Inflation Targeting under fixed exchange regime:
How can Chinese central bank do it?
July 2004
Meixing DAI
(∗)
Abstract: Chinese central bank is recently reported to abandon without announcement the
quantity of money supply as its intermediary goal and to adopt the framework of inflation
targeting. Generally, the later is associated in the inflation targeting literature with
flexible exchange rate regime. Inflation targeting under fixed exchange rate regime is a
new challenge in theory as well as in practice. We show in this paper, using a dynamic
setting, that under fixed exchange rate regime and with the help of some macro-economic
management measures, Chinese central bank can, even the task is hard, mimic inflation
targeting under flexible exchange rate regime.
JEL Classification : E52, E58, F41
Keywords: inflation targeting, fixed exchange rate regime, stability, optimal interest
rate rule, Chinese economy, China, macroeconomic management
measures.
(*) Meixing DAI, Associate Professor, Université Louis Pasteur (Strasbourg 1), BETA-Theme, 61,
Avenue de la Forêt Noire – 67085 Strasbourg Cedex, France, Tel : (33) 03 90 24 20 78; Fax : (33) 03
90 24 20 71, e-mail : dai@cournot.u-strasbg.fr .
1. Introduction
For a long time, one of important debates on monetary policy is the choice of
intermediate goal of monetary policy between interest rate and money supply. The attention
is now turning to inflation targeting, a new framework that a growing number of industrial
countries (including Canada, the United Kingdom, Sweden, Finland and Australia) have
adopted over the last decade to conduct monetary policy since New Zealand first adopted it in
19901. By anchoring their monetary policy to explicit quantitative inflation goals, the
adoption of this framework signals a deliberate attempt of central banks to improve their
inflation performance in a context where a low inflation environment is thought to be more
favorable for a durable economic growth in the long-run. Inflation targeting has also gained
the confidence of a growing number of emerging market countries (including Chile, Brazil,
Mexico, Israel, the Czech Republic, Poland and the South Africa) as an attractive framework
to guide the conduct of their monetary policy.
This shift in the monetary policy conduct is most motivated by the following changes.
Firstly, financial innovations have created ambiguity between different monetary aggregates.
The definition and the measurement of money supply are more and more difficult. The
diminution of interest rate elasticity of money demand as well as the change in the velocity of
money circulation has been reflected in the instability of the money demand function. It is
now difficult to control the money supply in order to realise the inflation and output stability
goals. Secondly, along with the financial liberalisation, firms have other financing channels
than loans from commercial banks. The central bank has difficulty to affect the firms’
investment in controlling the credit scale through the control of money supply. Thirdly, the
1
Some economists (Svensson, 2001) have suggested to the Bank of Japan to adopt inflation targeting in an
effort to stimulate the Japanese economy. And even the Federal Reserve has suggested introducing inflation
targeting in the United States (Meyer, 2001). The recent behaviour of European Central Bank is more and more
like inflation targeting.
1
economic and financial globalisation implies that capital can move massively and instantly
from one country to another, there is now feeble link between national economy growth and
national money supply. These changes signify that the central bank has weak control over the
money supply and the relationship between national money supply and economic growth is
broken. So, the money supply loses its initial significance and cannot be appropriately used
as the intermediary goal of monetary policy. These changes are also visible in China, so a
shift to inflation targeting might be an attractive alternative solution to the money quantity
control exercised by Chinese central bank in the past (Xia and Liao, 2001).
If the adoption of inflation targeting by industrial countries is often approved, its
application in the case of emerging countries is more controversial. In the case of emerging
countries using in the past dirty flexible or pegged exchange rate regimes as nominal anchor
and experiencing difficulty in the 1990s due to contagious financial crises in the context of
financial liberalisation, inflation targeting is an alternative nominal anchor (Mishkin and al.,
2002). The adoption of inflation targeting means abandoning unsuccessful exchange rate
targets and anchoring expectations in a floating exchange rate regime2. For Mishkin (2000),
since inflation targeting has the advantage of being easily understood by the public and is
thus highly transparent, it can bolster the credibility of monetary policy in emerging
countries, which have often a past history of monetary mismanagement. However, he notes
that the exchange rate flexibility required by inflation targeting might cause financial
instability. Masson and al. (1997) show that basic prerequisites (the central bank's scope for
conducting independent monetary policy and the undisputed primacy of the inflation
objective) may not be satisfied in emerging countries. Once these basic prerequisites are
2
See Schmidt-Hebbel and Werner (2002), Eichengreen (2001). Pegged exchange rate arrangements have been
common among emerging economies during the 1990s punctuated by a series of currency crises. For
economists, the time for such exchange rate arrangement is past since, through capital account liberalisation,
many emerging countries’ financial markets are narrowly integrated with international financial markets. This
is the reason for which Brazil, Chile and Mexico have adopted a floating exchange rate regime in the aftermath
of costly defence of their respective currencies in the later 1990s.
2
satisfied, it may lack some essential elements of inflation targeting framework at the
operational level. For these authors, inflation targeting is a framework that could be used to
conduct monetary policy in some high-to-middle-income developing countries. However, in
most developing countries, the preconditions for adopting such a framework are not yet
present.
