p.dev't nexus

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The Population-Development Nexus: Insights from a Multi-country Simulation Model

Brantley Liddle

Massachusetts Institute of Technology

Correspondence address:

5604 York Lane

Bethesda, MD 20814

USA

[email protected]

Fax: (603) 908-6573


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The Population-Development Nexus: Insights from a Multi-country Simulation Model

ABSTRACT. To gain greater understanding of important economic-demographic linkages and

their feedbacks, we develop a simulation model that borrows from economics, demography, and

political science. Long term, indirect impacts of population stem from the assumed life-cycle

relationship between age structure and investment. Short term, direct impacts depend on

whether per capita or aggregate effects of population dominate, i.e., whether people or

investments grow faster. We find evidence of a modified Malthusian effect, i.e., countries have

higher per capita incomes when their populations are lower. However, whether population

growth is good or bad for a countrys sustainedper capita income growth depends on that

countrys human capital and technology levels.

Key words: Population and Development, International Migration, Simulation Modeling.


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1. Introduction

If the population growth debate has progressed beyond the rather polemical positions of

population growth is bad (e.g., Ehrlich, 1971) vs. population growth is good (e.g., Simon,

1981, 1986, & 1990) over the past few decades, then it has been with the emergence of a

revisionist position. The fundamental conclusion of the revisionist position is that population

growth has an ambiguous effect on development: (1) population growth and size have both

positive and negative effects on development; (2) the impacts of these effects are both direct and

indirect and vary over the time horizon used; and (3) these impacts include feedbacks within

economic, political, and social systems (Kelley, n.d. & 1988). The key to moving the

population debate forward, according to Kelley (n.d.), involves gaining a greater understanding

of important economic-demographic linkages and their feedbacks. However, many of the

popular methodologies of economics are not appropriate for gaining such understanding since

tractable economic models are too simple to consider many different interactions or feedbacks,

and since econometric analyses suffer from a number of statistical and data problems (e.g.,

Kelley and Schmidt, 1994). In addition, it is hard to differentiate cause and effect between

population growth and economic growth, unless there is an effective way to explain questions

like whether, and if so how, economic growth would have changed if population rates were

lower/higher. Thus, simulation models are particularly suited to investigate the complex

interactions in the population-development system. As Simon (1977) argues, these models

allow us to compare the results of population growth structures that have not existed.

We have developed a simulation model to examine the population-development nexus

that is both complete (i.e., economic development and population are simultaneously

considered) and closed(i.e., all important parameters change endogenously). By borrowing


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from economics, demography, and political science our model calculates production,

consumption, investment, and population growth/change. Our model allows us to consider

populations impact on per capita consumption as well as the social interdependencies among

these variables. In our model the relationship between population and development depends on

three demographic variables: population size, rates of change, and age structure. Country initial

endowments affect how these per capita-aggregate population tradeoffs develop.

Through our simulations we identify short-run costs of rapid population growth and

long-term benefits from population growth. We find evidence of a modified, or weak form

Malthusian effect, in that countries have higher per capita incomes when their populations are

lower. However, whether population growth is good or bad for a countrys sustained per capita

income growth depends on the countrys development level. Perhaps the best examples of a

Malthusian-like trap are those results that indicate the perils ofnegative population growth, i.e.,

when population aging begins to put a strain on investment. For our model, the optimum

population profile is a combination of low birth rates and a young age structure. Thus, we find

that how population grows, not just how much it grows, is important in determining its effect on

development. Finally, the addition of a simple international migration module allows us to

examine migration induced population impacts on origin, origin anddestination, and destination

countries.

The following section briefly summarizes the major arguments for positive and negative

effects of population on development, and discusses some previous simulation models. The

next three sections describe our simulation model: first, a general overview that outlines the

sequence of events in the model is presented; then, the basic modules are described, and

important equations shown; finally, some results from the Base Case run are displayed and


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discussed. Section 6 presents the effect of different combinations of initial birth and death rates

and age structure on our models developed and developing countries, specifically, high growth

and young age structure on the developed countries, and low growth and advanced age structure

on the developing countries. Section 7 presents the results of a model experiment where

population structure and rates change via international migration. Section 8 concludes the paper

with a summary of the findings.

2. Background

2.1 Population growth debate

Population growth could have a negative impact if mouths increase faster than the

productivity of hands (Malthusian effect); if the dependency of a young population lowers

investment (youth-dependency effect); or if the average productivity of physical capital and

natural resources are lowered via diminishing returns (resource-shallowing effect). In

addition to the youth-dependency and resource-shallowing effects, Coal and Hoover (1958)

argue population growth could lead to an investment-diversion" effect, where investment is

shifted from more (immediately) productive areas like physical capital to (hypothesized) less

growth-oriented areas like education.

Population growth could have a positive impact if it stimulates the growth of other

factors, like physical capital investment or technology (resource-augmenting effect); if it

stimulates aggregate demand (size effect); or if there are economies of scale in either

production or investment (e.g., technology or physical capital). Some reasons for a less

pessimistic outlook on population growth have to do with more recent beliefs on the source of

economic growth--for example, the greater importance placed on human capital vis--vis natural

resources and physical capital (Kelley, n.d.). Also, endogenous technical change theories have


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led population optimists, like Simon (1986), to argue that population growth can stimulate

technical advancement as scarcity encourages innovation (the demand side) and that more heads

means more Einsteins (the supply side). Also, contrary to the youth-dependency effect,

population growth could have a positive effect on savings if a life-cycle model is considered

(e.g., Modigliani, 1970). In addition to financing children, families save for their old age; thus,

population growth could increase savings if it leads to a higher proportion of young workers to

retirees. This last (positive effect) is often not included in population growth-development

analyses, in part, because population is seen as a developing country problem, whereas

population aging is a largely, developed country phenomenon. Recent, empirical research on

the balance between positive and negative effects of population on savings has been mixed.

Williamson and Higgins (1997) found that demographic transition led to higher savings in East

Asia; however, Lee et al. (1997), who also examined East Asia, found that demographic

transition first increases savings, then decreases it.

