Return Migration as an Individual s Optimal Utility Maximizing Behavior. Yang Li and Wallace E. Huffman* December 31, 2000.

Transcription

1 Return Migration as an Individual s Optimal Utility Maximizing Beavior By Yang Li and Wallace E. Human* December 31, 2000 Sta Paper #339 *478C Heady Hall Iowa State University Ames, IA wuman@iastate.edu Abstract: Tis paper presents a model o location decisions o a multi-period, inite-lie, utility maximizing individual and an empirical azard rate analysis o return migration or Puerto Rican born males wo worked in te United States during te 1980s. A potential migrant is assumed to consume leisure, purcased goods, and local amenities and to be retired in is inal period o lie. We sow tat it is optimal or im to migrate in te irst period or to never migrate. Given tat migration occurs, return migration is likely wen e retires rom te labor market. Te reason is local amenities, including nearness to amily, riendly culture, pleasant climate, and amiliar places, wic are complementary wit leisure, weig eavily in consumption decisions at tis time. In te azard rate analysis, we ind tat actors aecting wage dierentials between te United States and Puerto Rico play a role, but te strongly convex eect o an individual s age on is azard rate or return migration supports te ypotesis o returning ome in retirement to consumer ome-country amenities. However, te azard o return migration is concave duration dependent. Keywords: Migration, return migration, United States, Puerto Rico, azard unctions, local amenities. Copyrigt 2000 by Yang Li and Wallace E. Human. All rigts reserved. Readers may make verbatim copies o tis document or non-commercial purposes by any means, provided tis copyrigt notice appears on all suc copies. IOWA STATE UNIVERSITY IS AN EQUAL OPPORTUNITY EMPLOYER Iowa State University does not discriminate on te basis o race, color, age, religion, national origin, sexual orientation, sex, marital status, disability, or status as a U.S. Vietnam Era Veteran. Any persons aving inquiries concerning tis may contact te Director o Airmative Action, 318 Beardsear Hall,

2 Return Migration as an Individual=s Optimal Utility Maximizing Beavior by Yang Li and Wallace E. Human * Large relatively new countries like te United States, Canada, and Australia were settled by immigrants, and immigrants and teir o-springs worked to develop tese countries into leading world powers. Also, te United States as a long istory o temporary worker programs, e.g., te bracero program o , and more recently te H-2A and H-1B programs. Illegal or undocumented immigration as been a growing problem in te U.S. since te termination o te bracero program because migration o Mexican workers did not end. Tis was igligted by te attempts by te Immigration Reorm and Control Act o 1986 to oer one-time amnesty to illegal workers wo could document teir past U.S. work istory and opes o ending illegal immigration (Fix and Passel 1994). In Western Europe, net emigration as been te experience until recently, wen legal and illegal immigrants ave come rom Nortern Arica and Central and Eastern Europe to provide signiicant sort and intermediate term increases in te labor orce. Currently about 8.5 percent o te U.S. population is oreign born (Passel and Edmonston 1994, pp. 37), but it is signiicantly iger in Canada, Switzerland, and France. * Te autors are Associate Proessor o International Business Studies at National Ci-Nan University, Taiwan, R.O.C., and Proessor o Economics at Iowa State University. Helpul comments were obtained rom Peter Orazem and oters. Financial assistance rom te Iowa Agriculture and Home Economics Experiment Station is grateully acknowledged.

3 3 Not all immigration is permanent; a signiicant sare o migrants return ome and a small sare goes elsewere. Some immigrant workers are under contracts tat stipulate te lengt o teir stay, e.g., U.S. H-2A and H-1B workers, and oters leave voluntarily. Most o te earlier studies o migration ave modeled location coice or migratory beavior as determined exclusively by income or real wage dierences between te ome and ost country, possibly incorporating selectivity, or example, see Scwartz (1976), Borjas (1994), Lalonde and Topel (1997), Borjas and Bratsberg (1996), Stark, Helmenstein, and Yegorov (1997), Encautegui (1993), Reagan and Olsen (2000). It as been unusual to empasize local amenities, consumption opportunities in retirement or inite lie in models o migration or return migration. However, given te reality o inite lie, retirement is an inevitable event or most males, and it represents a dramatic beavioral cange were uture wage prospects are greatly de-empasized and consumption opportunities, including easy access to amily, riends, amiliar places, comortable climate, and a riendly culture, weig eavily on coices. Wen previous studies o migration and re-migration ignored te importance o retirement on an individual=s location decisions, tey over-empasized wage or earning dierentials between ome and ost countries and unemployment or explaining migration and return migration. Te objectives o tis paper are to present a model o location beavior o a multiperiod inite-lie utility maximizing individual wo consumes leisure, purcased goods, and local amenities and is retired in te inal period o lie and to present empirical evidence rom a test using micro-data on return migration or Puerto Rican born males wo worked in te United States during te 1980s. Because te move is one o more tan

