## _wp0609

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---

### Introduction and context
- Major demographic transition characterized by:
  - slowing population growth;
  - changing age structure with the share of the young falling and that of the elderly rising.
- Timing and intensity vary by country and region:
  - Aging already well under way in most advanced countries.
  - East and southeast Asia and central and eastern Europe: significant aging from about 2020.
  - Many other developing countries: transition less advanced; working-age populations increase in coming decades.
- Analysis tools and calibration:
  - Four-country version of the MSG3 dynamic intertemporal general equilibrium model (DSGE extended with an OLG Blanchard approximation).
  - Demographic calibration to the “medium variant” of the United Nations population projections.
- Model innovations:
  - three-sector production technology;
  - rule-of-thumb behavior;
  - real and nominal rigidities;
  - different types of capital;
  - integrates features of real business cycle models and modern macroeconometric DSGE models.

### Key findings (four main results)
- Aggregate growth and regional divergence:
  - Population aging in industrial countries will reduce growth, beginning in Japan in the next decade and then the rest of other industrial countries by the middle of the century.
  - Developing countries will experience a “demographic dividend” as the relative size of their working-age populations increases, resulting in stronger growth over the next 20–30 years before aging sets in.
- Saving, investment, and capital flows:
  - Japan and, to a much lesser extent, the other industrial countries—the fastest aging countries—could see large declines in saving and a deterioration in their current account positions as the elderly run down their assets in retirement.
- Sensitivity:
  - Results are sensitive to assumptions about productivity growth and external risk premia.

### Modeling approach and scope
- Model overview:
  - Modified MSG3 (three-sector—energy, nonenergy, capital-producing—version of G‑Cubed).
  - World divided into four regions: Japan, the United States, other industrial countries, and the rest of the world (developing bloc).
  - Combines intertemporal optimization with short-run rule-of-thumb behavior and nominal/wage rigidities.
  - Core equations and calibration data available at www.gcubed.com (as stated in source).
- Demographic specification and counterfactual:
  - Baseline: UN mid-range demographic projection; simulations run 1985–2100; reported results 2005–2080.
  - Counterfactual (remove demographic transition from 1985) uses steady-state rates:
    - Child birthrate = 1.9 percent.
    - Adult maturity rate = 1.5 percent.
    - Constant probability of death of adults = 1 percent.
    - Constant probability of death of children = 0.46 percent.
  - Because model requires well-defined steady-state with identical demographics across countries, steady-state demographics are assumed identical across countries.
  - Results presented as difference between baseline (with demographic change) and alternative steady-state demographics; positive numbers indicate variables higher because of changing demographics.

### Simulation findings (2005–2080): aggregate and per-adult outcomes
- Aggregate GDP by 2050:
  - Japanese GDP is estimated to be 30 percent lower than would have been the case without the demographic transition.
  - Developing country GDP is estimated to be 60 percent higher as a result of the strong increase in the labor force due to the demographic transition.
- Growth rates:
  - Developing-country growth more than 2 percent higher by 2020 than without demographic change.
  - Japan’s growth falls after 2010 to reach a low point of 1.3 percent below the “no demographic change” scenario by 2040.
- Per-adult effects:
  - GDP per adult projected to be higher in Japan out to 2025 and still above what would have been experienced until 2050, underscoring importance of per-capita measures when labor forces fall.

### Investment, capital, and substitution effects
- Developing countries:
  - Increase in labor force raises marginal product of capital and stimulates higher investment.
  - Investment/GDP ratio 4 percent higher by 2025.
  - Real interest rates in developing countries 1.5 percent (150 basis points) above what they would have been because of demographic change; differential persists because of adjustment costs in physical capital accumulation.
  - Tobin’s q expected to rise especially in developing countries.
- Japan:
  - Initially increased investment as capital substitutes for a diminishing supply of workers; eventually investment falls as declining labor force needs less capital.
  - Capital/output ratio shows substitution of workers with capital.
  - Changing capital-labor ratios estimated to reduce real interest rates by up to 1.5 percent by 2050; long-term interest rates fall sooner due to expectations.
  - Equity markets fall below what they would have been by 2020 in Japan.

### Saving, consumption, and current accounts
- Japan:
  - Private saving-to-GDP ratio is 4 percentage points higher by 2005 due to the demographic transition, but by 2070 projected to be 11 percentage points lower.
  - Aggregate private consumption falls in Japan; per capita consumption rises initially and is only slightly lower by 2050.
  - Japanese current account in 2005 is 2.6 percent of GDP in surplus relative to the case of no demographic change; surplus narrows over time as saving falls.
- United States:
  - Saving-to-GDP ratio in 2005 is 3 percentage points lower due to demographic changes, but projected to be 5 percentage points higher by 2040 as more people move into high-saving years.
  - Aggregate private consumption rises to a lesser extent than in developing countries.
- Developing countries:
  - Private consumption rises as demographic transition increases labor force and income.
  - Developing country current account deteriorates initially as resources flow to developing countries (in scenario contexts described later).

