An n-Sector Migration Simulation ¨ A diploma thesis by Patrick Ohlinger under the supervision of Hardy Hanappi Vienna University of Technology, Austria May 22, 2008 Abstract Workers, considering costs of migration, tend to migrate to sectors where they expect higher wages. In revers, firms trying to increase profits, migrate to sectors with lower wages. The result of their com- bined movement will determine wages in each sector. This inductive behavior model with various strategies for wage expectations yields patterns of migration in an n-sectors scenario. Starting with a note on migration, this work analyses three influ- ential papers on migration1 and one on firm development2. It con- cludes with an agent based n-Sector Migration Simulation encapsu- lating ideas, concepts and approaches of stated papers. 1Migration, Unemployment and Development: A Two-Sector Analysis by Harris, To- daro; The Costs and Returns of Human Migration byLarryA.Sjaastad; Potential Migra- tion from Central and Eastern Europe into the EU-15 - An Update by Bru¨cker, Alavarez- Plata, Siliverstovs 2The Emergence of Firms in a Population of Agents: Local Increasing Returns, Unsta- ble Nash Equilibria, And Power Law Size Distributions by Robert Axtell 1 Contents 1 Migration 4 1.1 Migration in 60,000 BCE . . . . . . . . . . . . . . . . . . . . . 4 1.2 Motives for Migration . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Politics of Migration . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Emigration and Immigration . . . . . . . . . . . . . . . . . . . 6 2 A Two-Sector Migration Model 9 2.1 The Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Government Policies . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Wage Subsidy . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Government Policy: Migration Restriction . . . . . . . 14 2.2.3 A Combination of Policies . . . . . . . . . . . . . . . . 15 2.3 Adaptations for the n-Sector Migration Simulation . . . . . . 16 3 Firm formation and Agent-based Simulation 17 3.1 The Theory of the Firm . . . . . . . . . . . . . . . . . . . . . 17 3.2 A Variable Effort Model of Firm Formation . . . . . . . . . . 18 3.3 Agent based Simulation . . . . . . . . . . . . . . . . . . . . . 22 3.3.1 Computational Implementation . . . . . . . . . . . . . 23 3.3.2 Result of one representative Simulation . . . . . . . . . 26 3.3.3 Firm Size Distribution in the Aggregate . . . . . . . . 28 3.4 Adaptations for the n-Sector Migration Simulation . . . . . . 30 4 Costs and Returns of Migration 33 4.1 Migration: too much or too little . . . . . . . . . . . . . . . . 33 4.2 Costs of Migration . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2.1 Direct Costs of Migration . . . . . . . . . . . . . . . . 34 2 4.2.2 Indirect Costs of Migration . . . . . . . . . . . . . . . 35 4.3 Returns to Migration . . . . . . . . . . . . . . . . . . . . . . . 36 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5 Migration in Europe 37 5.1 Another Migration Model . . . . . . . . . . . . . . . . . . . . 38 5.2 Migration from CEEC 10 . . . . . . . . . . . . . . . . . . . . . 39 5.2.1 Migration from CEEC 10 to Germany . . . . . . . . . 40 5.2.2 Migration from CEEC 10 to EU 15 . . . . . . . . . . . 40 5.3 Simulation of Transitional Periods . . . . . . . . . . . . . . . . 41 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6 An n-Sector Migration Simulation 44 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.2.1 Workers following higher Wages . . . . . . . . . . . . . 44 6.2.2 Firms following lower Wages . . . . . . . . . . . . . . . 45 6.2.3 Wage Expectations . . . . . . . . . . . . . . . . . . . . 46 6.3 Results of the Simulation . . . . . . . . . . . . . . . . . . . . . 48 6.3.1 Wage Convergence . . . . . . . . . . . . . . . . . . . . 48 6.3.2 Social Networks and Information Constraints . . . . . . 49 6.3.3 Bounded Rationality: Strategies on Wage Expectation 51 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7 Appendix 56 7.1 Running the Simulation . . . . . . . . . . . . . . . . . . . . . 56 3 1 Migration 1.1 Migration in 60,000 BCE Human migrants started around sixty thousand years ago in Africa. Envi- ronmental changed vegetation and forced animals and the homo sapiens who feed on them to migrate. [Chan07] Figure 1: Out of Africa by the Genographic Project 2006 A global DNA survey by Genebase Systems tracked our ancestors and their early paths of migration. Starting in Africa our ancestors first moved to Central and Eastern Asia. From there over tausands of years the human species spread to Europe, Sibiria, North and than South America. Within fifty thausand years all five continents were occupied by humans. Sixtythousand years, i.e. a snapshot in evolutionary terms, hardly changed our DNA, evolution slightly adopted skin color and body size to account for differences in temperature and sun exposer in various regions. But un- derneath we are all distant relatives. Vasudhaiva kutumbakam, ”The whole world is a family.” This aphorism from the Indian Panchatantra is worth keeping in mind while tinkering with migration. The recent International Migration Outlook [OECD07] placed the number of foreign born, i.e. immigrants, at 200m world wide (that’s legal plus an ”educated guess” on illegal immigration). That sounds a lot, but it is really only 3% of the world population. The reasons for people to migrate hardly changed since our great great an- 4 cestors left Africa to follow their supply of food. Resources and security still dominate migration today. 