A POST-KEYNESIAN MACRODYNAMIC
SIMULATION MODEL FOR AN OPEN ECONOMY
Marcelo de Oliveira Passos
José Luís Oreiro
Marcelo de Oliveira Passos
PhD student at Department of Economics of Federal University of Paraná. (UFPR).
Project Development Analyst of Regional Development Bank of Extreme-South of
Brazil (Banco Regional de Desenvolvimento do Extremo Sul – BRDE). Professor of
Tuiuti University of Parana State (Universidade Tuiuti do Paraná – UTP). E-mail:
[email protected]. Website: http://marcelo-passos.sites.uol.com.br.
José Luís Oreiro
Phd in Economics (Federal University of Rio de Janeiro – UFRJ). Professor at
Department of Economics at Federal University of Paraná (UFPR). Researcher of
National Conseul of Technological and Scientific Development (Conselho Nacional
de Desenvolvimento Científico e Tecnológico – CNPQ). E-mail: [email protected]
and [email protected] Website: http://www.joseluisoreiro.ecn.br.
1
ABSTRACT: The objective of this article is to present the structure and first simulation
results of a post-keynesian macro-dynamic model for an open economy with floating
exchange rates and imperfect mobility of capital. The model to be presented integrates
both the real and financial aspects of post-keynesian economics in a dynamic
framework where real output is demand determined, investment is driven by Minsky´s
two price theory, money is endogenous, technical progress is determined by a Kaldorian
technical progress function and net exports are an important component of aggregate
demand. Domestic capitalists can store their wealth in foreign bonds, so there is
imperfect mobility of capital. After the presentation of the basic structure of model, one
can perform its computational simulation and, then, infer the dynamic trajectories of
endogenous variables. Simulated trajectories reflect some general features of the
dynamic of capitalists economies, especially the existence of irregular fluctuations of
the growth rates of real output. The analysis of the external sector of the economy
shows that the long-run dynamic interaction between the real exchange rates and the net
exports generates a real exchange rate appreciation, a fall in net exports and also a
reduction in the volatility of current account balance. Another important result that was
obtained from the model is the increasing share of financial assets in national wealth. In
other words, the model provides an economic result that suggests a growing share of
financial assets in the capitalists` aggregate wealth of this economy.
KEYWORDS: Open Economy Macroeconomics, Computational Economics, Simulation
Models, Post-Keynesian Economics.
JEL CODES: E12; F43, E37.
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1. Introduction
The objective of this paper is to present a post-keynesian macro-dynamic simulation model for an
open economy with a floating exchange rate regime and imperfect mobility of capital. After the
presentation of the theoretical structure of the model, we will proceed to a computational simulation in
order to calculate the dynamic paths of endogenous variables. Simulated paths replicate some general
features of capitalist dynamics as the occurrence of cyclical growth. An interesting result obtained from
the model at hand is the existence of a long-run tendency for increasing the share of financial assets in
total wealth.
The present article is structured in four sections, including the present introduction. In the second
section, we will present the six building blocks of the model at hand. This model is an extension of the
model originally developed by Oreiro and Ono (2007). Third section is dedicated to the presentation of
the results of computational simulation. Fouth section concludes the paper.
2. A Macrodynamic Simulation Model for an Open Economy
In this section we will structure a macro dynamic multisectoral model with a productive and a
financial sector in open economy with governmental activities. There are two available production
factors: capital and labor (both are homogeneous). Therefore, there is no asymmetry in the capital
lifetime neither differences in worker’s qualifications. Only one good is produced, consumed and
invested in this economy.
This model will be built starting from seven interconnected modules: (i) module 1 - the
components of the effective demand; (II) module 2 – the determination of the production level, the
income and the technological progress; (III) module 3 – income the determination of income
distribution; (IV) module 4 – inflation and monetary policy (v) module 5 – financial system; (vi)
module 6 - foreign sector, and (vii) module 7 – assets and debts of private sector.
The model admits recursive solutions. So, the values of the dependent variables in the t period can
be all expressed in terms of values of these same variables in the period t-1. We can compute time-paths
to all the dependent variables of the model, given the parameters values of the dynamic equations as
well the initial values of the dependent variables. We highlight two points on the model:
i)
The time-paths are not determined by attractors or pre-certain tendencies. By this way, the
model does not assume the existence of any kind of equilibrium in the economic system.
So, there is no “asymptotic position”or “steady state” in the model; and
ii)
the inclusion of a sixth module (the foreign sector), makes the model include some
variables related to the balance-of-payments: price-elasticity’s of demand for imports and
for exports; income-elasticity’s of demand for imports and for exports; foreign real interest
rate; foreign real exchange rate and the growth rate of the rest of world income. The
exchange rate is treated as endogenous.
In short, the model is a complex system of simultaneous difference equations, with the exogenous
variables being determined by a Monte Carlo process of random numbers` generation.
2.1. Module 1: Effective demand.
We initially assume that government consumption grows, in each period, by an exogenous rate (hC).
This consumption is autonomous in comparison to the current level of economic activity. Thus, we can
write the following equation:


GtC  1  h c GtC1
(1)
Where: GCt is the government consumption in t period .
Public investment is pro-cyclical. It experiences greater values when the economy grows.
So we have:
3
GtI  h I Yt 1 (2)
Where hI represents the induction factor of variations in the economic activity level of t-1
period, whereas public investment is made in t period. By hypothesis, we have 1>hI>0.
To enlarge the existing productive capacity, private investment is determined by a two-stage
process. In the first one, this process determines the investments chosen by businessmen, given their
expectations regarding future revenues of capital equipment, the state of confidence and the liquidity
preference (witch is given by a discount factor applied to the capital new equipment futures revenues).
In the second stage, businessmen compare their expected investments with the financial restriction to
invest. This restriction is given by the firm’s maximum sustainable level of debts. On the one hand, if
the desired investment is superior to the feasible investment1, firms will only be able to invest the
amount permitted by their financial restriction. On the other hand, if the desired investment is lower
than the feasible investment, the firm will be able to invest the amount that it wants.
The difference between desired capital stock in the current period and effective capital stock in
previous period is, by definition, the desired investment. Desired capital stock has two components. The
first one  0Yt 1 - K t 1 , denotes the accelerator effects of changes in the level of production over
investment decision. Thus,  0Yt 1 represents the production that the businessmen believe that they will
be able to sell in the current period.
This expectation depends on the sales executed in the previous period ( Yt 1 ) and of a sales
projection coefficient (  0 ). This coefficient is a random variable with uniform probability distribution,
defined in the interval [15, 20]. This random variable captures investors' animal spirits.
Thus, in each period, the businessmen will act with different values for the sales projection
coefficient, expressing the animal spirits` influence in investment decisions. The second term ( K t 1 )
represents the higher firm’s available production capacity. Therefore, the expression  0Yt 1 - K t 1
can be understood as a proxy of the expected utilization of productive capacity in the current period.
  Pt D

1 . It incorporates
  Pt

The second component describes the stock of desired capital,  1 
S
investment decision in to a general theory of portfolio choice. In this setting, purchase of capital goods
is seen as one of possible forms of wealth accumulation along time. The capital goods purchase
attractiveness depends on its profitability vis-à-vis the profitability of other forms of wealth
accumulation. With effect, the stock of desired capital depends on the ratio between demand price of
capital equipment and the offer price of this equipment.
Desired investment and desired capital stock can be expressed by:
I tD  K tD  K t 1 (3)
K tD

 Pt D

 S  1; se Pt D  Pt S



Y


K


 0 t 1
t 1
1


 Pt


 0Yt 1  K t 1 , caso contrario
(4)
onde :  0  0 ;  1  0
Where  is the social productivity of the capital (the inverse of capital-product ratio).
.
1
Feasible investment is provided by firm’s financial restriction.
4
Assuming a conventional behavior in expectations formation, one can compute the present
value of capital equipment’s expected revenues (the demand price of capital equipment). Future profits
will be equal to profits obtained in the last period (POSSAS, 1993). Therefore:
Pt D 
(1   )mt 1 Pt 1Yt 1
dt
(5)
Where:  is the tax rate over business profits , mt-1 is the profit share in the income of the
period t-1, Pt-1 is the general level of prices in t-1, Yt-1 is the real income in t-1 and dt is the discount
rate applied to expected revenues of capital equipment.
The equipment replacement cost (or the supply price of equipment) is equal to the value of
capital stock evaluated at current prices of this equipment. Since output is a homogenous good, the
supply price of capital goods is equal to the general level of prices. So, we have:
Pt S  Pt 1 K t 1
(5a)
The discount rate, applied to expected revenues of capital equipment, depends on two elements:
(i) The rate of interest of bank loans ( a proxy for opportunity cost of investment projects, it-1); and (ii)
the borrower’s risk, a weighted mean of the insolvency risk (t-1) and liquidity risk (ft-1). So we have
  i    Lt 1 
 L