China is quite successful in defending its fixed exchange rate regime (pegged to US
dollar) since the middle 1990s. The supposed unannounced transition in the early 2004 to an
inflation-targeting framework for monetary policy3 is not motivated by balance of payment
crisis but only due to domestic factors. In the 1990s, the financial development in China has
generated an unstable money demand function. The instability of the relation between the
money supply and the credits implies that it is more difficult to control the quantity of money
supply to attain macro-economic targets. The massive entry of foreign direct investment
(FDI) after the admission of China into the WTO adds to the turmoil. Xia and Liao (2001),
after having examined the conduct of Chinese monetary policy in the past, have concluded
that the quantity control of money supply is not suited any more for Chinese economy. A
feasible alternative is to target inflation. To achieve this transition, they suggest that Chinese
central bank does not announce (temporarily) the new intermediary goal, simulates the
inflation targeting in its current operations, diligently stabilises the inflation rate in a
reasonable zone and establishes a framework of monetary policy with an inflation target.
The adoption of inflation targeting in China is a practical and theoretical challenge to the
inflation targeting literature, as China seems to maintain the peg of yuan to US dollar for an
indefinite horizon. The studies of inflation targeting in open economies often associate
inflation targeting with flexible nominal exchange rate regime4. The present paper contribute
3
See for a report at http://finance.sina.com.cn/g/20040209/0743622538.shtml.
Most of the studies examine the inflation-targeting issues in small open economy and compare the effects, on
macro-economic variables, of alternative monetary policy rules, fixed exchange rates and inflation targeting.
See for example Rodseth (1996), Dueker and Fischer (1996), Ball (1998), Batini and Haldane (1998), Svensson
4
3
to the literature in analysing the dynamic implications of the atypical combination of inflation
targeting and fixed exchange rate regime and tries to give a rationale for this impure inflation
targeting framework, and supplies guidelines for monetary policy management in China.
The remainder of the paper is structured as follows. In section 2, we give out the model,
and we derive the optimal interest rate rule of the central bank, desiring to stabilise inflation
and output. In section 3, we discuss disequilibrium and dynamic stability issues under fixed
exchange rate regime. In section 4, we discuss the management of inflation targeting
framework in the Chinese context. Section 5 summarises the main results.
2. The Model
As the Chinese economy is more and more market oriented, we consider that a simple
traditional open economy model can describe it5. Inflation is governed by an expectationaugmented Phillips curve:
π = π eA + α ( y − y ∗ ) + ε π ,
where
π (≡ dp / dt )
is
the
inflation
rate
α > 0,
of
domestically
(1)
produced
goods,
π eA = ρπ e + (1 − ρ)(π ef + e& e ) the expected CPI inflation rate that is an average of foreign
inflation π ef and rate of change of nominal exchange rate ( e& e ) at the weight (1 − ρ) , and
domestic goods price inflation ( π e ) at the weight ρ . y is the actual (growth rate of) output,
y ∗ the natural rate of output and ε π an inflationary (or supply side) shock. Given the
definition of π eA , equation (1) can be rewritten as
(2000), Gali and Monacelli (2002), and Clarida, Gali, and Gertler (2001), Leitemo and Roisland (2002),
Obstfeld (2002), and Fernando, Driffill and Spagnolo (2002). For two country models, see Persson and Tabellini
(1996), Canzoneri, Nolan, and Yates (1997), Roisland and Torvik (2003).
5 More sophisticated models can be formulated in using recent developments of micro-economic foundations of
macroeconomics, see for example King (2000) for some of these possibilities in the framework of IS-LM
model.
4
π = ρπ e + (1 − ρ)(π ef + e& e ) + α ( y − y ∗ ) + ε π .
(2)
The output is equal to the aggregate demand which depends on the expected real interest
rate, (i − π e ) , and the real exchange rate, s , as follows:
y = −β (i − π e ) + γ s + ε d
β, γ > 0 ,
(3)
where, i is the domestic nominal interest rate, s ≡ p f + e − p , with p denoting the domestic
goods price level, p f the foreign goods price level in foreign currency and e the nominal
exchange rate and ε d a positive demand shock. The parameter β captures the financial
development in China. Since the end of 1990s, some important changes have taken place in
the financial sphere of Chinese economy. More and more households use credits to buy
houses and cars. Private enterprises have increasing access to credits to finance their
investments. Public enterprises are pushed to be market oriented. Under these conditions, β
is becoming more significant for Chinese economy and the effect of a variation of real
interest rate on Chinese aggregate demand not negligible.
