The effects of education subsidies on human capital accumulation: a numerical analysis of macroeconomy in China.

The effects of education subsidies on human capital accumulation: a numerical analysis of macroeconomy in China. 1. INTRODUCTION In this paper, we conduct a macroeconomic simulation using nationaldata from China based on the six-period overlapping generations (OLG)model of Bouzahzah et al. (2002) and human capital formation employed byDocquier and Michel (1999). Two types of education subsidy are examined:firstly, subsidy for expenditure on quality of education (SEQ), the mainform of subsidy provided by the Chinese government, and secondly,subsidy for opportunity cost of education in terms of foregone wageincome (SOC), which are at present not used in China. The effects ofthese subsidies on human capital accumulation are also compared with thecase of human capital accumulation dependent only on the factor ofeducation time as described in Bouzahzah et al. (2002). Since its market-oriented economic reform in 1978, China hasachieved outstanding economic development with an annual GDP growth rateof nearly 10 percent. This rapid development has been accompanied by anincrease in the demand for post-basic education. It is a demand that hasbeen growing sharply despite the abolishment of free higher education in1985. Because education is regarded as a key element determininglong-term economic growth, the government has also pushed to expand andimprove the quality of post-basic education by providing subsidies.1Consequently, it is critical for policy analysis that an adequate systemof assessing the subsidy policy is established. Such a system is alsovital for raising the country's economic competitiveness on theworld market. Auerbach and Kotlikoff (1987) extended Diamond's (1965) OLGmodel by introducing a dynamic simulation model and applied the model inthe field of public finance. Auerbach and Kotlikoff's (1987)seminal paper has been followed by an extensive literature discussingvarious public policies, including education. Docquier and Michel(1999), for example, was one of the first studies to examine thetradeoff between education subsidies for the younger generation andpensions for the elderly in European countries with aging societiesusing a simple three-period OLG model. The analysis indicates that inEurope higher economic growth can be achieved with the introduction of ablended policy comprising both SEQ and SOC on an equal basis. AlthoughDocquier and Michel's (1999) study was credited with contributingto the establishment of the dynamic endogenous growth model, the threeperiods of the lifecycle model was too simple a form by which the impactof education on the individual lifecycle could be examined. Otherstudies include those by Fougere and Merette (1999), who conducted asimulation in seven OECD countries using a 15-period OLG model, andSadahiro and Shimasawa (2001) who focused on Japan using a similarframework as Fougere and Merette (1999), but incorporated the element ofphysical capital in human capital formation. However, the role ofgovernment in financing education, which significantly affectsindividual incentives to accumulate human capital, was omitted fromthese analyses. Bouzahzah et al. (2002) extended the model of Docquierand Michel (1999) to a more realistic six-period OLG model and specifiedhuman capital formation as a function of the time invested in educationas in Fougere and Merette (1999). Bouzahzah et al.'s (2002) studyshowed that an endogenous growth model can serve an important role ineducation policy. However, by ignoring the quality input from the humancapital formation, which contradicts empirical evidence, the model mayfail to measure the human capital level appropriately. (2) Seeking to overcome the weaknesses in other models, we use thehuman capital formation used by Docquier and Michel (1999) based on thesix-period OLG model of Bouzahzah et al. (2002) and apply the model toChina. We then investigate the effects on human capital accumulation ofthe government's introduction of the SOC as described by Docquierand Michel (1999). The results obtained by the numerical analysis showthat, while there is no obvious difference in education time per personbetween the two subsidies, significant difference is found inexpenditure on quality of education. These results reveal that there isa strong possibility that growth will slow down with the implementationof SOC. As a consequence, it may be unwise to estimate human capitalwithout considering the quality aspect. The paper is organized as follows. Section 2 describes theframework of the model. Section 3 explains the process of parametersetting and calibration. Section 4 compares the impacts on economicgrowth between the two types of education subsidies. Section 5 concludesthe paper with limitations of the model and implications for policydevelopment. 