## 1. Education Spending and Migration in Developed and Developing Regions

## Source details

**Canonical URL:** [1. Education Spending and Migration in Developed and Developing Regions](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05140.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05140.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05140.pdf.json)

---

### I. Introduction — population aging, fiscal and political economy links
- World median age projected to rise from 26.4 in 2000 to 36.8 in 2050 (United Nations, 2002a).
- Old-age dependency ratios projected to increase approximately by 4 percent (developed regions) and 70 percent (developing regions) between 2050 and 2100.
- By 2150, medium fertility scenario old-age dependency ratios: 0.47 (developed) and 0.43 (developing).
- Example: share of the elderly population in the United Arab Emirates expected to rise from 2 percent to 28 percent by 2050 (Heller, 2003, p.13).
- Key links emphasized:
  - Aging raises fiscal pressure via higher social security and health care spending, potentially crowding out education.
  - Political economy: increasing political power of the elderly can reduce education spending (references: Gradstein and Kaganovich (2004); Holtz-Eakin, Lovely, and Tosun (2004); Razin, Sadka, and Swagel (2002)).
  - International spillovers and the relative neglect of labor migration versus capital mobility in previous literature (references cited).
- Paper contributions:
  - Emphasizes the aging–education–human capital link and the role of young migrant political participation in advanced economies.
  - Compares labor mobility model to open economy model with international capital mobility to treat factor mobility as a policy choice.

### II. Two-region overlapping-generations model — structure and mechanics
- Time and agents:
  - Two-period overlapping generations model (Diamond, 1965) extended to two regions with international labor mobility.
  - Political process: median-voter framework with voter heterogeneity (distribution of genetic ability levels).
- Human capital production:
  - h = Φ + a * (e g)^ψ  (ψ ≤ 1; expressed as equation (4)).
  - Ability a distributed uniformly on [0,1].
  - ψ specified at ψ = 0.5 in baseline.
- Fiscal institutions:
  - Social security spending per young is exogenously fixed (s_t^g); social security tax μ_t satisfies s_t^g = N_t μ_t.
  - Education tax τ_t finances education spending e_t^g = N_t τ_t; voters choose τ_t.
- Households:
  - Utility: ln C_t + δ ln C_{t+1} (equation (1)).
  - Optimal saving: S_{jt} = (w_t a_j l_{jt} (1−τ_t − μ_t)) / (1 + δ) (equation (6)).
  - Preferred education tax of young j: τ_jt = ((1−μ_t) a_j y_t) / (a_j y_t + ψ) (equation (8)); preferred τ increases in a_j and y_t, decreases in μ_t. Old prefer τ = 0.
- Producers and markets:
  - Production function: Y_t = Λ K_t^{α} H_t^{1−α} (equation (10)).
  - Aggregate human capital: H_t = N_t ∫_0^1 a f(a) l_{t}(a) da (equation (11)); human capital per worker in equation (12).
  - Factor prices equal marginal products (equations (13) and (14)); k and h denote capital per worker and human capital per worker.
  - Saving per worker: s_t = ∫_0^1 [ (1−τ_t − μ_t) w_t a (Φ + a e_t^g)^ψ ] / (1 + δ) f(a) da (equation (15)).
- International markets and migration:
  - Capital market equilibrium without international capital mobility: s^{A}_{t} N^{A}_{t} = k^{A}_{t+1} N^{A}_{t+1} and analogous for region B (equations (16)–(17)).
  - Assumption of perfect international labor mobility (one model period = 30 years).
  - Labor market equilibrium: net-of-tax wage equalization implied by source-based taxation; international labor flow constraint equalizes net-of-tax wages across regions (equation (19)).
  - Only the young move; ability distributions remain uniform across regions.

### III. Simulation design, parameterization, and baseline assumptions
- Population projections and horizons:
  - Simulations based on United Nations 2002 revision of World Population Prospects (United Nations, 2002a).
  - Two world regions: 28 developed and 141 developing countries.
  - Simulation horizons: two 30-year periods, 2000–30 and 2030–60, and the full period 2000–60.
  - One model period corresponds to 30 years.
- Population growth rates (preserve exactly):
  - Developed countries: 0.67 percent for the 2000–2030 period and then 0.38 percent for the 2030–60 period.
  - Developing countries: initial annual average rate of 2.47 percent, falling to 1.39 percent for the 2000–30 period and then to 1.27 percent for the 2030–2060 period.
- Elasticity and preference parameters:
  - The elasticity of output with respect to capital input is set equal to one-third (0.33α=).
  - The annual rate of time preference is chosen to be 4 percent.
  - Time preference and population growth are adjusted to the model period length (30 years).
- Human-capital parameter:
  - ψ = 0.5 (human capital elasticity w.r.t. government education spending and ability).
  - Rationale: compromise between Laitner (2000b) approximate 0.4ψ= and higher returns in low-income countries (Psacharopoulos, 1985).
- Social security calibration:
  - Social security spending s_t^g set exogenously.
  - Social security expenditure for 2000 compiled from Government Finance Statistics (IMF, 2003).
  - Future social security spending assumed to grow with population aged 65 and over using UN projections for 2000–30 and 2030–60.

