A DYNAMIC GENERAL EQUILIBRIUM ANALYSIS OF MIGRATION AND CAPITAL FORMATION: THE CASE OF CANADA. Stuart J. Wilson

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1 UNIVERSITY OF REGINA ISSN DEPARTMENT OF ECONOMICS A DYNAMIC GENERAL EQUILIBRIUM ANALYSIS OF MIGRATION AND CAPITAL FORMATION: THE CASE OF CANADA Suar J. Wilson Deparmen of Economics Universiy of Regina Regina, Saskachewan Canada S4S A2 econ@uregina.ca NOVEMBER 2 DISCUSSION PAPER #86

2 A Dynamic General Equilibrium Analysis of Migraion and Capial Formaion: The Case of Canada Suar J. Wilson * Deparmen of Economics Universiy of Regina Regina, Saskachewan, Canada S4S A2 November 7, 2 Suggesed Running Head: Migraion and Capial Formaion Conac: Suar J. Wilson Deparmen of Economics Universiy of Regina Regina, SK, S4S A2 Tel: (36) Fax: (36) suar.wilson@uregina.ca * The auhor would like o hank Alan Green, Allen Head, R.M. McInnis, and seminar paricipans a Queen s Universiy, a he 2 Meeings of he Sociey for Economic Dynamics, a he 2 Meeings of he Canadian Economics Associaion, and a he Fourh World Congress of Cliomerics, for helpful commens and discussions. None oher han he auhor can be held accounable for errors or oversighs. 1

3 Absrac A dynamic general equilibrium model is consruced o examine he impac of mass immigraion on capial accumulaion in life-cycle economies. The model economies are populaed by agens of overlapping generaions wih limied lifeimes, and are subjeced o a series of migraion shocks. The model is calibraed o mach Canadian demographic characerisics over The calibraed model is hen used o examine he impac of his demographic shif on domesic savings and foreign capial inflow raes. Model resuls sugges ha up o hree-quarers of he increase in he capial formaion rae and he foreign capial inflow rae, and all of he increase in he domesic savings rae, in he Canadian economy over , can be aribued o he dramaic inflow of migrans over his period. Key words: migraion; capial formaion; saving; life cycle. 2

4 1. Inroducion This paper presens a dynamic general equilibrium model o explain how migraion affecs capial accumulaion in life-cycle economies. The model absracs from business cycles, and earnings and employmen uncerainy o isolae he impac of migraion on he savings rae in a deerminisic environmen. The model is calibraed o mach Canadian demographic characerisics over To do so, I idenify age and gender-specific Canadian ne migraion paerns over During his period, Canada shifed from being a counry of ne emigraion, o one of ne immigraion, circa 1897, wih improved economic condiions leading up o he Firs World War. I hen use he model o examine he impac of his demographic shif on domesic savings and foreign capial inflow raes. Model resuls sugges ha up o hree-quarers of he increase in he capial formaion rae and he foreign capial inflow rae, and all of he increase in he domesic savings rae, in he Canadian economy over , can be aribued o he dramaic inflow of migrans over his period. Canada s experience during he four decades leading up o WWI consised of wo remarkably differen periods, wih 1897 as he defining year of change. In he hree decades following Confederaion in 1867, Canada was a ne supplier of migrans wih emigraion raes similar o hose of Norway and he Briish Isles (McInnis (1994), and Haon and Williamson (1994)). During his period, oal real income growh averaged hree percen per year, and capial formaion raes amouned o abou fifeen percen of real GNP (Urquhar (1988)). Afer 1896, he Canadian economy was dramaically alered. Canada became a ne receiver of immigrans wih a ne immigraion rae of 15.1% over (as a percenage of he 191 populaion). Canadian real oupu grew six percen per year. Gross capial formaion as a percenage of oupu grew seadily from welve percen in 1896 o hiry hree percen in 1913 (Urquhar (1988)). Figure 1 presens he Canadian gross domesic capial formaion, 3

5 domesic savings, and foreign capial inflows raes over Figure 2 shows he annual paern of migraion for Canada from Economeric analysis has concluded ha he increase in invesmen in Canada during his period was he resul of increases in he populaion, and innovaions o expors (Green and Sparks (1999)). The rise in he domesic savings rae was due in par o he dramaic increase in he working-age populaion (McLean (1994), and Wilson (2)). However, Canada, wih a young populaion, sill required foreign capial inflows o mee he increased capial requiremens during his period (Taylor and Williamson (1994)). Labor force growh raised capial requiremens and pulled capial from foreign sources, alhough wha role labor force growh played in accouning for he massive capial flows o he New World remains an open quesion (Taylor and Williamson (1994: 351)). This level of capial accumulaion has no been repeaed in Canadian hisory, nor has he rae of immigraion. Wha impac did migraion have on capial accumulaion? New immigrans would have o be equipped for producion, and social infrasrucure would need o be developed. Can he massive inflow of immigrans accoun for he surge in capial accumulaion ha Canada experienced prior o WWI? Can he age-composiion of immigrans explain he composiion of invesmen beween domesic and foreign sources? The economic effecs of immigraion have garnered much aenion in he US recenly. Work has focused on he impac of immigraion on wages and he migraion of naives in response o immigraion (see Borjas (1994), Friedberg and Hun (1995), Filer (1992), and Card(1997)), and on he fiscal impac of immigraion (Auerbach and Oreopoulos (1999), and Soresleen (2)). The massive reallocaion of labor ha occurred during he age of mass migraion, , has also been sudied a lengh. Elaborae compuable general equilibrium models have been developed o assess he impac of he massive reallocaion of labor on real wages in Ireland (Boyer, Haon and O Rourke (1994)), on wage differenials beween Briain and he Unied Saes (O Rourke, Williamson and Haon (1994)), 4

