Estimates of Human Capital in Canada: The Lifetime Income Approach

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1 Ctlogue no. 11F0027M No. 062 ISSN ISBN Reserch Pper Economic Anlysis (EA) Reserch Pper Series Estimtes of Humn Cpitl in Cnd: The Lifetime Income Approch by Wulong Gu nd Ambrose Wong Economic Anlysis Division 18-F, R.H. Cots Building, 100 Tunney s Psture Drivewy Telephone:

2 Estimtes of Humn Cpitl in Cnd: The Lifetime Income Approch by Wulong Gu nd Ambrose Wong 11F0027M No. 062 ISSN ISBN Economic Anlysis Division 18-F, R.H. Cots Building, 100 Tunney s Psture Drivewy Sttistics Cnd, Ottw K1A 0T6 How to obtin more informtion: Ntionl inquiries line: E-Mil inquiries: infostts@sttcn.gc.c June 2010 The uthors would like to thnk John Bldwin nd Rob Smith for their guidnce nd comments on the pper, nd thnk Mrc Frenette, Brbr Frumeni, Doug My, Chris Robson, Hui Wei nd prticipnts t workshop on the mesurement of humn cpitl orgnized by the OECD nd Fondzione Giovnni Agnelli for helpful comments. Authors nmes re listed lphbeticlly. Published by uthority of the Minister responsible for Sttistics Cnd Minister of Industry, 2010 All rights reserved. The content of this electronic publiction my be reproduced, in whole or in prt, nd by ny mens, without further permission from Sttistics Cnd, subject to the following conditions: tht it be done solely for the purposes of privte study, reserch, criticism, review or newspper summry, nd/or for non-commercil purposes; nd tht Sttistics Cnd be fully cknowledged s follows: Source (or Adpted from, if pproprite): Sttistics Cnd, yer of publiction, nme of product, ctlogue number, volume nd issue numbers, reference period nd pge(s). Otherwise, no prt of this publiction my be reproduced, stored in retrievl system or trnsmitted in ny form, by ny mens electronic, mechnicl or photocopy or for ny purposes without prior written permission of Licensing Services, Client Services Division, Sttistics Cnd, Ottw, Ontrio, Cnd K1A 0T6. L version frnçise de cette publiction est disponible (n o 11F0027M u ctlogue, n o 062). Note of pprecition Cnd owes the success of its sttisticl system to long-stnding prtnership between Sttistics Cnd, the citizens of Cnd, its businesses, governments nd other institutions. Accurte nd timely sttisticl informtion could not be produced without their continued coopertion nd goodwill. Stndrds of service to the public Sttistics Cnd is committed to serving its clients in prompt, relible nd courteous mnner. To this end, the Agency hs developed stndrds of service which its employees observe in serving its clients. To obtin copy of these service stndrds, plese contct Sttistics Cnd toll free t The service stndrds re lso published on under About us > Providing services to Cndins.

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4 Tble of contents Abstrct... 5 Executive summry Introduction Methodologies for estimting humn cpitl The income-bsed pproch to humn cpitl mesurement The cost-bsed pproch to humn cpitl mesurement Dt sources nd dt construction Empiricl results Summry of the dt Humn cpitl stock Investment nd chnge in humn cpitl stock Humn cpitl stock by gender, eduction nd ge group The contribution of humn welth to the welth ccounts Sensitivity nlysis Conclusions...41 References...42 Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

5 Abstrct This pper produces n estimte of mrket-bsed humn cpitl investment nd stock for Cnd over the period from 1970 to 2007 bsed on the lifetime income pproch nd compres it with tht of physicl nd nturl cpitl investment nd stock. It dopts the methodology developed by Jorgenson nd Frumeni, nd estimtes humn cpitl stock s the expected future lifetime income of ll individuls. Humn cpitl investment is estimted s chnges in humn cpitl stock due to the ddition of new members of the working ge popultion rising from the rering nd eduction of children nd the effect of immigrtion on humn cpitl. The min findings re s follows: 1. The volume of ggregte humn cpitl rose t n nnul rte of 1.7% in Cnd for the period 1970 to 2007, nd most of the growth is due to the increse in the number of individuls in the working-ge popultion. The rising eduction level of the Cndin popultion is lso significnt contributing fctor to the growth in humn cpitl. 2. The compositionl effects of ging of the Cndin popultion ( movement to popultion tht is older on verge) reduced humn cpitl growth by 0.6% per yer over the period 1980 to 2007, while the rising eduction level incresed humn cpitl growth by 0.7% per yer over the period. 3. Humn cpitl stock on per cpit bsis incresed t 0.9% per yer for the period 1970 to 1980, due to the rising eduction ttinment during the period. After 1980, humn cpitl stock per cpit ws virtully unchnged due to two offsetting fctors: rising eduction level which incresed humn cpitl stock nd the compositionl effects of popultion ging, which reduced humn cpitl stock. 4. The vlue of humn cpitl investment nd stock exceeds the vlue of physicl cpitl investment nd stock, nd the rtio of humn cpitl investment nd stock to physicl cpitl investment nd stock declined over time. In 2007, humn cpitl stock is bout four times s lrge s physicl cpitl stock while investment in humn cpitl is bout two times the mgnitude of investment in physicl cpitl. 5. The levels of humn cpitl investment nd stock estimtes re sensitive to the ssumptions mde bout expected future income growth nd the rte used to discount the future income when clculting humn cpitl, but the growth of the quntity nd price of humn cpitl investment nd stock is not sensitive to the ssumptions in these res. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

