A two-region model of economic growth and trade
Bo Hu Ying Qian
University of Federal Forces Munich Shanghai University
D-85577 Neubiberg, Germany CN-200444 Shanghai, China
bo.hu@unibw.de iris_qian@hotmail.com
Abstract
Trade protectionist tendencies are visible in a few countries around the world due to their increasing
current account deficit and their public and household debt. However, the long-term effect of such
a policy is quite unclear especially considering the feedback from the Rest of the World (ROW).
In this paper, using the US economy as a case, we present our two-region model of economic
growth and trade which uses Vensim’s subscripting language to depict the two regions: the USA
and the ROW. The model contains three major reinforcing loops responsible for endogenous
economic growth. It also outlines the mechanisms that explain the emergence of debt and its
negative impact on economic development. In order to model foreign trade, we introduce a factor
FTE (foreign trade effectiveness) to describe the extent to which one economy has market access
to another economy. The model is parameterized using historical statistic data of the US economy
and the World. On the whole, there is a fair match between the calibrated model outputs and
historical data. Our scenario simulations demonstrate that a higher share of non-investors’ income
in the US economy may help to reduce the debt-to-GDP ratio and accelerate the growth in the long
run. Import tariffs on foreign products may also have such positive effects if the tariff revenue is
distributed to the non-investors.
Keywords: foreign trade effectiveness, import tariff, capital share, indebtedness, endogenous
growth
1. Introduction
The US American economy and its trade relations to the Rest of the World (ROW) are — not only
in recent years — one of the main areas of interest in the public and in the economic research. Figure
1 shows the statistical data regarding GDP, non-investor debt, and investment (GCF, gross capital
formation) of the USA and the ROW as well as the import and export share on GDP of the USA
from 1970 to 2015 [8, 12, 15, 25]. The World is concerned about the increasing current account
deficit and the public and household debt of the USA, and in particular, about the consequences of
possible US policy changes regarding its international trade relations. Among others, two key
questions arise: What are the essential causes of the high debt ratio in the US economy? What is
the long-term impact of a possible US trade protectionism policy?
The development of a national economy is one of the major application areas of system dynamics.
A model for the national economy should, according to Forrester et al., include the following
sectors: production, labor, demography, household, finance, government, and foreign trade, in
particular, because (in the 1980s) “there are signs emerging that the United States is in the transition
stage. The transition stage is consistent with the social, environmental, and inflationary forces that
are developing.” [7]. In Saeed’s stock-and-flow structure representing Schumpeter’s concept of
creative destruction [20], the “capital” stock (and the investment into it) takes a central place in a
collection of “technology”, “unspent savings” and other three stocks reflecting workforce. Nathan
B. Forrester [5] translates, among others, Hicks’ IS-LM model [10] into a system dynamics model
with stocks “permanent income”, “employment”, “short-run expected demand”, “long-run
expected demand”, “capital” and “averaged output”. Weber presents a number of endogenous
growth models, including the Romer model [23, 19], as stock-and-flow diagrams with stock-
variables “capital stock”, “technical progress”, and “labor forces” resp. “human capital” [28].
Wheat [29] describes a feedback method of teaching macroeconomics. Based on a model with
stock variables including “savings”, “homes”, “govts”, “firms” and “inventories”, the wages are
identified as a key factor for consumption-driven economic growth. In Utama’s financial sector
sub model [26] five stocks namely “bank reserve”, “bank deposit”, “firm loan”, “firm deposit” and
“worker deposit” are included. A study by Kunte and Damani [14] uses three stocks “firm capital”,
“household capital” and “population” to model the growth ofa national economy. Randers’ concept
[17] provides further extensions in the area of social friction and environmental issues.