4 4 1,000 miles, we are modeling long distance migration. Te beavioral model is one o sequential optimization, return migration is conditional beavior, and a azard rate model o return migration provides te logical econometric ramework or carrying out tese tests. We ind strong empirical evidence or our teoretical model. Factors aecting wage dierentials between te United States and Puerto Rico play a role but te strongly convex eect o an individual s age on te azard rate or return migration supports te ypotesis o returning ome in retirement to consume ome-country amenities. Te paper unolds in te ollowing sections. A Multi-Period Finite-Lie Utility Maximizing Model o Migration and Re-Migration In tis section, a multi-period inite-lie model o migration and re-migration decisions o a utility maximizing individual wo is born in a particular (ome) country and contemplates migration to anoter (ost) country wit te prospect o eiter staying permanently in te ost country or returning to te ome country. Migrants may ave a deinite long-term location plan as tey embark on a sojourn to a ost country, e.g., to work or a ew years, save at an unusually ig wage rate, and return to te ome country to enjoy especially ig purcasing power o teir savings (see Stark et al. 1997). However, migrants, even tose wit strong etnic/amily transnational networks, ace considerable uncertainty or imperect inormation about uture economic events in te ost country, e.g., employment, wage rates, and utility generated rom consuming unamiliar culture, climate, and places in a ost country. Culture, topograpy (sea coast, mountains, plains), climate, and environmental quality in a potential ost country are experience good, wic can only be accurately assessed by sampling tem. Returning ome may be particularly attractive i te migrant experiences unanticipated

5 5 unemployment in te ost country or as e approaces retirement rom te labor orce and expects to ind ome country culture, places, relatives, and riends complementary wit increased leisure. An individual s lietime is split into ive periods, and e retires at te beginning o te last period. Lietime utility maximization is described as sequential decision-making over a ive-period planning orizon. Utility is a unction o an individual s leisure time, purcased goods, and local amenities. Te latter is not a coice at te margin, but is an indicator o location-speciic culture, social and political structure, linguistics, distance to relatives, climate, and environmental conditions tat aect te translation o leisure and goods into satisaction. To simpliy te decision problem in a plausible way, we assume te individual as ull inormation about is ome country, but incomplete inormation about te ost country, and e can become well or at least better inormed only by spending some time living in te ost country. Te optimal location strategy or te individual at eac decision time point is to coose te country tat provides im/er te greater expected utility over te remaining lietime. Te Framework Te individual s, potential migrant s, objective is to coose a place to live in eac period in order to maximize is expected present value o utility over te remaining lie span, discounted to te present at a constant discount rate β (0, 1). Tereore, te action space is given by A {, }, were = ome country, = ost (or oreign) country. Let s j (t) represent te state o inormation about country j in period t or j =, and t = 1,2,,5. Te state space or te decision process is ten given by

6 6 S S x S Were x is te Cartesian product, and te state space o country j, some inite or ininite dimensional vector space depending on te economic j S, is a subset o interpretation. Assume te state space S is a complete, separable metric space. Given a state o inormation s(t) S at decision time point t, wic describes te state o inormation or bot countries, te potential migrant will take an action in A according to a decision rule. Ten, te state o inormation s(t) migt cange rom period t to period t 1 according to a stocastic transition law, and te individual takes anoter action in A based on te state o inormation s(t 1). Assume te state o inormation or te two countries canges rom one period to anoter according to a Markovian decision process. In oter words, te stocastic law o motion is given by a sequence o transition probabilities { ( )} 5 t t = 2?, were P t (B s, a(s)) denotes te probability tat te state o inormation is B B(S) 1 during period t, provided te system is in te state o inormation s S during period t 1 and action a(s) A as been taken during tis period. Since te state transition probability is primarily based on subjective probability assessments o a potential migrant, it seems reasonable to assume tat only te state o inormation about te country j were te individual currently resides canges and e/se gains no inormation about anoter country. Assuming a omogeneous Markov process (te time index t can be omitted), say P ( ) and P : S P (S) is continuous w.r.t. te weak topology on P(S) were P(S) denotes te set o all probability measures on te measurable space (S, B(s)). Bot pecuniary and amenity dimensions o a location are key actors inluencing te individual s location/migration decision. Assume te state o inormation on country

7 7 j (witout uncertainty) in period t can be represented by te real wage rate, denoted by w j, and amenities, denoted by x j. For simplicity, as sume tat local amenities can be measured in wage units and tat te state o inormation o country j or te it period only depends on amenities. Tereore, te state o inormation or country j (witout uncertainty) at time t can be represented by te vector ( w, x ) j s j ( t) = x j j R R x R or ot t t = = 1, 2, 3, 4 Because o uncertainty about uture outcome states, te potential migrant will be modeled as te agent wo gaters inormation and ten makes te decision between te location/migration options. Let U j : S j R represent te individual preerences about te possible outcome states s j (t) in country j. Tis speciication implies tat te potential 5 migrant may eel dierently in dierent countries. I te state o inormation s j (t) is a probability distribution over ( w j, x j ), a nature candidate or te per period utility unction U j ( ) over te states in country j is von Neumann -Morgenstern expected utility U j ( s ( t)) = Uˆ( w, x ) ds ( t) j R x R j j j (1) were U ˆ( ) is te indirect utility unction over wage rates and amenity bundles. Ten, te bounded reward unction U ( ) o te Markovian decision process can be constructed by U : S x A R were U s, j) U j ( s ) or j A. Te objective o te migrant can ( j be restated as a migration strategy, or a sequence o action a ( s( t)) A, to maximize te expected discounted total reward 5 t β U( s( t), a( s( t)) ) (2) t = 1