### Real exchange rates, prices, and financial markets
- Real exchange rates by 2050:
  - Japanese real exchange rate appreciated by close to 60 percent.
  - Developing countries’ real exchange rate depreciated by close to 60 percent.
- Real interest rates:
  - Developing countries: real interest rates 1.5 percent (150 basis points) above counterfactual because of rising marginal product of capital.
  - Japan: real interest rates reduced by up to 1.5 percent by 2050 due to demographic-driven capital-labor changes.
- Financial asset prices:
  - Tobin’s q rises especially in developing countries; falls below counterfactual in Japan and other industrial countries as demographic transition matures.

### Selected numerical facts and parameter values emphasized
- Replacement level fertility: 2.1 births per woman in industrial countries and 2.4 births per woman in developing countries.
- Child dependency: children dependent for 17 years (period of childhood defined in appendix as "the first 16 years of an agent’s life" in other expressions).
- Simulation horizons and reporting windows:
  - World projection run from 1985 to 2100.
  - Results presented from 2005 to 2080 after initial asset adjustment.
- Key outcome magnitudes reiterated:
  - Global population growth: projected ¼ percent a year by 2050 vs. 1¼ percent at present.
  - Country population declines: over 30 percent in some central and eastern European countries; 22 percent in Italy; 14 percent in Japan (over the next 50 years).
  - Median world age: increase by over 10 years during 2000–50 to 37 years.
  - Japan GDP in 2050: 30 percent lower than without demographic transition.
  - Developing country GDP in 2050: 60 percent higher than without demographic transition.
  - Developing-country growth: more than 2 percent higher by 2020 due to demographic change.
  - Japan growth: 1.3 percent below counterfactual by 2040 (low point).
  - Investment/GDP ratio: 4 percent higher in developing countries by 2025.
  - Japan saving-to-GDP: 4 percentage points higher by 2005; 11 percentage points lower by 2070.
  - U.S. saving-to-GDP: 3 percentage points lower in 2005; 5 percentage points higher by 2040.
  - Japanese current account in 2005: 2.6 percent of GDP surplus relative to no demographic change.
  - Real exchange rates by 2050: Japan appreciated close to 60 percent; developing countries depreciated close to 60 percent.
  - Real interest rates: developing countries 1.5 percent (150 basis points) higher; Japan up to 1.5 percent lower by 2050.

### Alternative scenarios explored (post-2005 experiments)
A. Faster Global Growth through More Rapid Technological Convergence
- Scenario specification:
  - Productivity growth (labor-augmenting technical change) rises by "1 percent per year for 50 years from 2005 to 2054" in the developing country region.
  - Productivity growth rises by "0.1 percent per year over the same time in Japan and other industrial countries".
  - No change in underlying productivity growth from baseline in the United States.
- Key dynamics (percent deviation from baseline unless otherwise noted):
  - Real GDP:
    - Developing countries: growth begins immediately.
    - Rest of the world: GDP growth slightly lower initially as resources are channeled into developing countries; after a decade real GDP growth rises in the rest of the world.
  - Current account:
    - Developing country current account deteriorates initially as resources flow to developing countries.
  - Investment and savings:
    - Surge in growth initially reduces investment in all countries due to households raising consumption in anticipation of higher future income, reducing savings and raising real interest rates (crowding out private investment).
    - It takes "a decade" before investment rates rise above the baseline in developing countries.
    - Total savings/GDP and private consumption/GDP show anticipatory increases in consumption relative to baseline.
  - Capital and interest rates:
    - Capital-output ratios fall initially in all countries.
    - Higher real interest rates persist "for five decades" while productivity growth is high, then fall below baseline when the growth surge concludes.
    - Overshooting of interest rates and a sharp investment reversal after 2050 as capital accumulation overshoots.
  - Persistence:
    - Considerable persistence due to backward-looking households and firms despite presence of rational consumers and firms.
- Comparison with pure demographic transition:
  - "Higher productivity growth of 0.1 per year in Japan and the other industrial countries offsets half of the fall in GDP caused by demographic change."
  - For developing countries, the higher growth rate "almost removes the expected future decline in growth rates caused by their aging after 2030."