2.2 Simulation models

Two of the most famous simulation models treating population and development support

the extreme ends of the population debate, i.e., "population growth is bad" vs. the "population

growth is good". One very pessimistic model with regard to population growth (often described

as Malthusian) isLimits to Growth (Limits) by Meadows et al. (1972). Limits was

enthusiastically accepted by many in the scientific community, but was heavily criticized by

economists (particularly harsh in their criticism were Nordhaus, 1973 and 1992, and

Beckerman, 1972). Limits was criticized for, among other things, its failure to allow

substitution between abundant and limited resources (there was one necessary, nonrenewable

natural resource); lack of prices to allocate production and consumption decisions and warn of


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shortages; failure to allow for investments in technology, or resource exploration; and failure to

distinguish between developed and developing countries (it modeled the world as one

economy). In 1992 the Meadows group (Meadows et al., 1992) revised theLimits model by

addressing some of the above concerns. However, as Meadows et al. acknowledge, the models

behavior mode is still "overshoot and collapse" because of the programmed absolute limits on

technology, substitution, natural resource stock, and the earths ability to absorb pollution;

hence, Nordhaus (1992) criticism of the model as still tautological: when amount of, and

substitution possibilities away from, essential factors are limited, limited growth is guaranteed.

Simons (1977) model is much closer in spirit to ours than theLimits models are. His

model contains elements found in other population growth models (e.g., Coale and Hoover,

1958, and Enke et al., 1970), like diminishing returns and a negative effect of dependency on

investment. However, Simon also added, other elements that are generally agreed to be

important in qualitative discussions but that are omitted from previous models like a demand

effect on investment and an accelerator investment function (as opposed to a constant-

proportion-of-output function in Coale and Hoover). Simon found that a positive population

growth leads to higher per capita output in the long run (120 to 180 years) than a stationary

population, but in the short run (60 years), the stationary population performs slightly better. A

declining population does very poorly in the long run. A population doubling in 50 years

performs better in the long run than both a population doubling in 35 years and a population

doubling in 200 years. One criticism of Simons result is that what Keynes said of the long run

is true of Simons short run, i.e., according to Sirageldin and Kater (1982), Not many

developing countries could afford or be able to wait that long for improvement.


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Our model has a flexible economic system, world trade, and productivity-enhancing

investments. In addition, it has a complex, inter-linked demographic system that allows us to

examine a number of direct and indirect, short and long term impacts of population on a diverse

set of countries. More specifically, population feeds back into the model modules in several

ways:

1. population is a divisor for per capita measures like per capita GDP and

human capital;

2. a large graduating classs human capital has a greater impact on the total

work force;

3. population influences total GDP and, thus, investment in technology and

physical capital (where the total amount invested matters);

4. labor is a production factor, which can be grown faster and, in some

circumstances, cheaper than physical capital; and

5. population affects the share of GDP for investment directly through age

structure (young andold) and indirectly through per capita GDP.

3. Overview of Model

The model system comprises, for each of seven significantly different countries, the

following sets of relationships: (1) production of three kinds of commodities; (2) patterns of

international trade; (3) determination of consumption and investment; (4) allocation of

investment resources over four investment categories (physical capital, human capital, natural

resource capacity, and development of new technology); and (5) induced changes in population

growth and age distribution in each country. The analytical sequence of events in the model is

as follows: at the start of the initial period, each country has a given labor force, level of human


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capital, stock of physical capital, natural resource capacity, and state of technology. In each

country, there are three production sectors: resource intensive industry (producing a final good),

resource nonintensive (service) industry (also producing a final good), and natural resource

extraction industry (producing an intermediate good). There is also a set of international trade

prices, and a set of locally determined prices for labor and physical capital services. Prices,

production costs, and demand preferences determine exports and imports, and thus per capita

GDP in each country.

Consumers choose their consumption mix (between the two final goods) to maximize

their utility, derived from demand functions. The national optimal consumption mix is based on

national utility maximization reflected in consumer goods demand. Since we have no interest in

specific consumption preferences, we assume these demand functions all have unitary price and

income elasticities; thus, budgetary allocations to these goods are constant and, for simplicity,

are equal for the two goods in all countries.

Each country next determines the split between consumption and investment for this

total trade-modified outputviaa Keynesian consumption-investment function, modified bysocial provision for rates of population dependency. A national investor maximizes present

discounted value of all investments performed in each period, based on the marginal

productivity of different investment types. Each type of investment generates a lifetime

marginal value productivity via sectoral production functions and profit-maximizing levels of

output, which are transformed into present discounted values via a single social rate of discount

specified for each country as a function of its per capita GDP. Relative rates of return form the

basis of allocation. These investments endogenously change the following periods input

endowments.


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The level of per capita income and human capital affect population fertility and death

rates, and therefore set the stage for subsequent changes in the age distribution of the

population. Thus, at the end (and as a result) of this sequence of events, each country has a new

set of input endowments, including population level and age distribution, and a new set of

prices. In addition, there is a new set of international trade (final goods) prices. In this manner

the whole global system will generate 50-period (or year) national trajectories.

Assumed differences in our stylized countries have been chosen to show the importance

of initial conditions on influential variables in generating different long-run outcome

trajectories. The country initial conditions are based on judgmental stereotypes of Rich,

Middle, and Poor countries, as enhanced by empirical data on country factor endowments;

however, only the age structure and birth and death rates are taken directly from the empirical

data of specific countries. Since the various levels of development or per capita GDP (in our

model and empirically) are essentially definedin terms of technology, human capital, and

physical capital per capita, differences among countries at each level of development refer to

population size and resource (land) endowment. Thus, there are two Rich countries, one with

larger total population and higher resource endowment per capita; three Middle countries,

varying in population, resource base, and population growth; and two Poor countries, differing

in population size. The two Poor countries have the greatest resource endowment, followed by

Middle3, then Middle2 and Rich2; Middle1 and Rich1 have the smallest resource endowment.

Table 1 shows the initial country endowments (these data, as well as the simulation output, are

stylized and in generic units applicable to the specific variables they describe, e.g., units of

physical capital, production, consumption, etc.).

Insert Table 1


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The initial age specific birth and death rates and age structure are from Keyfitz and

Flieger (1990). The Rich countries are modeled after the European Community (EC) circa

1980, and thus, have low birth rates and advanced age structures. The three Middle countries

use data from Venezuela in 1985, Chile in 1980, and Taiwan in 1985, and thus, vary in the

degree to which they have undergone demographic transition. The Poor countries use data from

Guatemala in 1985, and thus, have high birth rates and young age structures. The left half ofTable 2 shows the initial total fertility rates and crude age structures used in the model.

