## wp18249

## Source details

**Canonical URL:** [wp18249](https://www.imf.org/-/media/files/publications/wp/2018/wp18249.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2018/wp18249.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2018/wp18249.pdf.json)

---

### 1. Introduction — Demographics, fiscal context, and policy options
- Demographic projections and dependency:
  - Japan’s population started declining around 2009 and is expected to fall by more than 25 percent, from 126 to 94 million, between 2017 and 2060.
  - Old age dependency ratio:
    - 44 percent in 2016 for Japan.
    - Projected to surpass 70 percent by 2060 for Japan.
    - Average for the next ten highest OECD countries forecasted to be 54 percent by 2060.
    - More than 10 percentage points higher than the average of the next 10 highest OECD countries (2016 comparison).
- Fiscal context:
  - Japan’s age-related government outlays are among the highest in the OECD.
  - Government debt-to-GDP ratio is the highest among OECD countries (at 2.4 times GDP).
  - Tax revenues are well-below the OECD average.
- Aging cost pressures:
  - Per adult spending on health and long-term care rises exponentially with age.
  - Recent estimates: health and long-term care costs could increase from roughly 9.5 percent of GDP in 2010 to a level in the range of 13 to 15.5 percent by 2030 (Nozaki and others, 2017).
- Policy options considered:
  - Increase consumption taxes.
  - Increase social security contributions to finance health care costs.
  - Increase copayment rates for health and long-term care.
  - Existing macro-indexing mechanism in pensions controls aggregate pension spending as percent of GDP but additional measures needed for universal health and long-term care funding.
- Preferred policy (baseline) and rationale:
  - Dynamic OLG model calibrated to Japan; consumption tax rates are the only variable adjusting to keep government debt stable at about 200 percent of GDP (current value of gross debt minus pension fund financial assets).
  - Consumption tax rate peaks at about 20 percent in this scenario.
  - Baseline stabilizes debt, has relatively benign macroeconomic and welfare effects, and yields substantial long-run gains relative to other financing options (GDP, private investment-to-GDP, welfare).

### 1. Introduction — Alternative scenarios and quantitative outcomes
- Social security contributions (SSC) increases scenario:
  - Implemented as gradual, even increases in effective tax rates on labor income over 20 years, peaking at an 8 percentage points increase and remaining indefinitely at that higher rate.
  - Consumption tax rates would still need to increase by roughly 8 percentage points to keep debt-to-GDP ratio stable.
  - Macro effects: labor income taxes are more distortive than consumption taxes; future generations face long-run GDP losses on the order of 7 percent relative to preferred policy.
  - Welfare: average welfare is 5 percent lower for future generations than under preferred policy.
- Further inaction (debt accumulation) scenario:
  - Consumption tax rates unchanged for about 15 years; thereafter debt grows at a constant pace until 2040.
  - Debt reaches 300 percent of GDP.
  - Private investment-to-GDP declines by up to 8 percent relative to preferred policy.
  - Consumption tax rates must increase to roughly 30 percent to stabilize debt-to-GDP.
  - Long-run GDP level is 20 percent lower than under preferred policy.
  - Distributional: retirees and older workers benefit at the expense of current workers and all future generations.
- Increasing copayment rates for the elderly:
  - Health copayment rate for people over 65 rises gradually over a 20-year period to same level as working-age population.
  - Required adjustment in consumption taxes reduced by more than 2 percentage points.
  - Policy is regressive: welfare losses for poor and middle-class workers can reach 6 percent of lifetime welfare.
- Sensitivity experiments:
  - More favorable fertility projections or efficiency improvements in health delivery reduce required consumption tax increases by roughly 3 percentage points relative to preferred policy.
  - Higher economy-wide productivity does not necessarily reduce fiscal burden substantially because pension transfers link to real wage developments and health transfers have grown faster than per capita GDP.

### 3.2 Portfolios and the return of assets — Asset structure, prices, and policy instruments
- Financial asset composition:
  - Individuals save in shares of a composite financial asset composed of fraction φ_t of government debt and fraction 1−φ_t of claims to flows from private firms’ capital.
  - Rate of return on composite asset is weighted average of returns on government debt and private capital.
  - Interest rate on government bonds exogenously given by sequence {i^d_t}; φ_t computed in equilibrium to satisfy market clearing given exogenous government debt and its interest rate.
- Relevant price sequences and policy instruments:
  - Equilibrium prices for households: {i^d_t, i^k_t} and wage rates {w_t}.
  - Policy specifies sequences:
    - Tax rates τ = {τ^c_t, τ^d1_t, τ^d2_t, τ^π1_t} where c denotes consumption, d distributions from businesses, and π profits; sector 2 businesses are not subject to corporate profit tax and must distribute all profits.
    - Effective labor income tax schedules {T^w_t(·)}.
    - Exogenous transfers {T^j,k,p_t, T^j,k,h_t} (pension and health/long-term care), time-, age-, and productivity-type dependent.
    - Government debt {B_t}.
    - Pure public good consumption {G_t} with G_t = φ^G_t GDP_t.

