Modeling the Dynamics of Poverty Trap and Debt
Accumulation
John Pastor Ansah
System Dynamics Group, School of Social Sciences
University of Bergen, Norway
Abstract
Absolute poverty is all pervasive in most developing countries and particularly in Africa
(Gore 2002; Sachs, Mcarthur et al. 2004) and Ghana is no exception. The poverty in
developing countries is exacerbated by poor GDP growth. For instance, the growth rate
per capita for sub-Saharan Africa was negative in the 1980s, i.e. about -2% per annum
and about -1% per annum during the 1990s (Birdsall, Claessens et al. 2002). Most
common explanation for why countries fail to achieve economic growth focuses on
corrupt leadership, inability to make productive use of loans and culture that impede
modem development (Korner, Maass et al. 1987; Sachs 2005). However, in recent years,
the idea that poverty itself causes economic stagnation has gain attraction and engages
the attention of researchers. In this paper, we developed a system dynamics model based
on the system dynamics adaptation of poverty trap and debt overhang theory to establish
the causal structural mechanism that explains poverty trap and determine internal poverty
trends and its link with public debt accumulation. A generic system dynamics model of a
developing economy whose microstructures incorporates basic mechanisms of
population, production and public debt accumulation is used as a basis for analysis. We
found out that the decline of per worker income in Ghana is attributed to significant
reduction of investment, which consequently decreases GDP growth, coupled with high
population growth. The policy analysis proposed increasing public investment or savings
as the best policy to reduce poverty and public debt accumulation.
Keywords: Poverty trap, Public Debt Accumulation, Modeling and Simulation
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1. Introduction
The economic literature on the nature of poverty and the idea that countries might be
stuck in an underdevelopment trap was widely discussed by development economist in
the 1950s (Nelson 1956; Lieberstein 1957). However, the continuous existence of
poverty in many countries in the world after countless attempt to eradicate poverty has
renewed the interest in search for causes of poverty trap in many developing countries
(Sachs 1989; Gore 2002; Sachs, Mcarthur et al. 2004; Sachs 2005). Absolute poverty is
all pervasive in most developing countries and particularly in Africa (Gore 2002; Sachs,
Mcarthur et al. 2004) and Ghana is no exception. The poverty in developing countries is
exacerbated by poor GDP growth. For instance, the growth rate per capita for sub-
Saharan A frica was negative in the 1980s, i.e. about -2% per annum and about -1% per
annum during the 1990s (Birdsall, Claessens et al. 2002). Most common explanation for
why countries fail to achieve economic growth focuses on corrupt leadership, inability to
make productive use of loans and culture that impede modem development (Komer,
Maass et al. 1987; Sachs 2005). Jeffrey Sachs in his book “the end of poverty” challenged
the common explanation for the failure of poor countries to achieve economic growth and
ask “if poverty itself causes economic stagnation”. Sachs concluded that poverty create
poverty trap and reinforces itself if steps are not taken to break the cycle. In most poor
countries, out of desperation to exit the poverty trap, loans are acquired to increase
resources for investment and consumption smoothing (Lindauer and Velenchik 1992; Jha
2001; Ghatak and Sanchez-Fung 2007). As a consequence public debt accumulates
causing a heavy debt burden.
The problem situation in Ghana is that Ghanaians are still about as poor as they were in
the early 1960s (Easterly 2002) coupled with high per capita public debt that surpass per
capita GDP as illustrated in figure 1. We took as a point of departure, the economic
performance of Ghana over the years, to understand the link between poverty, low per
capita GDP and public debt, i.e., how poverty contributed to the observed per capita GDP
and the per capita public debt. Of foremost importance for this paper is to answer the
question: what drives Ghana’s low GDP per capita and high per capita public debt?
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Figure 1 shows the development over time of per capita GDP and per capital public debt
in Ghana.
——GDP per capita (constant LCU) —a—per capita public debt
700 900
600 ty ee BNA + 800
oe AL aie
500 Po adl
> ] 4600 5
= 400 A 55 2
~
eral A
300 ron ra 400
a is We i
si pe “~ ~—_ A 300
/ 200
ite ZL on va
K ae 4 100
Z
0 0
1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999
Year
Figure 1: GDP per Capita (left side of y-axis) and per Capita Public Debt (right side of y-axis)
Source: World Bank, World Development Indicators 2002, Ghana Statistical Services
Note: LCU is Local Currency Unit, i.e. Cedi
In this paper, we developed a system dynamics model based on the system dynamics
adaptation of poverty trap and debt overhang theory to establish the causal structural
mechanism that explains poverty trap in Ghana and determine internal poverty trends and
its links with public debt accumulation. A generic system dynamics model of a
developing economy whose microstructures incorporates basic mechanisms of
population, production and public debt accumulation is used as a basis for analysis.