2. THE MODEL In this section, we develop a six-period OLG model of endogenousgrowth in discrete time with 10 years considered as one period. Weassume a perfectly competitive, closed economy. (3) The economy in themodel includes three kinds of economic agents: homogeneous individuals,a representative firm, and the government. The individuals conducteconomic activities for six periods from 15 to 74 years of age, with the0-14 age band being an economically nonproductive one. (4) It is assumedthat there is no uncertainty in the life span of the individuals. Forsimplicity, the population is assumed to remain unchanged; that is, thepopulation in each age group is normalized to one (e.g., age group 1 isfrom 15 to 24 years old, age group 2 is from 25 to 34 years old, etc.).(5) The firm and individuals have perfect foresight regarding governmentpolicy. 2.1 Human capital formation We define individuals who begin economic activities from period tas generation t. The individuals of generation t choose both theireducation time and expenditure for quality of education in the first agegroup. Thus, their human capital is formulated as: [h.sup.2.sub.t-1] = (1 + [B.sub.e.sub.t][q.sup.[theta].sub.t])[h.sup.1.sub.t] (1) [h.sup.f.sub.j] represents the human capital level of individualsin age group j in period t. Education time and expenditure on quality ofeducation are represented by [e.sub.t] and [q.sub.t], respectively. B(>0) is the human capital productivity parameter.[epsilon](0<[epsilon]<1) and [theta] (0<[theta[<1) areparameters for education time investment and for quality educationinvestment, respectively, and [epsilon] + [theta] < 1 indicates adecreasing return to scale. The inheritance of the human capital of theprevious generation in the first age group is regarded as a positiveexternality of education, and is expressed as [h.sup.1.sub.t] in thefollowing equation: [h.sup.1.sub.t] = (1+ [Be.sup.[epsilon].sub.t-1][q.sup.[theta].sub.t-1])[h.sup.1.sub.t-2]. After individuals formulate their human capital in the first agegroup given as (1), their human capital is accumulated throughon-the-job training. The parameters are exogenously given as[[sigma].sup.j] (j=2, 3, 4, 5, 6), where j denotes an age group. Hence,the human capital level in each age group is obtained as follows: (6) [h.sup.j.sub.t-j-1] [equivalent to] [[phi].sup.j] (1 + B[e.sup.[epsilon].sub.t] [q.sup.[theta].sub.t]) [h.sup.1.sub.t]. (2) 2.2 Firm A representative firm uses the constant-returns to scale technologyto produce a composite good that can be either consumed or used ascapital. The firm rents capital and effective labour to maximize itsprofit. Denoted by capital letters, the aggregate production function isgiven as: [Y.sub.t] = A [K.sup.[alpha].sub.t] [L.sup.1-[alpha].sub.t] (3) where [Y.sub.t], [K.sub.t] and Lt are respectively aggregateoutput, capital, and effective labour in period t. (7) A (>0) and[alpha] (0 < [alpha] < 1) are parameters for the exogenously giventechnology and capital income share. The lower case letter [k.sub.t] isdefined as being equal to the per effective labour variable, that is:[k.sub.t] = [K.sub.t],/[L.sub.t] which gives us [y.sub.t] =A[k.sup.[alpha].sub.t]. The labour market is assumed to be perfectly competitive. Thesupply of labour arises from individual tradeoffs between work andstudy. By normalizing one period as one time unit, the time not spent oneducation, 1- [e.sub.t], is allocated to labour in the first age group.The second, third, and fourth age groups inelastically supply one unitof their time. The fifth age group supplies 1 - [[zeta].sub.t] (0 <[[zeta].sub.t] < 1) of their fixed time for labour, and then retires.In sum, the aggregate effective labour time supply in period t is thusgiven by: Lt [equivalent to] [5.summation over (j=1)] [l.sup.j.sub.t[h.sup.j.sub.t], (4) where [l.sup.j.sub.t] is the labour supplied by individuals in agegroup j in period t, and ([l.sup.1.sub.t], [l.sup.2.sub.t],[l.sup.3.sub.t], [l.sup.4.sub.t], [l.sup.5.sub.t]) [equivalent to] (1 -[e.sub.t], 1,1,1,1 - [[zeta].sub.t]). Given that the profit-maximizing firm hires the factors ofproduction until their marginal productivities are equal to theirmarginal costs, we can derive the following two conditions: [delta] + [r.sub.t] = A [alpha] [k.sup.