### 3.2 The households’ problem, technology, and government accounting
- Household optimization:
  - Value function for age j and productivity k: v_j(a,s,k) = max_{a′, c, ` ≥ 0} { u(c,`) + β σ^j_t v_{j+1}(a′, s′, k) } subject to budget and constraints.
  - Budget constraint (as in source):
    - c + τ^c_t (c − T^j,k,h_t − χ^j,k,h_t) + a′ σ^j_t = { φ_t (1 + i^d) + (1 − φ_t)(1 + i^k) } a + y_t − T^w_t(y_t) + T^j,k,p_t + T^j,k,h_t
    - y_t = w_t l̄_{j,k}
    - c ≥ T^j,k,h_t + χ^j,k,h_t
    - s′ = F(s)
  - Health spending counted as part of consumption c for welfare calculations; health expenditures not subject to consumption taxes in Japan represented by τ^c_t (c − T^j,k,h_t − χ^j,k,h_t).
  - Savings are shares of asset paying conditional payments in retirement depending on survival probabilities.
- Technology and production:
  - Two production sectors with composite final good Y_t = Y_{1t}^{θ_1} Y_{2t}^{θ_2}, θ_1 + θ_2 = 1.
  - Sectoral Cobb-Douglas functions with tangible and intangible capital K_{iT}, K_{iI} and labor-augmenting technology Ω_t growing at rate γ with Ω_{t+1} = (1 + γ) Ω_t.
  - Capital accumulation and resource balance equations:
    - K_{iT,t+1} = (1 − δ_{iT}) K_{iT,t} + X_{iTt}
    - K_{iI,t+1} = (1 − δ_{iI}) K_{iI,t} + X_{iIt}
    - Y_t = C_t + X_{Tt} + X_{It} + G_t
- Government budget and corporate accounting:
  - Accounting profits and distributions defined; law of motion for government debt:
    - B_{t+1} = B_t + i_t B_t + G_t − ∑_{j,k} n_{j,k,t} ( T^j_t(w_t `_{j,k,t} ε_k) − (T^j,k,p_t + T^j,k,h_t) ) − τ^c_t (C_t − T^h_t − χ^h_t) − τ^π_{1t} Π_{1t} − τ^d_{1t} D_{1t} − τ^d_{2t} D_{2t}
  - Next period’s debt equals this period’s debt plus interest plus public consumption minus net tax revenues (labor, consumption excluding health transfers/copayments, corporate profits, corporate distributions, other business distributions).
- Equilibrium conditions:
  - Markets for labor, capital, and goods clear each period.
  - Household policy functions {a′ = f_j(s,k)}_j imply aggregate law of motion s′ = F(s).

### 3.2 Model parameters and calibration (macro overview; exact values preserved)
- National accounts and fixed asset shares (2015 baseline consistency):
  - Labor income comprises 53 percent of total adjusted income; 70 percent of households’ mixed income is classified as labor income.
  - Consumption comprises 75 percent of total adjusted product: private consumption 63 percent and public consumption 12 percent.
  - Investment comprises 25 percent of adjusted total product.
  - Private fixed assets amount to 229 percent of adjusted GDP (private corporates 68 percent, households 32 percent).
  - Government fixed assets amount to 112 percent of adjusted GDP.
  - Private + public fixed assets = 340 percent of adjusted GDP.
  - Including land, total capital stock = 566 percent of adjusted GDP.
- Demographics and preferences:
  - Long term population growth rate set equal to -1 percent.
  - Survival probabilities match demographic transition under medium fertility (stable at around 1.4) and medium mortality from IPSS projections.
  - Logarithmic preferences u(c,`) = log c + α log(1 − `) with α = 0.5.
  - β = 0.983.
  - JSNA reported average hours worked per employee in 2015 = 1,751 hours per year; discretionary time per week assumed 100 hours; fraction of time at work = 33.7 percent.
- Technology calibration:
  - Long run growth rate of labor-augmenting technology γ = 1 percent.
  - Combined with population growth -1 percent implies long run GDP growth rate = 0 percent.
  - Aggregate production share parameter θ_1 = 64 percent.
  - Tangible capital shares: θ_{1T} = 0.45 and θ_{2T} = 0.15.
  - Tangible depreciation rates: δ_{1T} = 0.06 and δ_{2T} = 0.05.
  - Intangible capital parameters calibrated following Arato and Yamada (2012).
- Fiscal parameters and taxes:
  - φ_B defined as gross general government debt minus financial assets held by public pension funds; φ_G held constant as percent of adjusted GDP.
  - Effective corporate income tax rate τ^π_1 = 25 percent.
  - Tax on corporate distributions τ^d_1 = 25 percent.
  - Tax rate on household business distributions τ^d_2 set to match an average labor income tax rate of 29 percent.

