Download Controls of capitals in emergent economies

Capacity Utilization, External Debt Capital Controls in Emerging Economies
An analysis based on computational simulations
*
Inácio Guerberoff **
José Luís Oreiro***
FIRST DRAFT
Abstract: This article analyzes the impact of capital controls over time-path of selected macroeconomic
variables, as well as the effects of these controls over the economy’s level of external fragility. First of all,
we present a Post-Keynesian Macroeconomic Model, which introduces capital controls as a choice variable
of economic policy. For computer simulation, we have selected a set of plausible values – in economic terms
- for the structural parameters of the model. Based on these parameters, we analyzed the dynamic behavior of
capacity utilization, external debt as a ratio of GDP, net exports as a ratio of GDP and level of domestic rate
of interest under different initial conditions for the level of external debt. After that, we analyze the degree of
economy’s fragility to external shocks as, for example, variations in the level of international rate of interest
and in the level of international trade flows. Based in this framework, we conclude that capital controls may
contribute to reduce the volatility of external debt (as a ratio of GDP) to exogenous shocks, but amplifies the
effects of these shocks over the level of capacity utilization. In this context, desirability of capital controls is
conditional to society’s preferences over capacity utilization and external debt volatility. If society has a
stronger aversion to output volatility than to external debt volatility, capital controls should not be used.
However, if society has a stronger aversion to external debt volatility than to output volatility, capital
controls can improve social welfare. Since emerging economies like Brazil and Argentina have a long lasting
problem of external constraint to economic growth, this last case seems more relevant for these economies.
Key Words: Capital controls, post keynesian economics, macroeconomic dynamics.
March, 2004
“It is ideas, not vested interests, which are dangerous for good or evil” (J.M.Keynes)
*
Paper to be delivered at Congress of Economic Growth and Distribution.
Graduate Student in Economics at Universidade Federal do Paraná, Curitiba, Brazil. E-mail: [email protected].
***
PhD in Economics at Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil and Associate Professor of Economics at
Universidade Federal do Paraná, Curitiba, Brazil. E-mail: [email protected]. Web-mail: www.joseluisoreiro.ecn.br.
**
1 – Introduction
The discussion on capital controls in Brazil and in the world has been made, usually, based with a
ideological bias – it is argued, for example, that its adoption would represent, for the country that adopts
them, an exclusion from international capital flows and, consequently, of the benefits of the process of
financial globalization – or with a purely technical bias, which advocates the impossibility of an effective
implementation of any form of controls, given the capacity of the investors to by-pass the established
regulations (cf. Edwards, 1999). Such discussion does not seem to take in consideration that some recent
experiences of capital controls had reached – in some degree – success in some countries, as Chile and
Malaysia, as recognized by a recent study made by technicians from the IMF (Ariyoshi etal, 2000). In other
words, the arguments against the intervention of the State in the movements of capitals between frontiers
seem to be supported more in preconceptions of ideological nature than in solid theoretical and empirical
arguments.
Nowadays, considering the typical financial/exchange instability of the recent world-wide experience,
even conservative agencies, like the IMF, accepts the possibility, in certain circumstances, of the temporary
use of certain types of capital controls. Even in the mainstream of economics profession, many economists
have criticized the benefits of the process of financial liberalization (Tobin, 1978; Rodrik, 1998; Stiglitz,
1999 and 2000) and defended the introduction of capital controls to increase the autonomy of the monetary
politicy and to reduce the external vulnerability of the emerging economies.
In the Brazilian case, the recent experience of exchange instability, since the Asian crisis, has
disclosed the difficulties of manegement of the macroeconomic policies in a country with high dependence of
foreign capitals, weak currency and an open capital account. A new style of economic policy becomes
necessary to create conditions for a sustainable and financially stable economic growth. The adoption of
some mechanisms of capital controls may help in the implementation of this policy, together with others.
Even though the reasons presented from its defenders may be correct reasons for the introduction of
capital controls, a deeper analysis on the desirability of them would demand the construction of a complete
macroeconomic model, where the effect of capital controls on variables like the degree of capacity
utilization, external indebtedness, net exports and etc could be evaluated. In fact, the debate on capital
controls has been lead sometimes based in a purely empiricist bias, where the effect of capital controls on the
macroeconomic performance of selected countries are availed with little or no theoretical content at all;
sometimes based in a simple theoretical framework, in which the secondary and/or of long-run effects of
these controls are not evaluated.
1
In this context, the objective of this article is increase our understaning of the macroeconomic effects of
the introduction of capital controls through the construction of a complete macroeconomic model. The model
that we will present will be used to answer two basic questions:
a)
What is the impact of capital controls on time path of selected economic variables like degree of
capacity utilization, external indebtedness as ratio of the GDP, domestic rate of interests and net
exports as a ratio of GDP?
b)
The capital controls can reduce the external fragility of the economy, that is, can reduce the
sensitivity of the economy to external shocks as, for example, variations of the international rate
of interests or variations in trade flows?
To achieve this target, we will proceed in two stages. Initially we will specify the structure of the
theoretical model from which this analysis will be lead, verifying the conditions of existence and stability of
the positions of long-run equilibrium. This verification will be made not only from the qualitative point of
view, but will also be complemented through computer simulation. The initial objective of these simulations
is to deduce a set of economically reasonable values for the parameters of the structural equations of the
model.
In the second stage, we will use the values deduced in the first stage (i) to compare the trajectory through
time of economic variables under different levels of capital controls: no controls and partial controls; (ii) to
analyze the sensitivity of the economy to external shocks under different levels of capital controls.
The present article is divided in four sections including this introduction. In section 2 we will present the
basic structure of the theoretical model used through out this article. Section 3 is dedicated to the simulation
exercises. The conclusions are in section 4.
2 – External indebtedness and Capital controls in a post-Keynesian macroeconomic model.
The model that will be developed in the present section is an extension of the model presented in
Oreiro (2004). The original version of the model presents a economy in the which (i) investment in fixed
capital is positively influenced by the ratio of external debt to GDP, due to the positive effect of a greater
diversity finance sources over borrower´s risk ; (ii) perfect capital mobility in the sense of Mundell (1968)
and Fleming (1962), i.e it is valid the so-called "uncovered interest rate parity"; (iii) the nominal exchange
rate is fixed and; (iv) the country-risk is endogenous, varying with the external debt as ratio of the GDP.
In the version of Oreiro´s model presented here, we will consider an economy that has capital
controls in the form of taxes over entry and/or exit of financial applications of the country.
2.1 Structure of the model and the short-term equilibrium
Let us consider an economy where the companies operate in oligopolized markets, determining their
2
prices based in a fixed mark-up over direct production costs, composed by labour costs and imported
materials. (cf.Taylor, 1983). So we have:
p  (1   )[ wb  ep0* a 0 ]
(1)
Where: p is the domestic price level, w is the rate of nominal wage, p* is the international price level, e
is the nominal exchange rate, b is labour requirement per unit of output, a 0 is the requirement of imported
raw materials per unit of output and  is the rate of mark-up.
Let r be the rate of profit and u the degree capacity utilization. It can be demonstrated that the profit
rate is given by:
r