The result from the analysis established that the decline of per worker income in Ghana
before the late 1990s was as a result of population growth rate exceeding GDP growth
rate. GDP on the average barely increased from 1960 to 1985, whereas from 1985 to
2000 GDP increased from 1.4% to 5.4%. On the other hand, population increased
between 2.3% to 2.5% from 1960 to 2000. The poor performance of GDP is attributed to
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low investment. According to the analysis, low investment is attributed to three main
reasons. First, the gradual decline of per worker income coupled with basic needs
consumption increased due to increases in household size as a result of population
increase reduced the ability of workers to save. Accordingly, the decline of savings
significantly reduced domestic investment which invariably affects investment. Second,
the dramatic decline of foreign direct investment during the early 1960s and subsequent
disinvestment in the economy contributed significantly to the low investment observed
during the simulation period. However, during the early 1990s, foreign direct investments
bounce back to the 1960 level. Lastly, the irregular public investment significantly
contributed to the observed behavior of investment over the simulation period.
The policy analysis established that increasing public investment or savings is the best
policy to reduce poverty and public debt accumulation. The policy analysis indicates that,
it is only when the capital base of the country increase significantly, causing production
and income to increase, and leading to per worker income significantly higher than basic
needs consumption, then, the economy tend to achieve growth.
The paper is organized as follows. Section 2 covers literature review on low level
equilibrium trap and poverty trap theory. Section 3 describes the causal structure of
poverty trap and debt accumulation while section 4 describes the stock and flow structure
and the equations of the model. Section 5 represents the validation of the model. Section
6 represents the base run behavior explanations. Section 7 represents the policy analysis
and discussion. Section 8 represents the conclusion.
2. Literature Review
Here, we will discuss two main theories: the low level equilibrium trap theory and
poverty trap theory. The low level equilibrium trap theory (Nelson 1956) discusses the
relationship between economic growth and demographic transition whereas the poverty
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trap theory (Sachs, Mcarthur et al. 2004) demonstrate how poverty causes economic
stagnation in poor countries.
growth
rate GDP growth rate
Population growth
rate
per capita
O . OM
Figure 2: Low Level Equilibrium Trap
Figure 2 shows the graphical model illustrating the low level equilibrium trap.
Considering the GDP growth curve for now, figure 2 implies that as per capita income (x-
axis of figure 2) increases, the rate of growth of GDP also increases. This is due to the
fact that as income increases, savings increases as well which facilitates the accumulation
of capital for production. As production increases, income rises which implies greater
human capital which further enhances production and income. On the population, the
model assumes that up to a certain level of threshold income, household will respond to
increased income by having more children. Also, it is hypothesized that as income
increases death rate decline further increasing population. But beyond certain level of
income (%) it is assumed that fertility will fall which consequently reduces
x
population.
From figure 2, the growth rate of per capita income can be estimated by subtracting
population growth rate from GDP growth rate. Therefore, per capita income is at
equilibrium when population growth rate equals GDP growth rate. Figure 2 shows two
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equilibrium states, i.e. (%) and Y6 | . Assuming per capita income is initially at
1 2
equilibrium (%) and through technology increase and investment, per capita income
1
temporarily increases wo( %) . Over time, if population growth rate exceed GDP
x
growth rate, per capita income will fall until it reaches the initial equilibrium ¥/ ) ‘
1
However, if the extemal forces applied to per capita income force it to the new
equilibrium{ ¥/ ) , the GDP growth rate will surpass the population growth. This will
Z
facilitate a period of sustained growth in per capita income.
The fundamental thinking of the poverty trap theory is that the economy grows in per
capita terms as long as savings per capita exceeds capital widening’ (Sachs, Mcarthur et
al. 2004). It is postulated that if savings is lower than capital widening the economy
experiences a decline in output per capita. According to the poverty trap theory, when
capital-labor ratio is very low, marginal productivity of capital also tend to be low
because a minimum threshold of capital is needed before modern production process can
be started. When the threshold capital is not present, small increments of capital-labor
ratio may have little effect. However, the theory hypothesized that once the basic
infrastructure and human capital are in place, the marginal productivity of capital may
indeed become very high in a low-income country.
| Capital widening is the amount of saving per capita that is needed to hold the capital-
labor ratio constant in the face of population growth and depreciation.
