is larger than on the rental rate of capital, matching the results from the first two cases. This suggests that the decline in welfare below autarky levels of utility in the sending country is due to the fact that one country is dynamically inefficient through part of the open economy adjustment period. 3.4. Case 4 Fixed benefit ratio The robustness of the welfare results above leads to the question whether a case can be constructed where in-migration does not substantially lower utility for younger generation in both countries. Razin and Sadka (1999) consider a situation where the social security system in one country is characterized by a fixed benefit ratio, i.e., the old receive a fixed percentage q of the wage of the currently young. The budget constraint for the old in the social security country then has to be modified to c 2tþ1 ¼ r tþ1 s t þ qw tþ1 ð11þ while the budget constraint for the young reads c lt þ s t ¼ w t ð1 z t Þ ð12þ The social security tax z now depends on the time period and is set in order to balance the government budget z t ¼ q=n t ð13þ

548 D. Geide-Stevenson, M. S. Ho This last equation shows that the social security tax z is lower the higher the population growth rate. Since the only source of population growth in the present model comes from migration, the social security country may benefit from immigration via lower social security taxes imposed on the young. In order to simulate case 4, it is assumed that the foreign country does not operate a social security system and is characterized by the same parameters as in Case 1. Steady-state utility in the foreign country is then V* ¼ 1.73892. The home country operates a fixed-benefit social security scheme where the old receive 2% of the wages earned by the currently young, i.e., q = 0.02. In the present example, this modest amount of social security is close to the optimal social security policy ensuring that n» r and that the home country ends up being the high-utility country. With q = 0.02, home country utility in the autarkic steady-state is V=1.73929, higher than in the foreign country and the home country is the receiving country. This opens up the possibility that the domestic young will benefit from immigration since they benefit from lower social security taxes as the population grows. For the simulation it is again assumed that both countries start in their respective autarkic steady-states. The pattern of migration is shown in Fig. 7. The utility calculations in Fig. 8 show that even in this case welfare for the young falls below the steady-state utility level from the sending country for 10 periods. Compared to Razin and Sadka (1999), in-migration does not benefit residents of the receiving country. This suggests that the positive tax-sharing effect is smaller than the negative effect coming from changing factor prices that induce temporary dynamic inefficiencies. Recall that in Razin/Sadka factor prices were assumed constant. The full two-country analysis suggests that welfare effects coming from changing factor prices are substantial when migration is not restricted. 12 10 Number of Migrants 8 6 4 2 Migrat 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 Time Fig 7. Case 4 (Home has fixed benefit ratio) Migration from foreign to home

International labor migration and social security 549 1.7395 1.739 Number of Migrants 1.7385 1.738 1.7375 V(open) V(home) V(foreign) 1.737 1.7365 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 Time Fig. 8. Case 4 (home has fixed benefit ratio) Utility levels during transition compared to autarkic levels 4. Discussion and conclusion This paper succeeds in simulating international migration patterns over time in a fully specified dynamic two-country general equilibrium model. While previous results determine the pattern of international migration when both countries are in steady-state, the transitional patterns of migration and welfare implied by the two-country overlapping generations models have not been studied. Our analysis indicates that the choice of the initial capital stocks in both countries only makes a difference for the level of migration in the first period. Other, fundamental differences between the two countries are responsible for prolonged patterns of migration over time. In particular, the cases studied above focus on fundamental differences in social-security policies. These fundamental differences imply that the two countries converge to different steady-state levels in their capital-labor ratios and utility levels of its residents. With these fundamental differences between countries, a consistent pattern of migration becomes apparent. In all cases studied, the level of migration is high in the first periods during which international migration is allowed. The level of migration typically declines monotonically in subsequent periods. While these models do not seem to be able to explain the observed waves of migration, they provide a framework in which one may incorporate stochastic shocks, or irreproducible factors like land, that will generate a richer set of patterns. The most surprising result is that in all cases studied, unrestricted labor migration generates welfare losses to all young, domestic and foreign, during a sometimes substantial transition period. In the receiving country the negative effect from a lower wage dominates the increase in the returns to capital,

