REAL EFFECTS OF DEVALUATION IN INDEBTED AND RISKY ECONOMIES

REAL EFFECTS OF DEVALUATION IN INDEBTED
AND RISKY ECONOMIES
José García-Solanes(*)
Universidad de Murcia
and
Fernando Torrejón-Flores
Universidad Católica San Antonio de Murcia
V JORNADAS SOBRE INTEGRACIÓN ECONÓMICA
INTECO
Universitat Jaume I de Castelló
27 and 28 November 2008
ABSTRACT
This paper develops a structural general equilibrium model to analyse the
effect of devaluation on output in Emerging Market Economies that have
limited access to world capital markets and have inherited external debt
denoted in strong foreign currency. Simulations of the model show that the
effect of devaluation on real activity may have either sign, but contraction
requires abnormally high values of some key parameters, especially the
sensitivities of the risk premium to relative effort in investment, the relative
dollar indebtedness, and the home bias. The paper also analyses the incidence
of the key parameters on other endogenous variables.
Key Words: Devaluation, Pass-through, Emerging market economies.
JEL classification: E52, F21, F33.
(*) Corresponding author: Departamento de Fundamentos del Análisis Económico, Facultad de
Economía y Empresa, Campus de Espinardo; 30100 Murcia, Spain. Tel: 34-968363782; Fax:
34-968363758: E-mail: [email protected]
1. Introduction
The debate on the effects of currency devaluation on economic activity is still alive in
emerging market economies (EMEs) despite the fact that an increasingly large number of
developing economies have moved toward flexible exchange rates during the last fifteen years.
The reasons are twofold: first, there is a representative group of EMEs that still have rigid
exchange rate regimes (Ecuador, El Salvador and Panama, for instance); and, second, some
countries that implement intermediate exchange rate arrangements, such as crawling pegs
(Bolivia and Costa Rica) or pre-announced crawling bands (Honduras), maintain the possibility
of devaluating the central rates of their regimes.
Developing countries are scared stiff of devaluations that inflict negative impacts on domestic
economic activity. Indeed, in the last decades there are several examples where devaluations –
triggered or not by currency crises – have been followed, at least in the short run, by severe
losses in terms of output and employment. For this reason, recent contributions attempt to
investigate whether this is a likely outcome under the current economic circumstances in
EMEs, and which factors could be responsible for it.
Theoretical analyses by Céspedes, Chang and Velasco (2003, 2004) – CCV hereafter - ,
stressed the important role of balance-sheet effects when imperfections in international capital
markets are particularly strong. The rationale for this result is simple: since the bulk of foreign
debt of EMEs is denominated in foreign (strong) currency, devaluation decreases the net worth
of firms, banks and governments and increases the risk premium, which in turn pushes down
the aggregate demand. When the negative balance sheet effects dominate the traditional
competitiveness one, the net result is contraction in real activity. To show their theoretical
results, CCV built an adapted IS-LM-BP model that removes the traditional perfect-capitalmobility assumption and incorporates balance sheet effects on the net worth of entrepreneurs.
Tovar (2005) constructed a New Open Economy Macroeconomics model which, in addition to
the expenditure switching and balance sheet transmission mechanisms, incorporates adjustment
costs in prices and wages – wage and price stickiness channel - and a reaction function of the
monetary authorities –monetary policy mechanism -. The latter is an interest rate rule that, in
addition to the traditional variables of a closed economy, also targets the nominal exchange
rate. Performing simulation and calibration exercises, the author showed that the probability of
expanding domestic output is higher in his model than in CCV (2003), and that the positive
response of output to devaluation increases with the fixity degree in the exchange rate system.
_______________________
2
Tovar (2005) justifies the two new complements of his model with simple “ad-hoc” functions.
To overcome this drawback, in the present paper we elaborate a general equilibrium stochastic
model for small open developing economy, where behavioural relationships are obtained under
the assumption that all agents maximize their utility or profits. We incorporate two important
novelties: first, in the production side of the economy we derive an aggregate supply function
that includes inertia in price setting in the spirit of the New Keynesian Phillips curve for open
economies. It turns out that the aggregate supply is steeper the higher the probability of price
adjustments. Second, we derive an optimal monetary policy function by assuming that the
central bank minimises inter-temporal losses created by output gaps and deviations of the
exchange rate around the value targeted by the central bank.
We solve for the deviations of the endogenous variables around their stationary level as
functions of the exogenous parameters, including the targeted exchange rate level. This
procedure allows us to clarify how the effects of devaluation – an increase in the targeted
nominal exchange rate – are transmitted through four channels before impacting on domestic
output. Let us describe the most important results. We obtain that the elasticity of the output
with respect to the level of the targeted exchange rate ( K sT ) decreases with the semi-elasticity
of the risk premium associated to the ratio investment/net wealth ( ι ), and with the ratio of
external debt over the net wealth of entrepreneurs ( χ ). Furthermore, the rate at which this
elasticity decreases with ι is higher for higher values of the home bias coefficient ( γ ).
Consequently, the range of the ι values for which the results of devaluation on output are
unambiguously positive crucially depend on the numerical values of χ and γ . For instance,
for χ = 1.25 and χ = 0.6 , the expansionary effects of devaluation are assured for levels of ι
below 1.75.
The effect of devaluation on the domestic consumer price index is positive but clearly lower
than unity, which reveals an incomplete transmission of exchange rate variations to increases
in domestic prices in the long run. For a given degree of exchange rate fixity, the size of passthrough from devaluation to domestic CPI decreases with the three key parameters, ι , χ and
γ . The sensitivity of the nominal interest rate to devaluation increases with both ι and χ ,
and decreases with γ for values of ι lower than 1.3.
The rest of the paper is organised as follows. Section 2 presents the theoretical model, and
solves it for the 8 endogenous variables as functions of thirteen exogenous variables; section 3
evaluates numerically the impact of changes in exogenous variables and of currency
devaluation on relevant endogenous variables. Finally, section 4 summarises the main
conclusions and derives some policy implications.
_______________________
3
2. The model
In this section we build and solve a stochastic structural model that illustrates the way
devaluation and different external shocks affect the endogenous variables. Our framework
extends the contributions of Céspedes, Chang and Velasco (2002, 2003), Fraga, Golfajn and
Minella – FGM – (2003) and Tovar (2005). We consider a small open economy that faces
imperfections in the international financial markets. The economy has five types of agents:
firms, households, entrepreneurs, government and a monetary authority. There is a large
number of firms that produce differentiated goods under conditions of monopolistic
competition. Firms rent capital from entrepreneurs and labour from households. Entrepreneurs
decide the size of investment, and finance it partly with their own resources (net worth), and
partly with foreign debt named in (strong) foreign currency. Goods are consumed by domestic
and foreign households and by domestic government. Domestic households issue bonds
expressed in strong foreign currency and optimise their actions by taking into account the intertemporal budget restriction of the government. The government levies lump sum taxes to
finance its consumption expenditures.