### 4.2 Micro Data — Income distribution, taxes, pensions, health transfers, and baseline financing
- Income distribution and tax estimation:
  - Labor income disaggregated using Tax Surveys published by NTA; labor income grouped in 14 income brackets.
  - Effective income tax rates across brackets estimated combining national personal income tax, local income taxes (derived via taxable income, number benefiting from income deductions, and maximum deduction), and social security contributions (recorded in Tax Surveys).
  - Empirical finding: despite progressivity of income taxes, social security contributions are regressive, with flat rates for middle incomes.
- Productivity types and calibration targets:
  - Four productivity types: low, medium, high, and top 1 percent.
  - Population shares over 18: low 32 percent, medium 31 percent, high 36 percent, top 1 percent the remaining 1 percent bracket.
  - Resulting shares in total labor income from lowest to highest types: 8, 25, 61, 6 percent, respectively.
- Pension and health transfer calibration and transition:
  - Transition period: 30 years up to 2048; after transition, per capita pension and health transfers grow at 1 percent (per capita GDP growth).
  - Pensions: basic pension (same amount for all retirees over 65) and employees’ pension (linked to lifetime labor income); calibrated to match aggregate benefit in 2015.
  - Pension macro-indexing and transition rules follow authority Scenario G from 2014 Actuarial Valuation; pension transition equations preserve macro-indexing and impose lower bound for older cohorts (80 percent floor for ages 68+ relative to age-65 benefit).
  - Health transfers estimated from FY2015 MHLW per capita spending and effective copayment rates:
    - Health transfers for those aged 65+ are about 6.8 times higher than those aged 18-64.
    - Transfers for aged 85+ are 4.4 times higher relative to those aged 65-69.
    - Effective copayment averages: adults 20-64 pay 17.3 percent; adults 65+ pay 9.5 percent (15.3 percent for 65-69, 9.3 percent for 70-74, about 8.5 percent for older individuals).
    - Per capita health transfers evolve at 1 percent plus excess cost growth of 0.7 percent over 30 years.
- Baseline financing through consumption taxes:
  - Baseline fiscal strategy: stabilize debt-to-GDP at current level of 2 times GDP; adjust consumption taxes (VAT).
  - Consumption tax rate required rises from baseline 8 percent to about 20 percent.
  - Half of required adjustment (consumption tax reaching 14 percent) occurs by 2030.
  - Aging costs (pensions + health + long-term care) increase slowly from 18 percent of GDP and peak at about 24 percent of GDP by 2057.
  - Up to 2030, most increase driven by health spending; by 2057 pensions and health contribute about equally.
- Macroeconomic impacts under baseline:
  - GDP is only 5 percent higher in 2040 than today (if labor force remained constant and TFP growth 1 percent, GDP would be 30 percent higher by 2040).
  - Hours worked per person decline; marginal product of capital falls; lower interest rates; lower investment-to-GDP ratio.
  - Private consumption-to-GDP increases (even excluding health and long-term care consumption).
  - Labor income and business tax revenues (shares of GDP) essentially unchanged with demographic transition because workers increase labor supply in response to anticipated taxes.

### 4.2 Scenarios: SSC increases, debt financing delay, and copayment increases — key quantitative outcomes and distributional effects
- Increasing Social Security Contributions (SSC scenario):
  - Labor income tax rate gradually increased by 8 percentage points over 20 years to finance health-driven aging costs.
  - Consumption taxes still need to increase by up to 8 percentage points to keep debt-to-GDP stable.
  - After 25 years, GDP about 4 percent lower than preferred (baseline); difference reaches 7 percent in longer horizon.
  - Welfare: retirees and older workers gain; young workers and future generations lose. Average welfare losses about 5 percent of lifetime welfare. Top 1 percent lose about 8 percent; bottom 30 percent lose close to 4 percent.
- Debt financing (delaying adjustment):
  - Continuous deficit financing until debt stabilized after 2040; resulting debt-to-GDP = 3.
  - Assumption: real interest rate on government debt remains 1 percent.
  - Consumption tax rate peaks at about 29 percent.
  - After 10 years GDP is 4 percent lower than preferred policy; after 20 years more than 15 percent lower.
  - Welfare: losses exceed 16 percent of lifetime welfare on average; older individuals may benefit but overall growth losses dominate.
- Increasing health copayment rates for elderly:
  - Raise copayments for 65+ to average level of 20-64 gradually over 20 years.
  - Permanent reduction in net health and long-term transfers of about 8 percentage points for relevant groups.
  - Consumption taxes still increase, peaking at about 17 percent.
  - Distributional impact: policy is regressive; bottom third experiences welfare losses as large as 6 percent of lifetime utility; most (bottom 99 percent) aged 18-90 would experience welfare losses, disproportionately young and lower-income workers.
  - Policy implication: safeguards for low-income households important if copayment increases pursued.
- Evaluation of other reform options:
  - More favorable demographics, health sector efficiency, or productivity improvements alone cannot fully address aging costs.
  - Recommendation: these measures can complement gradual consumption tax increases to form a policy package that minimizes economic distortions.

### 6.1 Alternative demographic pattern with higher fertility rate — effects and timing
- Scenario: IPSS favorable demographic scenario with high fertility (gradual improvement by mid-2020s to range of 1.6-1.7 live births per woman) and medium mortality; baseline uses IPSS medium fertility and medium mortality.
- Long-run population growth:
  - Favorable scenario long run population growth = -0.85 percent (instead of -1 percent in baseline).
- Effects on consumption taxes and public finance:
  - Differences in required consumption tax rates not very noticeable before 2040.
  - By 2065 required consumption tax to keep debt-to-GDP constant is about 3 percentage points lower than in baseline.
- Effects on GDP:
  - By 2065 GDP is 8 percent higher under favorable demographic scenario than baseline.
  - Higher long-run GDP mainly due to slower population shrinkage given same long-run TFP growth.
- Timing and transmission:
  - Population dynamics similar up to 2030 under both scenarios; transmission to economic differences is slow.
  - Recovery of population growth among workforce occurs in mid 2030s under favorable scenario, producing more material differences by mid-century.