6 Executive summry This pper develops mesure of the humn cpitl derived from the lifetime ernings pproch. It provides n estimte of the vlue of Cnd s totl welth ssocited with the lifetime lbour relted ernings of individuls tht cn be compred to the welth estimtes derived from produced physicl cpitl nd nturl cpitl. Investment in humn cpitl is seen to be s importnt for growth s the expenditures tht generte physicl cpitl such s mchinery nd equipment or nturl resources. While mesures of the ltter hve long ttrcted the interest of the sttisticl community, mesures of humn cpitl re less developed. Recently, member countries of the Orgnistion of Economic Co-opertion nd Development hve begun to experiment with such mesures. In the lte 1990s, the Cndin Productivity Accounts (CPAs) begn to ssess the contribution of investment in eduction nd trining to output growth nd productivity growth in Cnd. Investment in humn cpitl tht hs produced shift in the composition of the workforce towrds more educted nd more experienced workers hs been found to be n importnt source of productivity growth. The indices of lbour composition constructed by the CPAs of Sttistics Cnd re n essentil first step in incorporting investments in humn cpitl into empiricl studies of economic growth nd ntionl ccounts. This pper is n dditionl step in this direction. In the ntionl ccounting systems of Cnd nd other countries, expenditures on humn development nd relted intngibles re ll regrded s current expenditures (rther thn investment). This, in effect, mens tht outlys on eduction, child rering nd trining re ll clssified s consumption expenditures, either intermedite or finl. This pper trets humn development expenditures s investment (tht should be ccumulted into humn cpitl stocks) becuse the benefits of such expenditures ccrue to the individul over lifetime. This pper dopts the income-bsed pproch developed by Jorgenson nd Frumeni nd estimtes humn cpitl stock s the expected future lifetime income of ll individuls. Investment in humn cpitl is estimted s the chnges in expected future lifetime income due to the rering nd eduction of children plus the effect of immigrtion on humn cpitl ccumultion. The pper focuses on five questions. 1. Wht re the sources of humn cpitl growth in Cnd? Aggregte humn cpitl stock rose t nnul rte of 1.7% in Cnd for the period from 1970 to Most of the growth is due to the increse in the number of individuls in the working-ge popultion ged 15 to 74. The rising eduction level of the Cndin popultion is lso significnt contributing fctor to the growth in humn cpitl. Of the 1.7% growth in humn cpitl in the period from 1970 to 2007, 1.5 percentge points is ccounted for by the growth in the working-ge popultion, the remining 0.2 percentge points is due to the effect of the compositionl shift of humn cpitl (i.e.., rising eduction levels of the Cndin popultion). For the period 1970 to 2007, the rising eduction level incresed humn cpitl growth by 0.9% per yer. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

7 2. Wht ws the compositionl effect of the ging of the Cndin popultion on humn cpitl stock? The ging of the Cndin popultion ( shift in the popultion distribution towrds older workers) hs negtive effect on the growth of humn cpitl stock s older workers on verge hve lower humn cpitl stock (mesured by remining lifetime ernings) becuse of their shorter remining working life. Our estimtes show tht the ging of the Cndin popultion reduced humn cpitl growth by 0.6% per yer over the period 1980 to Wht ws the level of humn cpitl investment nd stock reltive to physicl cpitl investment nd stock? The vlue of humn cpitl investment nd stock exceeds the vlue of produced physicl cpitl investment nd stock. But the rtio of humn cpitl investment nd stock to physicl cpitl investment nd stock declined over time. In 2007, humn cpitl stock is bout four times s lrge s produced cpitl stock, nd investment in humn cpitl ws bout two times s lrge s investment in produced cpitl. The difference between humn cpitl nd produced cpitl ws higher in the erly 1970s. The rtio of humn cpitl stock to produced cpitl stock ws 5.7 to 1 in 1970, nd the rtio of investment in humn cpitl to investment in produced cpitl ws lso 5.7 to 1 in Wht ws the growth of humn cpitl investment nd stock reltive to the growth of physicl cpitl investment nd stock? The growth of humn cpitl investment nd stock ws slower thn the growth of produced cpitl investment nd stock. Over the period from 1970 to 2007, the volume of humn cpitl stock incresed 1.7% per yer, while produced cpitl stock rose t 2.8% per yer. From 1971 to 2007, humn cpitl investment in constnt dollrs grew t 0.4% per yer, while rel investment in produced cpitl rose t 3.9% per yer. 5. Are estimtes of the growth nd level of humn cpitl investment nd stock sensitive to lterntive ssumptions dopted for the estimtion? The levels of humn cpitl investment nd stock estimtes re sensitive to the ssumptions mde bout expected future income growth nd the rte used to discount the future income when clculting humn cpitl, but the growth of the quntity nd price of humn cpitl investment nd stock is much less sensitive to the ssumptions in these res. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

8 1 Introduction This pper develops mesure of the component of totl welth derived from the investments mde in humn development commonly referred to s humn cpitl nd provides n estimte of the vlue nd composition of Cnd s totl welth tht includes produced cpitl, nturl cpitl nd humn cpitl. Ech of these produces strems of erning tht re vilble to n economy for personl consumption, further investments nd support of government progrms. It is common to mesure the cpitl embedded in physicl nd nturl resource ssets nd include these in Welth Accounts. The cpitl vlue of n sset nd the flow of services t ny point in time differ. The net present vlue of the strem of ernings over lifetime of n sset such s physicl cpitl represents the vlue of this cpitl stock. The net present vlue of the strem of ernings of resource deposits is tken to be the vlue of these resources in the Welth Accounts. Similrly, ech individul hs lifetime ernings profile tht cn be thought of s the potentil mount tht cn be trnsformed into consumption, contributions to the government in support of needed progrms, nd svings tht cn be trnsformed into finncil welth to support retirement or contingencies tht short-run ernings will not cover. The net present vlue of these ernings then lso cn be thought of s the embedded cpitl of n individul wht is sometimes referred to in the economics literture s humn cpitl. The instntneous vlue of flows from n sset nd its cpitl vlue mesure different concepts. An individul ner the end of life my hve higher yerly income thn someone just strting out their working creer s result of the ccumultion of experience or eduction. But to the extent tht they hve fewer remining erning yers, the net present vlue of the remining ernings nd therefore the vlue of their humn cpitl will be lower. The individul my be just s productive over the course of the yer s he hs lwys been but the inexorble pssge of time nd the finiteness of life men tht his embedded humn cpitl diminishes with ge. Just s firms re not sustinble if their ssets ll re t the end of their working life nd no replcement hs occurred, if popultions consist lrgely of the elderly, the flow of ernings from tht popultion will not be sustinble s deth brings bout decline in popultion numbers. More recently, birth rtes hve fllen drmticlly in some countries to levels tht will eventully led to decline in their popultion. For this reson, estimtes of humn cpitl re seen to be importnt indictors of sustinbility tht complement other sttistics tht hve until now received more ttention. Estimtes of the mount of cpitl, its qulity, nd its ge hve been t the hert of investigtions into economic growth nd sustinbility in Cnd nd in the other member countries of the Orgnistion for Economic Co-opertion nd Development (OECD 1998, Skills Reserch Inititive 2008). Attention originlly focused on mesures of physicl cpitl. But more recently, experimentl estimtes hve been produced of the mount of humn cpitl. These estimtes require detiled dt on lbour remunertion cross different groups of workers. In the lte 1990s, the Cndin Productivity Accounts (CPAs) begn to ssess the contribution of improvements in eduction nd trining to output growth nd productivity growth in Cnd (Sttistics Cnd 2002; Gu et l. 2003). The CPAs constructed mesure of lbour input nd lbour composition tht focuses on chnges in the eductionl ttinment nd experiences of the Cndin workforce. Lbour input is disggregted by ge, eductionl Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