Monetary authorities are concerned with output and exchange rate stabilisation, which imply
that, after observing an external shock and/or modifying the pegged – central - exchange rate,
the central bank implements monetary actions to achieve the optimal combination of output
and nominal exchange rate.
In a short term perspective, we assume that prices adjust slowly because, as a result of various
costs, firms fully optimise prices only periodically and follow simple rules for changing their
prices at other times, in the tradition of Calvo (1983). The number of firms that change prices
in any given period is specified exogenously in this setting. On a long term horizon however,
prices adjust completely and developments of output and inflation are correctly anticipated.
The variables of the model are presented as linear deviations around their stationary state,
except for interest rates and risk premia1. The model is composed of the following equations2:
1
Et
2
{∑
∞
i =0
}
2
2
β i ⎡⎢ wy% ( y% t + i ) + ( st + i − stT+ i ) ⎤⎥
⎣
⎦
π tH = λr rt + λ y% y%t + λ y% y% t* + λq qt + β Et (π tH+1 ) + µt
*
(1)
(2)
1
Relative deviations around the stationary state are denoted with a low capital letter. For instance, for
variable X t , which has the stationary level X SS , relative deviation is defined as: xt = ( X t − X SS ) X SS .
Relative deviation may be expressed in a very approximate value by: xt = ln( X t / X SS ) .
2
These equations have been derived by assuming that all agents optimise their behaviour.
Derivations are presented in Torrejón, F., “Essays on exchange rates and inflation in Latin
American countries”, Ph D. dissertation, Universidad de Murcia, 2008, chapter 3.
_______________________
4
yt = sc hy Et ( yt +1 ) + sc hq Et (qt +1 ) + sc hb* Et (bt*+1 ) − sc hb* bt* −
sc
γc
rit + ( sq + sxη )qt
(3)
+ sx y + sg gt − sc hg Et ( gt +1 ) + scφt + sin int
*
t
rit − rit* = ψ [ Et (qt +1 ) − qt ] + ζ t
(4)
ζ t = ι [ (1 − γ ) + χ ] qt + ιint − ι (1 + χ ) yt + ιχ det + ϑt
(5)
int = Et ( yt +1 ) − [1 + (1 − γ )(1 − δ ) ] Et (qt +1 ) + [1 − (1 − γ )δ ] qt − rit* − ζ t .
(6)
Equation (1) is a central bank's inter-temporal loss function that penalises deviations of
inflation and nominal exchange rate from their targets. The output gap ( %yt ) is calculated with
respect to the long run or potential level ( yt ) and stT is the targeted nominal exchange rate
announced by the central bank. The inclusion of exchange rate deviations from the target in the
loss function of the central bank is justified by three groups of reasons: first, in the open
economies that we investigate, exchange rate fluctuations are likely to affect aggregate demand
and supply significantly; second, volatility in the nominal exchange rate modifies the net
wealth of entrepreneurs because their external borrowing is denominated in strong foreign
currencies; third, targeting the nominal exchange rate serves to anchor inflation expectations.
Although some authors have accorded relevance to exchange rate policy by considering that
the exchange rate must be an argument in the monetary reaction function (for instance: Ball
(1999), Obstfeld and Rogoff (1995), Svensson (2000), Mishkin and Savastano (2001) and
Caballero and Krishnamurthy (2005)), to our knowledge the model that we build here is the
first that incorporates the exchange rate in the loss function of the central bank. As a direct byproduct, we derive an interest rule that includes stT as an important variable. Edwards (2006)
remarks that in many instances the exchange rate does play a significant role in the monetary
policy reaction function (Taylor rules) although the central banks do not explicitly recognise it.
Et is the rational expectations operator in period t, β is the discount factor and w%y stands for
the relative weight attached to output variability. Since variations in w%y imply different
degrees of exchange rate flexibility, our specification of the loss function allows us, as in Tovar
(2005), to envisage a continuum of exchange rate regimes depending on the relative weight
assigned to exchange rate stabilisation3.
Equation (2) is an aggregate supply in the spirit of the New Keynesian Phillips curve that
incorporates inertia in price setting. Our version includes two variables of an open economy:
3
In Tovar’s model, the diversity of exchange rate regimes follows from the different weights assigned to
exchange rate stabilisation in his Taylor interest rate rule.
_______________________
5
the real exchange rate ( qt ), which transmits foreign disturbances, such as increases in foreign
prices, into domestic inflation, and the foreign output gap ( %y*t ). The real exchange rate is
defined such that an increase denotes a real depreciation of the domestic currency. The rate of
return on capital ( rt ) enters the equation as an additional cost pushing. The conventional part
of the equation may be derived assuming - as in Calvo (1983) – that firms maximise the
difference between their expected marginal revenue and unit costs and that only a fraction of
them, given exogenously, is allowed to adjust prices during each period4. All coefficients
λr , λ y% λ y% * and λq are positive and proportional to parameter λ, which is linked to the
probability of adjusting prices in the current period (1 − θ ) with this expression:
( λ = (1 − θ )(1 − θβ ) θ ). According to this, the aggregate supply becomes steeper ( λ y% goes up)
as the probability of adjusting prices rises5. Variable µt is an exogenous supply shock that
pushes up inflation.
Equation (3) indicates that the aggregate demand depends positively on the real exchange rate
(expenditure switching mechanism), expected output – due to consumption smoothing by
households6 –, the expected real exchange rate, the expected variation in the stock of foreign
debt denominated in foreign currency ( bt* ), foreign output ( y*t ), government expenditures
( gt ), domestic investment ( int ) and a demand shock ( φt ). The aggregate demand decreases
with increases in the real interest rate ( rit ) and in the expected government expenditures.
Equation (4) is the uncovered interest rate parity condition expressed in real terms. The
variable ζ t is the country risk premium, which is endogenously determined according to
equation (5). The last equation indicates that the risk premium unambiguously increases when
the value of current investment goes up and the real exchange rate deteriorates – real
depreciation increases the output value of debt repayments in case of liability dollarisation -; it
also increases with foreign indebtedness of entrepreneurs denoted in foreign currency ( det ),
and with a stochastic shock ( ϑt ). The risk premium decreases when domestic output increases,
since output is associated to the income and net worth of capitalists. As can be observed, the
4
Some recent papers adopt an alternative assumption, considering that the number of firms changing
prices in any given period is determined endogenously (state dependent pricing models). See, for
instance, Burstein (2002) and Goloslov and Lucas (2003). As emphasized by Eichenbaum and Fisher
(2004), empirically plausible versions of state dependent pricing models produce similar results to Calvo
(1983) for many experiments that are relevant in countries with moderate rates of inflation.