*Italic source attribution: IMF Working Paper — wp18249.*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Demographic challenges and fiscal context
- Japan’s population started declining around 2009 and is expected to fall by more than 25 percent, from 126 to 94 million, between 2017 and 2060.
- Old age dependency ratio (individuals aged 65 and over to individuals 15 to 64):
  - 44 percent in 2016 for Japan.
  - More than 10 percentage points higher than the average of the next 10 highest OECD countries.
  - Projected to surpass 70 percent by 2060 for Japan.
  - Average for the next ten highest OECD countries forecasted to be 54 percent by 2060.
- Japan’s age-related government outlays are among the highest in the OECD.
- Government debt-to-GDP ratio is the highest among OECD countries (at 2.4 times GDP).
- Tax revenues are well-below the OECD average.

### Nature and scale of aging-related cost pressures
- Per adult spending on health and long-term care rises exponentially with age, making these components particularly expensive given Japan’s demographics.
- Recent estimates: health and long-term care costs could increase from roughly 9.5 percent of GDP in 2010 to a level in the range of 13 to 15.5 percent by 2030 (Nozaki and others, 2017).

### Policy options under consideration
- Financing-side options discussed by Japanese policymakers and the IMF include:
  - Increasing consumption taxes.
  - Increasing social security contributions to finance health care costs.
  - Increasing copayment rates for health and long-term care.
- The government has implemented a macro-indexing mechanism in the pension system to control aggregate pension spending as a percent of GDP, but additional measures are required—especially to fund universal health and long-term care systems.

### Preferred policy scenario (baseline)
- Modeled using a dynamic general equilibrium overlapping generations (OLG) framework, parameterized to Japan’s macro and micro data.
- Baseline financing option: consumption tax rates are the only variable adjusting over time to keep government debt stable at about 200 percent of GDP (current value of gross debt minus pension fund financial assets).
- Consumption tax rate in this scenario peaks at about 20 percent.
- This preferred option allows debt to be stabilized, has relatively benign effects on macroeconomic activity and welfare, and yields substantial long-run gains relative to other financing options in terms of GDP, private investment to GDP, and welfare.

### Alternative scenarios and key quantitative outcomes
- Scenario: Increases in social security contributions to finance health and long-term care costs
  - Implemented as gradual, even increases in effective tax rates on labor income over 20 years, peaking at an 8 percentage points increase and remaining indefinitely at that higher rate.
  - Under this scenario, consumption tax rates would still need to increase by roughly 8 percentage points to keep the debt-to-GDP ratio stable.
  - Labor income taxes are more distortive than consumption taxes, causing significant GDP falls:
    - Future generations face long-run GDP losses on the order of 7 percent relative to the preferred policy.
    - Average welfare is 5 percent lower for future generations than under the preferred policy scenario.

- Scenario: Further inaction (debt accumulation)
  - Consumption tax rates remain unchanged for about 15 years; thereafter debt grows at a constant pace until 2040.
  - Debt reaches 300 percent of GDP.
  - Substantial crowding out of private investment:
    - Ratio of private investment to GDP declines by up to 8 percent relative to the preferred policy scenario.
  - Because long-run debt is higher, consumption tax rates must increase to roughly 30 percent to stabilize the debt-to-GDP ratio.
  - Long-run GDP level is 20 percent lower than under the preferred policy.
  - Debt- or higher-income-tax scenarios benefit retirees and older workers (who care mostly about current consumption) by delaying or lowering consumption tax increases, but at the expense of current workers and all future generations across the income spectrum.

- Scenario: Increasing health and long-term care copayment rates for the elderly
  - Health copayment rate for people over 65 rises gradually over a 20-year period to the same level as the working-age population.
  - Results in relatively small gains: required adjustment in consumption taxes is reduced by more than 2 percentage points.
  - Because health spending per adult is similar across the income spectrum, increasing copayments is regressive:
    - Welfare losses for poor and middle-class workers can reach 6 percent of lifetime welfare under this policy.

### Sensitivity experiments: demographics, health-sector efficiency, and productivity
- More favorable fertility projections or efficiency improvements in health delivery:
  - Require a smaller increase in consumption tax rates, by roughly 3 percentage points, compared with the preferred policy scenario.
- Higher economy-wide productivity:
  - Does not necessarily reduce the fiscal burden of aging costs substantially, because pension transfers are linked to real wage developments and health transfers have grown faster than per capita GDP.