'$100 0008 32.0%
bet a4=:
$10000B +—> + | + : 24.0%)
ic eeeeS>-—-
rt | |
ptt er
$10008 t 16.0%
i
| |
Le
} 1 een
$01008 8.0%
ai — ‘i
F, Sea
+4 i
‘GDPUSAdata _----- GDP ROW data debtUSAdata ----- debtROWdata
GCF USAdata GCF ROWdata import data (%) export Data (%)
$0010B ++ t ; a es a a eee ee i a 0.0%
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Figure 1: GDP, non-investor debt and GCF of the USA and the ROW (BS, logarithmic scale on
the left); import and export share on GDP of the USA (%, right scale) [8, 12, 15, 25]
Translating (and improving if necessary) existing economic models or creating models from
scratch are principle ways that system dynamics is used for economic modeling [16]. Some of the
modeling works focus on specific national economies or specific policy issues. A modified Harrod-
Domar model of growth by Rego & Vega [18] uses stock variables “capital” and “debt” for scenario
analyses of Argentina’s economy. Skribans [24] uses stock variables like “labor force”, “average
wage”, “average output”, “average consumption”, “inventories” and “debt capital” to show that the
European Union needs changes in its internal migratory policy. Yamaguchi shows in [30] that
under the current monetary system in the United States a significant debt reduction “inevitably
triggers economic recessions and unemployment” of American and foreign economies. Ansah
addresses the impact of fiscal policy on socio-economic development and fiscal sustainability of
Ghana [1]. Block et al. [4] address the debt crises in the euro-zone using stock variables including
“capacity”, “investor money”, “non-investor money” and “consumer debt” and find out that
achieving more income equality seems to be a better strategy meeting the challenge of the debt
crisis than a policy of austerity. However, this strategy may be undermined by free international
trade, as demonstrated by Arto et al. [2] using a two-country model containing stock variables
“capacity”, “non-investor money” and “consumer debt” for each of the countries. The higher the
degree of free movement of goods, the more likely the two countries will, as in a Prisoners’
Dilemma, choose the policy of austerity — the worse option. A small model [see, e.g., 6, 9] of the
dynamics of economic growth, foreign trading and indebtedness is presented in [11] and uses an
additional stock “offshore (capacity)” to model the development of the import into the USA.
In this paper, we present a two-region model of economic growth and trade for the USA and the
ROW. The model focuses on the development of and the relationship between the GDP, the level
of public and private debt, the import and export volumes, the income distribution, and the
investment propensity. The purpose of this model which we developed based on the models
presented in [2, 11], is to find out (1) whether a higher share of non-investors’ income in the US
economy may help to reduce the debt-to-GDP ratio and accelerate the growth in the long run, and
especially (2) what effects and side effects US tariffs on foreign products may have to the US and
World economy.
In the following, we describe our model in Section 2. In Section 3 we use statistical data of the US
and World economy to parameterize the model. In Section 4 we discuss several scenarios regarding
their possible effects to the US and World economy. Section 5 concludes this paper.
2. A two-region model of economic growth and trade
The system dynamics model which we present in this section uses Vensim’s subscripting language
[27] to depict two regions. All variables (but time, INITIAL TIME and FINAL TIME) in the
model are subscripted having subscript Region with the subscript elements USA and ROW.
Figure 2: Two connected stock-and-flow structures as a starting point of a two-region model.
The model is focused on the relations and driving forces between GDP and non- investor
debt which is the sum of government and household debt of a national economy and is equal in
magnitude to the stock variable non- investor money if the latter is negative (Figure 2). One
basic idea of the model is the division of economic actors into two categories: investors and non-
investors. One key difference between these two groups is that the members of the first group never
need to adjust their consumption level because of lack of money while the members of the second
group have to do that if necessary. The parameter Capital share describes the share of the
GDP which the members of the first group receive while the rest of GDP is considered the (sum of
working resp. tax) income of non-investors.
Notice that in this work we use a blue and opaque arrow in the figures resp. a 7 sign in the text (f.
i. from non-investor debt to interest) for positive influence, whilst a red and transparent arrow
resp. a \ sign (f. i. from non-investor money to non-investor debt) depicts a negative effect.