B. Improving Capital Market Access for Developing Countries
- Scenario specification:
  - Reforms reduce the risk premium associated with investing in developing country assets by "1 percent lower forever."
- Key dynamics:
  - Capital flows:
    - Reduction in risk premium encourages more capital to flow into developing countries.
    - Capital reallocation reduces real interest rates globally and has a considerable positive impact on real GDP in developing countries.
  - Domestic saving and returns:
    - Domestic saving increases for several decades in developing countries as the rate of return on domestic capital improves.
  - Current accounts and external balances:
    - Developing country current account positions deteriorate.
    - Advanced country regions—the suppliers of capital—experience improvements in their external balances.
  - Production and capital-output ratios:
    - Production relocates from industrial economies to developing countries.
    - Capital/output ratio rises in developing countries and falls in industrial countries.
  - Distribution of gains:
    - Unlike the productivity-growth scenario, the fall in developing country risk leads to a reallocation of global production and higher global income, but "all of the gains are captured by consumers in developing countries."

### Policy implications and conclusions (Section VI)
- Aggregate implications:
  - In advanced countries, population aging will likely reduce per capita growth rates.
  - In developing countries, increases in the relative size of the working-age population could lead to stronger per capita growth if additional labor is effectively utilized.
- International capital flows and external balances:
  - Large changes in saving, investment, and current account balances could occur "over the next 80 years" as a result of demographic change.
  - The impact critically depends on the reaction of private saving; it remains unclear how households will adjust behavior.
- Uncertainty and research needs:
  - The magnitude of potential changes should be compared with other shocks (e.g., changes in productivity growth).
  - "Substantially more research is required" to better understand demographic effects on economic performance.

### Appendix / Analytical approach: adult and child population dynamics, consumption, labor supply, and transfers
- Adult population dynamics:
  - Maturity rate b(s): size of newly matured cohort at time s relative to existing adult population N(s).
  - Mortality rate p: probability of an adult dying before the next period (common across adults).
  - Adult population evolution equation: Ṅ(t) = (b(t) − p)N(t).
- Child population and maturity:
  - Period of childhood denoted ∆; in simulations the period of childhood is defined as "the first 16 years of an agent’s life."
  - Aggregate children M(t) computed by integrating surviving children born within the last ∆ years.
  - Relationship: the maturity rate at time t depends on the birthrate and adult population size ∆ years earlier, adjusted for survival.
- Adult consumption and wealth (selected expressions preserved as in source):
  - Optimal consumption path: "[], ),(),()(),(tshtswptsc++=θ" (reported in source as equation (13)).
  - Human wealth h(s,t) defined as present value of expected future labor income (explicit integral form provided in source).
  - Aggregate relationships:
    - Aggregate consumption C_N(t) = ∫_{s=-∞}^{t} N(s,t) c(s,t) ds
    - Aggregate financial wealth W(t) = ∫_{s=-∞}^{t} w(s,t) N(s,t) ds
    - Aggregate human wealth H(t) = ∫_{s=-∞}^{t} h(s,t) N(s,t) ds
  - Aggregate adult consumption function: "[])()())(()(tHtWtptC N ++=θ" (reported in source as equation (18)).
- Labor supply and age-earnings profiles:
  - Effective labor supply of an adult follows a hump-shaped age-earnings profile with e^{μt} term where μ is technological progress.
  - Japan parameter estimates used for Japan: α1 = 0.073, α2 = 0.096, α3 = 0.085 and a1 = a2 = 200.
- Intergenerational transfers and aggregate consumption:
  - Children receive intergenerational transfer c(t) every period and completely consume it.
  - Transfer growth assumption: t ectc μ 0 )(=  (c(t) grows at the rate of productivity growth, μ).
  - Adults share burden equally: )(),(tjtsj = .
  - Aggregate consumption expression preserved as in source: )()()]()()[()(tMtctHtAptC+++=θ (equation (32)).
- Income and human wealth dynamics (preserved expressions):
  - Individual adult income y(s,t): )()()(),()()](1[),(tjttxttrtsltwttsy−−+−=τ (equation (33)).
  - Time derivative of individual human wealth h(s,t): ])([),(tjttxttrtsltwttshptrtsh−−−−−+= τ & (equation (35)).
  - Aggregate human wealth evolution: H(t) = r(t)H(t) -Y(t) + h(t,t)n(t,t) (equation (36)).
- Selected equation references preserved by number: (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36).
- Additional notation and presentation:
  - Some expressions in the source appear with typographic artifacts; preserved verbatim where quoted above.

*Source: IMF Working Paper chapter "2.  Population Structure, 1950–2050" (excerpt) and accompanying sections from the supplied IMF PDF content.*

### 2.  Population Structure, 1950–2050.....................................................................................

### 2.  Population Structure, 1950–2050

### Introduction and context
- The world is undergoing a major demographic transition characterized by:
  - slowing population growth;
  - changing age structure with the share of the young falling and that of the elderly rising.
- Timing and intensity of the transition vary by country and region:
  - In most advanced countries, aging is already well under way.
  - A number of developing countries in east and southeast Asia and central and eastern Europe will experience significant aging from about 2020.
  - In other developing countries the transition is less advanced and working-age populations will increase in the coming decades.
- The paper examines economic implications for Japan, the United States, other industrial countries (largely in Europe), and developing regions using:
  - a four-country version of the MSG3 dynamic intertemporal general equilibrium model (DSGE extended with an OLG Blanchard approximation);
  - demographic calibration to the “medium variant” of the United Nations population projections.
- Model innovations:
  - three-sector production technology;
  - rule-of-thumb behavior;
  - real and nominal rigidities;
  - different types of capital;
  - integrates features of real business cycle models and modern macroeconometric DSGE models.