6 and on growh and srucural change in Argenina (Taylor (1997)). These saic CGE models are useful in examining counerfacual assumpions of an economy a a poin in ime. Economeric models have been used o assess he role of migraion on real wages in Ausralia and Canada (Pope and Wihers (1994), and Green(1994)), economic growh in Canada (Green and Sparks (1999)), and growh and inequaliy in he Alanic economy (Williamson (1998)). Long-run demographic change and is influence on domesic savings raes and foreign capial flows in he US, Ausralia and Canada has also been modeled (McLean (1994), Taylor and Williamson (1994), and Wilson (2)). Using ime series daa, hese sudies examine dynamic ransiions of economies over ime. Dynamic general equilibrium models have been recenly developed and used o model he impac of demographic change on an economy. The effec of an aging populaion on social securiy (Auerbach, Kolikoff, Hagemann and Nicolei (1989)), and on capial accumulaion (Rios-Rull (1994)) has been modeled in a dynamic framework, as has he role of immigraion policy and is impac on fiscal policy (Soresleen (2)). Canada provides an enicing case sudy in he role of demographic change in an economy a he beginning of he wenieh cenury. This paper presens a dynamic (overlapping generaions) general equilibrium model ha examines he impac of immigraion on life-cycle economies. The model combines elemens used by Hugge (1996), where agens receive inergeneraional ransfers from accidenal bequess, and Soresleen (2), ha accouns for age-specific migraion. The model is calibraed o he Canadian economic environmen in he years leading up o he Grea War. Using census saisics of populaion, and esimaes of survival raes, feriliy raes, and immigran flow daa, he populaion process for Canada is recreaed for he period. The purpose of his paper is o isolae he effec of a migraion ransiion, holding echnological progress consan, and examine he implicaions of his change on capial accumulaion. 5

7 The conribuion of his paper o he exising lieraure is in idenifying age and gender-specific Canadian ne migraion paerns during he period of sudy, and in providing a preliminary answer o he open quesion of Taylor and Williamson (1994: 351). Resuls sugges ha up o hree-quarers of he increase in he capial formaion rae and he foreign capial inflow rae, and all of he increase in he domesic savings rae, in he Canadian economy over , can be aribued o he dramaic inflow of migrans over his period. Secion 2 presens he dynamic general equilibrium model and he soluion mehodology. Secion 3 discusses he calibraion procedure, and secion 4 presens he key modeling resuls. Secion 5 concludes wih direcions for fuure research. 2. An Overlapping Generaions Model 2.1. The Environmen The economy o be examined consiss of overlapping generaions of agens, following Auerbach and Kolikoff (1987), Hugge (1996) and ohers, who live up o a maximum of I periods. Agens are heerogeneous in age and sex, and agen ype is described by he subscrip h where i denoes age and h denoes gender. The age discriminaion is made as agens in he model economy save for life-cycle reasons, and asse holdings will vary according o age. Agens are discriminaed by sex in his model o accoun for age and gender-specific migraion paerns, he labor force paricipaion of young females, and allow for age-specific feriliy raes for females. The framework does no model household formaion bu models independen agens. The age disribuion of he populaion a a poin in ime is denoed by he (2I x 1) vecor µ, where µ = [ µ 1,f µ 2,f µ I,f µ 1,m µ 2,m µ I,m ] T. Agens of age i and gender h face a probabiliy s h of 6

8 surviving from he age of i o he age of i+1 ha is consan over ime. The uncondiional probabiliy of surviving o age k is s( k) = Π s. The vecor of age and gender specific feriliy raes is φ, and is k 1 j= 1 j assumed consan over ime. The number of newborns a ime is: k µ = φ (1) 1, k, h hµ h, 1 where k denoes he gender of he newborn, and h denoes he gender of he agen (birh-paren). The migraion process o be described is adaped from Soresleen (2) o sui he Canadian environmen. Each year, immigrans ener he economy, also heerogeneous by age and gender. Immigrans ener he economy wih he same skill and asse endowmens as he exising populaion heir own age. 1 The number of immigrans of age i and gender h in each age caegory is se o a fixed proporion θ i-1,h of he survivors of age i-1 o age i. The populaion of age i agens (where i > 1) a ime is: µ h, = s i-1,h (1+θ i-1,h )µ i-1,h,-1. (2) The law of moion of he populaion is represened by he marix Γ, where, Γ = s φ 1, f ( φ f 1, f 1 + θ m 1, f 1, f ) s φ 2, f ( φ f 2, f 1 + θ m 2, f 2, f ) s φ f I 1, f 1 + θ I 1, f ( I 1, f ) m φ I 1, f φ φ f I, f m I, f s φ φ 1, m ( f 1, m m 1, m 1 + θ 1, m ) s φ φ I 1, m ( f I 1, m m I 1, m 1 + θ I 1, m ) φ φ f I, m m I, m (3) so ha µ = Γµ -1. Emigraion can be modeled in a similar fashion, wih immigraion raes se o negaive values (i.e. θ < ). Agens maximize uiliy over a sandard composie good, wih ime separable preferences and discoun facor β. The composie good can also be used as capial, earning a risk-free one period reurn 7

