Influence of Workforce Ageing on Human Capital Formation

Transcription

1 International Intitute for Applied Sytem Analyi Schloplatz 1 A-2361 Laxenburg, Autria Tel: Fax: publication@iia.ac.at Web: Interim Report IR Influence of Workforce Ageing on Human Capital Formation Marcin Stonawki (tonawm@uek.krakow.pl) Approved by Wolfgang Lutz (lutz@iia.ac.at) Leader, World Population Program March 10, 2008 Interim Report on work of the International Intitute for Applied Sytem Analyi receive only limited review. View or opinion expreed herein do not necearily repreent thoe of the Intitute, it National Member Organization, or other organization upporting the work. International Intitute for Applied Sytem Analyi Regitration number: ZVR

2 Content Introduction... 1 Human Capital... 1 Method of Meuring Human Capital... 2 Method... 3 Formal education... 5 Acquiring new knowledge and experience during one profeional life... 5 Obolecence of knowledge Forgetting knowledge Health Individual Human Capital Profile Interaction Rate and Aggregated Human Capital Population Projection for Poland, Human Capital in Poland in Concluion Reference Appendix Appendix ii

3 Abtract Thi paper addree the quetion of how workforce ageing influence human capital formation, human capital deterioration, and future productivity growth. The method preented in thi paper focue on the magnitude of human capital that h been accumulated in an individual. It take into conideration education, acquiring knowledge and experience, knowledge becoming obolete or forgotten, well the impact of health. The etimated human capital curve (bed on the net effect of the variou determinant of human capital) h an inverted U-haped profile. The conequence of workforce ageing can be conidered in the hort and long term. In the hort term, the accumulated human capital could incree if well-educated worker from large cohort reach the age at which their human capital i the highet. However, in the long term, a decree in aggregate human capital i expected becaue the working-age population hrink. Thi could alo affect economic growth level in the future. iii

4 Acknowledgment The author would like to thank Wolfgang Lutz for the opportunity to work on thi project while participating in the IIASA Young Scientit Summer Program in Special thank alo go to Vegard Skirbekk, Warren Sanderon, Samir K.C., Alexia Prkawetz, and Thom Fent for their generou help while writing thi paper. iv

5 About the Author Marcin Stonawki participated in the Young Scientit Summer Program in He i currently an itant at the Department of Demography at Cracow Univerity of Economic, ul. Rakowicka 27, Cracow, Poland. v

6 Influence of Workforce Ageing on Human Capital Formation Marcin Stonawki Introduction The 21 t century i called by demographer the century of population ageing (Lutz et al. 2004). Population projection how that the hare of old people will incree dramatically in the future. Population ageing not only bring about demographic conequence, but affect all pect of ociety. One of the mot ignificant problem i the ageing of the workforce which generate a wide range of challenge in a ocial and economic context. The important iue i how the proce of ageing influence the accumulation of human capital tock in the workforce population, which i one of the main driving force of economic productivity growth. The hrinkage of available human capital in the labor market could caue lower or even negative economic growth in the future. The main objective of thi work i to e the influence of workforce ageing on human capital formation. The quetion arie when human capital reource incree or decree together with the proce of population ageing. In the following ection, the concept of human capital i preented, followed by a dicuion of the variou method of meuring human capital. We then decribe our propoed method of human capital meurement and elaborate on the individual human capital profile. Interaction rate and aggregated human capital are dicued. Uing the multi-tate demographic population method, we preent the population projection for Poland for and dicu human capital formation in Poland during the ame period. The paper end with concluding remark. Human Capital Although there are many tudie on human capital, there are not many definition of thi pecific kind of capital. Even the famou author G. Becker doe not pecify the exact definition of human capital. In hi book, Human Capital. A Theoretical and Empirical Analyi with Special Reference to Education, he define it in the context of invetment difference between variou kind of capital (Becker 1993). Human capital could be defined a capacity for work, including the capacitie, kill, peronality and capabilitie of a peron. The pecific feature of human capital i ineparability of the owner and indiviibility. In contrt to phyical and financial capital, it i not poible to eparate a peron from hi or her knowledge, kill, health or value (Becker 1993), which cannot be bought, old, etc. Important element that form human capital are experience, knowledge, health, peronality, and kill. In the 1