Insert Table 2

4. Model Modules

4.1 Production Module

As indicated above, there are three production sectors. Final goods and

processed natural resources are tradables, so their prices are the same for all countries; wage and

rent rates are determined locally. Because labor (but not capital) is completely mobile (within

each country), countries can shift production each period for competitive advantage. Since the

producers are treated as profit maximizing price takers, and since physical capital is fixed (in the

short term), the amount of each good produced by each country is a straight-forward

optimization calculation. The local wage rate for each country clears the labor market each

period. At the end of each period each countrys rent rate on physical capital is updated by

recalculating the average marginal value product of capital for the three sectors, weighted by the

total amount of capital in each sector. Lastly, world prices for the two final consumption goods

and the intermediate, natural resource good are calculated for use in the following period. These

prices are calculated iteratively by equating forecasted world supply and demand. This

(arguably simplified) solution method results in actual global supplies and demands that equate


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within +/- one percent. The national aggregate adjustments in equilibrium have many lags,

constraints, and uncertainties, making for varied speeds of adjustment. These adjustments are

too complex to model simultaneously; so we simplify by adjusting prices at the end of each

period, and leaving the direction of behavioral adjustments to these new prices to the next

period. Adjustments, therefore, lead to continued temporal changes--a main focus in the model.

The production functions for the two final consumer goods sectors, with all variables and

parameters specific to each period t, are:

Resource nonintensive service sector, S:

QS = AST (HLS)bls

KSbks

RSbrs

(1)

Resource intensive industry sector, I:

QI = AIT (HLI)bli

KIbki

RIbri

(2)

Where:

QS , QI : output for two sectors

AS,I : scaling factors to get initial positive profits in all sectors (currently set to 1)

T : input-neutral technological improvements (same for all sectors)

Lx, Kx, Rx (x = S,I) : labor, capital, natural resource input for individual sectors

H : human capital factor (same for all sectors)

bkx, blx, brx (x = s,i) : productivity exponents for three inputs and two sectors

The production function for the resource extraction sector, also specific to each period t, is:

( ) RHLaATKR nrRkr

R= (3)

Where:

R : amount of extraction

a : scaling factor to get initial positive profits (currently set to 1)


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A : country specific factor representing land endowment

T : input-neutral technological improvements (again, same for all sectors)

LR, KR : labor and capital input

H : human capital factor (again, same for all sectors)

nrkr , : productivity exponents for labor and capital

R : 8 year moving average of past extraction

: drag parameter based on the extent of recent extraction (less than -1).

The drag parameter () allows for heavy recent production to increase rapidly the cost of

further extraction, as too much extraction degrades the resource base. This parameter is

constrained to be less than -1.0 because we believe past extraction should have an increasingly

negative effect on productivity. This increasing cost to extract can lead to increasing prices for

the natural resource, despite its inexhaustibility. Lowering extraction temporarily reduces this

drag. The land endowment coefficient can be increased via investment.

All the production functions are assumed to have constant returns to scale. The

exponents used in the model were estimated from empirical data of factor shares using The

OECD Input-Output Database (1995). The resource intensive industry is less labor intensive

than the resource nonintensive one. Table 3 shows the exponent values used in the simulation

model (our results are similar to a number of other studies, e.g., Bernard and Jones, 1996;

Duchin and Lange, 1992; and McKibbin and Wilcoxen, 1995).

Insert Table 3

4.2 Investment Module

The share of a countrys total GDP allocated for investment depends positively on the

countrys per capita GDP relative to the initial per capita GDP of the richest country (a measure


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of a minimum consumption necessity), and negatively on the countrys young (ages 0-14) and

aged (65+) dependency (i.e., the ratio of those cohorts to the total population).

c = 0.34 + -0.071 ln(GDP/GDP0R

) + 0.7 xpop(0-14) + 2.1 xpop(65+) (4)

where c is the fraction of GDP for consumption, GDP is per capita GDP, GDP0R

is the initial

per capita GDP of the Rich country,pop(0-14) is the fraction of population aged 0-14, and

pop(65+) is the fraction of population over 65. The GDP ratio term as well as c are constrained

to be less than or equal to one.

The coefficients in Equation 4 were derived econometrically from panel data

(observations in 1985 and 1990) from World Bank (1994). All of the coefficients are

statistically significant at least at the five percent level (the adjusted R-squared for the regression

was 0.42). We normalize the per capita GDP term (1) to render its impact indifferent to the

magnitude of GDP and, thus, appropriate for the stylized values used in the simulation model,

and (2) to lessen some of the regression problems common when the dependent variables are a

combination of rates and levels. These results are similar to other econometric models, like

Kelley and Schmidt (1994) and Mason (1987 & 1988); however, we attribute a greater drag on

investment to aged dependency. Our formulation gives Middle countries (with per capita GDPs

about one-fourth of Rich countries) an opportunity to invest, but gives Poor countries (with per

capita GDPs 1/20 or less of Rich countries) very little chance to catch up.

The one exception to the model's lack of behavioral sensitivity occurs when the

coefficients in Equation 4 are adjusted (by one standard deviation from their means) in the way

that constrains investment the most. Under this scenario the rich countries' per capita GDP

displays "growth and then collapse," as their share of income for investment eventually reaches

zero (driven by their population aging).


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Each type of investment has a distinctive production function and cost function. From

these functions rates of return are calculated for each investment type. These different rates

determine the percentages of the total investment pool that are allocated to each investment

type. The resulting investment mixes differ for the various countries because of their different

circumstances in each period. Each countrys discount rate, at the end of each period, is

adjusted linearly for changes in per capita GDP. Initially, the Rich countries discount rate is

five percent, the Middle countries eight percent, and the Poor countries eleven percent.

Each production sector has its own physical capital allotment, which is increased

through investment and decreased by depreciation (set at five percent a year). Physical capital

created (by investment) at the end of one period is considered operational (included in the

production function) in the following period. The rate of return on physical capital for each

sector depends on the marginal value product of capital for that sector.

As stated previously, technology enters the production functions as a constant multiplier.