9 ttinment nd clss of workers (pid nd self-employed workers). Chnges in the composition of workers towrds more educted nd more experienced workers re found to be n importnt source of productivity growth. Over the lst 45 yers, it ccounted for qurter of the growth in lbour productivity in Cnd (Bldwin nd Gu 2007). The indices of chnges in lbour composition, constructed by the CPAs of Sttistics Cnd, re n essentil first step in incorporting more comprehensive mesures of humn cpitl using the lifetime ernings pproch into empiricl studies of Cndin economic growth nd the Welth Accounts produced by the Ntionl Accounts. This pper js n dditionl step towrds tht objective. It follows similr investigtions for the United Sttes (Jorgenson nd Frumeni, 1989). In the ntionl ccounting systems of Cnd nd other countries, expenditures on humn development nd relted intngibles re ll regrded s current expenditures (rther thn investment). This, in effect, mens tht outlys on eduction, child rering nd trining re ll clssified s current expenditures, either intermedite or finl. The min historicl nd institutionl resons for this clssifiction decision re: The clssifiction follows business ccounting conventions. Humn cpitl resources cnnot be bought nd sold on the mrket in the sme wy s nonhumn (physicl) cpitl. Certin expenditures, such s child rering, tht re required to sustin popultion growth re not directly mesurble nd would hve to be imputed. Yet the concept of humn cpitl hs been fmilir in economics for the pst 40 yers (e.g., Schultz 1961, 1961b; nd Becker 1964). The concept is bsed on n nlogy between investments in physicl cpitl nd investments mde to mintin popultions nd is motivted by common economic principle. When n individul (or economic entity) undertkes expenditures, the effects of such outlys cn be ctegorized into one of two types: The benefits of the expenditures re relized in the sme time period s when the outlys occur (e.g., period of one yer). The benefits re relized in future periods nd possibly fter considerble witing. The first type of expenditure is ctegorized s consumption : the second type of expenditure is defined s investment. This economic principle suggests tht expenditures on humn development should be clssified s investment (nd ppropritely ccumulted into humn cpitl stocks), becuse the benefits of these expenditures ccrue to the individul over lifetime. Severl different methodologies for mesuring humn cpitl hve been developed. Kendrick (1976) used cost-bsed pproch for the mesurement of humn cpitl nd estimted humn cpitl s the ccumulted vlue of ll expenditures relted to humn development, such s costs relted to the rering nd eduction of children. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

10 An lternte pproch bsed on lifetime income ws developed by Jorgenson nd, Frumeni (1989, 1992, nd 1992b) tht trets the net present vlue of incomes over lifetime s proxy for the ernings potentil nd thus the embedded cpitl inherent in the individul. The incomebsed pproch hs been used to estimte totl humn cpitl for Sweden (Ahlroth, Björklund nd Forslund 1997), Austrli (Wei 2004, 2007, 2008), New Zelnd (Le, Gibson nd Oxley 2002), for the United Kingdom (O Mhony nd Stevens 2009), nd for Norwy (Greker nd Liu 2008). This pper contributes to those recent studies on humn cpitl mesurement by pplying the Jorgenson nd Frumeni income-bsed pproch to mesure humn cpitl stock for Cnd. Previous studies hve developed mesure of humn cpitl for Cnd. Mcklem (1997) nd Bech et l. (1988) clculted ggregte humn welth s the expected present vlue of ggregte lbour income net of government expenditures. Mcklem (1997) found tht the vlue of humn welth ws bout six times s lrge s the vlue of non-humn welth over the period 1963 to While the concept of humn cpitl in those studies is similr to the one in this pper, those studies dopted mcro pproch nd filed to tke into ccount the effect on humn cpitl of shifts in the composition of the Cndin popultion towrds older nd more educted individuls, s this pper does. Lroche nd Mérette (2000) clculted n index of humn cpitl s weighted sum of the number of workers with different eduction levels nd experience. Unlike this pper, which weights individuls with their lifetime income, Lroche nd Mérette weighted the individuls with their current wge income. For the mesurement of humn cpitl stock, it is more pproprite to use expected lifetime income s weights. The wge income tht worker receives in one period only represents the flow of services from humn cpitl embodied in the worker t tht point in time. Tking longer time period recognizes tht worker s lifetime income my chnge becuse of the lifepth tht is tken over much longer period cused by life events such s eduction, trining nd the overll stte of the economy. The rest of the pper is orgnized s follows: The next section presents the methodologies for estimting humn cpitl investment nd stock. Section 3 presents the construction of dt used for estimtion. Section 4 presents the results. Section 5 provides summry of the findings. 2 Methodologies for estimting humn cpitl In generl, cpitl stock cn be vlued using two methods: It cn be vlued s the sum of dditions, minus the subtrctions, mde over time to initil stock (cost-bsed pproch). Alterntively, cpitl cn be vlued s the net present vlue of the income it is ble to produce over time (income-bsed pproch). The cost-bsed pproch is employed to estimte the vlue of physicl cpitl stock, while the income-bsed pproch is often used to estimte the vlue of nturl cpitl. In the former cse, the vlue of physicl cpitl is obtined by summing the vlue of investments nd subtrcting the deprecition from initil cpitl stock. This pproch is used becuse prices for physicl investments re vilble nd projections of future profits on physicl investments re more difficult to mke. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

