Migrations and FDI: what do we learn from an agent-based model?

Transcription

1 Migrations and FDI: what do we learn from an agent-based model? Léa Marchal December 20, 2013 PRELIMINARY VERSION Abstract Recently a new strand of the literature considers the stoc of FDI as an additional determinant of migrations. As some papers find either a positive or a negative relation between migrations and FDI, this paper aims to test under which conditions there is a substitution or a complementarity effect between the two factors. To this end, we build an agent-based model, which taes into account the endogenous lin between migrations and FDI. This new methodology allows to analyze complex adaptive systems, with a temporal scale, a spatial dimension and a large number of heterogeneous agents interacting with each others. Our model is ergodic and able to reproduce standard stylized facts. We observe FDI flows from the developed country to the developing country and migrations in the reverse direction (and return migrations in the long run. The model converges toward a quasi-stationary statistical equilibrium at the aggregated level. Preforming several tests, we find that FDI substitute migrations whereas migrations complement FDI in this process of remunerations equalization. In quantitative terms, migrations complement FDI, conversely we find no significant effect of FDI on migration. I am grateful to Hubert Jayet and Claire Naiditch for their helpful comments. All remaining errors are my responsibility. EQUIPPE, University of Lille I, Faculty of Economics and Social Sciences. Bât SH2, Cité Scientifique, Villeneuve d Ascq Cedex, France. lea.marchal@ed.univ-lille1.fr. 1

2 1 Introduction Foreign direct investments (FDI from developed to developing economies and migrations in the reverse direction, largely increased over the past decades. Between 1990 and 2010, the stoc of outward FDI of OECD 1 countries increased from 468, to 3, 858, millions of US dollars, a raise of more than 724%. The stoc of foreign individuals in OECD countries increased from 16, to 58, thousands of people, a raise of more than 252%. A new strand of the literature focuses on the lin between these two growing flows. Migrations are now considered as a determinant of FDI; FDI as a determinant of migrations. Most studies explaining the dynamic of migrations, whether empirical or theoretical attempts, have focused on determinants such as the wage differential, the distance, the share of a common history, a common culture or a common border and policy implementations. For instance, see Mayda (2010 for her empirical study on the determinants of migration inflows into OECD countries between 1980 and Recently, some papers consider the stoc of FDI as an additional determinant of migrations. In the short run, FDI generate externalities which can strengthen migrations. FDI allow the recipient country to developed: the average wage raises and people have access to education and to better jobs. Thus, it is easier for individuals to migrate as they can pay for the migration cost. In addition, FDI can vehicle cultural and ideological information between countries, which reduces ris and lessens migration costs. At a certain point, FDI allow the recipient country to develop enough and reduce incentives of migrations. FDI contribute to job creation which improves the labor maret condition, reduces wage differentials among countries and in fine lessens migrations. Some empirical studies confirm these mechanisms. Over the period , Sanderson and Kentor (2008 show that the stoc of FDI of a developing country positively impacts its emigration rate. D Agosto et al. (2006 study the lin between FDI and migrations over the period between OECD countries and developing countries. They find that a complementarity effect prevails through the development of the labour maret. Aroca and Maloney (2005 notice that FDI from the USA to Mexico in the framewor of the NAFTA 2, allow for job creations in the FDI recipient country and thus lessen migrations. However, if we were to consider FDI as a determinant of migrations, one should 1 Organization for Economic Co-operation and Development 2 North American Free Trade Agreement 2