7 Webter II New Riveride Univerity Dictionary (1984) we find the following definition of thee characteritic: a) experience knowledge or kill derived from active participation in event or activitie; the totality of uch event in the pt of an individual; b) health phyical and mental condition of the individual; c) individual knowledge knowledge derived from tudy, experience, or intruction; the um or range of what h been perceived, dicovered, or learned by an individual; d) peronality totality of qualitie or trait, of character or behavior, that are peculiar to an individual; e) kill collective et of art, trade, technique, or abilitie, epecially thoe requiring the hand or body. In the OECD report, The Well-being of Nation: The Role of Human and Social Capital, human capital i characterized in the following way: The knowledge, kill, competencie and attribute embodied in individual that facilitate the creation of peronal, ocial and economic well-being (OECD 2001: 18). Therefore, the iue i how to meure the accumulated tock of human capital on an individual level and on a population level, and which characteritic hould be taken into account in order to meure human capital appropriately. Method of Meuring Human Capital Variou method of meuring human capital can be found in the reearch paper of economit who try to explain the reon of economic growth, change in productivity and diproportion in development between countrie. In the early work on thee topic, human capital w equated with the labor force and counted a imple um of individual. Thi way of thinking h been changing gradually. Current reearch on human capital can be divided into three group: a) output-bed or education-bed meure; b) cot-bed meure; and c) income-bed meure. The mot widepread proxie of human capital bed on education are adult literacy rate (Azariadi and Drazen 1990; Romer 1990), chool enrolment ratio (Barro 1991; Mankiw et al. 1992), educational attainment and average year of chooling (Barro and Sala-i-Martin 1995; Krueger and Lindahl 2000). Thee proxie are imple and imperfect, but their acceibility to data make them popular in economic tudie. The cot-bed method take into conideration the cot incurred in the proce of human capital formation. Thu, the human capital of an individual equal thee cot. Stroombergen et al. (2002) indicate three tream of cot of human capital formation incurred by the individual or individual family, e.g., cot of tuition, foregone income; employer, e.g., upport of attendance at coure, on-the-job training; government, e.g., cot of running the education ytem. The drawback of thi approach are the unavailability of information about all cot, and the problem with human capital comparion between different time and population. For example, in a country where the cot are relatively low, an individual 2

8 with a high level of education h a maller tock of human capital than a peron with a imilar educational background in a country with higher cot. The income-bed meure treat human capital a variable expreed in unit of money. Thee method ume that human capital i valued by the market. The level of human capital equal the money (wage, earning) that omeone want to pay for it. Among thee method we find the dicounted tream of earning meure. Accumulated human capital i worth the ame the current value of all lifepan earning. In thi ce the market (relation between demand and upply) regulate the earning of individual. Employer price human capital, taking into conideration the productivity of employee. Thu, if an individual i more productive, he hould earn more, but if hi productivity decree, the earning hould be le. Thi method might ometime lead to incorrect concluion. The relatively larger cohort could experience a crowd effect on the labor market. The competition between people in uch cohort i tronger and lead to a decree in earning. Thi phenomenon i in accordance with the rule of the market which contitute that the price of good, whoe upply i relatively higher than demand, goe down. In thi ce, the earning cannot how the real value of human capital. It i poible that, among cohort with the ame educational tructure, ome have more human capital than other. Another iue i that the market i not perfect in the real world, therefore, earning are not perfectly dependent on the productivity of worker and upply-demand relation. Many factor can influence the level of wage, for example, the bargaining power of preure group uch labor union. In thi ce, worker who are in the majority and have the trong bargaining power can ecure their own financial tability. Thi lead to the ituation where individual with maller human capital reource and lower productivity can earn more than people who are better educated, more productive, and whoe power i maller. In the context of population ageing, it can be very problematic to meure human capital uing thi group of method becaue there will be more and more older worker who will have greater bargaining power than younger one. Method We preent a method that i bed on the magnitude of human capital that h been accumulated in an individual. It belong to the group of education-bed method, becaue the be of human capital accumulation i formal education (education during the year of chooling) (Kurkiewicz et al. 1999). But contrary to other method, it take into conideration other factor that influence the tock of human capital during a lifepan. Thi approach eem to be more adequate for tudying human capital formation in the context of population ageing becaue it include many different factor, but i not connected to earning. In the method preented here, the following factor are umed to influence individual human capital (ee alo Figure 1): learning during formal education; acquiring knowledge and experience during one profeional life; obolecence of knowledge; health; forgetting knowledge. 3

9 Learning Ability Acquiring Knowledge Acquiring Experience Formal Education Individual Human Capital Health Forgetting Knowledge Obolecence of Knowledge Figure 1. Outline of factor affecting human capital. We propoe to meure the human capital accumulated in an individual in the following way: h= h α β δ γ (1) where: h human capital accumulated in a peron at age a and education level ; h human capital accumulated during formal education; α rate of acquirement of knowledge and kill during profeional life; β rate of obolecence of knowledge; δ rate of forgetting knowledge; γ rate of an individual health condition. Thu, the tock of human capital i a product of five component which will be dicued in the ubection below. In thi method, the unit of meurement of human capital introduced by Polachek and Siebert (1993) i Ed. According to their definition: Ed repreent kill unit degree, qualification, on-job experience acquired by individual throughout life (Polacheck and Siebert 1993: 20). It i umed that 1 Ed equal one year of formal education. Thu, in the method preented in thi paper, all change (incree or 4