9 per uni, R, while he rae of reurn is r =R -1. The reurn is exogenously se on inernaional markes. Agens are endowed wih age and gender-dependen efficiency unis of labor e h, which hey supply inelasically beginning a age I w unil reiremen a age I r. Agens under he age of I w do no work, do no consume, and do no make any decisions. Agens preferences are summarized by he following uiliy funcion: E I w I I w j ( s( j + I w ) U ( c j I )) 1 σ c β, where U ( c) = w 1 σ. (4) j= + Producion is deerminisic and is governed by a consan reurns o scale echnology of he following form: α Y = F( K, L ) = A K L 1 α. (5) In order o isolae he impac of a change in migraion paerns on he economy, echnological progress, A, grows a a consan rae g, and capial depreciaes a a consan rae δ. The economy is a small open economy, so ha he rae of reurn on capial is exogenously fixed o he inernaional rae. Labor movemens are aken as exogenous in he model. Capial can freely flow in and ou of he economy. There is no role for governmen in he model economy. 2 In period, an agen chooses consumpion, c h,, and asse holdings, a i+1,h,+1, wih he following budge consrain: c + h, + ai+ 1, h, + 1 W = R a h, + ω e h T. (6) In his conex, W denoes wealh, and T is a lump-sum ransfer. Individuals receive wage rae ω per efficien uni of labor. Agens are liquidiy consrained such ha hey canno have negaive ne asse holdings a any age. The value of T is deermined by he amoun of accidenal bequess lef by hose who die in period, before he age of I. The value of hese bequess is hen disribued amongs he adul populaion (hose of age I w or older). 3 8

10 Agens make heir decisions on asse holdings for period +1 a ime and canno liquidae heir holdings unil ime +1. Immigrans a ime ener he economy wih foreign asse holdings, and heir asse holdings a ime +1 are hen considered o be held domesically. Emigrans a ime do no work domesically a ime, however, heir asse holdings are producive in he domesic economy a ime. Asses of emigrans are considered foreign a ime Equilibrium Pah A massive inflow of working age immigrans can drasically change he age disribuion of he populaion. No only do hose of working age save, hus increasing domesic savings, bu may require foreign capial flows o equip hem for producion. In order o compue a ransiion, iniial and erminal condiions mus be deermined. As such, he ransiion will occur beween wo seady-sae equilibria. The iniial seady-sae will involve a ne emigraion populaion process, and he erminal seady-sae will involve a ne immigraion process. The seady-sae age disribuions of he populaion, µ ss1 and µ ss2, he new law of moion for populaion describing he ransiion o he second seady-sae, Γ ss2, and he open economy environmen are aken as given. 4 Transiional equilibria are defined recursively. A a poin in ime, he populaion disribuion in he economy is defined by he vecor µ. The economy is also characerized by asse holdings of agens in each age and gender group, denoed by he vecor a, and given he open economy environmen, by he inernaional risk-free reurn, R. The sae of he economy is defined by (µ, a, R). The individual agen s sae is (e i, R, a i ), where a i denoes he individual s own holdings of asses. The agen s dynamic programming problem is now described. An agen s individual sae is denoed by (x, a), where x = (e, R). The funcions for consumpion, c ( x, h, a) and nex period s asse holdings, a ( x, h, a) are opimal decision rules ha solve he following dynamic programming problem, given ha in period I+1, he agen s value funcion is se o zero (V(x,I+1,h,a)=): 9

11 V x, h, a) = maxu( c) + β s E( V ( x, i + 1, h, a ) x) (7) ( h ( c, a') subjec o (1) c + a Ra + ω e( h) + T (8) (2) c, and a for all i. (9) Agens are liquidiy consrained such ha hey canno have negaive ne asse holdings a any age. The economy o be modeled is a small open economy, where he rae of reurn o capial is se exogenously on inernaional markes, and capial can freely flow in and ou of he economy. Definiion: A recursive open economy compeiive equilibrium is a se of value funcions, V(x,h,a,), a se of policy funcions for asse holdings, a ( x, h, a, ), a se of policy funcions for consumpion, c ( x, h, a, ), and laws of moion for he populaion, aggregae capial sock, aggregae labor inpu, domesic capial, foreign capial, ransfers, and funcions for prices, (Γ(), K(x,), L(x,), K d (x,), K f (x,), T(x,), ω(x,), R(x,)), such ha: (1) c ( x, h, a, ), a ( x, h, a, ) are opimal decision rules ha saisfy he agen s dynamic programming problem (equaion (7) subjec o (8) and (9)); (2) Inpu markes are compeiive: ω( ) = F2 ( K( ), L( )) and R ( ) = 1+ F1 ( K( ), L( )) δ, wih R se exogenously on inernaional markes; (3) The allocaions are feasible: (i) Domesic asse holding equal domesic capial, K ( + 1) = Σ, ( h, ) a ( x, h, a, ) ; d i hµ (ii) Foreign capial is he difference beween oal capial and domesic capial, K f ( ) = K( ) K ( ) ; d 1

12 (iii) Domesic wealh plus new immigran wealh equals consumpion and nex period asse holdings,ω(x,)l(x,) + R()K d (x,) + h µ(x,h,)(s(h)φ(h))a(x,h,)r(x,) = h µ(x,h,)c(x,h,a,) + h µ(x,h,) a (x,h,a,); (4) Effecive labor supply, L( ) = Σ i, µ ( h, ) e( h) ; h (5) Transfers o he adul populaion equal accidenal bequess, T ( + 1) = Σ (,, )(1 (, )) ( 1) i, hµ i h s i h R + a ( x, h, a, ) / N a ( + 1), where N a denoes he number of aduls in he populaion. The mehod of compuing he ransiion is adaped from Rios-Rull (1994, 1997). Firs, a sequence of populaion disribuions is calculaed using he populaion ransiion marix wih he firs seady-sae populaion disribuion as he saring poin. Nex, a guess for he sequence of ransfers is made. Given he sequence of ransfers, he sequence of opimal asse holdings of agens in he economy can be compued recursively. Then, he values of accidenal bequess (ransfers) are calculaed and compared o he guessed sequence of ransfers. If he wo sequences are equal he procedure is compleed, oherwise, he guessed sequence of ransfers is updaed and he compuaional procedure is repeaed unil convergence is achieved Calibraion Each period in he model economy corresponds o one year. Agens live up o a maximum of 95 years, begin supplying labor and making decisions a 15 years of age, and fully reire from he labor force a 9. 6 There is no earnings or employmen uncerainy in he model, and agens accumulae capial under he life-cycle moive. Agens do face uncerain lifespan, bu agens commonly know age and genderspecific moraliy raes. 11

