## 1.     Evolution of the Ratio of the World Population in Advanced Economies to the Population in Developing Economies

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### Population dynamics and data coverage
- Coverage: population growth comparison between advanced economies and developing economies for 1820 to 2000 (reference page 15).
- Historical decomposition: natural population growth and net migration for 1950 to 2005; projections for 2005 to 2050 (reference page 16).
- Scenario analysis excluding India and China: evolution of the ratio under different scenarios (reference page 17).
- Data sources: Maddison (2003) for 1820–2001; United Nations Population Division for 1950–2050.
- Classification rule: an economy is “advanced” if GDP per capita (1990 International Geary-Khamis dollars) > one-third of the “leading country” (UK for 1820–1900, US afterwards), and the country permanently remains above that threshold.

### Model summary and mechanism
- Chief route from poverty to wealth: integration with the world economy via non-traditional exports; successful exporters generate external learning spillovers that raise transition probabilities for other countries.
- Key model assumptions:
  - Countries transition one-way from developing to advanced.
  - Migration is from developing to advanced countries; advanced countries restrict migration to a proportion i of their population.
  - A developing country’s opportunity to integrate depends positively on the size of the advanced-country market (NA) and negatively on the number of competing developing-country suppliers (ND) — creating a development “queue.”
- Long-run outcomes hinge on:
  - transaction cost δ (barriers to trade),
  - transition mechanism captured by p(A(1−α)/(1+δ))1/α,
  - migration rate i,
  - natural population growth rates γA and γD,
  - initial proportion NA/ND.

### Technology, wages, and transition probabilities
- Technologies:
  - traditional: labor produces one unit of final good (both country types equally productive).
  - modern: Ymodern = A H^α L^(1−α) with A>2 and 0<α<1; requires complex task H (only advanced countries) and simple task L (either).
- Transaction cost for producing L in developing countries: δ units of the final good, giving production cost 1+δ.
- Transition probability: each period a developing country becomes advanced with probability p times the share of its population in the modern sector.
- Reservation wages and sectoral employment:
  - developing reservation wage wD = 1 (traditional sector).
  - number of developing workers in modern sector: NDM = (A(1−α)/(1 +δ))1/α NA.
  - wage in advanced countries: wA = α A^(1/α) ((1−α)/(1 +δ))^(1−α)/α.

### Evolution of world population — two-stage dynamics
- Stage 1 (not all developing countries integrated; three groups: advanced, integrated-developing, unintegrated-developing):
  - Dynamics:
    - ṄA/NA = γA + p(A(1−α)/(1 +δ))1/α + i
    - ṄD/ND = γD − (p(A(1−α)/(1 +δ))1/α + i) NA/ND
  - Condition for NA/ND to increase (move toward Stage 2):
    - NA/ND > (γD − γA) / (p(A(1−α)/(1 +δ))1/α + i − 1)  (equation (1))
  - Proposition 1: If NDM < ND, then NA/ND will increase over time iff condition (1) holds; otherwise NA/ND converges to zero unless (1) holds with equality.
  - Comparative statics: condition (1) is less strict when γD is lower; γA, p, i and A are higher; and α and δ are lower.
- Stage 2 (all developing countries integrated: NDM = ND):
  - Dynamics summarized:
    - ṄA/NA − ṄD/ND = −(γD − γA) + i(1 + NA/ND) + p(1 + 1/(NA/ND))
  - If:
    - i + p − 2√(p i) < γD − γA < i + p + 2√(p i)  (equation (3))
    then NA/ND grows without bounds (roots complex).
  - If either (3) or condition (4) hold, growth without bound obtains; otherwise NA/ND converges to a steady-state given by expression (5).
  - Wages when all integrated:
    - wA = A α (ND/NA)^(1−α)
    - wD = A (1−α) / (NA/ND)^α − δ
  - When NA/ND exceeds α/(1−α), advanced countries begin producing L; thereafter wA = wD + δ and the remaining wage premium equals δ.

### Differences across countries and the development queue
- Country-specific transaction costs δc induce an ordinal queue: advanced countries import L first from developing countries with lowest δc.
- Policy and distributional implications:
  - Small reductions in an individual country’s δc can yield large payoffs for that country (move it forward in the queue).
  - Similar reductions in average δ across all developing countries produce only small global gains because the speed of “graduation” is constrained by the population in advanced countries (NA).
  - Aggregate effects require changes that alter the size of the advanced-country market (NA); country-specific reforms mainly produce country-level gains.