8 8 were te state o inormation s (t) evolves according to te stocastic transition law P( s(t 1), a(s(t 1))) in time or t = 2,3,4,5. We assume te individual as ull inormation about is/er ome country, but is only partially inormed about te real wage and amenities in a potential ost country. Since a potential migrant can become better inormed only by spending some time living tere, assume s o represents te potential migrant s pre -immigration inormation state or ost country attributes at te beginning o te irst p eriod, but e/se does ave is/er own personal subjective probability distribution about w and x. Te migrant is assumed to be completely inormed about is wage prospects in te ost country ater living tere one period and about amenities in te ost country ater living tere two periods. We assume tat te migrant only cares about te wage rate during te second period o residence in te ost country. Ater e works or one period, e is ten concerned about amenities and te real wage rate. Denote k j R, wic is assumed to be known to te agent, as te cost o moving rom country i to country j. k and k are generally dierent, because k contains te searc cost and te moving cost, but k only includes te moving cost. 2 Tere are constant probabilities p and p, known to te potential migrant, o being unemployed in te ome country and te ost country, respectively, in te ourt period. To simpliy te model, we assume tere is at most one cycle o migrating moves, i.e., i a migra nt returns to is ome country, e cannot migrate again. Wit tis model structure, te state spaces or te ome country and ost country can be regarded as te subsets: S S ( R x R) { s } R ( R x R) R. o R, and

9 9 Te implication is te state o inormation or te ome coun try will be (w, x ) R x R until te last period wen it reduces to x R. Moreover, i e decides to stay in te ome country at te beginning o te irst period, is state o inormation or te potential ost country will be rozen at s o. However, i e decides to migrate to te ost country at te beginning o te irst period, te state o inormation or te ost country will cange rom s o to w R, and ten, te state o inormation will cange rom w R to (w, x ) R x R, provided e decides to stay one more period in te ost country. Ater te agent retires, is relevant state o inormation reduces to x R. Furtermore, te time-dependent action space or te potential migrant can be de scribed as: A 1 A t = = {, } { } {, } wen wen s( t) S s( t) S or t = 2, 3, 4, 5 and is per period utility unction U j : j S R or country j wit te state o inormation s j (t) are k or t = 1 U (s (t)) = w or t = 2 w x or t = 3, 4 x or t = 5 and U (s (t)) = w x or t = 1, 2, 3, 4 x or t = 5.

10 10 I te migrant re -migrates to is ome country at te beginning o period t, ten is utility unction at te beginning o period t in te ome country is w x k (or x k ). Te Optimal Migration Strategy Wat is te optimal migration strategy or te potential migrant? Te individual at eac decision time point cooses te country wic provides te larger expected presented value o remaining lie -time utility. Te optimal location i s ound by solving or te inal period and working backward, i.e., irst solve te re -migration problem at te beginning o period t 1, and based on tis solution solve te re -migration problem at te beginning o period t. 3 Because an individual can o nly migrate to te ost country during te irst period, we will only consider te re -migration beavior or te last our periods. Denote V t and V t to be te migrant s lie -time utility in te oreign country and te ome country in period t, respectively. Re-migration is te optimal strategy at te beginning o period t i and only i RM t = V t V t > 0 or t = 2, 3, 4, 5 (3) is satisied. Tereore, RM t can be interpreted as te net beneit rom re -migration in period t, given migration in te irst period. Similarly, migration is an optimal coice at te beginning o te irst period i and only i M = V V 0 (4) > is satisied. Hence, M 1 is te net beneit rom migration in te irst period. To complete te description o te potential migrant s strategy, solve or j V t, j =, and t = 1, 2,, 5. Since te individual is orced to retire at te beginning o te it period, te key actor inluencing i s well-being is local amenities, i.e.,

11 11 V = ( x k ), and (5) 5 V = x. (6) 5 Because te migrant aces te uncertainty o being unemployed in te ourt period, is presented value o remaining lie -time utility or bot countries at te beginning o te ourt period can be written as: V 4 = x β max{ x k, x } i ( w x ) β max{ x k, x } oterwise unemployed = x ( x k ) β ( RM ) i unemployed ( w x ) β ( x k ) β ( RM ) oterwise β 5 5 (7) V [ ( p ) w x k ] β x = 1 4. (8) Deine (X) to be max{x, 0}. Te max{x k, x } in V 4 captures te act tat te individual can stay or re -migrate in te next period i e decides to live in te ost country in te current period. At te beginning o te tird period, te migrant knows te amenities x ; e as all relevant inormation about te ost country. Te expected lie -time utility at te beginning o te tird period is: V 3 = (w x ) β[(1 p ) [(w x ) βmax {x k, x }] p max {x βmax {x k, x }, V 4 }] and (9) were V 3 = (w x k ) β[(1 p ) w x ] β 2 x, (10) V 3 represents te lietime utility rom period 3 onwards to a return migrant wo will stay in te ome country or te rest o is/er lie. On te oter and, V 3 represents te value wen te migrant decides not to return ome. Teoretically, tere

