Catalogue no. F009MIE No. 82 ISSN: 205-953 ISBN: 0-662-392- Research Paper Effects of Selecton Crtera and Economc Opportuntes on the Characterstcs of Immgrants by Abdurrahman Aydemr Famly and Labour Studes Dvson 2-J, R.H. Coats Buldng, Ottawa, KA 0T6 Telephone: 800 263-36 Ths paper represents the vews of the author and does not necessarly reflect the opnons of Statstcs Canada.
Effects of Selecton Crtera and Economc Opportuntes on the Characterstcs of Immgrants by Abdurrahman Aydemr No. 82 F009 No. 82 ISSN: 205-953 ISBN: 0-662-392- Famly and Labour Studes and Department of Economcs The Unversty of Western Ontaro Ottawa, Ontaro KA 0T6 How to obtan more nformaton: Natonal nqures lne: 800 263-36 E-Mal nqures: nfostats@statcan.ca October 2002 I would lke to extend my grattude to the members of my thess commttee: Professors James B. Daves, Chrs Robnson and Jeffrey Smth for ther advce. I would especally lke to thank my supervsor Professor Chrs Robnson for hs contnued support. I benefted from dscussons wth Audra Bowlus, James Heckman, Kevn Lang, Costas Meghr and Todd Stnebrckner, from comments of semnar partcpants at UWO, McMaster Unversty, U. of Vctora and U. Mane and from the comments of an anonymous referee. I would lke to thank the Famly and Labour Studes Dvson for ts fnancal support under a Statstcs Canada Research Stpend, and the Housng, Famly and Socal Statstcs Dvson for data support, especally Jane Badets, Peter Smth and Derrck Thomas. Ths paper represents the vews of the author and does not necessarly reflect the opnon of Statstcs Canada. Auss dsponble en franças Research Paper
Table of Contents. Introducton... 2. The Model... 2. Step () - The Decson to Apply (Applcaton)... 2.2 Step (2) - Host Country Chooses from the Pool of Applcants (Revew)...6 2.3 Estmaton of Parameters from the Two Steps...7 2. Specfcaton of the Frst and Second Selecton Indces...0 3. The Data...2. Estmaton of the Reduced Form Model...5. Reduced Form One-Step Model...5.2 Estmaton of the Reduced Form Model for Two-Step Mgraton Process...6.3 Polcy Analyss Usng Reduced Form Two-Step Model...20 5. Conclusons...2 Appendx - Immgraton Polcy of Canada...33 References...35
ABSTRACT Internatonal mgraton s a jont outcome of ndvdual s desre to mgrate and the host country s selecton process. The theoretcal focus of the earler lterature was just on the desre to mgrate, and the emprcal lterature focused on who actually mgrates, whch s the product of these two factors. The objectve of ths paper s to dentfy the components of ths two-step decson makng process by ncorporatng them n a model of mgraton that nvolves two steps. In the frst step potental mgrants apply to a host country and n the second step the host country chooses mgrants from the applcant pool. Parameters n the model relate drectly to polcy nstruments such as the ponts awarded for varous characterstcs. Gven the parameter estmates of the model, general analyss of mmgraton polcy, an analyss of the factors determnng the decson of ndvduals to apply can be done n a way that htherto has not been possble. Usng samples of mgrants and non-mgrants, the model s estmated for mgraton from two dfferent source countres, the U.S. and the U.K., to Canada. For mgrants a newly avalable longtudnal data set the Longtudnal Immgraton Database (IMDB) s used. The rchness of ths database, whch follows mmgrants to Canada over a long perod and contans nformaton on both ther applcaton and subsequent earnngs, permts the nvestgaton of a large range of questons that could not be frutfully addressed before. Estmaton of the two-step framework provdes mportant nsghts on the effects of the factors that determne the two steps. For example, for both source countres, more educated are more lkely to be observed as mgrants, a fact that can be observed from a smple probt. However, the two-step method shows that, n contrast to those from the U.K., hgher educated ndvduals from the U.S. are less lkely to apply, but because of the polcy stage the resultng mgrants are more educated. Ths may be related to returns to educaton n the varous countres, whch has to be nvestgated n future. The host country s selecton s also found to have sgnfcant mpact on characterstcs of the mmgrants. Ths result ndcates that parameters determnng the desre of ndvduals to mgrate cannot be properly dentfed wthout takng nto account the mpact of selecton by the host country. Further analyss wthn ths framework can address ssues such as the effect of changes n the polcy structure on mgraton outcomes, the effects of polces that ndrectly affect mgraton va effects on net-of-tax wage rates. Keywords: mmgraton, self-selecton, ponts system, bvarate probt, partal observablty JEL: J6, J68
. INTRODUCTION There are two related questons of nterest when studyng nternatonal labour mgraton n the context of an mmgrant recevng country. The frst one s the mpact of mmgraton on the economy, whle the second one addresses the ssue of how to set the level and composton of mmgrants. Ths study focuses on the second ssue. The am of ths paper s to understand the factors that nduce ndvduals to decde to mgrate n an nternatonal context whch determnes the pool of applcants for mmgraton, and the effect of selecton of mmgrants by the host country, and hence the effect of mmgraton polcy, on the observed characterstcs of mgrants. There s a large body of lterature studyng nternal mgraton that s free of any constrants mposed by mmgraton polcy as mgraton wthn a country s not restrcted. However, n an nternatonal context both the selecton of mgrants by the host country and the decson of ndvduals to mgrate jontly determne the characterstcs of mmgrant flows. Therefore, understandng the determnants of nternatonal mgraton requres takng nto account both of these factors. Immgrant recevng countres try to select the hgh qualty mgrants n the mmgrant pool who possess sklls that are n hgh demand n the host country. Ths s acheved through mmgraton polces that am to control the skll dstrbuton of ncomng mgrants. For example, under the current Canadan regulatons, non-refugee mmgrants are allocated to one of three broad admsson classes: famly class, ndependent class and asssted relatve class. Applcatons under ndependent and asssted relatve classes are assessed by a "pont system". Ponts are awarded to applcants based on personal characterstcs assumed to be assocated wth short and long run adaptaton to the Canadan economy such as educaton, age, experence, and