[alpha]-1.sub.t] (5) and [w.sub.t] = A(1 - [alpha])[k.sup.[alpha].sub.t] (6) where [delta] (0 < [delta] < l) is the invariant capitaldepreciation rate, and [r.sub.t] and [w.sub.t] are the rates of returnto capital and effective labour, respectively. 2.3 Individuals The individual preferences are given by the constant elasticity ofsubstitution (CES) utility function. The lifetime utility function isadditively separable in the instantaneous utilities which are discountedby a constant rate of time preference as: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7) [c.sup.j.sub.+j-1] is the per capita consumption level in age groupj in period t and [gamma](0 < [gamma] < 1) and [sigma] [member of]R are the time preference rate and intertemporal elasticity ofsubstitution, respectively. The individual lifetime budget constraint of generation t isexpressed as below: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8) The present value of the lifetime expenditure, shown on the lefthand side of the equation, is the sum of the gross consumption in eachage group and the expenditure for quality of education in the first agegroup, while the present value of the lifetime income, shown on theright, is the sum of the disposable income and public transfer.[[tau].sub.c,t] (0 < [[tau].sub.c,t] < 1) is the consumption taxrate in period t and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]is the expenditure for quality of education per effective labour unit.[w.sub.t] and [[tau].sub.w,t] (0 < [[tau].sub.w,t] <1) are thewage income rate per effective labour unit and the wage income tax ratein period t, respectively. T.sup.j.sub.t+j-1] consists of two types ofpublic transfers: education subsidies in the first age group and publicpension payments in the fifth and six age groups are shown as[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [v.sub.q,t] (0< [v.sub.qt] < 1)are the rates of SOC and SEQ. [p.sub.t] is thepublic pension payment rate per effective labour unit. Individuals maximize their lifetime utility in (7) under theirlifetime budget constraint (8) and human capital formation (2) withrespect to their choice of consumption, [c.sup.j.sub.t+j-1], educationtime, [e.sub.t], and expenditure on quality of education, [q.sub.t]. First of all, we can obtain the levels of [e.sub.t] and [q.sub.t]by simply maximizing lifetime budget as: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10) It is worth noting that [e.sup.*.sub.t] and [q.sup.*.sub.t] do notdepend on the human capital level; instead, their education time andexpenditure for quality of education are determined regardless of theirlevel of human capital. Next, the optimal distribution of per capita consumption for eachage group can be expressed by the following five Euler equations: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11) On the other hand, per capita assets for each age group are definedby: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12) Thus, the optimal asset level in per capita terms in each period isobtained by substituting [c.sup.*] and [q.sup.*] in (12). 2.4 Government In each period, the government levies taxes on consumption and wageincome and issues debts. It also provides education subsidies, pensionpayments, other government expenditures and interest payments for thedebt issues. Therefore, the government budget constraint in period is: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13) Where [C.sub.t]. [P.sub.t], [G.sub.t] and [D.sub.t] are aggregateconsumption, the exogenously given pension payment, the exogenouslygiven other government expenditures, and debt issues in period t,respectively. We simplify the analysis by assuming a balanced governmentbudget through the adjustment of debt issues in each period. Thisadjustment also allows the changes of debt level that influence capitalaccumulation to be examined. (8) The aggregate variables are expressedas follows: [C.sub.t] [equivalent to] [6.summation over (j=1)] [C.sup.j.sub.t],(14) [P.sub.t] [equivalent to] [6.summation over (j=5)] [[zeta].sub.t] +1) [p.sub.t] [h.sup.j.sub.t], (15) [G.sub.t] [equivalent to] [6.summation over (j=1)] [g.sub.t][h.sup.j.sub.t], (16) and [D.sub.t] [equivalent to] [5.summation over (j=1)] [d.sub.t][h.sup.j.sub.t], (17) [g.sub.