5
When the probability of adjusting prices is one, which means that all firms change their prices at every
moment (the case of full price flexibility), the aggregate supply is a line completely vertical (see, for
instance, Woodford (2003, chapter 2).
6
See, for instance, Fraga, Goldfajn and Minella (2003)
_______________________
6
incidence of all these determinants of the risk premium crucially depend on the value of
parameters ι and χ , which are, respectively, the semi-elasticity of the risk premium associated
to the ratio of investment to net wealth of entrepreneurs and the ratio of external debt over the
net wealth.
Finally, equation (6) is the investment demand equation, which can be easily derived from the
standard international arbitrage on rates of return. This relationship establishes that domestic
investment, undertaken by entrepreneurs, decreases in the international cost of capital (the sum
of world rate of real interest and the risk premium) - since entrepreneurs borrow abroad to
finance investment -, and in the expected real exchange rate because, ceteris paribus, a higher
expected qt today is associated with a higher expected real depreciation between today and
tomorrow, and hence a higher cost of foreign capital, when measured in terms of domestic
good. Moreover, domestic investment increases in the expected output and in the current real
exchange rate – because, ceteris paribus, a higher qt today is associated with a lower expected
real depreciation. Parameters γ and δ stand for the preference for domestic goods in
consumption (“home bias”) and the share of international flows of the home country in world
international trade.
Combining (5) and (6), we arrive at the BP curve, the locus of points ( yt ,int ) for which
financial markets are in equilibrium, everything else constant:
int =
1
ι (1 + χ )
1 + (1 − γ )(1 − δ )
Et ( yt +1 ) +
yt −
Et (qt +1 )
1+ι
1+ι
1+ι
[1 − (1 − γ )δ ] − ι [(1 − γ ) + χ ] q − ιχ de − 1 ri* − 1 ϑ
+
t
t
t
t
1+ι
1+ι
1+ι
1+ι
(7)
The BP schedule illustrates how the degree of imperfection in capital markets ( ι ) and the
international financial position of the country ( χ ) affect investment. In particular, like in CCV
(2003, 2004), investment may be increasing or decreasing in the real exchange rate. When
capital market imperfections and the inherited dollar debt are sufficiently high (large values of
ι and χ ), the balance sheet effect prevails over the expenditure shifting effect associated with
coefficient γ . In that case, the coefficient of qt is negative, and the economy becomes
financially vulnerable. Compared with the CCV (2003, 2004) framework, the coefficient of qt
in our model reinforces the influence of the expenditure shifting channel because we include
the parameter δ < 1 that is equal to unity in CCV (2003, 2004). An interesting particular case,
also stressed by CCV (2003, 2004), is the one in which financial imperfections are absent
( ι = 0 ), giving rise to a horizontal BP in the space ( yt ,int ).
_______________________
7
The model has thirteen exogenous variables: foreign output ( yt* ), foreign potential output
( yt* ), supply cost-augmenting shock ( µt ), average productivity of production factors (state of
the technology) ( at ), stock of bonds, denoted in foreign currency, issued by domestic
residents, which are held by foreigners (stock of foreign debt) ( bt* ), government expenditure
( gt ), demand shock in private consumption ( φt ), foreign real interest rate ( rit* ), rate of return
on capital ( rt ), foreign price level ( pt* ), foreign debt of entrepreneurs ( det ), targeted nominal
exchange rate ( stT ), and shock to the risk premium ( ϑt ). Moreover, all exogenous variables
(excep stT ) are governed by stationary AR(1) processes:
yt* = ρ y* yt*−1 + ε y* ,t , yt* = ρ y * yt*−1 + ε y* ,t , µt = ρ µ µt −1 + ε µ ,t , at = ρ a at −1 + ε a ,t
bt* = ρb* bt*−1 + ε b* ,t , gt = ρ g gt −1 + ε g ,t , φt = ρφ φt −1 + ε φ ,t rit* = ρ ri* rit*−1 + ε ri* ,t ,
rt = ρ r rt −1 + ε r ,t , pt* = ρ p* pt*−1 + ε p* ,t , det = ρ de det −1 + ε de ,t and ϑt = ρϑϑt −1 + ε ϑ ,t
The main steps in the solution of the model are explained in the Appendix to this paper. In the
following lines we present the solutions for six endogenous variables: domestic output ( ytE ),
nominal exchange rate ( stE ), domestic investment ( intE ), country risk premium ( ζ tE ), nominal
interest rate ( itE ) and domestic consumer price index ( p tH ) and the nominal interest rate ( itE ).
ytE = K y* yt* + K y * yt* + K µ µt + K a at + K b* bt* + K g gt + Kφ φt + K ri* rit*
+
+
-
+
-
+
+
-
+ K r rt + K p* p + K de det + K sT s + Kϑϑt
T
t
*
t
-
+
-
+
(8)
-
stE = S y* yt* + S y * yt* + S µ µt + Sa at + Sb* bt* + S g gt + Sφ φt + Sri* rit*
+
-
-
-
-
+
+
-
+ Sr rt + S p* p + Sde det + S sT s + Sϑϑt
T
t
*
t
-
+
-
+
(9)
-
intE = I y* yt* + I y * yt* + I µ µt + I a at + I b* bt* + I g gt + Iφ φt + I ri* rit*
+
+
-
+
-
+
+ I r rt + I p* p + I de det + I sT s + Iϑϑt
T
t
*
t
-
-
-
-
-
_______________________
8
+
-
(10)
ζ tE = Py yt* + Py yt* + Pµ µt + Pa at + Pb bt* + Pg gt + Pφ φt + Pri rit*
*
*
-
*
-
+
-
*
+
-
-
+
+ Pr rt + Pp* p + Pde det + PsT s + Pϑϑt
T
t
*
t
+
+
+
+
(11)
+
itE = Ty* yt* + Ty * yt* + Tµ µt + Ta at + Tb* bt* + Tg gt + Tφ φt + Tri* rit*
-
-
+
-
+
-
-
+
+ H r rt + H p* p + H de det + H sT s + Hϑϑt
T
t
*
t
+
+
+
+
(12)
+
H sT = γ BsT + (1 − γ ) S sT
(13)
Coefficients to the right of these equations measure the elasticities of the endogenous variables
with respect to each exogenous variable. Their arithmetic sign is indicated under each capital
letter.