Page 6 of 28
3. Structure of Poverty Trap and Debt Accumulation
Figure 3 show the fundamental loops that cause poverty and debt accumulation. The
conceptual framework of the model incorporates the debt accumulation process theory
(Saeed 1993) and the poverty trap theory (Sachs, Mcarthur et al. 2004). The information
relationships established in the model are explained below:
deaths
repayment
cat
cl + deaths loop
payment 2 7
oop births
population —-R4
public debt bits op =
+ income
+ ¢2 R3
+ interest loop 4 etngenetap income per
5 worker Ny
labor fi pak
R2 =
output per worker ssomgiias
Mt pital public
per capita investment
expenditure 3
+ deprecation -
loop
depreciation
Figure 3: Causal Structure of poverty trap and debt accumulation
3.1 Debt accumulation
The debt accumulation process is embodied in the feedback loops (R1, C1, and C2) as
shown in figure 3. Public debt increases through borrowing and interest accrual. As debt
increases, debt servicing consisting of repayment of principal and interest payments, rises
which consequently increases government expenditure. As government expenditure build
up without corresponding increase in revenue, budget deficit increases which create the
need for more borrowing the next year round. The counteracting loop C1 and C2 strives
to counteract the growth of public debt. Thus, as public debt increases, repayment of
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principal and interest payments increases which then reduces the stock of public debt
outstanding.
3.2 Poverty Trap mechanism
The poverty trap mechanism is represented by the interaction of the savings trap (R2) and
demographic trap (R3). The conceptual framework of the savings traps is the accelerator
principle (Hamberg 1971) which posit that investment is a function of rate of change of
income. The causal structure of the savings traps and demographic traps are described as
follows:
3.2.1 Savings Trap
The conceptual framework of the savings traps is the accelerator principle (Hamberg
1971) which posits that investment is a function of rate of change of income. In poor
countries, savings rate can be become very low or even negative when income is low,
because impoverished households use all of their income in the struggle to just stay alive
(Sachs, Mcarthur et al. 2004). Once basic needs, i.e. personal health, food intake and
shelter are met; poor households may save some of the excess income (Sachs 2002). The
causal loop (R2) demonstrates that low income per worker causes low savings which then
decreases investment and capital accumulation. Consequently, output per worker is
expected to decrease due to low capital accumulation coupled with high population
growth. As output per worker decreases over time, income per worker decreases as well
which causes low savings the next year round.
3.2.2 Demographic trap
The demographic trap shows how high population growth, with low capital can push a
country into the poverty trap. Based on the assumption that poor countries are
characterized by low income, it is proven that high fertility rates in the world are
observed among the world’s poorest people (Thompson 1928; Kamerschen 1972). With
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low income per worker, it is expected that fertility rate will increase causing birth rate to
rise. As birth increases, population increases. Population growth causes new entrants to
the labor market to increase, which consequently, increases employment, resulting in the
decline of capital-labor ratio. In the absence of technological improvement, which is
expected to be the case in poor countries, output per worker will decline. As a result
income per worker will decrease causing population to grow. It is important to note that
as the demographic trap loop becomes stronger over time, it strengthens the savings trap
which then reduces investment and capital accumulation further. The strength of the
demographic trap can only be counteracted by loop (C4) when death surpasses birth to
slow the growth of the population.
4. Overview of the Model Structure
This section briefly describes the model structure and the main assumption of the model.
The model consists of three parts, ie. population, production and public debt. Figure 4
shows the stock and flow structure of the model.
foreign drvct Public ivestment“¢——_
investment
lal domestic
Ae tvestment effec of per worker
sovestrent ‘ncom) pn bth rate
5 percapia savings
| basic meds \
aul ‘consumption \ |
perworkericome |
| \
deprecation av depose \ |
‘mrome ee )
|
goss domesic wes primey as |
CAPITAL, — mee as _ee | dei 1 pons eS |
ELASTICITY =, fms } * Pe
son interest
expendine
expen —* ‘Accnied
interest accural |_itrest
indicated _ _
productivity SS
labor force
Figure 4: Stock and Flow Structure of the poverty traps and debt accumulation model
Page 9 of 28
In the following paragraphs we describe and briefly discuss the structure of the model.
4.1 Population
The population sector models total population in a simplistic way. The growth of
population is determined by the relation between births rates and deaths rates (Meadows,
Randers et al. 1972; Szirmai 2005). Here, “births rate” and “deaths rate” are measured in
people per year. They represent the total rate at which population is being increased and
decreased. The population is represented in the model as:
P, =P, +(dt)BR,, —(dt)DR,, (1)
Here P, is the current population, P,_,is the previous year population, BR,_, is the births
rate and DR,_, is the deaths rate.
Births rate is determined by births rate normal (BRN), effect of per capita income on
births (f (IN)) and previous year population (P,_,). The births rate is called “normal” rate
because they correspond to a standard set of conditions at the initial model setting.
However, it is expected that income change will cause births rate to rise or fall from their
normal values. We assumed generally a negative relationship between per capita income
and births rate (Becker 1960). The equation representing births is:
BR, =[BRN * f(IN,_,)* P_, (2)
Deaths rate is a function of deaths rate normal (DRN,) and population. The equation
representing deaths rate is:
DR, =DRN,*P., (3)
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The labor force in the population module is a function of population and working age
population fraction. We assume that labor force equals employment. The equation
representing labor force is:
L, SWE,*P., (4)
4.2 Production
The production sector employs Cobb-Douglas production function to represent output.