10 decree) in human capital tock during a lifepan are related to the amount of human capital accumulated during one year of education. Formal education The main ource of an individual human capital i the education obtained during the firt tage of a lifepan. During thi period, a peron acquire new knowledge and kill from the imple and bic kill of reading and writing in primary chool to more precie and complicated iue which become the bi for one profeional life, well learning about ocial behavior and life in general. The importance of education during thi period for the accumulation of human capital h been emphized by many reearcher (Mincer 1981; Schultz 1960). Becker wrote that education and training i the mot important invetment in human capital (Becker 1993: 17). The method preented in thi paper take into conideration the factor of acquiring kill and knowledge during formal education. A mentioned earlier, the meurement unit of human capital i Ed, which equal one year of formal education. For example, if an individual h been tudying for eight year in primary chool and four year in econdary chool, he would accumulate 12 Ed. Thi imple calculation ume that all year of education add the ame amount of Ed to the accumulated human capital. However, it i difficult to etimate which tage of formal education i more important. We cannot ay that one year of tertiary education i more valuable than one year of primary imply becaue people with a higher education earn more than leeducated people. It i impoible to tart at a higher level without the bic kill and knowledge acquired from an elementary education. Thu, we treat every year of education an invetment; thi give an output of 1 Ed to human capital. Acquiring new knowledge and experience during one profeional life The completion of formal education doe not finih the proce of increing the human capital tock. Thi proce lt during the whole lifepan of an individual; only the pace of acquiition change. During one profeional life two factor play major role in the accumulation of human capital. Firt, an individual can acquire new knowledge through life-long learning activitie, uch taking part in coure and lecture that are connected with the profeional career or by broadening a particular knowledge of peronal, non-profeional interet, etc. All of thee activitie add human capital to the individual tock. The econd factor i experience, which i acquired during the permanent performance of action, dutie and work. Experience improve peronal efficiency, competence and productivity (Prkawetz and Lindh 2006). The acquiition of individual human capital through learning and gathering experience depend on one mental abilitie (Park et al. 2002; Skirbekk 2004). Thee abilitie can be divided into two group: the fluid abilitie which decree during the life cycle, and the crytallized abilitie which remain at the ame level until the older age. Park et al. (2002) have found that a continuou, regular decline occur in the peed of proceing, the working memory, and the hort- and long-term memory during the lifepan ( of the age of 20) (ee Figure 2). Only verbal knowledge incree acro the period of life. Thee function are reponible for the ability to learn which i ued a 5

11 proxy for the change in abilitie to acquire experience and learn new knowledge during one profeional life. 1,5 1 Working memory Long-term Memory Verbal Knowledge Short-term Memory Speed of Proceing 0,5 Z core 0-0,5-1 -1, Age group (year) Figure 2. Lifepan performance meure. A compoite view of the aforementioned meure. Source: Park et al. (2002). To meure the change in human capital acquiition caued by the ability to learn, we ue the linear function bed on Park et al. reult. It i umed that the decree in the ability to learn take place between the age of 25 and 60. Before 25, the ability i table on the highet level. We ume that after the age of 60, it i table on the minimal level. Thu, the pace of human capital decree linearly between the age of 25 and 60. The accumulation of additional human capital unit (Ed) begin immediately after the end of formal education. In the firt year after completion of formal education, an acquiition rate of human capital (r) i the highet and remain table to the age of 25. The acquiition rate are the ame for all peron. It i umed that an annual incree of human capital ( Δ C ) cannot exceed 1 Ed. Thi i very important becaue otherwie an individual would prefer to leave education earlier and tart working. In thi ce, a peron could accumulate more human capital annually than during formal education and receive additional earning. Thu, the annual acquiition rate i counted : Δ C <1 r<1 h 6

12 1 r< h where h tock of human capital accumulated during formal education, r annual acquiition rate of human capital during profeional life. Individual with a tertiary education have the highet tock of human capital. In order to count the acquiition rate we ue the tock for thi group. We umed that they accumulate 16 Ed which equal 16 year of chooling. Therefore, the acquiition rate i 16 r <1 r < Hence, the umption i that a maximal annual acquiition rate equal 6.24 percent. Thi value i the ame for all education level. To etablih the minimal value of the acquiition rate, we ume that everyone h the ability to learn until the end of their live. They can obtain new knowledge and acquire experience, but thi proce i not effective and doe not bring ignificant growth in human capital for people of older age. Thu, the minimal annual acquiition rate i etablihed at the level of 1 percent. Thi level i achieved by people at the age of 60 and i table until the end of their live (ee Figure 3) acquiition rate (r) age Figure 3. Human capital acquiition during a lifepan. Source: Author own calculation. 7

13 Depite the umption that the curve of learning ability i the ame for all level of education, there are difference in the mental capabilitie of people with different educational background. Thee difference can be noticed in the reult of tudie on human intelligence. Kaufman and Lichtenberger (2002) how the reult of pychological tet run by many reearcher, uch Matarazzo (1972), Jenen (1980), and Reynold (1987), who found ignificant difference in intelligence between people with different educational and occupational accomplihment (ee Figure 4). The mean IQ level for people with tertiary education i around , which i about three time higher than for people without education or with only primary education (performing imple carpentry, mowing lawn). In thi paper, the difference in mental capabilitie are expreed by the human capital tock accumulated during formal education. For example, an individual with tertiary education h 16 Ed and hi acquiition of capital in the firt year of working life ( Δ C ) equal 0.99 Ed (16 x 0.624), while a peron 16 with primary education with 8 Ed of tarting capital h an incree of 0.49 Ed. The tage of education and the tarting human capital tock are preented in Table 1. Ph.D or M.D. College Graduate Clerical/Sale High School Graduate Semikilled Work 50% Reach High School Harvet Vegetable Perform Simple Carpentry Mow Lawn Mean IQ Figure 4. Mean adult IQ (reult from the Wecler IQ tet) that correpond to different educational and occupational accomplihment. Source: Kaufman and Lichtenberger (2002). 8