Taking into account the equations that specify the equilibrium values of the endogenous
variables, it is easy to derive the elasticities of the endogenous variables with respect to the
targeted nominal exchange rate ( stT ):
λ y%
⎡⎣ λq ( P − R ) + λ y% ( M + N ) ⎤⎦
BsT = A
FsT
K sT =
S sT =
I sT =
λ y%
A
{B
sT
⎡⎣1 + λq ⎤⎦ − λq
{
(14)
}
1
λq wy% BsT ⎡⎣1 + λq ⎤⎦ + λ y%2
A
(15)
}
(16)
1
K T [1 + ι (1 + χ )] + ⎡⎣ S sT − BsT ⎤⎦ [ M 2 − M 1 ]
1+ι s
{
PsT = ι [ (1 − γ ) + χ ] ⎡⎣ S sT − BsT ⎤⎦ + I sT − (1 + χ ) K sT
_______________________
9
}
(17)
(18)
{
RsT = ι [ (1 − γ ) + χ ] ⎡⎣ S sT − BsT ⎤⎦ + I sT − (1 + χ ) K sT
}
(19)
H sT = γ BsT + (1 − γ ) S sT
(20)
TsT = RsT + H sT
(21)
Where:
FsT = g ( RR, A, P, β , λ y% , λq , R, N , wy% , M )
Furthermore:
⎡
s ⎤
B = ⎢ sin − c ι ⎥
γc ⎦
⎣
A = λq2 wy% + λ y%2
R = sc hy +
N = sc hq −
M =
sc
γc
RR =
B
(1 + ι )
sc
γc
ψ−
ψ −B
sc
γc
1 + (1 − γ )(1 − δ )
1+ι
ι [ (1 − γ ) + χ ] + ( sq + sxη ) + B
β
⎡ Rλ y% + Nwy% λq ⎤⎦
A⎣
⎡s
B ⎤
P = 1 − ι ( χ + 1) ⎢ c +
⎥
⎣ γ c (1 + ι ) ⎦
M1 =
M2 =
1 + (1 − γ )(1 − δ )
1+ι
[1 − (1 − γ )δ ] − ι [(1 − γ ) + χ ]
1+ι
_______________________
10
[1 − (1 − γ )δ ] − ι [(1 − γ ) + χ ]
1+ι
Before calibrating the model, it is worth noting that the values of these elasticities are a
compound of influences that flow through four different conduits. The first is the expenditure
channel, which conveys two expansionary effects. One of them is the initial rise in the nominal
value of domestic expenditures created by devaluation. The other is the usual expenditure
switching towards domestic goods, generated by the fall in the relative price of domestic
exports. This strengthening of real net exports subsequently boosts domestic output, which
eventually raises inflation and dampens the initial variation in the real exchange rate created by
nominal devaluation.
The second channel is the balance sheet effect, which has a negative impact on the demand for
domestic output because devaluation invariably increases both the value of external debt in
foreign currency and the risk premium of the country. Consequently, the strength of this
negative effect is directly linked to the semi-elasticity of the risk premium with respect to the
ratio of investment over net debt ( ι ) and to the ratio of external debt over the net wealth of
entrepreneurs ( χ ). The third conduit is the monetary policy channel, which operates through
the policy reaction of monetary authorities. Its contribution to the expansion of domestic output
is inversely related to the weight attached to fluctuations of output in the loss function of the
central bank ( wy% ). The lower the weight granted to output fluctuations, i.e. the less the
exchange rate is permitted to fluctuate, the higher the positive impact of devaluation on
domestic output. Finally, there is the aggregate supply channel, which strength is directly
related to price rigidity ( θ ), and indirectly to the elasticity of the aggregate supply schedule
( λ y% ) and to the home bias parameter (γ).
In order to obtain empirical results, we calibrate the model and derive responses of the
endogenous variables to some specific exogenous shocks. This task requires us to assign
reasonable values to the parameters, i.e. in the line of the relevant literature. Table 1,
presented in the Appendix, summarises the benchmark values that we adopt to
implement empirical exercises, and the original source from which we took it.
3. Simulation results
In this section we calculate and graphically report the effects of devaluation on selected
endogenous variables. More specifically we want to quantify the value of the elasticities given
by formulas (15) to (18), (21) and (22). Since we want to detect the specific incidence of the
relative indebtedness of entrepreneurs ( χ ), the sensitivity of the country risk premium to
relative investment ( ι ) and home bias ( γ ), we make calculations using different values of
these key parameters.
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11
Figure 1 depicts the results for the elasticity of domestic production with respect to the targeted
nominal exchange rate ( K sT ).
Figure 1
Elasticity of domestic output with respect to the targeted nominal
exchange rate ( K sT ) as a function of ι . Different combinations of χ and γ .
0.2
0.1
χ=2;γ=0.6
χ=1.25;γ=0.6
χ=2;γ=0.5
0
-0.1
KST
-0.2
-0.3
-0.4
-0.5
0
0.2
K sT =
0.4
0.6
0.8
1
ι
{
1
λ y% BsT ⎡⎣1 + λq ⎤⎦ − λq λ y%
A
1.2
}
1.4
1.6
1.8
2
(K sT = KST )
The three schedules represented in the graph, for different combinations of χ and γ , illustrate
four important features: a) K sT decreases significantly with increases in the semi-elasticity of
the risk premium associated to the ratio investment/net wealth ( ι ); b) in each case, the value of
K sT is positive for low levels of ι , but becomes negative, which indicates that devaluation may
contract output for higher levels of this parameter. For instance, for the benchmark values
χ = 1.25 and γ = 0.6 , the elasticity K s is negative for values of ι higher than 1.75; c) an
T
increase in γ makes the line steeper, indicating that higher preferences for home goods make
K sT more sensitive to variations in ι , but the home bias does not significantly alter the
threshold of ι that changes the sign K sT ; d) finally, an increase in χ (from the benchmark
1.25 to 2) shifts the line downwards and increases its slope, leading to a very significant
reduction in the sign threshold of ι (from 1.75 to 0.6). The general conclusion is, then, that
currency devaluation may cause either expansion or contraction in domestic production, but it
_______________________
12
is necessary that ι and/or χ reach uncommonly high values for the negative result in output
to emerge. Moreover, in all cases, the value of K sT is very sensitive to both ι and χ . Our
results deviate from those of Tovar (2005), in which devaluation always produces expansion in
domestic output, and they confirm the main conclusions of CCV. However, contrary to the
latter, we go a step further by quantifying the most relevant elasticities and thresholds.