### Key findings (four main results)
- Population aging in industrial countries will reduce growth, beginning in Japan in the next decade and then the rest of other industrial countries by the middle of the century.
- Developing countries will experience a “demographic dividend” as the relative size of their working-age populations increases, resulting in stronger growth over the next 20–30 years before aging sets in.
- Demographic change will affect saving, investment, and capital flows:
  - Japan and, to a much lesser extent, the other industrial countries—the fastest aging countries—could see large declines in saving and a deterioration in their current account positions as the elderly run down their assets in retirement.
- Results are sensitive to assumptions about productivity growth and external risk premia.

### Literature, model role, and scope
- Reviews recent literature on macroeconomic implications of demographic change.
- Uses the MSG3 four-region model developed by McKibbin and Nguyen (2004) to quantify effects.
- Analysis horizon and organization:
  - Baseline results estimate the impact of demographic change from 2005 until 2080.
  - Sensitivity analysis examines assumptions about growth and risk assessment in developing countries.

*Source: IMF Working Paper chapter "2.  Population Structure, 1950–2050" (excerpt).*

### Conclusions and policy implications follow (Section VI). Details of the model and the

### Conclusions and policy implications follow (Section VI). Details of the model and the calibration/estimation are contained in the appendix.

### II. Some background on global demographic change
- Historical context and broad patterns
  - Before 1900: slow world population growth, broadly constant age structure, relatively few people beyond age 65.
  - First half of the twentieth century: rising life expectancy boosted population growth with initially little change in age structure.
  - Second half of the twentieth century: fertility rates declined dramatically—by almost one-half—causing population growth to slow, the share of the young to decline, and the share of the elderly to increase; the share of the working-age population changed little.
- Regional heterogeneity
  - Fertility rates have fallen almost universally but remain much higher in developing than in advanced countries; advanced countries generally have fertility below the replacement rate.
  - Within developing countries: fertility high in Africa and the Middle East; below replacement in east Asia and central and eastern Europe.
  - Life expectancy has risen globally over the past 50 years, with largest gains generally in developing countries; exceptions: declines of more than 25 percent in some African countries due to HIV/AIDS, and declines in CIS countries.
  - Net immigration contributed importantly to population growth in North America, much less so in Europe and Japan.
- United Nations (mid-range / “medium variant”) projections (to 2050) — implications highlighted
  - Global population growth will continue to slow:
    - By 2050, global population growth is projected to be only ¼ percent a year, compared with 1¼ percent at present.
    - Population declines are projected in a number of countries over the next 50 years: by over 30 percent in some central and eastern European countries, by 22 percent in Italy, and by 14 percent in Japan.
    - Developing-country population growth remains robust (especially Africa and the Middle East, and parts of Asia) reflecting higher fertility rates.
  - The world’s population will continue to age:
    - Median age of the world expected to increase by over 10 years during 2000–50 to 37 years.
    - Elderly dependency ratio (population aged 65+ as a share of the working-age 15–64 population) projected to rise dramatically in Japan and Europe, with lesser increases anticipated in the United States.
    - Aging already under way in central and eastern Europe and expected to accelerate from about 2015; aging begins to accelerate in Asia and Latin America around 2015—China experiences particularly rapid aging; elderly shares remain relatively small in Africa and the Middle East.
  - Working-age population share:
    - Will fall in advanced countries (decline already started in Japan and some European countries and projected to accelerate).
    - In the United States, high immigration and higher fertility result in a more modest projected decline until 2025, after which the share stabilizes.
    - In developing countries, working-age share projected to increase until 2015 and then stabilize as declining youth share offsets rising elderly share.
- Caveats
  - Demographic projections become more uncertain further into the future; trends toward an increasing share of the elderly and declining share of the young are robust across plausible scenarios.
  - Elderly dependency ratios approximate support needs and do not adjust for continued work after age 65, non-employment in 15–64 group, or child labor; alternative economic-dependency measures are difficult to calculate, particularly for developing countries.