China experiences, since several years, large surplus in its balance of payment. The
increase of foreign exchange reserve is very rapid and the stock of foreign exchange reserve
is more than necessary for maintaining a viable and defensible fixed nominal exchange rate
of yuan vis-à-vis US dollar. Further, Chinese government is facing the pressure of foreign
governments (USA, Japan and EU) for a revaluation of yuan. Now, it may be the time for
China to equilibrate entry and exit flows of foreign exchanges. That does not necessarily
means a revaluation of yuan since other measures can be used to absorb the surplus of the
balance of payment. The foreign exchange market equilibrium is characterised by a
traditional equation describing the balance of payment with imperfect capital mobility. We
5
assume here and in the following that foreign exchange reserve ( R ) is kept constant with
R& = 0 , i.e. the time variation of the stock of foreign exchange reserve is zero. 6 That leads to
i − i f − e&e =
1
(η y y − ηs s − ε f ) ,
υ
ηs , η y > 0,
(4)
where η s and η y are respectively the real exchange rate-elasticity and the output-elasticity of
trade balance, i f the foreign interest rate, ε f a shock affecting foreign exchange market. The
parameter υ denotes the degree of capital mobility (or the degree of capital account
liberalisation). It is influenced by different measures of capital control or by institutional
rules prevailing on internal financial markets, which can be modified to limit the speed of
capital movements. In the case of China, capital movement is due principally to FDI and
capital flights, both foreign and Chinese, from China or into China. For FDI, the interest rate
differential has a role to play. But generally, the decision of entry into China is most
motivated by a the low cost of work in China, the importance of Chinese actual and future
internal market, and a potential long term revaluation of Chinese currency. The capital flights
may due to other reasons than economic. This equation captures imperfectly these capital
movements. As private agents have many ways to circumvent the official control of entry and
outflow of financial capital (through for example offshore swaps) and China is experiencing
to liberalize the financial capital movements, the interest rate differential and the expected
rate of change of nominal exchange rate will be more important determinants in the future.
The money market equilibrium is characterised by
m − p = l1 y − l 2 i + ε m ,
6
Equation
(4)
is
derived
*
l1 , l 2 > 0 ,
from
*
the
balance
*
(5)
of
payment
equilibrium
condition:
EP
EP
EP
R& = BC + BK =
X (Y f ,
) − H (Y ,
) + BK (i − i f − e& e ) = 0 , where the trade balance
P
P
P
EP *
BC depends on the income, Y , and the real exchange rate
and the balances capital balance BK
P
f
e
depends on the differential of yields on national and foreign bonds ( i − i − e& ).
6
where m represents the money supply7 and ε m is a white noise shock affecting money
demand. Even though Xia and Liao (2001) report the instability of money demand function in
China, we do not assume here that the parameters characterising the money demand function
( l1 and l 2 ) are submitted to random shocks. Money demand instability may be due to
economic instability and out-of-equilibrium situations. As it will be shown below, these
situations are possible when the framework of monetary policy is not well defined. Deriving
& = dm / dt = µ ,
equation (5) in relation to time, one obtains: m& − p& = l1 y& − l 2 i& + ε& m . Noting m
and ε& m = 0 (i.e., shocks without tendency), it yields
µ − π = l1 y& − l 2 i& .
(6)
Since money supply is endogenous in this framework, equation (6) implies that at the longrun stationary equilibrium, the growth rate of money supply must be equal to long term
current and expected inflation rates, i.e., µ = π = π e .
In the inflation-targeting framework, the nominal interest rate is treated as instrument by
monetary authorities in order to conduct its monetary policy. Chinese government is very
concerned to maintain a high economic growth rate and a weak inflation. Chinese monetary
authorities may act systematically to minimise fluctuations of output around the natural
(growth) rate, y ∗ , and inflation around its target, π T . This behaviour can be captured in
assuming that Chinese central bank minimises the discounted present value of the following
loss function:
L=
∫ 2 [ λ( y − y
∞
1
]
∗ 2
) + κ (π − π T ) 2 exp(−θ t )dt , λ , κ , θ > 0 ,
(7)
0
where preference parameters λ and κ denote respectively the importance that authorities
place on output and inflation stabilisation, and θ is the discount factor. This program
7
Here, m
reserve.
= log( F + R ) with F as the domestic counterpart of money supply and R the foreign exchange
7
corresponds to flexible inflation targeting in the sense that output and inflation targets are
simultaneously taken into account in the interest rate decision of the central bank. It can be
easily accommodated to reflect the framework of strict inflation targeting in assuming that λ
tends to zero. The first-order condition of the central bank’s minimisation problem (7) is
given by
λ
∂y
κα
( y − y ∗ ) = −κ (π − π T ) , ⇒ y = y ∗ −
(π − π T ) ,
λ
∂π
(8)
which leads to the following central bank’s optimal monetary policy rule (see, Appendix A):
i = πe +
κα
1

(π − πT ) − y ∗ + εd  .
γs +
β
λ

(9)
Equation (9) describes optimal reaction or optimal interest rate rule of the central bank. It
works quite similarly as Taylor’s rule8. Variants of the Taylor’s rule have been found to give
relatively robust and good results in different models. If a rule like that in (9) is adopted by
Chinese central bank, it has the advantage of being easily verified by outside observers and a
commitment to the rule would therefore be technically feasible (Masson and al., 1997, and
Svensson, 2002).