### IV. Full labor mobility simulation results — headline outcomes
- Migration pattern:
  - Perfect international labor mobility; migrant labor participates in the political system; labor migrates from the developing region to the developed region per population projections.
- Contribution of immigration to developed region labor growth:
  - Immigration makes up 46 percent of the 41.1 percent growth in the number of workers in advanced economies between 2000 and 2030.
  - Immigration makes up 61 percent of the 40 percent growth in the number of workers in advanced economies between 2030 and 2060.
  - Immigration accounts for 56 percent of labor growth in advanced economies between 2000 and 2060.
- Scale of immigration relative to developed region population and workforce:
  - The developed region receives 29 percent of its 2000 population between 2000 and 2060.
  - This inflow amounts to 48 percent of its working-age population.
- Impact on developing countries:
  - Developing countries experience lower domestic labor growth due to out-migration.
  - Example: of a potential 51.3 percent labor growth in the developing region between 2000 and 2030, 11.5 percent was lost due to out-migration, leaving a net 40 percent growth.

### V. Capital per worker, human capital, education tax rate, and education spending — quantitative results (labor mobility model)
- Capital stock per worker (Figure 5 / Table 2, column (1)):
  - Developed region: 2000–2030: -10.0 percent; 2030–2060: 4.2 percent; 2000–2060: -6.2 percent.
  - Developing region: 2000–2030: 48.7 percent; 2030–2060: 23.7 percent; 2000–2060: 84.0 percent.
- Human capital per worker (Figure 6 / Table 2, column (1)):
  - Developed region: 2000–2030: 7.8 percent; 2030–2060: -6.3 percent; 2000–2060: 1.0 percent.
  - Developing region: 2000–2030: -1.2 percent; 2030–2060: 3.8 percent; 2000–2060: 2.6 percent.
- Education tax rate (Figure 7 / Table 2, column (1)):
  - Developed region: 2000–2030: 18.5 percent; 2030–2060: -11.8 percent; 2000–2060: 4.5 percent.
  - Developing region: 2000–2030: -14.1 percent; 2030–2060: -0.4 percent; 2000–2060: -14.5 percent.
- Education spending per worker (Figure 8 / Table 2, column (1)):
  - Developed region: 2000–2030: 20.3 percent; 2030–2060: -14.7 percent; 2000–2060: 2.6 percent.
  - Developing region: 2000–2030: -2.8 percent; 2030–2060: 9.6 percent; 2000–2060: 6.5 percent.
  - Note: education spending in the developing region increases between 2030 and 2060 and between 2000 and 2060 despite tax rate decreases, mainly due to income growth.

### VI. Income per worker, consumption, and welfare effects
- Income per worker (Figure 9 / Table 2, column (1)):
  - Developed region: 2000–2030: 1.6 percent; 2030–2060: -2.9 percent; 2000–2060: -1.4 percent.
  - Developing region: 2000–2030: 13.1 percent; 2030–2060: 10.0 percent; 2000–2060: 24.4 percent.
- Consumption of young (Figure 10 / Table 2, column (1)):
  - Developed region: 2000–2030: -3.2 percent; 2030–2060: -0.5 percent; 2000–2060: -3.7 percent.
  - Developing region: 2000–2030: 18.9 percent; 2030–2060: 10.2 percent; 2000–2060: 31.1 percent.
- Consumption of old (Figure 11 / Table 2, column (1)):
  - Developed region: 2000–2030: 5.4 percent; 2030–2060: -6.5 percent; 2000–2060: -1.4 percent.
  - Developing region: 2000–2030: -16.3 percent; 2030–2060: 8.9 percent; 2000–2060: -8.9 percent.
- Sum of young and old consumption (Figure 12 / Table 2, column (1)):
  - Developed region: 2000–2030: 1.4 percent; 2030–2060: -3.8 percent; 2000–2060: -2.5 percent.
  - Developing region: 2000–2030: -3.0 percent; 2030–2060: 9.5 percent; 2000–2060: 6.2 percent.
- World consumption:
  - Growth in the sum of consumptions in the developing region dominates; world consumption decreases only slightly between 2000 and 2030 but increases between 2030 and 2060 and between 2000 and 2060.