14 Table 1. Human capital accumulated during formal education by level of education. Source: Author own calculation. Level of education () Human capital (in Ed) 1 - Primary not completed Primary Bic vocational Secondary Pot-econdary Tertiary 16 The proce of accumulation, mentioned earlier, begin immediately after the completion of formal education. Thu, the function of human capital acquiition take into conideration the length of time pent in the working life (i). In the time range between the firt year of profeional life and the age of 25, the value of the function i at the ame level in the firt year (1). i 1,E l, Δ Ci =ΔC1 (2) where: i duration of a working life, education level of a peron, E year of working life at the age of 25 [number of year pent in profeional life to l the age of 25], Δ C annual acquiition of human capital during the working period, i Δ C 1 acquiition of human capital during the firt year of working life [the rate equal 6.24 percent]. Annual acquiition decree between the age of 25 and 60, according to the linear function in the following form: i E l +1, E, ΔC i ( ΔC1 ΔC z ) E ( ) E + 1 ΔC1 ΔC z (3) = i+ ( ) ΔC z El + 1 l where E year of working life at the age of 60 [number of year pent on profeional life to the age of 60], Δ C accumulation of human capital during the year E of working period [the rate z equal one percent]. After the age of 60 to the end of life, the function i contant at the level achieved at the age of 60 (Eq. 3). 9

15 ) i + 1,, E Δ C = Δ (4) i C z We have acquiition rate for a particular year of working life, but it can be ueful to preent acquiition rate for a particular individual at age a and education level. The accumulated human capital for a peron at age a and education level i: E i= 1 * h = h + ΔC (5) i where * h amount of accumulated human capital that include Ed from acquirement of kill and experience, E year of working life of an individual at age a and education level, initial amount of human capital accumulated during the period of formal education. h Thu, the acquiition rate ( α calculation, ee Appendix 1): i 1,E l, i E l +1, E, 2ElΔC α = 1+ i + 1, E α = ), α ) are counted uing the equation (for the = 1+ Δ E C1 h ( ΔC1 ΔCz )( 2E ( El + 1+ E) ) ( E + 1) 1 + ( E l) 2 ΔC z l E ΔC h ( E )( ΔC +ΔC ) l 1 l 1 1+ z + ( E ) ΔC where α i the acquiition rate of human capital for an individual at age a and education level. The equation for the accumulated human capital for an individual at age a with education level i: h * = α (9) h z (6) (7) (8) Obolecence of knowledge Acquired kill and knowledge loe their relevance with the ping of time. A civilization develop, part of one knowledge and kill become inapplicable due to technological progre and development in cience. But not all acquired kill and knowledge depreciate over time. For example, during primary education, individual learn bic kill uch reading and writing, which are the bi for peronal development. Thee kill do not loe their uefulne. The kill required for computer 10

16 programming are another example. During education a peron learn how to program the computer in a particular language. The relevance of thi knowledge depend on the technological progre. If thi language i not ued becaue new, more ueful program are developed, the acquired knowledge of the old language become unimportant and will no longer be ued. However, the peron retain the bic of programming which are till relevant and can be ued a bi to learn a new language. Neverthele, the peron lot ome part of hi/her human capital and we hould take thi into conideration when counting the human capital. Outlining the peed and coure of the depreciation proce i problematic. The pace of thi proce depend on the development of technology and cience. It i a poitive relation. The fter the development, the fter the pace of obolecence. Thu, the different knowledge and kill depreciate at different peed. In thi paper we do not take into conideration the difference between an individual educational background and occupational tatu. We are conciou that thi i a huge implification becaue people are not homogeneou in thi repect. Individual with different level of education have different coure of human capital depreciation for example, phyician and high-tech engineer but it i impoible to pecify all difference when accounting for the human capital of a population. To ume the coure of the obolecence of knowledge, we bed our reult on reearch regarding the depreciation of technological knowledge. The method of etimating depreciation rate preented here are bed mainly on technological change theorie (e.g., technology cycle time) (Abernathy and Utterback 1978; Ayre 1994) uing patent renewal data (e.g., Boworth 1978; Pake and Schankerman 1984) and patent citation data (Park et al. 2006). Park et al. (2006) ue data from everal indutrie to analyze the depreciation rate of technology. They find that there i a gradual incree of thee rate over time, and within 12 year, the change w about 2-3 percentage point (ee Figure 5). Thu, we umed the linear depreciation of knowledge and treated it a whole. The pace of depreciation i contant for every unit of human capital. It i umed that knowledge gained during primary education (Ed number from 1 to 8) doe not become outdated becaue it repreent imple, bic abilitie (e.g., reading and writing) which are ued during a lifepan. The ftet pace of ageing i umed for knowledge which i acquired during tertiary education. Thi knowledge i very precie, particular and dependant upon the development of cience and technology. We have to take into conideration that even during tertiary education, the level of detail incree with the advancement of the tudent. Thu, the rate of human capital depreciation i different for the particular Ed accumulated during formal education. The proce of the obolecence of knowledge begin immediately after the accomplihment of formal education. The pace of depreciation i contant during the working life, but it i different for the particular Ed accumulated during formal education. 11