13 3.1. Populaion The populaion process for Canada was calibraed using esimaes of he populaion a census daes, esimaes of feriliy raes, crude birh raes, moraliy raes, and immigran flow saisics. The census populaion figures are aken from Urquhar and Buckley (1965), and are gender specific in five-year age cohor groupings wih he excepion of he elderly (i.e. he groupings are: under 5, 5-9, 1-14,, 65-69, and 7 and older). Survival raes were derived from he moraliy esimaes of Bourbeau and Legare (1982) a census years (i.e. 1871, 1881, ec.), and are also gender-specific in five-year age cohor groupings, wih he excepion of infans (under one year, and 1-5 age groups). The moraliy esimaes imply ha all agens die before 96 years of age. In he calibraed model, no agen survives pas his or her niney-fifh birhday. Feriliy raes were consruced using he 1926 age-specific feriliy raes of females from Urquhar and Buckley (1965) in five-year cohors from years of age, o years of age. The age disribuion of female feriliy raes is no available for Canada prior o 1926, and as such, he age disribuion of feriliy raes is assumed fixed for he period of sudy o he 1926 disribuion. These feriliy raes were hen scaled o mach he crude birh rae esimaes of McInnis (1999a, 1999b) for he years 1871, 1881, 1891, 191, and The male-female spli among newborns is se o 1.5:1. 7 Survival and feriliy raes were assumed consan over all ages in each cohor group. The esimaes of he populaion during a census year were derived by solving he following equaion in order o approximae he populaion wihin a cohor group (µ c ) according o survival raes: µ c = µ i + µ i+1 + µ i+2 + µ i+3 + µ i+4 = µ i + s i µ i + s i+1 s i µ i + s i+2 s i+1 s i µ i + s i+3 s i+2 s i+1 s i µ (1) so ha, µ i = µ c / (1+ s i + s i+1 s i + s i+2 s i+1 s i + s i+3 s i+2 s i+1 s i ). (11) 12

14 In cerain cases (i = 1 being he mos noable case), he esimae for µ i+4 was lower han he esimae for µ i+5, he firs esimae of he subsequen cohor group. This appears o be an indicaion of underenumeraion (Coale and Zelnik (1963)). In order o derive esimaes of emigraion over he las half of he nineeenh cenury, a no ne migraion populaion process was firs modeled over en year inervals, beween census daes for he 1861 o 191 period. The process was calibraed wih moraliy, feriliy and crude birh rae esimaes a he end of he decade, and iniial census populaion saisics for he decade. The resuling enh year populaion under he naural increase scenario was hen compared o he corresponding census saisics of age and gender-specific cohor groups. For example, he 1861 iniial populaion disribuion was used o model he populaion for he years 1862 o 1871, hen he 1871 resuls were compared o he acual 1871 census figures. Emigraion was derived as a residual. Then, a rough esimae of average annual emigraion raes was consruced by modeling he populaion process wih boh naural increase and emigraion parameers unil he esimaes converged o he corresponding census figures. 8 The esimaed emigraion raes were generally consisen over he , , and census years for he working age populaion, and were used o generae he firs seady-sae populaion disribuion µ ss1, and ransiion marix Γ ss1. The emigraion raes derived by using his mehodology are presened in Figure 3. Some explanaion of he raes is in order. The emigraion raes for females of working age were higher han hose of males. This arises because in 1871 and 1881, here were more working age females han males, and in 1891 and 191, his was reversed as here were more working age males han females. Emigraion was concenraed in he 2-39 age cohors. 9 Immigraion raes were derived in a similar manner, bu were se o be uniformly increasing over he period o mach he increasing number of immigrans over he decade. For example, average immigraion raes for he inercensal period were scaled by 1/5 for he firs year, 2/5 for he 13

15 second and so on, unil he raes for he enh year were wo imes he average raes. The average raes were hen adjused by modeling he populaion from 191 ill 1911, under his scaling mehod, o correspond o he census figures of The resuling immigraion raes for he year 1911 were hen used o define he populaion ransiion marix Γ ss2. The raes used for he second seady-sae are presened in Figure 4. The feriliy and moraliy raes were kep a he 191 raes in consrucing he populaion ransiion marices, Γ ss1 and Γ ss2, for he model economy. The composiion of immigrans was skewed owards young working age males, who have he highes employmen raes in he populaion. In 191 here were 47 housand more males han females beween he ages of weny and hiry-nine. In 1911, he corresponding figure rose o 269 housand. The derived age-specific immigraion raes also indicae high immigraion among males aged 4 o 45 and females aged 35 o 4. This suppors he evidence presened by Troper (1972). American families wih adul children were selling heir farms while land prices in he US were rising. They migraed o Canada, and bough a series of neighboring farms o provide for heir grown and growing children. Tha way, families were able o say close ogeher Earnings and Employmen The age-earnings profile is adaped from Green and McKinnon (1997). They found lile difference beween he earnings profile of immigrans and naives in Torono in 191, and found ha he profile flaens ou afer abou hiry years of age. Earnings of hose over he age of 65 were se o niney-four percen of wages earned by hose beween he ages of hiry and sixy-four. 11 The age-earnings profile for females was se equal o half ha of males. 12 Age and gender-specific employmen raes were se o he 1921 esimaes in Urquhar and Buckley (1965). Employmen raes for men over fify-five years of age were adjused using he esimaes repored in Cosa (1998) for US males in 19, o allow for a 14