According to equation (9), it is optimal for Chinese central bank to adjust nominal
interest rate upward to reflect fully expected inflation, and to adjust it positively to the gap
between current inflation and the inflation target ( π − πT ) as well as increases in the real
exchange rate ( s ) and increases in the output gap due to change of output potential ( y ∗ ) or a
positive demand shock ( ε d ). If increase in nominal interest rate is enough to raise the real
interest rate when current inflation rises, it can thereby contract the real economy. We note
that the reaction to other variables depends on the financial development parameter β . As
more important financial development signifies smaller interest rate variation, the recent
8
Taylor’s rule is empirically found by Taylor (1993) in studying the behaviour of the Fed in the 1980s.
8
financial development in China is favourable for the introduction of inflation targeting and
permits to avoid a too sharp rise of real interest rate when there is any inflationary tension.
If Chinese monetary authorities have a more pronounced preference for the achievement
of inflation target (more important value for κ / λ ), the interest rate will react more strongly
to current inflation. In this event, during the short-run adjustment, the nominal interest rate
may be subjected to more volatility. That will not be favourable for output (growth)
stabilisation. As China has an important unemployed population in the countryside, the
output stabilisation is then an important objective. Consequently, we think that Chinese
central bank must not be too eager to stabilise inflation rate. This will not endangers the
credibility of Chinese central bank as it has a quite good historical track of low inflation in
the past years. As many sectors are in over-capacity and Chinese economy only recently
comes out of soft deflation, it may be really preferable to not focus only on inflation target.
The reaction of nominal interest rate to the variation of real exchange rate does not
depend on the preferences of monetary authorities. The presence of real exchange rate (s) in
the optimal interest rate rule is due to the fact that it influences the demand for domestic
goods. Under floating exchange rate regime, a variation of nominal interest rate following
that of s makes it possible for the central bank to react not only to the shocks affecting the
goods demand but also to those affecting financial markets. Financial operators use economic
information quickly in their decisions of purchase and sale of assets so that all information is
integrated at every instant into the flexible exchange rate. But this mechanism is not
operational in the case of China as the nominal exchange rate of yuan is pegged to US dollar
and the movement of financial capital is controlled.
The inflation expectation of economic agents is crucial for the fixation of nominal
interest rate. Being now experienced with market economy, Chinese households and
enterprises are able to form rational expectations if they are given the right information. It is
9
in the interest of Chinese central bank to give enough information to economic agents in a
dynamic context, i.e., the Chinese economy is not in a situation of equilibrium. Out-ofequilibrium situation adds difficulty, together with persistent shocks, for economic agents in
their formation of inflation expectations. In out-of-equilibrium situations, economic agents
have to study the dynamic path of the economy before forming their expectations. If the
equilibrium is not stable or indeterminate, economic agents will not know where will be the
economy in the next period. So they cannot form good and consensual inflation expectations.
In the event of temporary shocks, if the economy is initially at a stable equilibrium, the
central bank can easily estimate the expected inflation rate by using its knowledge of the
economic model. In assuming rational expectations, the expected inflation rate will, a priori,
be equal to the inflation target of the central bank9, i.e. π e = π T .
However, it is important to notice that, if the shocks were not temporary, it would be
mistaken to suppose that economic agents continue to believe in the announcement of the
central bank without taking account of these shocks in their inflation expectations. Observing
persistent shocks, economic agents will take account, ex post, of the evolution of monetary
conditions, real income and current inflation rate to modify rationally their inflation
expectations. In order to determine the stabilising or destabilising effects of an optimal
interest rate rule, it is necessary to study how the economic system behaves when the shocks
are not temporary. As China is an economy in transition, both disequilibrium and shocks with
permanent effects are very important and must be taken into account when inflation targeting
is effectively introduced.
3. The out-of-equilibrium dynamics and stability analysis
9
In the inflation targeting literature, it is common to assume that shocks are random and temporary so that the
expected inflation rate becomes an exogenous variable and is equal to the inflation target of the central bank.
This approach is wrong when shocks are permanent or persistent since it assumes that the rational private agents
do not take account of these persistent shocks, which can affect greatly and durably their welfare.
10
3.1. The dynamic system
Equations (2)-(3) and (9) enable us to obtain the expression of inflation rate and output in
terms of expected inflation rate, exogenous variables and shocks as follows (see Appendix
A):
 e

λ
κα 2 T
e
e
&
(
1
)(
e
)
π=
ρπ
+
−
ρ
π
+
+
π
+
ε


π
f
λ
(λ + κα 2 ) 

y = y* +
[− ρπ
(λ + κα )
κα
2
e
(10)
]
− (1 − ρ)(π ef + e& e ) + π T − ε π .
(11)
Departing from an initial equilibrium where π e = π T , the expectation changes (due to
exogenous shocks) of economic agents will involve the variations of output and current
inflation rate. The interaction between expected inflation rate and other variables may induce
complex dynamics. In the event of persistent (or permanent) shocks, it is natural to recognise
that economic agents will not believe any more in the announced inflation target and modify
their expectations in taking account of the foreseeable evolution of inflation. Given that
monetary and financial markets provide a whole set of useful information, the economic
agents will use it when they revise their expectations following a shock.
In the inflation targeting literature, the money market described by equation (5) is only
used to determine in an endogenous way the money supply, which adapts to money demand.