the demand for the ntended occupaton of the applcant. Other major mmgrant recevng countres such as the Unted States and Australa also have polces that am to control the skll dstrbuton of mgrants. Australa has a system smlar to the Canadan pont system. Although the Unted States does not have a pont system, employers try to attract sklled mmgrants through specal vsas allocated to dfferent ndustres that have demand for sklled workers. Controllng the sze and skll dstrbuton of mgrants became a major polcy debate n the European Unon as a result of ncreasng mgraton between member countres as well as mgraton from non-member countres to the European Unon. Immgraton polces adopted by mmgrant recevng countres such as the ones dscussed above have potentally sgnfcant mpacts on the mmgraton outcomes. It s, therefore, of major mportance to estmate the mpact of polcy parameters on mmgraton. The earler theoretcal lterature studes the desre to mgrate, whle the focus of the emprcal lterature was on ether who actually mgrates or the mpact of mmgraton polcy. Both the Appendx provdes further nformaton about the Canadan Immgraton Polcy and the pont system as of 986-990 perod. Analytcal Studes Branch Research Paper Seres - - Statstcs Canada No. F009 No. 82
theoretcal work 2 and the emprcal work 3 on the determnants of nternatonal mgraton gnore the mpact of the host country s mmgraton polcy on mmgraton outcomes. Lucas (985) tres to assess the mpact of ndvdual characterstcs on who emgrates. Borjas (987) developed a self-selecton model of mgraton based on the model of Roy (95) that has been used extensvely n the lterature. Ths model assesses the mpact of ncome nequalty n the source countres on the skll content of mgrants controllng for source country-specfc aggregate varables that portray the poltcal and economc condtons. Startng wth Borjas (987), mplcatons of the Roy model were tested by varous studes that yelded conflctng results. Greenwood and McDowell (99), and Cobb-Clark (993) note that mmgraton polcy s not taken nto account n ths lterature and they nclude varables n ther reduced form equatons on an ad hoc bass tryng to capture these effects. Ther results suggest that mmgraton polcy s mportant n determnng observed outcomes. The other lne of emprcal research focuses on mmgraton polcy n an attempt to dentfy the effects of polcy on the skll levels of mgrants. There are two approaches n studes of polcy effectveness. The frst approach (e.g. Green and Green, 995) focuses on a sngle mmgrant recevng country, and dentfes perods of dfferent mmgraton polces. Varatons n the level and composton of mmgraton are attrbuted to the polcy changes. Although ths approach can control for the changng natonal orgn mx of mmgrants over dfferent perods, t s not possble to dentfy the ndvdual effects of the polcy changes from the changes n ncentves to mgrate. The second approach (e.g. Borjas, 993) studes mmgrant recevng countres that dffer n ther polces and attrbutes dfferences n outcomes to the dfferent mmgraton polces. In ths approach, usually censuses for each country are used, resultng n mmgrants who entered a country under qute dfferent polcy regmes beng napproprately combned together. Also, n census data due to absence of nformaton on the class of admsson of mmgrants conclusons cannot be drawn on specfc parts of the mmgraton polcy (e.g. the pont system n a Canadan context). Ths study establshes a framework that specfes mgraton as a two step process: Step () Applcaton: Potental mgrants apply to mgrate to a host country. Step (2) Revew: The host country chooses mgrants from the applcant pool. 2 For a revew of theoretcal models of mgraton see Bauer T. and K. F. Zmmerman (995), Massey et al. (993, 99). 3 See Lucas (985), O Grada (986), Taylor (986), Adams (993). The context of mmgraton s from less developed countres (LDC) to ether developed countres or to another LDC. Borjas (987) and Borjas (993) focus on mgraton to the U.S. from dfferent source countres. Ramos (992), Ortz (986), Rvera-Batz (989), Guterrez (983), Sands (973), Hernandez-Alvarez (967), Senor and Watkns (975), Fredlander (965), Melendez (99) focus on mgraton between Puerto Rco and the U.S. Papers before Borjas (987) are mostly motvated by the early bran dran lterature. Because Puerto Rcans are U.S. ctzens and can therefore move freely between the two "countres", sze and composton of mgrant flows can, n effect, be attrbuted entrely to dfferences n socal and economc factors between the sendng and recevng regons. Analytcal Studes Branch Research Paper Seres - 2 - Statstcs Canada No. F009 No.82
The observed dfferences n characterstcs of mmgrant flows across tme and across source countres n terms of skll content, age and occupatonal dstrbutons may be attrbuted to dfferent ncentves avalable to ndvduals n source and host countres that affect ther desre to mgrate or they may be a result of changng selecton rules of the host country. Wthn the twostep framework of ths study the mpacts of these factors determnng the two steps can be dentfed separately. Ths allows for predctng the effect of changng ncentves or changes n demographc factors such as a change n age dstrbuton on characterstcs of applcants from a source country. Gven a pool of applcants, the mpacts of dfferent selecton rules can also be predcted. The focus of the prevous emprcal lterature on who actually mgrates, whch s the product of applcaton and revew decsons, has two major drawbacks. Frst, t precludes analyss of the effects of mmgraton polcy on mgraton when changes n polcy are accompaned wth changng ncentves to mgrate. Second, by abstractng from the two step structure dentfcaton of the structural parameters of the applcaton step and revew step becomes mpossble. In the two-step framework of ths study, usng the selectvty-corrected returns to varous characterstcs for mgrants and non-mgrants, the opportunty wages of ndvduals, that s, the wages of mgrants had they stayed and non-mgrants had they mgrated can be estmated. Ths allows the estmaton of the responsveness of the ndvdual s desre to mgrate to the expected returns. The effects of polces that ndrectly affect mgraton va effects on net of tax wage rates can also be addressed. The model s estmated by poolng samples of male mgrants and non-mgrants, usng the U.K. and the U.S. Census data for non-mgrants and a new data set of mgrants to Canada, the Longtudnal Immgraton Database (IMDB). These data permt the nvestgaton of a large