1
u
( 2)
The goods market is in balance when the condition below is true:
pC  pI  pE  pX
(3)
Where: pC is the nominal value of the expenses in consumption, pI is the nominal value of the expenses in
investment, pE is the nominal value of the net exports and pX is the nominal value of the real income.
We will assume the existence of two social classes – capitalists and workers – which differentiates
among thenselves based on the origin of their income – profits or wages – and based on the propensity to
consume out of available income. In this context, we will assume that the workers "consume everything that
they earn" so that its propensity to consume is equal to one. 1On the other hand, the capitalists consume a
fraction cp of its incomes (which are constituted solely of profits), saving a fraction sp= (1-cp) of its income.
This way, the nominal value of the expenses of consumption is given by:
pC  wbX  (1  sc )rpK
(4)
Substituting (4) in (3) we have, after some algebra, that:
I
E

  sc
 qa 0  0
X X
1
(5)
The investment function is composed by three elements: an autonomous component (  0 ), one that
depends on the difference between the rate of profit and rate of interests ( 1[ri] ) and finally a component
that depends on the external indebtedness as ratio of GDP (  2 z ). We will assume that an increase of the
external indebtedness as ratio of the GDP will result in an increase less than proportional in investment, that
is, <1.
1
Or either, its propensity to save is equal the zero.
3
I
  0   1 [r  i ]   2 z 
X
0    1 (6) 2
The net exports function has an autonomous element (  0 ) and another element that depends inversely
on the level of capacity utilization, since an increase in economic activity will raise imports, leaving gross
exports unchanged. We have the folowwing equation:
E
  0  1u (7)
X
In a context where the mobility of capitals is not perfect due to the existence of capital controls, the
domestic rate of interests can be different from the level determined by the uncovered interest rate parity.
One of the reasons for the introduction of capital controls is exactly to give more autonomy to the conduction
of monetary politicy. Capital controls allows a greatter degree of freedom to fix domestic interest rates in
accordance to domestic objectives.
This way, we will assume that the domestic interest rate is formed by a weighed average between the
"desired interest rate" of the Central Bank, that is, the level of the domestic interest rate that is compatible
with the attendance of the objectives of the domestic economic policy, and the value given by the "uncovered
interest rate parity". This weighted average reflects the level of capital controls. The bigger are these
controls, greater is the weight of the rate of interests desired by the Central Bank in the determination of the
effective value of the domestic rate of interests.
Let i be the desired interest rate of the Central Bank and i *   (where i
*
it is the international
rate of interests and  the value of country-risk) the domestic interest rate compatible with the "uncovered
interest rate parity" in the absence of capital controls and assuming a regime of fixed exchange. The
domestic rate of interests can be written of the following way:
i  (1  k )(i *   )  k i
; 0  k 1
(8)
In respect to country-risk, we will assume that it possesss a minimum level  0 , equal to risk premiun
demanded by investors from sovering debt of countries with "investment grade". This minimum level of risk
will be obteined, in the present model, when the external debt as ratio of the GDP is zero. For positive values
of the external debt as ratio of the GDP, the risk premiun is an increasing function of the level of the external
indebtedness. In other words, the risk premiun is endogenous, so we have that:
   0  1 z
; 1  0
(9)
Substituting (9) in (8), we get the following expression:
i  (1  k )(i *   0  1 z )  k i
2
(10)
Regarding the micro foundations of this investment function see Oreiro (2004).
4
Substituting (10) in (6), we get an equation that determines the investment as ratio of the real GDP as
function of the external indebtedness and the profitability:
I
  0   1 [r  (1  k )(i *   0  1 z )  ki ]   2 z 
X
Placing u in evidence in the equation (2) and substituting the resultant in (7), we get:
E
(1   )
  0  1
r
X