[tau]] and [d.sub.t] are as other government expendituresand debt issues per effective labour unit, respectively. We define[p.sub.t] [h.sup.j.sub.t], [g.sub.t] [h.sup.j.sub.t], and [d.sub.t][h.sup.j.sub.t] as per capita expenditures to let [p.sub.t,] [g.sub.t]and [d.sub.t] be constant in the steady growth path, where the economicgrowth rate becomes constant over time. 2.5 Dynamics The dynamic system in this model is governed by both physicalcapital per effective labour unit and human capital. The former takes aconstant value, while the latter achieves a constant growth rate in thesteady growth path. Given that in this model the goods market clears, the capitalmarket equilibrium in period t is defined as the aggregate capital inthe next period being equal to the aggregate assets in the presentperiod less aggregate debt issues in the next period. T his isrepresented as: [K.sub.t+1] = [5.summation over (j=1)] [a.sup.j.sub.t] [D.sup.t+1](18) From (4) and (11), (18) can be rewritten in per effective labourunit as: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19) where [a.sup.j.sub.t] is the asset per effective labour unit. Second, modifying the dynamics of human capital accumulation in (1)using (4), (5), (6), (9) and (10), we can obtain the human capitalgrowth rate, namely, the economic growth rate which depends only on[k.sub.t] as: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20) Consequently, in the steady growth path [k.sup.*], [a.sup.*],[d.sup.*], [l.sup.*] and in (19) become constant. Moreover, substituting[k.sup.*] into (20), h takes a constant growth rate in the path. 3. PARAMETER SETTING AND CALIBRATION In this section, we describe the setting of parameters usingChinese data and calibrate the model explained in the previous sectionwith the parameters. Considering one period as 10 years in this model,we use the most up-to-date available data during the past 10 years from1998 to 2001, and input the annual average values into the model todetermine the parameter values. Unless otherwise specified, the data arefrom the China Statistical Yearbook from 1999 to 2008. The parametervalues are summarized in Table 1. First, we set the parameters of human capital formation. The datawe use are the average school life expectancy over a 10-year period(1998 to 2001), which is of 10.63 years (UNESCO, 2008), and the averageeducation expenditure per senior secondary student over the same period(China Statistical Yearbook). Because our interest lies in the long-termeconomic growth, we set the human capital/economic growth rate to matchthe long-term economic growth rate figure of 2.5 percent comparable tothat seen in many developed countries. The three values described aboveare assigned to (1), (9), and (10), which are then solved as a set ofsimultaneous equations to obtain values of the productivity parameter(B), and parameters for education time investment ([epsilon]) andquality education investment ([theta]). The parameter values ofon-the-job training or human capital depreciation ([[sigma].sup.j]) arefrom Ma's (2005) empirical data, which revealed, interestingly,that the wage profile in China does not follow an inverted U-shape oftenseen in developed countries but, instead, shows an increase with age. Second, the production function parameters are obtained based onthe national accounts to match the actual economic circumstances. Thelabour income share (1 - [alpha]) is calculated from the sum of theregional compensation of employees divided by the sum of the netregional products at factor cost. The capital income share ([alpha]) isdetermined for the production function to be homogeneous of degree one.Applying the elasticities and amount of total capital stock during thepast 10 years, we can compute the technology parameters (A). The capitaldepreciation rate ([delta]) is derived from the average depreciation offixed assets during the past 10 years. Since we lack empirical data for China, we cannot determine theparameters for the utility function in a straightforward manner. Due tothe lack of consistency in the values employed in various studies,controversy remains even in developed countries about the exact figureto use for these parameter values. Because we obtain realistic interestand saving rates later when we calibrate the model, the time preferencerate ([gamma]) and intertemporal elasticity of substitution ([sigma])are