Output depends on factors of production (capital’ and labor force) and productivity. The
Cobb-Douglas production function is represented as:
Y, =K,." * (at)L,.* * AG (5)
Here, Y, is the production, K,_,is the previous year capital, o is the capital elasticity,
L,., is the previous year labor force and A,_, is the previous year productivity.
In the production module, capital accumulates through capital acquisition and capital
depreciation. Capital acquisition depends on investment. Investment consists of domestic
private investment, public investment and foreign direct investment. Capital depreciation
is based on perpetual inventory estimation with a common geometric depreciation rate of
4% is assumed (Collins and Bosworth 1996) which gives an average life of capital of 25
years. The capital accumulation equation is represented as:
K, =K, (1-6) +(at bx, (6)
Here, K,is current capital, K,_, is the pervious year capital, 6, is annual depreciation
rate of capital and cK, is capital acquisition.
? Capital is defined as physical and human capital.
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In the model, public investment is determined by government decision on public
expenditure pattern, i.e. the decision to either invest or consume. Foreign direct
investment is an exogenous variable from historical data which is an indication of the
attractiveness of the local economy to foreign investors. However, savings is determined
in the model based on the assumption that: Households require a level of minimum real
consumption (C) to meet basic needs of personal health, food intake and shelter. When
income (N) is above (C), the household saves a constant fraction (¢) of the excess (N -
C). When income is below (C), household savings is zero, as household consumes as
much income as possible in order to come as close as possible to meeting basic needs
(Sachs 2002; Sachs, Mcarthur et al. 2004). Thus, savings (S) is represented as:
sl 0 if NX
“\@N-C) if NC
In the model, we assume that initial basic needs income will be 700 cedis and basic needs
income is expected to increase due to expected increase in household size. We assume
further that whenever per capita income is more than basic needs consumption, 40% of
the excess income is saved and the 60% is used for consumption smoothing.
4.3 Public Debt
The public debt model demonstrates transparently the mechanisms that generate public
debt. We assume that government finances its budget deficit by borrowing and depict it
as a result of a government budget constraint:
« D, = 3
pd, +, Dat ay An =Bd, =gB, (8)
Where pd, is primary deficit, i, is the interest rate, D,_, is the public debt of the previous
year, m is the debt maturity, Bd, is the budget deficit, gB, is the borrowing.
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We express the stock of total public debt (D,) from the government budget constraint
equation and the public debt model as follows:
D, = [>.. +(at)gB, atl?-¥f)] +{Al,, +(at)la, -(at)is,] (9)
Here Al,_, is accrued interest of the previous year, (dt)Ia, is the interest accrual, and
(dt)Is, is interest elimination.
The public debt model adopted the ‘co-flow structure’ (Sterman 2000) to account for
‘accrued interest’. As government borrows, it attracts an interest obligation, which is
referred to as ‘interest accrual’. The ‘interest accrual’ is stored into a stock of ‘accrued
interest’. ‘Accrued interest’ represent the total interest to be serviced per year. On the
other hand, when repayment on debt is made, it decreases ‘accrued interest’ through
‘interest elimination’. In sum, the co-flow structure helps us to keep track of ‘accrued
interest’ as an attributes of public debt.
5. Model Validation
System dynamic models are causal models and should endogenously generate the right
behavior for the right reasons. The validity of system dynamic models means validity of
its internal structure which comes from the descriptive knowledge about the system
structure (Barlas 1996; Sterman 2000). Greenberger et al. argue that validation is not a
general seal of approval but an indication of a level of confidence in the model’s behavior
under limited conditions and for a specific purpose. Moreover they argued that data
provide a tangible link between a model and its reference system, and a means for
gaining confidence in the model and its results. Hence, the comparison of the model
behavior with data portrays the behavior validity (Greenberger, Crenson et al. 1976).
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The purpose of this model is to identify the causal structure of poverty trap and debt
accumulation and design alternative policies to reduce poverty and public debt
accumulation. The poverty trap theory (Sachs, Mcarthur et al. 2004), debt accumulation
process theory (Saeed 1993) and accelerator principle (Hamberg 1971) provided the
theoretical, empirical and logical grounding of our approach to model the causal structure
of poverty trap and debt accumulation. This is the basis for the structural validity of the
model. Moreover, the formulation of the stock and flow structure of the model is
dimensionally consistent and performs as expected for the extreme condition test, another
validation measures (Barlas 1989; Barlas 1996; Ford 1999; Sterman 2000). On behavior
validity, the main variable in the model, i.e. gross domestic product correspond with the
historical data well with r-square of 0.874. The error analysis of the gross domestic
product shows RMSE? of 14% which is a strong indication that the model endogenously
tracks historical data quite well. The breakdown RMSE attributed 17.3% of the error to
bias, 37.3% to unequal variance and 45.4% to unequal covariance. The error analysis
indicates that major part of the error is with the covariation component as compared to
bias and unequal variance which are relatively small. This clearly shows that simulated
variable tracks the underlying trend well, but diverges by point-by-point. This might
indicate that the majority of the error is unsystematic with respect to the purpose of the
model, and it should not therefore be rejected for failing to match the data points.