11 The vlue of nturl resources is often estimted s the net present vlue of resource rents over n ssumed lifetime. This method is dopted becuse it is sometimes rgued tht simply summing developmentl costs would miss the rents ssocited with nturl resources nd thereby underestimte the returns to resources nd thus their intrinsic cpitl vlue. In well-functioning mrket, where physicl ssets re bought nd sold, the two methods (cost versus ernings) should yield pproximtely the sme results. Otherwise, if the net present vlue of income exceeds the cost of purchsing the sset, more physicl ssets re likely to be mnufctured nd employed thereby reducing returns (under the ssumption of diminishing returns) nd bringing the future strem of erning into equilibrium with the costs of producing the strem of returns. But in mrket, where there is reson to believe tht this cnnot or does not occur, lterntive methods re needed to vlue n sset. Becuse of the nture of lbour mrkets (mongst which is the length of childhood before newborns enter the lbour mrket), the ultimte ernings of individuls nd the costs of rering nd educting individuls my not equte t the mrgin. As result, Jorgenson nd Frumeni (1989, 1992 nd 1992b) estimted the vlue of humn cpitl directly in terms of lifetime lbour income for ll individuls. The dvntge of this pproch is tht it directly mesures the concept tht is being sought the lifetime ernings ssocited with lbour. Lifetime ernings ultimtely mesure the potentil economic vlue of the sset. 1 The disdvntge is tht it requires projections into the future. Whether this is importnt is n empiricl mtter tht cn be investigted by exmining the impct of lternte ssumptions on the estimtes of humn cpitl nd evluting the importnce of differences tht rise from these lterntives. The other dvntge of using the lifetime ernings pproch is tht it provides mesure of potentil ernings tht cn be used to chrcterize n individul s life course tht is chrcterized by grdul trnsformtion of humn cpitl potentil into consumption, investment in upgrding humn cpitl nd the trnsformtion of present ernings into finncil welth vi svings tht is vilble to support retirement. Descriptions s to how society prepres for retirement require n understnding of how income potentil (s mesured by lifetime ernings) is grdully trnsformed over lifetime into ctul prepredness (through sset cquisition tht will support retirement). Humn cpitl ccounts provide one of the two min ccounts required for this purpose. Using this income-bsed pproch to mesuring humn cpitl, Jorgenson nd Frumeni report tht their estimtes of humn cpitl were t lest 4 times the mgnitude of investment in nonhumn cpitl in the United Sttes; moreover, the vlue of humn cpitl stock is over 11 times the vlue of physicl or non-humn cpitl. More recently, the income-bsed pproch ws used to estimte humn cpitl for Sweden (Ahlroth, Björklund nd Forslund. 1997), Austrli (Wei 2004, 2007), New Zelnd (Le, Gibson nd Oxley 2002) nd Norwy (Greker nd Liu, 2008). Those studies confirmed the findings for the United Sttes nd found tht the vlue of humn cpitl using the income-bsed pproch is significntly greter thn the vlue of nonhumn cpitl stock. In relted context, O Mhony nd Stevens (2009) estimted the output of the eduction sector for the United Kingdom, nd Ervik, Holmøy nd Hægelnd (2003) estimted the output of the eduction sector for Norwy. Kendrick (1976) nd Eisner (1985) use the cost-bsed pproch to estimte investment in humn cpitl. The investment in humn cpitl includes the cost of child rering nd the cost 1. Economic vlue bsed on mrket prices my be quite different from inherent vlue bsed on other concepts. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