17 0,17 0,16 0,15 Depreciation rate 0,14 0,13 0,12 0,11 0, Indutrial ector Indutrie: 1 - food and beverage 8 - bic metal 2 - textile 9 - fabricated metal 3 - wood product 10 - machinery 4 - paper, printing and publihing 11- electrical, computing and communication 5 - chemical 12 - preciion 6 - rubber and pltic 13 - tranport equipment 7 - non-metallic mineral 14 - other manufacturing Figure 5. Changing pattern of depreciation rate acro indutrie in three-year interval. Source: Park et al. (2006). Table 2. Annual depreciation of human capital according to the number of Ed. Source: Author own calculation. Ed no. Annual depreciation *(9-8)/100=

18 1.1 1 l<=8 0.9 l= l=12 Ed 0.7 l= l=16 time Figure 6. Depreciation of particular unit of human capital which were accumulated during formal education. Source: Author own calculation. The depreciation of human capital i preented in Table 2 and Figure 6. We ume that the lt unit of human capital (accumulated during the lt year of tertiary education) decree by 50 percent over 100 year. The decree of the other unit are proportionally lower. Thu, the annual depreciation for a particular unit of human capital i counted in the following way: ( l 8), 100 where l i the number of Ed in order. The equation for accumulated human capital that conider the influence of the obolecence of knowledge i: h = 8+ h l= 9 [ 1 E ( l 8) ] Uing Eq. (9) we can calculate the depreciation rate ( β ) for an individual at age a and education level (the calculation can be found in Appendix 2): β = E ( h 7)( h 8) 2h (10) (11) Forgetting knowledge The next factor of human capital depreciation included in thi method i the proce of forgetting knowledge. In contrt to the obolecence of knowledge, which i 13

19 independent of an individual, forgetting knowledge depend on peronal abilitie. Forgetting i the decline of memory retention over time. The pace of forgetting i connected to the trength of one memory. The tronger the memory, the longer an individual can retain the knowledge. In the context of human capital meurement we have to take into conideration the long-term memory and the proce of forgetting during the lifepan. The firt ignificant reearch about memory retention and forgetting w run by Ebbinghau (1913), who publihed a book about thee topic in He argue that there exit an exponential nature of forgetting, which can be decribed : R e t / = (12) where R i memory retention, i trength of mind, and t i time. Ebbinghau made a hort-term tudy on the change in retention during the learning proce and the influence of repetition on the forgetting proce. The very important finding i that forgetting occur rapidly at firt and more lowly time goe on (Kahana and Adler 2002). Thi i till accepted in pychological cience, but the function equation i quetioned by many cientit (e.g., Wixted 1990; Rubin and Wenzel 1996). Some cientit are in favor of the power function equation, arguing that bed on the reult of their reearch, the power law can be applied to forgetting (Kahana and Adler 2002). One of the cientific paper that examine long-term memory i by Bahrick (1984). He reearched the retention (the ability to retain fact and figure in one memory) of the Spanih language learned at chool during a period of 50 year. He found that the highet pace of forgetting knowledge i oberved in the firt three year after completion of a language coure. During thi time, an individual loe about percent of hi/her knowledge (Figure 7). After that period the pace of forgetting i very low. At the end of the period under conideration, a peron till h about percent of all knowledge acquired at chool. Figure 7. Adjuted retention function. Source: Bahrick (1984: 10-11). 14

20 In the method preented in thi paper, we ume that the proce of forgetting knowledge tart immediately after the completion of formal education. The depreciation function i the ame for all education level. Taking the reult of Bahrick reearch into account, we ue the memory retention rate (γ ) bed on the power function: ( ) w γ (13) = z E where z, w are the parameter. The rate repreent the knowledge that i till remembered. Thu, the depreciation rate equal (1- γ ). Figure 8 how the memory a retention rate during the period of working life memory retention duration of profeional life Figure 8. Memory retention rate. Source: Author own calculation. In order to calibrate the function, we ume that during a period of 50 year of working life, an individual loe about 30 percent of hi/her human capital due to the proce of forgetting. We cannot be our finding exactly on the reult of Bahrick becaue we do not take the knowledge repetition proce into account (Jaber and Kher 2002). We ue the following equation: γ = ( E ) Health One of the mot important factor of human capital creation i an individual health. The importance of health i emphized by Becker (1993) and Mincer (1981). They treat expenditure on health improvement (e.g., medical care) an invetment in human capital. Human capital theory treat the tate of health tock-health capital. Thi tock depreciate over time at an increing rate in later age (Schultz 1981). 15