6. Baserun Analysis
The base run simulation shows the behavior of production, investment and savings and
public debt.
6.1 Production
The behavior of the production sector is evident in the simulation in figure 5.
3 Root-square mean error
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20B 80M
bt 80M
08 2,000
0 40M
1B 0
a 1,000
19601965 1970 1975 1980 i988 1990 1995 2000 1960 1965 1970 1975 1980 1985 1990 1995 2000
Tine (Year) Tine (Y eat)
gross domestic product :baserun. ————————_______ depreciation : baserun
Canta: tasean ———__crpilaopstion: basen
orfore: baseran), .
Labor Productivity : basen, —@£$@ @—-———— output per worker basen
Figure 5: Base run behavior of production sector
Gross domestic product remained relatively stable from 1960 to 1985 after which it
started increasing. The graph on the left hand side shows the behavior over time of gross
domestic product, capital, labor force and labor productivity. While labor force increased
consistently over the simulation period, capital stock declined significantly over the
simulation period. Since capital stock integrates capital acquisition and capital
depreciation, it is palpable that whenever capital is decreasing, it is as a result of excess
capital depreciation over capital acquisition. The graph on the right hand side, of figure 5
shows capital depreciation, capital acquisition and output per worker. From 1960 to
1990, capital depreciation surpassed capital acquisition, accordingly, capital stock
declined. However, from 1990 to 2000, capital acquisition increased significantly to slow
the decline in capital stock. The significant increase in capital acquisition during the
1990s is attributed to investment increase which will be discussed later. Labor
productivity decreased from 1960 to 1985. During the 1990s, the decreasing trend of
labor productivity reversed and surpassed the levels observed in the 1960s. The observed
behavior of labor productivity correlates with the observed behavior of output per
worker. The decline of capital stock and the corresponding output stabilization in the
midst of increasing labor force from 1960 to the 1980s, caused output per worker to
decrease. However, during the 1990s output increased significantly above the growth in
labor force causing output per worker to increase. As output per worker increased, lobor
productivity increased accordingly.
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It is apparent from the discussion that the poor performance of the gross domestic
product from 1960 to 2000 can be attributed to low capital base of the Ghanaian
economy. The decline of capital stock due to low capital acquisition as a result of
inadequate investment is the main cause of the poor performance of gross domestic
product.
6.2. Investment and Savings
Figure 6 shows on the left hand side investment and the various components of
investment i.e. total domestic investment, public investment and foreign direct
investment and population. On the right hand side of figure 6, the graph shows per
worker income, basic needs consumption and per worker savings.
2B
600M 2,000
1B
600 M
m PWR) Le
1,000
~ ot EL |
1960 1965 1970 1975 1980 1985 1990 1995 2000 1960 1970 1980 1990 2000
Time (Year)
Time (Year)
investment :baSer ———
total domesticinvestment:basenn ————————— __perworkerincome : baserun
public investment: baserun
igs tec eenact had basic needs consumption : baserun
Population :baserun. —_$_$_ _ _ _ perworker savings : baserun
Figure 6: Base run behavior of investment and savings
From 1960 to 1990, investment decreased in general amidst some fluctuations. The
decrease in investment is attributed to decline in savings, irregular public investment due
to government fiscal policy and dramatic decline of foreign direct investment. During the
1990s, investment as shown in figure 5 increased substantially mainly due to significant
increase in foreign direct investment, public investment and relative increase in savings.
The graph on the right hand side of figure 6 shows that over the simulation period, per
Page 16 of 28
worker income decreased until the 1990s when the trend was reversed while basic needs
consumption increased gradually over time, consequently, savings per worker declined.
We realized that per worker income in 2000 is at the same level as per capita income in
1960. The decline in income per worker is attributed to high growth rate in labor force
relative to the growth rate in disposable income. The rise of basic needs consumption is
understood to be caused by the increase in household size due to population growth. As
population increases, the dependency ratio (age-population ratio of those typically not in
the labor force, i.e. the dependent, and those typically in the labor force, i.e. the working
age) of workers increase, subsequently, more income is required to meet the basic needs
of the increased household size. As basic needs consumption increases given declining
per worker income, savings automatically decreases causing total domestic investment to
decrease below what is should have been, which, in tum decreases investment. As
investment decreases, capital accumulation is negatively affected which then causes
production to decrease. Production decrease causes disposable income to decrease, as
well as, per worker income. As per worker income decreases, it is hypothesized that
population increases due to the negative relationship between income and births rate. As
population increases, labor force increases, causing output per worker to decrease due to
lack of investment as a result of low savings. As output per worker decreases,
productivity is expected to decrease which negatively affect production.
