WORKING
PAPER
WP/02/10
DRAFT





Real Shocks, Credibility & Stabilization Policy
in a Small Open Economy


WAYNE ROBINSON1
Research Department
Bank of Jamaica

December 3 2001


Abstract

Intermittent exchange rate instability and attendant high interest rates have led some
observers to argue that there is need for an alternate monetary regime such as a
currency board or official dollarization. Against this background, this paper compares
the welfare costs of various stabilization policies for the Jamaican economy. The
analytic framework used is a stochastic model of a small open economy based on
micro-foundations. When calibrated to Jamaican data, the results suggest that policy
regimes that allow for some flexibility in monetary policy are superior, in terms of
welfare, to a currency board or the extreme of dollarization. Further, at low levels of
inflation policy could shift towards a full fledge inflation-targeting regime. The results
however rely on the critical assumption that the policy regime is credible. Thus whilst
dollarization may be inferior, policy makers are still confronted with the issue of the
credibility of their stabilization policies.



Keywords: Dollarization, Debt, Shocks, Welfare
JEL classification: F31, F32, F33, F34.









1 Address for Correspondence: Wayne Robinson, Research & Economic Programming Division, Bank
of Jamaica. Nethersole Pl. Kingston Jamaica. Telephone: 876-9670 823. Email: wayner@boj.org.jm.

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1. INTRODUCTION

Stabilisation policies in small developing economies have to varying degrees used
the exchange rate as a nominal anchor for prices and expectations2 with varying
success. However, the choice of an exchange rate regime for a small open economy
has recently re-emerged in the literature following the recent financial crises and the
debt problem in the currency board regime of Argentina.

One solution, which is to have no exchange rate, has recently emerged as an
alternate stabilization option within Latin America3. This is against a background that
dollarization underwrites the credibility of a government’s anti-inflationary policy by
ensuring monetary discipline. However, a number of studies4 has pointed to the role
of external shocks in explaining aggregate fluctuations in small open developing
economies. The inability to adjust to these shocks may result in a situation where the
welfare cost of losing monetary policy exceeds the benefits. Schmitt-Grohe and Uribe
(2001) argue that given that the shocks affecting the dollarized economy often differ
from the host country or have asymmetric effects on the two economies, dollarization
can result in higher macroeconomic instability. Further, Edwards and Magendzo
(2001) find that although dollarised economies have a lower rate of inflation,
economic growth tends to be lower due to the inability of the countries to
accommodate external disturbances such as terms of trade shocks and shocks to
capital flows5.


2 See Kiguel and Liviatan (1992) and Végh (1992).
3 Ecuador dollarized in 2001while Bolivia and Argentina have considered this option.
4 See for example Calvo, Leiderman and Reinhart (1993), Schmitt-Grohe and Uribe (2001) and
Agenor, McDermott and Prasad (1999)

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Following on these conclusions and given the vulnerability of the Jamaican
economy to external shocks, this paper evaluates alternate stabilization measures for
the economy. Specifically the paper compares the welfare costs of four policy
regimes: (i) inflation targeting (ii) money-based stabilization (iii) currency board and
(iv) a dollarized economy. Given that the economy is open, the policies considered
have as their objective some form of inflation/exchange rate stabilization.

Some of the more influential papers that studied the effects of different
stabilization policies include Calvo (1986), Calvo and Vegh (1994) and Uribe (1999).
Calvo (1986) focuses on the commitment and duration of an exchange rate based
stabilization programme. He shows that temporary stabilization is pareto inferior to a
permanent rate of devaluation, as a temporary policy gives rise to current account
deficits and lower consumption relative to that of a permanent monetary policy. Calvo
and Vegh (1994) extend Calvo’s (1986) model to include staggered prices and
currency substitution and show that temporary monetary based stabilization
programmes generate a contraction in aggregate demand. However, a temporary
exchange rate based programme results in an initial expansion followed by a
subsequent recession. Uribe (1999) extends this framework to allow for a one-time
jump in the money supply. He shows that the welfare gains of a permanent money
base policy exceed that of its rivals and that a temporary policy is more costly.