### Calibration, parameter estimates, and key numeric values
- Estimated transition rate proxy:
  - p(A(1−α)/(1 +δ))1/α estimated as 0.40% using 1952–2001 average (20th century average 0.37%, first half 0.34%, second half 0.40%).
- Demographic and migration estimates based on 2000–05:
  - γA = .29%
  - γD = 1.38%
  - i = 0.31%  (i excludes migration between advanced economies)
- Using these parameters and p(A(1−α)/(1 +δ))1/α = .0.40%, the right-hand side of condition (1) is 0.52, which is greater than the current NA/ND of 0.17 — implying that under baseline parameters the proportion of world population in developing countries would grow indefinitely absent parameter changes or shocks.

### Scenario analysis and sensitivity experiments
- Baseline scenario: demographic parameters as of 2000–2005; transformation average based on 1952–2001.
- Projected demographic changes: UN projections through 2050, then held constant at 2050 levels.
- Alternative sensitivity runs considered:
  - natural population growth gap halved,
  - immigration rate doubled,
  - transition rate doubled,
  - lowering δ to achieve equivalent effects.
- Convergence properties:
  - If the UN-projected narrowing of γD − γA occurs (projections held constant at 2050 thereafter), the world economy eventually reaches the prosperous steady state, but convergence is extremely slow (little change even over 100 years).
  - Dynamics improve under more optimistic parameter changes: halving the baseline γD − γA gap; doubling i; doubling p; or lowering δ.
- Large-country shocks:
  - If China instantaneously becomes advanced today, NA/ND would jump to 0.54, moving NA/ND just above the critical threshold; with baseline parameters condition (3) would hold and NA/ND would grow without bounds.
  - If both China and India became advanced, NA/ND would jump to 1.09 and induce a noticeable acceleration in the rate at which other economies develop.

### Main conclusions and policy-relevant implications
- Non-linearities and threshold effects: global development depends not only on country-specific reforms but crucially on the size of NA (the stage of the world economy).
- Individual-country reforms lowering δc can yield large country-level gains by moving the country forward in the development queue.
- Identical improvements across all developing countries yield only modest global gains because absorptive capacity is constrained by NA.
- Rapid transitions by very large developing countries (e.g., China and India) can dramatically improve prospects for other developing countries by expanding NA and altering global demand and terms of trade (e.g., rising prices for primary commodities and labor-intensive goods).
- Empirical caution: determinants of cross-country growth relationships may change as the world economy passes thresholds; countries unattractive today may become attractive later if they become among the last locations with inexpensive labor.

*Source: _wp0621 - 1.     Evolution of the Ratio of the World Population in Advanced Economies to the Population in Developing Economies; 5.     Effect of China and India Instantaneously Becoming Advanced Economies (IMF PDF).*

### 1.     Evolution of the Ratio of the World Population in Advanced Economies to the

### 1.     Evolution of the Ratio of the World Population in Advanced Economies to the Population in Developing Economies

### Population Growth in Advanced and Developing Economies from 1820 to 2000
- Coverage: population growth comparison between advanced economies and developing economies.
- Time span explicitly: 1820 to 2000.
- Reference page number: 15.

### Natural Population Growth and Net Migration from 1950 to 2005 and Projections for 2005 to 2050
- Coverage: decomposition into natural population growth and net migration.
- Historical period: 1950 to 2005.
- Projection period: 2005 to 2050.
- Reference page number: 16.

### Evolution of the Ratio of the World Population in Advanced Economies to the Population in Developing Economies Excluding India and China Under Different Scenarios
- Coverage: analysis of the ratio excluding India and China.
- Emphasis: different scenarios for the ratio’s evolution.
- Reference page number: 17.

*Source: _wp0621 - 1.     Evolution of the Ratio of the World Population in Advanced Economies to the Population in Developing Economies (IMF PDF).*

### 5.     Effect of China and India Instantaneously Becoming Advanced Economies

### 5.     Effect of China and India Instantaneously Becoming Advanced Economies on the Rest of the World

### Introduction and key mechanism
- Integration with the world economy via non-traditional exports is taken as the chief route from poverty to wealth; successful exporters generate external learning spillovers that raise transition probabilities for other countries.
- Model assumption: countries transition one-way from developing to advanced; migration is from developing to advanced countries and advanced countries restrict migration to a proportion i of their population.
- Core insight: a developing country’s opportunity to integrate depends positively on the size of the advanced-country market and negatively on the number of competing developing-country suppliers — creating a development “queue” and potential accelerating global growth as more countries become advanced.
- Long-run outcome hinges on:
  - barriers to trade (captured by transaction cost δ),
  - rate at which developing countries engaging in trade become advanced (captured via p(A(1−α)/(1+δ))1/α),
  - migration rate i,
  - natural population growth rates γA and γD,
  - initial proportion of world population in advanced countries NA/ND.