3 pay attention to the reflection lin as migrations positively influence FDI. Migrants networs vehicle information on foreign trade and investment opportunities between their origin and host countries, that are scarce and usually difficult to gather for companies. Diaspora soften the informational constraint faced by firms willing to invest abroad (Rauch, 2001; Dolman, 2008; Docquier and Lodigiani, De Simone and Manchin (2012 empirically show a positive effect between outward migrations and inward FDI, over the period for eastern and western European countries. See El Yaman et al. (2007 and Kugler and Rapoport (2005, 2007 for similar empirical studies. Kugler and Rapoport (2011 using the theoretical framewor of heterogeneous firms proposed by Helpman et al. (2004, 2008, highlight that migrants reduce fixed costs supported by firms setting up exports and FDI. Nonetheless, the two sides of the relation between migrations and FDI has been discussed in few papers. In particular, see Foad (2008; Javorci et al. (2011 for their empirical papers. See Federici and Giannetti (2010 for their theoretical model 3 in which they show that migrations strengthen FDI, through an information revealing effect. As some empirical studies find either a positive or a negative relation between migrations and FDI, we want to test under which conditions there is a substitution or a complementarity effect 4. To the best of our nowledge, this is the first attempt using an agent-based model (ABM. ABM allow to analyze complex adaptive systems i.e. systems with a spatial dimension, a temporal scale and a large number of heterogeneous agents interacting with each others. This rather new methodology presents efficient features to encompass the endogenous relation between FDI and migrations. It consists in defining micro behaviors of economic agents, which once defined result in migration decisions that are not constrained. At micro level, whenever an agent realizes an action, he impacts the context which is common to all agents. Any change of the context impacts in return the rest of the agents. Once aggregated, the sum of the agents actions results in emergent macro phenomena, such as migration and FDI flows. In addition, an ABM is an efficient tool to consider imperfect information. Agents have different geographic positions, they do not necessar- 3 Their ey assumptions are that migrations are temporary and that the capital stoc in southern countries is formed by FDI inflows from migrants hosting countries (northern countries. 4 In this paper, we use the definitions proposed by Wong (2006. He defines two factors as substitutes (1 when only one is necessary to allow for the equalization of remunerations, (2 or in the quantitative sens, when the exogenous increase of one factor implies the drop of the other factor. 3

4 ily have access to other agents, which restricts the transmission of information (Tesfatsion, 2003; Tesfatsion and Judd, Since the segregation model of Schelling (1971, agent-based computational economics has been used in a lot of economic fields such as maret optimization research, game theory applications and finance, see for instance Epstein and Axtell (1996; Duffy (2001 and Epstein (2001. Although this method seems adequate to model migrations, few papers use it. Klabunde (2013 measures the impact of networs on circular migrations. She proposes an ABM with an endogenous networ and shows that expected earnings, networ to other migrants and quality of relationships are three important determinants of the decisions to migrate and to return. Her model is calibrated for the case of Mexican migrants in the US from 1955 to Filho et al. (2011 propose an ABM to assess the importance of networing and communication transmission in the process of migration. Their model is calibrated for Brazilian internal migrations between two very similar regions, with the demographic census of Their results corroborate classical analytical models of migrations, based on wage differentials and job opportunities. Kniveton et al. (2011 propose an ABM built upon the theory of planned behavior and show that climate change strengthens regional and international migration flows, by influencing political, social and economical drivers of migrations. In the same vein, we propose an ABM built with Repast Simphony 2.1 for Java. We consider FDI as a determinant of migrations and migrations as a determinant of FDI. The following section introduces the model assumptions. Section 3 presents the calibration and the validation of the model. Section 4 presents the results. Section 5 details the robustness checs and section 6 concludes. 2 Model assumptions We feature a two-countries model. Countries are formalized by a 2D continuous square divided in two equal parts, one for each country ( and. The sides of the square are considered as impervious walls. We place a grid on this space, so that our environment is discrete. Both countries are endowed with capital and labor, respectively approximated by a given number of firms (F and individuals (L. We do not distinguish between silled and unsilled individuals. These agents are randomly placed on the grid at the start of the simulation. The world population is constant. Firms can realize FDI i.e. set up subsidiary companies abroad, thus the 4

5 number of firms can increase over time. The characteristics and behaviors of individuals and firms are described in the following subsections. Notice that the behavioral equations are not derived from an optimization process. We consider an environment under imperfect information thus these are intuitive i.e. heuristic rules. 2.1 Production function and factors remunerations at macro level At each period of time t, the technology of country is given by the following Cobb-Douglas production function: yt = A ( Ft α ( L 1 α t t, t = 1,..., T (1 with α the elasticity of substitution (0 < α < 1 and A the total factors productivity, a constant greater than unity. We assume constant returns to scale so that factors are remunerated to their marginal productivities. The average wage and the capital remuneration are given by: yt L t ( F = wt α = A (1 α t L t yt Ft ( L = ρ 1 α t = Aα t Ft We consider heterogeneous agents, and thus heterogeneous individuals and firms. Thus, we assume that the total factors productivity is an average of the firms and individuals productivities: A = A L + A F L t + F t = 1 2 L t i=1 a i L + t F t j=1 a j F t with A L the total labor productivity and A F the total firms productivity, a i the productivity of an individual i and a j the productivity of a firm j. 2.2 Individuals behaviors Wage and expected wage in the origin country We consider heterogeneous individuals. Thus, every individual i living in country gets a wage such that: 5