(7 a )
Substituting (6a) and (7a) in (5), and placing r in evidence we get the following expression:
r
1
( 1 m
1

 )
2


z    1 (1  k ) 1 z     1 ki  (1  k )(i *   0 )

(11)
1

ep *
is the real rate of exchange and m 
is the participation of the profits in income and
1
p
  0  0  sc m qa0 .
Where q 
Equation (11) presents the value of the current rate of profit for which the good market is in
equilibrium, that is, for which aggregate demand is equal to real income. It’s the short run equilibrium value
of the profit rate.
The shortrun equilibrium will be stable if  1m 1 1  0 .
Differentiating (11) with respect to r and z, we get the following expression:


r
1

 2 z  1   1 (1  k ) 1 (12)
1
z ( 1 m   1 )
The signal of
z increases
r
will depend on  2 z 1 1 (1 k ) 1 , which varies depends on z . This way, while
z
r
will pass from positive to negative, characterizing a nonlinear relation between the
z
profitability and the indebtedness with the format presented in Figure 1:
5
Figure 1 - Profitability as a function of the indebtedness
From (12) we know that
  2


z  
  1 (1 k ) 1 
1
1
 z*
r
 0 if the following condition is obeyed:
z
(13)
2.2 Long run dynamics and multiple equilibrium
To analyze the long-run dynamics of this economy, we will initially assume that goods market adjusts
slowly to the divergences between aggregate demand and real income. This way, the dynamics of the profit
rate is explained by the following differencial equation:
r   (EDB ) (14)
Where:



EDB  ( 1  1 m 1 )r   2 z  1 (1 k ) 1 z    1 ki  (1 k )(i *   0 )

is the excess of demand in the goods
market.
According to Simonsen and Cysne (1995), the differential equation that describes the dynamics of the
external debt is given by:
D  i e D  H (15)
Where: D
it is the accumulated external indebtedness, H is the liquid transfer of resources from abroad and
i e is the interest rate on external debt.
Differently from the domestic rate of interest, the external interest rate is not modified by the capital
controls, being determined, therefore, from the folowing equation:
i e  i *   (16)
Differentiating z with respect to the time, we get the following expression:
z 
D X D

X X X
(17)
Substituting (15) in (17) and assuming that the rate of growth of the product is exogenous and equal
to g 3, we get the following expression:
z  (i e  g ) z 
H
(18)
X
3
This assumption is necessary since the model presented here does not possess a equation capable to determine the rate of growth
of GDP. The usual assumption of post-Keynsian growth and distribution models is that the rate of growth of capital stock is equal
to the rate of growth of income. However, as capacity utilization is an endogenous variable in this model, then this equality is only
correct steady-state. Out of steady-state, the degree of capacity utilization can chenge over time, making the rate of growth of real
income to be greater or smaller than the rate of growth of capital stock.
6
The liquid transfer of resources from abroad is nothing more than, in the economy in consideration,
the value of net exports4. This way, the final expression for the dynamics of the external debt as ratio of the
GDP is given by:


z  i *   0  1 z  g z  0   1 m 1 r
(19)
In steady-state the rate of profit and the external indebtedness are constant through time. So, to
analyse the long-term equilibrium, we define two locus: r  0 and z  0 , whose inclinations are given
respectively by the following equations:

2 z 1  1 (1  k ) 1
 r 

 
(1   1m 1 )
 z  r 0

(20)


i *   0  g  2 1 z
 r 
(21)
  
 1m 1
 z  z 0
Previously we demonstrated that the locus that describes the combinations of r and z for which the
goods market is in equilibrium has the format of a parabola with down concavity. In the equation (21) we can
see that – assuming i *   0  2 1 z  g , condition for which i  g is enough – the locus that describes the
combinations of r and z for which the external debt is constant through time has negative inclination for all
the values of z.
This way, one of the possible configurations of the long-run equilibrium of the economy in
consideration would be the one in figure 2.
Figure 2 - Long-run equilibriums
In figure 2 we visualize the existence of two positions of long-run equilibrium. The first one is
characterized by a high profitability (r1) and a low level of external indebtedness (z1) – which we will call
equilibrium with low indebtedness - and the second is characterized by a low profitability (r0) and high level
of external indebtedness (z 0).
4
We are assuming that the balance of the invisible balance not-factors is equal the zero.
7
2.3 - Analysis of stability in the case where  < .
We will use the trace-determinant methodology to analyze the stability of the system.
The Jacobian matrix of the system is given by:
 r

J   r
 z

 r
r 
1
 1

z     ( 1  1 m )  ( 2 z  1 (1 k ) 1 ) 
z  
 1m 1
i *   0  g  2 1 z 

z 


Where:
 (1  1m1 )  0 (22)
 ( 2 z 1 1 (1 k )  ) (23)
i
 1m 1  0 (25)
*

  0  g  2 1 z  0 (24)
The values of the determinant and the trace of the matrix are:
DET ( J )  (22) * (24)  (23) * (25)
TR ( J )  (22)  (24)
The system will be unstable of the saddle path type if determinant of the Jacobian matrix is negative
(cf. Takayama, 1993).
If (23) is greater than zero, the determinant will be negative. Dividing (23) by gamma and isolating z,
we have:
  2


z  

(
1

k
)