12 12 exists a reservation qualit y o lie, * x wic is determined by 3 = V, suc tat te V 3 individual will re -migrate i * x x. I te migrant re -migrates at te beginning o te ourt period, e must retire in is ome country. However, i e decides to stay in te ost country in te ourt period, e as a coice to stay or to re-migrate in te next period. It can be sown, owever, tat re-migration is not a rational strategy at te beginning o te ourt period, i e does n ot suer an unanticipated layo. Te reason is tat te migrant knows all relevant inormation at te beginning o te tird period, and ence, i te ost country can provide a larger remaining lie -time utility, it sould also provide a larger remaini ng lietime utility in te ourt period, provided e is not unemployed. Proposition 1. Te immigrant will stay in te ost country during te ourt period (te year beore retirement) i e is not unemployed, provided e as lived in te ost country during te tird period (previous year). (See Appendix A or proo). According to proposition 1, te individual will re -migrate at te beginning o te ourt period i and only i e suers a layo and V 4 [x β(x k ) ( RM 5 ) ] > 0, since V 4 [(w x ) β(x k ) β( RM 5 ) ] is always negative. Tereore, te net value o re-migration in te ourt period (te year beore retirement) is deined by RM 4 = V 4 [x β(x k ) β( RM 5 ) ]. (11) Note tat altoug te individual is unemployed, e may not re -migrate because te ost country provides a iger remaining lie -time utility. Tus, te model describes wy some migrants coose to stay in a ost country wen tey a re unemployed but oters

13 13 decide to return ome. Te migrant s lie -time utility in te oreign country in period 3 (equation (9)) can be written as: V 3 = (w x ) β[(1 p ) [(w x ) β(x k ) β( RM 5 ) ] p V 4 p ( RM 4 ) ]. Te individual only as te inormation about te wage rate w and is own personal subjective distribution unction o x at te beginning o te second period. Denote G(x ) as te migrant s subjective cumulative distribut ion unction o x given w. Deine te expected remaining lietime utility at te beginning o te second period by V 2 = w β R max {V 3, V 3 } dg(x ) = w V 3 β β ( ) R RM 3 dg(x ), and (12) V 2 = (w x k ) β(w x ) β 2 [(1 p )w x ] β 3 x (13) were max{ V 3, V 3 } in V 2 represents te options o te individual living in te ost country in te current period and to stay or return ome in te next period. Because o uncertainty about x and risk neutrality, te mean o max{ V 3, V 3 } represents te uture utility in te ost country. Consequently, we can ind a reservation wage, * w wic is determined by V 2 = V 2, suc tat te individual will return ome i * w w. Tereore, some migrants return ome because te wage rate and/or amenities in te ost country are too low. Finally, te potential migrant as no inormation about te potential ost country at te beginning o te irst period, except is own pe rsonal subjective distribution unctions o w and x. Deine F(w ) to be conditional distribution unction o w given s o. Hence, V 1 and V 1 are given by

14 14 V 1 = k β max {V 2, V 2 } df(w ) R = k V RM 2 R β 2 ( ) β df(w ), and (14) 2 V 1 = t = 0 t β (w x ) β 3 [(1 p )w x ] β 4 x. (15) Equations (14) and (15) are similar equations to (12) and (13) except max{ V 2, V 2 } illustrates options to a potential migrant i e migrates in te irst period. Te mean o max{ V 2, V 2 } represents te uture lie time utility in te ost country. Overall, te conceptual model leads to some strong conclusions about migration and re-migration beavior. Given utility maximizing beavior over a ive -period lietime wit retirement at start o te last period, an individual will migrate in te irst period or never move, and given tat e migrates, e will most likely return ome at te start o te it or retirement period. Return migration during te second troug ourt periods is unlikely, unless e experiences unanticipated unemployment in te ost country, adverse wage outcomes in te ost country, or positive wage inormation rom te ome country. Comparative Static Results I te potential migrant is at te beginning o te decision process, is optimal migration strategy can be summarized by te migration decision tree in igure 1. Te H and F represent a decision to live in te ome country (H) or te ost country (F) in period t. He will return ome i te net value o tis move is greater tan zero, given tat once te migrant as returned to is ome country, e cannot migrate again. For analytical convenience, we assume tat M 1 0 and RM t 0 or t = 2, 3, 4, 5.