There is a number of recent applied papers that compares various monetary
arrangements and stabilization strategies for various emerging market economies
subject to exogenous shocks. Schmitt-Grohe and Uribe (2001), show that in the

5 See Robinson (2001) for a discussion on the pros and cons of dollarizing the Jamaican economy.

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presence of business cycle shocks, a credible exchange rate based stabilization
programme is to be preferred to inflation targeting, monetary stabilization and
dollarization in the case of Mexico. Mendoza (2001) arrives at the converse
conclusion when account is taken of financial market imperfections. Similarly, in the
case of Argentina, when account is taken of the shocks to risk premia, Ghironi and
Rebucci (2002) argue that dollarization is to be preferred to inflation targeting or a
currency board.

The theoretical framework used in this paper is a stochastic discrete time version
of the general equilibrium model of Calvo (1986). We extend this framework in two
important ways. First, foreign currency balances enter the utility function, similar to
Ghironi and Rebucci (2002), which gives rise to currency substitution and unofficial
dollarization that typify developing economies with a history of high inflation such as
Jamaica. Secondly, we introduce a stochastic production function similar to that in
Cooley and Hansen (1989) in which output and productivity are subject to exogenous
shocks, which give rise to business cycle fluctuations. In this model, exchange rate
and monetary policies can have real effects even in the long run6.

The model is calibrated to Jamaican data. To ensure the models validity, we
compare the observed business cycle trends to those predicted by the model.
Simulations are then done wherein the welfare cost of various stabilization regimes
are evaluated. The results show that policy regimes, which allow for some flexibility
in monetary policy, given the vulnerability of the economy to external shocks, are
superior in terms of welfare, to the extreme of dollarization. The most optimal policy

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from the perspective of consumer welfare is monetary stabilization. However, as
inflation falls, economic agents become indifferent between a monetary targeting and
an inflation-targeting regime. The results, howeve,r rely on the critical assumption
that the policy regime is credible. Thus whilst dollarization maybe inferior, the
Jamaican policy makers are still confronted with the issue of ensuring the credibility
of their stabilization policies.

The rest of the paper is organised as follows. Section 2 establishes the
vulnerability of the economy to shocks, by identifying the variables driving the
Jamaican business cycle in a structural VAR. Section 3 presents the theoretical model,
while section 4 outlines the calibration and the simulated results. Section 5 compares
the welfare costs of the different policy options. Some concluding comments are
given in Section 6.


2. AGGREGATE FLUCTUATIONS AND EXTERNAL SHOCKS

In this section we delineate the various sources of output fluctuations in the
Jamaican economy over the past twenty years. We estimate the share of k-quarters
ahead forecasts error variance in output (y) that is explained by fluctuations in
external price shocks -real exchange rate (rer) and terms of trade (tot), domestic
interest rates (r) and foreign output (y*). 7

We estimate a vector autoregression of the cyclical component and the
aggregate of the differences of the logs of these variables using annual data from 1970

6 See obstfeld (1981) for a similar model in which monetary policy can have real effects in the long
run.
7 The terms of trade was obtained from the Bank of Jamaica and the real exchange rate is calculated as
sP*/P. US real GDP is used foreign output and interest rates used were the domestic treasury bill rate.
Data on output, interest rate, exchange rates and prices were obtained from the IMF’s CD-ROM.