There is a ten period lag on technology investment, i.e., the technology multiplier is increased

based on technology investment ten periods ago, but the technology multiplier does not

depreciate if investment ceases. The increase in the technology multiplier is a logarithmic

function of the five-year average of technology investment (ten periods ago). The five-year

moving average reflects the fact that innovation is an interactive process that takes time to bear

fruit, i.e., labs must ramp up. Using a logarithmic relationship both bounds the increase in the

technology multiplier and agrees with available data. Data in Lederman (1987) shows a

logarithmic relationship between both nondefense R&D spending and technology intensive

exports, as well as nondefense R&D and total scientists and engineers for a number of

developed countries.


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A countrys human capital multiple,H, is based on the average per student spending on

education for the work force. Thus, the newHfor a country is the weighted (by population size)

average of theHof the graduating class and the currentHof the workforce. TheHof the

graduating class is based on the average per student spending (i.e., per student human capital

investment) for the class over their 12 periods in school. Hence, for human capital investment

both time lags and age structure are important. A one period increase in per student spending

will likely have a marginal effect on the graduating classsHsince it will be averaged together

with the per student spending for the previous 11 periods. Also, a graduating classsHhas a

greater impact on the countrysHas a whole when the graduating class is large relative to the

work force. In addition, the life of a human capital investment is limited by the life

expectancy of the graduating class.

Investment in the resource base increases land endowment,A. This investment is

analogous to exploration, but is limited by original land endowment and the sum of past

additions to land endowment (via rapidly diminishing returns); thus, countries with small

original land endowments but large amount of investment funds could not end up being the

major resource producing country. Finally, there is a five period lag between investment in

resource replenishment and increases to land endowment.

4.3 Population Module

The mortality rates for infants (0-1), children (1-5), and the aged (approximately 60 and

up) are updated every five periods according to changes in per capita GDP (negatively) and time

(negatively). Fertility is adjusted at five year intervals according to infant mortality (positively

affected) and human capital (negatively affected). Aging is performed based on one year

cohorts, i.e., instead of one-fifth of a cohort moving to the next one, the amount of people at


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each age is known. The school age population consists of 6-17, and the working population

consists of 18-64.

Although explicitly modeling population by the cohort method is certainly important, the

econometrically derived coefficients that adjust mortality and fertility rates have little impact (of

course, the individual countriesinitial population parameters and the ways population feeds

back into the model are also very important). Changing the coefficients in the fertility and

mortality rate adjustment equations by one standard deviation (or more in some cases) from

their means had a negligible impact on per capita GDP and only a small impact on total

population itself. Final populations for the various countries differed by only five percent or less

between the two sets of extreme settings (i.e., +/- one standard deviation), and final age structure

varied hardly at all. In fact, changing model parameters that lead to more income growth in the

poor countries had a much greater impact on the poor countriespopulations.

5. Base Case

Model behavior in the Base Case is characterized as divergence of welfare (or per capita

consumption) among development levels and "invest and you will grow". Both Rich countries

and all the Middle countries experienced per capita GDP growth; however, the gap between

Rich and Middle countries increased over time. On the other hand, the two Poor countries

experienced little per capita improvements. Initially, the Poor countriesconsumption levels

were too low to allow for much investment, and their continued, rapid population growth only

exacerbates this situation. In other words, the investment-population interaction creates a

poverty trap from which these countries are unable to extricate themselves. Thus, the motivation

for the population experiments discussed in Section 6.2 is to provide the Poor countries with

population growth slow enough so they can grow their economies faster than their mouths.


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The results from the Base Case show some indication of the long-run consequences of

negative population growth. The Rich countries and Middle3 saw their per capita GDP growth

slow down in the later periods because, as those countries aged, they invested a smaller share of

their GDPs. The two Rich countries total investment pool began to fall in Period 40, and

Middle3s in Period 36. Middle3s investment share of GDP peaked in period 21, at the highest

share of investment for any country, and then fell rapidly to an investment share equal to the

Rich countries'. The lower investment levels led to declining physical capital stocks and slowing

down of technology growth--both of which require investments of high aggregate levels, not

high per capita levels (like human capital investment). These three countries were able to sustain

per capita GDP growth in the late periods, despite lack of investment, primarily through the

decline in their total populations. Indeed, if the model were run longer (80 to 100 periods), lack

of investment would cause stagnated and then eventually declining per capita GDP in these

countries. Thus, the motivation for the population experiments discussed in Section 6.1 is

twofold: (1) to determine if higher initial endowments allow countries to grow per capita GDP

in the face of rapid population growth (and thus, avoid the poverty-trap discussed above); and

(2) to determine if some population growth in the rich countries will make their per capita GDP

growth more sustainable long-term.

The negative impact of aging on investment discussed above is seen most dramatically

in Figure 1, which shows the declining percentage of GDP used for investment for the two Rich

countries and Middle3 as their populations age. The trajectories of the two Rich countries were

right on top of one another since their population structures and rates of change were identical.

Middle3s curve in Figure 1 reflects that country's rapid population transformation. The extent

to which the countries undergo aging can be seen at a glance in Table 2 (introduced previously),


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which shows the initial and final total fertility rate and crude age structure of each country.

Middle1 and Middle2 had fairly even population growth throughout, and thus, sustained

reasonably high and steady fractions of investment (although Middle2s investment percentage

began to drop in the later periods because of aging). Again, because of their low per capita

GDPs neither Poor country had much investment. The shapes of the Poor countries trajectories

were identical, but only Poor2s (higher because of its larger per capita GDP) is shown.

Insert Figure 1

An other result from the Base Case germane to this discussion involves the fates of the

Middle countries. The three Middle countries, which all had essentially identical initial per

capita endowments, but different population profiles, comprise a population experiment in

themselves. Both Middle2 (with a lower population growth than Middle1) and Middle3 (with a

much lower population growth but a larger initial population (1.5 times) than Middle1) had final

per capita GDPs double that of Middle1 (20 and 21 to 10), as well as higher human capital.

Table 4 shows the final endowment stocks and per capita GDP for all countries in the Base

Case.

Insert Table 4

A large population has the benefits of a larger labor force (one of the production factors),

relatively lower wage rates, and a larger investment pool, which is important for physical

capital, technology, and land endowment investments. Middle1s final endowment stocks

emphasize the difference between how total and per capita GDP influence investment.