15 15 Te net present value o te migrat ion decision is increasing in p, µ w, or µ x, but decreasing in p, k, k, w, or x were µ w = w df w ) and µ x = x dg x ) are te expected wage rate and amenity values, respectively. Tese results are intuitively reasonable. For an increase in moving cost k or k, te ost country sould become less attractive because te expenditure on migration goes up, but an increase in µ w or µ x, or decrease in p will inlate te expected lie -time utility o te ost country residency at te beginning o te irst period. Moreover, te expected lie -time utility o living in te ome country at te beginning o te irst period will d ecline wen p increases (ome unemployment rate), w decreases, or x decreases. Te table also sows tat te net value o re-migration is decreasing in p, k, or µ x, but increasing in p (ost unemployment rate), w, or x. Tese results seem also to be intuitively plausible. Wen µ x increases or p decreases, te expected lie-time utility rom being in te ost country at te beginning o period t increases, but i p or k increases, te expected lie -time utility o te ome country at te begin ning o period t decreases. Te same argument can also be applied to * w and * x. Proposition 2, Part a. Te reservation wage p, but a decreasing unction o k, p, or µ x. Part b. Te reservation quality o lie ( ( * w is an increasing unction o x, w, or * x is an increasing unction o x, w, or p, wile a decreasing unction o k, or p. (See Appendix A or proo)

16 16 Te Empirical Analysis Migration as received considerable attention b y economists or more tan tree decades, but muc less is known empirically about te determinants o return migration, were a migrant returns ome ater spending some time in a ost country a type o conditional beavior. Hence, te ocus o our empiri cal researc is on testing predictions obtained rom te beavioral model were an individual makes a series o sequential decisions on location, leading to conditional statements about migration and return migration, given migration. 4 Econometric metods based on time-dependent azard unctions provide a natural approac to te analysis o data on return migration. Te Empirical Model During any given time interval a migrant as some probability o returning ome, and a azard rate representation o te p robability o returning ome is one particular representation o tis probability. Deine T as te duration or lengt o a completed spell o migration in a ost country wit associated c.d.. o F(t) and p.d.. o (t) were t is a realization o T. Ten te migrant s azard rate or return migration can be represented as te limiting probability tat a migration spell is completed in t, given tat te migrant as stayed in te ost country until time t: Pr( t < T t T > t) ( t) ( t) λ ( t) = lim = = (16) 0 1 F( t) S( t) were λ (t) is te individual s return migration rate at t, and S ( t) = Pr( T > t) is te migrant s survival unction in te ost country, expressing te probability tat a migration spell is o lengt at least t (Greene 2000, pp. 939; Kieer 1988). In our model, we wis to test or eects o a set o variables X on te return

17 17 migration azard rate. A proportional azard rate model is applied to construct te empirical speciication. Furtermore, te mixed model is used to consider te pos sible unobserved eterogeneity in te population o migrants. Heterogeneity is assumed to arise as (i) migrant -speciic unmeasured eects, e.g., intensity o psycic costs o being away rom ome and o being in ost country, (ii) measurement error in X, or (iii) measurement error in te duration o a migration spell in te ost country. I we impose te Weibull distribution on migrants duration ( t) in a ost country and let V, distributed as gamma wit unit mean and variance θ, represent te migrant -speciic unmeasured eterogeneity, te mixed migrant survival unction is: t S m ( t, X, β, σ, θ ) = exp v λ ( z, X, β, σ ) dz V ( v) dv 0 ( v[ t exp( X β )] ) 1 1 σ θ V ( v dv = 1 θ[ exp( X β )] σ = exp ) Te associated return migration azard unction is: t. (17) 1 λ 1 σ 1 [ exp( X β )] σ θ ( 1 ) 1 ( t, X, β, σ, θ) [ S ( t, X, β, σ, θ)] t σ m = m (18) (Greene 2000, pp ). 5 In particular, te eect o unmeasured migrant eterogeneity is increasing in θ > 0, but as θ goes to zero, eterogeneity vanises. 6 Hence, i θ is not signiicantly dierent rom zero, te azard o r eturn migration will be monotone in duration. Some o te variables in X or te i-t individual cange over time. I time dependent covariates are included in te econometric model, te corresponding azard and survivor unctions in general do not ave a closed-orm expression and requires numerical integration to evaluate it. One o two expedients is oten adopted to overcome

18 18 tis diiculty: replace covariates X (t) by its average witin a spell ; replace X(t) by its value at te beginning o a spell. However, te irst treatment can ave te undesirable eect o building in spurious relationsips between duration lengt and regressors, and te second treatment ignores te time eterogeneity in te environment (Heckman and Singer 1985). We will approximate te azard unction by step-unctions (Petersen1986), i.e., te time dependent covariates are assumed to be constant witin eac period, but may cange rom one period to te next. Te Data: Return Migration to Puerto Rico A large sare o re-migration is return migration (Borjas and Bratsberg 1996), and we propose to test our model o return migration using data on Puerto Ricans. Puerto Rico, a Caribbean island located about 1,000 miles souteast o Miami, Florida, can be seen as a periperal country receiving a large inlux o capital rom te United States and being a country wit a transnational migration network to te United States operating or more tan tree decades. Close political -economic relations, owever, ave not erased istorical linguistic, cultural, and income dierences. Puerto Rico was colonized by Spain in te 16 t Century, it remains largely Spanis speaking, and it as a strong Spanis lavor to its culture. 7 In contrast, te United States is Englis speak ing, and te culture is predominately Nortern European. In 1980, per capita income was 30 percent lower in Puerto Rico tan in te United States. Furtermore, minimum wage policies ave ad very dierent impacts on te labor orce in Puerto Rico tan i n te United States (see Castillo-Freeman and Freeman 1992). In 1980, 920 tousand native born Puerto Ricans were residing in te United States and 1.5 percent o Puerto Rico s 3.2 million people were return migrants. Te