Let us now give the economic explanation of these results using the structure and general
functioning of our model. Devaluation affects the demand for domestic output in two ways: on
the one hand, it increases the value of external debt in terms of domestic output, and reduces
their net worth. As a result, the risk premium increases – the higher ι is, the more it increases –
and domestic investment declines. This is the balance-sheet effect, and its negative impact on
domestic output is directly related to the size of ι and χ . On the other hand, devaluation
switches expenditure towards domestic output with an intensity that is directly related to the
elasticity of exports with respect to the real exchange rate ( η ). The expenditure switching
positively affects the demand for domestic output. For the benchmark values of
parameters ι , χ and η , the net effect on the aggregate demand is positive. Moreover, the
positive effect increases with lower values of ι , χ , and with higher levels of η . The
stimulus in the aggregate demand is matched by producers with combined increases in output
and in the price of internal goods. The steeper the aggregate supply – the slope is directly
related to the probability of not adjusting prices in the current period ( θ ) -, the higher the
effect on internal prices at the expense of output increases. Moreover, the aggregate supply
shifts upward and to the left due to the effect of devaluation on the unit cost of imported inputs.
Apart from this, the increase in the risk premium triggers capital outflows that depreciate the
nominal exchange rate, and the monetary authorities react by increasing the nominal interest
rate in order to obtain the optimal output and nominal exchange rate fluctuations. The strength
of monetary policy intervention and the effects on output and exchange rate depend on the
weight attached by the monetary authorities to output variability ( wy% ). The lower the weight
granted to output variability, i.e. the less the exchange rate is permitted to fluctuate, the higher
the impact of devaluation on domestic output. Consequently, the final effect on output depends
on the interaction of demand and supply forces and on the reaction of monetary authorities.
As can be seen, in our model the effects of currency devaluation on domestic output are
transmitted through four channels: the expenditure switching, which transmits positive impact;
the balance-sheet channel which creates negative influence; the pricing behaviour of domestic
firms, reflected in the slope of the aggregate supply ( λ y% = f (λ ) ); and the reaction of monetary
authorities, which is represented by the value of wy% . An inspection of the variables included in
_______________________
13
formula (24) reveals that the output impact of devaluation increases when wy% and/or λ
decreases.
Figures 2 to 6 show the elasticity of other endogenous variables as a function of ι , and the way
as the corresponding schedules are affected by the key parameters χ and γ .
Figure 2
Elasticity of the nominal exchange rate with respect to the targeted nominal
exchange rate ( S sT ), as a function of ι . Different combinations of χ and γ .
1.015
1.01
χ=1.25;γ=0.6
1.005
χ=2;γ=0.6
1
χ=2;γ=0.5
0.995
SST
0.99
0.985
0.98
0.975
0.97
0
0.2
S sT =
0.4
0.6
0.8
1
1.2
ι
{
1
λq wy% BsT ⎡⎣1 + λq ⎤⎦ + λ y%2
A
}
1.4
1.6
1.8
2
(S sT = SST )
Figure 2 shows the elasticity of the nominal exchange rate ( S sT ). As can be verified, the value
of this elasticity decreases as any of the two balance-sheet variables, ι and χ , increases, but
it keeps a positive sign for the whole range of feasible values of these parameters. Figure 3
plots the elasticity of domestic investment ( I sT ) with respect to the targeted nominal
exchange rate as a function of ι . It is apparent that the investment elasticity is always
negative and that, as expected, the negative value increases very significantly with any of the
two balance-sheet parameters.
_______________________
14
The elasticity of the risk premium ( PS T ) and the elasticity of the nominal interest rate ( TsT )
are shown in Figures 4 and 5, respectively. Quite reasonably, each of them is always a positive
value, which increases with any of the two balance-sheet parameters, ι and χ . However, the
incidence of the home bias parameter, γ , is not identical for each elasticity. Whereas an
increase in γ clearly increases PS T for levels of ι higher than 0.6, they affect positively TsT
for values of ι below 1.4.
Figure 3
Elasticity of domestic investment with respect to the targeted nominal exchange
rate ( I sT ), as a function of ι . Different combinations of χ and γ .
0
-0.5
χ=2;γ=0.6
χ=1.25;γ=0.6
-1
χ=2;γ=0.5
IST
-1.5
-2
-2.5
-3
I sT =
0
0.2
0.4
0.6
0.8
1
ι
1.2
1.4
1
K T [1 + ι (1 + χ ) ] + ⎡⎣ S sT − BsT ⎤⎦ [ M 2 − M 1 ]
1+ι s
_______________________
15
1.6
1.8
2
(I sT = IST )
Figure 4
Elasticity of the country risk premium ( PsT ) and real interest rate ( RsT ) with
respect to the targeted nominal exchange rate, as a function of ι . Different
combinations of χ and γ .
2
1.8
χ=2;γ=0.6
1.6
1.4
χ=2;γ=0.5
1.2
PST
RST
1
0.8
χ=1.25;γ=0.6
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
ι
1.2
1.4
{
PsT = RsT = ι [ (1 − γ ) + χ ] ⎡⎣ S sT − BsT ⎤⎦ + I sT − (1 + χ ) K sT
1.6
}
1.8
2
( PsT = PST , RsT = RST )
Figure 5
Elasticity of the nominal interest rate with respect to the targeted nominal
exchange rate ( TsT ) , as a function of ι . Different combinations of χ and γ .
2.4
2.2
2
1.8
1.6
TST 1.4
χ=2;γ=0.5
1.2
1
χ=1.25;γ=0.6
χ=2;γ=0.6
0.8
0.6
0.4
0
0.2
0.4
0.6
0.8
1
ι
TsT = RsT + H sT
1.2
1.4
1.6
(TsT = TST )
_______________________
16
1.8
2
Finally, Figure 6 shows the sensitivity of the consumer price index (CPI) with respect to
the targeted nominal exchange rate ( H sT ). The values are always positive, but
considerably lower than unity, which indicates a partial pass-through from devaluation
to internal CPI inflation. Furthermore, they decrease with any of the parameters ι , χ
and, particularly, with γ . The last influence is justified by the fact that, with a higher
weight of domestic goods in the consumption basket, the pass-through to the prices of
the imported component of the basket decreases considerably. One important implication
is that countries with high levels of external debt, risk premium and home bias will
exhibit levels of pass-through from devaluation to the internal CPI. The explanation is
that, as shown above, increases in the balance sheet parameters and in the home bias
reduce the strength of the internal demand created by devaluation.