1.2 Motives for Migration Formally we can identify three key motives for migration: First, refugees and asylum seekers, defined as those escaping prosecution but often including anybody forced to flee, for example from a war. Second, oftenunderestimated, familyreunification. Oneexamplecanbeseen in the data of US legal migration in 2005: Half of all legal US immigrants claimed to have relatives in the US. And third and most prominently those who seek an (economically) better life. As long as moving from a poor country to a rich one will increase income fivefold [Survey on Migration]. This motivator will persist. Thesearchforopportunitiesandprosperityishandsdownthestrongestforce of migration. This thesis will focus on this economic motivator of migration. It is generally the case (and data [OECD07] proves it) that young adults are most likely to migrate. They have a higher expected lifetime income differential than their older peers. The boundary with their home country is not yet as strong. Plus, they may be able to offer their children better opportunities as well. 1.3 Politics of Migration Thru-out history migration resulted in wars and fights over territorial domi- nation. More recently opinions against migration (particularly immigration) are driven by populist politicians trying to identify scapegoats for economic miseries. While borders my fall inside the European Union, borders are rising on the outside. The political force almost universally, it seems, is to close borders and stop immigration. Ironically, those countries who would benefit most from young working im- migrants, i.e. aging countries like Japan and most of central Europe, are those who oppose it the most. Not everyone is opposed, but enough to drive 5 politics in the direction of more selective immigration laws or in extreme cases outright opposal of everything foreign. Many politicians who inveighed against immigration now get closer to polit- ical power. In France Jean Marie Le Pen in 2002 run an anti-immigration campaign and reached the run-off stage of the presidential election. Running an election campaign based on comments against immigrants, Jo¨rg Haider’s ¨ far-right party FPO joined a coalition government in Austria in 2000. Both events steered controversy in and beyond Europe. Not so today, when hostility to immigration is spreading all over Europe. Britain’s Gordon Brown asks for ”British jobs for British workers”, Nicolas Sarkozy follows Le Pen in his arguments to save jobs for the french. Across the Atlantic, the 2008 presidential election candidates talk about ever increasing border con- trols and cracking down on illegal immigration. No debate without clapping down on migrants stealing jobs from native Americans. What is it that drives natives to oppose immigration? First it helps to group natives by income. Those well-off seem in general to benefit more from cheap labor provided by immigrants, while the poor feel the wage pres- sure particularly for low skill employment. A second worry is that migrants will put a strain on public services and the tax system. Locals complain if clinics and schools are overloaded. Although migrants often make a large contribution to the public purse. When a foreign worker arrives, dominantly as a young adult, fully educated and in good health, he makes few demands on schools or clinics. If allowed (i.e. he is a legal immigrant) he will pay taxes on his income. Even illegal immigrants will contribute by paying value added tax on their consumption. Immigrants as a whole, in the long term and counting the contributions of their children when they grow up and get jobs, are not a drain on public services. For rich countries with aging workforces in particular, gains from importingtheyoung,theenergeticandthosewillingtotakeriskscomfortably outweigh the cost. 1.4 Emigration and Immigration Migration always has two sides. To immigrate in one country one first has to emigrate from another. Ruffle 10% of the United Kingdom’s population is foreign born. On the other hand, about 10% of UK born folks currently 6 Figure 2: Net World Migration Rate: Immigration (+), Emigration (-) based on CIA factbook data, April 2006 life outside the UK. On average, of course, the number of immigration equals the number of emigrants world wide. However, when a fast majority is leaving one place to migrate to another. Problems occur. On both sides (although the source country usually already has problems to cause emigration in the first place). Benefits of Immigration • Jobs: Frequentlyeconomicimmigrantsarehighlymotivated,entrepreneurial, go getters (after all, they made the jump). About a quarter of Silicon Valley’s IT companies are founded by Chinese or Indian immigrants. Among them such as Sun Microsystems, Intel and Google. Bill Gates calculates, and respectable economists agree, that every foreigner who is given an H1B visa for America creates jobs for five regular Ameri- cans [Econ08]. • Talent: 40% of American PhDs in science and engineering go to immi- grants. 