In summary, we established a dynamic relationship between savings and investment. As
savings increases, investment increases over time creating the possibility for capital
accumulation and production increase. As production increases ceteris paribus per
worker income increases. This then causes savings to increase further the next year
round. In Ghana, the observed decline in savings was caused by increased basic needs
consumption due to household size increase emanating from population growth. The rise
in investment was due to increased government expenditure and increased foreign direct
investment which stimulated the economy to increase production causing per worker
income as well as savings to increase.
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6.3 Public Debt
The simulation result of the public debt accumulation is evident in figure 7.
2B 40B
6B 208
Od 4B
0 0
0 0
0 0
1960 1965 1970 1975 1980 1985 1990 199 2000 1960 1965 1970 1975 1980 1985 1990 1995 2000
Time (Y eat) Time (Year)
budget deficit: baserm —————— total public debt : baserun
interest payments : baseru. ——— Public Debt : basen
average interest rate : baseruy. ————— Accrued Interest : baserun
Figure 7: Base run behavior of population and public debt
The behavior of the budget deficit indicates that government expenditure exceeded
revenue and grants over the simulation period. As budget deficit increases, public debt is
accumulated. Total public debt increased shapely from 1960 to 1980. The growth of
public debt slowdown during the 1980s then increased shapely again in the 1990s. The
shape increase in public debt is attributed to government budget deficit. Interest payments
shows increasing trend over the simulation period due to increasing public debt and
interest rate charge on public debt. It is expected that as public debt increases over time,
interest payments will increase concurrently, causing goverment expenditure to
increase. As government expenditure increases mainly as a result of high public debt
burden, more resources are channeled to debt servicing which affect public investment.
As public investment decreases, production is expected to decrease which then decrease
per worker income and savings ceteris paribus. This scenario brings us back to the
vicious cycle of decreasing per worker income to low savings further decreasing income
and savings the next year round.
To summarize, we established that the decline of per worker income in Ghana before the
late 1990s was as a result of population growth rate exceeding GDP growth rate. GDP on
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the average barely increased from 1960 to 1985, whereas from 1985 to 2000 GDP
increased from 1.4% to 5.4%. On the other hand, population increased between 2.3% to
2.5% from 1960 to 2000. The poor performance of GDP is attributed to low investment
due to three main factors; first, the gradual decline of per worker income coupled with
basic needs consumption increase due to increase in household size as a result of
population increase reduced the ability of workers to save. The decline in savings
significantly reduced domestic investment which invariably affected investment. Second,
the dramatic decline of foreign direct investment during the early 1960s and subsequent
disinvestment in the economy contributed significantly to the low investment observed
during the simulation period. It was during the early 1990s that foreign direct investment
picked up again to the levels at the 1960. Lastly, the irregular public investment
significantly contributed to the observed behavior of investment over the simulation
period.
7. Policy Analysis and Discussion
7.1 Policy Simulation Setup and Description
The purpose of the policy analysis is to experiment and prescribe a policy or set of policy
initiatives to reduce poverty and public debt accumulation. The result from the policy
analysis is expected to help decision makers in choosing the best policy to reduce poverty
and public debt accumulation in Ghana. We tested six policies and evaluated their impact
on income, savings and public debt. Table 1 shows the six policies.
Policy Alternatives Value
1. Increasing public investment (P1) 12% of GDP by 2050
2. Increasing foreign direct investment (P2) 100% increase of FDI by 2050
3. Increasing spending rate (P3) 40% of GDP spending rate by 2050
4. Increasing effective tax rate (P4) 30% of GDP effective tax rate by 2050
5. Increasing savings (P5) 60% savings rate by 2050
6. Decreasing population (P6) 1% population increase by 2050
Table 1: Policy Simulation Setup
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7.1.1 Increasing Public Investment: This policy ensures that goverment
increase public investment to 12% of GDP by 2050. The assumption is that, at certain
stage of the economic growth, increases in public investment create the necessary human
and physical capital for economic growth to take off (Rostow 1990). High investment is
expected to aid accumulation of capital to facilitate production which will then increase
income to reduce poverty. This policy is implemented in the policy experimentation by
increasing the government decision variable, i.e. public investment fraction from 8.5% of
GDP in 2000 to 12% by 2050.