6 ( F wi, α t = a i (1 α t L i, i = 1,..., n ; t, t = 1,..., T t with a i the productivity of the individual. We assume the wage of the individual follows a Log-Normal distribution (Pinovsiy and Sala-i Martin, 2009, such that: w i, t ln N [ µ t, ( ξ 2 ] i, i = 1,..., n ; t, t = 1,..., T with a given standard deviation (ξ and a mean (µ t such that: The average wage is given by: µ t = log ( wt 1 ( ξ 2 2 w t = L t i=1 w i, t L t and should fluctuate around w t, the wage defined at macro level in section 2.1. The future wage in t + 1 of an individual i living in country is unnown at time t. His expected wage is an extrapolative anticipation of the future average wage such that: exp ( wi, ( ( t+1 = exp w i, t+1 = w t + b i w t w t 1 with b i a constant between zero and unity given randomly at the start of the simulation, reflecting the value the individual concedes to past information. Notice that the individual considers the mean wage of his country which is public information to calculate his expected wage, instead of considering his own wage as he nows he can get a lower or a higher wage in the next period Networ and expected wage abroad At each period, each individual randomly moves inside his country i.e. within his Moore neighborhood, at no cost. His Moore neighborhood is formed by the eight (twenty four, forty eight, etc. surrounding cells around his initial cell 5. Notice that an individual located at the border, can have a part of his neighborhood abroad. In this case, he is not allowed to move to this part of his neighborhood. This limited mobility restrains the individual in his geographic access to other individuals and therefore to information. 5 At the start of the simulation the individual is randomly placed in his country. 6

7 Each individual nourishes social relationships with a limited number of individuals. At each period, he creates lins with other individuals located close enough to him i.e. in an area of a given radius (Ω. The weight of this lin represents the quality of their relationship. Over time, if two individuals lined move too far away from each other, their relationship deteriorates until it vanishes. The networ of an individual i (N i, t is formed by all individuals with whom he is directly or indirectly lined, at time t. We tae into account two degrees of relationships (the relationships of the individual s relationships. The members of a networ exchange information on their wages. The connectivity pattern of the networ is local individuals need proximity to meet and random individuals move randomly inside their neighborhood to create new relationships. As there is no public information on the foreign wage, the individual interrogates his networ to collect information on the foreign wage (country. Among his networ, he interrogates all those living abroad (M i, t on their current wage, such that M i, t N i, t. With this information, he calculates an approximated mean wage abroad such that: w i t = Mi, t n=1 w n, t Mi, t n=1 n By interrogating his networ, the individual considers he has got a representative sample of the wage abroad. The future wage abroad is unnown, such that he calculates an expected wage, which is an extrapolative anticipation of the future average wage abroad based on the information gathered from the networ of the individual over time, such that: exp (w i, t Migration = exp ( w i, t+1 ( = w i, t + b i w i, t w i, t 1 Following the micro economic neo-classical theory of the migration decision, an individual is willing to migrate from his neighborhood in country to a random position in the foreign country, only if his expected gain is higher abroad than in his origin country (Harris and Todaro, The individual can migrate at the end of the period t if his expected gain is positive. In addition, he should be able to afford the migration cost c i, t. wi, t c i, t 0 (2 exp (w i, t+1 exp ( wi, t+1 > 0 (3 7