### Model structure and wages
- Two country types: advanced and developing.
- Two technologies:
  - traditional: labor produces one unit of final good (both country types equally productive).
  - modern: requires two intermediate tasks — complex task H (only in advanced countries) and simple task L (in either). Each unit of labor produces one unit of the respective intermediate good.
- Modern output: Ymodern = A H^α L^(1−α) with A>2 and 0<α<1.
- Transaction cost for producing L in developing countries: δ units of the final good, giving production cost 1+δ.
- Transition probability: in each period a developing country becomes advanced with probability p times the share of its population in the modern sector.
- Wages (stage where all developing countries integrated not enforced):
  - developing reservation wage wD = 1 (traditional sector), modern-sector developing labor must be paid this reservation wage.
  - number of developing workers in modern sector:
    - NDM = (A(1−α)/(1 +δ))1/α NA
  - wage in advanced countries:
    - wA = α A^(1/α) ((1−α)/(1 +δ))^(1−α)/α.

### Evolution of world population — two stages
- Stage 1: Not all developing countries integrated (three groups: advanced, integrated-developing, unintegrated-developing)
  - Dynamics:
    - ṄA/NA = γA + p(A(1−α)/(1 +δ))1/α + i
    - ṄD/ND = γD − (p(A(1−α)/(1 +δ))1/α + i) NA/ND
  - Condition for NA/ND to increase (move toward Stage 2):
    - NA/ND > (γD − γA) / (p(A(1−α)/(1 +δ))1/α + i − 1)  (equation (1) in the source)
  - Proposition 1: If NDM < ND, then NA/ND will increase over time iff condition (1) holds; otherwise NA/ND converges to zero unless (1) holds with equality.
  - Comparative statics: Condition (1) becomes less strict when γD is lower, γA, p, i and A are higher, and α and δ are lower.
- Stage 2: All developing countries integrated (NDM = ND)
  - Dynamics summarized by:
    - ṄA/NA − ṄD/ND = −(γD − γA) + i(1 + NA/ND) + p(1 + 1/(NA/ND))
  - If:
    - i + p − 2√(p i) < γD − γA < i + p + 2√(p i)  (equation (3))
    then NA/ND grows without bounds (roots complex).
  - If either (3) or condition (4) hold (see source), growth without bound obtains; otherwise NA/ND converges to steady-state given by expression (5).
  - Wages when all integrated:
    - wA = A α (ND/NA)^(1−α)
    - wD = A (1−α) / (NA/ND)^α − δ
  - When NA/ND exceeds α/(1−α), advanced countries begin producing L, after which wA = wD + δ and remaining wage premium equals δ.

### Differences across countries and the development queue
- Allowing country-specific transaction costs δc induces an ordinal queue: advanced countries import L first from developing countries with lowest δc.
- Small reductions in an individual country’s δc can have large payoffs for that country (move it forward in the queue), while similar reductions in average δ across all developing countries produce only small global gains because the speed of “graduation” from the queue is constrained by the population in advanced countries.
- Policy implication: country-specific reforms lowering δc can trigger large country-level growth, but aggregate effects require changes that alter the size of the advanced-country market (NA).

### Simple calibration and key parameter estimates
- Data sources: Maddison (2003) for 1820–2001; United Nations Population Division for 1950–2050.
- Classification rule: an economy is “advanced” if GDP per capita (1990 International Geary-Khamis dollars) > one-third of the “leading country” (UK for 1820–1900, US afterwards), and the country permanently remains above that threshold.
- Estimated transition rate proxy:
  - p(A(1−α)/(1 +δ))1/α estimated as 0.40% using 1952–2001 average (20th century average 0.37%, first half 0.34%, second half 0.40%).
- Demographic and migration estimates based on 2000–05:
  - γA = .29%
  - γD = 1.38%
  - i = 0.31%  (i excludes migration between advanced economies)
- Using these parameters and p(A(1−α)/(1 +δ))1/α = .0.40%, the right-hand side of condition (1) is 0.52, which is greater than the current NA/ND of 0.17 — implying that under baseline parameters the proportion of world population in developing countries would grow indefinitely absent parameter changes or shocks.