Seeking to develop their businesses investors put a certain share (reinvest share) of their
last (year’s) return as the investment in the production, service, and innovation
capacity [13]. Notice that the production into inventory [see, e.g., 21] is also included in the
term investment. Increasing capacity pushes increasing consumption. In our model, the supply-side
economic effects caused by increasing capacity can be parameterized by the lookup function
consumption add-on. The total consumption is the sum of investor consumption and
non-investor consumption. Considering that GDP is essentially made up of consumption
and investment we identify three reinforcing loops (Figure 3) which are the engines of endogenous
growth:
e R4.1: GDP Z return 7 return last (year in next year) 7 investment (in next year) 7 GDP
(in next year)
e R4.2: GDP 7 return 7 investment 7 capacity 7 consumption add-on 7 non-investor
consumption 7 GDP
e R4.3: GDP 7 return 7 investment 7 capacity 7 consumption add-on 7 investor
consumption 7 GDP
consumption
ISA
Figure 3: Three reinforcing loops as engines of economic growth
Since the relation from GDP to return is a part of all three reinforcing loops, a high level of capital
share can obviously accelerate the growth of a national economy significantly.
consumption
add-on
Figure 4: Adding debt/GDP, population and further variables to the model
At the same time, a high level of capital share means a low level of non-investors’ income which
can lead to indebtedness. The level of indebtedness of a national economy is characterized by
debt/GDP, as shown in Figure 4. Two lookup variables austerity and reinvest share
determine the strength of the negative impact of an increasing debt-to-GDP ratio on investment
and on non-investor consumption. CPI, interest rate, and population are added to the
model as exogenous time profiles. The dynamics of indebtedness is given by five additional
feedback loops among which one is balancing and four are reinforcing loops (Figure 5):
e B6.1 debt/GDP \ non-investor consumption \ non-investor money \ non-investor debt 7
debt/GDP
¢ R6.2 debt/GDP \ reinvest share 7 investment 7 GDP \ debt/GDP
e R6.3 debt/GDP \ non-investor consumption 7 GDP \ debt/GDP
e R6.4 debt/GDP \ reinvest share 7 investment 7 GDP 7 income 7 non-investor money \
non-investor debt 7 debt/GDP
e 6.5 debt/GDP \ non-investor consumption 7 GDP 7 income 7 non-investor money \
non-investor debt 7 debt/GDP
77 investment 2
capacity
returns USA
USA
en) non investor
consumption
GDP USA USA
X ee demand La
USA
investor
Figure 5: Five feedback loops in conjunction with non-investor debt
Notice that the relationship from GDP to income is contained in both reinforcing loops R6.4 and
R6.5. A lower capital share enhances the effect of these loops: pushing economic growth, reducing
non-investor debt and even increasing investment (see Section 3). In this way, R6.4 and R6.5
counteract the loops R4.1—R4.3. Furthermore, the balancing loop B6.1 has the stock variable non-
investor money as a part.
period
consumption
add-on
debvGDP
R64 consumption
pe start
non-investor consumption GDP
debt share start start
population
Figure 6: Foreign trade and tariff
As shown in Figure 6, we calculate the import into a region from the ratio between foreign and
domestic capacity. This ratio is multiplied by a certain factor which we introduce as FTE (foreign
trade effectiveness) to reflect that the foreign capacity does not have full access to a domestic
market because of diverse objective (f.i. habit, distance) and subjective (f.i. regulations) reasons.
Import tariffs are treated in our model separately.
demand USA
demand
USA
Figure 7: A two-region causal loop diagram (partial)
The import and export links between the two regions make the model very complex in terms of
feedback loops. Vensim counts several hundreds of them. In Figures 6 and 7 we can only specify
some of them:
e R7.1 import \ GDP 7 return 7 investment 7 capacity \ import
e B7.2 import \ GDP 7 return 7 investment 7 demand 7 import
e R8.1 export 7 GDP Z return 7 investment 7 capacity 7 export
e 9.1 tariff 7 income 7 non-investor money \ non-investor debt 7 debt/GDP \ reinvest
share 7 investment 7 capacity \ import 7 tariff
¢ B9.2 tariff[.USA] \ export[ROW] 7 GDP[ROW] Z return[ROW] 7 investment[ROW] 7
capacity[ROW] 7 import[USA] 7 tariff[USA]
It is obvious that there are more loops and side effects which make numeric simulations necessary.
3. Parameterization
Our model has a total of 36 essential variables, as listed in Table 1. These variables all have the
subscript Region with the subscript elements USA and ROW. Datasets from [8, 12, 15, 25] are
used directly as exogenous parameters or for the parameterization. To do this we modify the values
of the lookup tables and constants marked “fitting” in Table 1 to match the simulation results of
the model to the values marked “data to match”. During the parameterization, some or all these
variables can be replaced temporarily by the corresponding datasets.