8 The migration cost is given by: c i, t = ω ( w t + w t 2 = ω w t with ω an exogenous coefficient greater than unity and w t the world average wage at time t, such that the cost is indexed on the world average wage. When an individual i whose origin country is, meets the conditions 2 and 3, the probability he migrates from to, is given by: P i, t [ mig w i, t ci, t ; exp ( β (1 h i, t + γ Si, t S t ( exp w i, t+1 ] > 0 = w i, t+1 ( exp (w i, t+1 exp w i, t+1 + λ + δ (1 r i, t (4 exp (wi, t+1 This probability depends on four determinants, each of them weighted (β, γ, λ, δ such that the sum of the weighting coefficients is equal to unity. 1. An individual has a preference for his origin country (h i, t, which is a constant between zero and unity given randomly at the beginning of the simulation. When an individual has a low preference for his origin country, he is more prone to live abroad. His preference for the foreign country is then given by (1 h i, t. Over time, this home preference index changes. It decreases if the agent is surrounded by foreign firms or/and foreign individuals in his country of origin such that: h i, t = h i, t 1 h h i, t 1 Foreigners and subsidiary companies bring information on their origin country s culture (Sanderson and Kentor, Consequently, individuals are less scared by the foreign country which becomes more familiar. 2. In his networ, an individual may now people from his country who have already migrated (S i, t with S i, t M i, t N i, t, who can ease his arrival and establishment abroad. Over the population from his origin living abroad (S t the more persons he nows, the more he is prone to migrate 6 such that: 6 His relatives abroad minimize the ris and spread information which eases his access to formation, employment, housing, etc. Massey and Espana (1987; Beine et al. (2011 highlight this mechanism through the reduction of the migration cost. S i, t S t 8

9 3. An individual considers the magnitude of the wage differential between his country and the foreign country. He compares the gap between his expected wage abroad and his expected wage in his country such that: exp ( w i, t+1 exp ( wi, t+1 exp ( w i, t+1 4. When an individual migrates he nows his expected wage might differ from the wage he will actually gets i.e. he nows his prevision in terms of cost and revenue, may not realize. His ris aversion (r i is between zero and unity and given randomly at the beginning of the simulation. It influences his decision to migrate, such that: (1 r i, t His aversion decreases (increases if he gets a better (lower wage at the period following his migration. For instance, after a migration from to in t, the ris aversion of an individual increases (decreases of r if the individual gets a lower (better wage than what he anticipated to earn in his origin country such that: r i, t 1 + r r i, t 1 r i, t = r i, t 1 r r i, t 1 if wi, t < exp ( wi, t 1 if wi, t exp ( wi, t 1 Thus, the individual auto-adapts his strategy of migration according to his successes and failures, becoming more or less ris-averse (Epstein and Axtell, According to his probability to migrate (P i, t and probability of remaining in situs (1 P i, t, the individual draws from a Bernoulli distribution. The individual migrates to the foreign country only if he draws 1 from the distribution. This method allows us to introduce individuals heterogeneity or limited rationality of the agents, as two individuals with the same probability to migrate would not necessarily tae the same decision Return migration A similar mechanism is at play for the return migration. Although, the expected wage abroad of the individual is different when he already lives abroad. We consider that migrants have perfect information on their origin country. So, the 9

10 expected wage in country of an individual i whose origin country is, is based on the observed average wage in the origin country: ( ( exp (w i, t+1 = exp w i, t+1 = w t + b i w t w t 1 An individual is willing to return if his expected gain is null or positive i.e. if his expected wage in the foreign country exp ( wi, t+1 is equal or higher than ( his expected wage in his origin country exp wi, t+1 and if he is able to afford the migration cost. wi, t c i, t 0 (5 exp (w i, t+1 exp ( wi, t+1 0 (6 The cost of migration is identical. The probability to return depends on the same four determinants. The probability a migrant i from returns is such that: P i, t [return wi, t c i, t ; exp (w = βh i, t + γ S i, t S t exp + λ ( w i, t+1 i, t+1 exp ( wi, ] t+1 0 exp ( wi, t+1 + δ (1 r i, t (7 exp ( w i, t+1 Notice that the home preference index is now given by h i, t so that the migrant is more prone to return when his preference for his origin country is high. The individual draws from a Bernoulli distribution, according to his probability to migrate (P i, t and probability of remaining in situs (1 P i, t. The individual returns only if he draws 1 from the distribution. 2.3 Firms behaviors Capital remuneration and expected capital remuneration determination We consider heterogeneous firms. Thus, every firm j living in country gets a remuneration of its capital such that: ( L ρ 1 α j, t = a j α t Ft j, j = 1,..., n ; t, t = 1,..., T with a j the productivity of the firm. We assume the capital remuneration of the firm follows a Log-Normal distribution such that: [ ρ j, t ln N σ t, ( ς ] 2 j, j = 1,..., n ; t, t = 1,..., T 10