### Modeling approach and calibration
- The analysis employs a dynamic general equilibrium overlapping generations model with within-cohort heterogeneity by productivity type, calibrated to match Japan’s macro and micro data (including national income and product accounts and income distribution).
- Transitions computed from an initial state calibrated to Japan in 2015 (referred to as the “current Japanese economy”) incorporate demographic forecasts from the National Institute of Population and Social Security Research (IPSS) so that the old age dependency ratio reaches around 75 percent by 2060.
- Two business sectors are modeled because different legal categories of businesses face very different tax systems and thus different market valuations of equity and debt relative to capital stock.

*Italic final source attribution: IMF Working Paper — wp18249, 1. Introduction.*

### 3.2    Portfolios and the return of assets

### 3.2    Portfolios and the return of assets

### Portfolios and asset returns
- Individuals save in shares of ownership of a composite financial asset composed of:
  - a fraction φ_t of government debt, and
  - a fraction 1−φ_t of claims to the flows from private firms’ capital.
- The rate of return on the financial asset is a weighted average of the returns on government debt and private capital.
- The interest rate on government bonds is exogenously determined and given by the sequence {i^d_t}.
- Total asset holdings in the composite asset must equal government debt and private sector claims for financial market equilibrium.
- Given the exogenous stock of government debt and its interest rate, φ_t is computed in equilibrium to guarantee the assumed fractions of assets in the portfolio.

### Prices and policy instruments
- Relevant equilibrium price sequences for households: government debt and private capital interest rates {i^d_t, i^k_t} and wage rates {w_t}.
- Policy specifies the following sequences:
  - (i) Tax rates τ = {τ^c_t, τ^d1_t, τ^d2_t, τ^π1_t}, where c denotes consumption, d distributions from businesses to their owners, and π profits. Sector 2 businesses are not subject to the corporate profit tax and must distribute all their profits to their owners.
  - (ii) Effective tax schedules on labor income {T^w_t(·)}.
  - (ii) Exogenously given transfers (pension transfers and health (plus long term) care transfers) {T^j,k,p_t, T^j,k,h_t} that are time, age, and productivity-type dependent.
  - (iv) Government debt {B_t}.
  - (v) Pure public good consumption {G_t}, defined as a fraction of GDP: G_t = φ^G_t GDP_t.

### The households’ problem
- Household value function for age j∈{1,2,...,J} and productivity k∈{1,2,...,K}:
  - v_j(a,s,k) = max_{a′, c, ` ≥ 0} { u(c,`) + β σ^j_t v_{j+1}(a′, s′, k) } subject to the budget and constraints below.
- Budget constraint and definitions (as in source):
  - c + τ^c_t (c − T^j,k,h_t − χ^j,k,h_t) + a′ σ^j_t = { φ_t (1 + i^d) + (1 − φ_t)(1 + i^k) } a + y_t − T^w_t(y_t) + T^j,k,p_t + T^j,k,h_t
  - y_t = w_t l̄_{j,k}
  - c ≥ T^j,k,h_t + χ^j,k,h_t
  - s′ = F(s)
- ` denotes labor services; productivity profile is ε_{j,k} (denoted in source text as _{j,k}).
- v_{J+1} = 0.
- Savings are in shares of an asset that pays conditional payments in retirement depending on survival probability; the return on savings depends on asset return and survival probability.
- Households face labor income tax T^w_t(·) and receive pension and health transfers T^j,k,p_t and T^j,k,h_t.
- Health spending is counted as part of consumption c for welfare calculations. In Japan, health expenditures are not subject to consumption taxes, represented by τ^c_t (c − T^j,k,h_t − χ^j,k,h_t) on the left-hand side of the budget constraint.
- Consumption is constrained to be at least equal to health and long term care transfers including individual copayments χ^j,k,h_t.
- Pension and health/long-term care transfers are modeled as lump-sum transfers dependent only on time, household type, and age (an approximation consistent with data).
- Aggregate labor supply: L = ∑_{j,k} n_{j,k} `_{j,k} ε_{j,k}.
- The equilibrium law of motion of the aggregate state variable F is taken as given by private agents.

### Technology
- Two production sectors: sector 1 (subject to corporate income tax producing Y_{1t}) and sector 2 (producing Y_{2t}).
- Aggregate composite final good:
  - Y_t = Y_{1t}^{θ_1} Y_{2t}^{θ_2}, where θ_1, θ_2 > 0 and θ_1 + θ_2 = 1.
- Sectoral production functions (Cobb-Douglas) for i = 1,2:
  - Y_{it} = K^{θ_{iT}}_{iTt} K^{θ_{iI}}_{iIt} (Ω_t L_{it})^{1−θ_{iT}−θ_{iI}}
- Labor-augmenting technical level Ω_t grows at rate γ:
  - Ω_{t+1} = (1 + γ) Ω_t
- Capital accumulation for tangible and intangible capital for i = 1,2:
  - K_{iT,t+1} = (1 − δ_{iT}) K_{iT,t} + X_{iTt}
  - K_{iI,t+1} = (1 − δ_{iI}) K_{iI,t} + X_{iIt}
- Resource balance:
  - Y_t = C_t + X_{Tt} + X_{It} + G_t, where X_{Tt} = ∑_i X_{iTt} and X_{It} = ∑_i X_{iIt}.