range of questons that could not be frutfully addressed wth the prevously exstng data. In the IMDB, nformaton on characterstcs such as educaton s avalable at the tme of entry to the country, and also mgrants earnngs are traced through ther ncome tax returns, whch permts better estmates of lfetme ncome. It s also possble to dstngush the class of admsson of mmgrants. These features of the new data set allow a better treatment of selecton ssues and better measures of polcy tools. The tradtonal lterature on mgraton concentrated prmarly on the movement from less developed countres to developed countres. More recently mgraton between developed countres has become an mportant ssue. Estmatng the underlyng parameters of the decsons leadng to ths ever-ncreasng labour flow s therefore of major theoretcal and polcy nterest. The U.S. and the U.K. are major mmgrant source countres that provde sklled workers to Canada. Studyng these two countres also has the advantage of more readly avalable data on non-mgrants. Estmaton of the two-step framework provdes mportant nsghts on the effects of the factors that determne the two steps. For example, for both source countres, more educated are more lkely to be observed as mgrants a fact that can be observed from a smple probt. However, the two-step method shows that, n contrast to those from the U.K., hgher educated ndvduals from the U.S. are less lkely to apply, but because of the polcy stage the resultng mgrants are more educated. Ths may be related to returns to educaton n the varous countres, whch has to be nvestgated n future. The host country's selecton s also found to have sgnfcant mpact on characterstcs of the mmgrants. Ths result ndcates that parameters determnng the desre of Analytcal Studes Branch Research Paper Seres - 3 - Statstcs Canada No. F009 No.82
ndvduals to mgrate cannot be properly dentfed wthout takng nto account the mpact of selecton by the host country. In the next secton, the theoretcal model of ths study s outlned. Estmaton ssues are dscussed along wth a descrpton of the econometrc framework. Secton 3 descrbes the relevant characterstcs of the data utlzed. Secton presents the emprcal fndngs from the reduced form estmaton. Secton 5 concludes. 2. THE MODEL 2. Step ()- The Decson to Apply (Applcaton) Consder the choce problem for an ndvdual located n the source country (country 2) and consderng mgraton to the host country (country ). Assume, as n the exstng lterature, that the decson can be represented as a utlty maxmzng problem over the lfetme and that monetary equvalents can be used. The ndvdual then apples f the expected gan exceeds the applcaton cost, C a. The expected gan s the dfference between the expected ncome f the ndvdual apples and that expected f the ndvdual does not apply takng nto account movng costs. If the ndvdual apples, the applcaton s successful wth probablty P a. If the applcaton s successful, the mgrant receves an earnngs stream n the host country wth present value w and ncurs movng costs, C m. If the applcaton s unsuccessful the mgrant receves an earnngs stream n the source country wth present value w 2. The expected ncome f the ndvdual apples s thus: a P ( w -C m ) + (- a P ) w 2 The expected ncome f the ndvdual does not apply s smply, applyng s thus: a a P ( w -C m ) + (- P ) w 2 - w 2 w 2. The expected gan from Potental mgrants hence apply f: a P ( w -C m ) + (- a P ) w 2 - w 2 > C a () ( ) a P ( w - w 2 - C m ) > C a (2) If C = 0, the crteron reduces to: a ( w - w 2 - C m ) > 0 (3) Analytcal Studes Branch Research Paper Seres - - Statstcs Canada No. F009 No.82
a for non-zero P. The cost of applcaton C a, s ncurred at the tme of the applcaton. Ths s a varable cost dependng on the number of dependents and does not nclude costs of movng, foregone earnngs etc. whch are ncluded n C m. C a s generally small relatve to the lfetme w s and s assumed to equal zero n the rest of the analyss. 5 Thus, from (3), the probablty of an ndvdual makng an applcaton for mgraton depends postvely on the permanent ncome level he expects n the host country, and negatvely on hs permanent ncome level n the source country and the movng costs. The movng costs nclude travel expenses, foregone earnngs whle movng and also psychologcal costs of movement. The returns and costs dffer for each ndvdual as they depend on ndvdual characterstcs such as age, schoolng, gender, etc. Followng the prevous lterature, let 6 C m = cm where cm 0 and usng the approxmaton ln( + c) c (for small values of c ), rewrte the equvalent crteron for applyng as: w 2 ln w ln w c > 0 2 m Let the present value of log lfetme earnngs n the two countres be represented by the followng lnear functons: ln ln w X β + ε w2 X 2β 2 + ε 2 = (.) = (.2) And let cm X 3 β 3 + ε 3 = (5) where the X s are observable and the ε s are unobservable to the econometrcan. The β coeffcents represent the structural parameters of nterest n the applcaton step. 5 The assumpton of C a = 0 rules out any effect of revew by host country on applcaton decson. Relaxaton of ths ndependence assumpton can only be done wth more nformaton on costs and changes n the model, and s left for future research. 6 Robnson and Tomes (980) gve theoretcal and emprcal justfcaton for ths assumpton. One justfcaton s that the cost of mgraton s proportonal to the source country permanent ncome due to the exstence of source country specfc nvestment and/or endowments. The lnear specfcaton C m = cm w 2 follows from the convenence of functonal form. Analytcal Studes Branch Research Paper Seres - 5 - Statstcs Canada No. F009 No.82