### VII. Model comparisons and alternative mobility scenarios — key findings
- Models and variants compared (Table 2):
  - Full labor mobility model (baseline).
  - Capital mobility model (no labor mobility).
  - Labor mobility only after 2030.
  - Migrants' voting delayed by 30 years.
  - Fixed education spending per worker.
- Comparative outcomes:
  - Capital mobility model (no labor mobility) produces "significantly inferior outcomes for the developed region" relative to full labor mobility; developed-region outcomes improve in the full labor mobility case because labor inflows increase human capital when migrants participate politically.
  - Developing region benefits more under capital mobility (retains workers and receives capital inflows) but grows strongly under both models.
  - Delaying labor mobility until after 2030 can make the developed region "fare slightly better particularly after 2030" due to less downward pressure on net returns to labor.
  - Delaying migrant political participation by 30 years produces "rather adverse outcomes for the developed region" — sharp decreases in education tax rate, education spending, and human capital per worker — and leads to substantially higher labor inflows to equalize net labor earnings.
  - Fixing education spending exogenously removes human capital feedback and alters income change directions for developed region across periods.
- Select illustrative Table 2 entries (percent changes):
  - Number of workers, labor mobility model (developed region): 2000–2030: 41.1; 2030–2060: 30.9; 2000–2060: 84.7.
  - Number of workers, labor mobility model (developing region): 2000–2030: 39.8; 2030–2060: 34.4; 2000–2060: 87.8.
  - Capital stock per worker under capital mobility model (developed region, column (3)): 2000–2030: -35.5; 2030–2060: -6.7; 2000–2060: -39.8.
  - Education tax rate under migrants voting delayed 30 years (developed region, column (7)): 2000–2030: -81.5; 2030–2060: 236.4; 2000–2060: -37.6.

### VIII. Predicted versus actual labor flows to developed region
- Predicted average annual number of labor migrants to developed region (Table 3):
  - 2000–2030: 3,256,141
  - 2030–2060: 4,580,496
- Ratios to actual OECD 2000 figures (Table 3):
  - Ratio of predicted to actual foreign population inflows in 2000: 2000–2030 = 98.0 percent; 2030–2060 = 138.0 percent.
  - Ratio of predicted to actual foreign worker inflows in 2000: 2000–2030 = 190.0 percent; 2030–2060 = 267.0 percent.
- Interpretation: predicted average annual number of labor migrants is fairly close to actual inflows of foreign population (even below actual for 2000–2030 population inflows), while predicted worker inflows are substantially larger than observed worker inflows.

### IX. Sensitivities, welfare transfers, and parameter concerns
- Welfare transfers to migrants not modeled; considerations noted:
  - Transfers matter when labor inflows are large.
  - Politically enfranchised migrants may vote for lower transfers, offsetting transfer costs.
- Sensitivity to ψ:
  - Prior closed-economy results showed low ψ (<0.34) could produce "immiserizing steady state growth results."
  - Simulation with ψ = 0.4 reported: "results did not change significantly to alter the main conclusions of the paper."

### X. Summary conclusions
- Modeling perfect international labor mobility with politically responsive fiscal policy and UN population projections yields:
  - Migrants act as workers and savers and, when politically enfranchised, shift fiscal policy toward greater human capital accumulation.
  - Full labor mobility helps the developed region offset some aging effects through migrant-induced human capital increases, but the developed region still records an overall decrease in income per worker and consumption over 2000–2060.
  - Developing region experiences significant growth under both full labor mobility and capital mobility; it does relatively better under capital mobility but still grows substantially with labor mobility.
  - Political participation by migrants is crucial: delaying voting rights for migrants (30 years) yields inferior outcomes for the developed region.
  - Policy choice between labor mobility and capital mobility matters for assessing economic effects of population aging.

### XI. Appendix Table 1 — economies used in population projections (selected)
- Advanced economies listed include: Australia; Austria; Belgium; Canada; Cyprus; Denmark; Finland; France; Germany; Greece; Hong Kong SAR; Iceland; Ireland; Israel; Italy; Japan; Republic of Korea; Luxembourg; Netherlands; New Zealand; Norway; Portugal; Singapore; Spain; Sweden; Switzerland; United Kingdom; United States.
- Developing economies list includes a broad set of countries (Afghanistan through Zimbabwe) as provided; note overlaps where some economies (e.g., Singapore, Spain) appear in both lists in the supplied content.