### Government budget constraints and corporate accounting
- Relative prices of intermediate goods: p_{1t} and p_{2t}.
- Accounting profits:
  - Π_{1t} = p_{1t} Y_{1t} − w_t L_{1t} − X_{1It} − δ_{1T} K_{1Tt}
- Distributions to owners:
  - D_{1t} = (1 − τ^π_{1t}) Π_{1t} − K_{1T,t+1} + K_{1Tt}
  - D_{2t} = Π_{2t} = p_{2t} Y_{2t} − w_t L_{2t} − X_{2It} − δ_{2T} K_{2Tt}
- Law of motion for government debt:
  - B_{t+1} = B_t + i_t B_t + G_t − ∑_{j,k} n_{j,k,t} ( T^j_t(w_t `_{j,k,t} ε_k) − (T^j,k,p_t + T^j,k,h_t) ) − τ^c_t (C_t − T^h_t − χ^h_t) − τ^π_{1t} Π_{1t} − τ^d_{1t} D_{1t} − τ^d_{2t} D_{2t}
- Interpretation: next period’s debt equals this period’s debt plus interest plus public consumption minus net tax revenues (taxes on labor income, consumption excluding health transfers/copayments, corporate profits, corporate distributions, and other business distributions).

### Equilibrium conditions
- (i) Labor, capital, and goods markets clear at each point in time.
- (ii) Household policy functions {a′ = f_j(s,k)}_j imply the aggregate law of motions s′ = F(s).

### Model parameters and calibration (macro data overview)
- Calibration matches key features of Japan’s National Accounts (JSNA) and micro distribution from Tax Surveys in two steps:
  - Step 1: set parameters for demographics, preferences, firm technologies, government spending and debt shares, and capital income tax rates to match aggregate national accounts and fixed asset tables.
  - Step 2: set population weights, productivity levels, transfers, and labor income taxes to match micro data on population shares, labor income, transfer income, and tax rates.
- National account and fixed asset classifications and key shares (2015 baseline consistency):
  - Labor income comprises 53 percent of total adjusted income; 70 percent of households’ mixed income is classified as labor income.
  - Consumption comprises 75 percent of total adjusted product: private consumption 63 percent and public consumption 12 percent.
  - Investment comprises 25 percent of adjusted total product.
  - Private fixed assets amount to 229 percent of adjusted GDP (private corporates 68 percent, households 32 percent).
  - Government fixed assets amount to 112 percent of adjusted GDP.
  - Private + public fixed assets = 340 percent of adjusted GDP.
  - Including land, total capital stock = 566 percent of adjusted GDP.
- Demographics and preference calibration:
  - Long term population growth rate set equal to -1 percent.
  - Survival probabilities match demographic transition under medium fertility (stable at around 1.4) and medium mortality from IPSS projections.
  - Logarithmic preferences u(c,`) = log c + α log(1 − `) with α = 0.5 to match predicted hours of work.
  - β = 0.983 so model’s labor-capital income division matches Japan (Table 1).
  - JSNA reported average hours worked per employee in 2015 = 1,751 hours per year; with discretionary time per week assumed 100 hours, fraction of time at work = 33.7 percent.
- Technology calibration:
  - Long run growth rate of labor-augmenting technology γ = 1 percent.
  - Combined with population growth -1 percent implies long run GDP growth rate = 0 percent.
  - Aggregate production share parameter θ_1 = 64 percent (private corporates’ relative share).
  - Tangible capital shares: θ_{1T} = 0.45 and θ_{2T} = 0.15.
  - Tangible depreciation rates: δ_{1T} = 0.06 and δ_{2T} = 0.05.
  - Intangible capital parameters θ_{1I}, θ_{2I}, δ_{1I}, δ_{2I} calibrated following Arato and Yamada (2012) due to identification limits.
- Fiscal parameters and taxes:
  - φ_B defined as gross general government debt minus financial assets held by public pension funds; government consumption φ_G held constant as percent of adjusted GDP for all periods.
  - Effective corporate income tax rate τ^π_1 = 25 percent.
  - Tax on corporate distributions τ^d_1 = 25 percent.
  - Tax rate on household business distributions τ^d_2 set to match an average labor income tax rate of 29 percent.
- Simulation note: Using parameters in Table 3, the model’s national account and fixed asset statistics in 2015 closely match the JSNA Tables 1 and 2 for Japan.

*Source: IMF Working Paper — wp18249 (section 3.2–4.1.1).*

### 4.2    Micro Data

### 4.2    Micro Data

### Income Distribution and Tax Rates
- Labor income disaggregated using Tax Surveys published by NTA.
- Tax Surveys preferred over NSFIE because:
  - aggregate labor income is very close to JSNA;
  - straightforward estimation of labor income tax rates by income cohorts.
- Labor income grouped in 14 income brackets.
- Labor income taxes (including social security contributions) in each bracket estimated by:
  - (i) National personal income tax obtained directly from the Tax Surveys.
  - (ii) Local income taxes estimated by deriving taxable income from aggregate income in each cohort, number of workers benefiting from income deductions (proxied from national tax data), and the maximum amount of income deduction for local taxes; then multiplying taxable income by statutory tax rate.
  - (iii) Social security contributions estimated from the Tax Surveys since they record social security contributions in each income bracket for calculating income deductions.
- Empirical finding: despite progressivity of income taxes, social security contributions are regressive, with flat rates for middle incomes.
- The last column of Table 4 provides effective income tax rates across income brackets (used to set initial tax schedule).