According to Table 4, Middle1 passed the other two Middle countries in total physical capital

and stayed fairly close in technology, but fell behind in human capital. Because of its young age

structure and high total GDP, Middle1 had a sizable investment pool, but its per capita


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population growth was too great to achieve the per capita GDP growth or human capital level of

the other two Middle countries (which had much lower population growth). Thus, since the

more populated Middle1 was not able to catch or keep up with the other Middle countries in per

capita measures there is some evidence of a Malthusian effect.

6. Population Growth Experiments

6.1 Rich countries and population growth

The first of the two sets of population growth experiments involves the Rich countries.

Four different population scenarios were run for the Rich countries:

Scenario A: Rich country initial age structure with Middle1 initial growth (i.e.,

fertility and mortality) rates

Scenario B: Middle1 initial age structure and growth rates

Scenario C: Poor country initial age structure and growth rates

Scenario D: Middle1 initial age structure with Rich country initial growth

rates.

The final period results are summarized in the following two tables. Table 5 shows the

final endowment stocks and total investment pools for the two Rich countries under the four

scenarios, and Table 6 shows the final age structure and crude population growth rates for the

four scenarios (these data are the same for both Rich countries).

Insert Tables 5 & 6

The Rich countries experienced per capita GDP growth under all four scenarios, and this

growth, unlike in the Base Case, showed no signs of slowing down. Scenario D (the lowest

population growth scenario) had the greatest, by far, per capita GDP growth, and finished with

the highest per capita GDP. However, the Base Case (where population declined) finished with


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the second highest per capita GDP. On the other hand, Scenario C lagged behind the others in

per capita GDP from the beginning. Figure 2 shows the paths of per capita GDP for Rich1 under

the four population growth scenarios and the Base Case (again, although the numbers are

different, the shapes of the curves are the same for Rich2). The younger age structure solved the

Rich countries primary problem of a declining share of GDP going toward investment. In three

of the scenarios (B, C, and D) the investment share of GDP leveled off at a fairly high value (all

higher than in the Base Case), and in Scenario D the share, although falling, was considerably

higher than in the Base Case.

Insert Figure 2

All the population growth scenarios produced higher aggregate GDP than in the Base

Case; they all also produced continuously growing aggregate GDP, unlike in the Base Case

where aggregate GDP leveled off. Indeed, two scenarios (B and C, the highest population

growth scenarios) had the steepest aggregate GDP growth--significantly higher growth than the

Base Case.

Not surprisingly, Figure 3 displays larger investment pools for Rich1 in the four

scenarios than in the Base Case (again, the curves for Rich2 are the same, only the numbers are

higher).

Insert Figure 3

Indeed, the aggregate investment pool continued to increase in every scenario except for D (the

scenario with the highest per capita GDP growth), where it fell slightly in the last periods. The

(aggregate) investment pool path for the Base Case shows evidence of the long-run impact of

negative population growth discussed in the previous section. The stalled and then declining

investment pool indicates the beginning of a problem for the aging Rich countries. (Again, total


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investment begins to decline because aggregate GDP levels off, and population aging causes a

smaller share of GDP to be invested.) The reason per capita GDP has not (yet) begun to decline

is that the population is also declining.

The last column in Table 6, which indicates the percentage population growth between

the first and last periods (population declined in the Base Case), shows the importance of initial

age structure to population growth. Scenarios A and B have the same initial growth rates, but

population grew much less under Scenario A, which has a more advanced initial age structure.

Also, in Scenario D the populations grew despite having the original Rich country growth rates

(total fertility less than two), because the initial age structure was so young.

Beyond dependency ratios effect on investment (perhaps, the most important element in

the model), population impacts the model through differences between aggregate and per capita

variables. Both Rich countries benefited from the aggregate effect of population growth (higher

aggregate GDP) since their investment pools and physical capital levels were considerably

higher in all four scenarios than in the Base Case. Rich1 finished with a higher land endowment

in Scenarios B, C, and D, and a higher technology level in Scenarios B and D, than in the Base

Case. Rich2 finished with a higher land endowment in Scenarios B, C, and D, and a higher

technology level in Scenarios A, B, and D, than in the Base Case.

The per capita impacts of population growth, however, were more complex. In

Scenarios A and B the Rich countries finished with nearly the same per capita GDP as in the

Base Case. Yet, as shown in Figure 2, the scenario with the highest per capita GDP growth by

far, Scenario D, had the lowest population growth, and the scenario with the lowest per capita

GDP growth, Scenario C, had the greatest population growth. In Scenario B, one with high

population growth, the Rich countries finished with higher human capital levels than in the Base


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Case; here, the weighting effect of a larger graduating class ability to raise the overall human

capital level for the entire work force compensated for the per capita effect of having to spend

more in aggregate to achieve any specified per student level of spending. But in Scenario C,

which used the Poor country growth rates and age structure, final human capital levels were

lower than in the Base Case, as the per capita effect overwhelmed the weighting effect.

The Rich countries initial advantages in technology, human capital, and physical capital

meant that having the population growth rates of Middle1 (which had the lowest per capita GDP

growth of the Middle countries) had little effect on the Rich countries' human capital growth.

The Poor countries higher population growth rates appeared to be too great, however, although

the Rich countries still experienced GDP growth. Scenario D, which combined low birth rates

with a young age structure (similar to the situation in China), was an ideal situation for the Rich

countries since it combined the benefits of both low and high population growth (i.e., low

divisor growth for per capita measures and low dependency ratios, which insure high investment

levels).

6.2 Poor countries and population growth

The second set of experiments involves model runs with different population growth

conditions for the Poor countries. Two different population scenarios were run for the Poor

countries:

Scenario I: Poor country initial age structure with Rich country initial growth rates

Scenario II: Rich country initial age structure and growth rates.

Both Poor countries achieved much greater per capita GDPs under the two slower

population growth scenarios than in the Base Case, and per capita GDP increased throughout the

runs; Poor2 did particularly well, achieving approximately the initial Rich country per capita


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GDP both times. Poor2 finished with a per capita GDP of 7.8 in Scenario I and 6.5 in Scenario

II, compared to 1.5 for the Base Case; Poor1s final period results were 5.5, 3.3, and 0.9,

respectively. Under Scenario II both Poor countries experienced a slight population decline

between the first and last periods, whereas their populations increased by about 50 percent under

Scenario I over this period. In the Base Case the Poor countries populations increased nearly

five fold over the 50 periods. Table 7 shows the final endowment stocks, investment pools, and

per capita GDP for the two Poor countries under the two scenarios and the Base Case.

