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Jie Li
A monetary approach to the exchange market pressure index under capital control
624079
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Applied Economics Letters, 2011, 00, 1–5
A monetary approach to the
exchange market pressure index
under capital control
Jie Li
AQ2
AQ1
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10
15
20
Chinese Academy of Finance and Development, Central University of Finance
and Economics, 39, Xueyuan Nan Lu Road, Haidian, Beijing 100081, PR
China
E-mail: [email protected]
The conventional Exchange Market Pressure Index (EMPI), originated
from Girton and Roper (1977) and popularized by Eichengreen et al.
(1994, 1995) and Weymark (1995), uses weighted average of loss of
foreign reserves and depreciation of local currency to capture foreign
exchange market pressure. However, it does not take into account the
effect of capital control on foreign exchange market pressure. With
effective capital control, the conventional EMPI tends to under- or
overestimate the actual foreign exchange market pressure, depending on
the magnitude of capital control. We adopt a monetary approach to derive a
formula for new EMPI under capital control. Then we test the difference
between the old and the new EMPI with China’s data. The result shows that
the conventional EMPI overestimates the actual foreign exchange market
pressure by 91% in average.
Keywords: exchange market pressure; capital control; monetary model
JEL Classification: F31; F32; G15
I. Introduction
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With the rapid progress of globalization and financial
liberalization, currency crises hit the world often. To
empirically investigate the causes of crises, we need to
measure them well. In their pioneering study, Girton
and Roper (1977) proposed the definition of foreign
exchange market pressure, combining the changes in
exchange rates and foreign exchange reserves.
Weymark (1995) revised the Girton and Roper’s definition of the exchange market pressures and proposed
a general definition of exchange market pressure, a
country’s excess money demand under the current
exchange rate policy. Eichengreen et al. (1994, 1995)
popularized the practical use of Exchange Market
Pressure Index (EMPI) by introducing precisionweighting scheme to average loss of foreign reserves
and depreciation of domestic currency. They successfully avoided the use of structural parameters of economy when calculating EMPI, which makes possible the
computation of EMPI for a large set of countries. Since
then, EMPI becomes the standard index for measuring
the severity of foreign exchange market pressure.
However, EMPI does not take into account the
effect of capital control on foreign exchange market
pressure. Without doing so, EMPI tends to under- or
overestimate the actual market pressure. For an example, during financial market turmoil, a monetary
authority may close down its foreign exchange market
for the time being, which eliminates possibility of losing more reserve holdings and depreciation. EMPI,
averaging the loss of reserves and depreciation, cannot
capture the actual magnitude how the market would
have reacted without capital control.
Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online # 2011 Taylor & Francis
http://www.tandfonline.com
http://dx.doi.org/10.1080/13504851.2011.624079
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J. Li
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We try to fill the gap by incorporating capital control
into a simple monetary model setting and derive a new
EMPI which better reflects the actual magnitude of
foreign exchange market pressure. We test our new
EMPI with simulated data and confirm that the introduction of capital control does improve the accuracy of
estimating exchange market pressure. In addition, we
experiment the application of new EMPI with China’s
data and find that the old EMPI overestimates the
actual exchange market pressure by 91% in average.
The rest of the article is organized as follows:
Section II reviews some related literature. Section III
lays out a simple monetary model and derives a formula for the new EMPI, then we run an experiment
with China’s data. Section IV concludes.
II. Related Literature
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Girton and Roper (1977) first used the monetary
approach to analyse the Canadian exchange market
pressure and focused on the question that how much
pressure Canadian authority will suffer, keeping the
fixed exchange rate regime. Connolly and Dantas da
Silveira (1979) applied the theoretical model of Girton
and Roper for the case in Brazil during the period of
1955 to 1975. Modeste (1981) adopted a similar monetary model to test Argentina exchange market pressure in 1970s.
Kim (1985) derived the theoretical model of
exchange market pressure in South Korea, featured
by managed floating exchange rate system and small
open export-oriented economic characteristics.
Weymark (1995) established an EMPI based on
rational expectation and small open economy monetary model with the intervention of the central bank.
Through this model, she measured the bi-and multilateral intervention for the Canadian Central Bank
during 1975–1990. Based on Weymark (1995),
Spolander (1999) estimated the exchange market pressure and the intervention of the Finland Central Bank
during the period of implementing managed-float
regime. Stavarek (2007) applied Spolander’s methodology to four European countries (Czech Republic,
Hungary, Slovakia and Poland) during the period of
1993 to 2005.