 1

1
1
 z*
(26)
From (26) we observe that the equilibrium with low indebtedness, that is at left of z *, is necessarily
unstable of the type saddle path.
As the balance with high indebtedness is at right of z *, it may be stable, depending still on the trace
of the Jacobian matrix. For this equilibrium to be stable is necessary that the trace be negative. We have,
then, that:
 ( 1  1 m 1 )  i *   0  g  2 1 z
This will occur if:
z
 ( 1  1 m 1 )  i *   0  g  **
z
(27)
2 1
The condition (27) is necessary but not a sufficient condition for stability of the system. Moreover it
is necessary that determinant is positive, that is, z>z *. In other words, the equilibrium with high indebtedness
will be stable if z * < z **. For this to occur the following condition must be true:
8

1
  2
 1  ( 1  1 m 1 )  i *   0  g

 

(
1

k
)

2 1
1 
 1

Placing g in evidence, we have:
1
  2
 1
  ( 1  1 m 1 )  i *   0  g *
g  2(1 k ) 1 
  1 (1 k ) 1 
(28)
For the equilibrium with high indebtedness to be stable is necessary that the rate of growth of the real
product be bigger than a certain critical level g*, which depends, among others variables, on the level of
capital controls. If this condition is not true, the equilibrium with high indebtedness will also be unstable.
2.4 – Analysis of Stability in the case where   .
We will now abondon the hypothesis that the goods market adjusts slowly to the situation of excess of
demand, that is, we will assume that the degree of capacity utilization is always equal to its short-run
equilibrium value. This way, the dynamic system previously presented will be reduced to only one
differential equation – the expression (19) – where the dynamics of the external indebtedness depends only
on the value assumed from the variable z , since the profit rate will have assumed its value of balance, being
a nonlinear function of z in accordance with the equation (12).
In this context, the analysis of the stability of the system is simplified. This happens because the
economy will be operating continuously on the locus r  0 and its dynamic will be given only from the
equation (19). If the economy operates in a point of the lócus r  0 above the locus z  0 , the combination
external profitability-indebtedness will be such that the external debt as ratio of the GDP will increase
through time (Figure 3). However, if the economy operates in a point over the locus r  0 below the locus
z  0 , then the combination external profitability-indebtedness will be such that the external debt as ratio of
the GDP will diminish through time. This way, the equilibrium with high indebtedness will be stable, while
the equilibrium with low indebtedness will be unstable. This means that if the initial level of external
indebtedness is higher than the one of the balance with low indebtedness, the economy will converge to a
position of long-run equilibrium characterized by high external indebtedness.
9
Figure 3 - Dynamic of long stated period with instantaneous adjustment in the goods market
3 – Computational simulation of the Theoretical Model.
In this section we will use the differencial equations of the theoretical model developed in the
previous section to simulate in a computer the possible time paths of some relevant economic variables:
profitability, external debt as ratio of the GDP, domestic interest rate and net exports as ratio to GDP.
3.1 – The simulation methodology
The simulation of a economic model makes possible to analyze some practical properties of the
model, as well as verify the economical plausability of the dynamics studied in the qualitative analysis.
There are two ways to develop an economic simulation. In the first one, using a methodology that we
will call bottom-up strategy, a computational model with sights to the simulation is constructed. The
behavioral functions and some parameters are defined and drawn in the modeling process for the specific
objective of computational simulation. In general we get more precision in the resulting time series and more
flexibility of the behaviors of the system, but we lose analytical possibilities. The bottom-up strategy is used
when we want to take advantage of the flexibility of the computational language in comparison to the
algebraic one, as conditional behaviors, differentiated repetitions in diverse functions, among other behaviors
that could not be reproduced through the traditional algebra (or it would be unnecessarily complex to use).
The second way uses a methodology that we will call top-down strategy. The objective is to adapt an
existing economic model to a computer simulation. Without modifying the equations of the model, its
behavior is tested under real or reasonable parameters, and is verified the behavior in the time of the
economic variables. Because it is a numerical analysis of a qualitative work, sometimes we conclude that
certain conditions that were theoretically possible in the qualitative analysis are found to be impossible or
non-realistic through the computational simulation. This way, the top-down strategy is an important
complement to the qualitative analysis, because it allows us to have a clearer idea of the relevance of the
10
theoretical conditions in the which certain behaviors can or not be observed. Another result given by the
quantitative analysis with this method is the analysis of the reasonability of the dynamics observed in the