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to 2000. External shocks and foreign output are assumed to be exogenous. The
innovations in the terms of trade are not affected by domestic output since the
economy is a price taker, domestic interest rates and the real exchange rate. Domestic
interest rate fluctuations are assumed to respond to variations in prices and not
output8. With these identification assumptions the VAR structure is given by
X t = B(L)Xt−1 + ut
such that




E(u u′ ) = Σ
t t





Aut = vt




E(v v′ ) = Λ
t t

where X is the vector ( *
y , tot
t
t, rert, rt, yt)′ , ut residual vector, vt vector of own
innovations that are orthogonal, A is 5x5 lower triangular matrix, Σ is zero mean and
diagonal variance-covariance matrix and Λ a diagonal matrix. Likelihood ratio tests
and the Schwartz criterion favoured four lags.

Table 1 below shows the results of the fraction of the K-quarter ahead forecast error
variance of output explained by external shocks –terms of trade and US GDP, and
domestic shocks –interest rates and the real exchange rate, and own innovations to
GDP. The tables show that external shocks account for much of the fluctuation in
Jamaican GDP. In the case of aggregate GDP fluctuation, US GDP accounts for half
of the variations in Jamaican GDP, primarily through its effect on tourism and capital
flows. Terms of trade shocks are the second most important external source of
variation in both cases. The most significant domestic factor is the variation in
domestic interest rate, the effect of which is more prominent for the business cycle.

8 Monetary policy has been mostly concentrated on minimizing exchange rate and inflation and less on
output fluctuation.

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TABLE 1a
VARIANCE DECOMPOSITION OF JAMAICAN OUTPUT (Aggregate)
k y rer r tot y*
2 8.84 3.89 3.08 31.36 52.83
4 6.04 2.85 18.48 23.25 49.38
8 3.72 4.69 14.36 25.03 52.20
10 3.61 4.87 14.96 25.88 50.67

TABLE 1b
VARIANCE DECOMPOSITION OF JAMAICAN OUTPUT (Cyclical)
k y rer r tot y*
2 10.93 23.49 15.37 22.61 27.59
4 8.53 23.04 22.04 23.44 22.94
8 6.47 21.05 18.67 28.46 25.37
10 6.56 2.13 26.09 22.38 22.39




3. MODEL

We consider a small open economy of infinitely lived households that are
identical in preferences over consumption and money. In this model for simplicity the
population is normalized to one and the variables are in per capita terms. In this
economy there is a single consumption good, c, which is a traded good9. The
household’s wealth is divided between domestic fiat money, M, that pays no interest,
foreign currency M*, domestic government and internationally traded bonds (net), bg
and b* and physical capital k. There are no restrictions to capital and domestic and
foreign bonds pay a real rate of return per period of r and r*,10 respectively. The
economy is small and as such is a price taker and does not influence international
interest rates. The domestic price level then follows the PPP relation
*
P = S P , where
t
t t

9 See also Backus et al (1995) for another example in which there is a single traded good.
10 We assume at all time a positive interest rate, such that money is return dominated by bonds.

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S is the domestic currency price of one unit of foreign currency and P* is the foreign
price level. Assuming that foreign inflation is negligible the domestic rate of inflation
is given by P − P
P ≅ S − S
S
= ε
. The government gives a lump-sum
t
t−1
t −1
t
t −1
t −1
t
transfer to the household, issues domestic currency at the rate of ω per time period
(i.e. monetary policy) and sets the exchange rate policy. The amount of domestic
currency issued is equal to a portion, ψ, of the economy’s net foreign assets.


3.1 Households

Households have identical preferences over real consumption and real
domestic (M P)and foreign currency SM
( * P) holdings. The household maximises
its lifetime utility
∞

 M S * 
t
 t
t M



Et ∑ β U 
t 
c ,m
,

(1)
 t
 p
p

t =
t
t

0




Money enters the utility motivated by the same rationale as in Sidrauski (1967), i.e.
the liquidity services provided. U(.) is assumed to be strictly concave, continuously
differentiable and increasing in c and m, which are normal goods.