dt  it 1    t 1   (1   )  t 1
  it 1   t 1  (1   ) ft 1
 Pt 1Kt 1 
 mt 1Pt 1Yt 1 
(6),
Where: θ is the weight factor of insolvency and liquidity risk (it indicates the degree of
managerial aversion to the risk of insolvency vis-à-vis to liquidity risk); Lt is the total amount of debts
with the banking sector;  is the amortization coefficient of debts; t-1 is the ratio between firms` total
debts and their capital stock; and ft is a coefficient of financial fragility, given by the ratio between
firms´ financial debts and their operational profits.
Once determined the expected investment, firms should evaluate the real chance of
implementation of their investment decisions. The firms should determine: (i) the amount of new loans
that they can contract with the banking sector, having in mind the maximum level of debts that they are
willing to accept; and (ii) the amount of retained profits that are disposable for the financing of their
investment decisions. We suppose that government does not tax retained profits. Thus, the financial
restriction to investment is the sum of the increase in the level of indebtedness that firms are willing to
accept and retained profits. With effect, the investment, at the t period, that firms can support is
determined by:
Ft   max Pt 1 K t 1  Lt 1  Pt 1Yt 1  wt 1 N t 1  it 1   Lt 1  (7).
Where:  is the profits retention coefficient.
The equation (8) details the realized investment at the t period:
I t  min  I tD , Ft 
(8)
Regarding the consumption expenses, we suppose the existence of different propensities to
consume on, respectively, wages and profits (KALDOR, 1956 and PASINETTI,1962). Specifically, we
consider that “workers spend everything they earn” (their propensity to save is equal to zero). On the
other hand, we assume that productive capitalists (in other words, the non-financial company owners)
have a propensity to save on their operational profits equal to sc. These capitalists own a stock of
foreign assets2 that is inherited from previous period (A*t-1). Supposing that i * t 1 is the interest rate paid
over foreign bonds, than productive capitalists receive a foreign income equal to At*1it*1 measured in
2
Evaluated in foreign currency.
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foreign exchange and E t At*1it*1 measured in domestic currency, where E t is nominal rate of exchange
at t period.
Finally, we suppose that financial capitalists (i.e., the banks owners) have a propensity to save over
net receipts of financial intermediation (sf) Thus, the nominal expenses of consumption in the period t
are determined by the following expression:


Pt Ct  wt 1 N t 1  1  sc 1    1   Pt 1Yt 1  wt 1 N t 1  it 1   Lt 1   At*1it*1 Et 

1  s 1   .L
.i
t 1 t 1
f
(9)
Pt
The effective demand at the t period is determined by:
Z t  Ct  I t  Gtc  GtI  X t  M t
(10)
Where: Xt is the quantum of exports at the t period; Mt is the quantum of imports at the t period,
et 
Et Pt *
Pt
is the real rate of exchange; Pt
is the domestic price level; Pt * is the international
price level.
We suppose that (11) determines the quantum of imports:

 Et 1 Pt*1 
 Yt 1 (11)
M t  j

 Pt 1 
In which: j is a positive constant;  is the income-elasticity of demand for imports (positive);
 is the price-elasticity of demand for imports (negative); Pt is the price of exports (in domestic
currency) .
The exports function, in a similar manner, is

 E P* 

X t    t 1 t 1  Yt*1 (12)
 Pt 1 
In which we have: x as a positive constant;  as the income-elasticity of demand for exports (positive);
 as the price-elasticity of demand for exports (positive); and Yt *1 representing the external demand
defined in the previous period.
2.2. Module 2: Production, Income and Technological Progress.
According to the principle of effective demand, the production level is determined by effective
demand for goods and services (PASINETTI, 1997, p.99). This occurs if and only if there is no full
utilization of productive capacity (i.e, there is a “idle” capacity). We suppose that firms attend to the
change in demand for their products with change in production. The limit to aggregate production is
given by the economy production potential level.
However, there are two limitations to determine the potential output: (i) the manpower
available; (ii) the maximum level of capacity utilization.
With regard to the first limitation, there is a minimum level to the unemployment rate. This rate
(Umiin) will determine the full-employment level of output Yt max, l given by,
Yt max, l 
Nt
1  U min 
qt
(13),
Where qt is labor requirement per-unit of output.
6
The variable qt is not constant, but changes through time due to the occurrence of technical
progress, which will be modeled here by means of a Kaldorian technical progress function (KALDOR,
1957) as the one written above:
 (1  ) K t 1  I t  Gti

qt  qt 1   0 
 1    qt 1 (14)
i
 (1  ) K t 2  I t 1  Gt 1

In expression (14), we can see that any increase in the stock of aggregate capital will reduce the
labor requirement per unit of output, i.e. will increase the productivity of labor.
The uncertainty surrounding the process of technical change will be modeled by means of a
random variable ( ), which is assumed to have a uniform distribution in interval [-1;1].
Another assumption, just as emphasized by STEINDL (1952), is the existence of an upper limit
to the level of capacity utilization. Firms wish to operate with a certain level of idle capacity (in the
long-term) due to the indivisibilities in investment decision. Hence, the growth of installed capacity is
larger than the demand growth. So the maximum output compatible with the normal level of capacity
utilization is given by:
Yt max, c  u max Yt 1 (15)
In equation (15), umax is the normal level of productive capacity utilization; Yt max, c is the level of
output compatible with a normal level of capacity utilization and Yt 1 is the potential output at period
t-1.
Potential output Yt 1 is given by:
Yt 1  K t 1 (15a)
In which  is “social productivity of capital”, a technical coefficient that describes the amount of
product that can be obtained through the utilization of one unit of capital.
In this context, the maximum level of output compatible with both restrictions will be the smaller value
between (13) and (15):
N