21 In the method preented in thi paper, change in health are a factor of depreciation of human capital. Together with ageing, the condition decree and becaue of that, accumulated human capital become maller. A very important factor in determining incentive to invet in human capital and the value of it tock i the life expectancy of a population (Schultz 1981). Thu, we meure the influence of health on human capital formation uing information from the period life table. In our method the intenity of depreciation i proportional to the mortality of a population. It might be better to ue the data from health life table (healthy time, ickne-free time) which take into account the change in health condition of a population, but they are not commonly ued. The equation for the rate i: L( a) δ = L( a where L (a) tationary population at age a ) L( a E ) tationary population at age a E Thi meure how how much human capital i till poeed by an individual at age a. Thu, the depreciation rate h the form: 1- δ. It i umed there are no health difference between people with different level of education (but of coure it i poible to ue pecific education life table in our method). The only difference implemented in the meure i the duration of formal education which influence the value of L( a E ). Uing Eq. (14) we compare the health condition of an individual at age a with the value from the beginning of hi/her profeional life. The improvement in mortality caue an incree in the health rate δ and hamper the proce of human capital depreciation. (14) Individual Human Capital Profile Uing data from Poland we etimate the tock of human capital by age and level of education. We ume ix age group: 15-25, 25-35, 35-45, 45-55, 55-65, and 65 and older. Inide each particular group, people are at the median (e.g., it i umed that in group 15-25, people are 20 year old). There are alo ix education group: primary not completed, primary, bic vocational, econdary, pot-econdary and tertiary. We count the human capital accumulated during formal education by taking the duration of chooling on the different level in 2002 (ee Table 1). It i umed that rate of acquiring experience and learning new knowledge during the profeional life ( α ), obolecence of knowledge ( β ), forgetting knowledge ( γ ) are the ame for all population. There are no difference between population in thi repect, with biological abilitie (cognitive abilitie) connected to acquiring experience and learning, and forgetting knowledge. The technological progre affect all population in the ame way. The differentiation factor are duration of the formal education and health condition. In thi exercie we ue the period life table for male in

22 Taking all of thee factor into account, we etimate ix education-pecific human capital profile (ee Figure 9). The reult ugget that human capital follow an inverted U-haped profile where the ignificant decree of the tock are found after the age of 45. It i independent of the education level. But there are difference between the profile: The better the education, the teeper the curve. The very flat profile i found for people with primary not-completed education. The teeper profile i oberved for tertiary education. The peak of human capital tock i achieved in the age group Figure 9. Education-pecific human capital profile. Source: Author own calculation. In the context of population ageing, it i very important to undertand how improvement in the health condition of a ociety and the fter pace of progre in cience and technology could influence human capital formation. In the method preented in thi paper, the development in health condition i hown through an incree in the health rate δ (ee Eq. 14). We preent three level of life expectancy at birth which could how the progre of health condition (life expectancy equal 60, 70 and 80 year). Uing the human capital profile for tertiary education, thi phenomenon can be een in Figure 10. An incree in life expectancy ignificantly affect the human capital profile. There are change in the hape of the curve and in the level of human capital for all age group. The curve become more flat the decree in human capital at older age low down. The level of human capital are the highet when life expectancy equal 80 year. For example, there i a growth of about 32 percent in the age group The mot important finding i that the peak of the human capital profile change with the progre in life expectancy. The peak hift to the older age group. 17

23 Ed LE= 60 LE=70 LE=80 ag e Figure 10. Human capital profile for tertiary education by level of life expectancy. Source: Author own calculation. Another important factor i the influence of technological and cientific progre on ociety. The acceleration of progre give rie to the fter pace of the obolecence of knowledge. Thu, the human capital tock decree fter under the ceteri paribu umption. In the method preented in thi paper, we ume that the latet accumulated unit of human capital decree by 50 percent during 100 year, but we alo tet other cenario that ume a more rapid pace of knowledge obolecence. The following cenario were prepared: I. The latet accumulated unit of human capital decree by 50 percent during the next 100 year of an individual life. II. The unit decree by 80 percent during the next 100 year. III. The unit equal 0 after 100 year; and then IV. The unit decree by 80 percent during the next 50 year. The reult are preented in Figure 11 and 12. We ume that the human capital tock of people with low education doe not depreciate becaue their knowledge i bic. Thu, we can focu only on the econdary and tertiary education level. There i a very weak effect of the progre of acceleration on the human capital profile of individual with a medium education level (ee Figure 11). People with a higher education could loe more human capital with accumulated tock during the acceleration, becaue part of their knowledge i very pecific and depreciate quickly. The effect are connected to the peed of progre: The fter the progre, the higher the loe of human capital. The overall influence i rather moderate. Change are viible particularly in the older age group (ee Figure 12). 18

24 25 Ed age I II III IV Figure 11. Human capital profile for level of econdary education by the peed of the obolecence of knowledge. Source: Author own calculation. 25 Ed I II III IV age Figure 12. Human capital profile for level of tertiary education by peed of the obolecence of knowledge. Source: Author own calculation. 19