19 19 return migration lows were relat ively stable during te 1970s, ranging rom 21,802 to 29,928 persons per year. Te return lows grew during te 1980s to more tan 35,000 per year (see table 2), and may ave been aected by canging labor conditions in te United States due to te Immigration Reorm and Control Act o 1986, wic legalized or work more tan 3 million largely low skilled Spanis speaking workers rom Mexico and Central America. For tis study, a return migrant is deined as a male age 18 to 64 years old in 1990 wo was born in Puerto Rico and as lived/worked in te United States or six or more consecutive monts but ad re-migrated rom te U.S. mainland during te 1980s. Males wo were in te armed orces, sel-employed, or enrolled in scool are excluded. Te data are drawn rom te percent sample o te Public Use Microdata Samples (PUMS) or Puerto Rico and te United States. Te azard rate model is applied to migration/working spells in te United States o Puerto Rican born males. A total o 12,108 mig ration/working spells are used in te empirical analysis o wic 2,544 are rom te Puerto Rico sample and 9,564 are rom te U.S. sample. Te duration o te migration/working spell is deined as: were min { T S, ( ENDAGE 6 ED), ( ENDAGE 18) } S T is te duration recorded in te survey, ED is te individual s years o ormal scooling completed, and ENDAGE is te individual s age in 1990 or te U.S. sample and te age wen te last migration spell was complete or te Puerto Rico sample. Ater applying te above deinition o te duration o a migration spell, we still ave 1,183 let - censored spells, wic are adjusted to complete te sample (see Appendix B or a discussion). 8

20 20 Te Empirical Speciication Altoug te wage at ome and in te prospective ost country play a central role in an individual s location decision in our conceptual model, predicted wage rates rom an equation itted to cross-sectional data seem raugt wit diiculties. Te primary reason is tey provide a snapsot o te wage structure at only one point in time. Te coeicients in edonic wage equations may reasonably be constant, wen adjusted or inlation, over periods modest in lengt but seem unlikely to be constant over orty years wic is te l engt o time spent on te mainland by te Puerto Rican migrant wit te longest duration in our sample. An alternative approac is to consider a edonic wage equation and ten replace te predicted wage by te set o regressors tat are predictors taking a reduced-orm approac. By applying tis metodology, we can solve several problems. Tere is, owever, no ree lunc and te price we pay is tat we cannot obtain direct estimates o te impact o te U.S. and Puerto Rican wage rates on te azard rate or re-migration. Prime candidates or regressors in te wage equation are an individual s own uman capital and local - and birtplace - labor market conditions. An individual s years o scooling completed represent general uman capital tat is valuabl e in te labor market o te United States and Puerto Rico. Castillo-Freeman and Freeman (1992) ave sown tat or Puerto Rican born men, te economic return to scooling in 1970 and 1980 rom working in Puerto Rico is iger tan rom working in te Uni ted States, and te gap was increasing during te decade o te 1970s. An individual s education also aects inormation processing skills tat can reduce transactions costs associated wit eicient decisions to relocate (Human 1985). Furtermore, De tang-dessendre and

21 21 Molo (1999, 2000) ave sown empirically tat an individual aving iger levels o education increase te probability o long distance migration (but as no eect on sort distance migration). An individual s age is strongly correlat ed wit potential labor market experience, wic generally as a quadratic marginal eect on an individual s wage. An individual s age also proxies individual and amily lie -cycle eects on work, including retirement, and consumption, and given tat u man lie is inite, an individual s age is an indicator o expected lengt o remaining work lie and o lie over wic beneits rom return migration can be obtained. An individual s Englis proiciency is a valuable skill in te U.S. labor market and being bilingual is a skill o some value in te Puerto Rican labor market. Linguistics is one part o social capital wic can be expected to aect migration and return migration (see Stevens 1994; Borjas 1994; Dustmann 1999). Individuals wo ave greater Englis proiciency ave greater tendency to immigrate to te United States, and once in te U.S. teir proiciency wit Englis tends to increase (Stevens 1994). For a migrant, an increase in is Englis proiciency will increase is U.S. wage rate by mo re tan is Puerto Rican wage rate. Good ealt is also uman capital (Strauss and Tomas 1998) aecting an individual s wage rates and te quality o lie. Wen an individual is disabled, is labor productivity is lower, and disability can be expected to reduce te size o te U.S. Puerto Rico wage dierential. Disability also increases te cost o migration, and it may aect an individual s location preerences because o dierences in entitlements tat are associated wit living in a particular lo cation. Te job growt rate, unemployment rate, and minimum wage policies o Puerto Rico and te United States are also determinants o expectations about te wage rate tat