Yt max  min  t 1  U min ; u max Kt 1  (16)
 qt

If the level of output is smaller than the maximum level of output - determined by equation
(16a) - than real output in period t will be determined by the effective demand of this same period given by equation (10). However, we have to consider another restriction. Real output cannot increase
between periods at any rate. In fact, there is a maximum rate of increase of real output between periods
due to the existence of adjustment costs. These costs are related to selecting, contracting and training
new workers. Therefore, we will consider the existence of a maximum real GDP growth rate between
periods, gmax. In this way, the production level at the t period will be determined by:


 
Yt  min Z t , Yt max , 1  g max Yt 1
(16a)
2.3. Module 3: Income distribution
According to a classical-marxist view, in an industrial economy, just as the one supposed by the
model at hand, national income should be conceived as the wealth expressed in material terms
(products) and created along a certain period. Hence, there are only two kinds of income in an industrial
economy: wages and gross profits. The government and the financial sector do not create wealth,
because they do not create added value. They just appropriate of a share of the profits (constituted by
7
taxes and interests). Taxes and interests do not affect the profits amount. By this perspective, the
income evaluated in nominal terms and generated along the period t is just wages plus gross profits. So,
we have: Pt Yt  wt N t  rt Pt K t
(17)
Where rt is the profit rate and w is the nominal wage rate.
Profit rate rt can be seen as the product between profits share in the income (mt), the level of
productive capacity utilization (ut) and the “social productivity of capital” (σ). Thus, we can re-write the
expression (17):
mt  1  Vt qt
(18) ,
Where: Vt is the real wage rate.
Equation (18) shows that, given the labor productivity, there is an inverse relationship between real
wage and profits share.
2.4. Module 4: Inflation and Monetary Policy
In order to determine the rate of inflation of the economy at hand, we will suppose that:
(i)
Exports and imports are made only with final goods. So, variations in nominal
exchange rate do not have any direct impact upon production costs of firms;
(ii)
International mobility of labor is zero so that nominal and real wages are determined
only in accordance with the conditions prevailing in domestic labor markets.
(iii)
Domestic firms operate under an oligopolistic market structure, so they have
market-power. In other words, firms are price-makers in goods market.
(iv)
Due to the existence of uncertainty regarding the level of demand for their products
(which is the direct result of strategic interaction between price-decision of firms
under oligopoly), firms fix the prices of their products by means of a mark-up rate
over unit direct costs.
Based on this discussion, we have:


Pt  1  ztf wt qt
(19).
Where: zft is the mark-up rate set by firms of the productive sector.
The prices fixed by productive firms change according to: (i) variations of wages between
periods; (ii) variations of mark-up rates between periods; and (iii) variations of unitary requirement of
labor between periods. So, inflation rate in period t is given by:
1   t  




 1  ztf   wt   qt 
Pt




Pt 1  1  ztf1   wt 1   qt 1 
(20)
Where:  is the inflation rate in the t period.
The first step to determine the inflation rate at the t period t is to compute the wage inflation
(in other words, the rate of variation of the nominal wages between period t and the period t-1). Then,
we suppose that the nominal wages are the result of a bargaining process among firms and unions. In
this negotiation process, unions demand higher wages to cover the inflation losses of the previous
period and to increase the real wage rate to a certain target rate. This target rate is determined by the
conditions prevailing in the labor market and by productivity growth. Greater is the bargaining power of
unions, greater will be the target real wage in the determination of nominal wages.
In this sense, we have:
8
 wt  wt 1   Pt 1  Pt 2 

  
   Vt  Vt 1 
 wt 1   Pt 2 
(21)
Where: Vt is the target real wage in the period t.
Target-real wage is determined by:
Vt  1  0U t 1  2
1
(21a)
q
Using (19), (21) and (21a) in (20), we arrive at the following expression:
 1  z 0  z1f u t 1  z 2f  t 1 

1
t  
  t 1  1  1  0U t 1   2  Vt 1 
f
f
q

1  z 0  z1 u t  2  z 2  t  2 

 1   K t 1  I t  Gti

1   0 
  1

1
 1   K  I  G


t 2
t 1
t 1



(20a)
Equation (20a) is a kind of Phillips curve for the economy at hand. In fact, inflation rate at
period t is, among other variables, a function of unemployment rate at period t-1. We have also to notice
the presence of inflation inertia since inflation rate at period t depends on inflation rate at period t-1.
Finally, we have to notice that changes in capacity utilization and the aggregate stock of capital also
cause changes in the rate of inflation.
Regarding the operation of monetary policy we will suppose that monetary policy is conducted
in a Inflation Targeting Regime by means of fixing the short-term interest rate according to a Taylor's
Rule (TAYLOR, 1993). The equation for interest rate rule is given by:
 