the same values as those of the European case described by Bouzahzahet al (2002). Lastly, we assign seven policy variables as follows. Theconsumption tax rates ([[tau].sub.c]) and wage income tax rate([[tau].sub.w]) are computed based on the final consumption expenditure,total wages and the amount of each tax revenue during the past 10 years.The rate of the SOC ([v.sub.e]) are calculated from the governmenteducation expenditure per senior secondary student divided by the percapita net compensation of employees. The rate of the SEQ ([v.sub.q])is the share of government education expenditure per senior secondarystudent of the total education expenditure, including tuition andmiscellaneous fees. The pension payment (p) is obtained from the totalpension payment divided by the population over 65 years of age. (9) T heretirement ratio ([zeta]) is set as 0.5 because the average retirementage for male workers is 60 years of age. (10) The figure for other formsof government expenditure (g) is derived from total governmentexpenditure minus total education expenditure, pension payments, anddebt issues divided by the population. Using these parameter values, we conduct calibration to obtainequilibrium values in the steady growth path. We define the steadygrowth path with the SEQ as the base case reflecting the currenteducation system in China, and the SOC as the simulation case. Firstly,[h.sup.1.sub.i] is normalized as one to calibrate the relative valuesper person because [h.sup.1.sub.t]] grows at a constant rate in thesteady growth path. (11) We then obtain the capital stock per effectivelabour unit ([k.sup.*.sub.0]) as 4.263 for the base case and 4.448 forthe simulation case. (12 13) In addition, we obtain the equilibriumvalues of the rest of the endogenous variables and the humancapital/economic growth rates. 4. SIMULATION RESULTS 4.1 Difference in human capital accumulation in the steady growthpath In this section, we compare the base case with the simulation casein human capital accumulation in the steady growth path. Figure 1 showsthe difference in relative levels of human capital per person in eachage group in the steady growth path when [h.sup.1.sub.i] is set to one.Table 2 summarizes the difference in the equilibrium values of the humancapital variables. [FIGURE 1 OMITTED] The first finding was that, while individuals accumulate humancapital through on the job training from the second age group to thefifth age group, the decisions regarding education made in the first agegroup are a critical factor for accumulating human capital. Although, asshown in the first row of Table 2, there is no obvious difference ineducation time per person, (2.28 years for the base case and 2.22 yearsfor the simulation case), nearly a six fold difference between the basecase and simulation case exists in expenditure on quality of educationper person (as shown in the second row of Table 2). Indeed, the nethuman capital/economic growth rate during the 10 years in the third rowis 31.5 percent in the base case and 23.7 percent in the simulation casein the steady growth path. (The growth rate per year traces anequivalent 2.8 percent and 2.2 percent.) Similarly, the educationsubsidies per person decrease from 10,910 yuan to barely 2,550 yuan, asshown in the fourth row. Furthermore, although a smaller amount ofresources is needed for educational investment in the simulation case,the debt issues per person is larger than those in the base case. 4.2 Welfare difference in the steady growth path We next turn our attention to the differences in utility level ineach age group between the two types of education subsidies. Figure 2shows how the instantaneous utilities increase with advancing age inboth cases. However, the utilities of the base case are consistentlyslightly larger at each age group than those of the simulation case. Thesmoothing over of consumption patterns that occurs during the lifecycleof individuals can be interpreted as stemming from the difference ininterest rates. In fact, interest rates during the 10-year simulationperiod are 93.0 and 89.6 percent for the base case and simulation case,respectively (Refer to the fifth row of Table 2.). Even if we take thedifference in interest rates into account by examining the lifetimeutility at present, the utility is still larger in the base case than inthe simulation case, that is, 12,529 in the base case and 12,339 in thesimulation case in the sixth row of the table. Consequently, the basecase can be considered superior to the simulation case in terms ofwelfare level, a result that can be attributed to the higher humancapital accumulation in the base case. (14) [FIGURE 2 OMITTED] These results suggest that by not considering the quality aspect,the model fails to measure the human capital level appropriately.Because both the SEQ and SOC can cause a distortion in education demand,we must examine carefully how the distortional effect is associated withchanges in behaviour of individuals. 