*Source: _wp05140 (IMF Working Paper content unit excerpt provided).*

### 1. Education Spending and Migration in Developed and Developing Regions ......................20

### 1. Education Spending and Migration in Developed and Developing Regions

### 1. Education Spending and Migration in Developed and Developing Regions (page 20)
- Main section title as listed: "Education Spending and Migration in Developed and Developing Regions".
- (No substantive findings or numeric results provided in the supplied content unit beyond the section heading and page reference.)

### 2. Comparisons with Alternative Factor Mobility Models (page 21)
- Section title as listed: "Comparisons with Alternative Factor Mobility Models".
- (No substantive findings or numeric results provided in the supplied content unit beyond the section heading and page reference.)

### 3. Comparison of Predicted and Actual Labor Flows to Developed Region (page 23)
- Section title as listed: "Comparison of Predicted and Actual Labor Flows to Developed Region".
- (No substantive findings or numeric results provided in the supplied content unit beyond the section heading and page reference.)

### Figures (pages 24–29)
- Figure 1: "Population Growth Rates in Developed and Developing Regions" (page 24).
- Figure 2: "Composition of the Change in the Number of Workers in the Developed Region" (page 24).
- Figure 3: "Ratio of Immigrant Labor to Developed Region Population" (page 25).
- Figure 4: "Composition of the Change in the Number of Workers in the Developing Region" (page 25).
- Figure 5: "Change in Capital Stock Per Worker in Developed and Developing Regions" (page 26).
- Figure 6: "Change in Human Capital Per Worker in Developed and Developing Regions" (page 26).
- Figure 7: "Change in Education Tax Rate in Developed and Developing Regions" (page 27).
- Figure 8: "Change in Education Spending Per Worker in Developed and Developing Regions" (page 27).
- Figure 9: "Change in Income Per Worker in Developed and Developing Regions" (page 28).
- Figure 10: "Change in Consumption of Young in Developed and Developing Regions" (page 28).
- Figure 11: "Change in Consumption of Old in Developed and Developing Regions" (page 29).
- Figure 12: "Change in Sum of Young and Old Consumption in Developed and Developing Regions" (page 29).

### Appendix and Appendix Table (pages 30–31)
- Appendix: "The Effect of Increasing Dependency Ratio on the Ability Level of the Median Voter" (page 30).
- Appendix Table 1: "List of Economies Used in Population Projections" (page 31).

*Source: _wp05140 - 1. Education Spending and Migration in Developed and Developing Regions ......................20*

### References..............................................................................................................

### References

### I. INTRODUCTION
- Population aging:
  - World median age projected to rise from 26.4 in 2000 to 36.8 in 2050 (United Nations, 2002a).
  - Old-age dependency ratios projected to increase approximately by 4 percent (developed regions) and 70 percent (developing regions) between 2050 and 2100.
  - By 2150, a medium fertility scenario shows old-age dependency ratios of 0.47 (developed) and 0.43 (developing).
  - Example: share of the elderly population in the United Arab Emirates expected to rise from 2 percent to 28 percent by 2050 (Heller, 2003, p.13).
- Fiscal and growth implications:
  - Aging raises fiscal pressure through higher government spending on social security, health care, and other welfare programs for the elderly, potentially reducing spending on programs that benefit the young (education highlighted).
  - Political economy links: increasing political power of the elderly can affect education spending (Gradstein and Kaganovich (2004); Holtz-Eakin, Lovely, and Tosun (2004); Razin, Sadka, and Swagel (2002)).
  - International spillovers: aging analyzed in open economy frameworks (Cutler et al. (1990); Börsch-Supan (1996); Kenc and Sayan (2001); Elmendorf and Sheiner (2000); Jelassi and Sayan (2004); Tosun (2001, 2003); Van Groezen and Leers (2000)).
  - Labor migration underexamined relative to capital mobility (Leers, Meijdam, and Verbon, 2004; Storesletten, 2000).
- Paper contributions:
  - Brings out political economy of aging through the aging–education–human capital link, emphasizing young migrant political participation in advanced economies.
  - Compares labor mobility model to open economy model with international capital mobility to examine factor mobility as a policy choice.