11 with a given standard deviation (ς and a mean (σ t such that: σ t = log ( ρ 1 ( t ς 2 2 The average capital remuneration is given by: ρ t = F t j=1 w j, t F t and should fluctuate around the capital remuneration ρ t, defined at macro level in section 2.1. At time t, the future capital remuneration of a firm is unnown ( ρ j, t+1. The firm has perfect information on its country, thus it nows it could get a higher or a lower remuneration in the next period. It realizes an extrapolative anticipation of the future average remuneration such that: exp ( ρ j, t+1 = exp ( ρ j, t+1 = ρ t + b i ( ρ t ρ t 1 with b j a constant between zero and unity given randomly at the start of the simulation, the value the firm j concedes to past information Expected profitability of a foreign investment The firm has perfect information on the capital remuneration in the foreign country. Thus, the expected remuneration of a foreign investment is an extrapolative anticipation of the future average capital remuneration abroad such that: ( exp (ρ j, t+1 = exp ( ρ j, t+1 = ρ t + b i ρ t ρ t Foreign investment The objective of a firm is to realize sustainable investments abroad. Only the most productive firms realize FDI (Helpman, Among all firms introduced at the start of the simulation in both countries, we consider a group of firms (θ which is the x percent of firms with the highest remunerations of their capital. Thus to realize an FDI, a firm should be part of the lucy few i.e. this highly performing group. Its remuneration should( be at least equal to the remuneration of the least productive firm of the group ρ θ t, such that: ρ j, t ρ θ t (8 At time t, if a firm j located in country is productive enough to set up a subsidiary company abroad in t + 1, it can realize an investment if it is able to 11

12 pay for the cost of establishment abroad and if its expected returns on capital in its country are lower than abroad: The cost of investing abroad is given by: ( ρ t + ρ t f j, t = z 2 ρ j, t f j, t 0 (9 exp (ρ j, t+1 exp ( ρ j, t+1 > 0 (10 = z ρ t with z an exogenous coefficient greater than unity and ρ t the world average returns to capital, such that the cost is indexed on the world average capital remuneration. When the firms j located in country meets the necessary conditions 8, 9 and 10, the probability it realizes an FDI in country is given by: P j, t [F DI ρ j, t ρ θ t ; ρ j, t f j, t 0; exp (ρ E = η ( ρ j, t+1 j, t+1 E ( ρ j, t+1 + ν L t E ( ρ j, t+1 L t exp ( ρ ] j, t+1 > 0 + ι F j, t Ft + τ w t w t w t (11 This probability depends on four causal factors, each of them weighted (η, ν, ι, τ such that the sum of the weighting coefficients is equal to unity. 1. The firm considers the magnitude of the capital remuneration differential between its country and the potential destination of investment, such that: ( E ρ j, t+1 E ( ρ j, t+1 E ( ρ j, t+1 2. Migrants bring information on their origin culture which can ease the establishment of the firm abroad (Docquier and Lodigiani, 2010; Kugler and Rapoport, Thus, the firm considers the presence of foreign indi- ( viduals L t compared to the total population of its country ( L t. All firms have identical information on the foreign presence, but this information changes over time with migrations and returns. 3. If a firm has already realized an FDI abroad, it is more prone to repeat it. The past experiences of investment abroad bring more information on the practices of the foreign country. In addition, when a firm owns 12

13 an important maret share abroad, its investments are facilitated. Thus, we consider the number of FDI already realized by the firm j abroad (F j, t over the number of firms in the destination country (Ft. This information is different for each firm. Kinoshita and Mody (2001 notice that investment decisions are based on public information remuneration differential, competition or maret size and private held information past experience of investment or nowledge of the foreign country. 4. As an estimation of its production costs, the firm considers the magnitude of the wage differential between its country and the potential destination of investment: w t w t w t According to its probability to invest abroad (P j, t and probability to do nothing (1 P j, t, the firms draws from a Bernoulli distribution. It realizes an FDI to a random position in the other country only if it draws 1 from the distribution. This condition allows us to introduce firms heterogeneity. For the sae of simplicity, we do not consider local investment (Federici and Giannetti, At the end of each period, the firm s capital that has not been invested abroad is lost. Also, a subsidiary company cannot realize FDI. 2.4 Model operating The algorithms 1 and 2 summarize the schedule of actions replicated over time by every type of agent. Notice that agents are autonomous, in the sens they are not governed by any central authority. Algorithm 1 Individual schedule Moves inside his Moore neighborhood (at no cost. Creates relationships with individuals close enough to him. Gets a wage (from the wage distribution of his country of residence. Calculates his expected wage abroad, thans to information provided by his relationships. Calculates his probability to migrate. Taes a decision: migrates to the other country or remains in situs. 13