22 22 an individual migt earn in te United States and Puerto Rico, respectively. Fo llowing Topel (1986), a iger expect job growt rate or an area or lower expected unemployment rates is associated wit a iger expected wage rate or an area, oter tings equal. Te anticipated eects o unemployment are incorporated into wage structures, but tey ave dierent eects tan unanticipated unemployment. Castillo - Freeman and Freeman (1992) ave sowed tat a major increase o te minimum wage in Puerto Rico created a marked spike in te distribution o earnings near te minimum wage. Also, a ig minimum wage as employment eects, leading to iger unemployment rates in te sort run (see Ramos 1992, Castillo -Freeman and Freeman 1992) and substantial loss in employment over te long term (see Reynolds and Gregory 1965; Castillo-Freeman and Freeman 1992). Te symbols used to deine te variables in te empirical azard rate model are presented in table 3, and te systematic part o te azard rate unction is: X i ( ti ) β = β 0 β 1AGEi ( ti ) β 2 AGESQi ( ti ) β 3EDi β 4ENGi β 5 DISAB i β 6PJRUSi ( ti ) β 7PURUSi ( ti ) β 8PJRPRi ( ti ) β 9PURPRi ( ti ) β 10PRMIN i ( ti ) β 11PRMINURi ( ti ) (19) were PRMINUR is an interaction term between PURPR and PRMIN. 9 ED, ENG, and DISAB take on a particular value at te beginning o a migration spell and are uncanged over te remainder o te spell. AGE, AGESQ, PURUS, PURPR, PJRPR, PURPR, PRMIN, and PRMINUR vary over time and across (spells) individuals. Tey take on end o migration spell or 1990 values. Te expected sign o te coeicients in equation (19) is: β 1 > 0 β 2 < 0; β 3 < 0, β 4 > 0, β 5 > 0, β 6 > 0, β 7 < 0, β 8 < 0, and β 11 > 0. We cannot directly predict β 9 or β 10 since tere exists te minimum wage -unemployment interaction

23 23 eect. We can only expect tat bot te real minimum wage and te unemployment in Puerto Rico ave negative eects on te azard rate or re-migration, evaluated at sample mean. Table 3 presents sample mean values o te caracteristics o Puerto Rican migrants wo returned to Puerto Rico during te 1980s (at te time o re -migration) and or Puerto Rican migrants wo remained in te United States in Te returning migrants were on average younger, less scooled, less proicient in Englis, and more likely to be disabled tan migrants wo remained in te United States. Tese dierences are roug conirmation o te selectivity o bot migration and return migration. Te Results Te maximum likeliood estimates o te coeicients or te empirical return - migration azard -rate unction itted to te 12,108 observations on migration/working spells are reported in table 4. All o te estimated coeicients are signiicantly dierent rom zero, including θ, te eterogeneity parameter. Hence, we conclude tat eterogeneity exists in te return -migration azard unction. Wen te predicted azard rate, evaluated at te sample mean, is graped against duration, te relationsip is an inverted U (igure 2, part b), or concave duration dependent. Te maximum azard rate or re-migration (0.8%) occurs wen a Puerto Rico-born man as lived/worked in te United States or 3.75 years. Tereater, te azard -rate declines or additional duration. Tis grap suggests tat migration is generally a success in te sense tat individuals tend to stay or a signiicant lengt o time in te ost country beore eeling a strong unmeasured pull to return ome. Tis is long enoug to capture some positive beneits on te initial migration costs associated wit moving rom Puerto Rico to te United

24 24 States. In contrast, i omogeneity were imposed, te implication is te igest probability o returning ome occurs during te irst year, and it decreases as time in te U.S. accumulates (see igure 2, part a). Our oter estimated coeicients provide enligtening new insigts on determinants o return migration. Te concave eect o a migrant s AGE on expected duration in te United States implies tat duration increases wit is age up to 28, but or an individual wo is older tan 28 years, duration decreases wit age. Tus, wen a Puerto Rican is younger tan 28 years, te conditional probability o im returning ome decreases wit eac birtday. Ater e turns 28 years, te probability o return migration increases wit eac birtday, increasing rapidly during te 40s and 50s and becoming relatively large or an individual wo is 60 years o age (see igure 3). 10 Reagan and Olsen (2000) obtained somewat similar results. Te strongly convex relationsip between te azard rate or return migration and te migrant's age is inconsistent wit in ter-country wage dierences being te major actor driving return migration. Te eect is, owever, consistent wit inite lie and a dramatic cange in consumption bundle in retirement were ome -country amenities weiging eavily on location decisions. We suggest tese results provide strong empirical evidence or te predictions rom te beavioral model developed in te previous section. Te results are also consistent wit conclusions in Tienda and Wilson (1992) and Pissarides and Wadswort (1989). Increasing an individual s scooling by one year reduces by 4.5 percent te duration o a Puerto Rico-born male s migration spell in te United States and increases is probability o return migration. Tis result supports Castillo-Freeman and Freeman s