qualitative models, like convergent cycles and oscillations.
The methodology used in this work is the second. Starting with a theoretical model written in
mathematical form, we use reasonable numbers for the parameters of the behavioral functions of the model.
5
Some of these parameters, however, are of an unknown magnitude. For these parameters, we use the
methodology of Samuelson´s correspondence principle, that is, we use the values that are needed for the
time path to be realistic.
For example, attributing values for the "observable" parameters of the model based on what seems
reasonable for a country like the Brazil, and adjusting the values of the parameters for which no a priori
estimate can be made based on the conditions of existence of the equilibriums with low and high
indebtedness; we verify that the stability of the equilibrium with high indebtedness in the case where   
would only be possible with unreasonable values for the parameters of the model. In effect, the attendance of
the condition (28) demands that the rate of growth of the real GDP to be significantly bigger that 6 %. Still, if
we add the necessary condition that the equilibrium point with high indebtedness to be situated in the region
between z * and z ** , we need a rate of growth of the GDP of 24% a year ! This way, we have a model
without stable equilibrium for reasonable parameter values.
The economists, usually, have a great discomfort with equilibrium positions that are not stable. This
discomfort is based on two positions. The first one, defended by Samuelson (1945), establishes that an
unstable equilibrium is a transitory position and, as such, not observed empirically. The second, defended by
Blatt (1983), establishes that (unbounded) instability generates a dynamics such that the endogenous
variables of the economic system converges to an impossible state in a finite interval (even, in some cases,
very long) of time.
This reasoning, however, does not seem enough convincing to justify the abandonment of a
theoretical model in which the equilibrium positions are not stable. Let us consider, for example, the
theoretical literature that deals with the issue of the hiper-inflation. This literature is based on models of
representative agent with infinite horizon of planning, in the which the currency is the only asset, that is, the
only way in which the representative agent can carry purchase power in the long-run (cf. Blanchard & Fisher,
1989 pp.239-245).
This class of models admits the existence of a position of stationary in which the real value of the
monetary balances is constant through time. This equilibrium is, however, unstable: if the real value of the
5
This attribution is made on the basis of the existing countable estimates regarding the values of the same ones.
11
monetary balances gets lesser of that of equilibrium, then the economy will enter in a dynamic path such that
this value will converge to zero in a finite interval of time. That is, the value of the currency will tend to zero
in the long-run. This position is clearly impracticable in the economic point of view, since it means the
reversion of exchange technology to direct barter, what it is not compatible with the high degree of
specialization and division of the work in a capitalist economy. However, this instability is not seen as an
anomaly or something that puts down against the utility of this class of models. This is because hiperinflation, even being a rare event, is not a phenomenon impossible to occur. In fact, in century XX we can list
at least half dozen of historical experiences of hiper-inflation.
Based in this analogy, we can affirm that the analytical utility of a model that presents unstable
equilibrium consists exactly in showing the necessity of the accomplishment of structural reforms, led or not
by government, with the objective to stabilize the economic system, thus preventing the emergency of
economically impracticable states in the long-run.
In the simulations that follows, we will analyze the behavior of the endogenous variables in an
interval of time short enough to prevent that these variables assume impossible or unreasonable values. The
objective is to make what we will call comparative dynamics, that is, we will compare the trajectories
through time of the endogenous variables that can be gotten from different values of the parameters on the
model. A particular interest will be devoted to the comparative dynamics of the capital controls. In other
words, we will compare the trajectories of the diverse endogenous variables that can be gotten from different
values for the level of the capital controls.
3.2 – The process of choice of the values of the parameters.
Taking as base the principle that the values of the parameters must be numbers that are reasonable
under economic point of view, and considering that the economy in analysis is an emerging country, that
possess a great (but not perfect) mobility of capitals and a high external indebtedness; we considered the
following set of parameters in the simulation exercises:
Parameter
Description
Value
Parameter
Description
Value
sc
Propensity to save of the
capitalists
0.15
0
Autonomous determinant of
net exports
0.1
m
Profit share
0.5
1
Sensitivity of the imports to
the activity level
0.33
i*
International interest rate
0.02