### II. THE TWO-REGION MODEL
- Model structure:
  - Two-period overlapping generations model (Diamond, 1965), extended to two regions with international labor mobility (Galor (1986, 1992); Crettez et al. (1996, 1998)).
  - Political process modeled via median-voter framework with voter heterogeneity (distribution of genetic ability levels).
  - Human capital production depends on individual ability and government education spending per young, with functional form: h = Φ + a * (e g)^ψ (expressed in text as equation (4)); ψ ≤ 1.
  - Social security spending is exogenously fixed per young (s_t^g); social security tax μ_t determined by s_t^g = N_t μ_t. Education tax τ_t finances education (e_t^g = N_t τ_t); voters choose τ_t.
- Households:
  - Utility: ln C_t + δ ln C_{t+1} (equation (1)); individuals live two periods.
  - Budget constraints (first and second period) shown in text (equations (2)).
  - Optimal saving of individual j: S_{jt} = (w_t a_j l_{jt} (1−τ_t − μ_t)) / (1 + δ) (equation (6) as given).
  - Preferred education tax rate of young individual j: τ_jt = ((1−μ_t) a_j y_t) / (a_j y_t + ψ) (equation (8) as given); preferred τ increases in a_j and y_t, decreases in μ_t. Old prefer τ = 0.
- Political process:
  - Median voter a_m defined by integral condition (equation (9)).
  - Aging without migration: median voter becomes lower-ability, prefers lower education tax.
  - With migration: inflow of young workers can raise median voter ability relative to no-migration case; whether it exceeds pre-aging level is ambiguous.
- Producers and markets:
  - Production: Y_t = Λ K_t^{α} H_t^{1−α} (equation (10)).
  - Aggregate human capital: H_t = N_t ∫_0^1 a f(a) l_{t}(a) da (equation (11)); human capital per worker expressed in equation (12).
  - Factor prices equal marginal products (equations (13) and (14)); variables k and h denote capital per worker and human capital per worker.
  - Saving per worker: s_t = ∫_0^1 [ (1−τ_t − μ_t) w_t a (Φ + a e_t^g)^ψ ] / (1 + δ) f(a) da (equation (15) as given).
- International goods and labor markets:
  - Capital market equilibrium without international capital mobility: s^{A}_{t} N^{A}_{t} = k^{A}_{t+1} N^{A}_{t+1} and analogous for region B (equations (16)–(17)).
  - Assumption of perfect international labor mobility (one period = 30 years makes this viable).
  - Labor market equilibrium and net-of-tax wage equalization implied by source-based taxation; international labor flow constraint ensures equalized net-of-tax wages across regions (equation (19) as given).
  - Only young move; ability distributions remain uniform across regions (migration does not change ability distributions).

### III. GLOBAL AGING AND LABOR MIGRATION
- Simulation inputs and design:
  - Simulations based on United Nations 2002 revision of World Population Prospects (United Nations, 2002a).
  - Two world regions: 28 developed and 141 developing countries.
  - Population growth rates implied by the projections (Figure 1 referenced in text).
  - Simulation horizons: two 30-year periods, 2000–30 and 2030–60, and the full period 2000–60.
  - Starting point uses average population growth rates for 1970–2000 period.
  - Notation: one model period corresponds to 30 years (text note).
- Mechanisms highlighted:
  - A decrease in population growth affects labor flows and capital accumulation directly (fewer workers → higher marginal product of labor → labor inflows) and indirectly via political economy (aging shifts median voter identity → lower τ → lower education spending → effects on human capital and growth).

*Source: _wp05140 - References (excerpt) — content as provided in the supplied PDF excerpt.*

### 0.67 percent for the 2000–2030 period and then to 0.38 percent for the 2030–60 period. In

### _wp05140 - 0.67 percent for the 2000–2030 period and then to 0.38 percent for the 2030–60 period. In

### Model parameterization and baseline assumptions
- Population growth rates:
  - Developed countries: 0.67 percent for the 2000–2030 period and then 0.38 percent for the 2030–60 period.
  - Developing countries: initial annual average rate of 2.47 percent, falling to 1.39 percent for the 2000–30 period and then to 1.27 percent for the 2030–2060 period.
- Elasticity and preference parameters:
  - The elasticity of output with respect to capital input is set equal to one-third (0.33α=).
  - The annual rate of time preference is chosen to be 4 percent.
  - The rate of time preference in the utility specification and the population growth rate are adjusted to the length of the model period (30 years).
- Ability distribution and human capital:
  - Ability level, a, is assumed to be distributed uniformly on the interval [0,1].
  - Human capital elasticity with respect to government spending on education and ability level (ψ) is set to ψ = 0.5.
    - Rationale: Laitner (2000b) corresponds approximately to 0.4ψ= in this model; Psacharopoulos (1985) suggests higher returns in low income and developing countries, motivating the compromise ψ = 0.5.
  - Note: Holtz-Eakin, Lovely, and Tosun (2004) provide sensitivity analysis on this parameter.