### Parameters Based on Income Distribution and Tax Data
- Model assumes four productivity types: low, medium, high, and top 1 percent.
- Calibration targets:
  - low type: matches share of lifetime labor income for brackets under ¥2 million; comprises 32 percent of population over 18.
  - medium: matches ¥2 million to ¥4 million; population share 31 percent.
  - high: matches ¥4 million to ¥15 million; population share 36 percent.
  - top 1 percent: matches over ¥15 million.
- Resulting shares in total labor income from lowest to highest types: 8, 25, 61, 6 percent, respectively.
- Age-earnings profiles:
  - regular workers: productivity paths correspond to quadratic interpolations of Basic Survey on Wage Structure.
  - non-regular workers: assume flat profiles (earnings paths do not grow much with age).
- Initial tax schedule parameterization:
  - assume T_j0(·) depends only on labor income, T_j0(y) = T_w(y), where T_w(y) = β_i y on each income interval [y_i, ̄y_i], i = 1,...,14.
  - uniform tax rates assumed on distributions from corporations and household business.

### Pension Benefits, and Health and Long-term Care
- Transition period: 30 years up to 2048; pension and health transfers treated separately.
- After transition, per capita pension and health transfers assumed to grow at 1 percent (per capita GDP growth).
- Pensions in model: basic pension and employees’ pension.
  - Per capita basic pension at initial period: same amount for all retirees over 65, regardless of productivity.
  - Per capita employees’ pension linked to lifetime labor income.
  - Per capita transfers calibrated to match aggregate benefit in 2015.
- Pension indexing and “macroeconomic slide”:
  - real wage growth proxied by labor-augmenting technology growth of 1 percent.
  - follow authority Scenario G from 2014 Actuarial Valuation for macro-indexing adjustments.
- Pension transition equations:
  - For j = 65,...,67:
    T_{j,k,p,t+1} = T_{j−1,b,t}(1 + γ)M_{b,t} + T_{j−1,k,e,t}(1 + γ)M_{e,t}
    where T_{j,b,t} and T_{j,e,t} are basic and employees’ pension benefits, and M_t is macro-indexing adjustment factor.
  - For j = 68,...:
    T_{j,k,p,t+1} = max(T_{j−1,b,t}M_{b,t}, 0.8 T_{65,b,t+1}) + max(T_{j−1,k,e,t}M_{e,t}, 0.8 T_{65,k,e,t+1})
    (Pension benefits for those aged 68 or above are no longer adjusted with real wage growth; lower bound set to 80 percent of benefit for those aged 65.)
- Health transfers:
  - Estimated from per capita spending for health and long-term care and effective copayment rates in FY2015 published by MHLW.
  - Health transfers for those aged 65 or above are about 6.8 times higher as those aged 18-64.
  - Transfers for aged 85 or above are 4.4 times high relative to those for aged 65-69.
  - Effective copayment averages: adults 20-64 pay 17.3 percent; adults 65+ pay 9.5 percent (15.3 percent for 65-69, 9.3 percent for 70-74, about 8.5 percent for older individuals).
  - Per capita health transfers assumed to evolve at rate of 1 percent (per-capita GDP growth) plus excess cost growth of 0.7 percent over 30 years.
  - Note: excess cost growth rate of 0.7 percent aligns with ex-post excess cost growth over past 5 years; may overestimate future excess cost growth.

### Baseline: Financing the Costs of Aging through Consumption Taxes
- Baseline fiscal strategy: stabilize debt-to-GDP ratio at current level of 2 times GDP; adjust consumption taxes (VAT) to satisfy government constraint.
- Consumption tax rate required rises from baseline 8 percent to about 20 percent.
- Half of required adjustment (consumption tax reaching 14 percent) occurs by 2030.
- Aging costs (pensions + health + long-term care):
  - increase slowly from 18 percent of GDP and peak at about 24 percent of GDP by 2057.
  - up to 2030, most increase driven by health spending due to macroeconomic slide dampening pension growth; by 2057 pensions and health contribute about equally.
- Macroeconomic impacts:
  - GDP is only 5 percent higher in 2040 than today (if labor force remained constant and TFP growth 1 percent, GDP would be 30 percent higher by 2040).
  - Hours worked per person decline; marginal product of capital falls; lower interest rates; lower investment-to-GDP ratio.
  - Private consumption-to-GDP increases (even excluding health and long-term care consumption).
- Labor income and business tax revenues (shares of GDP) essentially unchanged with demographic transition because workers increase labor supply in response to anticipated taxes.