Insert Table 7

Under Scenario II, however, the improvement seems almost entirely attributable to the

per capita effect (simply having smaller populations). Indeed, in most aggregate measures (e.g.,

physical capital stocks, land endowment, technology, and investment pool) the countries

finished with nearly the same as or less than in the Base Case. However, in Scenario II both

countries finished with lower aggregate GDPs than in the Base Case (the Base Case overcame

Scenario II in period 34 for Poor1 and in period 40 for Poor2), and by the end of the run the

investment share of GDP and the investment pool had dropped to the point where they were

being overtaken by the Base Case.

On the other hand, in Scenario I (a population profile similar to Scenario D, the high

GDP growth case for the Rich countries), there was evidence of aggregate as well as per capita

growth for the Poor countries. Not only did per capita measures like human capital and per

capita GDP improve relative to the Base Case, but there were much higher final levels of

physical capital (except for resource nonintensive capital in Poor2), land endowment, and

technology. In Scenario I both countries had significantly higher aggregate GDP, a much greater


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share of GDP going toward investment, and thus, much larger investment pools than in the Base

Case.

The lack of aggregate growth under Scenario II is important for several reasons. First,

although the countries achieved much greater levels of per capita consumption, by such

measures as infrastructure (i.e., physical capital) and technology, they are still

"underdeveloped". Second, much more so than with the Rich countries under population

decline, the Poor countriessustained per capita income growth seems particularly vulnerable

given their low levels of many productive endowments combined with a falling investment pool.

Third, the relative low levels of investment under Scenario II leads, in our rather simple model

of economic structure, to even less diversity in production than under the Base Case for the

smaller Poor country. Under Scenario II the two countries specialized, nearly exclusively, in

natural resource extraction, while in the Base Case both countries developed a resource

nonintensive industry. In fact, in both countries, resource nonintensive production and physical

capital investment began to decline at the same time their total populations reached a plateau

and then fell (beginning in periods 16-24). It appears that the natural resource extraction

industry is so superior to the two final goods industries that, when the labor pool is not too large,

the extraction industry can bid up the wage rate to a level at which the other industries cannot

produce profitably. Under Scenario I both countries did experience some population growth,

and Poor1 (the larger Poor country) had a growing resource nonintensive industry throughout

the run (which finished at a much higher level of production than in the Base Case). However,

Poor2 again concentrated virtually entirely on extraction (although Poor2 did produce more of

the resource nonintensive good than in Scenario II). Poor2s work force was still small enough

that the extraction industry, made more profitable by higher technology and human capital,


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could employ the entire country. In other words, Poor2 had a comparative advantage in the

extraction industry (a large natural resource endowment), but with a small population lost its

comparative advantage in the resource nonintensive industry (a low wage rate), as the export

demand for the natural resource drove up its wage rate.

7. International Migration

The population growth scenarios presented in Section 6 are rather artificial. A more

policy-oriented way for countries to alter their population profiles would be through

international migration. Indeed, international migration is sometimes defended as a way to

address the population imbalance problem, i.e., the imbalance between the rich, small,

declining, and aging populations of the developed world and the poor, large, growing, and

young populations of the developing world.

To examine the effects of migration-induced changes in countries populations a simple

migration module was added. It is assumed that the motivation for a workers migrating is to

maximize his human capital adjusted wage. The human capital adjusted wage is the countrys

wage rate divided by its human capital multiple. This operation reflects the fact that lower

skilled immigrants expect lower wages than the higher skilled indigenous population. In

addition, migrants are assumed to come only from the 20-35-age cohort and be evenly split

between men and women. Besides the obvious impacts of a larger and younger population,

migrants affect their host countries in more subtle ways. Migrants bring with them their

countrys human capital multiple and fertility rates, thus affecting the host countrys (through a

simple weighted average).

The direction of migration will be from countries with a lower human capital adjusted

wage to countries with higher ones. The destination country of the migrants is determined from


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a logit model. Besides the relative weighted wage, migrants are attracted to countries where

there is a history of past migration from their country and their cultures are similar (as measured

by a ratio of the countries respective human capital and technology multiples and their total

fertility rates). Migrants are discouraged from a particular host country if that country makes an

effort to restrict their migration. Countries restrict migration when past migrants are large

compared to the indigenous work force, the population density is high (as measured by the

population divided by the initial natural resource endowment), and the prospective migrants

culture is very different from their own. Migration is encouraged when a host countrys retired

population is large relative to its total population.

To calibrate and test the limits of the new migration parameters (as was done for each

model module earlier), a series ofnested, two-level, full andfractionalfactorial experimental

designs were used. Factorial designs allow study of the effects of changes in levels of

independent factors as well as interaction effects. This method is described in detail with

examples in Schmidt and Launsby (1992). The magnitude of an effect is calculated by taking

the difference in the average of some model output (usually per capita GDP) for the runs

containing low values and for the runs containing high values of the factor. This factorial

analysis showed two parameters to be by far the most important. One of these parameters is the

maximum percent of people migrating each period, i.e., given a very large difference in adjusted

wages, the maximum percent of the 20-35-age cohort a country (or our model) will allow to

leave. The other important parameter is thepercent of migrants remaining in the system.

Because of the limited number (relative to the real world) of destination countries in our model,

we believed that all migrants could not be accounted for without rather extreme changes in

population occurring. Thus, we allowed the model to be open in this one respect: only a certain


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percentage of migrants will actually find their way to one of the other six countries; others will

simply be lost.

Another two-level, full factorial experiment was performed on only these two

parameters. Table 8 shows the experimental design. The (-) sign corresponds to the low setting

for a parameter, and the (+) sign corresponds to the high setting. For thepercent of migrants

remaining in the system (% In System, in the table), the low setting is 0.05, and the high setting

is 0.50; for the maximumpercent of people migrating each period(Max % Migrating) the low

setting is 0.05, and the high setting is 0.40. Table 9 shows the resulting final period per capita

GDP and population for each country in each of the four runs.