In each time period t, the household allocates its income towards current
consumption and wealth accumulation. Income is derived from the output of the
economy, y,11 government lump-sum transfers (net of taxes and other claims), g, and
returns on financial assets and capital. Similar to Schmitt-Grohe and Uribe (2001)
capital accumulation is given by

i
= k - (1- δ )k
(2)
t +1
t +1
t

11 For simplicity and without loss of generality, we assume that the household owns the firm.

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The household therefore faces the following inter-temporal budget constraint

*

*
M
S M
M
M

*
t
t
t
t -1
*
 *
t -1
S
+ b
+ i
+
+
≤ (1 +
)b
+
+ (1 +
)S

t
b
t
gt
t +1
t
r
gt -1
t
r
t
b
t
-1 +
t
P
t
P
t
P

t
P



k
+
k + g + y − c
t
r
t
t
t
t
(3)
and the no-Ponzi –game condition Lim (1
+ r)-T b
= 0 and
gt +T
T →∞
Lim (1
+ r*)-T b*
= 0 .
gt +T
T →∞

The household chooses the paths for c, m, k, b and b* to maximise (1) subject
to (2), (3) and the transversality condition. The first order conditions for the
household’s maximisation problem are

Uc(ct , t
m ) = λt








(4)
λ S
t
= β E λ
S
(1 + r* )
t t
t t +1 t +1
t







(5)
λ = E
β λ
(1 + r )
t
t t +1
t








(6)
1
*


M
S M
t
t
t
1
1
U


m (ct , t
m ).mm/p
,
+ βEtλt
=
+
λ
1
t



(7)
t
P
t
P
t
P


t
P +1
t
P
S
*


t
M
S M
(1 +
t
t
t


t
r )St+1
St
U m t
(c , t
m ).m *
m /p
,
+ E
β tλt
=
+
λ
1
t



(8)
t
P
t
P
t
P


t
P +1
t
P
λt [1−φ (k
- k
k
t +1
t ]
) = β E λ
(f (k
) + r* -
+
+
φ (k
- k ) - (1 -
+
δ ))
t t t 1 k
t 1
t
k
t 1
t

(9)

where λt is the Lagrange multiplier.

Using equation (4) and the first order condition for holding domestic bonds
given in equation (6) we obtain the Euler equation for the optimal consumption path
U (c ,m ) = β(1 + r )E U (c
,m
)
c t
t
t
t c t +1
t +1

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which is the standard intuitive result that the rate of growth in consumption is a
function of the rate of interest. In an open economy, this is a function of the returns on
a substitutable foreign bond and the expected price of the consumption good in terms
of the foreign currency. This can be seen by combining equations (5) and (6) to yield
the following no-arbitrage condition for holding domestic and foreign currency bonds




1 + r =
E
+ ( + *
r )
tε t +
1
1

Additionally, given equation (4) and the fact that U(.) is twice continuously
differentiable and c and m are normal, then there exists some function,




U (c,
ε
L(c, + r*)) = λ
c

Since U(.) is concave and Lc>0, Li<0, then the implicit partial derivative of the above
expression satisfies
c
∂
sign
= −signUcm
∂ε
(see Calvo(1986) ). This implies that the effect of monetary/exchange rate policy on
consumption depends on the value of the cross derivative Ucm(.). Specifically, policy
will be non-neutral if U
(.) 0 which implies that c and m are Edgeworth
cm
≠
dependent.


3.2 Firms

Without loss of generality the production function is highly simplified in this
economy. Because we want to focus on exogenous shocks to the economy, we
abstract from business cycle fluctuations arising from the labour market. For
simplicity we assume that there is a freely accessible constant returns to scale
technology and that output can be costlessly transformed into either consumption or
investment. The production function in intensive form is therefore given by y = f(µ,k),

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Document Outline

• WORKING PAPER WP/02/10DRAFT
• Real Shocks, Credibility & Stabilization Policy
• in a Small Open Economy
  • • • • • December 3 2001
      • 3.1 Households
      • 3.2 Government
      • 3.3. Equilibrium

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