### Social security spending specification
- Social security spending (stg) is set exogenously in the model.
- Calibration:
  - Social security expenditure for developed and developing economies is compiled for the year 2000 using Government Finance Statistics published by the International Monetary Fund (2003).
  - Future social security spending is assumed to grow by the growth rate in population aged 65 and over.
  - United Nations population projections are used to derive social security spending for the periods 2000–30 and 2030–60.

### Full Labor Mobility Simulation Results — key outcomes
- Migration pattern:
  - Perfect international labor mobility with migrant labor participating in the political system.
  - Labor migrates from the developing region to the developed region based on the population projections.
- Contribution of immigration to developed region labor growth:
  - Immigration makes up 46 percent of the 41.1 percent growth in the number of workers in advanced economies between 2000 and 2030.
  - Immigration makes up 61 percent of the 40 percent growth in the number of workers in advanced economies between 2030 and 2060.
  - Immigration accounts for 56 percent of labor growth in advanced economies between 2000 and 2060.
- Scale of immigration relative to developed region population and workforce:
  - The developed region receives 29 percent of its 2000 population between 2000 and 2060.
  - This inflow amounts to 48 percent of its working-age population.
- Impact on developing countries:
  - Developing countries experience lower domestic labor growth due to labor outflows to the developed region.
  - However, the loss in labor growth is described as a relatively small portion of overall labor growth in developing countries.

*Source: IMF Working Paper content unit _wp05140*

### 51.3 percent labor growth that would have been seen in the developing region between 2000

### _wp05140 - 51.3 percent labor growth that would have been seen in the developing region between 2000

### Labor movements, population growth, and capital per worker
- Developing region: "51.3 percent labor growth that would have been seen in the developing region between 2000 and 2030, 11.5 percent was lost due to out-migration of labor, leaving this region with a net 40 percent growth."
- Developed region: labor influx between 2000 and 2030 leads to a decrease in capital stock per worker in that period because "capital stock is determined by saving in the previous period (1970–2000)".
- Capital per worker changes (Figure 5 / Table 2, column (1) labor mobility model):
  - Developed region: 2000–2030: -10.0 percent; 2030–2060: 4.2 percent; 2000–2060: -6.2 percent.
  - Developing region: 2000–2030: 48.7 percent; 2030–2060: 23.7 percent; 2000–2060: 84.0 percent.
- Explanation: the developing region’s capital stock per worker rises 2000–2030 because "the capital stock in the period 2000–2030 is utilized by fewer workers" after out-migration; the subsequent period 2030–2060 exhibits smaller capital growth due to "considerable population growth decrease (from 2.47 percent to 1.39 percent) in developing countries coupled with labor emigration between 2000 and 2030".

### Human capital, education tax rate, and education spending
- Human capital dynamics (Figure 6 / Table 2, column (1)):
  - Developed region: human capital per worker 2000–2030: 7.8 percent; 2030–2060: -6.3 percent; 2000–2060: 1.0 percent.
  - Developing region: human capital per worker 2000–2030: -1.2 percent; 2030–2060: 3.8 percent; 2000–2060: 2.6 percent.
- Political economy mechanism: human capital is a function of government spending on education; median voter ability declines with aging, reducing support for education spending, but migrant labor (young voters) can offset this by changing tax choices in favor of the young.
- Education tax rate changes (Figure 7 / Table 2, column (1)):
  - Developed region: 2000–2030: 18.5 percent; 2030–2060: -11.8 percent; 2000–2060: 4.5 percent.
  - Developing region: 2000–2030: -14.1 percent; 2030–2060: -0.4 percent; 2000–2060: -14.5 percent.
- Education spending per worker (Figure 8 / Table 2, column (1)):
  - Developed region: 2000–2030: 20.3 percent; 2030–2060: -14.7 percent; 2000–2060: 2.6 percent.
  - Developing region: 2000–2030: -2.8 percent; 2030–2060: 9.6 percent; 2000–2060: 6.5 percent.
- Note: "education spending in the developing region increases between 2030 and 2060 and between 2000 and 2060 despite the tax rate decreases in these periods. This is mainly due to income growth in this region."