Insert Tables 8 & 9

This stylized migration tends to be a good strategy for the individual migrants

themselves, but not necessarily for the countries; migration is particularly damaging for origin

countries. Migration impacts the system most when % In System is set high (thus, there is a

lot of in-migration) and Max % Migrating is set high (thus, there is a lot of out-migration).

Conversely, in Run 4 where both parameters are set low, not surprisingly, migration has little

impact on the system, and thus, the results are essentially the same as for the Base Case. The

Rich countries do experience the benefit of a younger population leading to a higher percent of

GDP going toward investment; indeed, for Run 1 this percentage never dropped below 20

percent. Yet, per capita GDP is much higher for the Rich countries in Runs 2 and 3 where they

experience much less in-migration. Migration impacts the Rich countries both directly and

indirectly through gradual assimilation, as discussed above. For example, in Run 1 Rich1s

final period total fertility rate is more than twice as high as the Base Case (3.09 to 1.48), and its

final period human capital is 5.29 compared to 7.2 in Base Case. Again, this lower human


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capital is not simply a result of a larger population, but a reflection of having to assimilate

migrants with lower human capital. Indeed, in the highest population growth scenario discussed

in the previous section (scenario C), Rich1s population was more than a third higher but

finished with a human capital of 6.0. Finally, as a destination country for many origin countries,

migrations effect on the Rich countries is a function of the prospects in the Middle countries.

In scenarios where the Middle countries have lower incomes, more of the Rich countries in-

migrants come from these middle countries and thus are closer (than migrants from the Poor

countries) to the Rich countries indigenous fertility rates and human capital.

Origin countries did not realize any of the benefits of lower populations or population

growth seen in the scenarios of Section 6.2. These benefits were not realized because of the

assumed nature of migration: a high number of out-migrants meant the remaining population

was skewed against investment, i.e., since 20-35-year-olds were leaving, youths and retirees

made up a greater share of the population. This phenomenon was particularly devastating to the

Middle countries in Runs 1 and 3, where the influx of peoples from the Poor countries could not

off-set the effects of their own out-migration. In these runs, the Middle countries investment

pools went to zero as their populations declined and the share of aged increased, despite having

total fertility rates above replacement value. For example, in Run 3 roughly 11 percent of the

major birth cohort (or approximately two percent of the total population) left Middle1 each year.

As a result, the workforce became only 46 percent of the population, while the aged became 13

percent, causing the share of (a declining aggregate) GDP for investment to fall below five

percent; meanwhile, the total fertility rate fell only to 2.93 (from 3.58).

8. Conclusions

Three aspects of population affect development: population size, fertility and death rates,

and age structure. Age structure is particularly important in our model since population aging


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30

reduces the share of GDP that goes toward investment. Also, age structure along with fertility

and death rates determine whether and how the aggregate population grows.

The long term and indirect impacts of population in our model mostly stemmed from this

relationship between age structure and investment (i.e., the life cycle model). Short term and

direct impacts mostly had to do with whether per capita or aggregate effects of population

dominated. Population growth may make per capita income or human capital growth more

difficult by increasing the capita, but since labor is a productive input, it can lead to greater

aggregate GDP. This larger aggregate GDP leads to a larger investment pool, which, in turn,

can lead to more physical capital and a higher technology level (investments dependent

primarily on the total amount committed), and thus, eventually higher per capita GDP.

Whether population growth was good or bad for a countrys sustained per capita income

growth depended on the countrys development level, or more specifically its human capital and

technology levels. The Rich countries performed well (their per capita income level grew)

under all population growth scenarios, and this income growth appeared to be more sustainable

(because of the younger population) than in the Base Case where population aging began to put

a strain on investment. However, in general the scenarios with the lower populations had the

higher per capita incomes. On the other end of the spectrum, the Poor countries performed

much better than in the Base Case with the Rich countries population profiles (of negative

population growth) simply by lowering the number of heads, and in one scenario performed

better on an aggregate level too.

Thus, the model supports a modified, or weak form Malthusian effect, in that we found

little evidence of (positive) population growth dooming a country; however, we found plenty of

evidence of countries performing better (on a per capita basis) when their populations were


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31

lower. One might find evidence of a traditional or strong form Malthusian effect in the Poor

country population experiments (Section 6.2), where a scenario (II) with (slightly) negative

population growth produced considerably higher per capita GDP than the Base Case. However,

another scenario (I) with population growth (albeit much lower than in the Base Case)

outperformed the negative population growth scenario in terms of both per capita and aggregate

measures.

Perhaps the best examples of population causing a "doom" scenario were those results

that indicated the perils ofnegative population growth. In the Base Case, the population decline

and aging in the Rich countries and Middle3 led to declining investment pools in those

countries. An aging populations negative impact on investment really created a spiral of doom

for the Middle countries in some of the migration scenarios (discussed in Section 7), where, as

the working-age cohort became a minority, the investment pools were driven toward zero, and

physical capital stocks fell rapidly.

With respect to Simons results (e.g., 1977), our model generally agrees with the view

that positive population growth is better than stationary in the long run, but that stationary

growth is better in the short run, and that declining population growth performs poorly in the

long run (given that our model runs are equivalent to Simons short run). (However, we could

not agree with Simons argument on which population-doubling term is best since our model

has a more sophisticated demographic system, and since, in particular, age structure impacts our

model directly through population growth and indirectly through our life-cycle investment

model.) For our model, the Middle countries population growth seemed to be the best (with

Middle2s slower growth than Middle1 and slower aging than Middle3 being most ideal).

Typically, Middle countries' younger populations led to a higher percent of GDP going toward


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32

investment than the Rich countries, and unlike the Poor countries, the Middle countries were

able to increase production faster than mouths. Arguably, the population profile that produced

the best results in our model (Scenario D, discussed in Section 6.1) was a combination of low

birth rates and a young age structure. This combination led to small aggregate population

growth and a high share of GDP being invested. Importantly, this profile led to population

growth because of the age structure, not the fertility and death rates, since in the Base Case the

same growth rates coupled with an older age structure led to population decline in the Rich

countries. Thus, how population grows, not just how much it grows, is important in determining

its effect on development.

Finally, a simple model of international migration could come close to replicating the

benefits of increased population growth for high human capital, aging destination countries.