### III. Modeling the economic impact of demographic change
- Model overview
  - Modified version of the MSG3 model (a three-sector—energy, nonenergy, capital-producing—version of the G‑Cubed model).
  - World divided into four regions: Japan, the United States, other industrial countries (largely Europe), and the rest of the world (essentially the developing bloc).
  - Combines intertemporal optimization (forward-looking producers and consumers) with short-run rule-of-thumb behavior and nominal/wage rigidities.
  - Core equations and calibration data available at www.gcubed.com (as stated in source).
- Main model features
  - Demographics:
    - Economic agents possess finite lifespans; income varies with age.
    - Follows Faruqee (2003a, 2003b) extension of Blanchard (1985) with aging considerations.
    - Children are dependent on working parents for 17 years; children become adult at a maturity rate m.
    - Each adult has age-specific productivity that rises over life and then gradually deteriorates towards zero as they age.
    - Death occurs with a fixed probability.
  - Explicit intertemporal optimization by consumers and firms.
  - Rule-of-thumb agents to capture inertial short-run dynamics due to myopia or borrowing constraints.
  - Cash-in-advance constraints: money required to purchase goods; holdings of financial assets including money explicitly modeled.
  - Nominal rigidities: short-run nominal wage rigidity (degree varies by country) allowing protracted unemployment depending on labor market institutions.
  - Two types of capital: sticky physical capital (within sectors and countries) vs. flexible financial capital (flows immediately where expected returns highest).
  - Estimation/calibration: key parameters (e.g., elasticities of substitution) estimated to reproduce historical dynamics.
- Fiscal sector and assumptions
  - Fiscal sector articulated without a public pension scheme; government expenditures held constant as a share of GDP; tax revenues fluctuate with labor and corporate incomes.
  - Lump-sum tax on households adjusts to finance additional interest costs of any changes in government debt that result.
  - Fiscal sustainability is imposed to focus on macroeconomic adjustments to demographic change.
- Modeling approach for simulations
  - Baseline projection: world economy simulated from 1985 to 2100 using UN mid-range demographic projection and productivity growth assumptions by sector and country.
  - Counterfactual: rerun model removing demographic transition starting in 1985 by setting birthrates of adults and children equal to long-run steady-state rates at 2200:
    - Child birthrate assumed 1.9 percent.
    - Adult maturity rate assumed 1.5 percent.
    - Constant probability of death of adults 1 percent and of children 0.46 percent.
  - Because model requires a well-defined steady-state with all countries growing at same rate, steady-state demographics are assumed identical across countries (centuries into the future).
  - To separate expectations revision from pure demographic effect, model allowed to run until 2005 so much of initial asset adjustment to 1985 information revision is completed; all reported results presented from 2005 to 2080.

### IV. How will demographic change affect the global economy? — simulation findings (2005–2080)
- Key simulation setup notes
  - Results expressed as difference between baseline (with demographic change) and alternative scenario with demographic variables at steady-state growth rates.
  - Positive numbers indicate variables higher because of changing demographics.
  - Results reflect both own-country demographic change and cross-border spillovers.
- Aggregate and per-adult outcomes
  - By 2050:
    - Japanese GDP is estimated to be 30 percent lower than would have been the case without the demographic transition.
    - Developing country GDP is estimated to be 60 percent higher as a result of the strong increase in the labor force due to the demographic transition.
  - Growth rates:
    - Growth in developing countries more than 2 percent higher by 2020 than without demographic change.
    - Japan’s growth falls after 2010 to reach a low point of 1.3 percent below the “no demographic change” scenario by 2040.
  - Per-adult (proxy for per-capita) dynamics differ from aggregate results:
    - GDP per adult projected to be higher in Japan out to 2025 and still above what would have been experienced until 2050, illustrating importance of focusing on per-capita measures when labor forces fall.
- Investment, capital, and substitution effects
  - Developing countries:
    - Increase in labor force raises marginal product of capital and stimulates higher investment.
    - Investment/GDP ratio 4 percent higher by 2025.
    - Real interest rates in developing countries 1.5 percent (150 basis points) above what they would have been because of demographic change; differential persists because of adjustment costs in physical capital accumulation.
    - Tobin’s q (equity markets) expected to rise especially in developing countries.
  - Japan:
    - Initially increased investment as capital substitutes for a diminishing supply of workers; eventually investment falls as declining labor force needs less capital.
    - Capital/output ratio shows substitution of workers with capital.
    - Changing capital-labor ratios estimated to reduce real interest rates by up to 1.5 percent by 2050; long-term interest rates fall sooner due to expectations.
    - Equity markets fall below what they would have been by 2020 in Japan.
- Saving and consumption
  - Japan:
    - Private saving boosted in recent years as working-age cohorts move through high-saving years.
    - Saving-to-GDP ratio is 4 percentage points higher by 2005 due to the demographic transition, but by 2070 projected to be 11 percentage points lower.
    - Aggregate private consumption falls in Japan; per capita consumption rises initially and is only slightly lower by 2050.
  - United States:
    - Saving-to-GDP ratio in 2005 is 3 percentage points lower due to demographic changes, but projected to be 5 percentage points higher by 2040 as more people move into high-saving years.
    - Aggregate private consumption rises to a lesser extent than in developing countries.
  - Developing countries:
    - Private consumption rises as demographic transition increases labor force and income.
- Current accounts and global capital flows
  - Japanese current account:
    - In 2005, Japanese current account is 2.6 percent of GDP in surplus relative to the case of no demographic change.
    - Over time, as saving falls in Japan and investment rises then falls, the current account surplus narrows.
  - United States and developing countries see an improving current account position; other industrial countries’ position deteriorates modestly.
  - Reallocation of global capital: aging economies repatriate capital to maintain consumption in face of falling labor incomes.
- Real exchange rates and prices
  - Key mechanism: all goods enter consumption bundles by country of origin—shrinkage in supply of a country’s goods tends to raise relative price of those goods.
  - By 2050:
    - Japanese real exchange rate appreciated by close to 60 percent.
    - Developing countries’ real exchange rate depreciated by close to 60 percent.
  - Income repatriation to aging economies reinforces appreciation of aging economies’ real exchange rates.
- Financial market implications
  - Real interest rates:
    - Developing countries: real interest rates 1.5 percent (150 basis points) above counterfactual because of rising marginal product of capital.
    - Japan: real interest rates reduced by up to 1.5 percent by 2050 due to demographic-driven capital-labor changes.
  - Equity markets: Tobin’s q rises especially in developing countries; falls below counterfactual in Japan and other industrial countries as demographic transition matures.
- Overall interpretation
  - Demographic transition is already affecting and will increasingly affect global growth distribution.
  - Savings, investment, current account balances, capital flows, exchange rates, and asset prices are all materially influenced by demographic change.
  - Results depend on myriad model assumptions; sensitivity analysis is required to contextualize magnitudes.