Table 1: Essential variables of the model of economic growth and trade
tora | 2282"-] 22 | ring | coro roan | 2222+] 422° | ering | conc
7 Jeusterity el a 18 [import a
7 apa at fresne
espa aa fs
4 _ [capital share a DZ [22 interest rate Z ic]
= |eonsumption add-on a [22 [investment ey
1 Jenaunein pe te nese comune
7 ens sare peje
E as Be Jones oncGTS
Peco aT fries de z
70 esd perce ney
7 eres fone money a z
7 jecregs a8 FI z ted a
[ee Z pepo ze
44 [FTE 32_|reinvest share g a
75 Fe pa a eo [Ce oun
FE set fer
7760 Sepa
78 [GDP stat a [36 [tant rate g a
We calculate the datasets for the ROW as the difference between the World and the USA [12, 15].
One of these datasets — non-investor debt of the ROW — attracts our special attention: Being a stock
variable, debt development can hardly be as volatile as the data (blue curve in Figure 8). The reason
for this is that the figures are in US dollar and thus include currency fluctuations. To model the
economic development of the ROW properly we introduce a virtual currency for the World (WCU)
of which the exchange rate to US dollar (violet curve in Figure 8) is defined in such a way that the
development of the debt stock of the ROW is smoothed (red curve in Figure 8).
aac TTTTITTT TTT
_ pete iss) J 46
<a ||| axon ia
A
Figure 8: Smoothing the development of debt stock using virtual currency for the ROW (WCU)
As shown in Figure 9 there is a fair match between the calibrated model outputs and historical data
in the cases of GDP, debt and GCF. The divergence between the model and data in the cases of
import and export is within a 30% range and can be seen as acceptable.
$100 0008
$10000B = 24%
—
a
=?
$10008 16%
JS Mi
— i
A Beas
aie
{| > ea |
ey Corr | ed
$01008 = i EEE I t 8%
7 a |—GDP USA —GDPUSAdata === GDPROW —— GDP ROWdata
i I——debtusa debtUSAdata --= debtROW debt ROW data
I ——ccF usa ——GCFUSAdata. === GCFROW —— GCF ROW data
|—— import Usa (%) —— import data (%) —— export USA (%) export Data (9)
$00108 0%
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Figure 9: Fair consistency between the data (see Section 1) and the model simulations
Figure 10 shows the results of a sensitivity analysis using scatterplots [22, 3]. All three inputs of
interest — FTErow to usa, FTEusa to Row and capital share — are implemented as lookup tables in our
model. For the sake of clarity, we choose three input variables: a shift in the percentage of capital
share from 1970 to 2015 and two multiplicative factors of both FTEs. Two output metrics are non-
investor debt at the end of 2015 and the GDP of 2015 since our focus is on economic growth
without indebtedness. The model’s behavior is apparently quite sensitive to both FTEs. This
requires closer investigation and the development of tool-based parameterization techniques to
improve the simulation results.
Gop USA Gop usa
Figure 10: Scatterplots of GDP and non-investor debt versus FTE of both the USA and the ROW
as well as versus shift of capital share of the USA
4. Scenario simulations
In this section, we present the results of two scenario analyses of the US economy using the model
described in Sections 2 and 3.
The first scenario analysis deals with the question about whether a change towards more
distributive equality in the US economy may help to reduce the debt level while keeping economic
growth. Specifically, in this scenario analysis, the non-investor income should increase and the
capital share should decrease by 5% resp. 10% from 2018 to 2020. In fact, our simulations show
that compared to the scenario, where no decrease (0%) takes place, such a change may reduce the
debt-to-GDP ratio significantly (Figure 11, top left). Regarding the development of the GDP, we
see a worse-before-better pattern in the long run (Figure 11, top right). There is a counterintuitive
behavior of the system as well: a lower capital share may help to reduce the debt level and in this
way keep the investment propensity at an acceptable level (Figure 11, bottom left). A very small
advantage for the ROW economy, regarding both the debt-to-GDP ratio and the GDP, comes from
the reduced GCF on the side of the USA, which in turn leads to a reduced export and an increased
import of the USA (Figure 11, bottom right).
debt/GDP GDP (2015=100%)
CLM POL PAP DO fd PS SASL ADMD PP OA a OP
PSP PP Sg? PP. dP ota? g? gf PP SPP GP. Sg? ah GPa? ct a? Pg!