### Increasing Social Security Contributions (SSC scenario)
- Scenario: labor income tax rate (personal contributions) gradually increased by 8 percentage points over 20 years to finance expected health-driven aging costs.
- Key results:
  - Consumption taxes still need to increase gradually by up to 8 percentage points to keep debt-to-GDP stable (roughly half the increase needed under baseline).
  - Effective labor income tax rate rises; progressive labor income taxes are more distortive macroeconomically than consumption taxes.
  - After 25 years, GDP is about 4 percent lower than under preferred (baseline) policy; difference reaches 7 percent in longer horizon.
  - Short-run GDP differences small because young workers increase labor supply and save more anticipating higher future income taxes.
- Welfare impacts:
  - Retirees and older workers gain (they value consumption); consumption taxes remain lower than in preferred policy.
  - Young workers and future generations lose: average welfare losses about 5 percent of lifetime welfare.
  - Top 1 percent of earners lose about 8 percent of lifetime welfare on average.
  - Bottom 30 percent lose close to 4 percent.

### Debt Financing (delaying adjustment)
- Scenario: continuous deficit financing until debt stabilized after 2040; resulting debt-to-GDP ratio is 3.
- Assumption: real interest rate on government debt remains 1 percent.
- Consequences:
  - Consumption tax rate peaks at about 29 percent.
  - Large crowding out of private investment: households must hold larger stock of government debt, raising cost of capital for private sector.
  - Macroeconomic costs sizeable and rapid: after 10 years GDP is 4 percent lower than preferred policy; after 20 years more than 15 percent lower.
- Welfare impacts:
  - Delaying adjustment is very costly; most individuals lose.
  - Losses exceed 16 percent of life-time welfare on average.
  - Older individuals might benefit from lower consumption taxes, but overall lower aggregate growth outweighs benefits.

### Increasing Health Copayment Rates
- Baseline copayment averages: adults 20-64 pay 17.3 percent; adults 65+ pay 9.5 percent.
- Scenario: raise copayments for 65+ to average level of 20-64 (gradually over 20 years at a constant rate).
- Fiscal effect: permanent reduction in net health and long-term transfers of about 8 percentage points for relevant groups.
- Macroeconomic/fiscal outcomes:
  - Debt-to-GDP ratio held constant; consumption taxes adjust to satisfy government budget constraint.
  - Consumption taxes still increase, peaking at about 17 percent.
  - Policy yields only modest fiscal gains relative to needed adjustment.
- Distributional/welfare effects:
  - Policy is regressive because net health transfers do not vary much by income conditional on age.
  - Bottom third of population experiences large welfare losses, as large as 6 percent of lifetime utility.
  - Most (bottom 99 percent) of population currently aged 18-90 would experience welfare losses, disproportionately affecting young and lower-income workers.
- Policy implication: safeguards for low-income households are important if copayment increases pursued.

### Evaluation of Other Reform Options
- Considered sensitivities: more favorable demographic trends, improvements in health sector efficiency, improvements in economy-wide productivity.
- Finding: none of these options alone can fully address Japan’s aging costs.
- Recommendation: these measures can complement the preferred policy of gradually increasing consumption taxes; a policy package should minimize economic distortions and include broader reforms.

*Source: wp18249 - 4.2    Micro Data*

### 6.1    Alternative Demographic Pattern with Higher Fertility Rate

### 6.1    Alternative Demographic Pattern with Higher Fertility Rate

### Overview
- Scenario studied: IPSS "favorable demographic scenario" with a high fertility rate (gradual improvement by the mid-2020s to the range of 1.6-1.7 live births per woman in her lifetime) and medium mortality.
- Baseline uses IPSS medium fertility and medium mortality.
- The favorable scenario is labeled “demographics” in the figures.
- The 2014 Actuarial Valuation provides estimates for implied changes in pension transfers; these estimates are introduced into the simulations.
- Baseline and favorable scenarios imply very similar population dynamics in the medium term (up to 2030).

### Long-run population growth and pension transfer mechanism
- Long run population growth under the favorable scenario: -0.85 percent (instead of -1 percent in the baseline).
- Because of the macro-indexing mechanism in Japan’s pension system, different demographics imply different future flows of pension transfers.
- The macro-indexing adjustment reflects projected decreases in the number insured and increases in life expectancy; the 2014 Actuarial Valuation scenarios inform the simulations.

### Effects on consumption taxes (VAT) and public finance
- Differences in required consumption tax rates under the alternative demographic scenario are not very noticeable before 2040.
- By 2065 the required consumption tax (to keep debt-to-GDP ratio constant) is about 3 percentage points lower than in the baseline.
- Figure references in source: Figure 17 summarizes VAT/consumption tax adjustments.

### Effects on GDP
- By 2065 GDP is 8 percent higher under the favorable demographic scenario than in the baseline.
- The higher long-run GDP under the favorable scenario is mostly due to slower population shrinkage while assuming the same long-run growth rate of TFP across scenarios.
- Explanation: long-run GDP growth is the product of the change of TFP growth and population growth; a less negative population growth yields larger GDP.

### Timing and transmission
- Demographic trends are essentially the same until 2030 under both scenarios; population changes permeate slowly through the economic system, so near-term differences in policy requirements are small.
- The recovery of the growth rate of the population entering the workforce occurs in the mid 2030s under the favorable scenario, producing more material differences by mid-century.

*Source: IMF staff simulations and analysis in "6.1    Alternative Demographic Pattern with Higher Fertility Rate."*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18249.pdf_