12 of eduction, including erning forgone by students. The dt on investment in humn cpitl is then ggregted using the perpetul inventory method to derive estimtes of humn cpitl stock. More recently, the cost pproch ws used by Kokkinen (2008) to construct mesure of humn cpitl stock for Finlnd in n empiricl nlysis of humn cpitl nd economic growth. In ddition to those pproches, previous empiricl studies hve used number of proxy mesures of humn cpitl, including eductionl ttinment, verge yers of schooling, nd litercy scores (e.g. Brro nd Lee 1996; Coulombe nd Trembly 2006; nd, for review, see OECD 1998). 2.1 The income-bsed pproch to humn cpitl mesurement This study dopts vrint of the Jorgenson nd Frumeni (1989, 1992 nd 1992b) incomebsed pproch for the mesurement of humn cpitl nd estimtes the vlue of humn cpitl stock s the expected future lifetime income of n individul. This pproch trets individuls s entities tht embody cpitl with n erning potentil tht is derived from mrket ctivities, nd ssigns price 2 to their lifetime lbour using their ctul ernings profile. 3 As outlined bove, the vlue of n sset cn be estimted either from the strem of ernings it produces or the costs of producing or buying it,. For physicl cpitl, the vlue of the sset is observed directly from mrket trnsctions in investment goods. The cost of cpitl services from the sset is then derived using the user-cost-of-cpitl eqution. For humn cpitl, the vlue of the sset is not observed from trnsctions in lbour mrkets; the cost of producing the lbour is not directly observed becuse humn trfficking is illegl nd therefore the vlue of lifetime services cnnot be observed from mrket trnsctions. Therefore, the vlue of humn cpitl ssets is estimted here s the net present vlue of the wge rtes over lifetime (or lifetime lbour income). 4 Lbour income is defined s the concept tht is used in the Ntionl Accounts. 5 To construct lifetime lbour incomes nd humn cpitl embodied in the Cndin popultion, we will exclude the vlue of non-mrket ctivities nd focus on the humn cpitl embodied in the working-ge popultion, ged 15 to The extended ccounts of Jorgenson nd Frumeni include the vlue of non-mrket ctivities nd the vlue of humn cpitl embodied in ll individuls. The vlue of non-mrket ctivities is bsed on the ssumption tht individuls llocte time between work nd non-mrket ctivities so tht the mrginl vlue is equlized between the two types of ctivities. The issue of vluing non-mrket ctivities is controversil. Furthermore, it cn be rgued tht humn cpitl embodied in the working-ge popultion is more relevnt for mesuring the productive cpcities of the Cndin popultion. As such, we will exclude the vlue of non-mrket ctivities in our mesure of humn cpitl nd focus on the humn cpitl of the working-ge popultion. 2. Assigning price to humn effort s vlue ccords with the norml prctice of the Ntionl Accounts which uses the prices of products tht re exchnged in mrkets to vlue reltive worth. 3. Jorgenson nd Frumeni ssume tht humn cpitl such s skills, knowledge nd competencies embodied in n individul with given gender, eduction nd ge group does not chnge over time. To ccount for such chnge in the qulity of humn cpitl in n individul would require the use of hedonic methods s in the estimtion of price indices for computers nd semiconductors (Wei 2008). 4. In this pproch, no deduction is mde for the mintennce of lbour. This llows the income strem derived from lbour to be compred to the income strem from other ssets like physicl nd nturl cpitl. 5. For discussion of this concept, see Gu et l The end yers re rbitrrly chosen. While the verge ernings of 74 yer olds re not exctly zero, they re very close to zero nd chnging the limits will hve very smll effect on the estimtes produced here. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

13 We estimte mrket lifetime lbour income for ll individuls ged 15 to 74 with cross-sectionl dt benchmrked to Ntionl Accounts totls. We ssume tht expected incomes in future periods re equl to the incomes of individuls of the sme gender nd eduction, with the ge tht the individuls will hve in the future time period, djusted for increses in rel income. The lifetime incomes cn be clculted by bckwrd recursion, strting with ge 74, which is ssumed to be the oldest ge before retirement. The expected income for person of given ge is their current lbour income plus their expected lifetime income in the next period multiplied by survivl probbilities. For exmple, the present vlue of lifetime income of 74-yerolds is their current lbour income. The lifetime income of 73-yer-olds is equl to their current lbour income plus the present vlue of lifetime income of the 74-yer-olds, djusted for increses in rel income. Formlly, we use the following eqution for estimting verge humn cpitl per cpit for cohort of individuls with gender (s), ge (), nd eductionl ttinment (e): h w y w y sr h (1 g)/(1 r) (1) e e e e e, 1, 1, 2, 2,, 1 e, 1 where e = eductionl ttinment levels (1 to 5): 1 = zero to eight yers of school, 2 = some or completed high school, 3 = some post-secondry eduction below bchelor s degree, 4 = bchelor s degree, 5 = mster s degree or bove; = ges: 15 to 74; h e, = verge humn cpitl or verge lifetime lbour income per cpit for individuls with ge () nd eduction level (e); w = probbility of engging in pid employment for individuls with ge () nd eduction e 1, level (e), defined s the number of pid workers over the popultion for tht cohort; y = nnul lbour compenstion of pid workers with ge () nd eduction level (e); e 1, w = probbility of engging in self-employment for individuls with ge () nd eduction e 2, level (e), defined s the number of self-employed workers over the popultion for tht cohort; y = nnul lbour compenstion of self-employed workers with ge () nd eduction level e 2, (e); sr, 1 = the probbility of surviving one more yer from ge (); nd g = rel income growth rte; r = discount rte. This formul is then pplied to ech genertion of individuls t point in time ssuming tht ech individul progresses through time using the reltive incomes of ll succeeding cohorts nd the relevnt probbilities of moving to different sttes of eduction nd employment sttus tht re pplicble t tht point in time. The eqution is estimted seprtely for mles nd femles. This formul requires estimtes of the future growth rte of rel income. Here it is ssumed to equl lbour productivity growth in the Cndin business sector, which ws 1.7% per yer for our estimtion period of 1970 to Rel income growth in the pst followed the growth in productivity very closely over long Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

14 periods of time (Sttistics Cnd, 2007). We will set the rel discount rte equl to 5.1%, which is the weighted verge of rel rtes of return to equity nd debt (Bldwin nd Gu 2007). 7 During their working life, individuls my pursue further studies to increse their ernings. To incorporte the extr humn cpitl of those individuls, the formul for bckwrd recursion in (1) is modified (Jorgenson nd Frumeni 1989, 1992, 1992b; Le, Gibson nd Oxley 2002; Wei 2004): where h w y w y (1 senr ) sr h (1 g) / (1 r) e e e e e e, 1, 1, 2, 2,, 1 e, 1 M e m1 senr / M sr h (1 g) / (1 r) e m m e, m e1, m e senr = school enrolment rte, which is defined s the proportion of individuls with eduction level (e) who re studying for higher eduction level (e+1); M e = number of yers tht the individuls with eduction level (e) spend to complete higher eduction level (e+1). (2) When individuls pursue further studies, they fce two possible ernings strems: one with the current eduction level (e), nd the other with the higher eduction level (e+1) with dely becuse of schooling. Averge humn cpitl per cpit mong cohort of the individuls is weighted sum of these two ernings strems, with weights being the probbility of school enrolment. In Eqution (2), we mke the ssumption tht students enrolled in n eduction level re evenly distributed cross different study yers, except for certin young ges. For exmple, 22 yer-old students with bchelor s degree studying for mster s degree re ssumed to be in their first yer. 8 To estimte humn cpitl for Cnd, we hve clssified individuls in the Cndin popultion into five eduction levels: zero to eight yers of schooling, some or completed high school, some post-secondry school below bchelor s degree, bchelor s degree nd mster s degree or bove. We will ssume tht individuls with zero to eight yers of schooling tke three yers to complete the next eduction level (some or completed high school); tht individuls with some or completed high school tke two yers to complete some postsecondry eduction; tht individuls with some post-secondry eduction tke two yers to 7. Schreyer (2001) provided detiled discussion bout the conceptul issues of discount rte. 8. Specificlly, we mde the following ssumptions bout school enrolment: For n individul with eduction level 4 nd enrolled in school, he or she is ssumed to be in the first yer of study if he or she is less thn or equl to 22 yers of ge, in the second yer if he or she is 23, nd in the first nd second yer with equl probbility if he or she is 24 or older. For n individul with eduction level 3 (some post-secondry eduction) nd enrolled in school for bchelor s degree, he or she is ssumed to be in the first yer of study if he or she is less thn or equl to 20 yers of ge, in the second yer if he or she is 21, nd in the first, nd second yers with equl probbility if he or she is 22 or older. For n individul with eduction level 2 nd enrolled in school, he or she is ssumed to be in the first yer of study if he or she is 15, nd in the first nd second yer with equl probbility if he or she is 16 or older. For n individul with eduction level 1 nd enrolled in school, he or she is ssumed to be in the first, second nd third yers of study with equl probbility. In our empiricl nlysis, we find tht this chnge to the ssumption of even distribution of students cross different school yers hs little effect on the estimted stock of humn cpitl for Cnd. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