Pentecost et al. (2001) used the principal component
analysis to construct a measure of the exchange market pressure. They estimated the exchange market
pressure of German Mark in five members in the
European exchange rate mechanism. Tijmen et al.
(2008) argued that the traditional measure of
1
exchange market pressures has defects that their measurement does not include the definition of exchange
market pressures under different conditions.1
III. A Simple Monetary Model
The model used in this section is built on a simple
monetary setting for a small open economy with capital control. Domestic output and the foreign price
level are assumed to be exogenous.
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The model
This model is extended from Waymark (1995).
115
mdt ¼ pt þ b1 yt b2 it þ vt
ð1Þ
pt ¼ a0 þ a1 pt þ a2 et
ð2Þ
mst ¼ dt þ rt
ð3Þ
rt ¼ rt et
ð4Þ
it it ¼ lt ðEst etþ1 et Þ
ð5Þ
where asterisks denote the variables in foreign countries
and Et is the rational expectation operator at time t.
mt is the logarithm of the money stock in period t
with the superscript s and d denoting supply and
demand, respectively.
pt is the logarithm of the domestic price level in
period t.
yt is the logarithm of real domestic output in period t.
it is the logarithm of the domestic interest rate level
in period t.
vt is the stochastic money demand disturbance in
period t.
et is the logarithm of the period t exchange rate
expressed as the domestic currency cost of one
unit of foreign currency.
t1 Dt1
dt ¼ ht Dt h
, where ht is the money multiplier
Mt1
in period t and Dt is the stock of the domestic
credit.
t1 Rt1
rt ¼ ht Rt h
, where Rt is the stock of foreign
Mt1
exchange reserves in period t.
t is the policy authority’s time-variant response
r
coefficient.
lt is the measure for capital control. lt is greater
than 0. If there is no capital control, lt equals 1
and Uncovered Interest Parity (UIP) holds.
Another large strand of the literature focuses on the relationship between the authority reaction and exchange market pressure;
see Aizenman and Hutchison (2010) among others for different applications.
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AQ3
EMPI under capital control
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3
Equation 1 is the standard money demand function
for a small open economy. The money demand is
positively related with domestic price (pt) and domestic output (yt), negatively related with domestic interest rate (it). Equation 2 characterizes the movement of
domestic price that is determined by foreign price ðpt Þ
and exchange rates (et). This characterization allows
the domestic economy to deviate from Purchasing
Power Parity (PPP). Nevertheless, it reduces to PPP
when a0 ¼ 0, and a1 ¼ a2 ¼ 1. Equation 3 is the usual
representation of changes of monetary base, consisting of changes in domestic credit and foreign reserves.
Equation 4 is the monetary authority’s policy response
function, reflecting its preference in exchange market
intervention. Under a pure float exchange rate regime
with rt ¼ 0, the monetary authority refrains from
intervention, letting exchange rate (et) to fluctuate
while keeping constant foreign reserves ðrt ¼ 0Þ.
too small), or on future capital inflows (domestic currency is expected to be overdepreciated or Et etþ1 is too
large). When lt ¼ 1, the interest rate spread is exactly
offset by expected future depreciation, leading to
UIP. With UIP, the model condenses to Weymark
(1995).
Combining Equations 1, 2 and 5 yields
mdt ¼ a0 þ a1 pt þ a2 et þ b1 yt
b2 ½lt ðEt etþ1 et Þ þ it þ vt
ð6Þ
In money market equilibrium, we have
mdt ¼ mst
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ð7Þ
From Equation 3, 4, 6 and 7, we can get the
following:
160
et ¼
rt b2 lt ðEt etþ1 Þ dt þ a1 pt þ b1 yt b2 it þ vt
a2 þ b2 lt
ð8Þ
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With rt ¼ 1, the monetary authority intervenes
exchange market at all times keeping exchange rate
constant. rt falls between 0 and 1, indicating that the
small open economy adopts an intermediate exchange
rate regime.
The introduction of lt in Equation 5 allows us to
incorporate capital control,2 the common practice of
an emerging/developing country in the real world, into
consideration of capital flows across borders. When
lt >1, the positive interest rate spread between domestic and foreign country cannot be fully explained by
expected depreciation of domestic currency. This may
be due to the existence of two kinds of capital controls.
First, current capital inflows are restricted to the
extent that the current domestic exchange rate (et)
does not appreciate enough. In another word, et is
greater than it would have been without capital controls. Second, due to restrictions on capital outflows in
the future, the expected future depreciation ðEt etþ1 Þ is
not big enough. The combination of controls in current inflows and future outflows may aggravate the
deviation from UIP, leading to a higher value of lt.