In this paper, in addition to this role, following Dai and Sidiropoulos (2003), the money
market (and so the implicit financial markets) is considered as a co-ordination place for the
formation of good and consensual inflation expectations of economic agents. In the Chinese
context, this is even more necessary to use the money market to help economic agents to have
good inflation expectations. What Chinese central bank can do is to give more information
about its open-market operations, i.e., when Chinese central bank injects or withdraws
liquidity at given repo interest rate, it announces the amounts injected or withdrawn as well
11
as the repo interest rate. The information about the amount of liquidity constitutes indicators
that the economic agents use in forming appropriately their inflation expectations10.
By taking the mathematical expectation of equation (6), one has, µ e − π e = l1 y& e − l 2 i&e .
In examining this equation, equations (6) and other equations of the model, one can find that
the amount of liquidity injected in the economy depends on expected inflation rate, and
expected inflation rate depends on the expected amount of liquidity present in the economy.
One simple way to break this cycle is to assume that economic agents adopt a learning rule:
the expected growth rate of liquidity is equal to that announced by the central bank, i.e.
µ e = µ . In fact, information about the growth rate of liquidity can be communicated by the
central bank at short intervals of time (daily, weekly, monthly etc.) over which other macroeconomic variables are not easily observable. Consequently the learning rule assumption with
µ e = µ is not irrational: when information is quickly available, economic agents can wait for
it instead of guessing it. This simple learning process is a good choice since it is reasonable
and keeps the model simple. This gives us an equation describing the dynamic adjustment of
expected inflation rate of domestically produced goods11.
Following the preceding analysis, the economy can be described by equations (4)-(5) and
(9)-(11) completed by a dynamic system of real exchange rate and expected inflation rate.
The dynamic behaviour of the economy can be summarised by two differential equations in
real exchange rate, s , and expected inflation rate, π e . Thus, under fixed exchange rate
regime, the reduced dynamic model is given (in admitting e& e = π& ef = &e&e = 0 ) as follows12
π& e =
λ (1 − ρ) + κα 2 e
λ
κα 2 T
π −
[(1 − ρ)π ef +
π + επ ] ,
ΩΨ
ΩΨ
λ
10
(11)
See Dai and Sidiropoulos (2003), they argue that the money supply is endogenous when central bank
provides the liquidity to satisfy the needs of the economy and it constitutes an exogenous data when the agents
formulate their inflation expectations because they use them in this case like indicators.
11
The equation governing the dynamics of
12 The equation governing the dynamics of
π e is derived in Appendix B.
s is derived in Appendix B.
12
s& = π ef − π e ,
where Ω =
(12)
l1 l 2 κα
−
≥ or < 0 , and Ψ = −λ (1 − ρ) − κα 2 < 0 .
α β λ
In admitting that private agents expect the continuation of the fixed exchange rate
regime, i.e., e& e = 0 , the balance of payment equilibrium condition13 or equation (4) leads to
i −if =
1
(η y y − η s s − ε f ) .
υ
(13)
In using equations (7), (9) and (10) in (13), we have for R& = 0 the following relation:
κα(1 − ρ)(υ + βη y ) e κα(υ + βη y ) T
(λ + κα 2 )( γυ + βη s )
π =−
s−
πf +
π
Θ
Θ
Θ
κα(υ + βη y )
(λ + κα 2 )(υ + βη y ) * υ(λ + κα 2 )
βυ(λ + κα 2 )
−
επ +
y −
εd +
if
Θ
Θ
Θ
Θ
β(λ + κα 2 )
−
εf.
Θ
e
(14)
where Θ = βυ(λ + κα 2 ) + καρ(υ + βη y ) . This equation permits us to better analyze
disquilibrium situations in distinguishing the area where the balance of payment is in deficit
from the one where it is in surplus.
3.2. The dynamics in the absence of stationary equilibrium
Under fixed exchange rate regime, we can show that when foreign and domestic inflation
rates are different, the economy cannot find a stationary equilibrium. Consider the case where
in the long run, the foreign inflation rate is superior to the domestic one.
13
The stock of foreign exchange reserve will be kept constant with R&
13
= 0.
R& = 0
πe
E2
π ef
s& = 0
E1
πe
π& e = 0
s
s
Figure 1a. Weak inflation aversion:
πe
π ef
κ β l1
<
.
λ α 2l2
R& = 0
E2
s& = 0
E1
πe
π& e = 0
s
s
Figure 1b. Strong inflation aversion:
κ β l1
>
.
λ α 2l2
At the point E1 in Figures 1a and 1b, foreign exchange reserve remains unchanged
( R& = 0 ) and domestic expected inflation rate is stationary ( π& e = 0 ) and so is the realised
inflation rate. But as π e < π ef , we have s& > 0 . Similarly, at the point E2 where foreign
exchange reserve and real exchange rate are stationary (correspondingly R& = 0 and s& = 0 ),
but expected and realised inflation rates will change at positive (Figure 1b) or negative rate
14
(Figure 1a) according to the central banker’s relative preference for output and inflation
targets and depending on subjacent economic conditions.