15 complete bchelor s degree nd tht individuls with bchelor s degree tke two yers to complete mster s degree or bove. The totl vlue of humn cpitl is just the sum cross ll individuls in the popultion being counted (in our cse, yer olds). For given popultion, the vlue of humn cpitl will be smller if there is lrger proportion of the popultion t n older ge since this group hs smller proportion of their erning yers before them. While the ltter my seem counterintuitive since the flow of services from the stock of the humn cpitl my be no different in two countries tht differ only in terms of the ge composition of their popultion, the vlue of the humn cpitl is indeed lower in the ltter sitution since its popultion hs lower remining lifetime. An nlogy cn be found in comprison of physicl cpitl stocks derived from onehoss shy type ssets tht is, where the sset yields more or less constnt flow of services over lifetime but dies suddenly t the end of its physicl life. Two compnies tht possess the sme physicl units of this type of sset but tht differ in terms of the ge structure of the sset (one sy owning n units with 20 yers remining life nd the other possessing n units with only 1 yer left) will differ in terms of their sustinbility. The former will be ble to continue to produce for 20 yers without further investment but the other is going to hve to mke mjor investments or go out of business within 2 yers. A comprison of flows derived from humn cpitl in these two situtions would conclude tht the two countries re eqully well off when, in relity, the production volume of one is much less sustinble thn other. It is for this reson tht students of sustinbility rgue tht mesure of humn cpitl re needed to supplement flow mesures tht re trditionlly used to study economic growth especilly in n er where birth rtes hve fllen in mny countries to levels tht will not sustin the present popultion. Differences in humn cpitl per cpit cross countries rise from the sme sources tht determine differences in wges rtes cross individul workers. Higher incomes my be relted to greter experience or higher levels of eduction or superior bilities. Differences re lso function of the mount of cpitl intensity of country or its nturl resource endowment. For mny purposes, vlues of chnges in humn cpitl rther thn levels of humn cpitl re required. And chnges cn occur either becuse of movements in prices or volumes. A volume estimte provides mesure tht bstrcts from chnging prices tht is chnging reltive lifetime ernings cross individuls. A mesure of the chnge in the volume of humn cpitl is obtined using the Tornqvist ggregtion method. 9 The growth rte of the volume index of ggregte humn cpitl stock is clculted s the weighted sum of the growth rtes of the number of individuls cross different ctegories of the popultion (gender, ge nd eduction) using their shre of the nominl vlue of humn cpitl stock s weights: ln K v ln L s e s, e, s, e, (3) where K denotes the volume indices of ggregte humn cpitl stock, L s,e, the number of individuls with gender (s), ge (), nd eduction level (e), nd denotes first difference, or chnge between two consecutive periods, for exmple: 9. Diewert (1976) shows tht the Tornqvist index is n exct superltive index number. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

16 ln K ln K( t) ln K( t 1) (4) The weights re given by the verge humn cpitl shre of ech ctegory of popultion in the nominl vlue of ggregte humn cpitl stock: 1 vs, e, vs, e, ( t) vs, e, ( t 1), vs, e, 2 h s e L s, e, s, e, h L s, e, s, e, (5) where {h s,e, } is the set of verge lifetime lbour income of different types of individuls, crossclssified by gender, ge nd eduction, clculted using Eqution (2). Ceteris pribus, this index will increse if the number of individuls increses over time. Concomitntly, countries with declining popultions will experience declines in this index. Alterntely, popultions with chnges in composition towrds those tht hve incresingly lrge remining lifetime ernings will experience increses in the volume index. This my occur if growth in the popultion occurs in those who hve greter lifetime ernings becuse they re t n erly stge of their creer pth or in those who hve more erning power becuse of increses due to eduction or experience. The difference between the growth of this weighted popultion counts nd the growth of unweighted popultion counts mesures the growth of humn cpitl per cpit. The growth in humn cpitl per cpit reflects the effect of demogrphic chnges in popultion such s ging compositionl effects nd rising eduction levels. Humn cpitl per cpit will increse if there is shift in the composition of the popultion towrd younger or more educted individuls with higher expected lifetime income. Formlly, ggregte humn cpitl per cpit is defined s: CK K / L (6) where L is the number of individuls in the popultion. The evolution of humn cpitl per cpit is sometimes used s n indictor of whether n economy is on pth of sustinble development. According to some, n economy is on sustinble development pth if totl cpitl (including produced cpitl, nturl cpitl nd humn cpitl) per cpit does not decline (Arrow et l, 2007; UNECE, 2009). The chnges in humn cpitl per cpit cn be trced to demogrphic chnges in popultion such s compositionl ging effects nd rising eduction levels in popultion. To exmine the effect of the demogrphic chnges on chnges in humn cpitl per cpit, we construct the prtil indices of ggregte humn cpitl stock corresponding to popultion chrcteristics such s gender, ge nd eduction seprtely. For exmple, prtil index of the volume of ggregte humn cpitl stock corresponding to gender is defined s follows: sex ln K v ln L s s vsln Ls,, e s e s (7) Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