### Selected numerical facts and parameter values emphasized in the analysis
- Replacement level fertility: 2.1 births per woman in industrial countries and 2.4 births per woman in developing countries.
- Child dependency specification: children dependent for 17 years.
- Steady-state rates used to remove demographic transition:
  - Child birthrate = 1.9 percent.
  - Adult maturity rate = 1.5 percent.
  - Constant probability of death of adults = 1 percent.
  - Constant probability of death of children = 0.46 percent.
- Simulation horizons and reporting windows:
  - World projection run from 1985 to 2100.
  - Results presented from 2005 to 2080 after initial asset adjustment.
- Key outcome magnitudes:
  - Global population growth: projected ¼ percent a year by 2050 vs. 1¼ percent at present.
  - Country population declines: over 30 percent in some central and eastern European countries; 22 percent in Italy; 14 percent in Japan (over the next 50 years).
  - Median world age: increase by over 10 years during 2000–50 to 37 years.
  - Japan GDP in 2050: 30 percent lower than without demographic transition.
  - Developing country GDP in 2050: 60 percent higher than without demographic transition.
  - Developing-country growth: more than 2 percent higher by 2020 due to demographic change.
  - Japan growth: 1.3 percent below counterfactual by 2040 (low point).
  - Investment/GDP ratio: 4 percent higher in developing countries by 2025.
  - Japan saving-to-GDP: 4 percentage points higher by 2005; 11 percentage points lower by 2070.
  - U.S. saving-to-GDP: 3 percentage points lower in 2005; 5 percentage points higher by 2040.
  - Japanese current account in 2005: 2.6 percent of GDP surplus relative to no demographic change.
  - Real exchange rates by 2050: Japan appreciated close to 60 percent; developing countries depreciated close to 60 percent.
  - Real interest rates: developing countries 1.5 percent (150 basis points) higher; Japan up to 1.5 percent lower by 2050.

### V. Sensitivity and considerations for policy implications (introductory remarks)
- The analysis highlights sensitivity to key assumptions (e.g., productivity growth, capital adjustment costs, demographic projections).
- The magnitudes reported should be interpreted in context of model structure, calibration choices, and aggregation across heterogeneous countries within regions.
- Further sections (beyond provided excerpt) explore sensitivity to alternative assumptions (for example, differential productivity growth outside the United States) to benchmark the size of demographic effects.

*Source: IMF working paper content (Section II–V, model description and simulation results).*