The problem of absence of stationary equilibrium under fixed exchange rate regime can
be resolved in adjusting the domestic inflation rate target so that in the long run domestic
expected and realised inflation rates are equal to foreign ones. Under this condition, the two
curves π& e = 0 and s& = 0 coincide. Further, in adjusting different control variables (nominal
exchange rate, output target, import taxes and export subsidies), we can have a unique
stationary equilibrium where expected inflation rate, real exchange rate and foreign exchange
reserve will not change over time. This equilibrium can be locally stable or not according to
the preferences of monetary authorities for inflation and output targets.
3.3. The dynamic stability of managed equilibrium
In adjusting different control variables (inflation target, output target, import taxes and
export subsidies, nominal exchange rate, etc.), Chinese central bank can replicate an
equilibrium that is similar to that under floating exchange rate. However, there is a major
difference in the behaviour of nominal and real exchange rates under these two regimes.
Under floating exchange rate regime, the nominal exchange rate e (and therefore the real
exchange rate, s ) is a forward-looking variable. In other words, as the nominal exchange rate
is a price that clears an efficient international financial market, it is not a predetermined state
variable. It is free to make discrete jumps in response to “news” which includes all previously
unanticipated current or future changes in exogenous variables and policy instruments. This
function of nominal and real exchange rates as jumping variables is questionable under fixed
exchange rate regime. Since the nominal exchange rate is pegged, the real exchange rate is
adjusted only in passing by price (i.e. the inflation rate) adjustment. In a low inflation
environment, π and so π e is a mostly like a backward-looking variable. The expected
15
inflation rate is assumed to be predetermined14 at a point in time and is continuously updated
by the system of dynamic equations (11)-(12).
The path followed by inflation rate and real exchange rate depends on the sign of Ω . The
crucial role is played by the relative inflation aversion of monetary authorities,
κ
, in
λ
relation to other economic conditions. There are two qualitatively distinct phase diagram
configurations in the π e − s space, as shown in Figure 2a, b.
a) Central bank has weak aversion for inflation
The dynamic adjustment of the economy is characterised by a saddle-point configuration
when Ω is strictly positive. That leads to
κ β l1
<
.
λ α 2l2
(14)
If the central bank prefers strongly output target relative to inflation target, the condition
(14) will be realized. The value of the ratio
κ
compatible with saddle-point equilibrium
λ
depends also on others parameters ( β , l1 , α and l 2 ). If β and l1 have stronger values and α
and l 2 weaker values, the central bank can give greater relative weight to inflation target. We
note that, a stronger β corresponds to a more important financial development and weaker l 2
to a smaller interest rate elasticity of money demand. The quick financial development and
the diminution of interest rate elasticity of money demand15 give then more liberty to Chinese
14
In assuming expected inflation rate as a predetermined variable, reacting to economic news slowly without
jumps, one admits that the prices adjust with lags due to menu costs or other rigidities. It reacts to economic
news slowly without jumps. In the present model, the expected inflation rate in the Phillips curve is formed
before the arrival of shocks. The empirical studies (Gordon, 1997) show an inertia of the adjustment of
inflation rate. In this paper, output and realised inflation rates can jumps initially to share the adjustment due
to an inflationary shock. See also Buiter and Panigirtzoglou (2003) for a similar assumption concerning
inflation rate. This behavior corresponds well to the situation in a low inflation period in contrast to high
inflation or hyperinflation experiences.
15 See Xia and Liao (2001).
16
central bank in defining its inflation targeting framework without creating a new source of
macro-economic instability.
In the case of weak inflation aversion, the equilibrium may have a unique converging
path (cc in Figure 2a). As we consider the artificial or managed stationary equilibrium
solution, s& = 0 and π& e = 0 locus coincide and both have a zero slope (Figure 2a). Under the
condition (14), the dynamic system has one zero root and one stable root
(
λ (1 − ρ) + κα 2
< 0 ). If we have one predetermined and one non-predetermined variable, the
ΩΨ
transversality condition and the rationality of economic agents imply that only the stable
solution is chosen. In other words, the jump variable will always attain the value required to
put the system on the unique convergent trajectory.
Under fixed exchange rate regime, this faculty of economic agents in finding the
converging path is very problematical as nominal and real exchange rates cannot adjust
instantaneously. Of course, as we will show later, macro-economic managements can come
as substitutes in order to remedy to this failure. The managed equilibrium is difficult to attain
due to the fact that the real exchange rate cannot adjust rapidly under the fixed exchange rate
regime. The managed equilibrium is extremely fragile and will not survive to a shock without
help. In the case of China, when there is many negative inflationary shocks (e.g., the pressure
to the diminution of prices in the manufacturing sectors) and under-evaluation of national
currency, Chinese central bank can help in fixing temporarily higher targets for domestic
output and inflation so that Chinese economy returns to equilibrium.
17
R& = 0
πe
c
E1
π e = π ef
π& e = 0
s& = 0
c
s
s
Figure 2a. The case of weak inflation aversion.