LLL LLL ML LM LH HS KS LLL LL LMS MMH HM SN 8
reinvest share, GCF/GDP USA import/GDP, export/GDP USA
15% 20%
aK Lf == 19%
39% —— 18% SaaS
36% — 17% on
33% 16% [|
30% 15% —t
27% 1%
24% 13%
21% 12% +F
18% — 1%
15% e 10%
2% } = o%
‘9% 1 ——rein share 10% ——reinv.share-5% —reinv.shareO% || an —import-10% —import-5% —imporox [
ox Ly om
Set ccr-se cers = ere [] | —ennor-s0% —enpor-sx ——ernonon |
a a 1
CLM P PLP MPD OLS PPS SP MP PPD MD PP PA o_O
PP SP PPM SP PPP Hg? 08 FPF PPP PrP PPP HPP 08
LLL LILI ML LLL LN HS HS LLL LL LLL LI LN MN YS
Figure 11: More distributive equality may help to reduce the debt level while keeping economic
growth
In the second scenario analysis, we consider the effects of import tariffs for the economies of the
USA and the ROW. We compare five scenarios:
No (additional) import tariff is imposed.
An (additional) import tariff will be imposed by the USA and the tariff rate will increase
from 0% to 20% from 2018 to 2020 and then be kept at 20%. No reaction from the ROW.
The ROW reacts with a tariff rate which will increase from 0% to 10% from 2018 to
2020.
The ROW’s tariff rate will increase from 0% to 20% from 2018 to 2020.
The ROW’s tariff rate will increase from 0% to 30% from 2018 to 2020.
Our model outputs show that the 2™ scenario, in comparison to the 1*, baseline scenario,
will reduce the debt-to-GDP ratio significantly while accelerating economic growth (Figure
12, left side). Notice that the tariff revenue flows completely into the US treasury according
to our model. Even the 3" scenario still brings some advantages for the US economy.
However, the advantage turns to a disadvantage if the ROW should respond with an equally
high or even higher tariff to the American import, as in the 4" and 5" scenarios. Expressed
as a percentage, the effect of such a change on the ROW is noticeably smaller than that on
the US, as shown in Figure 12 (right side).
USA: debt/GDP ROW: debt/GDP
‘00% Corr i C1
380% |{ ——a%/0% —20Ko% | 380% | {— amon 200%‘
350% —20%/10% —20%/20% | Fushi —20%/10% —20%/20% |
340% i oe | —2o%/s0% |
PP Pia PH SPP cP PP ch PPS? PsP
SPP SPH HPS PHS SPP SP HS
OPP PIMP PS
HPP PP Ocho? cS
eS $
Figure 12: import tariffs and their impacts on the economic development
5. Conclusion and outlook on future research
In this paper, we presented a two-region model of economic growth and trade which uses Vensim’s
subscripting language to depict the two regions: the USA and the Rest of the World (ROW). The
model basically contains three reinforcing loops responsible for endogenous growth. It also
outlines the mechanisms that explain the emergence of debt and its negative impact on economic
development. In order to model foreign trade, we introduced a factor FTE (foreign trade
effectiveness) to describe the extent to which one economy has market access to another economy
(Section 2).
The model was parameterized using historical statistic data of the US economy and the World. In
total there was a fair match between the calibrated model outputs and historical data. The sensitivity
analyses showed that the behavior of our model is quite sensitive to FTE (Section 3). Our scenario
simulations demonstrated that a higher share of non-investors’ income in the US economy may
help to reduce the debt-to-GDP ratio and accelerate the growth in the long run. Import tariffs on
foreign products may also have such positive effects if the tariff revenue is distributed to the non-
investors (Section 4).
Despite the rather simple division of the world into only two regions, the present model seems to
provide some interesting insights into the US economy and its trade relations to the ROW. Future
research could take the next step by having a closer investigation of the factors FTE and developing
tool-based parameterization techniques. Based on this, we will then face the challenge of creating
a three-region model to look at the development of two economies with their bilateral trade
relationship in the context of world trade.
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