Figure 6
Elasticity of domestic consumer price index rate with respect to the targeted
nominal exchange rate ( H sT ) ,as a function of ι . Different combinations of χ and γ .
0.55
χ=2;γ=0.5
0.5
0.45
HST
χ=1.25;γ=0.6
0.4
0.35
χ=2;γ=0.6
0
0.2
0.4
0.6
0.8
1
ι
H sT = γ BsT + (1 − γ ) S sT
1.2
1.4
1.6
1.8
2
(H sT = HST )
Let us now analyse the effects of some external shocks on domestic output. We will focus on
the elasticities of domestic output with respect to three individual shocks: foreign output ( yt* ),
foreign real interest rate ( rit* ) and the foreign price level ( pt* ). The results are given by
_______________________
17
formulas (34), (35) and (36) of the Appendix, respectively. We realise that the signs of these
variables are unambiguously positive, negative and positive. This means that decreases in yt*
and in pt* , and increases in rit* , will impact negatively on domestic output. Taking into account
our previous analysis, it follows that, if the economy is hit by some of these negative shocks
and the balance-sheet parameters correspond to the non-vulnerable economy case, their
authorities can resort to devaluation for countercyclical purposes. In other words, in countries
that are financially robust, devaluation may play the role of shock absorber. The effectiveness
of devaluation increases with fixity of the exchange rate regime (lower values of wy% )
5. Concluding remarks
Cespedes, Chang and Velasco (2003) launched the challenge of improving their basic IS-LMBP model to understand better the precise circumstances under which devaluation might
depress investment and output in emerging market economies. We have dealt seriously with
this task by building and simulating a structural general equilibrium framework in the stream
of the New Open Economy Macroeconomic modelling. Our framework includes two new
channels through which the effects of devaluation are transmitted to real economic activity.
The first is sluggish adjustment of prices in the short run, captured by an aggregate supply à la
Calvo (1983) that we extend with several elements of open economies. The second is a
monetary policy reaction function derived from an optimising behaviour of the central bank.
The second channel allows us, like Tovar (2005), to bring into the picture different degrees of
flexibility in the exchange rate regime.
We restate the main conclusion of CCV that, with important imperfections in international
financial markets and large inherited dollar debts, devaluations may contract domestic output.
However, we go some steps further and find that, under reasonable parameters drawn from the
recent literature, which include, among others, the probability of adjusting prices in the current
period and the weight that the central bank attaches to the variability of output, devaluation
depresses output when the semi-elasticity of the risk premium with respect to the relative effort
in investment, surpasses 1.75. This is a rather high threshold, because it implies abnormal
increase in the risk premium for even small boosts in investment. For instance, a three percent
increase in the ratio of investment over the net worth - a modest amount compared with the
catching up requirements in EMEs - would generate a 5.25% increase in the risk premium,
which is higher than the risk-free interest rate currently prevailing in the international financial
markets.
We also find that the two balance-sheet parameters affect positively the elasticities of the risk
premium and of the nominal interest rate, and negatively the sensitivities of the nominal
_______________________
18
exchange rate, of domestic investment and of the consumer price index, with respect to
devaluation. The last influence indicates that the two balance-sheet parameters contribute to
lower the pass-through of devaluation to internal CPI inflation and, thus, to make devaluation a
useful tool to modify the real exchange rate.
Consequently, in essence, our findings for financially robust EMES do not overturn the
conventional wisdom that devaluation can be used to mitigate the negative effects on output
caused by adverse external shocks; or that flexible exchange rates are a desirable device to
absorb external disturbances and to stabilise the economy.
_______________________
19
Appendix
I. Solution of the model
The model has thirteen exogenous variables: foreign output ( yt* ), foreign potential output
( yt* ), supply cost-augmenting shock ( µt ), average productivity of production factors (state of
the technology) ( at ), stock of bonds, denoted in foreign currency, issued by domestic
residents, which are held by foreigners (stock of foreign debt) ( bt* ), government expenditure
( gt ), demand shock in private consumption ( φt ), foreign real interest rate ( rit* ), rate of return
on capital ( rt ), foreign price level ( pt* ), foreign debt of entrepreneurs ( det ), targeted nominal
exchange rate ( stT ), and shock to the risk premium ( ϑt ). Moreover, all exogenous variables
(excep stT ) are governed by stationary AR(1) processes:
yt* = ρ y* yt*−1 + ε y* ,t , yt* = ρ y * yt*−1 + ε y * ,t , µt = ρ µ µt −1 + ε µ ,t , at = ρ a at −1 + ε a ,t
bt* = ρb* bt*−1 + ε b* ,t , gt = ρ g gt −1 + ε g ,t , φt = ρφ φt −1 + ε φ ,t rit* = ρ ri* rit*−1 + ε ri* ,t ,
rt = ρ r rt −1 + ε r ,t , pt* = ρ p* pt*−1 + ε p* ,t , det = ρ de det −1 + ε de ,t and ϑt = ρϑϑt −1 + εϑ ,t .
Let us now solve the model mathematically and obtain the equilibrium value of seven
endogenous variables. First, we derive the equation that specifies the equilibrium value of ptHE
using the indeterminate coefficients method. The procedure is as follows: Minimise the loss
function (1) subject to the aggregate supply (2) to derive the optimal trajectories for domestic
output gap and nominal exchange rate:
y% t =
st =
λ y%
⎡π tH − β Et (π tH+1 ) − λr rt − λq pt* − λ y%t* − µt + λq ptH − λq stT ⎤
y%
⎦
λ wy% + λ y%2 ⎣
*
2
q
(A1)
w%
y
⎡ λ π H − βλq Et (π tH+1 ) − λr λq rt − λq2 pt* − λ λq y% t* − λq µt + λq2 ptH ⎤
y%
⎦
λq2 wy% + λ y%2 ⎣ q t
*
+
λ y%2
λq2 wy% + λ y%2
(A2)
T
t
s
Now, substitute the risk premium (5) into the uncovered interest rate parity (4), and insert the
result in the aggregate demand (3). Then, combine the resulting expression with the BP
_______________________
20
equation (7) and solve for ytHE . Insert (A1) and (A2) in the resulting expression and solve for
Et ( ptH+ 2 ) . We reach:
Et ( ptH+ 2 ) = d1 Et ( ptH+1 ) + d 0 ptH + C y* yt* + C y * yt* + Cµ µt + Ca at + Cb* bt* + Cg gt + Cφ φt
+ Cri* rit* + Cr rt + C p* pt* + Cde det + CsT stT + Cϑϑt
(A3)
Define:
ptH = By* yt* + By * yt* + Bµ µt + Ba at + Bb* bt* + Bg gt + Bφ φt + Bri* rit*
+ Br rt + B p* pt* + Bde det + BsT stT + Bϑϑt
(A4)
Et ( ptH+1 ) = By* ρ y* yt* + By * ρ y * yt* + Bµ ρ µ µt + Ba ρ a at + Bb* ρb* bt* + Bg ρ g gt + Bφ ρφ φt
(A5)
+ Bri* ρ ri* rit* + Br ρ r rt + B p* ρ p* pt* + Bde ρ de det + BsT stT + Bϑ ρϑϑt
Et ( ptH+ 2 ) = By* ρ y2* yt* + By * ρ y2* yt* + Bµ ρ µ2 µt + Ba ρ a2 at + Bb* ρb2* bt* + Bg ρ g2 gt + Bφ ρφ2φt
+ Bri* ρ ri2* rit* + Br ρ r2 rt + B p* ρ p2* pt* + Bde ρ de2 det + BsT stT + Bϑ ρϑ2ϑt
(A6)
Now, substitute equations (A4) to (A6) into (A3). On applying the indeterminate
coefficients methodology we derive the coefficients of ptHE ( B j ), with:
Bj =
Cj
ρ 2j − d1 ρ j − d 0
Where j = y* , y * , µ , a, b* , g , φ , ri* ,r , p* , de, ϑ . For sT , B j = C j [1 − d1 − d 0 ] .
