Equity across Generations and Uncertainty within a Generation: A Welfare Analysis of the National Pension System

Kwon, Kyooho Article Equity across Generations and Uncertainty within a Generation: A Welfare Analysis of the National Pension System KDI Journal of Economic Policy Provided in Cooperation with: Korea Development Institute (KDI), Sejong Suggested Citation: Kwon, Kyooho (2019) : Equity across Generations and Uncertainty within a Generation: A Welfare Analysis of the National Pension System, KDI Journal of Economic Policy, ISSN 2586-4130, Korea Development Institute (KDI), Sejong, Vol. 41, Iss. 2, pp. 1-39, https://doi.org/10.23895/kdijep.2019.41.2.1 This Version is available at: https://hdl.handle.net/10419/201711 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-sa/4.0/ KDI Journal of Economic Policy 2019, 41(2):1 – 39 http://dx.doi.org/10.23895/kdijep.2019.41.2.1 1 Equity across Generations and Uncertainty within a Generation: A Welfare Analysis of the National Pension System† By K YOOHO K WON * This paper utilizes a life-cycle overlapping-generations model to quantify the welfare effects of plans to postpone the depletion of the National Pension Fund. In order for the model to incorporate the rapidly changing demographic structure of Korea fully, we build and calibrate a model in transition directly. The model is considered suitable for analyzing the effects of demographic changes on the Korean economy and the effects of plans to change the National Pension System. According to a simulation of the model, to postpone the depletion of the National Pension Fund for 30 years, the premium rate must be increased to 18.3% from the current rate of 9%. By postponing the depletion of the fund reserve, young and future generations gain significantly at the expense of the older generations. The simulation results should be, however, interpreted as meaning that the current system is unjustifiably partial to the older generations. Moreover, given the current premium rate, it is desirable to strengthen the incomeredistribution function of the National Pension System. Key Word: Heterogeneous Agent Models, Population Aging, National Pension System, Pension Reform JEL Code: C68, E21, J11 I. Introduction he long-term financial outlook of the National Pension System is a grave concern. According to the Third Official Fiscal Projections in 2013 by the Ministry of Health and Welfare, the National Pension Fund will begin to run a deficit in 2044 and will run out of funds and enter insolvency by 2060 under the current system. The projected path of the National Pension Fund in proportion to the nominal GDP is shown in Figure 1. Also shown in the figure is the author’s extension * Associate Fellow, Korea Development Institute (e-mail: [email protected]) * Received: 2018. 11. 29 * Referee Process Started: 2018. 12. 3 * Referee Reports Completed: 2019. 1. 14 † This paper is a revised and translated version of Kwon (2016), Research Monograph 2016-11, Korea Development Institute. T 2 KDI Journal of Economic Policy MAY 2019 of the path employing the officially projected macroeconomic variables if the current premium rate (9%) is maintained after the depletion of the reserve funds. As the deficit will explode, the debt issued by the National Pension will increase rapidly after 2060 and reach an unsustainable amount, exceeding 100% of GDP by 2080. The long-term fiscal problems of the National Pension System are attributable in part to the rapidly changing demographic structure of Korea. According to Statistics Korea, as of 2010 the working-age (15~64) population, which largely determines the size of the labor force, is forecast to shrink at an accelerated rate due to a persistently low fertility rate, dwindling to 21.8 million by 2060, a mere 59% of its peak of 37.0 million in 2016. It is approximated that the working-age population will decrease by 0.3 million, or 1~2 percent per annum, over the next 45 years. Korea’s demographic structure is also changing at an unprecedentedly rapid pace, even by international standards. In terms of the old-age dependency ratio, Korea is projected to become one of the most aged countries by 2050 among OECD member countries, as shown in Figure 2. Korea's old-age dependency ratio is the 27th lowest among the 32 OECD members as of 2014, but it is expected to become the third lowest in 2050. In addition to the rapid population aging, the long-term fiscal problem is deepened by the structural issues of the National Pension System, which has been referred to as the “low burden but high benefits” issue. Despite the two revisions of the National Pension Act in 1998 and 2007, current generations are expected to receive generous pension benefits compared to their contributions. According to Choi and Shin (2015), the cohorts born between 1930 and 1990 are expected to receive benefits much more than the twice their contributions if measured by the present value term. As a result, workers who will be working in the labor market after 2060 must bear a considerable burden to maintain the current system. As stated in the Third Official Fiscal Projections, if the National Pension System becomes a pay-as-you-go system after it is depleted, it is projected that the premium rate must rise sharply to 21.4~22.9 percent from the current level of 9 percent in order to balance the budget until 2083. FIGURE 1. THE PROJECTED PATH OF THE NATIONAL PENSION FUND (% OF NOMINAL GDP) Note: The dashed line is a projection by the author based on the projected macro-variables by the Ministry of Health and Welfare. Source: Third National Pension Fiscal Projection, The Ministry of Health and Welfare, 2013. -120 -90 -60 -30 0 30 60 2013 2020 2030 2040 2050 2060 2070 2080 A Projected Path with 0% Interest Rate A Projected Path with Positive Interest Rate (% of GDP) VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 3 FIGURE 2. PROJECTION OF THE AGED DEPENDENCY RATIO FOR OECD COUNTRIES Note: The horizontal axis indicates the old-age dependency ratio in 2014. The vertical axis indicates the old-age dependency ratio in 2050. Source: Kwon (2017). In Japan, where the pension fund is being depleted, it is reported that the functioning of its pension system is being threatened because only 40 percent of the young insured are paying their scheduled pension premiums. In order for the National Pension System to be sustainable for a longer period of time, it seems inevitable to reform the current system in some way. The purpose of this paper is to analyze plans to postpone the exhaustion of the National Pension Fund and study welfare implications from an intergenerational perspective. Because a reform of the National Pension System will affect macroeconomic variables as it will affect the labor supply, consumption and savings behavior of the majority of workers, it is desirable to study this within a general equilibrium framework. To do this, we build a life-cycle overlapping-generations macroeconomic model populated by heterogeneous agents. In addition to the differences across generations arising from the differences in the macroeconomic environment over time, such as changes in the GDP growth rate, wage growth rate, and the interest rate, the model economy is composed of heterogeneous economic agents in terms of income histories and wealth holdings, even within a generation. The macroeconomic models in this class have been widely applied to analyses of the macroeconomic effects and to the study of welfare implications. Examples include population aging, pension reforms, and labor market institutions. For example, Nishiyama and Smetters (2007), Nishiyama (2003), Imrohoroglu and Kitao (2012) analyze and evaluate plans to improve the Social Security System. Heathcote, Storesletten, and Violante (2010) study the welfare implications of the rising wage inequality starting in the 1970s. However, this type of model has not been popularly applied to the Korean economy thus far. Notable exceptions are Kim and Chang (2008) and Hong, Lee, and Kang (2016). Kim and Chang (2008) analyzed the macroeconomic effects of the introduction of the EITC policy and Hong, Lee, and Kang (2016) analyzed the macroeconomic effects of the extension of the retirement age. 0 10 20 30 40 50 60 70 80 0 102030 4050607080 Korea Germany Italy S p ain USA Japan 4 KDI Journal of Economic Policy MAY 2019 There are many papers which present research on the macroeconomic effects of reforms of the National Pension System employing a structural macroeconomic model such as a variant of Auerbach and Kotlikoff (1987). These include Shin and Choi (2010), Chun and Yoo (2004), Choi, Shin and Kwon (2015), and Hong (2016) to name a few. Most previous studies are, however, silent with regard to how much the model economy can explain the growth path of the Korean economy. Moreover, by unrealistically assuming the complete capital market, this model ignores the effect of labor market uncertainties on individual welfare considerations and may not properly gauge the social value of the National Pension System. Concerning the building of the structural model in this paper, we attempt to incorporate the features listed below in addition to those of the typical overlappinggenerations model. First, workers are heterogeneous in terms of income history and asset holdings, and the modelling of the National Pension System is based on the actual system. Second, because a reform in the National Pension System involves the future growth path of Korean economy, the model economy should have at least some explanatory power of Korea's past growth path. , in order to reflect the rapid changes in the population structure, not only changes in the population due to changes in fertility rates but also changes in life expectancy should be modelled explicitly. To the best of our knowledge, this study is the first attempt to build a macroeconomic model encompassing these features. Moreover, given that the Korean economy is never considered to have reached a steady state, it is inadequate to calibrate a structural macroeconomic model of Korea based on the steady state assumption. If the steady state assumption is adopted to calibrate a model, it is practically impossible to replicate the rapid demographic transition of Korea, which is unacceptable when evaluating the fiscal reforms of the National Pension System. To bypass this difficulty, we directly build and calibrate a model economy in transition by adopting the calibration strategy suggested by Kwon (2017). According to the model simulations of this study, the National Pension System should be reformed in the direction of a more equitable system across generations and changed to strengthen the income redistribution function within a birth cohort even at the current premium rate. We simulate the model economy to evaluate plans to fiscally stabilize the National Pension System. Because there is no explicit agreement pertaining to the definition of the fiscal stabilization of the National Pension system, we calculate the equilibrium premium rate to delay the depletion of the reserve funds for 30 years from the date of insolvency in the benchmark model economy. According to the model simulation, we find that it is necessary to raise the premium rate by 9.3 percentage points from the current premium rate of 9 percent. In order to push back 50 years instead of 30 years, a rate increase of 11.0 percentage point is required. Although these plans are not strong enough to prevent the National Pension Fund from becoming depleted, they will enhance equity across generations significantly. Aside from the goal of postponing the depletion of the reserve funds, we also evaluate a plan to strengthen the income redistribution function of the system. By redistributing more income within a cohort, the welfare of the young and future generations can be expected to increase, as this effort reduces the uncertainty of the consumption path within a generation. This paper is organized as follows: Section 2 specifies the model economy; VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 5 Section 3 calibrates the model based on various macroand micro-datasets; Section 4 reports the benchmark model simulation results; Section 5 conducts a welfare analysis based on the model economy; Section 6 concludes the paper. II. A Macroeconomic Model of the National Pension System A. Demographic Structure Time t is discrete and the model period is one year. The model economy is populated by D J overlapping generations. Individual workers may live up to D J periods and face mortality risks in each period. Let (,) T j t ψ denote the conditional probability that an individual of age j in period t survives to the next period 1t+. Let () T nt denote the growth rate of the population of age 1 in period t. Let ,(1 ) jt D NjJ≤≤ denote the population of age j in period t . The total population in period t is calculated as 1, D J j tjt NN =  =. Then, the population of each age evolves over time, as follows: 1, 1 1, [1 ( 1)] tT t NntN +=+ + 1, 1 , (,) ,1 1 jt T jt D NjtNjJ ψ ++=≤≤− 1, 1 0 Jt N++= We refer to the population of age j in period t as the th k cohort. Note that age, time, and cohort indices are not independent given the one-to-one function that 1ktj=−+ . In order to simplify the notations and present the model clearly, individual workers’ utility maximization problems are laid out with cohort and time indices, whereas macro-variables are done so with age and time indices. B. Individual Worker’s Problem An individual worker is a unit that makes independent economic decisions concerning consumption-savings and the labor supply. Each worker starts to participate in the labor market at the age of W J and retires at the exogenous age of R J . Enrollment in the National Pension is determined at the age of W J i f t h e worker starts working after the introduction of the system. Otherwise, the enrollment is determined at the time of the introduction. We assume that the enrollment decision is not a choice but an exogenous assignment. 6 KDI Journal of Economic Policy MAY 2019 Utility Maximization Problem of a Retired Worker At the exogenous age of R J , workers retire from the labor market and make consumption and savings decisions. Retired workers who are eligible for National Pension benefits q are characterized by the individual state vector (, ;,)aq jk , where a is the amount of asset holding, q is the amount of National Pension benefit, j denotes the person’s age, and k is the cohort index. Let t r denote the market interest rate, and borrowing is not allowed. The tax rate for asset income is denoted as a t τ . A retired worker’s decision problem is formulated recursively. Let R K V denote the value function of the retired agent in the state of (, ;,)aq jk . The decision problem can be represented as , (, ;,) max{(,) (;) ( , ; 1,)} RR KKK ca Vaqjk uch jkVaqj k βψ ′ =+ ′′+ s.t. [1 (1 ) ] , a tt t ca rab q τ +′≤ + − + + 0, 0, ,ha qq=′≥ =′ where ,ca′ and t b denote the consumption, savings, and transfer income other than the pension benefit, respectively. The parameter β denotes the preference discount rate, and (;) K j k ψ denotes the conditional probability that an individual in the th k cohort of age j survives to the next period.1 The amount of q′ i s equal to q, which is determined at the time of each worker’s retirement. ()u⋅ is the instantaneous utility function, which is separable with regard to consumption and hours of work. It is determined as follows:2 111 (, ) log() /(1 )uch c Bh γ γ + =− + This type of utility function is chosen to support a balanced growth path. The parameter γ denotes the intertemporal substitution elasticity of work hours. The decision rules that solve this problem are expressed as (, ;,) R K ccaqjk= and (, ;,) R K aaaqjk′= . 1(;) (; 1)jk j k j KT ψψ ≡+− . 2Note that 0h= for a retired worker. VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 7 Let NR K V denote the value function of a retired worker who is not eligible for pension benefit. The decision problem of this type can be recursively written as , (;,) max{(,) (;) ( ; 1,)} NR NR KKK ca Vajk uch jkVaj k βψ ′ =+ ′+ s.t. [1 (1 ) ] a tt t ca rab τ +′≤ + − + 0, 0.ha=′≥ The decision rules that solve this problem are (;, ), (;, ) NR NR KK ccajka cajk=′= . Utility Maximization Problem of a Worker Individual workers begin participating in the labor market at the age of W J and retire from the market at the age of R J. Workers are heterogeneous in terms of labor market productivity. Labor market productivity measured in efficiency units is assumed to be composed of three parts. First, a type-dependent fixed effect z is determined at the age of W J drawn from the probability distribution, () zz π . Second, an age-dependent component j ε is assumed to be deterministic, a persistent idiosyncratic shock x evolves following the conditional probability distribution, (, ) X x x π ′. We assume that there is no difference in the labor market productivity structure across generations.3 When an individual worker aged j supplies h hours to the labor market, he supplies jzxh ε units of efficiency labor and earns tj wzxh ε , where t w denotes the market wage rate for an efficiency unit of labor in period t . If he is enrolled in the National Pension, his pension contribution is calculated as { } min , ttjt wzxhy τε , which is not part of his taxable income under current Korea tax law. Here, t τ denotes the pension premium rate. The amount of income over the predetermined level t y is exempt from pension contributions. Hereafter, following the National Pension Act, we refer to t y as the maximum Standard Yearly Income and { } min , tj t wzxhy ε as the Standard Yearly Income. We assume that individual workers begin their economic lives with no financial assets, and borrowing against the future labor income is not allowed. A worker enrolled in the National Pension is characterized by the state vector 3Therefore, the difference in the labor market productivity rates among cohorts reflects the differences in the level of the total factor productivity and the degree of capital deepening. 8 KDI Journal of Economic Policy MAY 2019 (, ,,;,)apxzjk. The variable p denotes his average Standard Yearly Income up to the age of 1 j −, which summarizes his individual labor income history. Let W K V denote the value function of a worker in the state of (, ,,;,)apxzjk. The decision problem of the agent can be recursively represented as ,, (, ,,;,) max{(,) (;) ( 1,)} W KK ca h Vapxzjk uch jkNVFj k βψ ′ =+ + s.t. (;1,) , 1 (1,) (, ) ( , , ,; 1,), 1 R KR W XK R x Vaqj k ifjJ NVF j k xxV a p x z j k if j J π ′ ′, ′ + = −  += ′′′′+ <−   [1 (1 ) ] (1 )( ), al tt t t tj ca rab wzxh ττεθ +′≤ + − + + − − { } min , , ttjt wzxhy θτ ε = () 1[()] () 1 () K K KT A k ppjJk j Jk At θ  ′= − +  −+  (;), 1, KR qQpkifjJ′= ′ = − 01,0,ha≤≤ ′≥ where () K Jk denotes the age at which th k cohort workers are enrolled in the National Pension, () T A t denotes the Average Yearly Income, which is the average Standard Yearly Income of all insured workers in period t . () K A k denotes the three-year average value of the Standard Yearly Income of all th k cohort workers immediately before their retirement. It is determined using the equation below. 3 1 1 () [ ([ 1] )] 3 KTR Ak A k J τ τ = =+−−  The decision rules that solve this problem are expressed as (, ,,;,), (, ,,;,), (, ,,;,). WW W KK K c c apxz jk h h apxz jk and a a apxz jk== ′= The pension contribution reflecting the optimal working hours is denoted as (, ,,;,). W Kapxzjk θ VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 15 (6) ,, (,,; 1, 1) (,) (, )1[ (,,;,) ] (,,;,) NW T NW NW TXT T axz Naxzjt j txxaaxzjtaNaxzjt ψπ ′′′ + + =′=′  The distribution of the population aged W j J= in period 1t+ is determined as follows: For any z, (7) , , (0, 0, , ; , 1) ( ) ( 1)[1 ( 1)] , (0, , ; , 1) ( )[1 ( 1)][1 ( 1)] , W W W TWZTTJt NW T W ZT TJt N x z J t z t n t N and NxzJt z t ntN πχ πχ += + + + += − + + + where (1) Tt χ + denotes the insured rate by the National Pension Service for the birth cohort who will become aged W J in period 1t+ . Here, x denotes the average value of the persistent part of the individual productivity, . x E. Definition of the Competitive Equilibrium Let ( ) { ( ), ( , ), , , , , , , , , , , } l TTT ttttttttttt St nt jkA d yBKL SF α ψδτ ττ = be the aggregate state of the model economy in period .t We assume that economic agents perfectly foresee the entire path of the state of the aggregate economy, 0 {()}. TtT St∞ = Given the path of the aggregate state of the economy, the equilibrium of the economy consists of the value functions {,, , }; WRNWNR TTT T VVV V the associated decision rules {,, , }, W R NW NR TTT T ccc c {,, , }, W R NW NR TTT T aaa a and {, }; WNW TT hh the sequence of the production plans for firms {,}; tt KL the factor prices {} t w, {} t r, the National Pension System {, , }; tt t ySF τ transfer income {}; t B and the population measures {,, , } W R NW NR TTT T NNN N such that 1. Given the path of the aggregate state of the economy and the factor prices, the value functions and the decision rules solve the workers’ dynamic problems. 2. Given the path of the factor prices, {,} tt KL denotes the solution to the representative firm’s profit maximization problems. 3. Given the path of the factor prices, the factor markets clear and satisfy ,. s dsd tt tttt KK KLLL== == 4. The goods market clears as follows: for all t, , tttt YCIG=++ where t C denotes private consumption, t I denotes investment, and t G denotes government 16 KDI Journal of Economic Policy MAY 2019 expenditures. t C and t I are calculated as follows: 1 ,,, , 1 ,, , (, ,,;,) (, ,,;,) (,;,) (,;,) (,,;,) (,,;,) (; ,) (; ,) R W R R W R J WW tT T jJ apxz J WW RR jJ aq J NW NW TT jJ axz J NW NW RR jJ aq CCapxzjtNapxzjt CaqjtNaqjt C axz jtN axz jt CajtNajt − = = − = = = + + +     1(1 ) tt tt I KK δ + =−− 5. The National Pension Funds evolves following the equation (3) and switches to a pay-as-you-go system if it is depleted. 6. The government’s budget maintains a period-by-period balance for all t: 1 ,,, 1 ,, () (, ,,;,) (, ,,;,) (,,;,) (,,;,) R W R W s ttttt J lW W tT T jJ apxz J lNW NW tT T jJ axz GrK apxzjtN apxzjt axz jtN axz jt α τδ τψ τψ − = − = =− + +   7. The amount of accidental bequests is equal to the amount of transfers to the living population: 1 ,,, , 1 ,, , (, ,,;,) (,;,) (, , ; ,) (; ,) R WR R WR JJ sd W W t t tT tT jJ apxz jJ aq JJ NW NR tT tT jJ axz jJ aq B BbNapxzjtbNaqjt bN a x z j t bN a j t − == − == == + ++     8. The distribution of the population over the state space evolves following the equations (4), (5), (6), and (7). VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 17 In order to quantify the model economy, we must specify the characteristics of the balanced growth path to which the model economy eventually converges. First, we assume, in the end, that the net fertility rate and the conditional survival probabilities converge and become constant such that the following conditions are satisfied. ** * () , ( ,) ( ) 1 . TT R n t n j t j for j J and all t T ψψ == ≤≤ ≥ After passing D J periods upon satisfaction of these conditions, we have *** 1(1 ) , tt NnN +=+ **** ,1 1 , // j tt jtt NNNN ++ = In other words, the growth rate of the total population is equal to the net fertility rate, and the age distribution of the population becomes stationary. Second, we assume that the growth rate of the total factor productivity converges in the end, i.e., ** 1/. ttA A A for all t T γ +=≥ Suppose that a stationary population distribution is achieved and that the growth rate of total factor productivity is constant over time. In such a case, the stationary recursive competitive equilibrium is recursive competitive equilibrium in which the following characteristics are satisfied. For all ,t the consumption and savings of the representative household increase in proportion and the supply of labor remains constant: * (, ,,; 1, 1) (, ,;, 1,), WW Tct Capxzj t Capxzj t γ ++= + * (,; 1, 1) (,;, 1,), RR Tct Caqj t Caqzj t γ ++= + * (, ,,; 1, 1) (, ,;, 1,), WW Tat aapxzj t aapxzj t γ ++= + * (,; 1, 1) (,;, 1,), RR Tat aaqj t aaqzj t γ ++= + (, ,,; 1, 1) (, ,;, 1,), WW Tt hapxzj t hapxzj t++= + * (,,; 1, 1) (,;, 1,), NW NW Tct C axz j t C axz j t γ ++= + * (; 1, 1) (;, 1,), NR NR Tct Caj t Cazj t γ ++= + 18 KDI Journal of Economic Policy MAY 2019 * ( , , ; 1, 1) ( , ; , 1, ), NW NW Tat aaxzjt aaxzjt γ ++= + * (; 1, 1) (;, 1,), NR NR Tat aaj t aazj t γ ++= + (,,; 1, 1) (, ,;, 1,), NW NW Tt haxzjt hapxzjt++= + where 1 ** * 1 () , ca A α γγ γ − == for all i and *.tT≥ Fourth, the National Pension Service operates as a pay-as-you-go system on the balanced growth path. Finally, with the conditions above being satisfied, the aggregate supply of savings also increases at a fixed rate and the factor prices are determined as follows: ** 1 ,, ttwt rrw w γ + == where 1 ** 1 () WA r α γ − = F. A Welfare Measure In order to analyze the welfare implications of changes to the National Pension Service, a welfare criterion must be defined beforehand. The welfare function in this study is the total utility obtainable during a lifetime of an individual, which is expected at the time the individual initially become economically active. In order to specify the welfare function, some notations must be introduced. An allocation of individual consumption and labor supply during a lifetime can be expressed as (, ) { , } . D W J jjjJ ch c h = ≡7 The lifetime utility ()W obtainable with this allocation is, then, calculated as [( , )] ( , ). D J W jJ W jJ jj Wch uch β = − ≡ As there is some uncertainty about individual labor productivity, there is also uncertainty in the above allocation. The expected lifetime utility reflecting this uncertainty is expressed as follows and used here as a welfare measure of a given cohort. [( , )] { [( , )]} ( , ) D W W J jJ jj jJ E Wch EWch E uch β − =  ≡=    This measure has the following characteristics. First, because the consumption of goods and the consumption of leisure are assumed to be normal, the expected lifetime utility increases as the consumption increases or the working hours decreases. Second, the uncertainty of the allocation (, )ch reduces the expected lifetime utility because we assume a risk-averse utility function. 7In this subsection, subscripts for cohorts are omitted for convenience. VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 19 In order to quantify the change in welfare according to a reform of the system, this study applied the certainty equivalent variation, CEV , which can be regarded as the answer to the next question: “In order to avoid a change of the expected lifetime utility after a reform of the system, how much consumption should be increased or decreased from the optimal allocation before the reform?” Specifically, we denote the optimal allocation during a lifetime in the benchmark economy as 00 (, )ch and the optimal allocation in the new equilibrium after a reform as ** (, )ch . At this point, the changes in welfare due to institutional changes can be measured as () () ** ** 00 00 [(,)] (,) (1 ) , (1 ) , . D W W D W W JjJ jJ JjJ jj jJ EWch E uch EuCEVch EW CEV c h β β − = − =  =   =+    =+    We can decompose CEV into the component () C CEV resulting from the change in consumption from 0 c to * c and the component () H CEV resulting from the change in labor supply from 0 h t o * h . These components are calculated as follows:8 *0 00 ** *0 [( , )] [((1 ) , )] [( , )] [((1 ) , )] C H EW c h EW CEV c h EW c h EW CEV c h =+ =+ The part of the welfare change due to the change in consumption schedule, C CEV , can be further decomposed into a component reflecting the change in the consumption level () CL CEV and a component reflecting the change in consumption schedule uncertainty () CD CEV as follows: 00 00 *0 *0 ˆ [(,)] [((1 ),)] ˆ [(,)] [((1 ),)] CL CD E Wch EW CEV ch E Wch EW CEV ch =+ =+ {} * 00 0 0 ˆˆ , D D W W J Jj jj jJ jjJ c cc c c = =    =≡       where 0 j c and * j c are the average consumption values of the populations whose 8,CEV CEVc, and H CEV are related such that (1 )(1 ) cH CEV CEV++ or . cH CEV CEV CEV≈+ 20 KDI Journal of Economic Policy MAY 2019 ages are j before and after the system change, respectively. Similarly, the welfare change due to the change in labor supply, H CEV , can be divided into H L CEV and . H D CEV III. Calibration A. Demographic Transition The demographic transition of the model economy is calibrated to match the history and the projection by Statistics Korea as of 2010. To solve the model, projections of fertility and survival probabilities are required to produce the age distribution of the population at each period. The net fertility rates () T nt are calculated to match the growth rate of the one-year-old population until 2060. However, to completely solve the model economy quantitatively, we need information beyond 2060. Between 2060 and 2100, the net fertility rate projections are obtained from the Statistical Research Institute. After 2100, they are assumed to be fixed at zero. The conditional survival probabilities, (,), T j t ψ are drawn from the life tables projected by Statistics Korea. Because the projected life tables are in five-year periods, the probabilities for the interim periods are approximated by linear interpolation. After 2060, the survival probabilities are assumed to remain fixed at the 2060 levels. Under the assumptions specified above, the population distribution reaches a steady state in 2200, wherein the population growth rate is zero percent and the age distribution of the population does not change over time. B. Utility and Labor Market Productivities The parameter γ denotes the intertemporal substitution elasticity of work hours. Micro-estimates of γ range from 0.1 to 0.7. We choose a value of 0.4, which is a widely accepted value for the class of the model economy considered in this paper. We choose the weight parameter for disutility from working, B , such that the average number of hours of work is 1/3 between 1989 and 2014 in the model simulation. The preference discount factor β is set such that the average K/Y ratio of the model economy during 1989~2014 matches the average value of the K/Y ratio data for the same period, which is 2.9. Note that the average K/Y ratio of the model economy between 1989 and 2014 is pinned down, but the dynamics is determined endogenously in the model. The definition of the capital stock for calculating the K/Y ratio is the private production capital stock from the National Balance Sheet. As specified in the previous section, individual workers are heterogeneous along three dimensions that affect their labor productivity: a deterministic age-dependent component 65 24 {} , jj ε = a type-dependent fixed effect z , and a persistent idiosyncratic shock, x . These specifications and the calibration strategy are adopted from Conesa, Kitao, and Krueger (2009). For the type-dependent fixed effect, we VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 21 consider two ability types 1exp( ) z z σ =− and 2exp( ) z z σ = with an equal population mass of 0.5. We assume that [ln( )] 0Ez= and 2 [ln( )] . z Var z σ = For the persistent idiosyncratic shock, we specify the stochastic process such that ln( ) x follows the AR(1) process, as follows: 2 ln( ) ln( ) , ~ (0, ). xxx xx N ε ρ εε σ ′= + We discretize the AR(1) process with seven nodes using the method suggested by Rouwenhorst (1995). We further assume that x is equal to the unconditional average () x ≡ when workers enter the economy. The variance of logged productivity is, then, determined along the age dimension as follows: (8) 1 22 2 0 [ln( ) ln( ) ln( )] 0 j h j jz x h Var z x ε εσσ ρ − = ++ =++  In order to quantify the specified labor productivity, we need the parameter values for 65 24 {} jj ε = are determined in such way that the model-generated age profile of log earnings in 2014 matches the data. In Figure 3, the age earnings profile from the model simulation is represented by the thick straight line and the calibrated values of 65 24 {} jj ε = put into the model are represented by the thick dashed line. Moreover, the values of 2,, zx σ ρ and 2 ε σ are calibrated jointly to match the cross-sectional variance of individual labor earnings. As shown in the panel on the right in Figure 3, the cross-sectional variance of logged individual labor earnings increases almost linearly along the age dimension. To mimic this pattern, we must have 1, x ρ ≈ as implied by equation (8). We, however, limit the value to 0.99 for the parameter FIGURE 3. NORMALIZED LIFE-CYCLE PROFILE AND VARIANCE OF LABOR EARNINGS Source: Korean Labor & Income Panel Study, 2012 and 2015. -0.9 -0.6 -0.3 0.0 0.3 0.6 25 30 35 40 45 50 55 60 65 KLIPS 2011 KLIPS 2014 Benchmark Model (2014) Benchmark Model(epsilon_j) 0.0 0.2 0.4 0.6 0.8 1.0 25 30 35 40 45 50 55 60 65 KLIPS 2011 KLIPS 2014 Benchmark Model (2014) ㅋ 22 KDI Journal of Economic Policy MAY 2019 x ρ for technical reasons. The parameter 2 z σ is determined to match the variance for the age of 24, which is 0.1, and the calibrated value is 20.1. z σ = Finally, the parameter 2 ε σ is calibrated for the model-generated variance for the age of 60 to match the data, making this value 0.6. The calibrated value for the parameter 2 ε σ is 0.016. C. National Pension System The National Pension System was introduced in 1988 and has since been revised twice through reforms, in 1997 and in 2007. The model parameters determining the contributions and benefits are calibrated to mimic the current system, which includes the changes put into place by the two reforms. The premium rates are set to 3%, 6% and 9% for the periods of 1988~92, 1993~97, and 1998 onwards, respectively. Note that the system is switching to a pay-as-you-go system if the National Pension Fund becomes insolvent. In such a case, the premium rate is set endogenously to ensure the period-by-period budget constraint. Between 1988 and 1998, the value of A α was 0.43, but the value has been set to 0.5 since then. The pension reform in 1997, therefore, strengthened slightly the income-redistribution role of the National Pension System. When the National Pension was introduced, the value of the proportional constant t d was set to 0.35, which implied an income replacement ratio of 35% for the 20years-of-enrollment period. As part of the first reform in 1997, the value was lowered to 0.30. With the second reform in 2007, the value of t d was set to decrease annually by 0.005 until reaching the level of 0.2 in 2028. After 2028, it is assumed to remain fixed at the value of 0.2. Given the time-series of t d , the values of () K Dk are calculated using equation (2). Figure 4 reports the calculated income replacement ratios () K Dk across birth cohorts. When the system was introduced in 1988, an income replacement ratio of 35% after the 20-years-of-enrollment period was targeted, but it is slated to be reduced to the level of 20% eventually. Because the system must honor the previous contributions at the time of the reform, only the future proportional constants had to be decreased to cut the pension benefits, which implied a loss in benefits for the young and for future generations. In the model economy, the proportion of the insured in each cohort is determined exogenously. For each birth cohort, it is calculated by dividing the number of insured by the number of the population when the cohort reaches the age range of 55~59, as shown in Figure 5. For the 1962~1970 cohort for whom the values are not yet realized, this proportion is assumed to increase to 70%. For those born after 1970, it is assumed to stay at 70%, which is in line with official projections. The maximum Standard Yearly Income t y is approximately the twice of the Average Yearly Income () T A t in 2014. We assume that this ratio is maintained for all simulation periods. VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 23 FIGURE 4. THE PROJECTED INCOME REPLACEMENT RATIO BY BIRTH COHORT (() K D k) Note: Based on the author’s calculation. An insured period of 20 years before retirement is assumed. Source: The National Pension Act, 1988, 1997, and 2007. FIGURE 5. THE ENROLLMENT RATE IN THE NATIONAL PENSION BY BIRTH COHORT Note: The enrollment rates for the age group of 55~59 are reported in the figure. Source: 1995~2015 National Pension Statistics Facts Book, National Pension Service. D. Production function and other parameters With the Cobb-Douglas production function assumption, if the goods and factor markets are competitive, the output elasticity of capital α turns out to be equal to the capital income share. We choose a value of 0.35, which is the average capital income share between 2000 and 2014. The definition of the capital income share we employ is 1 (labor income + self-employed income) / .GDP− The total factor productivity (TFP) is calculated with the standard growth 0.15 0.20 0.25 0.30 0.35 0.40 1930 1940 1950 1960 1970 1980 1990 2000 2010 (Birth Cohort) 0.2 0.3 0.4 0.5 0.6 0.7 1995 2000 2005 2010 2015 1937~41 Cohorts 1942~46 Cohorts 1947~51 Cohorts 1952~56 Cohorts 1957~61 Cohorts (%) 24 KDI Journal of Economic Policy MAY 2019 accounting method. In this paper, the TFP is assumed to be identified as the Solow residual. Thus, different measures of labor and capital input yield different values of the TFP. To maintain consistency with the model economy, we define the labor input as the total number of employees weighted by the age-productivity profiles. For the future values of total factor productivity, we adopted the TFP growth rate from Cho (2014) until 2035 and assume that there is continued growth thereafter at a constant rate of 1.3 percent per annum. The depreciation rate of capital stock is calculated to match the average private gross real fixed investment of national accounts during the period of 1989 and 2014, which is 29%. The calculated depreciation rate is 8%. We used a value of 5.5% before 2000 to reflect the rising pattern of the depreciation rate in the data. Given the value of the output elasticity of capital of 0.35 and the mean value of the capital-output ratio of 3 after 2000, the implied marginal productivity of capital is about 4% between 2000 and 2015. The labor income tax rate and capital income tax rate are set to 15%. Model simulations require the initial asset holdings by age in the year 1989. We use Statistics Korea's Household Asset Survey of 2006 to determine the age-asset distribution in 1990; although this survey was conducted for the year 2006, to the best of our knowledge, it is the earliest data available. The aggregate wealth of the model economy in 1989 is then then rescaled to match the K/Y ratio in 1990, which is 2. Within each cohort in the year 1989, the assets are evenly distributed. IV. Benchmark Model Simulation A. In-sample Performance of the Model We compare the simulated aggregate variables with the relevant historical data, in this case the employment growth rate and the real GDP growth rate. Panel A in Figure 6 shows the time series of the GDP growth rate. The model captures the downward trend in the GDP growth well, as the endogenous variables of the model react in a consistent manner with the actual data when the demographic structure and the TFP are fed into the model. Panel C of Figure 6 depicts the aggregate labor growth rate of the model economy and the employment growth rate from the Economically Active Population Survey.9 Also shown in the figure is the growth rate of the population aged 24~64 in the model economy. The employment growth rate exhibits a slow downward trend and short-run fluctuations. The trend in the employment growth rate is well captured by the growth rate of the population aged 21~64 of the model economy. As reported in Table 2, the contribution of labor to GDP growth was 1.0% per annum in the 1990s and 0.8% per annum in the 2000s. In the model economy, the corresponding numbers are 1.3% and 0.9%, respectively. However, not well replicated by the model economy are the relatively high employment growth rates in the first half of the 2010s. During this period, we observe a slowdown in GDP growth and a relatively 9 A closer empirical counterpart for our aggregate labor here can be constructed using total working hours weighted by the age-productivity profile. However, the time series of average working hours can be obtained for the years after 2004, which is much shorter than the in-sample time horizon. VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 31 National Pension System by raising the premium rate. Because there is no explicit agreement on the definition of fiscal stabilization as it pertains to the National Pension System, we adopt the definition suggested by the Third National Pension Improvement Committee in 2013. It suggested as a goal to maintain a reserve fund at more than twice the projected annual expenditure until 2083. In this subsection, we calculate the equilibrium premium rate necessary to remain solvent for another 30 and 50 years from the date of the depletion in the benchmark model economy. More specifically, we find the minimum premium rates that allow the National Pension Fund to avoid depletion until 2080 (Plan 1) and 2100 (Plan 2). We then analyze the welfare consequences based on the welfare criterion presented in Section 3. To simplify the problem, we assume that the government will announce a one-time unexpected premium rate increase in 2021 and implement the plan immediately. Reported in the left panel of Figure 11 is the equilibrium premium rate after the reforms. It was found that is necessary to raise the premium rate by 9.3%p for Plan 1 and 11.0% p for the Plan 2 from the current premium rate of 9%. The macroeconomic effects of the Plan 1 are reported in Table 4. The numbers reported in Table 4 are the percentage deviation in levels from the benchmark model for the selected years. The numbers in the parentheses are the simulation results, in which the wage growth rate and the interest rate are fixed at the level of the benchmark model. If the price variables are not allowed to vary, the capital stock increases by 19.2% in 2060 compared to the benchmark model mainly due to the large increase in the National Pension Fund. In the long run, the capital stock, however, converges to the level of the benchmark model given that Plan 1 is only a temporary measure. The labor supply is low relative to the benchmark model until 2049, when the fund depletes in the benchmark model. However, the labor supply increases significantly between 2050 and 2080 in response to the drop in the premium rate compared to the benchmark model. Like the capital stock, the labor supply returned to the same level as the benchmark economy in the long run. With regard to GDP, the effect of the increase in the capital stock outweighs that of the decrease in the aggregate labor input. Therefore, output also increases except for a few periods FIGURE 11. PATH OF THE EQUILIBRIUM PREMIUM RATE (LEFT) AND THE BENEFITS-COST RATIO (RIGHT) 0 5 10 15 20 25 30 35 2013 2050 2100 2150 2200 Plan 1 Plan 2 Benchmark Model 0 1 2 3 4 1950 2000 2050 2100 2150 Plan 1 Plan 2 Benchmark Model 32 KDI Journal of Economic Policy MAY 2019 TABLE 4—CHANGES IN MACROECONOMIC VARIABLES: PLAN 1 (Unit: %, %p) Period GDP Labor Capital Wage Premium Rate(τ) Real Interest Rate 2021 -0.4 (-0.1) -0.72 (-0.30) 0.00 (-0.05) 0.23 (0.00) 0.09 (0.09) -0.04 (0.00) 2030 0.8 (2.1) -0.58 (-0.33) 3.46 (6.44) 1.42 (0.00) 0.09 (0.09) -0.26 (0.00) 2040 1.6 (3.9) -0.88 (-0.97) 6.67 (13.23) 2.64 (0.00) 0.09 (0.09) -0.47 (0.00) 2050 4.3 (7.3) 3.11 (2.91) 8.93 (18.08) 2.35 (0.00) -0.11 (-0.11) -0.42 (0.00) 2060 3.8 (7.0) 2.01 (1.59) 9.03 (19.23) 2.67 (0.00) -0.12 (-0.12) -0.49 (0.00) 2070 2.8 (5.8) 1.33 (0.93) 6.71 (16.23) 2.01 (0.00) -0.11 (-0.12) -0.38 (0.00) 2080 1.6 (3.9) 0.61 (0.31) 3.69 (10.97) 1.11 (0.00) -0.07 (-0.07) -0.22 (0.00) 2090 0.4 (1.7) -0.41 (-0.76) 1.53 (6.02) 0.63 (0.00) 0.01 (0.01) -0.12 (0.00) 2100 0.2 (0.9) -0.08 (-0.15) 0.48 (2.79) 0.18 (0.00) 0.00 (0.00) -0.03 (0.00) 2150 0.0 (0.0) 0.00 (0.00) 0.00 (0.12) -0.01 (0.00) 0.00 (0.00) 0.00 (0.00) 2200 0.0 (0.0) 0.00 (0.00) -0.01 (0.00) 0.01 (0.00) 0.00 (0.00) 0.00 (0.00) Note: The results for Plan 1 are reported on the right side of the parentheses. Reported in the parentheses are the partial equilibrium results for Plan 1. The percentage deviation levels from the benchmark model are reported. VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 33 immediately after the implementation of Plan 1. In the general equilibrium case, the adjustments in prices to clear markets significantly dampen the response of the macroeconomic variables. As the National Pension Fund expands, the equilibrium interest rate falls sharply as capital stock relative to labor input increases rapidly. The equilibrium interest rate falls by 0.5%p in 2060, when its difference reaches the maximum. On the other hand, the increased wages induce workers to supply more labor to the market. The expansionary output effect reaches its maximum relative to the benchmark simulation in 2050, and the GDP increases by 4.3%. To increase the GDP by 4.3% in 30 years, it must grow more rapidly by approximately 0.15% per annum from 2021 to 2050, which is a significant growth effect given the low growth rate projection in the benchmark model economy. The macroeconomic effects of the implementation of Plan 2 are reported in the appendix. In order to facilitate comparison with Plan 1, the results for Plan 1 are reported again in the parentheses. Table 5 shows the changes in the average premium rate and the benefits-cost ratio according to Plan 1 and Plan 2. Recall that the equilibrium premium rate to implement Plan 1 is 18.2%. Because the transition to the pay-as-you-go system is delayed for 30 years, the equilibrium premium rates between 2050 and 2080 drop significantly. As a result, the average premium rates during a lifetime for the generations working for that period are significantly lower. For example, the average premium rate for the 2030 cohort fell by 7.1%. However, the effect on the average premium rate for the 2050 cohort was insignificant, as they start working in the mid2070s. As shown in Figure 11, Plan 1 is not a long-term solution to the fiscal problems of the system, though it postpones the depletion of the fund. On the other hand, the average premium rate for the generations born before 2000 increases due to the reform. For example, in case of the 1980 cohort, the average premium rate rises by 5.3%p by Plan 1, which is still lower than the long-run steady state premium rate of 18.3%. With the implementation of Plan 2, the fund’s insolvency is postponed until 2100 TABLE 5—BENEFITS AND COSTS OF THE NAT IO N AL PENSION BY COHORT: REFORMS (Unit: %) Birth Cohort 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 ⋯ 2200 Income Replacement Ratio 30.3 28.1 25.4 22.4 20.7 20.1 20.0 20.0 20.0 20.0 20.0 ⋯ 20.0 Average Premium Rate Benchmark Model 8.0 8.3 8.6 9.0 11.5 16.6 21.5 25.8 28.4 27.7 27.0 ⋯ 18.3 Plan 1 8.0 9.3 11.7 14.3 16.5 18.2 18.2 19.2 21.3 23.5 25.6 ⋯ 18.3 Plan 2 8.0 9.5 12.3 15.3 17.9 20.0 20.0 20.0 20.0 20.8 22.6 ⋯ 18.3 Benefits-Cost Ratio Benchmark Model 2.9 2.6 2.3 2.0 1.4 1.0 0.7 0.6 0.5 0.6 0.6 ⋯ 0.8 Plan 1 2.9 2.3 1.7 1.2 1.0 0.9 0.8 0.8 0.7 0.6 0.6 ⋯ 0.8 Plan 2 2.9 2.3 1.6 1.2 0.9 0.8 0.8 0.8 0.8 0.7 0.7 ⋯ 0.8 34 KDI Journal of Economic Policy MAY 2019 and the premium rate rises to 20%. As shown in the panel on the right in Figure 11, the premium rate and the benefits-cost ratio are greatly equalized across generations, despite the fact that Plan 2 does not avoid the depletion of the reserve fund. Note also that the benefits-cost ratios for the young and future generations become similar to the long-run steady-state value under Plan 2. We now turn to look at the welfare implications of the reforms. The change in welfare in terms of CEV for the selected birth cohorts are reported in Table 6 and Table 7. The patterns of welfare changes among the generations are similar to the changes in the average premium rate reported in Table 5. The welfare of the 2020~2050 cohorts, who supply labor actively between 2050 and 2080, increases significantly due to the reform as the burden of paying a premium falls sharply. For example, the welfare gain of the 2030 cohort is found to be 9.3% in terms of CEV , which means that the gain amounts to an increase in consumption of 9.3% for every possible contingency during the lifetime of this cohort. Note that most of the welfare change is explained by the increase in consumption, C CEV . Further decomposition of C CEV shows that the gain from the reduction in uncertainty, CD CEV i s negligible relative to CL CEV . However, note that CD CEV is positive for the TABLE 6—CHANGES IN WELFARE FOR THE SELECTED COHORTS: PLAN 1 (Unit: %) Birth Cohort 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 1998 -2.2 -2.3 -2.0 -0.3 0.1 -0.1 0.2 2000 -1.4 -1.4 -1.2 -0.2 0.1 -0.1 0.2 2010 3.1 3.2 3.3 -0.1 -0.1 -0.3 0.2 2020 6.7 7.0 7.1 -0.1 -0.3 -0.4 0.1 2030 9.3 9.3 8.4 0.8 0.0 0.0 0.0 2040 6.2 6.0 5.4 0.6 0.1 0.1 0.0 2050 2.6 2.4 2.1 0.4 0.1 0.1 0.0 2060 -0.1 -0.1 0.0 -0.1 0.0 0.0 0.0 2100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2150 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TABLE 7—CHANGES IN WELFARE FOR THE SELECTED COHORTS: PLAN 2 (Unit: %) Birth Cohort 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 1998 -3.4 -3.5 -3.4 -0.2 0.1 0.0 0.2 2000 -2.6 -2.7 -2.5 -0.2 0.1 -0.1 0.2 2010 1.8 1.9 2.0 0.0 -0.1 -0.3 0.2 2020 6.7 6.9 6.8 0.1 -0.2 -0.3 0.1 2030 10.7 10.7 9.8 0.8 0.0 -0.1 0.1 2040 8.7 8.7 8.1 0.5 0.0 -0.1 0.1 2050 6.0 6.0 5.5 0.5 0.0 0.0 0.0 2060 3.6 3.6 3.4 0.2 0.0 0.0 0.0 2100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2150 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 35 2030~2050 cohorts; moreover, the magnitude is not too small so as to be ignored. As the average premium rates for these cohorts drop sharply, their ability to accumulate savings to buffer the effects of productivity shocks on consumption is improved significantly. The decomposition of welfare change shows that for the young and future generations, the reduction in the burden to support the National Pension System greatly improves their welfare. Of course, they benefit from the reform at the expense of the older generations. However, the welfare analysis in Table 6 together with the changes in the benefits-cost ratios reported in Figure 11 clearly indicate that the current system is unjustifiably partial to those in the older generations. Shown in Table 7 are the welfare changes caused by the implementation of Plan 2. As expected, the results are qualitatively similar to those of Plan 1 and are quantitatively larger than those of Plan 1. However, the results in Table 5 are interpreted as meaning that Plan 2 distributes more evenly the burden of supporting the National Pension System than Plan 1 across generations, as the benefits-cost ratios become closer to the steady-state value for many more generations. However, in the model economy, older cohorts that start working before 2021 lose due to the reforms. If the implementations of Plans 1 and 2 are determined by voting in 2021, it turns out that even Plan 1 is not implementable, as the future generations are not eligible to vote. We also attempted to find ways to achieve the goal of Plan 1 by reducing the benefits of the National Pension, i.e., by adjusting the proportional constant t d . However, if the system is to be modified akin to how the second National Pension reform was in 2007, this goal cannot be achieved. The reform in 2017 guaranteed proportional constants before the reform and announced a lowering of the proportional constants for the years to come. By honoring this vested right, we could not achieve the goal of postponing the depletion of the reserve fund for 30 years. B. Strengthening Income Redistribution As noted in the previous section, the degree of income redistribution is determined by the weight parameter A α in equation (1). If the weight parameter were 1, regardless of individual earnings histories, the amounts of pension benefits would be identical for all beneficiaries within a birth cohort. At the other extreme, if the weight parameter were 0, the amount of pension benefits only depends on the individual earnings history, and there would not be any income redistribution by the National Pension System. In this subsection, the change in welfare is measured when the weight parameter changes to the value of 0.99 from the current value of 0.5. As the value of A α increases, it turns out that the welfare evaluated by CEV for future generations increases. Therefore, we only report the simulation results of A α being equal to the value of 0.99. We assume that the government will announce unexpectedly the change in the weight parameter in 2021 and implement it immediately in that year. We further assume that only the beneficiaries who retire after the announcement are affected by the reform. We refer this reform as Plan 3 hereafter. 36 KDI Journal of Economic Policy MAY 2019 The macroeconomic effects of Plan 3 are summarized in Table 8. As in Table 4, the percentage deviations in levels from the benchmark simulation are reported. Unlike the fiscal stabilization plans in the previous subsection, the reform in this subsection changes the system permanently and the macroeconomic variables are affected even in the long run. The aggregate labor supply and savings increase, resulting in an increase in the total output compared to the benchmark model. The wage rate is higher and the interest rate is lower than in the benchmark simulation as the aggregate labor supply relative to capital stock increases. Researchers who are familiar with the class of model in this paper may see the results shown in Table 8 as counterintuitive. Because the uncertainty about allocation is expected to decrease due to the reform, the workers directly affected by the reform would supply less and save less as the precautionary motive decreases. However, the results in Table 8 are considered to be a somewhat special case because there is an upper limit on the Standard Yearly income () t y. We checked the case in which there is no maximum Standard Yearly Income in equation (1). In that model economy, the reform caused decreases in the labor supply, savings and output. Reported in Table 9 are the changes in welfare in terms of CEV for the selected TABLE 8— CHANGES IN THE MACROECONOMIC VARIABLES: PLAN 3 (Unit: %, %p) Period Output Labor Input Capital Stock Real Wage Real Interest Rate 2021 0.07 0.01 0.00 -0.02 0.00 2030 0.20 0.02 0.34 0.08 -0.01 2040 0.34 0.00 0.71 0.19 -0.04 2050 0.50 0.05 1.06 0.29 -0.05 2060 0.66 0.15 1.42 0.39 -0.07 2070 0.76 0.17 1.65 0.46 -0.09 2080 0.80 0.16 1.76 0.50 -0.10 2090 0.78 0.12 1.77 0.51 -0.10 2100 0.78 0.13 1.74 0.50 -0.10 2150 0.70 0.11 1.58 0.45 -0.09 2200 0.57 0.07 1.22 0.35 -0.07 TABLE 9—CHANGES IN WELFARE FOR THE SELECTED COHORTS: PLAN 3 (Unit: %) Birth Cohort 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 𝐶𝐸𝑉 1998 1.5 1.6 0.2 1.4 -0.1 0.0 0.0 2000 1.6 1.7 0.2 1.4 -0.1 0.0 0.0 2010 1.7 1.8 0.4 1.4 -0.1 -0.1 0.0 2020 1.8 1.9 0.5 1.4 -0.1 -0.1 0.0 2030 1.9 2.0 0.5 1.5 -0.1 -0.1 0.0 2040 2.0 2.1 0.6 1.4 -0.1 -0.1 0.0 2050 2.2 2.3 0.6 1.6 -0.1 -0.1 0.0 2060 1.9 2.1 0.7 1.4 -0.1 -0.1 0.0 2100 1.9 2.0 0.6 1.3 0.0 -0.1 0.0 2150 1.9 1.9 0.4 1.5 0.0 0.0 -0.1 2200 1.5 1.5 0.5 1.0 -0.1 -0.1 0.0 VOL. 41 NO. 2 Equity across Generations and Uncertainty within a Generation 37 cohorts who start working after 2021. The welfare increases for all cohorts in Table 9 and the improvement show consumption increases of approximately 1.5% to 2.2% for every possible contingency compared to the benchmark economy. This increase in expected lifetime utility is attributable to the increase in consumption ( C CEV ) rather than to a change in working hours. However, unlike the effects of fiscal stabilization reforms, the improvement in welfare arises from a reduction in the uncertainty of consumption path ( CD CEV ) as opposed to being an effect of the level of consumption ( CL CEV ).This result implies that in addition to the self-insurance mechanism through adjustments to the labor supply and savings, the National Pension System plays a role in providing additional insurance from labor market productivity shocks. Given the calibrated labor income process, workers in the benchmark economy desire more insurance to be provided by the National Pension System, which is reflected in the increase in the expected lifetime utility by the reform. The majority (64.3%) of the current population in 2021 are found to be in favor of the reform in the benchmark model simulation. VI. Summary and Conclusion The long-term financial outlook of the National Pension System is a grave concern. According to the Third Official Fiscal Projection in 2013 by the Ministry of Health and Welfare, the National Pension Fund will begin to run a deficit in 2044 and will run out of funds in 2060 under the current system. The long-term financial problems associated with the National Pension are attributable in part to the rapid change in the demographic structure of Korea. In addition to the rapid population aging, the long-term financial problems are deepened by certain structural issues of the National Pension System, referred to the “low burden but high benefit” issue here. The purpose of this paper is to analyze plans to postpone the depletion of the National Pension Fund and to study welfare implications across generations. To do this, we build a life-cycle overlapping-generations macroeconomic model populated by heterogeneous agents. The model economy is composed of heterogeneous economic agents in terms of income histories and wealth holdings even within a generation. According to simulation results, as in many other studies, it is desirable for the National Pension System to be improved in order to increase the equity across generations, and it should be promoted to strengthen the income redistribution function within a birth cohort, even at the current premium rate. We calculate the equilibrium premium rate to delay the depletion of the fund reserve for 30 years from the year of depletion in the benchmark model economy. We find that it is necessary to raise the premium rate by 9.2%p from the current premium rate of 9%. Although the plan is not strong enough to prevent the National Pension Fund from depletion, it enhances the equity across generations significantly. Aside from the goal of postponing the depletion of the fund, we also evaluate a plan to strengthen the income redistribution function of the system. A shortcoming of the welfare measure 38 KDI Journal of Economic Policy MAY 2019 in the paper is that it does not reflect the overall welfare of the current and future population. To overcome this difficulty, Nishiyama and Smetters (2007) introduce what they term the Lump-Sum Redistribution Authority (LSRA) to analyze the social welfare of the older and future generations in a single framework. We leave a welfare analysis of this type for future research. APPENDIX TABLE A1—CHANGES IN MACROECONOMIC VARIABLES: PLAN 2 (Unit: %, %p) Period GDP (%) Labor (%) Capital (%) Wage Real Interest Rate (%p) 2021 (-0.4) -0.5 (-0.7) -0.9 (0.0) 0.0 (0.2) 0.3 (-0.0) -0.1 2030 (0.8) 1.0 (-0.7) -0.6 (3.5) 4.2 (1.4) 1.7 (-0.3) -0.3 2040 (1.6) 2.1 (-0.9) -1.0 (6.7) 8.2 (2.6) 3.2 (-0.5) -0.6 2050 (4.3) 5.1 (3.1) 3.1 (8.9) 11.3 (2.4) 3.2 (-0.4) -0.6 2060 (3.8) 4.8 (2.0) 2.0 (9.0) 12.3 (2.7) 3.8 (-0.5) -0.7 2070 (2.8) 3.9 (1.3) 1.0 (6.7) 10.5 (2.0) 3.4 (-0.4) -0.6 2080 (1.6) 2.8 (0.6) 0.5 (3.7) 7.9 (1.1) 2.6 (-0.2) -0.5 2090 (0.4) 2.0 (-0.4) 0.6 (1.5) 5.1 (0.6) 1.6 (-0.1) -0.3 2100 (0.2) 1.1 (-0.1) 0.4 (0.5) 2.5 (0.2) 0.8 (-0.0) -0.2 2150 (0.0) -0.1 (0.0) 0.0 (0.0) -0.0 (-0.0) -0.0 (0.0) 0.0 2200 (0.0) 0.0 (0.0) 0.0 (-0.0) -0.0 (0.0) 0.0 (0.0) 0.0 Note: The results for Plan 1 in Table A1 are reported in the parentheses for comparison. 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