it*  1   it*1    0  t 1   *  1 gt 1      2

(22)3.
Where: i* is the basic interest rate determined by the Central Bank;  is the interest rate inertia factor4;
The coefficients 0>0 and 1>0 represents, respectively, the given weight, in interest rate composition,
to the divergence of inflation rate of the previous period concerning the “natural” growth rate (); and
the to the divergence of the growth rate of real output (at the previous period) concerning the natural
growth rate. 2 is a constant.
2.5. Module 5: Financial sector and Fiscal Deficit.
Just as in the case of the productive sector, we suppose a oligopolistic structure of the banking
sector. Thus, banks are price-makers too. Therefore, they fix the interest rate of their loans to the
productive sector. The commercial banks define the interest rate charged by their loans (it) through the
application of a mark-up (zbt) over the short-term interest rate fixed by the Central bank (ROUSSEAS,
1986, pp.51-52). Thus, we have the equation:


it  1  ztb it* (23)
Banking mark-up is not constant through time. It varies between periods according to the
economic conjuncture and/or to the banks market power. Just as ARONOVICH (1994), we suppose that
banking mark-up is countercyclical, varying in the opposite direction of productive capacity utilization.
In fact, increases in the level of productive capacity utilization are related to sales increase and, by
3
The only restriction to the application of equation ( 22) as a rule for fixing the short-term interest rate is that nominal
interest rates can never be negative. So we can define a roof for the short-term interest rate. We will define this minimum value
for short-term interest rate as i*min, so the value of short-term interest rate in period t is given by:
*
it*  max imin
; 1   it*1    0  t 1   *   1 g t 1      2 

4

According to BARBOSA (2004), Central Banks operate monetary policy in a manner to smooth interest rate
changes over time. This interest rate smoothing generates a certain level of inertia in interest rate determination.
9
extent, to a reduction of productive sector`s firms default risk. This reduction allows to banks reduce
their spreads.
Other assumption in this module: increases in the inflation rate induce the commercial banks to
increase mark-up's rate. The intuition here is a higher inflation forces the Central Bank to increase the
short-term interest rate. Such action is accomplished in the attempt to prevent a divergence between
current inflation and inflation target. But it increases the volatility of the short-term interest rate,
contributing for an increase of “interest risk” (ONO et alli, 2005). In response to this increase,
commercial banks charges higher spreads. Banking mark-up is described just as it follows:


b
ztb  max zmin
; z1but 1  z2b t 1 (24)
Once fixed the loans interest rate, commercial banks attend the entire demand for loans of the
productive sector. That means that there is no kind of credit rationing, just as we see in new-keynesian
macroeconomic models. Therefore, the effective volume of credit conceded by commercial banks at the
t period is entirely determined by credit demand. Such assumption is in consonance with the hypothesis
of endogenous supply of money (KALDOR, 1986 and Moore, 1988). Creation of demand deposits is,
therefore, determined by expansion of banking credit. So, we have:
Dt  Dt 1  Lt  Lt 1 (25)
Where Dt is demand deposits at period t.
The government's fiscal deficit (DGt), by hypothesis, is entirely financed by the expansion of
the monetary base (Ht) at period t:
DGt  H t  H t 1 (26).
2.6. Module 6: External sector
The economy considered in the model at hand is a small open-economy with a floating exchange
rate regime that operates in a setting of imperfect mobility of capital. With regard to the degree of
openness of capital account, we adopt the assumption that only capitalists of productive sector are
authorized by law to use a part of the distributed profits by their firms to buy foreign assets. Direct
investment is the only way by which the capitals can flow out the domestic economy. There is no
interest-rate arbitrage5 .
Hence, the prices and the international inflation are determined by the next equations:
Pt*  (1   * t ) Pt*1 (27)
 *t   *   t
(28)
In which:  t is a white noise and  * is the inflation of the rest of the world (an exogenous and
random variable with constant average and variance).
The average rate of growth of the world economy is given by g t* , as follows:
Yt *  (1  g t* )Yt *1
(29)
g t*  g *   t
(30)
In which  t is the term of white noise related to the growth process.
Similarly, we suppose that the international interest rate fluctuates in random manner around a
constant value (an exogenous variable):
it*  i *   t (31)
5
So, the transfer of liquid funds from one monetary center (and currency) to another to take advantage of
higher rates of return or interest is prohibited by law.
10
where: i * is the prevalent average interest rate in international economy and  t is a white
noise associated with the international interest rate movements.
The current account balance is given by:
(32)
STC  Et Pt*  X t  M t   Et it*1 At*1
Since savings of productive capitalists are always positive, the economy in consideration is a
capital exporter. So, capital account balance will be always negative. The result of the capital account is
determined by:
SKC   Et At*  At*1 (33)
We assume the existence of a pure floating exchange rate regime. Because of that, the result of
the balance-of-payments is necessarily equal to zero, once the monetary authorities do not intervene in
the exchange market. So, we can write:



Et Pt*  X t  et M t   Et it*1 At*1  Et At*  At*1

(34)
Productive capitalists allocate their savings in foreign assets, so that capital account balance can
be written as:



Et At*  At*1  s c 1    1   Pt 1Yt 1  wt 1 N t 1  it 1   Lt 1   Et it*1 At*1

(35)
Combining the expressions (11), (12) and (35) in (34), with some calculus we have:

   E P* 


 Et 1 Pt*1 
 *

* 
t 1 t 1
 Y t 1  j 
 Yt 1    it*1 At*1   1   
Et  Pt   




 Pt 1 
   Pt 1 

1   Pt 1Yt 1  wt 1 N t 1  it 1   Lt 1   Et it*1 At*1
 

(36)

In the equation (36) the nominal rate of exchange (at the t period) is the variable that adjusts the
result of current account balance to the result of capital account in order to maintain the equilibrium in
the balance of payments. Solving the equation (36) to Et, we obtain:
Et 
1   1   Pt 1Yt 1  wt 1 N t 1  it 1   Lt 1 
   E P* 
 *  t 1 t 1 
Yt *1
 Pt   

P
   t 1 
 

E P
 j 
 Pt 1
*
t 1 t 1






Yt      it*1 At*1






(37)

We use the Monte Carlo method to generate the random values for the exogenous variables of
the model. The determinations of model`s parameters and the fixation of initial conditions follows
Samuelson´s Correspondence Principle (SAMUELSON, 1947) and the method of calibration
(HANSEN and HECKMAN, 1996, p.2).
Below, the table 1 describes the exogenous variables of the model (most of then generated by
Monte Carlo method). Inflation of the rest of the world is constant (equal to 0,025). The values of white
noises were also generated by Monte Carlo method (from an interval of [0; 0,01]).The terms used for
white noises were: , and 
11
Table 1 – Exogenous variables obtained by the Monte Carlo Method
t
g*t
i*t




Inflation of the rest of world (fixed at 0,025)
Growth rate of international economy (random numbers generated from the [0,005; 0,045] interval).
International nominal interest rate (random numbers generated from the [0,01; 0,12] interval).
Price elasticity of demand for exports (random numbers generated from the [-0,55; 0,7 ] interval).
Price elasticity of demand for imports (random numbers generated from the [-0,7; 0,85] interval).
Income elasticity of demand for exports (random numbers generated from the [1,85; 1,95] interval).
Income elasticity of demand for imports (random numbers generated from the [1,65; 1,51] interval).
2.7 Module 7: Private Sector`s Assets and Debts
The private sector of the economy has three social classes: productive capitalist, financial
capitalists and working class. Working class` propensity to save is zero. Workers have only their own
capacity to work; they do not have any other kind of wealth. Productive and financial capitalists own,
respectively, productive firms and banks, which existence is totally independent and distinguishable of
their owners. In this way, assets and debts of firms and banks are completely separated of the personal
wealth of their owners.
Productive firms own only capital stock as asset. It is financed by retained profits (net wealth,
F
Wt ) and bank loans (Lt). Therefore, their balance sheet can be expressed by:
Pt K t  Lt  Wt F (38)
Bank assets are represented by loans to productive firms and by bank reserves. Bank liabilities
are composed by net wealth ( Wt B ) and demand deposits (Dt). In algebraic terms:
Lt  Rt  Dt  Wt B (39)
The productive capitalist use its savings for the purchase of foreign currency assets. Thus, we
have:
Et At*  Wt cp (40).
Where Wt cp is the wealth of productive capitalists.
Finally, financial capitalists allocate his wealth ( Wt cf ) in two assets: demand deposits and cash
( M t ). So, we can write:
Dt  M t  Wt cf
(41)
Aggregating all assets and debts, we have:
Wt  Wt B  Wt F  Wt cf  Wt cp  Rt  M t  Pt K t  Et At*
(42),
Where Wt is the net wealth of private sector.
Monetary base (Ht) is equal, by definition, to the sum of bank reserves and cash owned by the
public. In this way, we have:
H t  Rt  M t (43).
As we have seen, only banks and financial capitalists take portfolio decisions. Productive
capitalists and firms allocate their wealth entirely in only one asset.
With regard to financial capitalists, we suppose that the amount of cash that they wish to hold
(at the t period) is equal to the stock of money they retained (at the previous period) plus the saved share
of net profit (at the previous period). Hence,
M t  M t 1  1   s f it 1 Lt 1 
(44)
Finally, with some calculus, from (26), (44) and (43), we have:


Rt  H t 1  M t 1   DG t   1   s f it 1 Lt 1  (45)
12
3. Simulation`s Results
Computational simulation model results6 can be synthesized in two parts. The first refers to
internal macroeconomic dynamics of the model. The second, described from exogenous variables
computed by Monte Carlo simulation processes, is related to external macroeconomics dynamics of the
model.
3.1. Internal Macroeconomic Dynamics
From Graph 1, that describes the evolution of real GDP along 73 periods, we extract conclusions
that are similar to the original Oreiro-Ono`s model for a closed economy. We note an irregular growth
and a non-explosive path of real GDP. Nevertheless, in this open model there is narrower fluctuations,
what does not occur in closed model.
Graph 1 – Real GDP
Gráfico 1 - Dinamica do PIB
6.000.000
5.000.000
4.000.000
3.000.000
2.000.000
1.000.000
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Source: model results estimated by authors.
Concerning to GDP growth, graph 2 demonstrates, initially, an explosive growth (a take-off, just
as described by ROSTOW, 1960). After that, a stagnation period, followed by an abrupt fall (economic
depression, at the 11th period) and an expansionist period with a sharply cyclic GDP growth path. Soon
after, we have a second depression, with smaller duration than the first. Then, the economy begin to
grow with larger volatility than the simulation of closed (and without endogenous technical progress)
Oreiro-Ono`s model.
6
To run this model, the software we employed was Excel 2002.
13
Graph2 – Growth rates of GDP
Gráfico 2 - Taxa de Crescimento do Produto Real
0,15
0,1
0,05
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
-0,05
-0,1
-0,15
-0,2
-0,25
-0,3
Source: model results estimated by authors.
The unemployment path describes peaks and “valleys” related to the performance of real activity
(graph 2). The growth rates “valleys” are near to the rate of 2,5%, that is equivalent to unemployment
level obtained by economies that exhibits cycles of high expansion (Japan, in the postwar; China, since
the final of 80`s; South Korea, from the final of 70`s; Ireland, in the middle of 90`s; Spain and Chile,
from the beginning of 90`s). The four peaks registered in simulation become smaller, what allows us to
suppose that - with the development of the economy - the unemployment rate volatility tends to
decrease (graph 3).
Graph 3 – Unemployment rates
Gráfico 3 - Taxa de Desemprego
0,450
0,400
0,350
0,300
0,250
0,200
0,150
0,100
0,050
0,000
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Source: model results computing by authors.
Graph 4 presents a slow, progressive and cyclical fall of financial fragility. We can see a tendency
of reduction of subjective rate of discount trajectory.
14
Graph 4 – Financial fragility (ft) and subjective rate of discount (dt)
Gráfico 4 - Fragilidade (ft) e Desconto (dt)
6,00
5,00
4,00
3,00
2,00
1,00
0,00
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73
ft
dt
Source: model results estimated by authors.
With three axes, graph 5 demonstrates the inverse relationship between interest rates and
investment. Furthermore, as the theory of investment predicts, we can see a lag-response (of about one
period) of investment to impulses of real interest rates.
Graph 5 – Investment (solid line) and real interest rates (dotted line)
Gráfico 5 - Juros reais e Taxa de Investimento
1.800.000
0,3
1.600.000
0,25
1.400.000
1.200.000
0,2
1.000.000
0,15
800.000
600.000
0,1
400.000
0,05
200.000
0
0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73
Taxa de investimento
Juros reais
Source: model results estimated by authors.
In the long term, we also see the underutilization of productive capacity. Again, the difference
regarding to the closed model is the cyclical outline of the graph. With the rise of real interests and the
disinflation at the 3rd period, there is a period of GDP growth stagnation, when the capacity utilization
degree arises (graph 2). Given the rising of inflation among periods 25 and 32, and the increasing of
15
real interest, this degree abruptly decreases and the real wage grow. Real interest and inflation, from the
period 54, show an unstable trajectory. Thus, the capacity utilization falls and the real wage arises again
(graph 6).
Graph 6 – Real interest (solid line) and profit rates (dotted line)
Gráfico 6 - Juros reais e Participação dos Lucros da Renda
0,5
0,4
0,3
0,2
0,1
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
-0,1
-0,2
Taxa de Lucro
Taxa de Juros
Source: model results estimated by authors.
3.2. External Macroeconomic Dynamics
In long-term, the dynamic interaction between real exchange rate and net exports is described by
the graph 10. In the periods where a real exchange rate appreciation occurs, we notice that net exports
decreases. Furthermore, its volatility tends to increase a lot.
Graph 7 – Exchange rates (solid line ) and net exports (dotted line)
Gráfico 7 - Câmbio real x Saldo Comercial
90,000
3.000.000
80,000
2.000.000
1.000.000
70,000
0
60,000
-1.000.000
50,000
-2.000.000
40,000
-3.000.000
30,000
-4.000.000
20,000
-5.000.000
10,000
-6.000.000
0,000
-7.000.000
1
3
5
7
9
11
13 15 17
19 21
23
25 27 29
31 33 35
37 39
câmbio real
41 43 45
47 49 51
53 55 57
59 61
63 65 67
69 71 73
75
saldo comercial
Source: model results estimated by authors.