5. CONCLUSION In this paper, we conducted a macroeconomic simulation usingnational data in China based on the six-period OLG model of Bouzahzah etal. (2002) with human capital formation employed by Docquier and Michel(1999) and analyzed the effects on human capital accumulation/economicgrowth and welfare by comparing two types of education subsidies, theSEQ and SOC. It was revealed that the quality of education per persondeteriorates and the economic growth can be expected to slow down withthe introduction of the SOC in China. Because both the SEQ and SOC causedistortion in education demand, it may be precipitous to estimate humancapital without considering the quality aspect. Although this model was able to offer several long-termimplications for the education policy based on Chinese data, certainimportant aspects were not considered. The most crucial concern is thatonly the extreme cases are compared in our analysis. We might expectdifferent results if a blended policy (implementation of SOC and SEQ ona 50-50 basis) such as that described by Docquier and Michel (1999) wereinitiated. Another difficulty is that the transitional period was notincluded in the analysis. Because intergeneration conflict arises,especially when there is a wide gap in education quantity and qualitybetween generations, we must take into consideration thegovernment's short and mid-term policies. In spite of theselimitations, this study has shown the potential significance of anumerical analysis that offers plausible and meaningful interpretationsof economic growth and education policy in China. ACKNOWLEDGEMENTS I am grateful to Profs. Hideya Kato, Mark Rebuck, TsuyoshiShinozaki, Nobuhito Takeuchi, Makoto Tawada, Shigemi Yabuuchi andMitsuyoshi Yanagihara for their useful comments and suggestions. I alsoappreciate the participants of the PRSCO 2009 Conference for theirvaluable comments. This research was supported by Nagoya University Fundfor Promotion of Science. REFERENCES Auerback, A.J. and Kotlikoff, L.J. (1987) Dynamic Fiscal Policy.The MIT Press: Cambridge. Azariadis, C. and Drazen, A. (1990) Threshold externalities ineconomic development. The Quarterly Journal of Economics, 105 (2), pp.501-526. Barro, R.J. and Lee, J. (2000) International data on educationalattainment updates and implications. NBER Working Paper Series, 7911,ppl-36. Barro, R.J. and Sala-i-Martin, X. (2004) Economic Growth. The MITPress: Cambridge. Bouzahzah, M., De la Croix, D. and Docquier, F. (2002) Policyreform and growth in computable OLG economies. Journal of EconomicDynamics & Control, 26, pp. 2093-2113. Central Intelligence Agency. (2008) The 2008 World Factbook. De la Croix, D. and Michel, P. (2002) A Theory of Economic Growth:Dynamics and Policy in Overlapping Generations. Cambridge UP: Cambridge. Diamond, P.A. (1965) National debt in a neoclassical growth model.The American Economic Review, 55, pp. 1126-1150. Docquier, F. and Michel, P. (1999) Education subsidies, socialsecurity and growth: the implications of a demographic shock. TheScandinavian Journal of Economics, 101 (3), pp. 425-440. Fougere, M. and Merette, M. (1999) Population ageing and economicgrowth in seven OECD countries. Economic Modelling, 16, pp. 411-427. Glomm, G. and Ravikumar, B. (1992) Public versus private investmentin human capital: endogenous growth and income inequality. The Journalof Political Economy, 100 (4), pp. 818-834. Gradestein, M., Justman, M. and Meier, V. (2005) The PoliticalEconomy of Education: Implications for Growth and Inequality. The MITPress: Cambridge. Lucas, R.E. (1988) On the mechanics of economic development.Journal of Monetary Economics, 22, pp. 3-42. Ma, X. (2005) Chugoku toshibu niokeru danjokan chingin kakusa noyouin bunkai. KUMQRP Discussion Paper Series, pp. 1-22. National Bureau of Statistics of China. (1999-2008) ChinaStatistical Yearbook. China Statistics Press. Sadahiro, A. and Shimasawa, M. (2002) The