For example, By* is the elasticity of the domestic price with respect to the foreign
output. With this information, on applying the parametric values that we explain below
(Table1), we derive the signs of the partial derivatives in (A4):
ptHE = By* yt* + By * yt* + Bµ µt + Ba at + Bb* bt* + Bg gt + Bφ φt + Bri* rit*
+
-
+
-
-
+
+
-
+ Br rt + B p* p + Bde det + BsT s + Bϑϑt
T
t
*
t
+
+
-
+
(A4)
-
To obtain the equilibrium equations of the domestic output and the nominal exchange rate,
substitute ptHE from (A4) into (A1) and (A2), respectively. The result is:
_______________________
21
ytE = K y* yt* + K y * yt* + K µ µt + K a at + K b* bt* + K g gt + Kφ φt + K ri* rit*
+
+
-
+
-
+
+
-
+ K r rt + K p* p + K de det + K sT s + Kϑϑt
T
t
*
t
+
-
-
+
(A7)
-
stE = S y* yt* + S y * yt* + S µ µt + Sa at + Sb* bt* + S g gt + Sφ φt + Sri* rit*
+
-
-
-
-
+
+
-
(A8)
+ Sr rt + S p* p + Sde det + S sT s + Sϑϑt
T
t
*
t
-
-
+
+
-
To obtain the equations for domestic investment and the risk premium, substitute (A4), (A7)
and (A8) into (7) and into (5) to obtain (A9) and (A10), respectively:
intE = I y* yt* + I y * yt* + I µ µt + I a at + I b* bt* + I g gt + Iφ φt + I ri* rit*
+
+
-
+
-
+
+
-
(A9)
+ I r rt + I p* p + I de det + I sT s + Iϑϑt
T
t
*
t
-
-
-
-
-
ζ tE = Py yt* + Py yt* + Pµ µt + Pa at + Pb bt* + Pg gt + Pφ φt + Pri rit*
*
*
-
*
-
+
-
*
+
-
-
+
(A10)
+ Pr rt + Pp* p + Pde det + PsT s + Pϑϑt
T
t
*
t
+
+
+
+
+
To derive the equation for the real interest rate, substitute (A4), (A8) and (A10) into (4):
ritE = Ry* yt* + Ry * yt* + Rµ µt + Ra at + Rb* bt* + Rg gt + Rφ φt + Rri* rit*
-
-
+
-
+
-
+ Rr rt + R p* p + Rde det + RsT s + Rϑϑt
T
t
*
t
+
+
+
+
-
+
(A11)
+
To obtain the equation for the equilibrium rate of inflation ( π tE ), substitute (A4) into the
equation of the aggregate rate of inflation,
π t = γπ tH + (1 − γ )(π tH * + s&t ) ; where:
π tH , π tH * and s&t are the rate of inflation of the home goods, the rate of inflation of foreign
goods, and the depreciation rate of the nominal exchange rate, respectively. Assuming
ptH−1 = 0 y st −1 = 0 , we arrive at:
_______________________
22
π tE = H y yt* + H y yt* + H µ µt + H a at + H b bt* + H g gt + H φ φt + H ri rit*
*
*
+
*
-
+
-
-
*
+
+
-
+ H r rt + H p* p + H de det + H sT s + Hϑϑt
T
t
*
t
+
+
-
+
(A12)
-
Finally, to derive the nominal interest rate rule (monetary policy reaction of the central bank),
substitute (19) and (20) in the relationship between nominal and real interest rates,
it = rt + E (π tE+1 )
(A13)
The result is:
itE = Ty* yt* + Ty * yt* + Tµ µt + Ta at + Tb* bt* + Tg gt + Tφ φt + Tri* rit*
-
-
+
-
+
-
-
+
+ H r rt + H p* p + H de det + H sT s + Hϑϑt
T
t
*
t
+
+
+
+
(A14)
+
Taking into account the equations that specify the equilibrium values of the endogenous
variables, it is easy to derive the elasticities of the endogenous variables with respect to the
targeted nominal exchange rate ( stT ):
λ y%
⎡⎣ λq ( P − R ) + λ y% ( M + N ) ⎤⎦
BsT = A
FsT
K sT =
S sT =
I sT =
λ y%
A
{B
sT
⎡⎣1 + λq ⎤⎦ − λq
{
(A15)
}
1
λq wy% BsT ⎡⎣1 + λq ⎤⎦ + λ y%2
A
(A16)
}
(A17)
1
K T [1 + ι (1 + χ )] + ⎡⎣ S sT − BsT ⎤⎦ [ M 2 − M 1 ]
1+ι s
{
PsT = ι [ (1 − γ ) + χ ] ⎡⎣ S sT − BsT ⎤⎦ + I sT − (1 + χ ) K sT
_______________________
23
}
(A18)
(A19)
{
RsT = ι [ (1 − γ ) + χ ] ⎡⎣ S sT − BsT ⎤⎦ + I sT − (1 + χ ) K sT
}
(A20)
H sT = γ BsT + (1 − γ ) S sT
(A21)
TsT = RsT + H sT
(A22)
Where:
FsT = g ( RR, A, P, β , λ y% , λq , R, N , wy% , M )
Furthermore:
⎡
s ⎤
B = ⎢ sin − c ι ⎥
γc ⎦
⎣
A = λq2 wy% + λ y%2
R = sc hy +
N = sc hq −
M =
sc
γc
RR =
B
(1 + ι )
sc
γc
ψ−
ψ −B
sc
γc
1 + (1 − γ )(1 − δ )
1+ι
ι [ (1 − γ ) + χ ] + ( sq + sxη ) + B
[1 − (1 − γ )δ ] − ι [(1 − γ ) + χ ]
1+ι
β
⎡ Rλ y% + Nwy% λq ⎤⎦
A⎣
⎡s
B ⎤
P = 1 − ι ( χ + 1) ⎢ c +
⎥
⎣ γ c (1 + ι ) ⎦
M1 =
M2 =
1 + (1 − γ )(1 − δ )
1+ι
[1 − (1 − γ )δ ] − ι [(1 − γ ) + χ ]
1+ι
Following the same procedure, we derive the elasticities of each of the three variables,
the price of the domestic good, the domestic product and the nominal exchange rate,
_______________________
24
with respect to each of the foreign parameters: foreign product, the foreign real interest
rate and the price of the foreign good:
Elasticities of the price of the domestic good ( ptH ) with respect to yt* , rit* and pt* :
λ y%
⎡λ y% ( P − R ρ * ) − λq wy% ( M + N ρ * ) ⎤ + sx
y
y ⎦
⎣
A
B y* =
Fy*
Bri*
*
⎡s
B ⎤
−⎢ c +
γ (1 + ι ) ⎥⎦
= ⎣ c
Fri*
(A23)
(A24)
λq
⎡ λ y% ( P − R ρ * ) − λq wy% ( M + N ρ * ) ⎤ + M + N ρ *
p
p ⎦
p
⎣
B p* = A
Fp*
(A25)
Where:
Fj = g ( RR, ρ j , A, P, β , λ y% , λq , R, N , wy% , M ) , and j = y* , ri* , p* .