70 of the 300 Americans who have won Nobel prizes since 1901 were immigrants [Econ08]. • Additonal tax income from legally employed immigrants. • GDP growth, albeit not necessarily on a per capita bases. 7 Drawbacks of Immigration • Lower wages for some native workers (less so in the long term). Benefits of Emigration • Higher wages for staying natives (less so in the long term). • Remittance payments to poor or developing countries ($301.4bn world- wide in 2006 [IFAD06]). • Back-flow of knowledge and business opportunities [BoST05]. Drawbacks of Emigration for source country Brain drain, the emi- gration of trained and talented individuals. Sometimes this ”drain” can be offset by knowledge backflow. As South African President Thabo Mbeki asked for in his 1998 ’African Renaissance’ speech: ”In our world in which the generation of new knowledge and its application to change the human condition is the engine which moves human society further away from barbarism, do we not have need to recall Africa’s hundreds of thousands of intellectuals back from their places of emigration in Western Europe and North America, to rejoin those who remain still within our shores! I dream of the day when these, the African mathematicians and computer specialists in Washington and New York, the African physicists, engineers, doctors, business managers and economists, will return from London and Manchester and Paris and Brussels to add to the African pool of brain power, to enquire into and find solutions to Africa’s problems and challenges, to open the African door to the world of knowledge, to elevate Africa’s place within the universe of research the information of new knowledge, education and information.” 8 2 A Two-Sector Migration Model Harris and Todaro[HaTo70] found the conventional economic models with their singular dependence on the achievement of a full employment equilib- rium through appropriate wage and price adjustments insufficient to explain migration to highly unemployed urban areas. Their work is focused on tropical Africa rural-urban migration but can be seen more abstract as a poor to rich migration, with the added twist of unemployment in the urban area. Clearly what is driving migration are not wage differentials per se, but more specifically the expected wage differentials between rural and urban employ- ment. I was drawn to this work while looking into migration patterns in the Eu- ropean Union, during and after the inclusion of 10 new countries of mostly lower wage eastern European countries. There like in Harris and Todaro, unemployment in the host countries particular Germany played a role. The foundation of the model is that migration continues from rural to urban areas for as long as the expected wage in urban areas We is higher than u in rural areas. Or as Harris and Todaro put it: ”prospective rural migrants behave as maximizers of expected utility.” As an added twist, urban wage has a lower sealing set by the government i.e. a minimum wage (a market intervention that causes unemployment). After showing the model the authors analyse potential government policy to reduce unemployment, while keeping the minimum wage set. The eco- nomically more efficient solution of price flexibility is rejected as political impossible. The effects of partial wage subsidies (for example via direct government employment) and restrictions to free migration are analytically shown with their model. Nether wage subsidies nor restrictions on migration can yield the desired result. But interestingly a combination of both measures can, under certain conditions, lead to the desired result. 2.1 The Basic Model The basic model used by Harris and Todaro is a two-sector internal trade model with unemployment. The two sectors are the permanent urban and 9 the rural. The urban sector produces manufactured goods, part of which is exported to the rural sector in exchange for agricultural goods. The crucial assumption made by Harris and Todaro is that rural-urban mi- gration will continue so long as the expected urban real income We exceeds u real agricultural product W . A The following formulation of the model is an excerpt from Harris and To- daro’s work. Agricultural Production Function: X = q(N ,L¯,K¯ ),q(cid:48) > 0,q(cid:48)(cid:48) < 0 (1) A A A where, X is output of the agricultural good, A N is the rural labor used to produce this output, A ¯ L is the fixed availability of land, ¯ K is the fixed capital stock, A q(cid:48) is the derivative of q with respect of N , its only variable factor. A Manufacturing Production Function: X = f(N ,K¯ ),f(cid:48) > 0,f(cid:48)(cid:48) < 0 (2) M M M where, X is output of the manufactured good, M N is the total labor (urban and rural migrant) required to produce this M output, ¯ K is the fixed capital stock, and M f(cid:48) is the derivative of f with respect of N , its only variable factor. M 10