Rate of decrease of the
investment with
indebtedness
0.2
0
Risk premium of countries with
investment grade
0.03
i
Target interest rate
0.03
12
1
Sensitivity of risk premium to
the total debt
0.2
a0
Unitary requirement of raw
materials
0.5
0
Autonomous determinant of
the investment
0.067
q
Real exchange rate
0.2
1
Sensitivity of the investment to
the difference between interest
and profitability
0.6
g
Growth rate of the GDP
0.035
2
Sensitivity of the investment to
the total debt
0.1

Speed of adjustment in the
goods market
0.1
Table 1 - Parameters of simulation
In Table 1 the values of the parameters  1  2 , 1  1 , and  had been chosen in a way to allow the
existence of two positions of long-run equilibrium, such as in the developed theoretical model in the previous
section. The other parameters had been chosen based on reasonable values for an emerging economy as, for
example, the Brazilian economy. Using k = 0,1 get the result presented in Graphic 4 below at the result
presented in figure 4:
Figure 4 - Curves with the parameters used in the simulations and k=0.1
In Figure 4, we see the existence of two equilibriums. In the first one, with low indebtedness, the
relation debt/GDP is equal to 0.75% and the profitability is 16,65%. In the second, with high external
indebtedness, the relation debt/GDP is of 52,75% and profitability of 7,03%.
3.3 Compared dynamics for the case of  <  under different levels of capital controls
In the analysis of comparative dynamics we will use the values of the parameters defined previously
(except the value of the capital control, k), and we will analyze the trajectory of the endogenous variables
under two different scenarios for the initial value of the external debt as ratio of the GDP: 10% and 25% of
the GDP (corresponding to z = 0.1 and z = 0.25). In each of these scenarios we will analyze the impact of
different levels of capital controls (no controls: k = 0, or partial: k = 0.1) on the dynamics of the economic
variables. It is good to note that the initial point corresponds to a situation of equilibrium in the goods
market.
13
Scenario 1: Low Initial Indebtedness
In figure 5 we observe that in the initial periods of the time path of the interest rate, the absense of
capital controls generates a higher interest rate than the one than the one generated by a situation of partial
capital controls. This happens because capital controls allows the Central Bank to fix an interest rate lower
than the one that would prevail in a situation of perfect capital mobility. In fact, in t = 0 the domestic interest
rate in a regime of no capital controls would be of 6,98% per period, while in a regime of partial capital
controls, it would be 6,59% per period, with the parameters used in the simulation. This happens because the
capital controls modifies the initial interest rate directly, as it can be seen in (8).
As time passes, however, this relation is reverted: the domestic rate of interests in a regime of absense
of capital controls is lower than the one resulted in the other regime. This behavior is consequense of the
dynamics of the degree of use of the productive capacity and the external indebtedness: because the domestic
interest rate is lower in the initial periods in the case of partial capital controls than in the case of absense of
it, the investment and the degree of use of the productive capacity will be higher in the first case. A bigger
level of use of the productive capacity will generate a smaller value for the liquid exportations as ratio of the
real GDP and generate, therefore, a faster accumulation of external indebtedness. This explanation is proven
by the analysis of Figures 6, 7 and 8:
Figure 5 - Interest rate
Figure 5 - Liquid exportations (E/X)
Figure 6 - External debt
Figure 7 - Profit rate
14
Scenario 2 : High Initial Indebtedness
The dynamics of the interest rate under different levels of capital controls in the case where the initial
level of external indebtedness is 25 % of the GDP is shown by Figure 9:
Figure 8 - Interest rate
Figure 9 -
Figure 10 - External debt
Figure 11 - Profit rate
Liquid exportations (E/X)
As in the previous case, we observe here that in the initial periods of the simulation the interest rate is
smaller in a regime of partial capital controls than in a regime of perfect capital mobility The difference with
the previous case is in the initial level of the interest rate in both cases. In the case of no capital controls, the
initial value of the domestic interest rate is 10% per period. In a regime of partial capital controls the value is
only 9.3% per period.
In figure 10 we observe the time path of the net exports under different levels of capital controls. We
can see that net exports as ratio of the GDP on both regimes keeps a smaller deficit, in comparison with the
case of low initial indebtedness. The reason for this apparently "good behavior" of the commercial balance is
due to the effect of the higher interest rate on the degree capacity utilization. Because the country-risk is
higher in the case where z(0) = 0,25 than in the case where z(0) = 0.1; the interest rate will be higher in the
first case that in the last one. This way, the investment and, consequently, the degree of capacity utilization
15
will be lower in scenario 2 than in scene 1. As net exports are inversely related to the degree of capacity
utilization, the trade balance will be higher in the scenario with high initial indebtedness than in the scenario
of low initial indebtedness.
3.4 Comparative statics for the case where  - >  for different conjunctural scenarios
As seen in section 2.4, relaxing the assumption of slow adjustment in the goods market, we have the
occurrence of stability in the equilibrium with high indebtedness. In fact, when running the dynamic
simulation with the same initial parameters of the analysis of section 3.3 and using the instantaneous
adjustment in the goods market, we verify a convergence with low oscillation:
Figure 12 - Profitability in time
Figure 13 shows only the behavior from t=20 in order to point the small damped oscillations that
occur due to the adjustment caused by the dynamics of the external indebtedness (equation (19)).
We can analyze the different positions of equilibrium where economy is taken in different
conjunctural and structural situations.
The tables in page 19 shows the results of these simulations. Each table analyzes the impacts of
variations in one determined exogenous variable. Table 2, for example, shows the values of equilibrium in
three scenarios: the standard scenario for international rate of interest used in the work ( i *  0.02 ), an increase
*
*
of 0,5 percentile point ( i  0.025 ) and a fall of 0.5 percentile point ( i  0.015 ). In each one of the three cases,
the table informs the equilibrium values of r and z in the cases of absence of capital controls ( k  0 ) and
*
in the case of partial capital controls ( k  0.1 ). For example, when i  0.015 and there are partial capital
controls the values of equilibrium of the profitability and of the indebtedness they are 5.87% and 57.24%,
respectively.
The tables also shows the percentile variations in the endogenous variables in relation to the basic
case (enhanced in the tables with the edge in boldface) in fields " r1 / r and z1 / z " and " r2 / r and z 2 / z ".
The variations with subscript 1 (for example r1 / r ) relate to the first case of variation (that is, the value to
16
the right of the basic case), and with subscript 2 (for example z2 / z ) relates to the second case of variation.
For example, we can see in Table 3 that, when the independent value of the liquid exportations passes from
 0  0.11 to  0  0.1 in the absence of capital controls, the equilibrium profit rate increases in 19,15%, and the
equilibrium debt has a -38,37% fall.
Scenario 1 – Variations in the international rate of interest
We analyze the impact of a variation (up and down) of international interest rate ( i * ) in 0,5 percentile
points. The results are presented in Table 2
We see here an interestning result: when the international interest rate increases the equilibrium
profitability increases and the equilibrium debt decreases. It is important to stand out that we are analyzing an
equilibrium position, and not instantaneous effects. At first, there is a reduction of the profitability (that has
instantaneous adjustment). Because the profitability is smaller than the one that leads to the equilibrium of
the debt, the economy enters in a trajectory of reduction of the debt and increase in profitability, that results
in a smaller debt and a bigger profitability than the initial values.
Scenario 2 – Variations in trade flows
The variable of the model that reflects changes in international trade is  0 , the autonomous
component of net exports, given that the term  1u reflects imports, that are induced by variations in the
degree capacity utilization.
The first comment that can be made on the results (see Table 3) is the huge impact of changes in
exports over equilibrium values. This happens because the profitability that balances the goods market is
more sensible to net exports than the one that balances the debt6. This behavior can be visualized in the
comparative graph of the two situations (Figure 14).
 0 in  0 modifies r of balance in
6
An alteration of
e
1  0 , we have that
 0
 0
1
in r  0 , and
in. z  0 As  1 m 1  0
1
1
 1 m  1
 1m
 0
 0
, resulting, of this form, in. r|r 0  r| z 0