Elasticities of the domestic product ( yt ) with respect to yt* , rit* and pt* :
K y* =
K ri* =
K p* =
λ y%
{B
A
y*
⎡1 + β (1 − ρ * ) + λq ⎤ − λ *
y
⎣
⎦ y%
{
}
(A26)
}
1
λ y% Bri* ⎡⎣1 + β (1 − ρ ri* ) + λq ⎤⎦
A
λ y%
A
{B
(A27)
⎡1 + β (1 − ρ * ) + λq ⎤ − λq
p
⎣
⎦
p*
}
(A28)
Elasticities of the nominal exchange rate ( st ) with respect to yt* , rit* and pt* :
S y* =
S ri* =
S p* =
λq
A
λq
A
λq
A
{w B
y%
y*
{w B
y%
ri*
{w B
y%
p*
⎡1 + β (1 − ρ * ) + λq ⎤ − λ * wy%
y
⎣
⎦ y%
}
}
⎡⎣1 + β (1 − ρ j ) + λq ⎤⎦
(A29)
(A30)
⎡1 + β (1 − ρ * ) + λq ⎤ − λq wy%
p
⎣
⎦
_______________________
25
}
(A31)
TABLE 1
Parameter values
Parameter
Value
1<θ < 0
0.75
β <1
0.99
0 <α <1
0 <η <1
χ=
0.8
0.2
γc >1
2
γn >1
1
0 < δ <1
0.01
0 < γ <1
0.6
wy%
0.3
ι
0.51
Q SS DE SS P SS DE SS
=
NE SS
NE SS
0 < scr =
sbr =
Explanation
Probability of not adjusting the price of
domestic product. Fraga et al. (2003).
Inter.-temporal discount factor. Fraga et al.
(2003), Batini et al (2001)
Elasticity output-labour. FGM (2003).
Elasticity net exports-real exchange rate.
Fraga et al. (2003), Batini et al (2001).
Inverse value of the Inter.-temporal elasticity
of consumption. Céspedes and Soto (2005).
Inverse value of the elaticity of labour with
respect to the real wage. Céspedes and Soto
(2005).
Share of the domestic international trade on
the world international trade.
Degree of preference for domestic goods in the
consumer basket (home bias). Tovar (2005),
Céspedes and Soto (2005)
Weight assigned to output stabilisation in the loss
function of the central bank. Fraga et al. (2003)
Semielasticity of the risk premium with respect to
the ratio capital over net worth..Tovar (2005)
Ratio foreign debt of entrepreneurs over net worth
of the stationary state. Measured in domestic
currency and in nominal terms. Tovar (2005)
Ratio of total private consumption over
domestic output in the stationary state. Both
variables are measured in domestic currency.
1.25
PASS C SS
<1
P H , SS Y SS
0.65
P*SS B*SS
>1
( PASS / S SS )C SS
Ratio of foreign debt over private
consumption in the stationary state. Both
variables are measured in foreign currency.
Ratio og private investment over domestic
product inthe stationary state. Both variables
are measured in domestic currency.
0.63
PASS I SS
=< 1
P H , SS Y SS
X SS
0 < sx = SS < 1
Y
G SS
0 < sg = SS < 1
Y
0 < sc = γ scr < 1
0.6*0.65=0.39
0 < sin = γ sir < 1
0.6*0.2=0.12
0 < sq = (1 − γ )( sc + sin ) < 1
0.4*(0.39+0.12)=0.204
0 < sir =
0.2
Y SS
1
=
>1
SS
scr
C
sg
G SS
0 < hg = SS =
<1
scr
C
hy =
0.26
Share of exports over domestic output in the
stationary state.
0.14
Share of government consumption over domestic
output in the stationary state.
Share of consumption of domestic goods over
domestic output
Share of investment on domestic goods over
domestic output
Elasticity of the demand for domestic goods with
respect to the real exchange rate
1/0.65=1.538
Ratio of domestic output over total private
consumption
0.14/0.65=0.215
Ratio of government expenditures over total
private consumption
hq = γ sbr > 0
0.6*0.63=0.378
hb* = sbr > 0
0.63
Marginal effect of real depreciation on
consumption of domestic goods caused by
valuation effects in foreign bonds
Marginal effect of variation of foreign debt on
total private consumption
ρ y = 0.95, ρ y% = 0.95, ρ y = 0.98, ρ µ = 0.95, ρ a = 0.95, ρ b = 0.8,
*
*
*
*
ρ g = 0.5, ρφ = 0.3, ρ ri = 0.5, ρ r = 0.7, ρ p = 0.9, ρ de = 0.8, ρϑ = 0.8
*
*
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26
Acknowledgements
Financial support of the Spanish Ministry of Education, Project SEJ 2006-15172, is gratefully
recognised.
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