7.1.2 Increasing Foreign Direct Investment: With this policy, we speculate
that foreign direct investment will double by 2050. This policy is based on the
assumption of the economic convergence (Barro and Sala-i-Martin 1991; Sachs and
Wamer 1995) at play in the world economy such as the potential for capital inflows into
capital-scarce countries. This policy will ensure that the government creates the necessary
enabling environment for foreign investors to invest in the country. The policy is
implemented in the policy experimentation by increasing foreign direct investment from
1.17e+012 in 2000 to 2.34E+12 by 2050.
7.1.3 Increasing Spending Rate: The spending increase policy guarantees that
goverment expenditure increase as a result of increasing spending rate as a percentage
of income to 40% by 2050. It is hypothesized that as goverment expenditure increases,
public investment, capital accumulation and production will increase as well. On the flip
side, this policy is likely to increase budget deficit if goverment revenue remains
unchanged. This policy is implemented in the policy experimentation by increasing
govemment decision variable spending rate from 33.7% in 2000 to 40% by 2050.
7.1.4 Increasing Effective Tax Rate: The policy of tax increase is expected to
increase the effective tax rate to 30% of income by 2050. It is expected that as effective
tax rate increases, tax revenue generated by government will increase to enable
govemment finance all expenditure from goverment revenue to reduce public debt build
up. Moreover, as tax revenue increases, government expenditure is expected to increase
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concurrently; therefore, public investment is expected to increase creating the possibility
for the accumulation of human and physical capital to stimulate growth and economic
prosperity. The downside of this policy is that, as tax revenue increases, disposable
income available to the households will decrease, consequently, per worker income will
decline causing private savings and domestic investment to decrease. This policy is
implemented in the policy experimentation by increasing the effective tax rate from 19%
of income in 2000 to 30% by 2050.
7.1.5 Decrease Population: Population increase without corresponding income
increase, is seen as one of many factors responsible for poverty (Sachs, Mcarthur et al.
2004). This policy will ensure that government implement strategies to reduce population
over time by decreasing fertility rate. We assume that by implementing this policy, birth
rate will reduce to 1%. The policy is implemented in the policy experimentation by
reducing birth rate normal from 2.5% in 2000 to 1% by 2050.
7.2 Results and Discussion
The outcome of the policy experimentation and simulation is presented in table 2. Three
main indicators are used to assess the success and impact of the policies on poverty and
public debt. The indicators are; per worker income, per worker savings and debt-GDP
ratio. Figure 8 shows the behavior over time of the policy analysis.
Per worker Per worker Debt-GDP
Policy Alternatives income savings Ratio
1. Increasing public investment (P1) 2626** 410 3
2. Increasing foreign direct investment (P2) 2470 348
3. Increasing spending rate (P3) 2444 337 4
4. Increasing effective tax rate (P4) 2007 163 yer
5. Increasing savings (P5) 2586 502** 3
6. Decreasing population (P6) 2261 264 4
Table 2: Result of Policy Simulation
Page 21 of 28
Per Worker Income
4,000
2,000 all
0
1960 1971 1983 1994 2005 2016 2028 2039 2050
Time (Y ear)
per worker ince: PL
arwotkrinmme: P2
erworer ince 3
arworkrinmme: Pt
pervs ince; 25 ———————————
exc: 2S ——————————
Per Worker Savings
600
300
0
1960 1971 1983 1994 2005 2016 2028 2039 2050
Time (Y ear)
pe worker savings : PL
BE Worker savings: P2
Worker savings :P3
Worker savings: PA
BE Worker savings: PS
er worker savings: PS
Debt-GDP Ratio
0
1960 1971 1983 1994 2005 2016 2028 2039 2050
‘Time (Y ear)
“abt ra": PL
bt ai: P2
“abd ao”: 6
Figure 8: Policy Simulation result for Income, Savings and Public debt
The policy analysis established that, the policy to increase public investment (P1) is the
policy option that gives the highest sustainable per worker income over the simulation
period compared to the other policies. The underlying mechanism that explains the
results obtained from P1 is, as public investment increases over time, capital is
accumulated to facilitate production which in tun generates prosperity, i.e. income. As
income increases ceteris paribus, savings increases as well, which further enhance the
ability to invest and accumulate capital and technology to boost production. Also, policy
P1 is the second preferred policy to increase per worker savings and reduce public debt
compared to the other policies.
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The policy simulation analysis indicates that foreign direct investment policy (P2) is the
third favorable policy to increase per worker income and per worker savings. However,
conceming public debt reduction, policy P2 is comparable to the results obtained for P1
and P5, which demonstrate that P2 is among the second best policies to reduce public
debt given the current condition. The foreign direct investment policy, i.e. (P2), attracts
the scarce capital unavailable in the local economy to increase investment and capital
accumulation. The performance of (P2) clearly indicates that, doubling the foreign direct
investment currently available in Ghana will not be as effective as P1 and P5 to reduce
poverty. However, this policy can be implemented along side other policies to pull
together investment opportunities for the economy to take off to the path of sustained
economic growth and prosperity.