Next, defne the followng ndex: I * = X + ε X 2β 2 ε 2 X 3β 3 ε 3 β W π + ε (6) so that the crteron for step () s * I > 0, orε > Wπ. Ths can be estmated as a structural ndex f the separate terms X β, X 2 β 2 and X 3 β 3 can be measured, and the β coeffcents can be recovered under certan condtons (dscussed later). * Otherwse we have to work wth the reduced form ndex I π + ε and estmate π. 7,8 W 2.2 Step (2) - Host Country Chooses from the Pool of Applcants (Revew) We assume that host countres have mmgraton polces that characterze the revew step. Ths results n a mechansm for choosng mmgrants from the pool of applcants. Assume that ths mechansm can be represented by the ndex where parameters and I = X β + ε > 0 (7) * 2 X are observable characterstcs of the potental mmgrant and any measurable polcy ε are unobservable to the econometrcan. 9 In the Canadan pont system, f an ndvdual gets a suffcent number of ponts (whch s constant for all applcants n an admsson category) then admsson s granted to the ndvdual. Ponts for relevant characterstcs are determned and added together to fnd the total number of ponts an ndvdual gets. For example, as of 990 an ndvdual gets 6 ponts f 9 years old, 8 ponts f 20 years old and 0 ponts f the age s between 2-. One of the sources of uncertanty leadng to ε s the extra ponts generated as a result of the assessment of the applcant by the mmgraton offcer. The mplct assumpton n the above specfcaton of the selecton ndex * I 2 s that ε s not correlated wth X. If the mgraton offcer tends to gve hgher ponts for "personal sutablty" 7 Earler lterature on nternatonal mgraton estmates the reduced form ndex Y W π + ε s f an ndvdual mgrates, 0 otherwse. Later n the text, ths model s referred to as Reduced Form One-Step Model. 8 The decson makng for applyng for mgraton n ths paper s at the ndvdual level rather than beng at the famly level because the data on mgrants doesn t nclude nformaton that allows to dentfy any famles. 9 The specfcaton of the selecton ndex depends on the context of the study. In the Canadan context, the pont system can be approxmated by such an ndex. In other cases where reasonable approxmatons are not possble, one may wsh to dentfy a structure f there s enough nformaton on the process. Where estmaton of structural ndces s not possble, a reduced form model can be utlzed. Analytcal Studes Branch Research Paper Seres - 6 - Statstcs Canada No. F009 No.82
to the applcants who are close to the threshold value n the pont system, ths rases a potental non-zero correlaton between ε and X. However, snce the story can be told n the opposte drecton, t s not possble a pror to determne the sgn of ths potental correlaton. Usng the dstrbuton of pont scores, the correlaton between ε and ndvdual components of X as well as the total number ponts obtaned from X are nvestgated and no sgnfcant correlaton s found. 2.3 Estmaton of Parameters from the Two Steps Gven the above formulaton, we can consder the ndvdual and the host country as two decson makers ( j =,2), each faced wth a bnary choce I = 0,. Let j * I j = f I j > 0 = 0 otherwse Each ndvdual s decson corresponds to a unvarate probt model (f we assume normalty for ε s), and the two decsons taken together correspond to a bvarate probt model. I = f the ndvdual apples and I f the ndvdual s accepted. = 2 Full observablty corresponds to the case where for every ndvdual whether that ndvdual appled or not, and what decson s made by the host country for each ndvdual applcant, can be observed. Gven a random sample ( I, I 2 W, X ), ( =,2,..., n), f the usual dentfcaton condtons hold (e.g. one of the vectors ( W or X ) excludes at least one exogenous varable appearng n the other vector) and subject to a normalzaton rule n each equaton, π and β are dentfed (Heckman, 976, 978; Amemya, 978). Under certan condtons the structural parameters of the applcaton step can be estmated. In the case consdered here the choces I and I 2 cannot be fully observed. For example, those who appled but were turned down s not known. The only nformaton avalable s who actually mgrated (that s who appled and was admtted) and who dd not. Ths leads to the partal observablty framework of Porer (980). Followng Porer, partal observablty can be represented by the sngle bnary random varable Z = I * I 2 =,2,..., n Z = ff I = I 2 =, that s f the ndvdual mgrates and zero f not. Thus Z s the observed mgraton varable and the probablty of mgraton s the jont probablty: ( I, I = ) = Pr( I = I = ) Pr( I = ) = Pr( Z ) Pr 2 2 = = Thus, the probablty dstrbuton of Z s: Analytcal Studes Branch Research Paper Seres - 7 - Statstcs Canada No. F009 No.82
Pr Pr m ( Z = ) = Pr( I = and I 2 = ) P m ( Z = 0) = Pr( I = 0 or I = 0) = Pr( I = and I = ) = P 2 Gven a random sample of observatons on Z, the log lkelhood for the sample can be specfed gven dstrbutonal assumptons on the ε s. Assume that each ndvdual n the source country draws a realzaton of the par ( ε,ε ) from the bvarate normal dstrbuton ( ε ε, ρ) ε. 0 g,, where ρ s the correlaton between ε and Gven a random sample of observatons ( Z W X )(,2 n) sample s: L n =,..., 2, =, the log lkelhood for the ( π, β, ρ) = { Z lng( W π, X β ; ρ) + ( Z ) ln[ G( W π, X β ; ρ) ]} (8) Lettng θ = [ π, β ρ ],, the parameter vector θ s to be estmated. The lkelhood functon presented above n (8) presupposes an exogenous samplng process Z of ther where a sequence of ndvduals are drawn at random and the jont outcomes ( ) choces over applcaton and the host country s decson over grantng admsson are observed. In contrast, a choce-based samplng process s one where a sequence of chosen alternatves are drawn and the characterstcs of the decson makers selectng those alternatves are observed (Mansk and Lerman, 977). In choce-based samples the usual ML estmates wll mpart some bases n estmated parameters. Mansk and Lerman ntroduced an alternatve estmator for these cases whch provdes consstent estmators. Ths method modfes the famlar ML estmator by weghtng each observaton s contrbuton to the log-lkelhood functon. If the outcome assocated wth observaton n s the alternatve, that s mgrant or non-mgrant, then the weght mposed s () H() Q, where Q () s the fracton of the decson-makng populaton wth outcome and H () s the fracton for the choce-based sample. Ths method assumes that the analyst knows these two fractons. 0 Varous assumptons regardng components of ε and ε that are known to the ndvdual but unknown to the econometrcan can be made. For example, ε may contan some personal characterstcs unobserved to the econometrcan, but known to the applcant that are relevant for the ponts system n addton to a subjectve assessment component by the partcular mmgraton offcer that s unknown to the potental mgrant and not revealed untl the applcaton process has occurred. Compared to the case wth fully observed choces, the maxmum lkelhood estmates from (8) wll be neffcent (Porer, 980). Also, ssue of dentfcaton arses whch s dscussed later n the text. Analytcal Studes Branch Research Paper Seres - 8 - Statstcs Canada No. F009 No.82
