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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 country’s sustained per capita income growth depends on that
country’s 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
population’s 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 country’s sustained per capita
income growth depends on the country’s development level. Perhaps the best examples of a
Malthusian-like trap are those results that indicate the perils of negative 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 and destination, 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 model’s 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-à-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) is Limits 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 the Limits model by
addressing some of the above concerns. However, as Meadows et al. acknowledge, the model’s
behavior mode is still "overshoot and collapse" because of the programmed absolute limits on
technology, substitution, natural resource stock, and the earth’s 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.
Simon’s (1977) model is much closer in spirit to ours than the Limits 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 constantproportion-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 Simon’s result is that what Keynes said of the long run
is true of Simon’s 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 class’s 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 and old) 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 output via a Keynesian consumption-investment function, modified by
social 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 period’s 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 defined in 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 of
Table 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 country’s 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)blsKSbksRSbrs
(1)
Resource intensive industry sector, I:
QI = AIT (HLI)bliKIbkiRIbri
(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:
R = aATK R
αkr
(HLR )αnr R β
Where:
R : amount of extraction
a : scaling factor to get initial positive profits (currently set to 1)
(3)
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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)
αkr ,αnr : productivity exponents for labor and capital
R : 8 year moving average of past extraction
ß : drag parameter based on the extent of recent extraction (less than -1).
The drag parameter (ß) 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 country’s total GDP allocated for investment depends positively on the
country’s 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 country’s 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 x pop(0-14) + 2.1 x pop(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 country’s 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 country’s human capital multiple, H, is based on the average per student spending on
education for the work force. Thus, the new H for a country is the weighted (by population size)
average of the H of the graduating class and the current H of the workforce. The H of 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 class’s H since it will be averaged together
with the per student spending for the previous 11 periods. Also, a graduating class’s H has a
greater impact on the country’s H as 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 countries’ initial 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 countries’ populations.
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 countries’ consumption 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
Middle3’s in Period 36. Middle3’s 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.
Middle3’s 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 Middle2’s 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 Poor2’s (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. Middle1’s 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:
é Scenario A: Rich country initial age structure with Middle1 initial growth (i.e.,
fertility and mortality) rates
é Scenario B: Middle1 initial age structure and growth rates
é Scenario C: Poor country initial age structure and growth rates
é 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
22
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
23
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:
é Scenario I: Poor country initial age structure with Rich country initial growth rates
é 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
24
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; Poor1’s 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
25
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 countries’ sustained 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). Poor2’s work force was still small enough
that the extraction industry, made more profitable by higher technology and human capital,
26
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 worker’s migrating is to
maximize his human capital adjusted wage. The human capital adjusted wage is the country’s
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
country’s human capital multiple and fertility rates, thus affecting the host country’s (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
27
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 country’s 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 of nested, two-level, full and fractional factorial 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 the percent 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
28
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 the percent 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 maximum percent 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 Rich1’s
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
29
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), Rich1’s 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,
migration’s 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 inmigrants 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
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 country’s sustained per capita income
growth depended on the country’s 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
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 of negative 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 population’s 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 Simon’s 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 Simon’s short run). (However, we could
not agree with Simon’s 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
Middle2’s 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
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 outmigration as a way to alleviate population growth pressures were found to be counterproductive,
if not detrimental, in the long run.