25 Interaction Rate and Aggregated Human Capital When etimating human capital for a population treated a whole, it i neceary to take into account the ocial pect of an individual. A particular peron i not iolated from the other member of a ociety. The ource of additional human capital tock of a population could come from the interaction between people. In the proce of human capital formation, the effect of ynergy can exit (Fuller 1975; Hkell 1972). Thu, the tock of human capital of peron acting together i greater than a imple um of individual human capital. Thi concept i imilar to the ocial capital term that i ued mainly by ociologit and economit. Coleman (1988) et apart three form of capital: Phyical capital, created by change in material to form tool that facilitate production; Human capital, created by change in peron that bring about kill and capabilitie that make them able to act in new way; and Social capital, that come about through change in the relation among peron who facilitate action. It exit in the relation among peron. The manifetation of ocial capital are, among other, authority relation, relation of trut, norm, and tie between group. Many cientit emphize the influence of ocial capital on economic activity (Ben-Porath 1930; Baker 1984; Putnam et al. 1993). For example, Knack and Keefer (1997) examine the relation between ocial capital and economic performance uing two very important variable of ocial capital: trut and civic norm. They have found that trut and civic cooperation have ignificant impact on aggregate economic activity. In thi paper we ue the concept of ocial capital in a different way. We do not eparate human and ocial capital, but we notice the product of the interaction between peron additional human capital on the level of population. The ynergy effect of human interaction i very hard to meure. We ue the interaction rate propoed by Kurkiewicz et al. (1999), which take into account only imple pair of interaction. The main umption of thi meure are: a) Interaction exit only inide the population; b) The value of the interaction i not dependent on age and ex but rather on the level of education. It equal the arithmetic mean of the input of the group taking part in the interaction; c) The interaction rate i counted ingle interaction, all with all; and d) The interaction of people with tertiary education double the number of human capital. Thi influence i proportionally lower for individual with lower education. The interaction are meure according to following equation: 6 6 bij ( hi + h j ) i= 1i= 1 I = 1+ (15) r bij i= 1i= 1 where 20

26 b ij Pi Pj = 0,5 Pi ( Pi 1) P i and i j i= j P j number of people with education level i or j b ij number of available interaction of people with education i and j. In order to meure aggregated human capital we ue the equation n n HC= Ir h p a= 1= 1 (16) where p i the number of people in age group a on education level. Population Projection for Poland, In order to project change in human capital formation in Poland, we prepare a population projection by age, ex and education. The mot important iue i to include educational differential for mortality and fertility. We ue the multi-tate demographic population method where individual tate are level of education. The education ytem h been changed in Poland, but the level from 2002 are ued in the projection. An individual may chooe one of the ix tage of education preented in Figure 13. Te rtiary Se condary Primary not completed Primary completed Bic vocational Pot-e condary Figure 13. Outline of the ix level of education. The tranition rate between tate are calculated uing the method bed on the education attainment progreion ratio (EAPR) firt introduced by Lutz et al. (2007). In thi paper only one cenario of the projection i preented. In thi cenario we ume that the pace of fertility change within education group following the UN projection (medium variant) for the Polih population. Thu, the relative difference in age-pecific fertility rate between education group are table at the 2002 level during the period The pace of change i the ame for all education-age-pecific fertility rate. It i umed that life expectancy for all education group i table at the 2002 level (ee Table 3). 21

27 Table 3. Life expectancy at birth by level of education. Source: Author own calculation uing data from the Central Statitical Office in Poland. Level of Education Male Female Tertiary Pot-econdary Secondary Bic Vocational Primary Completed Primary Not Completed The flow of migration i alo at the 2002 level. The cenario i very optimitic about fertility becaue it i bed on the UN umption that the total fertility rate (TFR) will incree and reach a level of 1.85 at the end of the period under conideration. However, it i peimitic about life expectancy becaue it doe not predict the progre of the lifepan duration. Thu, the cenario ume a lower pace of population ageing than could happen in the real world in the future. The data for the tarting population come from the Central Statitical Office in Poland. The data for the population tructure by age, ex and education in 2002 come from the National Population Cenu The age pyramid for 2002 (ee Figure 14) how that progre h been made in the educational development of Poland. Among the age group 65+ a hare of the people with low education (primary not-completed and primary) i more than 50 percent (54 percent for male and 71 percent for female). In the younger age group the hare of people with low education i ignificantly lower. Among medium age group the people with a medium level of education predominate. Another finding i that more women have tertiary education than men. For example, in the population aged 25-29, the hare of female with a higher education i 25 percent, where for male it i only 17 percent. During the next 50 year there will be ignificant change in the population tructure (ee Figure 15 and 16). The hare of people 65+ will incree from 12.7 percent in 2002 to 18 percent in 2027 and 23.3 percent in The population will decree from 38 million to about 30 million. At the ame time, the working population (aged 15-64) will decree by 8 million to the level of 18 million. Thu, the hrinkage of population and population ageing i projected. The level of education will incree. In 2052 the hare of the population with a tertiary education will be about 25 percent for male and 38 percent for female. 22