However, for countries that were both origin and destination countries, migration tended to

benefit the individual migrants at the expense of those countries. Policies to encourage out-

migration as a way to alleviate population growth pressures were found to be counterproductive,

if not detrimental, in the long run.


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33

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Kelley, A. C., (1988), Economic Consequences of Population Change in the Third World,

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McKibbin, W. J. & Wilcoxen, P.J. (1995).Environmental Policy and International Trade

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Table 1: Initial Country Endowments

Technology

multiplier

Human

capital

Physical

capital

Population Land

endowment

Rich1 3 3 160 182 2.5

Rich2 3 3 249 300 10

Middle1 2 2 60 204 5

Middle2 2 2 60 200 10

Middle3 2 2 90 300 15

Poor1 1.2 1 58.3 465 20

Poor2 1.2 1 22 200 20


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Table 2: Initial and Final Population Structures for Base Case

Country Initial Final

TFR 0-5 6-17 18-64 65 plus TFR 0-5 6-17 18-64 65 plus

Rich1/Rich2 1.81 6.4% 23.7% 56.2% 13.7% 1.48 5.5% 12.2% 62.2% 20.1%

Middle1 3.58 14.8% 35.5% 46.3% 3.4% 2.57 11.3% 21.2% 58.7% 8.8%

Middle2 2.47 10.0% 30.1% 54.1% 5.7% 1.67 7.1% 15.0% 63.3% 14.6%

Middle3 1.88 8.5% 28.0% 57.5% 6.1% 4.67 5.4% 12.3% 62.9% 19.4%

Poor1/Poor2 5.96 18.0% 38.5% 40.6% 2.9% 4.42 19.1% 29.9% 47.7% 3.3%


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Table 3: Production Function Exponents

Extraction/resource

replenishment

Resource

intensive

Resource

nonintensive

Labor share 0.3 0.45 0.6

Capital share 0.7 0.20 0.3

Material share 0.35 0.1


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Table 4: Final Country Endowments and Per Capita GDP for Base Case

Resourcenonintensive

capital

Resourceintensivecapital

Extractioncapital

Humancapital

Landendowment Technology Population

PerCapitaGDP

Rich1 870 914 293 7.2 8.6 5.3 164 54.8Rich2 1,397 1,534 1,014 7.3 33.4 5.4 271 64.1Middle1 931 293 586 2.9 16.1 3.5 513 10.4Middle2 737 289 973 4.1 33.3 3.7 280 19.6Middle3 702 318 938 4.2 50.4 3.9 333 21.0Poor1 140 11 274 1.0 51.6 1.9 2,354 0.9Poor2 60 0.2 273 1.1 50.9 1.7 969 1.5


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Table 5: Final Endowment Stocks and Per Capita GDP for Rich Countries Population Growth

Experiment

Scenario

Resourcenonintensivecapital


Extractioncapital

Humancapital

Landmultiple

Techmultiple

Totalinvestmentpool Pop

PerCapitaGDP

Rich 1

A 1,783 1,718 457 7.0 8.4 5.3 3,160 377 43.5B 3,695 3,167 855 7.6 10.6 5.5 6,269 540 51.3C 3,462 2,981 841 6.0 18.0 5.3 7,004 1,016 30.9D 3,038 2,663 668 8.6 10.6 5.7 3,426 273 82.3Basecase

870 914 293 7.2 8.6 5.3 800 164 54.8

Rich 2A 2,612 2,650 1,590 7.1 33.0 5.5 5,251 554 51.6B 5,424 4,941 3,094 7.9 35.6 5.7 9,888 794 57.3C 5,051 4,571 2,897 6.1 34.6 5.4 10,188 1,494 32.1

D 4,552 4,289 2,527 8.9 35.7 5.9 5,903 402 94.2Basecase

1,397 1,534 1,014 7.3 33.4 5.4 1,500 271 64.1


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Table 6: Final Age Structure and Overall Percentage Increase for Rich Countries Population

Growth Experiment

Scenario % 0-5 % 6-18 % 18-65 % 65 plus Crude % increase

A 12.4% 22.6% 55.4% 9.6% 182%B 12.7% 22.5% 56.5% 8.3% 259%C 19.6% 29.9% 47.0% 3.5% 485%D 5.8% 12.1% 65.0% 17.1% 135%Base case 5.5% 12.2% 62.0% 20.3% -10%


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Table 7: Final Endowment Stocks and Per Capita GDP for Poor Countries Population Growth

Experiment

Scenario

Resourcenonintensivecapital


Extractioncapital

Humancapital

Landmultiple

Techmultiple

Totalinvestmentpool Pop

PerCapitaGDP

Poor 1

I 533 0.6 1,313 1.6 62.0 2.4 908 700 5.5II 25 0.8 362 1.6 57.0 2.2 184 451 3.4Basecase

140 11 274 1.0 51.6 1.9 241 2,354 0.9

Poor 2I 14 0.1 1,472 1.7 55.6 2.2 553 301 7.8II 3 0.2 335 2.1 53.8 2.0 179 194 6.5Basecase

60 0.2 273 1.1 50.9 1.7 200 969 1.5


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Table 8: Migration Parameters Experiment Design Matrix

Run % In System Max % Migrates

1 + +

2 + -

3 - +

4 - -


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45

Table 9: Final Period Response Values for Migration Parameters Experiment

Per Capita GDP Population

Country/Run 1 2 3 4 1 2 3 4

Rich1 32.7 45.9 47.9 52.2 703 324 209 180

Rich2 39.8 50.8 52.2 61.7 898 455 328 291

Middle1 3.8 7.8 5.4 9.1 262 558 151 442

Middle2 7.0 13.9 10.2 17.9 336 391 122 258

Middle3 7.6 16.2 11.7 18.1 374 438 136 303

Poor1 1.0 0.9 1.0 0.9 238 1593 224 1590

Poor2 1.7 1.5 1.9 1.6 170 724 119 669


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46

Figure 1: Share of GDP for investment for all countries in the Base Case.

Figure 2: Per capita GDP for Rich1 under various population scenarios.

Figure 3: Total investment pool for Rich1 under various population scenarios.


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47

0,05

0,1

0,15

0,2

0,25

0,3

0,35

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Period

Rich1/Rich2

Middle1

Middle2

Middle3

Poor2


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