Choce-based samplng s relevant n ths study for the subpopulatons of those who mgrate and those who do not. The model s estmated wth approprate weghts for choce-based samplng. 2 m The weght for a mgrant ( ) a s equal to the fracton of mgrants n a certan group (such as males, aged 8 to 65) n source country populaton over the fracton of mgrants n the sample nm a s calculated (wth prevous restrctons) used for estmaton. The weght for a non-mgrant ( ) smlarly. The data provde the number of mgrants from a source country over a perod of tme. Gven the sze of the source country populaton the weghts can be calculated. The lkelhood functon takng nto account choce-based samplng becomes: L n = { } (8 ) m nm ( π, β, ρ) = Z a lng( W π, X β ; ρ) + ( Z ) a ln[ G( W π, X β ; ρ) ] For dentfcaton of π and β at least one varable n W s requred not to be n X or vce versa (Porer, 980). Estmaton of π and β s referred as "reduced form estmaton" n the rest of the text. Estmaton of the parameters of the applcaton step β, β 2 and β 3, along wth β s referred to as "structural estmaton". A 3-step estmaton procedure s suggested to obtan consstent estmates of β s. Ths method s an extenson of the Heckman 2-stage method for sample selectvty. The earnngs functons cannot be estmated for all ndvduals orgnally resdent n the source country. For the mgrants we observe ln w and for the stayng we observe ln w 2. Estmaton of the earnngs equatons requres takng nto account the double selecton process. Equaton (.) s estmated on the sample of mgrants: * * E ln w Z = = E ln w I 0 and I2 0 > > X E I 0 and I 0 9 * * = β+ ε > 2 > Equaton (.2), on the other hand, must be estmated on the sample of stayers: [ w Z 0] = X β + E[ ε Z 0] (0) E ln 2 2 2 2 = = () where * * ( 2 ) * * ( > 0 2 < 0) * * ( I < 0 and I2 < 0) Z = 0 f I < 0 and I > 0 or I and I or 2 Choce-based samplng also requres a correcton for the standard errors. The correct standard errors for the choce-based samplng are calculated and reported later n the text wth the parameter estmates. Analytcal Studes Branch Research Paper Seres - 9 - Statstcs Canada No. F009 No.82
To get consstent parameter estmates, Heckman s (979) two stage procedure for a sngle selecton rule has to be extended to two selecton rules. 3 The consequences of partal observablty of the type dscussed above are essentally two-fold. Frst, the maxmum lkelhood estmators obtaned from (8 FRPSDUHGWRWKRVHREWDLQHGLQWKH case of fully observed choces, are neffcent. The extent of effcency loss cannot be addressed wthout reference to a partcular data set. Second, dentfcaton problems arse that were dscussed earler. 2. Specfcaton of the Frst and Second Selecton Indces The earnngs functons for the two countres follow the sem-log form proposed by Mncer (97): ln w = j X j β + ε j j where X j = {schoolng, degree, experence, language, tranng} and hgher order terms n experence. The language varable s n general mportant n a Canadan context. However, t s omtted n ths study snce the focus s on mgraton from the U.S. and the U.K. to Canada and mgrants destned to the French speakng provnce of Quebec are excluded. Data reveal that mgrants from the U.S. and the U.K. who have French language sklls or those who are blngual are almost always destned to Quebec. Remanng mgrants from the U.S. and the U.K. destned to elsewhere n Canada are ether natve Englsh speakers or speak Englsh very well. Snce there s no nformaton on tranng n the data sets ths varable s also omtted. The varables ε and ε 2 nclude general unobserved ablty and unobserved country specfc captal. It s assumed that, over the entre populaton of ndvduals ntally located n the source country, ε and ε 2 have zero means, varances σ, σ 22 and covarance σ 2. No restrctons are mposed on the sgn of σ 2. If unobserved sklls that make an ndvdual more productve n the source country also make an ndvdual more productve n the host country, then σ 2 > 0 (vewng unobserved sklls as undmensonal); a theory of comparatve advantage wth multdmensonal unobserved sklls would permt σ 2 < 0 (Robnson and Tomes, 982). The 3 Catsaps and Robnson (982) extend Heckman s procedure to cases wth multple selecton rules where they assume full observablty on I and I. Consstent parameter estmates are obtaned by addng correcton terms n * * 2 an ordnary least squares (OLS) regresson. Tunal (986), dscusses estmaton under varous assumptons of observablty. There s a techncal appendx that gves the detals of the proposed 3-step estmaton method for the case of partal observablty that s avalable from the author upon request. Analytcal Studes Branch Research Paper Seres - 0 - Statstcs Canada No. F009 No.82
parameters β and β 2 are not constraned to be equal, allowng rates of return for each characterstc to vary by country. For example, the locaton where the hghest degree and tranng are completed can be mportant n the mmgraton context. Due to the lack of nformaton on the qualty of educaton acqured n dfferent source countres, prospectve employers at the source and host countres may value the same number of years of schoolng dfferently. The factor of proportonalty c m s gven by: cm = X 3 β 3 + ε 3 where X 3 ={famly sze, language, martal status, schoolng} ε 3 ={unobservable cost components} ε 3 s assumed to have zero mean, varance σ 33 and covarances σ 23, σ 3. It s argued that the presence of chldren, due to changng schools, etc., nhbts mgraton. Also, there s emprcal evdence that the exstence of a spouse ncreases costs of mgraton (Mncer, 978). Schoolng and language are hypotheszed to reduce the nformaton costs va better nformaton and job prospects and lower the cost of movng. Agan n the U.S.-Canada and the U.K.-Canada context the language varable s dropped. Gven the above specfcatons for X, X 2, X 3 and replacng experence wth age n the reduced form estmaton, W n (6) s gven by: W ={schoolng, degree, age, famly sze, martal status} The second selecton ndex s represented as: * I 2 = X β + ε where X ={schoolng, age, occupaton, degree} ε ={unobservable components affectng admsson} The varables n X correspond to the characterstcs evaluated n the pont system. More educated ndvduals get hgher ponts. In general, applcants n whte-collar occupatons (Executve and Admnstratve, Professonal Specalty, Teachng and Related Occupatons) are awarded hgher ponts compared to those n sales and blue collar occupatons. Those who have arranged employment are more lkely to be admtted as they are awarded extra ponts. It s assumed that the probablty of havng arranged employment depends on occupaton, experence and degree. Younger applcants get hgher ponts under the age factor, whereas older applcants who are relatvely more experenced are awarded hgher ponts under the experence factor. An Analytcal Studes Branch Research Paper Seres - - Statstcs Canada No. F009 No.82