### 2005. The second assumption we explore is what happens if there is a fall in the country risk

### _wp0609 - 2005. The second assumption we explore is what happens if there is a fall in the country risk

### A. Faster Global Growth through More Rapid Technological Convergence
- Scenario specification:
  - Productivity growth (labor-augmenting technical change) rises by "1 percent per year for 50 years from 2005 to 2054" in the developing country region.
  - Productivity growth rises by "0.1 percent per year over the same time in Japan and other industrial countries".
  - No change in underlying productivity growth from baseline in the United States.
- Key dynamic outcomes (percent deviation from baseline unless otherwise noted):
  - Real GDP:
    - Developing countries: growth begins immediately.
    - Rest of the world: GDP growth is slightly lower initially as resources are channeled into developing countries; after a decade real GDP growth rises in the rest of the world.
  - Current account:
    - Developing country current account deteriorates initially as resources flow to developing countries.
  - Investment and savings:
    - Surge in growth initially reduces investment in all countries due to households raising consumption in anticipation of higher future income, reducing savings and raising real interest rates (crowding out private investment).
    - It takes "a decade" before investment rates rise above the baseline in developing countries.
    - Total savings/GDP and private consumption/GDP show anticipatory increases in consumption relative to baseline.
  - Capital and interest rates:
    - Capital-output ratios fall initially in all countries.
    - Higher real interest rates persist "for five decades" while productivity growth is high, then fall below baseline when the growth surge concludes.
    - There is an overshooting of interest rates and a sharp investment reversal after 2050 as capital accumulation overshoots.
  - Persistence:
    - Considerable persistence due to backward-looking households and firms despite presence of rational consumers and firms.
- Comparison with demographic transition:
  - Higher productivity growth in developing and modestly higher productivity growth in developed economies can offset demographic impacts on aggregate GDP.
  - "Higher productivity growth of 0.1 per year in Japan and the other industrial countries offsets half of the fall in GDP caused by demographic change."
  - For developing countries, the higher growth rate "almost removes the expected future decline in growth rates caused by their aging after 2030."
  - Aggregate consumption outcomes are similarly improved, but with more upward pressure on real interest rates in the short run.

### B. Improving Capital Market Access for Developing Countries
- Scenario specification:
  - Reforms reduce the risk premium associated with investing in developing country assets by "1 percent lower forever."
- Key dynamic outcomes:
  - Capital flows:
    - Reduction in risk premium encourages more capital to flow into developing countries.
    - Capital reallocation reduces real interest rates globally and has a considerable positive impact on real GDP in developing countries.
  - Domestic saving and returns:
    - Domestic saving increases for several decades in developing countries as the rate of return on domestic capital improves.
  - Current accounts and external balances:
    - Developing country current account positions deteriorate.
    - Advanced country regions—the suppliers of capital—experience improvements in their external balances.
  - Production and capital-output ratios:
    - Production relocates from industrial economies to developing countries.
    - Capital/output ratio rises in developing countries and falls in industrial countries.
  - Distribution of gains:
    - Unlike the productivity-growth scenario, the fall in developing country risk leads to a reallocation of global production and higher global income, but "all of the gains are captured by consumers in developing countries."

### VI. Conclusions and Policy Implications
- Demographic shifts will be wide-ranging:
  - In advanced countries, population aging will likely reduce per capita growth rates.
  - In developing countries, increases in the relative size of the working-age population could lead to stronger per capita growth if additional labor is effectively utilized.
- International capital flows and external balances:
  - Large changes in saving, investment, and current account balances could occur "over the next 80 years" as a result of demographic change.
  - The impact critically depends on the reaction of private saving; it remains unclear how households will adjust behavior.
- Uncertainty and research needs:
  - The size of potential changes should be considered against other shocks (e.g., changes in productivity growth).
  - "Substantially more research is required" to better understand demographic effects on economic performance.

### Appendix: The Analytical Approach
- Model and documentation:
  - Key features of the MSG3 model summarized; more detailed documentation referenced in the source.
- Adult population dynamics:
  - Maturity rate b(s): size of newly matured cohort at time s relative to existing adult population N(s).
  - Mortality rate p: probability of an adult dying before the next period (common across adults).
  - Adult population evolution equation: Ṅ(t) = (b(t) − p)N(t) (interpreted as adult population grows at maturity rate less mortality rate).
- Child population and maturity:
  - Period of childhood denoted ∆; in simulations the period of childhood is defined as "the first 16 years of an agent’s life."
  - Aggregate children M(t) computed by integrating surviving children born within the last ∆ years.
  - Relationship: the maturity rate at time t depends on the birthrate and adult population size ∆ years earlier, adjusted for survival.
- Adult consumption and wealth:
  - Adults maximize expected lifetime utility with logarithmic utility and discount by survival probability.
  - Budget constraint includes consumption c(s,t), wage income, returns on financial wealth w(s,t) at interest rate r(t), and an effective rate p on financial wealth due to life insurance market.
  - Optimal consumption path: c(s,t) = θ[w(s,t) + h(s,t) + p t ?] (expression reported in source as equation (13): "[], ),(),()(),(tshtswptsc++=θ" — preserve exact structure in source).
  - Human wealth h(s,t) defined as present value of expected future labor income (explicit integral form provided in source).
  - Aggregate relationships:
    - Aggregate consumption C_N(t) = ∫_{s=-∞}^{t} N(s,t) c(s,t) ds
    - Aggregate financial wealth W(t) = ∫_{s=-∞}^{t} w(s,t) N(s,t) ds
    - Aggregate human wealth H(t) = ∫_{s=-∞}^{t} h(s,t) N(s,t) ds
  - Aggregate adult consumption function: C_N(t) = θ[W(t) + H(t) + p t ?] (reported in source as equation (18): "[])()())(()(tHtWtptC N ++=θ")
- Labor supply and age-earnings profiles:
  - Age-earnings/hump-shaped profiles introduced so income varies with age; only adults earn labor income; children dependent.
  - Effective labor supply of an agent adult since s at time t given by nonlinear functional form (equation (19) in source) including e^{μt} term where μ is the rate of technological progress.
  - Parameters for hump-shaped profile (Japan estimates, as used in paper):
    - α1 = 0.073, α2 = 0.096, α3 = 0.085 and a1 = a2 = 200.
- Notes on modeling choices:
  - Continuous age-earnings profiles used rather than discontinuous retirement cutoff to reflect varied retirement ages and to avoid implementation complications.
  - Technological progress raises the value of effective labor supplied by all agents over time.