25 25 (1992) inding or Puerto Rico-born men tat te economic return to scooling in Puerto Rico is iger tan in te United States, and given tis inormation, it also supports predictions rom our conceptual model wen te wage in te ome country rises rel ative to wage in te ost country. It also supports scooling reducing transactions costs associated wit long-distance migration (Detang -Dessendre and Molo 1999), and Ramos (1992) inding tat native born Puerto Ricans wo migrate and return to Puerto Rico tend to be more skilled tan tose wo remain in te United States. An individual s Englis proiciency plays a signiicant role in return migration decisions or Puerto Rico-born men. Greater Englis proiciency increases a migrants time in te Un ited States (because it increases te wage rate in te U.S. by more tan it increases te wage rate in Puerto Rico) and reduces is azard -rate or return migration. Duration in te United States or Puerto Rico-born males aving Englis proiciency is 2.22 times longer tan or tose wit poor Englis proiciency. Tis empirical result supports te prediction rom our conceptual model tat an increase in te U.S. wage relative to Puerto Rican wage reduces te azard rate or return migration. It also supports te ypotesis tat language proiciency is an important orm o countryspeciic uman capital aecting re-migration rates (Ciswick and Miller 1993; Regan and Olsen 2000; Dustmann 1999). Te results suggest tat tat a migrant s disability lengtens is duration in te United States by about 18.3 percent, and reduces is azard rate or return migration. Overall, te result supports te prediction tat disability raises te cost or/and reduces te beneit to return migration. It is also consistent wit better entitlement programs or disabled individuals in te United States tan in Puerto Rico. Te coeicient, owever, is

26 26 signiicantly dierent rom zero only at te 10 percent signiicance level. Te empirical results yield strong evidence or te eect o labor market conditions on re-migration decisions. A 0.1 percentage point increase in te predicted U.S. job growt rate, wic increases te migrant s expected U.S. wage rate, lengtens te migration spell in te United States b y 28 percent, and tereby reducing is azard rate or return migration. A similar increase in te predicted job growt rate or Puerto Rico, wic increases te migrant s expected wage rate i e sould returns ome, reduces is duration in te United States by 40 p ercent and increases is azard rate or return migration. Tese results support predictions rom our beavioral model about ost and ome country wage eects on te return migration decision. Te empirical results sow tat a 0.1 percentage point increase in te predicted U.S. unemployment rate reduces by about 9 percent te duration o migration to te United States, and increases te azard rate or return migration. Te proportional eect o te predicted Puerto Rican unemployment rate on migrant s time in te U.S. is β 9 β 11 PRMIN. Wen we evaluate tis eect at te sample mean o PRMIN or1980 and 1990, we obtain Hence, a one-percentage point increase in te predicted unemployment rate or Puerto Rico lengtens te migration spell by 4.1 percent and reduces te azard rate or return migration. Similarly, a proportional increase o te real minimum wage in Puerto Rico impacts te lengt o te U.S. spell duration as β 10 β 11 PURPR. At te mean o PURPR rom 1980 to 1990, wic is , te results sow tat a 10 cents increase in te Puerto Rican real minimum wage lengtens te U.S. migration spell by 19.7 percent and 11 decreases te azard rate or return migration. Te estimate o β 11 wic is te coeicient o te interaction term between

27 27 te Puerto Rican predicted unemployment rate and real minimum wage, is positive. Given tat te estimates o β 9 and β 10 are negative, tis interaction eect as a moderating eect. Conclusions and Implications Return migrati on requently occurs at te time an individual retires rom te labor orce. Teoretical models o location, including migration and re -migration, and empirical analyses o tese events ave inrequently incorporated te eects o inite lie and retirem ent wit its dramatic cange in te consumption bundle. In contrast, tis paper as presented a conceptual model o an individual s multi -period lietime utility maximizing location decisions were ome and ost locations are eterogeneous in amenities an d retirement occurs at te beginning o te inal (it) period. We obtained te prediction tat an individual will migrate in te irst (adult) period or never migrate, and given e migrates, e is most likely to return ome at te start o te inal or retirement period. Return migration at oter times is unplanned but may be optimal wen economic socks cange ost and ome country real wage opportunities and employment prospects. Empirical evidence was presented in a azard rate analysis o return migration or Puerto Rico-born males wo worked in te Untied States during te 1980s. Te empirical evidence was consistent wit te predictions o te beavioral model improved ost labor market conditions reduced te azard o return and improved ome country labor market conditions increased te azard o return. Also, te strongly concave relationsip between te azard o return and te migrant s age is evidence o te very important role played by inite lie and retirement wen ome and ost locat ions

28 28 dier greatly in culture, language, access to amily, and a comortable climate. Altoug te azard rate wit eterogeneity exibited concave duration dependents, we conclude it does not contradict te beavioral model. Te study as major implic ations or internal migration. Te teoretical model is directly application witout modiication, provided te ome and prospective ost areas are eterogeneous in location-speciic amenities wic is true or all large countries, e.g., United States, Canada, Australia, European Union, Brazil. Te model, owever, seems most applicable were uman, economic, and social mobility are occurring at not more tan a modest rate because tis permits local eterogeneity to maintain considerable persistence over t ime, e.g., France, Germany, United Kingdom, European Union. An individual wo migrates at an early age can return ome in retirement to amiliar local amenities and not be disappointed. In contrast, i uman geograpic, economic, and social mobility ar e occurring too rapidly over time, te unique attributes o ome/originating areas will be canging rapidly. Hence, any ome area will lose most o its attractiveness to retiring migrants, wo let te area at a young age, because tere is noting amil iar to return to, e.g., United States, Brazil.

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