33
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37
Table 1: Initial Country Endowments
Technology
Human
Physical
Population
Land
multiplier
capital
capital
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
endowment
38
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%
39
Table 3: Production Function Exponents
Extraction/resource
Resource
Resource
replenishment
intensive
nonintensive
Labor share
0.3
0.45
0.6
Capital share
0.7
0.20
0.3
0.35
0.1
Material share
40
Table 4: Final Country Endowments and Per Capita GDP for Base Case
Rich1
Rich2
Middle1
Middle2
Middle3
Poor1
Poor2
Resource
nonintensive
capital
870
1,397
931
737
702
140
60
Resource
intensive
capital
914
1,534
293
289
318
11
0.2
Extraction
capital
293
1,014
586
973
938
274
273
Human
capital
7.2
7.3
2.9
4.1
4.2
1.0
1.1
Land
endowment Technology Population
8.6
5.3
164
33.4
5.4
271
16.1
3.5
513
33.3
3.7
280
50.4
3.9
333
51.6
1.9
2,354
50.9
1.7
969
Per
Capita
GDP
54.8
64.1
10.4
19.6
21.0
0.9
1.5
41
Table 5: Final Endowment Stocks and Per Capita GDP for Rich Countries Population Growth
Experiment
Resource
nonintensive
capital
Resource
intensive
capital
Extraction
capital
Human
capital
A
B
C
D
Base
case
1,783
3,695
3,462
3,038
870
1,718
3,167
2,981
2,663
914
457
855
841
668
293
7.0
7.6
6.0
8.6
7.2
Land
multiple
Rich 1
8.4
10.6
18.0
10.6
8.6
A
B
C
D
Base
case
2,612
5,424
5,051
4,552
1,397
2,650
4,941
4,571
4,289
1,534
1,590
3,094
2,897
2,527
1,014
7.1
7.9
6.1
8.9
7.3
Rich 2
33.0
35.6
34.6
35.7
33.4
Scenario
Tech
multiple
Total
investment
pool
Pop
Per
Capita
GDP
5.3
5.5
5.3
5.7
5.3
3,160
6,269
7,004
3,426
800
377
540
1,016
273
164
43.5
51.3
30.9
82.3
54.8
5.5
5.7
5.4
5.9
5.4
5,251
9,888
10,188
5,903
1,500
554
794
1,494
402
271
51.6
57.3
32.1
94.2
64.1
42
Table 6: Final Age Structure and Overall Percentage Increase for Rich Countries Population
Growth Experiment
Scenario
A
B
C
D
Base case
% 0-5
12.4%
12.7%
19.6%
5.8%
5.5%
% 6-18
22.6%
22.5%
29.9%
12.1%
12.2%
% 18-65
55.4%
56.5%
47.0%
65.0%
62.0%
% 65 plus
9.6%
8.3%
3.5%
17.1%
20.3%
Crude % increase
182%
259%
485%
135%
-10%
43
Table 7: Final Endowment Stocks and Per Capita GDP for Poor Countries Population Growth
Experiment
Resource
nonintensive
capital
Resource
intensive
capital
Extraction
capital
I
II
Base
case
533
25
140
0.6
0.8
11
1,313
362
274
Land
multiple
Poor 1
1.6
62.0
1.6
57.0
1.0
51.6
I
II
Base
case
14
3
60
0.1
0.2
0.2
1,472
335
273
1.7
2.1
1.1
Scenario
Human
capital
Poor 2
55.6
53.8
50.9
Tech
multiple
Total
investment
pool
Pop
Per
Capita
GDP
2.4
2.2
1.9
908
184
241
700
451
2,354
5.5
3.4
0.9
2.2
2.0
1.7
553
179
200
301
194
969
7.8
6.5
1.5
44
Table 8: Migration Parameters Experiment Design Matrix
Run
% In System
Max % Migrates
1
+
+
2
+
-
3
-
+
4
-
-
45
Table 9: Final Period Response Values for Migration Parameters Experiment
Per Capita GDP
Country/Run
Population
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
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.
47
0,35
0,3
0,25
Rich1/Rich2
Middle1
Middle2
Middle3
Poor2
0,2
0,15
0,1
0,05
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49
Period
48
6FHQDULR$
6FHQDULR%
6FHQDULR&
6FHQDULR'
%DVHFDVH
3HULRG
49
6FHQDULR$
6FHQDULR%
6FHQDULR&
6FHQDULR'
%DVHFDVH
3HULRG