14 Algorithm 2 Firm schedule Gets a remuneration of its capital (from the capital remuneration distribution of its country. Calculates its expected remuneration abroad. Calculates its probability to invest abroad. Taes a decision: realizes an FDI or does nothing. In our model, firms and individuals influence each others, through their common environment. The following figure (1 illustrates this mechanism. A country hosts firms and individuals. Individuals can decide to migrate, firms to invest abroad. These actions impact their origin and destination countries. For instance when an individual migrates, he decreases the total population of his origin country and increases the population of his destination country. Similarly, when a firm realizes an FDI, it increases the number of firms in the destination country. These changes impact the agents remunerations and their preferences, which influences their next decisions. In a model with endogenous relationships between agents, the Who acts first? question matters. Allowing one type of agents to act before another can sew the result of the simulation. To solve this issue, we have constructed our model such that individuals and firms act (migrate and invest at the same time. Figure 1: Model operating diagram 14

15 3 Model calibration In this section, we present the value of the parameters we tae for the initial state of our model simulation. Notice that our parameters do not have concrete meanings. We cannot calibrate our model with a specific database, as it has been built for a qualitative calibration (to observe patterns of migrations and FDI rather than a quantitative calibration. Our space is 150 cells large and 150 cells high. Each country is formed by half of this space over which its population and firms are placed. We simulate a developed country ( and a developing country (. We assume the ratio of capital per capita to be larger in the developed region than in the developing region. Thus at the start of the simulation, the developed country as a small population (450 individuals and a large share of capital (225 firms compared to the developing country (1080 individuals and 90 firms. Notice that the population density matters 7. The average capital remuneration is higher in the developing region, whereas the average wage is higher in the developed region. The developing country has an average wage six times lower than the developed country. This calibration approximatively relates the wage differential between the High income and the Low & Middle income countries groups in 2010 (World Development Indicators database of the World Ban, Second, we fix the behavioral parameters of firms and individuals. The set of parameters is presented in Appendix 1. For the chosen parameters, we calculate means and standard deviations of our macro variables (the average wage and the average capital remuneration for 100 runs of the model: 2nd period Variables Obs Mean Std. Dev. Min Max ρ ρ w w The chosen set of parameters allows the model to tend toward a statistical equilibrium (we have a quasi-stationary equilibrium. The transition period toward 7 On the one hand, a too small density does not allow individuals to communicate and thus to migrate. It does not result in an ergodic model. On the other hand, a too large density gives too precise information to the individuals, such that they migrates and returns a lot, which reduces their preference for their origin country. In the long run, they do not differentiate between their country of origin and the foreign country. 15

16 350th period Variables Obs Mean Std. Dev. Min Max ρ ρ w w th period Variables Obs Mean Std. Dev. Min Max ρ ρ w w the statistical equilibrium also called transients, is about 350 periods, after which the wage and the capital remuneration converge. Hundred simulations have been performed which gives similar trajectories and similar equilibrium values of the average wage and capital remuneration. Over 100 runs of the model, the cross-sectional variance of variables is small. Thus, the model can be qualified of self-organized i.e. ergodic. In other words, the model is stable with respect to seeds 8 i.e. the seed does not influence the result of the model. 4 Results First, the model allows to reproduce standard theoretical results nown in the migration theory, second it permits to test the behavior of the model to macro shocs. 4.1 Reproduction of standard theoretical results To assess the consistency of our model, we want to reproduce two standard stylized facts. We now that factors flow where their remunerations is the highest. FDI negatively affect the average capital remuneration and positively affect the job maret of the receiving country. Also migrations positively affect the average wage of the sending country and negatively affect the average wage of the recipient country. First, we want to observe FDI flows from the developed 8 Seed values are integers taen to calculate pseudo-random numbers. 16