1
 1m 1  1m 1
17
Figure 13 - Effect of reduction in the independent component of the liquid exportations
In a context of depression in international markets, the presence of capital controls improves the
response of the level of activity to the new situation in the equilibrium. On the other hand, the reduction of
the equilibrium indebtedness is smaller. In the case of an increase in exports, however, we observe the
opposite. In section 3.5 we analyze these different behaviors under the perspective of the social welfare.
3.5 Welfare Analysis
The results gotten in the simulations on section 3.4 allowed the observation of relations of cause and
consequence for qualitative analysis and conjunctural considerations. The variations verified while
comparing the results in the presence and in the absence of capital controls were, however, non-conclusive.
In cases like variation of the international rate of interest, the capital controls intensified the variation in the
rate of capacity utilization, but on the other hand it attenuated the variation in the external indebtedness.
18
Results of the simulations for the case r 
K 0
r
z
K  0.1
z1 / z e z2 / z
i *  0.02
i *  0.025
10,61%
11,51%
9,70%
8,58%
41,13%
36,55%
45,51%
-11,13%
i *  0.015 e
z1 / z e z2 / z
i *  0.015 e
i *  0.02
i *  0.025
-15,73%
7,03%
8,19%
5,87%
16,50%
-28,33%
24,51%
52,75% 48,13%
57,24%
-8,76%
18,93%
Table 2 - Variations in the international interest rate
K 0
r
z
K  0.1
z1 / z
 0  0.11
 0  0.1
 0  0.12
10,61%
12,63%
7,73%
19,15%
41,13%
25,35%
55,11%
-38,37%
e
z2 / z
z1 / z
z2 / z
 0  0.11
 0  0.1
 0  0.12
-38,80%
7,03%
10,61%
2,01%
50,92%
-81,06%
117,40%
52,75%
35,16% 69,39%
-33,35%
97,35%
e
e
e
Table 3 - Variations in the world commerce
19
Welfare analysis of capital controls demands, therefore, a method of quantification of it. For this,
initially we will assume that the society desires stability of the endogenous variables of the model (activity
level and external indebtedness). The weight that the society gives for these variations, however, can change.
Two cases illustrate this behavior: German society, for example, seems to show a very low tolerance for the
oscillations in the inflation levels, probably because of two traumatic moments in its history
–
the
hiperinflations of 1923 and 1948. The North American society, on the other hand, seems to show little
tolerance with high oscilations in unemployment rate, due to the experience of the 1929 crisis.
This way, we will analyze the different levels of welfare for changing weights that societies can give
to the volatileness of two variables of the model.
The volatileness of z in a change of economic scenario is the difference between the greater and the
lesser value that it acquires and is given by the equation (29). In the same way, the volatileness of r in a
change of economic scene is given by the equation (30):
Vz 
z1 z 2

z
z
(29)
Vr 
r1 r2

r
r
(30)
We will assume that the cost of the volatileness on these variables for the society increses with their
value. This means that an alteration of 2% in a variable has a social cost bigger than the double of the cost of
a 1% alteration. We will call the weight that the society gives for the volatileness of the level of use of the
productive capacity  r and for the volatileness of the external indebtedness  z . Our function of social cost
is of the following form:
CS   rVr   zV z
2
2
(31)
Welfare can be given by the negative of the social cost:
BE  CS (32)
Joining (29) and (30) in (31) (remembering that, when taking a square leaves the need to use the
module) and substituting in (31) we have the welfare equation that we will use:
2
  z1 z 2  2
 r1 r2  

BE    z 


 r 

  z
z
r
r


 