π
R& = 0
e
E1
π e = π ef
s
π& e = 0
s& = 0
s
Figure 2b. The case of strong inflation aversion.
b) Central bank has strong aversion for inflation
The dynamic behaviour of the economy is characterised by an unstable configuration
(Figure 2b) under the following condition:
κ β l1
>
.
λ α 2l2
(15)
This is the case when the central banker has a strong aversion for inflation. The dynamic
system (11)-(12) possesses two unstable engenvalues and the economy has an unstable
18
stationary equilibrium. Strong preference of the central bank for inflation stabilisation,
considered as favorable for the reinforcement of credibility of the central bank in the
economic literature16, will not ensure the economic stability. When the output target is
neglected, the adjustments following any shock will not lead to the equilibrium and can
induce the economy into any direction. As the money supply is endogenous in the inflationtargeting framework, all inflationary expectations can be auto-realised.
In fact, when the central bank reacts excessively to an increase in inflation rate in raising
strongly nominal interest rate, it can reduce the output further than necessary. The restrictive
monetary policy can increase in this case the expected inflation rate, since the economic
agents may not reduce their expected nominal money demand and so the expected nominal
money supply facing the diminution of output and the rise of nominal interest rate, which
diminish the real money demand. This kind of reaction will bring further rise in inflation rate
and interest rate and as a consequence more important economic disequilibrium.
It is preferable then in the case of China to give a balanced focus over inflation and
output targets. An attitude like that of the American Federal Reserve (Fed) is preferable than
that of the European central bank (ECB). Even though taking the Fed’s kind of attitude is not
sufficient to guarantee the convergence to the stationary equilibrium under fixed exchange
rate regime, it is however better than taking the ECB’s attitude. If no endogenous element of
dynamic stability is present, more intensive use of macro-economic management measures
will be necessary.
4. The management of inflation targeting under fixed exchange rate regime
As we have shown before, the equilibrium is unstable under the fixed exchange rate
regime with inflation targeting. This is particularly the case when goods price (and so
16
According to Roisland and Torvik (2003), a low credibility central bank must give higher priority to
achieving inflation target than a high credibility central bank.
19
inflation rate) is not adjusting quickly to absorb the disequilibrium, given that real exchange
rate follows the movement of goods prices under the fixed exchange rate regime. Several
solutions might permit the central bank to re-establish the equilibrium once the economy is
situated in disequilibrium. We take example of Chinese economy in a situation with underevaluation of national currency and low inflation.
4.1. The choice of an appropriate inflation target
As we have shown in the precedent section, if the stationary national expected inflation
rate is inferior to that of foreign country, the real exchange rate will continue to evolve. There
is no equilibrium where all variables are stationary. In order to have a unique equilibrium, the
central bank must fix, according to equation (11), an inflation target at foreign level in taking
account of domestic supply shocks, i.e., πT = π ef −
λ
ε π . In the long run, the domestic
κα 2
expected and realised inflation rates are equal to foreign ones. In modifying the inflation
target, the R& = 0 locus will move to the right. An appreciation of real exchange rate is
possible when domestic inflation rate is higher than foreign inflation rate so that the domestic
goods become cheaper. In temporarily fixing the domestic inflation target higher than
πT = π ef −
λ
ε π , for a given level of nominal exchange rate, the real exchange rate will
κα 2
diminish from s 0 to s1 . This solution may not be sufficient so the economy may be at a new
disequilibrium E0' . If the present measure is appropriately and flexibly used, the desirable
equilibrium E3 can be attained. At this equilibrium, the balance of payment is in equilibrium
and real exchange rate and inflation rate will not evolve any more (Figure 3).
20
πe
R& = 0
E2
π ef
E3
E1
πe
s
E0'
s& = 0
π& e = 0
E0
s1 s 0
π& e = 0
s
Figure 3. The adjustment of inflation target.
4.2. Revaluation of Chinese national currency
This solution is to some extent equivalent to re-establishing the role of forward-looking
variable for real exchange rate. As we have shown in the previous figure, further measures
may be necessary to attain the stationary equilibrium. One measure frequently advanced by
foreign governments to diminish the surplus of Chinese balance of payment is a revaluation
of Chinese national currency (yuan). This solution can be valuable when used together with
the precedent measure, i.e. the alignment of national inflation target at the level of foreign
inflation level in taking account of shocks affecting national supply. A revaluation of yuan
can permit Chinese economy to find a stationary equilibrium at the point E3 in Figure 3.
If the revaluation of yuan is taken place alone, the following adjustment cannot establish
a durable macroeconomic equilibrium and may induce the Chinese economy on unstable
adjustment path. One important objection among the economists to the revaluation of yuan is
that it might create financial instability. This cannot be shown directly in this simple model.
But as the Chinese economy can enter into deflation after a revaluation of yuan and Chinese
financial system is fragile (with quite important percentage of bad debts), the risk of financial
instability is obviously very important.
21
πe
π ef
R& = 0
E2
s& = 0
E0
E1
πe
s
s0
π& e = 0
s
Figure 4. The revaluation of yuan.