16 general decline in he raes. 13 Labor endowmen is calculaed as he produc of age and gender-specific employmen raes and earnings. These parameers are presened in Figure Preferences and Technology The values of β and σ were se o 1.11 and 1.12, following he esimaes esablished by Hurd (1989). The producion funcion is a sandard Cobb-Douglas wih he share o capial, α, se o.15. The value used by Green (1999) is.21 for he wenieh cenury as a whole. An esimae of α from Urquhar and Buckley (1965), by dividing he sum of corporae profis before axes, ineres and oher invesmen income, and capial cos allowances, by GNP, was.22 for 1926 and rises o.26 for 196. High values for α lead o high capial-oupu raios. Values higher han.16 cause he replacemen of depreciaed capial o exceed en percen of income. This would imply ha more han jus domesic savings in he period were needed o mainain he capial sock. Higher values for α also lead o excessively large values for gross domesic capial formaion. The parameer was se o.15 and generaes a raio of depreciaed capial o oupu of 8%. This is consisen wih he Green and Urquhar (1976) esimaes of depreciaion of beween eigh and nine percen of oupu over The value for g, echnological progress, is se o.185. The average annual growh rae in real GNP per worker over was 1.8% (Urquhar (1988)), and he average rae of growh in real wages over was 1.86% (Williamson (1998)). The average capial cos allowance as a proporion of gross indusry capial was abou six percen beween 1926 and Capial cos allowance also ranged from eigh o welve percen of oupu during his period (Urquhar and Buckley (1965: 13, 139)). Wih a capial-oupu raio of 3, his would amoun o an allowance of hree o four percen of capial. The wo model economies have a depreciaion rae of.32 wih he reurn o capial se o 2.8%. 14 The values for R and δ are calibraed 15

17 o provide reasonable gross domesic formaion raes and curren accoun balances, and o closely resemble he esimaes made by Urquhar (1988) before he change in migraion paerns Transiion The GE model was used o model he economy wih he populaion now o be described. A ime =19, he populaion disribuion is se equal o he firs seady-sae disribuion, µ ss1. For = 19-j, j>, he populaion is se o (Γ ss1 ) -j µ ss1. A ime =191, here is no ne migraion. Then, he immigraion process grows as described above from =192 o =1911. The raes for he 1912 and 1913 were calibraed o 1.1 imes he raes for 1911 (o coninue he general upward rend in migraion from 1911 o 1912), and hereafer migraion follows he process implied by Γ ss2, corresponding o he second seady-sae. The ne migraion figures from he model economy wih his migraion process, denoed Model Economy A, are compared o oher migraion esimaes in Figure 6. A second model economy, denoed Model Economy B, has a migraion ransiion where age and gender-specific migraion raes during he ransiion period are scaled in order o mach he overall ne migraion esimaes of Firesone (1958) over 191 o For example, he age and gender-specific migraion raes from Model Economy A, corresponding o he year 192, were muliplied by a facor of 3.1 o generae he raes for Model Economy B o mach he Firesone esimaes of overall ne migraion rae for 192. So, he migraion ransiion described by Model Economy A is a gradual one, wih migraion increasing over he period o correspond o he generally increasing paern in he official gross immigraion series over The migraion ransiion described by Model Economy B resembles ha implied by he Firesone ne migraion series from 191 o This is no mean o imply ha he Canadian economy was in a seady-sae in he years leading up o 191, nor was he economy in a seady-sae in 1911 or soon hereafer. However, in order o compue a migraion ransiion, seady-saes are needed as saring and ending poins. 15 The focus of 16

18 his exercise is o model a migraion ransiion similar o ha for Canada over , and examine he impac of his change on capial accumulaion. 4. Resuls The dynamic model produces several series ha will now be defined. Real naional income is se equal o oal labor income, ωl, plus he reurn on domesically held capial, (R-1)K d and will hereafer be simply referred o as naional income. Gross domesic capial formaion a ime is equal o he increase in he capial sock from ime o ime +1, plus depreciaed capial. The capial formaion rae is equal o gross domesic capial formaion divided by naional income. The domesic savings rae a ime is defined as he increase in he sock of domesically held capial from ime o ime +1, plus depreciaed capial, all divided by naional income a ime. The ne foreign capial inflow rae a ime is defined as he increase in foreign-held domesic capial (ne of domesically-held foreign capial) from ime o ime +1, divided by naional income a ime Seady-saes Firs, a descripion of he seady-saes defining he iniial and erminal condiions of he compued ransiions is in order. Table I provides a summary of he key model seady-sae resuls. Given he parameers se above, he model economies have a capial-oupu raio of 2.5. The firs seady-sae is characerized by an annual populaion growh rae of.4%. This is lower han he acual populaion growh rae of Canada over , due o he assumpion of consan survival and feriliy raes, se o he raes of 191, and o he difficulies in calibraing o census daa. The annual populaion growh rae in he second seady-sae, corresponding o a populaion ransiion as described by Γ ss2 is 3.5%. 17