We established that the policy to increase government expenditure (P3) in the fourth
favorable policy to increase per worker income and per worker savings. On public debt,
P3 is the third and least favorable policy to reduce debt-GDP ratio. The underlying
mechanism of P3 is that, by implementing this policy, govemment expenditure is
significantly increased to stimulate the economy to the path of growth. However, when
expenditure increases, budget deficit increases as well due to excess spending over
revenue. Deficit spending builds up public debt, which, consequently, increase interest
payments and repayments that takes significant portion of government expenditure, as a
result, decreasing non-interest expenditure available for spending and investment. The
outcome of the policy analysis indicates that, increasing goverment spending is not
necessarily the best policy to reduce poverty and public debt.
The policy analysis result establishes that, the policy to increase government revenue
through increasing effective tax (P4), is the least favorable policy to increase per worker
income and per worker savings. Nonetheless, P4 is the most effective policy to reduce
public debt. The mechanism underlying P4 is that, increasing effective tax reduces per
worker income and savings because as tax revenue increases, disposable income
available to the household’s decreases, concurrently, as a result, per worker income
decreases ceteris paribus. As per worker income decreases ceteris paribus, savings is
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expected to decrease which in turn decreases investment, capital, production and
disposable income to household's the next year round. On the other hand, as effective tax
increses, government revenues rise; this then reduces budget deficit and public debt
accumulation.
The policy to increase savings (P5) is evidently the most successful policy to increase per
worker savings. Also, we found that P5 is the second favorable policy to increase per
worker income and reduce public debt. The mechanism underlying P5 is explained as
follows: as savings increases over time, investment increases, this then facilitate the
accumulation of capital for production. As production increases, income to households
increases causing disposable income to rise further creating the condition for more
savings. On the flip side, increases in production are accompanied by income increases
which then increase government tax revenue. Increases in government revenue enable the
government to reduce deficit spending ceteris paribus. As deficit spending declines,
public debt reduces below what it would have been.
The policy analysis shows that decreasing population (P6) is the second least favorable
policy to increase per worker income and savings. Moreover, P6 is the least favorable
policy to reduce public debt. The result indicates that the expected decrease in population
from the implementation of P6 is not significant enough to increase income and savings.
Moreover, the decline in population from implementing P6 is not significant enough to
reduce government spending, which will consequently, reduce public debt.
Based on the results from the policy analysis, we established that, the best policy(s) to
reduce poverty and public debt accumulation is: to increase public investment (P1) or to
increase savings (P5). P1 yields the highest per worker income and is the second best
policy to increase per worker savings and reduce public debt. On the other hand, P5
yields the highest per worker savings and is the second best policy to increase per worker
income as well as reduce public debt.
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In summary, we established that, when an economy begins with a low capital base, low
GDP growth, and high population growth, both capital stock and per worker savings tend
to decline over time. Lack of capital accumulation coupled with population growth
further erodes the income base. The outcome of the policy analysis confirms that it is
only when capital base of the country increase above a certain threshold which leads to
per worker income significantly higher than basic needs consumption then the economy
tend to achieve growth.
8. Conclusion
The system dynamics model presented in this paper represent an integration of poverty
trap and public debt accumulation, to clarify the dynamic mechanisms underlying
observed trends and project the trends into the future under variety of policies to assess
their impact on poverty and public debt.
We established that the decline of per worker income in Ghana before the late 1990s was
as a result of population growth rate exceeding GDP growth rate. GDP on the average
barely increased from 1960 to 1985, whereas from 1985 to 2000 GDP increased from
1.4% to 5.4%. On the other hand, population increased between 2.3% to 2.5% from 1960
to 2000. The poor performance of GDP is attributed to low investment due to three main
reasons; first, the gradual decline of per worker income coupled with basic needs
consumption increase due to increase in household size as a result of population increase
reduced the ability of workers to save. The decline in savings significantly reduced
domestic investment which invariably affected investment. Second, the dramatic decline
of foreign direct investment during the early 1960s and subsequent disinvestment in the
economy contributed significantly to the low investment observed during the simulation
period. It was during the early 1990s that foreign direct investment picked up again to the
levels at the 1960. Lastly, the irregular public investment significantly contributed to the
observed behavior of investment over the simulation period.
Page 25 of 28
The policy analysis proposed increasing public investment or savings as the best policy to
reduce poverty and public debt accumulation. This is for the reasons that, when an
economy begins with a low capital base, low GDP growth, and high population growth,
both capital stock and output per worker tend to decline over time. Lack of capital
accumulation coupled with population growth further erodes the income base. The
outcome of the policy analysis confirms that it is only when capital base of the country
goes above a certain threshold which leads to per worker income significantly higher than
basic needs consumption then the economy tend to achieve growth.
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