16
The relationship between the exchange-rate and GDP growth rates approaches the conclusions of
McCombie-Thirwall`s model. When the real exchange rate appreciates, the real GDP tends to decrease.
It happens in several periods (graph 8). The reciprocal reasoning is also true. Simulation results
demonstrated that, after successive periods of rapid growth, there are periods of appreciation of
exchange rates because of the fall of net exports. In such periods, the price elasticities of demand for
exports were larger than the price elasticities of demand for imports. At the same time, the income
elasticity for imports is larger than income elasticity for exports. In the simulation process, those
elasticities was generated by the Monte Carlo method, with results that suggest a causal relation
between the increase of real exchange rate and the decrease of volatility of the level of openness of
current account.
It is possible to verify that the strong recession of period 13 was preceded by two cycles of
exchange rate depreciation (in the periods 8 and 11, respectively). These two cycles provoked a
reduction of the net exports (as we described in graph 7).
Graph 8 - Exchange (solid line) and growth rates (dotted line)
Gráfico 8 - Câmbio Real (Et) x Crescimento real do PIB (gt)
90,000
0,12
80,000
0,1
70,000
0,08
60,000
0,06
50,000
0,04
40,000
0,02
30,000
0
20,000
-0,02
10,000
0,000
-0,04
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
crescimento
41
43
45
47
49
51
53
55
57
59
61
63
65
67
69
71
73
75
câmbio real
Source: model results estimated by authors.
Two hyperdevaluations of exchange rates occurred in the periods 8 and 11. They cause a arise in
the exports and, for consequence, provoked an increase of the degree of openness of the current account
and of its volatility (graph 9).
17
Graph 9 – Degree of openness in the current account (solid line) and exchange rates (dotted line)
Gráfico 11 - Corrente de Comércio (% do PIB) x Câmbio real
140,0
6,000
120,0
5,000
100,0
4,000
80,0
3,000
60,0
2,000
40,0
1,000
20,0
0,0
0,000
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
Câmbio real
39
41
43
45
47
49
51
53
55
57
59
61
63
65
67
69
71
73
75
Corrente de comércio
Source: model results estimated by authors.
Note: foreign transactions as a percentage of GDP.
To conclude, we can observe a long-run tendency for the increase in the share of financial wealth
in total wealth. This increase is the result of the fact that productive and financial capitalists use their
personal savings only to buy financial assets. Productive assets are bought only by means of investment
decision of productive firms. This result is consistent with the ‘stylized facts´ of capitalist long-run
dynamics; according to which financial wealth tends to increase in importance in the long-term.
Graph 10 – Financial wealth share in total wealth
Gráfico 13 - Índice de Financeirização da Riqueza
1,2
1,0
0,8
0,6
0,4
0,2
0,0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75
Source: model results estimated by authors.
18
4. Final considerations
The central goal of this article was to build a simulation macrodynamic model for an open
economy with governmental activities, a flexible exchange rate-regime, inflation targeting, endogenous
technical progress and imperfect capital mobility. This model is an extended version of Oreiro & Ono`s
seminal model.
Oreiro & Ono`s model do not have exogenous variables. To build the open model, we apply a
Monte Carlo simulation to generate these variables.
With the model results, we verify that, under a internal macrodynamic view, there emerges a
cyclical, irregular and non-explosive growth path, which are more volatile than the Oreiro-Ono`s model
one.
In the open model, financial fragility exhibits a slow, progressive and cyclical tendency to fall,
while the discount rate series demonstrates a progressive reduction of its volatility.
Just as in Oreiro-Ono's original model, this open model also shows that there is no full capacity
utilization in the long term. The results of both models shows the stability of profit rate and profit share
in the long-term.
However, with regard to model`s external macrodynamics, we analyze the interaction among real
exchange rate and net exports in the long term. It allows us to conclude that, when a appreciation of real
exchange rate occurs, net exports falls and its volatility decreases.
In long-term, the dynamic interaction between real exchange rate and net exports shows that the
appreciation of exchange rate foregoes the decreasing of net exports. Therefore, the volatility of net
exports tends to increase a lot.
The conclusions of McCombie-Thirwall`s model are close to the results of the dynamic
interaction between exchange rates and GDP growth rates. In fact, when the real exchange rate
appreciates, the real GDP tends to decrease. The inverse dynamic is valid.
Two hyperdevaluations occurred. They enlarged exports and provoked an increase of the
commerce and its volatility.
Finally, there is a long-run tendency for increase of the share of financial wealth in total wealth.
This result is consistent with the ‘stylized facts´ of capitalist long-run dynamics; according to which
financial wealth tends to increase in importance in the long-term.
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