28 primary not completed primary completed bic vocational econdary pot-econdary tertiary Figure 14. Age and education pyramid for Poland in Source of data: The Central Statitical Office in Poland, primary not completed primary completed bic vocational econdary pot-econdary tertiary Figure 15. Age and education pyramid for Poland in Source: Author own calculation. 23

29 primary not completed primary completed bic vocational econdary pot-econdary tertiary Figure 16. Age and education pyramid for Poland in Source: Author own calculation. Human Capital in Poland in Uing data from the population projection and education-pecific human capital profile, we calculated the human capital tock for the Polih population at age in Figure 17 how change in the working population and adjuted population for human capital in Poland. It i umed that the average individual human capital in 2002 equal 1. The working population incree lightly to 2012 and then it decree gradually to the level of 18 million people. The pace of incree of the adjuted population i higher than the working population becaue of the progre of education. After 2012 human capital decree, but the pace i lower than the change in the working population. The reult how that aggregated human capital in Poland will decree in the next 50 year. 24

30 Million Population Human Capital Figure 17. Working population (aged 15-64) and human capital (aged 15-64) in Poland in Source: Author own calculation. From an individual human capital formation point of view, the future for Poland will be very optimitic. The average human capital per capita will incree about 22 percent (ee Figure 18). The convex part of the line indicate thoe year in which welleducated people with large cohort reach the age where individual human capital i the highet. 1,25 1,2 1,15 1,1 1, Figure 18. Average human capital per capita in Poland in Source: Author own calculation. 25

31 The ituation eem to be rather peimitic when we conider the aggregated human capital for population. Figure 19 how the relative change in human capital with reference to the year 2002 (HC=1). Human capital peak in 2012 with an incree of 10 percent. After 2012 a decree i oberved. The reon for thi decree i the projected development of education in Poland, well a decree in the ize of the workforce. In 2037 (after 35 year) the level of human capital i the ame it w at the beginning of the period under conideration! Then human capital decree even fter and in 2052 reache a level that i 15 percent lower than in Thu, the potential of human capital that can be ued in creating economic growth will hrink within the next 50 year. The conequence could be very negative for the Polih economy, which i trying to catch up to the level of development of the old EU countrie. 1,2 1,1 1 0,9 0,8 0,7 0,6 0, Figure 19. Aggregated human capital (workforce) in Poland in Source: Author own calculation. Concluion We preent a modified method of human capital meurement. In contrt to other education-bed method, rather than conidering only one factor, our take into account the following factor affecting human capital formation: education, acquiring knowledge and experience, obolecence of and forgetting knowledge, and the impact of health. The complexity of the human capital formation proce require implification and umption which could be diputable, but the method preented in thi paper eem to be uitable for following through thi formation in the ituation of workforce ageing. The reult ugget that individual human capital follow an inverted U-haped profile where the ignificant decree of the tock are found after the age of 45. It i 26

32 independent of an education level, but there are difference between the profile the better the education, the teeper the curve. The very flat profile i found for people with primary not-completed education. The teeper profile i oberved for thoe with a tertiary education. The peak of human capital tock i achieved in the age group The procee of population ageing and de-population will influence more and more ocietie and economie. In the labor market it will caue a hrinkage of the workforce and change in workforce tructure. An incree in a population level of education can low down the negative conequence of thi demographic proce, but it cannot top them. Conequence of workforce ageing can be conidered in the hort and long term. In the hort term, accumulated human capital could incree if well-educated worker from large cohort reach the age at which their human capital i the highet. However, in the long term, a decree in aggregate human capital i expected becaue the working-age population hrink. Thi could alo affect economic growth level in the future. Reference Abernathy, W. and J. Utterback Pattern of indutrial innovation. Technology Review 80: Ayre, R.U Toward a non-linear dynamic of technological progre. Journal of Economic Behavior and Organization 24(1): Azariadi, C. and A. Drazen Threhold externalitie in economic development. The Quarterly Journal of Economic 105: Bahrick, H.P Semantic memory content in permtore: Fifty year of memory for Spanih learned in chool. Journal of Experimental Pychology: General 113(1): Baker, W.E Floor trading and crowd dynamic. Page in P.A. Adler and P. Adler (ed.), The Social Dynamic of Financial Market. Greenwich, CT: JAI Pre. Barro, R.J Economic growth in a cro ection of countrie. The Quarterly Journal of Economic 106: Barro, R.J. and X. Sala-i-Martin Economic Growth. New York: McGraw-Hill. Becker, G.S Human Capital. A Theoretical and Empirical Analyi with Special Reference to Education. Chicago: Univerity of Chicago Pre, 3 rd edition. Ben-Porath, Y The F-connection: Familie, friend, and firm and the organization of exchange. Population and Development Review 6: Boworth, D.L The rate of obolecence of technical knowledge. A note. Journal of Indutrial Economy 26: Coleman, J.S Social capital in the creation of human capital. American Journal of Sociology 94: