key: cord-0435378-9062rvlv
authors: Iiboshi, Hirokuni; Ozaki, Daisuke
title: The Impact of the Social Security Reforms on Welfare:Who benefits and loses across Generations, Gender, andEmployment Type?
date: 2022-05-17
journal: nan
DOI: nan
sha: 67af566fa115e710b385d1f54d1f60e3c12c3262
doc_id: 435378
cord_uid: 9062rvlv

We quantitatively explore the impact of social security reforms in Japan, facing rapid aging and the highest government debt among developed countries, using an overlapping generations model with four types of agents distinguished by gender and employment type. We find that social security reforms without extending the retirement age raise the welfare of future generations, while the reforms with raising copayment rates for medical and long-term care expenditures, in particular, significantly lower the welfare of low-income groups (females and part-timers) of the current retired and working generations. In contrast, the reform reducing the pension replacement rate lead to a greater decline in the welfare of full-timers. The combination of these reforms and the extension of the retirement age is expected to improve the welfare of the current working generations by 2--9% over the level without reforms.

of aging and public pension reform in the U.S., they adopted a general equilibrium overlapping generations (OLG) model with four types of households distinguished by the wealth class. The feature of their model is rich parameterization which enable calibration corresponding to both macro-level data and micro-level income data, e.g., application of the progressive tax bracket to the labor income tax rate. By applying their model to Japanese policy reforms, our study provide empirical outcome under more practical situations than previous Japanese studies.

And we extend McGrattan and Prescott (2017) to four types of households distinguished by gender (male and female) and employment types (full-timer and part-timer), as well as to include medical and LTC insurance besides public pensions. We then quantitatively analyze the impact of social security reforms associated with population decline on the welfare of over generations: the current working, retired, and future generations.

In our paper, the reform of the pension, medical insurance, and LTC insurance are considered according to the two scenarios: firstly, a baseline scenario based on the current system. Secondly, a scenario in which the extension of the retirement age from 65 to 70. Under these two scenarios, we calculate three options of the reforms: (1) a reform to gradually lower the pension income replacement rate from the current 62% up to 50.8% until 2047; (2) a reform to raise the copayment rate for medical expenses for the elderly uniformly to 30% for all ages; and (3) a reform to increase the copayment rate for LTC expenses uniformly to 30%.

According to our simulation, by the mid-2040s when population and output levels are at their lowest, the output will be about 75% of its 2020 level, and extending the retirement age and reforming social security have little effect on raising GDP. On the other hand, extending the retirement age has improved the welfare of the current working-age population in particular. Focusing on social security reform, the reduction in the pension income replacement rate reduces the welfare of full-timers by a relatively large amount, and the increase in the copayment rate for medical and LTC expenditures lowers the welfare of the current retired generation. We also find that med-ical and LTC insurance reform significantly lowers the welfare of females and part-timers with relatively low incomes and assets.

The contributions of our paper are that it shows, based on quantitative analysis, what types of households should be more cared for, when conducting social security reforms subject to fiscal sustainability constraints, and that in light of past previous empirical research outcomes, we calculate and present practical policy implications by exploring above three options of social security reforms on household's welfare based on the two scenarios, classified by four kinds of households over generations including the current working, retired and future generations.

The rest of this paper is organized as follows. section 2 summarizes Japan's demographic data and institutional background and shows the contribution of this study to previous studies. section 3 describes our model. section 4 provides an explanation of the calibration and parameterization based on the data and institutional background for the analysis, and calculates the steady state.

section 5 computes the transition path based on the steady state. Then, we conduct simulations assuming the several scenarios and social security reforms described above. section 6 discusses the conclusions of our paper and future research.

In this section, we describe two things that provide the motivation and background for our study.

First, there are the demographic data and medical and LTC expenditures per capita to clarify the arguments that our paper focuses on. Second, we summarize the literature review for the relevant field, in particular, for Japan.

As discussed in section 1, the population decline associated with graying leads to a decrease in the labor force. According to the projection by IPSS, the population aged 20-64, consisting mainly of workers, will decrease monotonically in the future, while the population aged 65 and over, consisting mainly of retirees, will increase as Figure 2 Panel (a). This trend is reflected clearly in the transition of the old-age dependency ratio. 4 While this ratio is about 50% in 2015, it is projected to exceed 80% by around 2050 as Figure 2 Panel (b). Because these demographic changes give significant impacts on the public pension, and medical and LTC insurance systems, this topic must have been considered as one of the most urgent policy agenda in terms of fiscal sustainability.

Institutional background In Japan, citizens are required to be covered by some form of public medical insurance. As of 2021, the copayment rate for medical expenses is set at 30% for those under 70 years old, 20% for those between 70 and 75 years old, and 10% for those over 75 years old (preschool children under 6 years old are required to pay 20%). However, due to the passing 4 Where the old-age dependency ratio ≡ population aged over 65 / population aged 20-64. of a revised law on June 4, 2021, it was agreed that the copayment for the aged 75 and over will be raised to 20% in the latter half of 2022, to reduce the burden on the covered persons in the medical insurance system. In addition, LTC insurance is mandatory from age 40. The copayment rate for LTC expenditures is set at 10% for all ages 40 and over ( Figure 3 ).

Public LTC insurance was introduced in Japan in 2000. After that, there were increasing concerns about the financial sustainability of LTC insurance with the aging of the population, and the reform of the program has been implemented frequently until now. the copayment rate for the elder people earning the equivalent level of incomes as the working-age generations, etc. 6

The above social security reforms to maintain fiscal sustainability could have a significant impact on aggregate flows such as consumption and saving over the household life-cycle. And the reforms also would affect aggregate stock variables such as capital accumulation which forms future output. Since declining population and labor force could also hurt economic growth, we have to examine effect of reforms comprehensively. In fact, outlooks by the government, such as the Cabinet Office's "Medium-and Long-Term Economic and Fiscal Outlook" and the Bank of Japan's "Outlook for Economic and Price Conditions," indicate a slowdown in GDP growth in recent years and a decline in the total factor productivity (TFP) growth rate. For example, the Bank of Japan's Outlooks shows particularly low values ranging from 0.01-0.43% from 2015 onward. 7 Therefore, additional social security reforms are likely to be implemented simultaneously declining population and a further slowing of economic growth. We think that investigating the effects of such reforms on people's consumption and saving behavior or welfare could have important implications for future policy discussions. 8

There are large literature to analyze the impact of the population aging on fiscal administration in Japan. By using a neoclassical growth model, Hansen and Imrohoroglu (2016) focused on the aging and fiscal sustainability. They find that the consumption tax rate of about 40% is needed to sustain the fiscal balance when reforms such as the expansion of the tax base and the reduction of social security benefits are implemented. They also showed that the consumption tax rate of about 60% would be needed if those reforms are not carried out.

Using a general equilibrium OLG model, Braun and Joines (2015) simulated the fiscal impact of an aging population on Japan's social security system, including public pensions, medical insurance, and LTC insurance. And they analyzed the impact on fiscal sustainability of reforms such as raising the consumption tax and increasing the copayment rate for medical expenditures.

They conduct policy simulations under the assumption that public finances are balanced by the consumption tax rate, and they show that consumption tax rates of 30-45% would be necessary to sustain fiscal balance. Furthermore, they find that if reforms to raise the copayment rate for medical expenditures for the elderly to 30% are simultaneously implemented, the consumption tax rate needed to sustain the fiscal balance would be around 20%. Kitao (2015) quantitatively explored the fiscal impacts of demographic change in Japan, focus- 6 Fu et al. (2017) analyze the impact of these LTC insurance reforms on labor supply using microdata. 7 Bank of Japan, "Supply-Demand Gap and Potential Growth Rate" (https://www.boj.or.jp/research/ research_data/gap/index.htm/ accessed June 29, 2021). 8 Of course, COVID-19 would significantly affect social security administration and demographic dynamics. However, we aim to analyze the impacts of social security reform by focusing on demographics from a more long-term perspective. For this reason, our study does NOT consider the effects of COVID-19 and uses data until 2019.

ing on the pension reform. She showed that the consumption tax rate needed to maintain public finances would rise to a maximum of nearly 50% without pension reforms, and that raising the pension starting age together with a 20% benefit reduction would result in the consumption tax rate rise of only less than 30%. And, Kitao (2018) also focused on the pension reform and incorporated uncertainty about the timing of beginning reforms to reduce pension benefits into the analysis to quantitatively illustrate the welfare losses that would result from a delay in reforms.

As focusing on labor policy against a declining labor force, Imrohoroglu et al. (2017) measured the effects of labor force growth due to the immigration of guest workers on fiscal sustainability and welfare changes among native Japanese in a shrinking population. They assume that guest workers work in Japan for ten years and return to their countries without receiving social security benefits. They conduct a scenario analysis distinguishing between high and low skill levels of guest workers, and show that an influx of high-skilled guest workers lowers the consumption tax rate in particular and improves the welfare of native Japanese in the future.

From an accounting approach based on micro data, Imrohoroglu et al. (2019) found that higher labor productivity and female labor force participation become more effective factors in improving fiscal sustainability, for achieving reforms of medical and LTC insurance systems as well as pension system.

Using OLG model with household heterogeneity differentiated into four types in terms of their wealth class, Prescott (2017, 2018) examined the policy effect of transition from a PAYG public pension system to a private funded system. They calculated the extent to which a change to a private funded system has improved social welfare for different households with income and wealth inequality. To capture the Gains and Losses between public pension contributions and benefits over the life-cycle with higher degree of accuracy, they incorporated a progressive labor income tax rate into their model and also set up two-sector firms, i.e., the corporate sector and a government/household business (self-employment) sector in which both tangible and intangible assets form their capital. These fine-grained settings using macro and micro data allow the model to examine much practical policy simulations fitted to both sides of actual macro and micro economy. (e.g. Moriguchi, 2017; Kitao and Yamada, 2019) In fact, several studies focus on differences by gender and employment type. For instance, Kitao and Mikoshiba (2020) examined the impact of labor market changes on the Japanese economy and the fiscal situation using an OLG model that includes males and females with different labor participation, employment types, labor productivity, and life expectancy. They showed that higher labor participation rates and labor productivity, especially among females and the elderly, are significant factors for improving the fiscal situation.

Of course, gender heterogeneity is thought to be key element in other countries, too. For example, Braun et al. (2017) , analyzed the efficient level of old-age income compensation programs for medical and LTC expenditures, spousal bereavement, and other risks faced in old age in the U.S., also points to the importance of gender differences.

Turning to studies dealing with medical and LTC costs from different perspectives, there are studies on the retirement savings puzzle, which indicates actual medical and LTC expenditures higher than derived by the standard life-cycle model. For example, De Nardi et al. (2010) explained the saving behavior of elderly households in the context of precautionary savings to finance medical expenditures that may arise during old age. And, Kopecky and Koreshkova (2014) found that the LTC expenditures account for large portion of precautionary savings among the elderly. They also showed that expanding Medicaid, which is the U.S. health insurance program for low-income households, could improve the welfare of future generations. On the other hand, Braun et al. (2017) showed that expanding the social security with the means test could improve welfare because of taking into account aging risks such like death or longevity of a spouse.

For Japan, Iwamoto and Fukui (2018) shows average medical and LTC expenditures. 9 Figure   4 depicts per capita medical and LTC expenditures by age group. As the figure, medical and LTC costs are higher for the elderly. In particular, LTC costs rise rapidly after the age of 80s. Increasing the expected spending in old age must have influenced on saving and consumption amount at his young age. Similar to this, increases in copayment rates for medical and LTC could have much greater impact on them at his young age. We take these things into account in our study, by incorporating the medical and LTC costs into our model.

In this section, we describe the model used in our quantitative analysis. First, we show the settings that describe the social security system. Next, we set up households and firms, and describe the budget constraints of the government managing the social security system. Finally, we define the equilibrium conditions.

As mentioned in the previous section, our model is a deterministic OLG model following McGrattan and Prescott (2017) and modified to fit into Japan's original system. The households 9 Iwamoto and Fukui (2018) is calculated on data from the Ministry of Health, Labour and Welfare (Basic Data on Medical Insurance and Statistics of Long-term Care Benefit Expenditures). This is the sum of the copayment and insurance contribution. Figure 4 : Per capita medical and LTC expenditure 0 -4 5 -9 1 0 -1 4 1 5 -1 9 2 0 -2 4 2 5 -2 9 3 0 -3 4 3 5 -3 9 4 0 -4 4 4 5 -4 9 5 0 -5 4 5 5 -5 9 6 0 -6 4 6 5 -6 9 7 0 -7 4 7 5 -7 9 8 0 -8 4 8 5 -8 9 9 0 -9 4 9 5 -9 9 1 0 0age bracket sector, whose capitals are formed from tangible and intangible assets. The government runs the social security systems (pension, medical insurance, and LTC insurance) as well as conducts finance by issuing government bond and provides benefits for households.

We assume that households decide in perfect foresight and representative firms in both sector produce with a constant return to scale technology under perfect competition. The government implements a credible fiscal policy. Time is discrete, and one period in the model is one year. And we also assume that the economy is on a balanced growth path with a constant labor-augmented productivity growth rate γ and a constant population growth rate n in the long run.

First, let t and j denote time period and the age of the agents at maximum age J, respectively.

g ∈ {m, f } represents gender. m and f denote male and female. s j,g t represents the probability that an agent of gender g entering the economy at age j = 1 will survive until the next period. The unconditional survival probability at age j in period t is given by

(1)

And we denote n j,g,h t the size of the population at age, where h ∈ { f ull, part} denotes the employment types, and full and part represents a full-timer and a part-timer, respectively. The size of the new cohort n j,g,h t for j = 1 grows at a rate γ n t .

Following Kitao and Mikoshiba (2020) , we set up pension benefits households are assumed to receive a public pension benefit after they reach normal retirement age J R . p j,g,h t is the public pension benefit received at age j in period t where by g denotes gender and h, employment type.

The public pension benefit is given as

where κ t is the replacement rate of the past average earnings. Accumulated labor income earned by the heterogeneous households during their lifetime, W j,g,h t

, are defined recursively as

where w t is wage rates in period t. l j,g,h t and e j,g,h are the labor supply, or working hours, and labor productivity of the households differentiated by age, gender, and employment type, respectively.

Therefore, the aggregate public pension expenditure provided by the government in each year can be defined as

As in Kitao (2015 Kitao ( , 2018 , we introduce the total healthcare cost faced by every household each period: that consists of both medical costs m H j,t and LTC costs m L j,t . And the fractions λ H j,t and λ L j,t represent the copayment rates for medical and LTC expenditures. The remaining expenditures are covered by public medical insurance and LTC insurance. The aggregate healthcare cost is the sum of households' copayments and government contributions M g t , and defined as

Following Kitao (2015 Kitao ( , 2018 , Braun and Joines (2015) , and , we assume that households allocate a fraction ψ t of their assets to government debt and the rest to corporate equity.

Thus, the after-tax gross return on personal assets is given by

For households, a single period of risk-free assets may be traded. This asset is assumed as a composite of an investment in corporate capital and a holding of government debt, paying gross interest r t after taxes. We also assume that borrowing against future income or transfers is not allowed, and assets must be non-negative. The state vector of an agent x (= { j, a t , g, h}) consists of age j, assets a t , gender g, and employment types h. The agent chooses the optimal path of consumption c t , assets a t+1 , and labor supply l t to maximize lifetime utility, where l t indicates the working hours, or intensive margin, and l t ≥ 0. Labor supply of households after reached their retirement age J R is assigned l t = 0. The problem is solved recursively, and the value function v t (x)

without policy uncertainty is defined as

where the value function v J+1 at the final age is equal zero. Agents can allocate a unit of disposable time to labor supply and leisure each period.

We assume that agents know with certainty the profile of the labor efficiency e j,g,h that depends on its age, gender, and employment type. Private capital and government bond are shares of ownership in an asset that pays out at the time of their retirement, and the return on assets is provided to the still alive members of their same cohort. Thus, the return depends not only on the size of the capital and bond, but also on the probability of survival.

For the left-hand side of equation (8), we show that agents only pay out-of-pocket for medical and LTC expenditures and receive healthcare services; following Braun and Joines (2015) , this is not reflected in the utility function as in normal consumption. That is, we assume that health care costs are always incurred by households, although the amount varies by age and gender. The above budget constraint of households is also set to be consistent with the fact that health care costs is not subject to consumption tax. On the other hand, as for the right-hand side of equation (8), the first term is the after-tax gross income on the assets (1 + r t ) a t explained above, and the next term y t is the labor income, which indicates that households receive an income transfer of pension benefit T p

Following Mc Grattan and Prescott (2017) and Mc Grattan et al (2019), we set up two sectors of production in our economy. Sectors 1 and 2 produce intermediate goods Y 1t and Y 2t , respectively.

Sectors 1 denotes corporate sector, while Sector 2 denotes household business sector. And the aggregate production function of the composite final good is given by

where η 1 = 1 − η 2 , that setting indicates constant return to scale and both parameters, η 1 and η 2 , are positive. And the production function in Sector i (i = 1, 2) is formed by the Cobb-Douglas function with inputs of tangible denoted as T and intangible denoted as I capital stocks, i.e., K iT t K iIt , and labor L it , as below.

The levels of TFP and labor force growth technology in period t for Sector i are, respectively, A t

and Ω t , that grow at rates of γ A , γ Ω .

The tangible and intangible capital stocks depreciating at certain rates, δ iT , δ iI in Sectors i are given as

where X iT t and X iIt are tangible and intangible investments for i = 1, 2, respectively. In addition, from the resource constraint, output Y t , and gross domestic product (GDP t ) are expressed as

where

The government in our economy collects revenue through consumption taxes, labor income taxes, social security premiums, corporate and dividend taxes, and the issuance of risk-less debt B t+1 . Its revenue is used by the government to purchase goods and services G t , to pay for principal and interest on debt, (1 + i d )B t , as well as for public pension benefits P g t , medical and LTC insurance benefits M g t .

Labor income tax and social security premium We assume a labor income tax based on a progressive taxation system, which includes social security premium. The details of the progressive taxation system will be explained in the next section.

The accounting profit of Sector 1, the corporate sector, in period t is given by

where p 1t is the relative prices of intermediate goods to final goods in Sector 1. 10

Let us now write the corporate tax of Sector 1 as τ π 1t , and the dividend of the shareholders in this sector D 1t , can be expressed by the following equation.

Similarly, the dividend D 2t , for Sector 2, household business sector, is given by

where p 2t is the relative prices of intermediate goods to final goods in Sector 2.

In our economy, the profits of the corporations in Sector 1 are taxed at the rate τ π 1t . And the dividends D It of Sector i are taxed at the rate τ d It .

Government Debt From the above public expenditures and revenues, the equation for government debt can be derived as follows.

Labor income progressive tax and capital tax rates and the ratio of government consumption to GDP are given exogenously, while government debt, private capital interest and wage rates, and consumption tax rate are determined endogenously so that market equilibrium is completed.

A competitive equilibrium, for a given sequence of demographics, TFP levels

• wage rates {w t } ∞ t=1 , interest rates {r t } ∞ t=1 , and

In this section, we describe the procedure for calibrating and parameterizing the model. And we explain the sources of data used for the calibration. The quantitative results of the transition path for our policy analysis are illustrated in the next section.

We conduct the calibration of the steady state and transition path in our model based on the three steps below, following Prescott (2017, 2018) . The first step is to calculate the initial steady state. To be more precise, we calculate the initial steady state by setting parameters based on Japan's demographics and economic statistics such as the National Accounts (JSNA).

That is, we use the demographic structure as of 2015 and the average value of the JSNA from 2015

to 2019 as the beginning (initial) steady state data. The second step is to approximate a balanced growth path. Based on the initial steady state calculated in the first step, we assume balanced growth given the expected growth rate of technological productivity (the TFP growth rate γ A and the labor-intensive technology growth rate γ Ω ) and the population growth rate (γ n ) and derive a balanced growth path of the economy up to 240 years from base year set as initial steady state. The third step is to perform a full-fledged calculation of the transition path. Based on the equal growth paths derived in the second step, we calibrate the transition path based on annual projections of population dynamics and other factors. In this step, we further calculate policy simulations for retirement age extension and social security reform by changing the condition settings.

In the above calibrations, we parameterize in the following two aspects in terms of both macro and micro sides. First, in order to fit to actual aggregate data representing as the national accounts and fixed asset tables shown in Tab1es 1 and 2, we select the parameters pertaining to demographics, household preferences, firm technology, government spending and debt shares, and capital income tax rates. Second, for micro-side, we set the levels of labor productivity, labor supply, and progressive labor income tax to match the corresponding data for the population share, average labor income, and average working hours classified by gender and employment type. Table 1 shows the national income and product accounts for Japan after some standard adjustments to make the model measures and concepts consistent with the JSNA. With the 2016 revision of the JSNA, which adopted the 2008 SNA, the capital stock now includes both tangible and intangible capital. However, the intangible assets assumed in our model are a broader concept than those included in the JSNA. Therefore, we use the 2018 JIP (The Japan

Industrial Productivity) database. 11 The share of private capital in adjusted GDP is 232%, of which 68% is held by private firms and 32% by households and non-profit organizations. The 

We suppose households enter the economy at age 20, and they live up to a maximum age 120. In the notation of our model, this corresponds to age j = 1, 2, . . . , 100. The four types of households are characterized by (1) survival rates, (2) labor productivity, and (3) lifetime expected medical and LTC expenditures. Figure 5 shows (1), (2) and Figure 6 shows (3). First, we assume that agents are characterized by the age and gender specific survival rates s j,g,t and the growth rate of a new cohort n g,t are based on the population distribution and survival rate projections of IPSS (2017 estimates). 13 Next, to set up heterogeneous agents by dividing households into gender, and employment type, the population is assigned to the four types based on the composition ratio of each type described in the Basic Survey on Wage Structure Statistics (2019) by the Ministry of Health, Labor and Welfare.

We use the per capita medical and LTC expenditures presented by Iwamoto and Fukui (2018) .

And expected medical expenditure m H j,t is obtained by multiplying the gender-specific survival rates presented in Figure 5 Panel (a) and the per capita age-specific expenditures data shown in Figure 4 . Furthermore, expected LTC expenditures m L j,t , is obtained by multiplying the genderspecific survival rates, the certification rate of LTC need, and the per capita age-specific expenditures data mentioned above. Figure 6 Panel (a) and (b) show expected medical and LTC expen- 12 We also include land in the capital stock because it is in large part a produced asset associated with real estate development. With land included, the total capital stock is 566% of adjusted. 13 By reference, the IPSS future population projections are formal estimates for the period 2015-2065, and are calculated assuming that the death and birth rates at that time will remain at the same rate after 2065. ditures per capita, respectively. 14 Because survival rates are higher for females than for males, especially for those aged 60 and older, expected medical and LTC expenditures are also higher for females.

As shown in equation (22), an agent's utility function is composed of consumption and labor supply, and while the log function is used for consumption, the CES function is adopted for the disutility of labor. Kuroda and Yamamoto (2008) estimated the value of Frisch labor supply elasticity ζ g (g ∈ {m, f }; hereafter, Frisch elasticity), which differs between males and females, using data from Japan. Therefore, we conduct our analysis based on their estimation results. Frisch elasticity in gender units is set as ζ m = 0.03 for males, and ζ f = 0.05 for females, and preference parameter of leisure γ = 10 for both males and females.

The labor supply at the initial steady state of the four heterogeneous agents calculated using the parameters described above is shown in Figure 7 Panel (a). As can be seen in this figure, regardless of the increase in labor income with age, gender, employment type, or the age of the worker, agents spent working around eight hours a day (about one-third of a day). In addition, the labor supply is higher for males than for females. These are consistent with the results of empirical studies such as Kuroda and Yamamoto (2008) .

14 The certification rate of long-term care/support need that we use is defined by dividing the number of people in each age group who LTC (you-kaigo) level from one to five, excluding those who requiring support (you-shien), by the population in each age group. 

The technology parameters in Table 3 govern the technology growth rate (γ A = 0.3%), investment rate, and capital income share by both sectors. The long-run growth rate for labor-intensive technology γ Ω is set at 0.7%. By combined the two technology growth rates with the long-run population growth rate γ n indicating the demographic parameters as −1.0%, then the long-run GDP growth rate is offset as just 0%.

In Table 3 , the share parameter of the aggregate production function η 1 (which determines the relative share of income to Sector 1) is set to 64%. This parameter is based on the share of operating rates that produce investment rates consistent with the Japanese data are δ 1T = 0.08 and δ 2T = 0.05. The tangible capital share and depreciation rate in Sector 2 include housing costs for the household business sector. The intangible capital ratio and depreciation rates, θ 1I , θ 2I , δ 1I , and δ 2I , cannot be uniquely identified with the data we have. In our baseline model, we calibrated these parameters following Arato and Yamada (2012) who derived estimates of tangible and intangible assets for Sector 1. To obtain calibration of intangible assets in Sector 2, we assume the same ratio of intangible assets and non-land fixed assets in Sector 2. As a result, we set these parameters to 

In our model, e j,g,h represents the efficiency units supplied to the labor market by a group of agents of age j, gender g, and employment type h. In order to establish labor productivity by the four types, i.e., combinations of male or female, and full-timer or part-timer, we calculate hourly wages for each type of worker. This result is shown in Figure 5 Panel (b). For data on wages and working hours, we use the Basic Survey on Wage Structure Statistics (2019) by the Ministry of Health, Labor and Welfare. From this data, hourly wages are calculated for males and females, and for fulltime and part-timers, and then labor productivity was calculated based on the method presented by Hansen (1993) and used by Yamada (2011 ), Braun et al. (2006 , and others. Figure 7 Panel (b) shows the age distribution of labor income calculated at the initial steady state based on this labor productivity. Kitao and Mikoshiba (2020) used not only the Basic Survey on Wage Structure

Affairs and Communications to determine the productivity of the self-employed, whereas, in our (2018) . The values of the labor supply parameters are derived from the estimation of the labor supply elasticity of Kuroda and Yamamoto (2008) .

paper, the four types of productivity described above are determined based solely on data from the BSWS. In our analysis, since the baseline retirement age is set uniformly at 65, labor productivity is set so that it would reach zero at age 65. For both male and female full-timers, hourly wages, and labor productivity decline sharply after reaching age 60, but this is thought to reflect the decline in wages due to reemployment after the retirement age 60, that is actually adopted by most of companies.

The distribution of assets for each agent at the initial steady state is shown in Figure 7 Panel (c). This distribution depicts that male full-timers accumulate fewer assets at a younger age than female full-timers and that they begin to increase rapidly after age 40. After age 50, the assets of male full-timers are higher than those of female full-timers. The reason for this lies in the shape of the labor productivity curve shown in Figure 5 (b) and the labor income shown in Figure 7 Panel (b). That is, productivity and income of male full-timers increase significantly by the peak in their early age 50 compared to female full-timers. Male full-timers behave knowingly about this, and thus are able to allocate a larger share of their income to consumption in their younger years.

Public Pension System The government operates a PAYG pension system. In the baseline simulation, the normal retirement age J R , equivalent to age 65, is set at 46. As shown in Figure 7 Panel ( Labor and Welfare, and are calculated using the method presented in Iwamoto and Fukui (2018) .

In our quantitative analysis, we set the upper limit of the government debt-to-GDP ratio at 1.5

in the steady state. In addition, we assume that the fiscal balance is adjusted by changes in the consumption tax during the transition process.

Progressive taxation Progressive taxation is set according to the income bracket of the household. use income and promotion tax tables estimated by IMF staff using National Tax Agency data. In our study, we also use the tax rates per income bracket estimated here. The details are shown in Table 4 . Here, we assume the progressive labor tax of our model includes mainly national tax, local tax such as inhabitant tax, and public pension, public medical insurance, and LTC insurance premiums.

The capital tax rates are shown in Table 3 . The effective corporate income tax rate τ π 1 is set at 25% to bring the modeled values in line with the taxes paid by corporations in the JSNA on corporate income tax and other corporate taxes. In addition, investors in corporations where distributions are paid in the form of dividends will pay an additional tax on distributions. These tax (2018), the second column "Share" are obtained from the distribution of labor income based on the Tax Surveys published by National Tax Agency. And the third column "Tax rate" are also the estimates of effective income tax rates across 14 income bracket by . The fourth and fifth columns "α" and "β", which are calculated from tax rate, are referred to as intercept and slope of the progressive tax structure, respectively. Table 3 also contains the fiscal policy parameters. ψ B is defined as the total debt of the general government minus the financial assets held by public pension funds. These assets are accumulated for future pension obligations. However, in our model, future pension liabilities are also incorporated. The level of government consumption ψ G is set to a constant percentage of adjusted GDP over the entire period.

In this section, we describe the quantitative results of a policy simulation for the transition process.

Our analysis is based on two scenarios: baseline and extension of the retirement age. For these two scenarios, we conduct policy simulations for three options of social security reforms described below. Then, we calculate the impact on the current working, the retired, and future generations for the four types of households distinguished by gender and employment type, and evaluate the extent to which differences in the impact are generated for the four types.

We proceed the following three aspects. First, we outline the economic circumstances underlying the two scenarios and the three options of social security reforms. Second, we show how the transition paths of key aggregate economic variables would change if one of the three reforms is implemented in the two scenarios. In particular, we focus on changes in real GDP and the level of the consumption tax rate. Third, we compare the impacts of the different reforms on the welfare for the current working, retired and future generations. We then discuss the effects of the reforms, focusing on heterogeneity of households in terms of inter-generations and intra-generations.

Here, we describe the two scenarios and three social security reforms in our analysis. As mentioned in section 4, we assume that (i) the TFP growth rate γ A is 0.3%, the retirement age J R is age 65, and the long-run population growth rate γ n is −1 in the baseline scenario. In the extended retirement age scenario, (ii) the only change from the baseline is that the retirement age J R increases from 65 to 70 in 2030.

Under these two scenarios, we conduct policy simulations the cases of the three reforms as well as the case in that reforms are not implemented. That is, (1) preservation of the current policy,

(2) gradual decrease of the pension income replacement rate κ t , (3) increase in the copayment rate λ H j,t for medical expenditures, and (4) increase in the copayment rate λ L j,t for LTC expenditures. In policy (1), we suppose that the pension income replacement rate κ t is constant at 62%, the copayment rate for medical expenditures λ H j,t is 30% for those aged 20 to 70, 20% for those aged 70 to 75, 10% for those aged 75 and over, and 10% for LTC expenditures λ L j,t . Policy (2) is a reform to reduce the pension income replacement rate from 62% as of 2015 to 50.8% in 2047. 16 Policy (3) is a reform to raise the copayment rate for health care expenditures for the elderly in 2030 to a uniform 30% for all ages. Policy (4) is a reform that would set the copayment rate for LTC expenditures at 30% in 2030.

Here, we show the simulation results for the transition path of real GDP, its growth rates, and the consumption tax rates, under the demographic projection in which population growth rates are adopted that of IPSS (2017) 

The first of all, we focus on the transition path of the output. Figure 8 Panel ( that the level of GDP transition into the future is highest when the retirement age is extended and the reduction of pension income replacement rate is introduced. Figure 9 shows the growth rates of output at the baseline scenario, and the contribution decomposition of factors including intangible assets. Based on the production function described in section 3, the growth rate of output is decomposed into TFP A t , tangible assets K iT in sector i, TFP  KT1  KT2  KI1  KI2  L1  L2 pop GDP growth rate intangible assets tangible assets K iI , labor force L i in sector i, and population growth.

The total of the TFP growth rate and the labor-intensive technology growth rate (light green bars) is stable with about 1% for the contribution, based on our setting. In contrast, the growth rate of the population (dark gray bars) is shown as −1% for the contribution. And these two contributions are approximately offset to zero percent growth. On the other hand, a major factor depressing the growth rate of output through 2050 is the growth rate of tangible assets in Sector 1 (light gray bars) and tangible assets in Sector 2 (yellow bars).

This is because both of a decrease in the labor force population and an increase in the retired population makes aggregate saving rate, or capital accumulation drop rapidly in this period. Our simulations show that the size of negative contribution of tangible and intangible assets to the output is much larger than that of the negative contribution the labor force shown the blue and brown bars.

Next, we turn to the consumption tax rates. These transition paths are shown in Figure 10 , where the consumption tax rates rises to around 42-43% at the peak in mid-2050 under both scenarios if the current policy is maintained. Previous studies such as Braun and Joines (2015) also show generally consistent trends, albeit with differences in population growth rates and policy simulation assumptions. 18

The impact of the reforms on the consumption tax rate can be summarized as follows three points. First, all reforms would also reduce the peak level and lower the tax rate over the long run compared to the current policy. Second, among the three reforms, the effect of reducing the pen- 18 Simulations of the consumption tax rates in Braun and Joines (2015) and others show results reach around 45% in the 2060s. We think this is caused not only by differences in assumptions about demographics, but also by the higher contribution of capital in our model, especially since it takes into account intangibles. 

By comparing with no reform case as a benchmark, we assess the impact on the welfare of three social security reforms for all generations distinguishing by the current working, the current retired, and the future generations, under the two scenarios. And we add the heterogeneity of the four types of households, categorized by gender and employment type to this consideration.

At first, let us deal with the reform by the reduction in the pension income replacement rate.

This reform results in a significant fall in the welfare of individuals around retirement age in the present in both scenarios (Figure11 Panel (a) and (b)). We consider the impact to be that individuals in this age group have already paid most of their pension contributions, while they begin to receive pension benefits when the benefit is reducing. In the baseline scenario, welfare declines in almost all ages of the current retired and working generations, albeit in the extended retirement scenario, each types of agents' welfare improves by about 2-5% for the working generation. This pension reform also brings a significant decline in benefits for full-timers than for part-timers for both the male and female groups. As discussed in section 4, we deduce that the reason for this is that fulltimers, who have relatively higher incomes, pay more in pension contributions, despite receiving reduced benefits.

Next, we move to the reform by raising copayment rate in the medical insurance. Figure 12 Panel (a) shows a similar trend to the pension reform in the baseline scenario. In particular, there is a significant decline in the welfare of the current retirees. The reform also shows a substantial decrease in welfare for both male and female part-timers. For instance, the welfare of female parttimers declines by at most 4%. In the extended retirement scenario, the welfare of the current working-age population improves, similar to the pension reform ( Figure 12 Panel (b)).

Finally we describe the reforms by increasing copayment rate of LTC insurance. In the baseline scenario, Figure 13 Panel (a) shows a decline in welfare for the current older age groups compared to the medical care case. This result is consistent with the LTC expenditures being higher per capita expenditures for those aged 90 and older compared to health care, as discussed in section These three results indicate that the welfare of future generations improves with all of three social security reforms under two scenarios. On the other hand, we find that all of the social security reforms in the baseline scenario reduce the welfare of the working-age population to a greater extent. In particular, the welfare decline is significant for those aged 60 and over at the current point, with heterogeneous effects for different types of agents among them. Again, we find that the welfare of full-timers with relatively high incomes falls markedly upon the pension reform, whereas the welfare decline of female and part-timer with relatively low incomes is more significant upon the medical and LTC insurance reforms.

We turn to discussion about implications due to our policy simulation as described above. There are the following three arguments.

First, demographic change impacts on savings and labor force. The decline in combination of tangible and intangible capital stocks attributed by reduction of savings are major factors in the decline in output up to around 2050, as well as the downward of labor force.

Second, the pension reform makes the highest consumption rate the most moderate. The medical insurance reform is the second position, and the LTC insurance reform is the third one. This pattern is observed under both scenarios. And the transitions of the consumption tax rates do not show significant differences among all of the three reforms.

Third, the welfare analyses show that all social security reforms raise the welfare of future generations consistently. However, all of social security reforms without retirement age extension larger decrease the welfare of the working-age population than no reform. In particular, the medical and LTC insurance reforms significantly bring the welfare losses of the agents with relatively low incomes. The pension reform lowers the welfare of full-time male workers the most severe of all types of households. In contrast, in the case of retirement age extensions, the pension reform improve the welfare of the working-age generation by 2% to 5% relative to no reform. Now, we consider the extent to which the differences are generated among impacts of the pension reform and the medical and LTC insurance reform on welfare. We suppose that during the working period, individuals pay pension contributions to the government based on their income level, and during the retirement period, they receive pension benefits based on the average of each agent's lifetime earnings multiplied by the pension income replacement rate. And, when higher lifetime income earners face a reduction in the pension income replacement rate, the decrease in pension benefits influence on him more significant, although the contributions they pay years remain at the same amount during their working. This is why full-time male workers with higherincome would face greater reductions in welfare from the reform than part-time male and female workers with relatively lower-income. Therefore, we confirm that the households with relatively low income and savings (part-time male and female workers) react to the medical and LTC insurance reform, which would have increased expected spending during retirement by consuming less during their working period to prepare for future expenses.

Our policy simulations also show that females consistently suffer more significant declines in welfare than males under all cases of reforms. These differences between gender come from our settings. Again, we set up heterogeneity according to their labor productivity (hourly wage), employment types, and gender-specific survival rates, based on Japan's data. Although the amount of pension benefits during retirement make difference, gap in survival probabilities between males and females also lead to differences in expected medical and LTC expenditures, particularly in the retirement period. As a result, we confirm that females with relatively lower-wage growth, also suffer a larger decline in welfare than the case of males, because of the reduction in consumption over the life-cycle due to the social security reforms. This is paralleled in the decline in welfare for part-time male workers than for full-time ones.

Thus, we conclude that the medical and LTC insurance reforms that increase expected spending in retirement lead to a significant welfare decline among socially vulnerable females and parttimer households through changes in their consumption and savings behaviors, and that although the social security reforms should be conducted to maintain fiscal sustainability in the face of an aging population and for future generations, such reforms might have significant negative impacts on the welfare of the current generations. Our policy simulations suggest that when implementing the social security reforms, we should pay sufficient attention to intra-generations such as low-income individuals (females, part-timers) who are relatively socially vulnerable.

This paper quantitatively examines the impact of the implementation of pension, medical, and LTC insurance reforms on household's welfare in Japan, where the population is aging remarkably, through policy simulations using an OLG model with four types of households distinguished by gender and employment type.

Our policy simulation shows that three options of social security reforms consistently raise the welfare of future generations, in contrast have a particularly negative impact on relatively low-income groups, say, females, part-timers, in the current working-age population. Females are also found to be consistently and significantly negatively affect in all social security reforms. In addition, we find that simultaneously extending the retirement age improves welfare by 2-5%, particularly by mitigating the negative impact on the current working-age population. Our policy simulations suggest that the negative impact of the implementation of social security reforms on social welfare could be reduced by paying enough attention to the impact on females and parttimers, who are relatively socially vulnerable groups.

However, our study has the following challenges . Firstly, since future medical and LTC expenditures depend on uncertain factors such as individual health status, there are many implications of focusing on future uncertainty, especially in the context of the retirement saving puzzle, for that field the literature has recently accumulated (e.g. De Nardi et al., 2010; Kopecky and Koreshkova, 2014) . In contrast , our model is set up as deterministic without uncertainty. Next, our model also discards the effects of risk-sharing of future spending through marriage and other factors. For example, Braun et al. (2017) quantitatively explores the risk of becoming single after retirement.

In order to analyze such effects more rigorously, it is necessary to use microdata on household consumption, income, medical and LTC expenditures, etc. Our analysis, however, is based on aggregate data. Overcoming for above aspects would provide more practical and useful policy implications for conducting social security reforms, while mitigating negative impacts as much as possible. We would like to make these challenges as our next research subject.

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