19 The real income growh rae in he firs seady-sae is 2.3% per year, while he rae is 5.4% in he second seady-sae. These raes are equal o he growh rae in he populaion plus he growh rae in per capia income, in his case, he rae of echnological progress. The growh rae in per capia real income in boh seady-saes is 1.85%. The calculaed raes of capial accumulaion and domesic savings are gross raes, herefore include he replacemen of depreciaed capial. The raio of capial accumulaion o naional income is 15.4% and 27.2% in he firs and second seady-saes. This rise is due o he increased annual ne inflow of working age migrans in he second seady-sae compared o he firs. Capial requiremens are increased o equip hese migrans for producion, and for housing and oher social overhead needs. The domesic savings rae in he firs seady-sae is 12.7% of naional income, and 16.9% in he second seady-sae. The increase in he domesic savings rae does no mach ha of he capial formaion rae. Since migrans are primarily in he 2-45 age group, he capial requiremens o equip hem for producion and for he developmen of social infrasrucure ouweigh he supply from domesic sources. Domesic sources of invesmen funds canno mee he increased invesmen requiremens in he second seady-sae, and so he ne capial inflow rae rises from 2.7% in he firs seady-sae, o 1.3% in he second Transiional Dynamics The economies were hen modeled o generae he ransiion from he firs seady-sae equilibrium under he ne emigraion scenario, o he second seady-sae under he ne immigraion scenario. The period of ineres is he years of he ransiion in he model economies, corresponding o 1899 o 1911 for Canada. The sar dae of 1899 is chosen since he model economy ransiion begins in 191 and capial requiremens for producion in 191 mus be planned in 19. So, 1899 is he las period where formaion raes are unchanged from he previous period in he model economies. The migraion 18

20 ransiion described by Model Economy A is a gradual ransiion, wih migraion increasing over he period o correspond o he generally increasing paern in he official gross immigraion series over The migraion ransiion described by Model Economy B resembles ha implied by he Firesone (1958) ne migraion esimaes over (see Figure 6). The massive inflow of working age immigrans in he open economy framework has he impac on key economic variables as depiced in Figure 7. The model resuls show ha foreign capial inflows are more responsive o populaion movemens han domesic savings. Immigrans were primarily young aduls and young families, who generally hold lile capial. Young workers do no hold enough capial o supply hemselves in producion, nor o fully provide for he developmen of social infrasrucure. The gross domesic capial formaion, domesic savings and foreign capial inflow raes generaed by he model economies are compared o he acual Canadian raes in Figures 8, 9, and 1. The Canadian raes are smoohed by using hree-year cenered averages. This is done in order o reduce he sochasic yearo-year variaion in he acual series and o beer enable a comparison wih he deerminisic series generaed by he model economies. The upward rend in gross domesic capial formaion raes of he model economies are similar o he rend exhibied in he acual series as shown in Figure 8, however, for Model Economy B, he rae of capial formaion declines in 197 and is much lower han he acual rae hereafer. This is he resul of a fall in he ne migraion esimaes of Firesone. The gross domesic capial formaion rae in Canada increased by.16 over he period. The rae of he model economies increased by.12 and.6 for Economies A and B respecively over his decade. These resuls sugges ha up o 79% of he increase in he gross domesic capial formaion rae over can be aribued o a gradual migraion ransiion, bu only 36% would be due o a migraion ransiion implied by he Firesone esimaes (see Table II). 19

21 The Canadian domesic savings rae rose o 16% in The general increase in he rae from 1899 o 1911 was 3.9 percenage poins over he rae in The rae generaed by he model economies increased by 4.2 percenage poins for Model Economy A, and 2.7 percenage poins for Model Economy B from 1899 o These resuls, also presened in Table II, sugges he migraion ransiion in Canada can be responsible for beween hree-quarers and all of he oal increase in he domesic savings rae during he period of sudy. The Canadian foreign capial inflow rae is compared o ha of he model economies in Figure 1. The acual rae increased by 12.3 percenage poins during he period of sudy, while he rae for Model Economy A rose by 8.6 percenage poins, and he rae for Model Economy B rose by only 3.1 percenage poins. These resuls sugges a gradually increasing inflow of migrans can explain abou hree-quarers of he rise in he foreign capial inflow rae in Canada during he firs decade of he wenieh cenury (see Table II). However, by accouning for he ime paern of migraion implied by Firesone, only one-quarer of he rise in he rae can be aribued o he rise in ne migraion. The resuls generaed by model economies A and B are sensiive o he pah of migraion, however, boh generae he same level of oal capial sock a he end of he period in 1911 because he populaion is idenical in 1911 in boh cases. A comparison of he resuls from Model Economy B (using he ime pah of migraion implied by Firesone) wih he acual esimaes suggess ha foreign capial flows were delayed ino Canada. When ne migraion ailed off afer 197, foreign capial coninued o pour ino he counry consisen wih he gross immigraion flows in he laer half of he decade. By 1912, Canada was preparing for 4, immigrans in one year, an addiion of 5% o he populaion, and enough o calm fears a he ime ha oo much foreign capial was enering Canada (Field (1914: 237-8)). The resuls for Model Economy B, however, sugges oherwise. Emigran flows were no recorded a he ime, as i was easy for people o cross he border beween Canada and he US. While he Canadian economy was preparing for an increasing flow of immigrans, i was no preparing 2

22 for a corresponding increase in he flow of emigrans. As such, he model resuls sugges foreign capial inflows were sensiive o he percepion of coninued increasing immigraion wihou he expecaion of increasing emigraion. The resuls of he model economies during he period of ransiion give us an indicaion of he relaive amouns of immigran wealh brough ino he economy wih respec o foreign capial inflows. In he open economy environmen, he rise in he domesic savings rae is he resul of immigran wealh coming ino he counry and being held by new residens of he counry. 16 During he period, ne immigran receips amouned o $252 million. Cumulaed ne long-erm foreign capial inflows for he period were $2.1 billion (Urquhar (1993: Table 1.4)). The raio of immigran capial o ne foreign capial inflows for he period is.12. The corresponding raio for Model Economy A is.21, while ha for Model Economy B is.19. The model economy raios are higher because he model economies do no replicae he surge in foreign capial over The raio for Canada over is.17, more consisen wih he model economy resuls. Canada experienced a dramaic fall in immigraion wih he oubreak of World War I. Are he resuls sensiive o he assumpion of a coninued high rae of immigraion ino Canada? The answer is no for he pre-war period. A model economy wih migraion raes se o zero afer 1914 will exhibi a decline in he capial formaion rae, domesic savings rae and he foreign capial inflow rae, bu only afer During he period, hese raes vary no more han.1 percenage poins from he scenario wih a coninued immigraion process as defined by Model Economies A and B. The resuls during he sudy period are no sensiive o he assumpions of he second seady-sae populaion process in he open economy environmen, bu o he ransiion environmen iself. These resuls mus be reaed wih cauion. The acual Canadian series exhibi sochasic paerns, while he series generaed by he model economy are deerminisic. This makes a comparison enaive. The model does no capure he surge in he domesic savings rae ha occurred over

23 192. This was a period of recovery for Canada, as i pulled ou of a depression in he mid-189s. As such, his surge may be reflecing a business cycle. The model does perform well in explaining he role of changing migraion paerns and i s impac on he capial formaion rae, he domesic savings rae, and he foreign capial inflow rae. The resuls confirm he findings of Green and Sparks (1999) ha populaion innovaions were a significan facor in shifing up he growh pah of invesmen during he wo decades prior o WWI. The New World wih a younger populaion was relian on he Old World for capial. The ime paern of increased foreign capial flows coincides closely wih ha of rising annual immigraion. Since foreign invesmen in Canada was primarily in governmen and railroad securiies and oher populaion-sensiive invesmen, i appears ha populaion growh was he primary force in pulling in foreign capial. 17 This paper sheds ligh on he open quesion of how labor force growh, hrough immigraion, can accoun for massive capial inflows in he desinaion counry, while a he same ime, accoun for an increasing domesic savings rae. In he open economy environmen, he rise in he domesic savings rae is he resul of wealh coming ino he counry wih working-age immigrans, who are also ne savers in he economy. The domesic savings rae does no change as a resul of fundamenal changes in he consumpion-saving decision of individuals. 5. Conclusion A dynamic general equilibrium model is consruced o examine he impac of mass immigraion on capial accumulaion. The model is calibraed o mach Canadian demographic characerisics over During his period, Canada shifed from being a counry of ne emigraion, o one of ne immigraion, circa 1897, wih he prospec of profiable farming in he Prairies and he developmen of a ransconinenal economy. As a resul of modeling he Canadian populaion process over , I idenified age and gender-specific migraion paerns. The resuls indicaed ha emigrans over

24 191 were predominanly individuals beween he ages of 2 and 3, wih ne emigraion raes of females higher han hose of males. Resuls also indicaed ha immigraion over was predominanly concenraed among males aged 16 o 3 and 4 o 45, and females aged 16 o 25 and 35 o 4. Moreover, he rae of adul male ne immigraion was much higher han ha of adul females. The calibraed model was hen used o examine he impac of his shif in migraion on he domesic savings rae, and he foreign capial inflow rae. Model resuls sugges ha up o seveny-five percen of he rise in he capial formaion rae, and up o all of he rise in he domesic savings rae, in Canada over , can be aribued o he dramaic inflow of migrans over his period. The resuls also sugges an answer o he open quesion pu forh in Taylor and Williamson (1994): labor force growh, hrough immigraion, appears responsible for up o hree-quarers of he rise in he foreign capial inflow rae. The resuls confirm he findings of Green and Sparks (1999) ha populaion innovaions were a significan facor in shifing up he growh pah of invesmen during he wo decades prior o WWI. Model resuls have demonsraed how sensiive capial formaion is o he ime pah of migraion. I appears much of he dramaic rise in he gross domesic capial formaion rae and he foreign capial inflow rae were he resul of expecaions of a coninued upward rend in immigraion. The Canadian economy was no expecing a corresponding upward rend in emigraion. This paper has demonsraed he abiliy of a calibraed dynamic equilibrium model o assess he impac of changing migraion paerns on capial accumulaion. The resuls sugges direcions for furher research. This sudy reas labor movemen as exogenous, and capial as endogenous. Land and naural resources are reaed as exogenous and are incorporaed ino A, he parameer describing echnological progress in equaion (5). A naural quesion is: wha s exogenous? If one were o rea land and resources as exogenously given and capial and labor as endogenous, one would need o model boh labor and capial movemens as a resul of resource discovery and model hese implicaions on he reurns o labor and capial. In his sudy, his endowmen discovery is included in he growh rae 23

25 of echnological progress for Canada, given ha oupu per worker increased by 1.8% per annum in he firs decade of he wenieh cenury. 18 The Canadian populaion experienced an immigraion shock afer boh World Wars, along wih a baby boom in he pos-wwii period. The Canadian savings rae also surged following boh wars, accompanied by increases in foreign capial inflows. A dynamic GE model can be consruced o examine he impac of hese migraion shocks on world economies. More recenly, policymakers and economiss have been concerned wih he general decline in personal and aggregae savings raes in developed naions since he 197s. During his ime, social policies have become more widespread. Governmen pension and social securiy programs affec he life cycle savings moive of individuals, while unemploymen insurance programs affec he precauionary savings moive. The model presened in his paper can be adaped o examine hese insiuional changes and heir effec on capial accumulaion. Appendix 1: Compuaion of Equilibria A1.1. Solving for he Seady-sae The variables are ransformed as follows o remove he effecs of growh in he populaion and of echnology: ~ L ~ = L / L, K = K ~ / L A, T = T / A, a~ = a / A, c ~ = c / A, ~ ω = ω / A, ~ µ = µ / L, N ~ = N / L. As such, an agen s dynamic programming problem may now be described. An agen s sae is denoed by x = ( a ~, e, R ), producive capial asse holdings, labor endowmen and he inernaional risk-free reurn. The funcions for consumpion c ~ ( x, h ) and asse holdings a ~ ( x, h ) are opimal decision rules 24