17 where v v s s 1 2 e v ( t) v s v s,, e s ( t 1) The prtil volume index corresponding to gender cptures the shift of the popultion distribution between the two genders lone. Similrly, the prtil volume indices for eduction nd ge mesure the shift between ge groups or between eduction levels. The difference between the growth of the prtil indices of ggregte humn cpitl for ech chrcteristic (gender, ge nd eduction) nd the growth of the number of individuls in the popultion mesures the contribution of tht chrcteristic to the chnge in humn cpitl stock per cpit. The sum of the contribution tht ech chrcteristic mkes to the chnge in humn cpitl stock per cpit will differ from the overll chnge in humn cpitl stock per cpit, s the sum of the contribution of chrcteristics represents the first-order pproximtion to the index of humn cpitl stock per cpit. To exmine the evolution of humn cpitl stock over time nd present n ccumultion ccount of humn cpitl, we will decompose the chnges in humn cpitl stock into three components: investment in humn cpitl, deprecition on humn cpitl nd revlution of humn cpitl. The methodology for decomposing the chnge in humn cpitl stock is similr to the one for decomposing the chnge in non-humn cpitl stock nd ws developed by Jorgenson nd Frumeni (1989). For comprison, we will first present the method for decomposing the chnge in non-humn cpitl stock (Christensen nd Jorgenson 1973). For single cpitl good, the vlue of stock is the sum of vlues of investment goods of ech vintge, summed over ll vintges: W p A (8) t t, v tv v0 where p t,v is the price of the investment good of vintge v in period t. A t-v is the quntity of the investment good of vintge v in period t. The chnge in the nominl vlue of cpitl stock from period to period my be written s: W W p A p A t t1 t, v tv t1, v t1 v v0 v0 = p A p A p A t,0 t t, v1 tv1 t1, v t1 v v0 v0 Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062 = p A ( p p ) A p p A t,0 t t1, v t1, v1 t1 v t, v1 t1, v1 tv1 v0 v0 The first term in the lst expression is gross cpitl formtion. The second term is the deprecition on cpitl goods of ll vintges, which represents the chnge in the vlue of n sset ssocited with the ging of the sset nd the resulting decline in its efficiency. The third term is the revlution of ssets of ll vintges, which represents the chnge in the vlue of n sset ssocited with everything other thn ging, including pure infltion, obsolescence nd ny other impct on the vlue of n sset tht is not ssocited with ging (Frumeni 1997; Diewert 2005; Schreyer 2001). (9)

18 According to Eqution (9), the chnge in the nominl vlue of cpitl stock is the sum of net cpitl formtion (gross cpitl formtion minus deprecition) nd sset revlution. The methodology for decomposing the chnge in the vlue of non-humn cpitl stock (Eqution [9]) cn be used to decompose the chnge in the vlue of humn cpitl stock. Similr to non-humn cpitl stock, the chnge in humn cpitl stock cn be decomposed into three components: investment in humn cpitl, deprecition on humn cpitl nd revlution for humn cpitl (Jorgenson nd Frumeni 1989). Humn cpitl investment reflects the increse in humn cpitl stock rising from the rering of children, forml eduction, voctionl nd on-the-job trining, helth nd migrtion. For this pper, our mesure of humn cpitl investment reflects dditions to the working ge popultion due to the rering of children (the rrivl of new members of the ntive born popultion into the workforce), forml eduction (skills upgrding from schooling post high school) nd migrtion (new members of the popultion from outside Cnd). This is estimted s the sum of chnges in lifetime incomes rising from forml eduction, lifetime incomes of ll individuls who reched working ge nd chnges in humn cpitl due to immigrtion. The second component of the chnge in humn cpitl rises from deprecition of humn cpitl, which is the chnge in humn cpitl stock becuse of ging, deth nd emigrtion. It is clculted s the sum of chnges in lifetime lbour incomes ssocited with ging for ll individuls who remin in the working-ge popultion nd lifetime lbour incomes of ll individuls who die or emigrte. Recll tht the humn cpitl of everyone in the popultion will suffer reduction in their totl lifetime strem of ernings ech yer tht they live becuse they hve fewer erning yers left in their life due to the finite nture of humn working life. The third component of the chnge in humn cpitl is the revlution of humn cpitl, which represents the chnge in humn cpitl over time for individuls with given set of demogrphic chrcteristics gender, eduction nd ge. It is clculted s the sum of chnges in lifetime lbour incomes from period to period for individuls with given set of demogrphic chrcteristics. These chnges cn occur for mny resons. Economic business cycles my cuse reduction in ernings during downturns. Or genertionl effects my suddenly ffect new lbour force entrnts. An exmple of such chnge is provided by Picot nd Heisz (2000) who document decline in prticiption rtes nd slow growth in worker ernings in Cnd during the erly 1990s, prticulrly for the younger mle cohort. This will give rise to smll or negtive revlution term for humn cpitl in tht period, prticulrly for the younger mle cohort. Whether these chnges re only temporry or re long-lived is n empiricl mtter tht will be investigted lter. To derive the eqution for decomposing the chnge in humn cpitl stock, we strt with the definition of humn cpitl stock. Humn cpitl stock in current dollrs in period t is the sum of discounted lifetime lbour incomes for ll individuls in the working-ge popultion: P K h L t t t t K s, e, s, e, s, e, (10) where P is the price index of ggregte humn cpitl stock, t K ggregte humn cpitl stock. t K is the volume index of Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