(33)
We now analyze two cases of societies´s preferences: aversion to volatileness in the external indebtedness
and aversion to volatileness in the capacity utilization.
Welfare
K 0
Variations in i *
Welfare
K  0.1
-0.11004 -0.10775
Variations in i *
K 0
K  0.1
-0.07608
-0.1699
21
Variations in  0
-1.90378 -1.71665
Table 4 - Aversion to volatileness in the external
indebtedness
Variations in  0
-0.85847 -1.73347
Table 5 - Aversion to volatileness in the level of
capacity utilization
Case 1: Aversion to volatileness in the external indebtedness
In this in case we take the following values for the parameters:  z  0.75 and r  0.25 .
The results shown in Table 4 show that, in a society with aversion to volatileness in the external
indebtedness, a bigger capital controls increases welfare in variations of the international interest rate and in
the external commerce.
Case 2: Aversion to volatileness in the level of capacity utilization
In this case we take the following values for the parameters:  z  0.25 and r  0.75 . The results
can be seen in Table 5.
In the case of society with aversion to volatileness in the level of capacity utilization, the absence of
capital controls resulted in a bigger welfare in variations in all the analyzed exogenous variables.
4 – Conclusion
The present work had the objective of making a theoretical analysis of the impact of capital controls
in an emerging economy. The methodology used to reach this objective was of analysis of results of
simulation in computer of a theoretical model.
The results had shown that the effects of capital controls in a economy can be very complex.
In sections 3.3 and 3.4, for example, we saw that, in the initial periods of the dynamic analysis, the
capital controls can increase the level of capacity utilization. Through time, however, this increase in the
level of capacity utilization leads to a reduction of trade balance, that leads to an increase in external
indebtedness and a reduction in the level of capacity utilization.
As the results relating to changes in the volatileness of the macroeconomic variables were not
immediately conclusive, we have to made a welfare analysis that showed that the option for capital controls
depends on the level of society´s aversion to the volatileness of different macroeconomic variables. In this
context, if the society have a strong aversion to the volatileness of the external then capital controls will be
preferable to a situation perfect capital mobility. However, if society have a strong aversion to the
volatileness of the degree of capacity utilization, giving little value to the volatileness of the external debt
then absence of capital controls will be the choice that maximizes the welfare of society.
This way, the choice between capital controls and capital mobility cannot be based solely on technical
arguments, because it depends on social preferences.
22
References
Ariyoshi, A., K. Habemeier, B. Laurens, I. tker-Robe, J. Canales-Kriljenko, e A, Kirilenko (2000). Capital
Controls: Country Experiences with Their Use and Liberalization. Washington: IMF.
Bresser, L.C; Nakano, Y. (2002). Uma Estratégia de Desenvolvimento com Estabilidade. Revista de
Economia Política, Vol. 22, N.3.
(2003). Crescimento Econômico com Poupança Externa? Revista de Economia
Política, Vol.23, N.2.
Blanchard, S; Fisher, F. (1989). Lectures on Macroeconomics. MIT Press: Cambridge.
Blatt, J. M. (1983). Dynamic Economic Systems: a post Keynesian approach. M.E. Sharpe : Nova Iorque.
Calvo, G. (2001). “Crises de Balanços de Pagamentos em Mercados Emergentes” In Krugman, P. (Org.).
Crises Monetárias. São Paulo: Makron Books.
Carvalho, F. C. e J. Sicsú (2003). “Controvérsias Recentes sobre Controle de Capitais”. IE/UFRJ, mimeo.
Eaton, J. (1993). “Soveirgn Debt: a primer”. The World Bank Economic Review, Vol. 7, n .2.
Edwards, S. (1999). “How Effective are Controls on Capital Flows? An evaluation of Chile’s experience”.
Mimeo.
Fleming, M. (1962). “Domestic financial policies under fixed and under floating exchange rates”. IMF Staff
Papers, 9.
Kaldor, N. (1957). A Model of Economic Growth. Economic Journal, Vol. 67.
Keynes, J.M. (1973). The Collected Writings of John Maynard Keynes. Editado por D.E.Moggridge.
Macmillan: Londres [no texto é referenciado por CWJMK]
Lima, G. T. (1999). Progresso Tecnológico Endógeno, Crescimento Econômico e Distribuição de Renda in
Macroeconomia Moderna: Keynes e a Economia Contemporânea. Campus: Rio de Janeiro.
Marglin, S. (1984a). Growth, Distribution and Prices. Harvard University Press : Nova Iorque.
Mundell, R. A.(1968). International Economics. Nova Iorque : Macmillan Publishing Co.
Neely, C. J. (1999). “An Introduction to Capital Controls”. Federal Reserve Bank of St. Louis, 13-30,
nov./dez.
Oreiro, J.L (2002). Prêmio de Risco Endógeno, Metas de Inflação e Câmbio Flexível. Revista de Economia
Política, Vol. 22, N.3.
Oreiro, J.L; Sicsú, J.S; De Paula, L.F. (2003). Uma Alternativa Keynesiana para o Crescimento Sustentado
da Economia Brasileira. Anais do VIII Encontro Nacional de Economia Política. Florianópolis.
Oreiro, J.L. (2004). Poupança Externa e Performance Macroeconômica. Revista de Economia Política, no
prelo.
23
Paula, L.F.; Oreiro, J.L. Jonas, G. (2003). “Fluxos e Controles de Capitais no Brasil: avaliação e proposta de
política” in Sicsú, J.; Oreiro, J.L; Paula, L.F. Agenda Brasil: políticas econômicas para o crescimento
com estabilidade de preços. Manole: São Paulo.
Possas, M.L. (1987). Dinâmica da Economia Capitalista. Brasiliense: São Paulo.
Rodrik, D. (1998). “Who Needs Capital-Account Convertibility?“. Essays in International Finance no. 207,
pp. 55-65, Princeton.
Samuelson, P. (1983). Fundamentos da Análise Econômica. Abril Cultural : São Paulo [ Edição Original:
1945].
Simonsen, M.H; Cysne, R.P. (1995). Macroeconomia. Atlas: São Paulo.
Shone, Ronald (1997) Economic Dynamics. Cambridge University Press: Reino Unido.
Stiglitz, J. (1999).”Bleak Growth Prospects for the Developing World”. International Harold Tribune, 10 de
Abril, p.6.
. (2000) “Capital Market Liberalization, Economic Growth and Instability”. World Development,
vol. 28, n. 6, pp. 1075-1086.
Takayama, A. (1993). Analytical Methods in Economics. The University of Michigan Press: Michigan.
Taylor, L. (1989). Macroeconomía Estruturalista. Trillas: Cidade do México.
Tobin, J. (1978). A Proposal for International Monetary Reform. Eastern Economic Journal, vol. 4.
24