When 0<lt <1, the positive interest rate spread is
overcompensated by expected depreciation of domestic currency, indicating restrictions on current capital
outflows (domestic currency is overappreciated or et is
2
In Equation 8, the exogenous disturbances to the
economy are changes in the foreign price level pt ,
changes in the level of domestic output yt , changes in
the foreign interest rate level it and changes in the
domestic credit dt and random money demand
shock vt .
Rewrite Equation 7 as
et ¼ rt þ Wt
205
ð9Þ
where ¼ ða2 þ b2 lt Þ1 and Wt ¼ b2 lt ðEt etþ1 Þ þ
dt a1 pt b1 yt b2 it vt :
¼ @et =@ rt ¼ ða2 þ b2 lt Þ1 is the elasticity
that converts observed reserve changes into equivalent
exchange rate units while keeping money market equilibrium. And Wt represents the combination of factors
other than reserves that influence the change of
exchange rates in money market equilibrium.
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215
Definition of EMPI
According to Weymark (1995),
Exchange market pressure measures the total
excess demand for a currency in international
markets as the exchange rate change that
Instead of the multiplicative form of right-hand side of Equation 5, some interpret it as risk premium using additive form. See
Chinn and Meredith (2005) for applications.
220
J. Li
4
8.00
Old EMPI
New EMPI
6.00
4.00
2.00
Feb-08
Aug-08
Feb-07
Aug-07
Feb-06
Aug-06
Feb-05
Aug-05
Aug-04
Feb-04
Feb-03
Aug-03
Aug-02
Feb-02
Aug-01
Feb-01
−4.00
Aug-00
−2.00
Feb-00
−
−6.00
−8.00
−10.00
−12.00
Fig. 1.
Comparison of the old and new EMPI for China from January 2000 to December 2008
would have been required to remove this excess
demand in the absence of exchange market intervention, given the expectations generated by the
exchange rate policy actually implemented.
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EMPI is thus defined as
EMPIt ¼ et þ Rt
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ð10Þ
The first part of right-hand side of Equation 10
captures the magnitude of exchange rate changes and
the second part measures the foreign exchange market
intervention by a monetary authority. While this general formula is the same with Weymark (1995), the
derivation of differentiates our model from her’s.
The following are the EMPI in Weymark (1995) without capital control and our new EMPI with capital
control.
EMPIt ¼ et ða2 þ b2 Þ1 rt
ð11Þ
EMPIt ¼ et ða2 þ b2 lt Þ1 rt
ð12Þ
A simple comparison of Equations 11 and 12 tells us
that in a world of capital control, particularly in emerging/developing countries, the traditional EMPI tends
to overestimate actual exchange market pressure when
lt >1 and underestimate it when 0<lt <1.
An experiment of the new EMPI in China
245
To test for the difference between the new EMPI and
the old one, we apply our method to China’s data from
year 2000 to 2008.3 For simulating the new EMPI, we
need structural parameters of China’s money demand
function and PPP.
Dai (2000) estimated China’s money demand function. The empirical results show that estimated
3
b2 ¼ 0:179, while Liu (2004) obtained a2 ¼ 0:781 by
estimating China’s PPP.
As shown in Fig. 1 in the presence of capital controls, the old EMPI may not reflect the actual pressure
in the foreign exchange market. The simulation above
shows that, without taking into account capital control, the old EMPI overestimates China’s exchange
market pressure from January 2001 to December
2008 by 91% in average.
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255
IV. Conclusion
In this article, we construct a new EMPI through a
simple monetary model, taking into account capital
control. We find that the old EMPI overestimates
China’s exchange market pressure by 91% in average
from year 2000 to year 2008. Our new index better
reflects the actual exchange market pressure with capital control.
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265
Acknowledgements
Excellent research assistance by Zhongyuan Yuan
and Shuzhan Zhou is greatly appreciated. The
author would like to thank Thomas Willett, Barry
Eichengreen, Ramkishen Rajan, Alice Ouyang and
Liqing Zhang for sharing their insights. The author is
also grateful for the comments from the participants of
the fifth and sixth annual conferences of Asia–Pacific
Economic Association, and the 84th annual conference
of Western Economic Association. Financial support
from the China National Social Science Fund
(11CJL037) is greatly acknowledged. All errors remain
the author’s.
The capital control index from Chinn and Ito (2008) is updated until year 2008.
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275
EMPI under capital control
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