*Source: Authors' estimates and the supplied content from the IMF PDF chapter.*

### 0.10076 and a1 = a

### _wp0609 - 0.10076 and a1 = a

### Evolution of individual and aggregate labor supply
- Equation (22): 213
  aaa−−=  
- Individual adult labor-supply evolution (equation (23)):
  - ∑ = − = 3 1 ),()(),( i ii tsltslαμ &  
- Aggregate effective labor supply L(t) (equation (24)):
  - ∑ ∫ = ∞− = = 3 1 )( ),(),()( i i t tL dstsltsntL  
- Definition linking cohort effective labor to aggregate term (equation (25)):
  - dstsltsntL t ii ∫ ∞− =),(),()(  
- Aggregate decomposition (equation (26)):
  - )()()()()()()()( )()()()( 332211 321 tNtbetLptLptLp tLtLtLtL t i μ α μα μα μ +−−+−−+−−= ++= &  
- Intuition:
  - Aggregate labor supply changes as the population ages and as new agents mature into the labor force.
  - Application uses the estimate age earnings profile for Japan and the U.S. age-earnings profile for all other regions as an approximation.

### Intergenerational transfers
- Children:
  - Do not supply labor and do not hold financial wealth.
  - Receive intergenerational transfer c(t) every period and completely consume it.
- Transfer growth assumption (equation (27)):
  - t ectc μ 0 )(=  (c(t) grows at the rate of productivity growth, μ)
- Adult payment specification (equation (28)):
  - )(),(tjtsj =  (adults share burden equally; j(s,t) is payment by an adult who became adult at s, at time t)
- Aggregate budget constraint for transfers (equation (29)):
  - ∫ ∞− = t dstsntjtMtc),()()()(  
- Implied expression (equation (30)):
  - ∫ ∞− = t dstsn tMtc tj ),( )()( )(  
- Relationship tying j and c (equation (31)):
  - )()()(ttctjδ=  

### Aggregate consumption
- Aggregate consumption C(t) (equation (32)):
  - )()()]()()[()(tMtctHtAptC+++=θ  
  - Aggregate consumption equals aggregate adult consumption plus aggregate child consumption and other components as specified.

### Income, individual income definition, and human wealth
- Individual adult income y(s,t) (equation (33)):
  - )()()(),()()](1[),(tjttxttrtsltwttsy−−+−=τ  
  - Components: after-tax labor income, government transfers tr, lump sum taxes tx, intergenerational transfers j.
  - Distribution of tx and tr is uniform across population.
- Aggregate adult income Y(t) (equation (34)):
  - dstsntsytY t ∫ ∞− =),(),()(  
- Time derivative of individual human wealth h(s,t) (equation (35)):
  - ])([),(tjttxttrtsltwttshptrtsh−−−−−+= τ &  
  - Interpretation: (r + p) growth term because future earnings are discounted less as time passes; current income is subtracted as it ceases to be human wealth.
- Aggregate human wealth evolution (equation (36)):
  - H(t) = r(t)H(t) -Y(t) + h(t,t)n(t,t)  
  - Intuition:
    - Aggregate human wealth grows at rate r because future income draws nearer.
    - Death (p) does not affect aggregate human wealth due to insurance-company redistribution.
    - Each period new-matured cohort brings new human wealth h(t,t)n(t,t).

### Model assumptions and data choices
- Age-earnings profiles:
  - Japan estimate used for Japan.
  - U.S. age-earnings profile used for all other regions (noted as a crude approximation due to data limitations).
- Simplifying assumption on adult payments:
  - Adults of all ages contribute equally to child support (contrast noted with Bryant and Velculescu (2001) who make most child expenses fall on younger adults).

### Key referenced equations (by number)
- (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36)

*Source: _wp0609 - 0.10076 and a1 = a (PDF chapter/section).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp0609.pdf_