17 country to the developing country and migrations in the reverse direction 9. Second, we want to observe an equalization of remunerations in the long run. The model shows the expected trends. After approximatively 350 periods, the average capital remuneration tends to equalize between the two countries and then stay stable over time. FDI tae place from the developed country to the developing country, where the capital remuneration is the highest. The two following figures shows the variation of the capital remunerations and the FDI stocs (figures 2 and 3 for one particular simulation. Migrations tae place from the developing to the developed country. The average wage first equalizes around the 350th period. Then, the wage progressively increases over time, which is due to the development of the recipient country of FDI (figure 4. In the short run, migrations increase up to reach the point when wages equalize between countries. In the long run, migrations slow down and returns tae place (figure 5. This result corroborates the idea of Federici and Giannetti (2010, according to which migrations are only temporary. Also, we can assume that once a certain amount of capital is reached in the developing country, migrations slow down and returns tae place, as FDI participate to the development of the FDI recipient country. Notice that we observe noise on the remunerations graphics (figures 2 and 4. Fluctuations can be interpreted as exploratory behaviors or wrong expectations of agents. This is due to the determination of probabilistic behaviors in our model. 9 See for instance De Simone and Manchin (2012 for stylized facts over the period for eastern and western European countries. 17

18 Figure 2: Evolution of the average capital remuneration for a simulation of 1000 periods Figure 3: Stoc of foreign firms for a simulation of 1000 periods 18

19 Figure 4: Average wage evolution for a simulation of 1000 periods Figure 5: Migrants stoc for a simulation of 1000 periods In addition, migrations occur faster when we increase the level of communication between individuals (size of the Moore neighborhood, minimal distance to create a relationship and relationship depreciation over time. In this model, the formation of endogenous networs allows the spread of information on wages of the foreign country. When the communication is high the networs are bigger, information is more precise and migrations occur faster. As a result, the equalization of remunerations happens faster, although the evolution is the same in the long run. This result has been emphasized by Filho et al. (2011. Thus spatial interactions are important. 19

20 4.2 Macro economic shocs Substitution and complementarity in the process of remunerations equalization Restrictions on foreign investments. In order to test if migrations can substitute FDI in the process of remuneration equalization, we run the model without FDI by prohibiting firms to invest abroad (x = 0, which is similar to tae a prohibitive FDI cost. We observe that although individuals are allowed to migrate, very few of them actually move. Most of them are not able to afford the migration cost and are stuc in a poverty trap. Remunerations do not equalize. To ensure this effect does not result from a too high migration cost, we reproduce the test for a cost of migration equal to zero (ω = 0. In this case, there are still not enough individuals that migrate to equalize wages and capital remunerations between countries. They may stay in the developing country because of their preference for their origin country, their ris aversion and the lac of information on the foreign country. In both cases, the few individuals who migrate do not return, as FDI do not allow for the development of their origin country. Thus, migrations only complement FDI in the process of equalization of remunerations. If we reestablish the possibility for firms to invest abroad, the economy converges again toward an equilibrium (figures 6 and 7. Figure 6: Evolution of the average capital remuneration for a simulation of 1000 periods (FDI authorized at the 500th period 20

21 Figure 7: Average wage evolution for a simulation of 1000 periods (FDI authorized at the 500th period Restrictions on labour mobility. In order to now if FDI can replace migrations in the process of factor price equalization, we test our model with a prohibitive migration cost such that no migration occurs (ω = 100. We observe an equalization of remunerations. Although this process taes more time compared to the a situation with authorized migrations because it only taes place through capital transfers. In the long run, equilibrium values of the wage and capital remuneration are similar to a situation with migrations. Thus, FDI substitute migrations in the price equalization process Substitution and complementarity in quantitative terms Sensitivity of foreign investments to migration cost variations. In order to test the quantitative relation between FDI and migrations, we run the model for different migration costs, ω = 0; 0.5; 1; 1.5; 2. On the one hand, when the cost of migration increases, less migrations occur as less individuals can pay for their migration. In parallel, less foreign investments occur. This results corroborates the empirical study of Neumayer (2011, who shows that visa restrictions have a negative effect on trade and FDI. On the other hand, when the cost of migration drops, more migrations tae place as more individuals can afford their migration cost. In parallel, we observe that foreign investments are strengthened. Thus in the quantitative sens, migrations complement foreign investments. 21