550 D. Geide-Stevenson, M. S. Ho while in the sending country the negative effect from a lower return to capital dominates the increase in the wage rate. Thus, these two-country OLG models do not generate an immigration surplus, but rather an immigration deficit during the transitional period. This result is robust when different discount factors and both dynamically efficient and inefficient steady-states are considered. The analysis reveals that this result can be attributed to the dynamic inefficiency of the receiving country during part of the adjustment path for the open economy. Based on these results, a strong case for harmonizing social security systems can be made when countries allow unrestricted migration. 7 Alternatively, countries could restrict the number of people leaving the country, i.e., even the emigration country has an incentive to regulate migration even though labor is homogenous. This should be contrasted with other models where welfare losses for the emigration country are generated by a brain drain, i.e., the emigration of the skilled portion of the work force. Endnotes 1 Cremer and Pestieau (1998) discuss a country s choice of a social security system in the context of labor mobility and distinguish between rich and poor migrants. However, they do not use an OLG model for their analysis. 2 The model consists of a set of dynamic equations that must be solved simultaneously. The transition to the steady state is gradual and we choose a terminal period that is sufficiently far out to represent the steady state. The GAMS program was used to solve the model. 3 Also, Homburg (1991) shows that dynamic inefficiency can be ruled out in more complex cases. 4 This is discussed in more detail in Geide-Stevenson (1998) on p. 410. 5 Blanchard and Fisher derive the comparative statics results for the general model. 6 Assuming a smaller discount factor is more realistic since the average time span between the two time periods is roughly between 20 and 30 years. 7 As Homburg and Richter (1993) point out, harmonization of public pension benefits is only efficient when jurisdictions (countries) are characterized by the same population growth rates which, absent migration, is assumed in the present paper. References Blanchard OJ, Fischer S (1989) Lectures on Macroeconomics. MIT Press, Cambridge, MA Borjas GJ (1995) The Economic Benefits from Immigration. Journal of Economic Perspectives 9(2):3 22 Cremer H, Pestieau P (1998) Social Insurance, Majority Voting and Labor Mobility. Journal of Public Economics 68(3):397 420 Friedberg RM, Hunt J (1995) The Impact of Immigrants on Host Country Wages, Employment and Growth. Journal of Economic Perspectives 9(2):23 44 Galor O (1986) Time Preference and International Labor Migration. Journal of Economic Theory 38(1):1 20 Galor O (1992) The Choice of Factor Mobility in a Dynamic World. Journal of Population Economics 5(2):135 144 Galor O, Ryder HE (1989) Existence, Uniqueness, and Stability of Equilibrium in an Overlapping-Generations Model with Productive Capital. Journal of Economic Theory 49(2):360 375 Galor O, Stark O (1991) The Impact of Differences in the Levels of Technology on International Labor Migration. Journal of Population Economics 4(1):1 12 Galor O, Stark O (1994) Migration, Human Capital Formation, and Long-Run Output. In: Siebert H (ed) Migration: A Challenge for Europe. J.C.B. Mohr, Tuebingen, 59 70

International labor migration and social security 551 Geide-Stevenson D (1998) Social Security Policy and International Labor and Capital Mobility. Review of International Economics 6(3):407 416 Homburg S (1991) Interest and Growth in an Economy with Land. Canadian Journal of Economics 24(2):450 459 Homburg, S, Richter WF (1993) Harmonizing Public Debt and Public Pension Schemes in the European Community. Journal of Economics, Supplement 7:51 63 Kemp MC, Kondo H (1989) An Analysis of International Migration: The Unilateral Case. In: Zimmermann KF (ed) Economic Theory of Optimal Population. Springer, Berlin Heidelberg New York, 153 165 Kondo H (1989) International Factor Mobility and Production Technology. Journal of Population Economics 2(4):281 299 Razin A, Sadka E (1999) Unskilled Migration: A Burden or a Boon for the Welfare State. NBER Working Paper Series No. 7013 Reichlin P, Rustichini A (1998) Diverging Patterns with Endogenous Labor Migration. Journal of Economic Dynamics and Control 22(5):703 728 Scholten U, Thum M (1996) Public Pensions and Immigration Policy in a Democracy. Public Choice 87(3 4):347 361 van Dalen H (1993) International Migration, Economic Policy and Human Capital Accumulation A Simulation Study. Economic Modelling 10(4):417 429 Zimmermann KF (1995) Tackling the European Unemployment Problem. Journal of Economic Perspectives 9(2):45 62