computable overlappinggenerations model with an endogenous growth mechanism. EconomicModelling, 20, pp. 1-24. UNESCO Website, Retrieved June 21, 2009(http://stats.uis.unesco.org/unesco/ReportFolders/ReportFolders.aspx),. Wendner, R. (1999) A calibration procedure of dynamic CGE modelsfor non-steady state situations using GEMPACK. Computational Economics,13, pp. 265-287. Zhai, F. and He, J. (2008) Supply-side economics in thePeople's Republic of China's regional context: a quantitativeinvestigation of its VAT reform. Asian Economic Paper, 7 (2), pp.96-121. (1) China has nearly achieved universal basic education. Theaverage school life expectancy from primary to tertiary is 11.2 years in2006 from UNESCO (2008). (2) Barro and Lee (2000) showed the importance of not only quantityof education but also quality in the human capital formation. (3) Although China is an open economy, this assumption isacceptable for our modelling purposes. (4) This assumption is based on a life expectancy in China of 73.18years as estimated by The 2008 World Factbook. (5) Although China is an aging society, a negative populationgrowth rate is not considered in order to avoid eventually reaching azero population situation. (6) Note Bouzahzah et al. (2002) assume that the human capitalstock in the sixth age group is defined as 0. It is assumed that thesixth age group can hold the same human capital level as the fifth, asituation that most probably reflects reality. (7) Because our aim is to ensure a constant long-term economicgrowth, we do not include an intratemporal externality where averagehuman capital increases productivity as shown by Lucas (1988). (8) It is also possible to assume that the debt level isexogenously given, whereas tax levels are endogenously determined.Bouzahzah et al. (2002) set the wage income tax, which directlyinfluences the selection of education time, as an endogenous variable. (9) The recipients of pension payments include only retirees ofgovernment agencies and institutions covered by the government budget. (10) The retirement age for females is 55 years. (11) The absolute value can be obtained by multiplying the relativevalue by the k) level in a specific period. (12) The subscript 0 in k0* indicates an initial value. (13) By changing the exogenously given parameters of educationinvestment (e), we examine values of k0* to check the robustness of themodel. When the parameter value changes from 0.650 to 0.640 and 0.660 inthe base case, the value ofk* becomes 4.311 and 4.218. Therefore, weconclude that the model is sufficiently robust. (14) Because the economic growth rate is higher in the base casethan in the simulation case as shown in Table 2, we can confirm that thewelfare levels in the base case exceeds the simulation case in eachperiod. Yuko Shindo Graduate School of Economics, Nagoya University, Furo-cho,Chikusa-ku, Nagoya, Aichi 464-8601 JAPAN.Table 1. Parameter and Policy Variable Values Parameter/policy variable Value[beta] Human capital productivity 0.784[epsilon] Parameter for education time investment 0.650[theta] Parameter for quality education investment 0.150[phi].sup.2] OJT/human capital depreciation in age group 2 1.061[phi].sup.3] OJT/human capital depreciation in age group 3 1.201[phi].sup.4] OJT/human capital depreciation in age group 4 1.325[phi].sup.5] OJT/human capital depreciation in age group 5 1.429[phi].sup.6] OJT/human capital depreciation in age group 6 1.429A Technology parameter 9.573[alpha] Capital income share 0.331[delta] Capital depreciation rate 0.390[gamma] Time preference rate 0.840[sigma] Intertemporal elasticity of substitution 1.500[[tau].sub.c] Consumption tax rate 0.128[[tau].sub.w] Wage income tax rate 0.399[v.sub.e] The rate of subsidy for opportunity cost of 0.201 education (SOC)[v.sub.q] The rate of subsidy for expenditure on 0.786 quality of education (SEQ)p Pension payment per effective labour unit 0.343[zeta] Retirement ratio 0.500g Other government expenditures per effective 1.273 labour unitTable 2. Difference in human capital equilibrium values Base SimEducation time per person (yrs) 2.28 2.22Expenditure for quality of education per 1.388 0.234person (10,000 yuan/10 yrs)Human capital/economic growth rate (%/10 31.5 23.7yrs)Education subsidies per person (10,000 1.091 0.255yuan/10 yrs)Debt issues per person (10,000 yuan/10 5.262 5.541yrs)Interest rate (%/10 yrs) 93.0 89.6Lifetime utility per person in present 12.529 12.339value (60 yrs)