26 ha solve he following dynamic programming problem, given ha in period I+1, he agen s value funcion is se o zero (V(x,I+1)=): ( ~ 1 σ V ( x, h) = max u c ) + β (1 + g) s ( c ~, a ~ ') h E( V ( x, i + 1, h) x) subjec o (1) c ~ ~ + (1 + g) a ~ Ra~ + ωe( h) + T (2) c ~, and a ~ for i=i. The addiional erm (1+g) 1-σ in he objecive funcion appears due o he ransformaion of he variables o remove growh. In he seady-sae, he ransformed variables for capial and labor inpus, for ransfers and for he age-disribuion of agens in he economy are consan over ime. The unransformed variables herefore all grow a consan raes. Definiion: A seady-sae open economy equilibrium is ( c ~ ( x, h ), a ~ ( x, h ), ~ ω, R, ~ K, ~ L, ~ T ) such ha: (1) c ~ ( x, h ), a ~ ( x, h ) are opimal decision rules; (2) Inpu markes are compeiive: ~ ω = F ( ~, ~ 2 K L) and R = 1+ F K 1, L ) δ, wih R se on inernaional markes, and here assumed consan; (3) The allocaions are feasible: ~ (i) Domesic asse holdings equal domesic capial K = Σ ~ µ ( h) a ~ ( h) /(1 ) ; d h + n (ii) Foreign capial is he difference beween oal capial and domesic capial: ~ ~ ~ K = K K ; f d 25

27 (iii) Domesic wealh plus new immigran wealh equals consumpion and nex period domesic asse holdings: ~~ ~ ωl + RK + Σ ~ µ ( h)( s( h) φ( h)) a ~ ( h) R = Σ ~ µ ( h) c ~ ( h) + Σ (1 + g) ~ µ ( h) a ~ ( d h h h h ~ (4) Effecive labor supply: L = Σ ~ i µ ( h) e( ) = 1;, h h (5) Transfers o he adul populaion equal accidenal bequess: ~ ~ T = Σ ~ µ ( h)(1 s( h)) Ra~ ( h) / N (1 ), where N a denoes he number of aduls in he i, h a + n seady-sae populaion. ) ; In order o compue he seady-sae of he model economy, he seady-sae age disribuion of his economy mus be derived. To do his, he eigenvalues and eigenvecors of he marix describing he law of moion of he populaion are compued. The larges eigenvalue of he marix Γ is equal o he seady-sae growh rae of he populaion. The seady-sae age disribuion of he populaion is defined by he produc µ* = Γ ~ b µ, where each elemen of Γ ~ is equal o he corresponding elemen of Γ scaled by is larges eigenvalue, and where b is sufficienly large so ha Γ ~ b+1 µ - Γ ~ b µ (). In he small open economy framework he reurn on capial is deermined on inernaional markes. Given he seady-sae age disribuion, he aggregae seady-sae capial sock is calculaed by solving he equaion ha defines he reurn on capial. Wages are se o he marginal produciviy of labor. Seady-sae equilibria are compued using he following algorihm: (1) Guess he value for he ransfer of accidenal bequess, T ~. (2) Calculae he opimal decision rules, c ~ ( x, h ), a ~ ( x, h ), of agens aged I w o I, wih he values of a ~ and ~ Iw 1 a I +1 se o zero. These rules are achieved by recursively solving a series of 26

28 second order difference equaions, from he Euler equaion of he opimizaion problem, of he following form: 1/ σ ~ (1 + g) ( Ra~ ~ (1 ) ~ i + T + ω ei + g ai+ 1) 1 σ 1/ σ ~ ~ ( β Rs (1 + g) ) ( Ra + T + ~ ω e i i+ 1 i+ 1 (1 + g) a ~ i+ 2 ) = (3) Calculae he value of T ~ implied by a ~ ( x, h ) from sep (2). (4) If he value of T ~ calculaed in sep (3) differs from he iniial guess in sep (1), repea he procedure using he resul from sep (3) as he iniial guess unil convergence is achieved. A1.2. Compuing he Transiion The mehod of compuing he ransiion is as follows: (1) Compue he sequence of vecors { } b+ µ = 1 1, given he calibraed populaion ransiion sequence and Γ ss2, he law of moion of populaion ha describes he second seady-sae. 1 (2) Guess a sequence of ransfers { + } =, wih T b 1 T < = T ss1, he level of ransfers in he firs 1 seady-sae, and T > b + = T ss2 1, he level of ransfers for he second seady-sae. 1 (3) Solve for he vecor of opimal asse holdings, sequence { 1 + } =, so ha he Euler equaions hold for all h, and. 1 (4) Compue he impued sequence of ransfers { 1 + } =, where T b 1 a b 1 T = Σ µ s R a / N where N w is he number of hose aged 2 and over. 1 h h, 1 ( 1 h ) h, 1 w T 1 (5) If { 1 + } b = = 1 { } b + T 1 seps (1)-(5) unil convergence. = hen sop, else updae he guess for he sequence of ransfers and repea 1 27

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