### Income per worker and consumption/welfare effects
- Income per worker changes (Figure 9 / Table 2, column (1)):
  - Developed region: 2000–2030: 1.6 percent; 2030–2060: -2.9 percent; 2000–2060: -1.4 percent.
  - Developing region: 2000–2030: 13.1 percent; 2030–2060: 10.0 percent; 2000–2060: 24.4 percent.
- Consumption of young (Figure 10 / Table 2, column (1)):
  - Developed region: 2000–2030: -3.2 percent; 2030–2060: -0.5 percent; 2000–2060: -3.7 percent.
  - Developing region: 2000–2030: 18.9 percent; 2030–2060: 10.2 percent; 2000–2060: 31.1 percent.
  - Mechanism: "perfect labor mobility dictates that the net labor earning of a young worker gets equalized between the two regions"; out-migration increases net labor earnings (and young consumption) in the developing region and reduces them in the developed region.
- Consumption of old (Figure 11 / Table 2, column (1)):
  - Developed region: 2000–2030: 5.4 percent; 2030–2060: -6.5 percent; 2000–2060: -1.4 percent.
  - Developing region: 2000–2030: -16.3 percent; 2030–2060: 8.9 percent; 2000–2060: -8.9 percent.
  - Mechanism: increases in capital per worker in developing region depress interest rates and net return on saving, reducing old-age consumption 2000–2030.
- Sum of young and old consumption (Figure 12 / Table 2, column (1)):
  - Developed region: 2000–2030: 1.4 percent; 2030–2060: -3.8 percent; 2000–2060: -2.5 percent.
  - Developing region: 2000–2030: -3.0 percent; 2030–2060: 9.5 percent; 2000–2060: 6.2 percent.
- World consumption: "growth in the sum of consumptions in the developing region dominates and the world consumption decreases only slightly between 2000 and 2030 but increases between 2030 and 2060 and between 2000 and 2060."

### Model comparisons and labor mobility scenarios
- Models compared (Table 2):
  - Full labor mobility model (no capital mobility) — baseline (columns (1) and (2)).
  - Capital mobility model (no labor mobility) — columns (3) and (4).
  - Variants of labor mobility model: mobility only after 2030 (columns (5)-(6)); migrants voting delayed 30 years (columns (7)-(8)); fixed education spending per worker (columns (9)-(10)).
- Key comparative findings:
  - Capital mobility model (no labor mobility) produces "significantly inferior outcomes for the developed region" compared to the full labor mobility model; labor inflows in the full model offset aging’s adverse effects via human capital and political participation.
  - Developing region benefits more under the capital mobility model (no labor mobility) because it retains workers and receives capital inflows; still experiences strong growth under both models.
  - Delayed labor mobility until after 2030 (column (5)) may make the developed region "fare slightly better particularly after 2030" due to lower overall labor growth and less downward pressure on net return on labor.
  - Delaying migrant political participation by 30 years (column (7)) produces "rather adverse outcomes for the developed region" — sharp decreases in education tax rate, education spending, and human capital per worker — and leads to substantially higher labor inflows as the differential in net labor earnings must be closed by greater labor movement.
  - Fixing education spending exogenously (columns (9)-(10)) alters the direction of income changes in the developed region for 2000–30 and 2030–60 relative to the labor mobility model because "there is no human capital feedback" in the fixed-spending case.
- Table 2 illustrative entries (select highlights, all numbers are percent changes between period years):
  - Number of workers, labor mobility model (developed region): 2000–2030: 41.1; 2030–2060: 30.9; 2000–2060: 84.7.
  - Number of workers, labor mobility model (developing region): 2000–2030: 39.8; 2030–2060: 34.4; 2000–2060: 87.8.
  - Capital stock per worker under capital mobility model (developed region, column (3)): 2000–2030: -35.5; 2030–2060: -6.7; 2000–2060: -39.8.
  - Education tax rate under migrants voting delayed 30 years (developed region, column (7)): 2000–2030: -81.5; 2030–2060: 236.4; 2000–2060: -37.6.

### Predicted vs actual labor flows to developed region
- Predicted average annual number of labor migrants to developed region (Table 3):
  - 2000–2030: 3,256,141
  - 2030–2060: 4,580,496
- Ratios to actual OECD 2000 figures (Table 3):
  - Ratio of predicted to actual foreign population inflows in 2000: 2000–2030 = 98.0 percent; 2030–2060 = 138.0 percent.
  - Ratio of predicted to actual foreign worker inflows in 2000: 2000–2030 = 190.0 percent; 2030–2060 = 267.0 percent.
- Interpretation in text: "predicted average annual number of labor migrants is fairly close to actual inflows of foreign population. It is even below the actual figure for the 2000-2030 period" for population inflows; predicted worker inflows are larger (about double for 2000–30 and about 2.7 times for 2030–60).

### Sensitivities, welfare transfers, and parameter concerns
- Welfare transfers to migrants are not modeled; paper notes two countervailing considerations:
  - Transfers matter if labor inflows are large.
  - Migrants might vote for lower transfers (social security) when politically integrated, offsetting transfer costs.
- Sensitivity to human-capital return parameter ψ:
  - Prior closed-economy study: low values (ψ<0.34) produced "immiserizing steady state growth results."
  - Paper reports a simulation with ψ=0.4: "results did not change significantly to alter the main conclusions of the paper."