22 Sensitivity of migrations to investment cost variations. We run the model for different costs of investment abroad (z = 0; 0.5; 1; 1.5; 2 to test the sensitivity of migrations to FDI. Surprisingly, we find that foreign investments do not have any significant effect on migrations. 5 Robustness checs 5.1 Sensitivity of the model to the wage/capital remuneration differential We test the robustness of the model for a higher wage differential between the two countries. In particular, we calibrate the developing country to have a wage twenty seven times lower than the developed country, by allowing more capital per capita to the developed country (450 individuals and 289 firms compared to the developing country (1080 individuals and 26 firms. It approximatively relates the wage differential between the High income and the Low income countries groups in 2010 (World Development Indicators database of the World Ban, The behavior of the model stays the same. As there is a larger gap between the two countries, more individuals have to come out of the extreme poverty to be able to pay for the migration cost. During this time, more FDI tae place toward the developing country. After a run of 1000 periods, the model shows slightly different equilibrium values, a lower average capital remuneration ( ρ = and a higher average wage ( w = , due to the bigger FDI flow (values are average of 100 runs. 5.2 Sensitivity of the model to the wage/capital remuneration distributions We test the model with a Gamma distribution of remunerations (Pinovsiy and Sala-i Martin, 2009 instead of the Log-Normal distribution, to see if it is sensitive to the distribution chosen. The wage distribution is such that: [( ( ] µ wi, 2 ξ 2 t Γ ξ 2, i, i = 1,..., n ; t, t = 1,..., T µ The mean of the distribution is given by µ = E ( w t and the standard deviation ξ is fixed as a parameter to 0.8. Similarly, the capital remuneration distribution is given by: [( σ ρ 2 j, t Γ, ς 2 ( ς 2 σ ] j, j = 1,..., n ; t, t = 1,..., T 22

23 The mean is σ = F ( ρ t and the standard deviation ς is fixed as a parameter to 0.8. The same trends emerge from the model. FDI tae place from the developed to the developing country, in parallel to migrations in the reverse direction. At a certain point, FDI toward the developing country allow for return migrations. Remunerations equalize after a run of 1000 periods, at the same level than with Log Normal distributions. 6 Conclusion In this paper, we build an agent-based model considering the endogenous lin between FDI and migrations. As some empirical studies find either a positive or a negative relation between migrations and FDI, we test under which conditions there is a substitution effect or an effect of complementarity, using a bottom-up approach. The definition of the micro behaviors of individuals and firms and the parametrization we propose, result in an ergodic ABM. In addition, the model allows us to reproduce standard stylized facts. FDI flow from the developed country to the developing country and individuals migrate in the reverse direction. The remunerations of individuals and firms equalize in the long run. In particular, the less developed country catches up the developed country in term of wages. The model converges toward a quasi-stationary statistical equilibrium at the aggregated level. In addition, migrations occur faster when we increase the level of communication between individuals (size of the Moore neighborhood, minimal distance to create a relationship and relationship depreciation over time. Also we notice that the population density matters, because of the networ patterns. Preforming several tests, we find that FDI substitute migrations whereas migrations complement FDI in this process of remunerations equalization. In quantitative sens, migrations complement FDI, conversely we find no significant effect of FDI on migrations. Several extensions of this model could be done. For instance, we could consider individuals qualifications. Some papers show that different effects could be at play between labour and FDI when qualifications are considered (El Yaman et al., 2007; Kugler and Rapoport, Our ABM can easily be modified to tae into account new agents characteristics such as qualifications of individuals or the sector of the firms. 23

24 A Appendix Table 1: Set of parameters for the reference scenario Environmental parameters elasticity of substitution between factors α 0.5 number of individuals in the developed country L t 1000 number of individuals in the developing country L t 3000 number of firms in the developed country F t 200 number of firms in the developing country F t 100 standard deviation of the wages distribution ξ 0.8 standard deviation of the capital remunerations distribution ς 0.8 share of the world average wage (giving the migration cost ω 1.0 share of the world average capital remuneration (giving the FDI cost z 0.5 % of firms allowed to mae FDI x 0.05 Individual s parameters home preference effect β 0.3 networ effect γ 0.3 wage differential effect λ 0.2 confidence effect δ 0.2 home preference depreciation index h 0.1 confidence appreciation/depreciation index r 0.1 size of the Moore neighborhood (1 = 8, 2 = 24, 3=48 surrounding cells 2 radius of the area in which the individual is able to create a lin Ω 2 weight of a relationship at its creation 1 depreciation of a relationship over time 0.5 Firm s parameters capital remuneration differential effect η 0.3 foreign presence effect ν 0.2 networ of firms effect ι 0.3 wage differential effect τ

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