dentfcaton problem arses f experence, age and schoolng are entered smultaneously snce experence s calculated as (age (- )years of schoolng (-) 6). The personal sutablty factor whch s determned by the mmgraton offcer at an ntervew, factors that affect arranged employment that can not be captured by the characterstcs n X, such as motvaton, other factors such as medcal condton preventng admsson of an applcant, etc. contrbute to the error term n the second selecton ndex. The mean of the personal sutablty and arranged employment ponts are captured n the ntercept term. The remanng error component s assumed to have zero mean and constant varance over the populaton of the source country. 3. THE DATA The reduced form model s estmated on pooled samples of mgrants and non-mgrants from the U.S. to Canada and the U.K. to Canada. For estmaton of the model, a sample n the source country at tme t would deally need to be observed. Then the same sample would be observed at a later date t 2 to dentfy those who mgrated and those who ddn t, where the latter group s composed of people who ether ddn t apply to the host country for mgraton or appled but were rejected. Such a sample doesn t exst snce source countres don t keep track of people leavng the country and host countres are only nterested n who gets n rather than who s left out. Ths s a major dffculty for studes of nternatonal mgraton. In ths study we set t to 986 and t 2 to 990. Usng Canadan data we obtan a sample of ndvduals who appled from the source country startng n 986 untl the end of 990 and who are accepted by the host country. Ths forms the mgrant sample. The non-mgrant samples are drawn from the 990 U.S. Census and the 99 U.K. Census. The mgrant and non-mgrant samples for a gven source country are then pooled together whch results n the choce based sample used for estmaton of the model. The model s then estmated for the U.S. and the U.K. separately. Immgrant samples used n the reduced form estmaton are obtaned by matchng the Landngs Records (LIDS) wth the admnstratve fle on mgrants, the Immgraton Data System Overseas (IDSO). For the estmaton of the structural model, mgrant records are obtaned from the Longtudnal Immgraton Database (IMDB) whch matches mgrant records n the LIDS wth the earnngs nformaton n tax fles. As data sets from dfferent countres are used, several data avalablty/comparablty ssues arse that are dscussed below. A concern here s that n the census data, e.g. n the 990 U.S. Census, there may be ndvduals who appled, say, n 989 and have not mgrated by the census date because ther applcaton s not fnalzed. However, gven the small number of people mgratng from the source country to Canada relatve to the sze of the source country populaton, the number of such people n the non-mgrant sample and the resultng contamnaton bas s neglgble. Analytcal Studes Branch Research Paper Seres - 2 - Statstcs Canada No. F009 No.82
In LIDS each landng record contans demographc data (e.g. age, martal status, last permanent resdence), program data (mmgrant category, specal program codes, prncpal applcant code) and personal characterstcs (ntended occupaton, years of schoolng, level of educaton, selfassessed knowledge of an offcal language). These data are recorded as of the date of ssue of the landng vsa and are avalable for all landngs n Canada. The IMDB combnes nformaton from landng records of mmgrants wth nformaton recorded on the personal ncome tax returns (T). Tax returns provde nformaton on employment earnngs, UI benefts, self-employment earnngs and, snce 992, ncome assstance data. The database currently covers the perod 980 to 995. 5 IDSO provdes the ponts awarded to prncpal applcants for each characterstc assessed under the pont system. It also provdes other admnstratve nformaton such as the date the applcaton was receved, and the date of landng. The dstngushng features of the IMDB, LIDS and IDSO are the ncluson of mmgrant class/category, the specal program codes, the prncpal applcant codes, the ponts and the longtudnal data on earnngs. Immgrant class determnes the selecton crtera that apply to an mmgrant. Prncpal applcant nformaton ndcates whch mmgrants are assessed and whch are dependents. Specal program codes ndcate cases admtted under relaxed crtera. The longtudnal feature of IMDB provdes several observatons on earnngs for an ndvdual (e.g. up to ten observatons for a mgrant who landed n 986). Hence, t permts better measures of lfetme earnngs. Most mgraton analyses have been carred out usng census data. In census data t s not possble to dentfy the class of admsson of mgrants and t s not possble to dstngush the prncpal applcants from dependents. Wthout ths nformaton t s not possble to determne whch ndvduals go through the pont system. The admsson crtera for dfferent classes are substantally dfferent from each other. For example, a mgrant under famly class s admtted on the bass of havng a famly member n the country and a sponsorshp guarantee from that famly member. The pont system doesn t apply to ths class. An ndependent mgrant who s the prncpal applcant, on the other hand, has to pass the ponts test. Also, n the census data nformaton about educaton, occupaton etc. are as of the tme of the census. Addtonal nformaton provded n the IMDB, LIDS and IDSO allows for a detaled and more careful analyss of the mmgraton polcy and labour force outcomes of mmgrants. 5 It should be noted that the characterstcs of mmgrants n the IMDB devate from those of the landed mmgrant populaton snce the populaton as a whole mmgrants and non-mmgrants alke does not necessarly fle a tax return. To be ncluded n the IMDB a mgrant has to fle at least one tax return startng from the date of applcaton. A study done by Carpenter and Pnsonneault (99) fnds that the IMDB s representatve of the tax-flng populaton. Average characterstcs n the IMDB resemble those generally found n the labour force. Analytcal Studes Branch Research Paper Seres - 3 - Statstcs Canada No. F009 No.82