### Summary conclusions (section IV)
- The paper models perfect international labor mobility with a politically responsive fiscal policy (median voter) and uses UN population projections for developed and developing regions.
- Main conclusions:
  - Labor mobility has dual effects: migrants contribute as workers and savers and, when politically enfranchised, shift fiscal policy (education) toward greater human capital accumulation.
  - Full labor mobility model helps the developed region offset some aging effects through migrant-induced human capital increases, but developed region still records an overall decrease in income per worker and consumption over 2000–2060.
  - Developing region experiences significant growth under both full labor mobility and capital mobility (no labor mobility); it does relatively better under capital mobility but still grows substantially with labor mobility.
  - Political participation by migrants is crucial: delaying voting rights for migrants (30 years) yields inferior outcomes for the developed region.
  - Choice between labor mobility and capital mobility matters for assessing the economic effects of population aging.

*Source: Computed simulation results, figures, and text from the IMF working paper content unit provided.*

### Appendix Table 1: List of Economies Used in Population Projections

### Appendix Table 1: List of Economies Used in Population Projections

### Advanced economies
- Australia
- Austria
- Belgium
- Canada
- Cyprus
- Denmark
- Finland
- France
- Germany
- Greece
- Hong Kong SAR
- Iceland
- Ireland
- Israel
- Italy
- Japan
- Republic of Korea
- Luxembourg
- Netherlands
- New Zealand
- Norway
- Portugal
- Singapore
- Spain
- Sweden
- Switzerland
- United Kingdom
- United States

### Developing Economies
- Afghanistan
- Albania
- Algeria
- Angola
- Argentina
- Armenia
- Aruba (not listed; omitted)
- Azerbaijan
- Bahamas, The
- Bahrain
- Bangladesh
- Barbados
- Belarus
- Belize
- Benin
- Bhutan
- Bolivia
- Bosnia and Herzegovina (not listed; omitted)
- Botswana
- Brazil
- Burkina Faso
- Burundi
- Cambodia
- Cameroon
- Cape Verde
- Central African Rep.
- Chad
- Chile
- China
- Colombia
- Comoros
- Congo, Rep. of
- Congo, Dem. Rep. of
- Costa Rica
- Cote d'Ivoire
- Croatia
- Czech Republic
- Djibouti
- Dominican Republic
- Ecuador
- Egypt
- El Salvador
- Equatorial Guinea
- Eritrea (not listed; omitted)
- Estonia
- Ethiopia
- Fiji
- Gabon
- Gambia, The
- Georgia
- Ghana
- Guinea
- Guinea-Bissau
- Haiti
- Honduras
- Hungary
- India
- Indonesia
- Iran, Islamic Rep. of
- Iraq
- Jamaica
- Jordan
- Kazakhstan
- Kenya
- Kiribati (not listed; omitted)
- Korea, Democratic People’s Rep. (not listed; omitted)
- Kuwait
- Kyrgyzstan
- Lao People's Dem. Rep.
- Latvia
- Lebanon
- Lesotho
- Liberia (not listed; omitted)
- Libyan Arab Jamahiriya
- Lithuania
- Madagascar
- Malawi
- Malaysia
- Maldives
- Mali
- Malta
- Mauritania
- Mauritius
- Mexico
- Moldova
- Mongolia
- Morocco
- Mozambique
- Myanmar
- Namibia
- Nepal
- Netherlands Antilles
- Nicaragua
- Niger
- Nigeria
- Oman
- Pakistan
- Panama
- Papua New Guinea
- Paraguay
- Peru
- Philippines
- Poland
- Qatar
- Romania
- Russian Federation
- Rwanda
- Saint Lucia
- Saint Vincent and the Granadines
- Samoa
- Saudi Arabia
- Senegal
- Sierra Leone
- Singapore (listed under Advanced economies as well)
- Slovak Republic
- Slovenia
- Somalia
- South Africa
- Spain (listed under Advanced economies as well)
- Sri Lanka
- Sudan
- Suriname
- Swaziland
- Syrian Arab Republic
- Tajikistan
- Tanzania
- Thailand
- Togo
- Tonga
- Trinidad and Tobago
- Tunisia
- Turkey
- Turkmenistan
- Uganda
- Ukraine
- United Arab Emirates
- Uruguay
- Uzbekistan
- Venezuela
- Viet Nam
- Yemen
- Zambia
- Zimbabwe

*Source: United Nations (2002a).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05140.pdf_