19 The chnge in the vlue of humn cpitl stock from period t-1 to period t my be written s: P K P K h L h L t t t1 t1 t t t1 t1 K K s, e, s, e, s, e, s, e, s, e, s, e, = h L h L ( h h ) L t t t t1 t t1 t1 s, e, s, e, s, e, s, e, s, e, s, e, s, e, s, e, s, e, s, e, t t t t1 t1 t t1 t t1 t1 = hs, e, Ls, e, hs, e, 1 sr, 1 Ls, e, hs, e, Ls, e, hs, e, 1 sr, 1 Ls, e, s, e, s, e, s, e, s, e, s, e, ( h h ) L t t1 t1 s, e, s, e, s, e, The first term in the lst expression is investment in humn cpitl in current prices. The second term is the deprecition of humn cpitl. The third term is the revlution of humn cpitl stock, which is the sum of chnges in lifetime lbour incomes from period to period for individuls with given set of demogrphic chrcteristics gender, eduction nd ge. (11) According to Eqution (11), the chnge in humn cpitl is the sum of gross investment in humn cpitl net of deprecition nd the revlution of humn cpitl. To interpret the term for investment in humn cpitl, we rewrite it s: h L h sr L t t t t1 t1 s, e, s, e, s, e, 1, 1 s, e, s, e, s, e, h L h ( L sr L ) t t t t t1 t1 s, e, s, e, s, e, s, e, 1, s, e, 1 s, e, 15,, 15 s e (12) Investment in humn cpitl in period cn be clculted s the sum of the chnges in lifetime incomes becuse of eduction, lifetime incomes for ll individuls who reched working ge in the period nd the effect of immigrtion. The first term on the right side of the eqution is lifetime incomes of ll individuls who reched working ge (15 yers of ge). It cptures the effect on humn cpitl investment of the rering nd eduction of children up to ge 15. The second term is the ddition to humn cpitl stock due to increses in eduction nd immigrtion. This is estimted s the verge lifetime lbour income of individuls multiplied by the chnge in the number of grdutes t given eduction level nd immigrtion to Cnd. 10 The term for the deprecition in humn cpitl my be written s: h L h sr L t t1 t t1 t1 s, e, s, e, s, e, 1, 1 s, e, s, e, s, e, = t t t1 t1 t t1 t1 t1 hs, e, hs, e, 1 sr, 1 Ls, e, hs, e, Ls, e, sr, 1 Ls, e, s, e, s, e, (13) The deprecition on humn cpitl is estimted s the sum of two terms. The first term is the chnge in lifetime lbour incomes tht occurs with ging for ll individuls who remin in the working-ge popultion. The second term is the lifetime lbour incomes of ll individuls who die, emigrte or rech the ge of We did not collect dt on immigrtion for this pper nd will not estimte the seprte effect of immigrtion nd eduction on humn cpitl investment. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062

20 The nominl vlue of investment in humn cpitl, deprecition nd revlution of humn cpitl cn be seprted into two components ssocited with price nd quntity indices. t Treting verge lifetime lbour income h s, e, s the price component of investment in humn t 1 1 cpitl nd the terms ssocited with popultion counts L se,,14 nd ( t t t Ls, e, sr 1, Ls, e, 1) s the quntity component of investment in humn cpitl in Eqution (12), we cn pply the Tornqvist ggregtion formul to dt on individuls to obtin the price nd quntity index for investment in humn cpitl. To obtin the price nd quntity index for deprecition, we tret terms t t t ssocited with lifetime incomes hs, e, 1 hs, e,, hs, e, s the price component, nd the terms ssocited with popultion counts s the quntity component. Similrly, treting the chnges in t t 1 verge lifetime lbour income of individuls cross time periods ( h h ) s the price component of revlution nd the number of individuls ( ) 1 L t s, e, s, e, s, e, s the quntity component, we obtin the price nd quntity index of revlution for ll individuls in the working-ge popultion. The mesure of investment in humn cpitl in this pper excludes the effect of on-the-job trining nd helth on humn cpitl investment becuse of lck of consistent time series dt on trining nd helth. The importnce of trining for humn cpitl investments ws discussed in Becker (1964) nd Mincer (1962, 1989). Mincer (1989) provided survey on the incidence nd impct of on-the-job trining. Rosen (1989) noted tht investment in trining is included in the deprecition estimtes for the Jorgenson nd Frumeni method for humn cpitl mesurement. Hui Wei (2008) mde the sme point nd estimted the component of the deprecition term tht is ssocited with the effect of work experience on humn cpitl investments for Austrli. Abrhm nd Mckie (2005, editors, Chpter 6) discussed helth cre (such s exercise, diet nd medicl cre) s form of humn cpitl investment. 2.2 The cost-bsed pproch to humn cpitl mesurement The cost-bsed pproch to estimting humn cpitl stocks nd flows is similr to tht often used to estimte physicl cpitl stocks nd flows. The pproch estimtes the stock of humn cpitl s the ccumulted vlue of the expenditures spent on those items defined s investment in humn cpitl. The cost-bsed pproch ws used by Kendrick (1976) nd Eisner (1985) to estimte humn cpitl stock for the United Sttes. Kendrick (1976) included in investments in humn cpitl the following items: the costs of rering children, expenditure on helth nd sfety, mobility, eduction nd trining, nd ernings forgone by students ttending school. It is reltively esy to mesure dequtely most forms of investment in humn cpitl using vrious dt sources t Sttistics Cnd. Public nd privte spending on forml eduction is reltively well-documented. Spending by enterprises on job-relted trining progrmmes my lso be quntified. The work of Mincer (1962) shows tht informl, on-the-job trining contins n implicit investment spect, s workers ccept lower wges to gin working experience. Indeed, eduction results not only from schooling nd trining, but lso from generl experience both t work nd in leisure-time ctivities. But the expenditures relted to informl on-the-job trining re not redily vilble. Economic Anlysis Reserch Pper Series Sttistics Cnd Ctlogue no.11f0027m, no. 062