### Scenario analysis and sensitivity
- If the UN-projected narrowing of γD − γA occurs (projections available through 2050 and held constant thereafter in simulations), the world economy eventually reaches the prosperous steady state, but convergence is extremely slow (little change even over 100 years).
- Dynamics improve under more optimistic changes:
  - halving the baseline γD − γA gap,
  - doubling i,
  - doubling p,
  - or lowering δ to achieve an equivalent effect.
- Large-country shocks:
  - If China instantaneously becomes advanced today, NA/ND would jump to 0.54, moving NA/ND just above the critical threshold; with baseline parameters condition (3) would hold and NA/ND would grow without bounds.
  - If both China and India became advanced, NA/ND would jump to 1.09 and induce a noticeable acceleration in the rate at which other economies develop.
- Figure-based scenarios (as described in the source):
  - Baseline scenario: demographic parameters as of 2000–2005; transformation average based on 1952–2001.
  - Projected demographic changes: UN projections through 2050, then held constant at 2050 levels.
  - Alternative sensitivity runs: natural population growth gap halved; immigration rate doubled; transition rate doubled.

### Main conclusions and policy-relevant implications
- The model implies strong non-linearities and threshold effects: the global development process depends not only on country-specific reforms but crucially on the stage of the world economy (size of NA).
- Individual-country policy improvements that reduce transaction costs δc can yield large country-level gains by moving the country forward in the development queue; however, identical improvements across all developing countries yield only modest global gains because the absorptive capacity is constrained by NA.
- Rapid transitions to advanced status by very large developing countries (e.g., China and India) can dramatically improve the prospects for other developing countries by expanding NA and altering global demand and terms of trade (e.g., rising prices for primary commodities and labor-intensive goods).
- Caution is warranted in interpreting empirical growth determinants from country-level studies because growth drivers may change as the world economy passes thresholds; countries unattractive today may be attractive later if they become among the last locations with inexpensive labor.

*Source: _wp0621 - 5.     Effect of China and India Instantaneously Becoming Advanced Economies*

### REFERENCES

### REFERENCES

### Listed References
- Aitken, Brian, Gordon Hanson and Ann Harrison, 1997, “Spillovers, Foreign Investment, and Export Behavior,” Journal of International Economics, Vol. 43(1), pp. 103–32.
- Galor, Oded and David Weil, 1996,”The Gender Gap, Fertility and Growth,” American Economic Review,  Vol. 86(3), pp. 374–87.
- Galdón, Sánchez, José and James Schmitz, 2002, “Competitive Pressure and Labor Productivity: World Iron-Ore Markets in the 1980’s,” American Economic Review,  Vol. 92(4), pp. 1222–35.
- Grossman, Gene and Elhanan Helpman, 1991b, “Innovation and Growth in the Global Economy,” MIT Press, (Massachusetts: Cambridge).
- ———, 1995, “Technology and Trade,” in Handbook of International Economics, Vol. 3 (Gene Grossman and Kenneth Rogoff, editors), Amsterdam: Elsevier Science Publishers B.V.
- Hausmann, Ricardo and Dani Rodrik, 2003, “Economic Development as Self-Discovery,” Journal of Development Economics, Vol. 72(2), pp. 603–33.
- Kremer, Michael, Alexei Onatski and James Stock, 2001, “Searching for Prosperity,” Carnegie-Rochester Conference Series on Public Policy, Vol. 55, pp. 275–303.
- Lucas, Robert E., 1993, “Making a Miracle,” Econometrica, Vol. 61(2), pp. 251–72.
- ———, 2000, “Some Macroeconomics for the 21st Century,” Journal of Economic Perspectives, Vol. 14, pp. 159–68
- Maddison, Angus, 2003, “The World Economy: Historical Statistics,” Paris and Washington D.C., Organization for Economic Cooperation and Development.
- Parente, Stephen and Edward Prescott, 1994, “Barriers to Technology Adoption and Development,” Journal of Political Economy, Vol. 102(2), pp. 298–321.
- Quah, Danny, 1993, “Empirical Cross-Section Dynamics in Economic Growth,” European Economic Review, Vol. 37, pp. 426–34.
- Rhee, Yung Whee and Therese Belot, 1990, “Export Catalysts in Low-Income Countries: A Review of Eleven Success Stories,” World Bank Discussion Papers No. 72.
- Tamura, Robert, 1996, “From Decay to Growth: A Demographic Transition to Economic Growth, Journal of Economic Dynamics and Control, Vol. 20, pp. 1237–62.

* _wp0621 - REFERENCES_

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