The sample of mgrants used n the reduced form estmaton conssts of male mmgrants aged 8 to 65 whose applcaton for mgraton was receved between 986 and 990. 6,7 Unted States mgrants are those mgrants whose country of last permanent resdence s the U.S. Unted Kngdom mgrants are those whose country of last permanent resdence s England, Scotland, or Wales. Mgrants whose last country of permanent resdence s Northern Ireland are excluded from the sample snce the U.K. Census ndvdual fle doesn t nclude ndvduals from Northern Ireland. The mgrant samples are further restrcted to sklled workers admtted under the ndependent class, who are prncpal applcants. The ndependent class conssts of workers who are seekng admsson on the bass of ther labour market sklls. Immgrants whose ntended destnaton s Quebec are excluded. Immgrants who are admtted under specal programs or those that pass the pont test only wth the mmgraton offcer s dscreton are also excluded. The reasons for these excluson restrctons are dscussed below. The resultng mgrant sample from the U.S. conssts of 2,500 records, the mgrant sample from the U.K. conssts of 5,78 records. Over the perod covered by the data set (980-995) there were several changes n the pont system. Although the characterstcs assessed remaned mostly the same, the ponts assocated wth them were altered. Over the perod 980 to 990, the perods 980-98, 982-985 and 986-990 can be dentfed as perods over whch the selecton crtera remaned the same. We avod the perod 982-985 snce durng ths perod applcants were requred to have arranged employment, otherwse rejecton of the applcaton was automatc. Ths requrement resulted n substantal reductons n the number of people beng admtted. Ths restrcton was lfted on January st, 986. In ths paper the perod 986-990 s studed. Over ths perod the selecton crtera dd not change for the ndependent class. Quebec has ts own selecton crtera, dfferent from the rest of Canada. Applcants whose ntended destnaton s Quebec are assessed by Quebec and have to satsfy the provncal requrements to be admtted. For ths reason mmgrants who are destned to Quebec are excluded. Immgrants enterng under specal programs are assessed under relaxed crtera. Independent class applcants may be accepted even f they don t have enough ponts, by way of the mmgraton offcer s dscretonary power. Ths dscreton, whch s exercsed very rarely, s dfferent from the mmgraton offcer s regular evaluaton for personal sutablty. An example of a specal program would be acceptng mmgrants from a country that had a natural dsaster. For the admsson of these mgrants some or all of the characterstcs n X may be rrelevant, and these mgrants are excluded from the sample as well. 6 An analyss of mgraton by females s beyond the scope of ths study. It would requre ncorporatng a thrd selecton problem, snce a szeable fracton of women are non-labour force partcpants. 7 There s a concern that older people may have weak labour force attachment, and thus they wll not be representatve of the ndvduals who are mgratng for economc reasons. In order to test the robustness of results presented later n the paper to the age restrcton 8 to 65, the models are estmated by restrctng the sample to males between ages 20 and 55. All the qualtatve results (not presented) reman the same. Analytcal Studes Branch Research Paper Seres - - Statstcs Canada No. F009 No.82
From the /00 U.S. Census a /60 random sample s drawn that s restrcted to males aged 8 to 65. Smlarly, from the 2/00 U.K. Census a /6 random sample s drawn that s restrcted to males aged 8 to 65. These samples refer to non-mgrants, that s ndvduals who ddn t apply or who appled but were rejected for mmgraton to Canada. The resultng non-mgrant sample from the U.S. conssts of 0305 records and the non-mgrant sample from the U.K. conssts of 837 records. Pooled mgrant-nonmgrant samples consst of 2,805 and 2,065 records for the U.S. and the U.K., respectvely. Tables and 2 gve the defntons of varables n the pooled samples for the U.S. and the U.K. as source countres respectvely. Tables 3 and present the descrptve statstcs for the mgrants and non-mgrants for the two source countres. Tables 3 and reveal that mgrants are composed of younger, more educated ndvduals concentrated n whte-collar occupatons that are more lkely to be marred relatve to nonmgrants. The major dfference between the U.S. and the U.K. mgrants s that, those from the U.K. are much younger.. ESTIMATION OF THE REDUCED FORM MODEL. Reduced Form One-Step Model Frst a reduced form model gnorng step (2) s estmated. Ths model s referred to as the Reduced form one-step model and s gven by: Y = W π + ε where Y s equal to f an ndvdual s observed as a mgrant; 0 otherwse. W s dentcal to the vector W n the frst selecton ndex n equaton (6) presented n secton 2.. As ndcated earler ths s the model employed n the prevous lterature. It provdes a benchmark for comparson of the results obtaned from the two step model suggested n ths study wth the results avalable n the lterature. Tables 5 and 7 present the probt estmates of the reduced form one-step model for the pooled sample of mgrants-nonmgrants from the U.S., and from the U.K., respectvely. The frst columns show the parameter estmates whle the thrd columns present the margnal effects, 8 both corrected for choce based samplng. Standard errors are gven n parentheses. 8 E[ Y ] Margnal effects are equal to β β. Partal dervatves wth respect to the vector of characterstcs are computed at the means of the characterstcs n the sample. Indcator varables are beng set at ther sample proportons. Because of the exstence of ndcator varables, margnal effects are approxmatons of the mpact of the bnary co-varates on the probablty of observng an ndvdual as a mgrant. Also, note that the margnal effects n Tables 5, 7, 9 and 2 are to be nterpreted n the followng context: Gven the ncdence of mgraton of males from the U.S. to Canada over the 986-990 perod, the probablty of observng a male n the U.S. as an mmgrant n Canada by 990 s.5e-5. Smlar fgure for the U.K. s 3.9e-. Analytcal Studes Branch Research Paper Seres - 5 - Statstcs Canada No. F009 No.82
The coeffcent of yrssch n Table 5, and the coeffcents on unv_np and postgra n Table 7 are postve, ndcatng that ndvduals wth hgher educaton are more lkely to mgrate. 9 If the host country s assumed to play no role n the observed selectvty of mgrants, then these results would be nterpreted as more educated ndvduals have more ncentves to mgrate. Ths suggests a postve selecton among the ndvduals from the source country populatons that mples the returns to human captal characterstcs are hgher n the host country than the source countres. However, f host country affects the observed selectvty of mgrants, t s not possble to dstngush whether postve selecton n terms of educaton s a result of hgher returns to educaton n host country, or a result of host country s selecton of hghly educated ndvduals from the pool of applcants. Results also suggest that ncreasng age ncreases the probablty of mgraton untl age 35 (3) for the U.S. (U.K.) case, beyond whch t contrbutes negatvely to the probablty of mgraton. Marred ndvduals are more lkely to become mgrants and havng dependents decreases the probablty of beng a mgrant. Marrage may be expected to nhbt mgraton as more ted stayers are expected to be less moble relatve to sngle, wdowed or separated people. However, Mncer (978) ponts out that sngle ndvduals may also be ted stayers. Tables 6 and 8 present the model ft for the reduced form one-step model for the U.S. and U.K. cases. 20 The model for the U.S. (U.K.) has a correct predcton rate of 8.% (59.8%) for nonmgrants and 8.5% (78.8%) for mgrants. Overall the correct predcton rate n the unweghted pooled sample s 8.2% (6.3%). The model ft s worse for the U.K. case compared to the U.S. case, possbly due to unavalablty of co-varates, such as years of schoolng..2 Estmaton of the Reduced Form Model for Two-Step Mgraton Process The estmates from the model presented n the prevous secton have been nterpreted n the lterature as f the host country plays no role on the observed mgraton outcomes. If parameters 9 To test the robustness of the results regardng educaton varables the model for the U.S. case was estmated wth a dfferent specfcaton. A new varable unv was created, equal to f ndvdual has a unversty degree or a post graduate degree; 0 otherwse. The unv varable replaced the yrssch varable to capture the effect of educaton. The estmated coeffcent of the varable unv has a postve sgn, suggestng that the more educated are more lkely to mgrate gnorng the selecton by the host country. A smlar exercse was done for the U.K. case that provdes better comparablty between the results for the U.S. and the U.K. cases. The model for the U.K. was re-estmated wth a dfferent specfcaton where a new varable seced was created, equal to f the ndvdual has a unversty degree or a postgraduate degree, replacng the prevous educaton varables unv_np and postgra; 0 otherwse. Ths varable s comparable to the educaton varable unv n the last specfcaton for the U.S. case where yrssch varable s dropped. The estmated coeffcent of seced s postve, suggestng that the more educated are more lkely to mgrate. 20 In order to estmate whether an ndvdual s a mgrant or not, the probablty of observng an ndvdual as a mgrant s calculated usng the model specfcaton and the parameter estmates, gven the characterstcs of the ndvdual. If ths probablty s greater than the proporton of mgrants n the weghted sample, then the ndvdual s predcted to be a mgrant; otherwse a non-mgrant. These predcted probabltes are cross-tabulated wth actual (observed) outcomes n the sample to obtan the model ft. Analytcal Studes Branch Research Paper Seres - 6 - Statstcs Canada No. F009 No.82
of nterest are the factors that determne ndvduals decson to mgrate, then estmaton of the model n secton. cannot provde any answers. Also, one-step model precludes analyss of the effects of mmgraton polcy on mgraton. In ths secton, the reduced form two-step model s estmated assumng that the dstrbuton of ε s the same among mgrant and non-mmgrant populaton. 2,22 The coeffcents of the frst selecton ndex n the two-step reduced form model ndcate the total effect of the exogenous varables on the probablty of applyng, actng through the wage dfferental for mgratng versus stayng and through the cost of movng. The coeffcents of the second selecton ndex gve the effect of exogenous varables on the probablty of acceptance. 2 As noted earler, subjectve assessment by the mmgraton offcer of "personal sutablty" of a potental mgrant contrbutes to ε. IDSO provdes ponts for personal sutablty of those ntervewed. Normalty of ponts from personal sutablty s tested usng the Bowman and Shenton ch-squared statstc. The null hypothess of normalty can not be rejected at the % level. Ponts from personal sutablty have a mean of 7.0 and a standard devaton of.2. The number of ponts from personal sutablty (pts_pers) s assumed to be equal to: pts _ pers = pts _ pers + ε where pts _ pers = 7 and ε s dstrbuted as normal wth mean zero and constant varance for the mgrant and non-mgrant populatons. The random error term ε and factors that affect arranged employment whch are not captured by the model jontly determne ε, whch s assumed to have a normal dstrbuton wth mean zero and constant varance. We also nvestgate the mplct exogenety assumpton n the model that s the exogenety of pts _ pers (or ε ). We calculate the correlaton coeffcents between pts _ pers and ponts from other characterstcs (ponts from educaton, specfc vocatonal preparaton, experence, age, occupatonal demand, knowledge of Englsh, knowledge of French, arranged employment), as well as the correlaton between pts _ pers and total of ponts from all other characterstcs ( ). Below table presents the results: pt _ all pt_edu pt_svp pt_exp pt_age pt_occd pts_pers -.27 -.27 -.02 -.03 -.0 pt_eng pt_fr pt_arre pt_all - pts_pers.02.05 -.06 -.2 - The null hypothess of zero correlaton can not be rejected at 5% level for all pars of correlaton coeffcents n above table. We also test the dependence between pts _ pers and other ponts lsted n the above table. We calculate Hoeffdng's D statstcs for all pars and we can not reject the null hypothess of ndependence. 22 The results obtaned n ths and the prevous subsectons are subject to the dstrbutonal assumptons made regardng the error terms. One of the referees suggested usng Census data for estmaton that wll allow a larger proporton of mmgrants n order to test senstvty of results to the dstrbutonal assumptons. However, as ndcated before, Census data doesn't have nformaton on the category of mmgrants, e.g. ndependent mgrants, refugees etc., therefore t s not possble to know who actually goes through the ponts test. The model could be estmated wth a larger number of mmgrants by studyng a longer perod of mmgraton (e.g. perod of 980-990, rather than the 986-990 perod studed n ths paper). There s, however, a trade-off between more observatons and problems assocated wth havng dfferent mmgraton polces effectve over a longer perod. Moreover, the ncrease n fracton of mmgrants over a longer perod wll be very small gven the large source country populatons. Analytcal Studes Branch Research Paper Seres - 7 - Statstcs Canada No. F009 No.82