Using Figures 1a,b, we can show further that, a revaluation of Chinese national currency
leading to a temporary equilibrium E1 , where the balance of payment is in equilibrium, will
not be a durable solution. At E1 , as the Chinese inflation rate is inferior to the foreign,
Chinese products may quickly gain in competitiveness ( s& > 0 ). The domestic inflation rate
can go into different directions according to the inflation aversion of Chinese central bank.
4.3. The diminution of reimbursement of taxes for exports
This is the measure used by Chinese government in 2003 as a first answer to foreign
pressure for a revaluation of Chinese national currency. This measure is equivalent to a
negative shock affecting the foreign exchange market ( ε f < 0 ). This moves the locus R& = 0
to the right and reduces the surplus of balance of payment (Figure 5). If the effect of
diminution of reimbursement of taxes for exports is sufficiently strong, the Chinese economy
can return temporarily to the partial equilibrium E0 , where Chinese foreign exchange market
22
is at equilibrium. Nevertheless, as the economy is not at a steady state, the reduction or
elimination of disequilibrium on the foreign exchange market will be only temporary.
R& = 0
πe
E2
π ef
E3
E0
E1
πe
s& = 0
π& e = 0
s0
s
s
Figure 5. The diminution of export subsidies or tax exoneration.
πe
π ef
R& = 0
E3
E2
E1
πe
s
s& = 0
E1'
E0
s0
π& e = 0
s
Figure 6. A higher output target.
4.4. Higher national output target
As we have shown in Figure 3, the realignment of domestic inflation target at the foreign
level is not necessarily sufficient to attain the stationary equilibrium. One supplementary
solution is to increase the national output target (Figure 6). If the national output target of the
23
Chinese central bank is sufficiently high, the R& = 0 locus will move to right so that the
equilibrium point coincide with E0' in Figure 3. Of course, if the national output target is too
high, the R& = 0 locus will move temporarily to the right of E0' and the balance of payment
will be in deficit.
5. Conclusion
Using a simple open economy model, we analyse the monetary policy management of a
central bank adopting inflation targeting as the framework of its monetary policy under fixed
exchange rate regime. This seems to be the case of Chinese central bank in its recent openmarket operations. After all, Chinese central bank is now interest rate guided rather than
quantity guided. We have shown that under fixed exchange rate regime, the different markets
may not be in equilibrium when inflation and output targets are not compatible with steady
state equilibrium and national currency is under-evaluated. A stable unique saddle-point
equilibrium becomes problematical under fixed exchange rate regime as nominal and real
exchange rates cannot behave like jumping variable to equilibrate foreign exchange market
and place the economy on a converging path to the stationary equilibrium. If floating
exchange rate regime is adopted, only a central bank with weak inflation aversion can
guarantee the macro-economic stability to Chinese economy. As China has an important
unemployment rate in the countryside, the output stabilisation is then an important objective.
So we think that Chinese central bank must not be too eager to stabilise the inflation rate.
This will not endangers the credibility of Chinese central bank as it has a quite good
historical track of low inflation in the past years. As many sectors are in over-capacity and
the Chinese economy comes out of soft deflation only recently, it may be preferable to not
focus only on inflation target. As Chinese financial market develops quickly and the interest
rate elasticity of money demand diminishes in time, Chinese central bank can increase in the
24
future its preference for inflation target (more aversion for inflation) without endangering the
macro-economic stability conditions, which are helpful for Chinese economy even though it
continues to operate under fixed exchange rate regime. For instance, China is not ready to
abandon this regime.
The adopting of inflation targeting under fixed exchange rate regime, if not impossible, is
really a new challenge in theory as well as in practice, since the conventional wisdom in the
inflation targeting literature is that inflation targeting is associated with flexible exchange rate
regime. We have shown, using a dynamic setting, that under fixed exchange rate regime and
with the help of some macro-economic management measures, Chinese central bank can
mimic inflation targeting framework under flexible exchange rate regime. The fundamental
measure is to align domestic inflation target at foreign level in taking account of domestic
supply shocks. Departing from a situation characterised by weak inflation and undervaluation of Chinese national currency, this measure, if used flexibly in the sense that
Chinese central bank fixes temporarily an inflation target higher than the foreign level, can
restore alone the economic equilibrium. Three other measures (revaluation of Chinese
national currency, diminution of export subsidies or tax exoneration, a higher output growth
target), if they are not, used separately, sufficient to restore global equilibrium, can restore
temporarily the equilibrium or reduce the disequilibrium on Chinese foreign exchange
market. If they are used together with the first measure, the charge of adjustment for each
measure will be smaller17 and the speed of adjustment towards the equilibrium will be higher.
The possibility of using these four management measures, and perhaps others, to restore the
equilibrium permits us to say that inflation targeting can be practised under fixed exchange
rate regime. However, the task for Chinese central bank is much harder than that of other
central banks adopting inflation targeting under flexible exchange rate regime.
17
In the presence of uncertainty affecting the coefficients of transmission of monetary policy, it is preferable
according to Brainard (1967) to diversify the instruments and to reduce the intensity of utilisation of each
instrument. This kind of uncertainty is not considered explicitly in our model.
25
Appendix A. Derivation of the optimal monetary policy rule
The optimal monetary policy is the solution to the sequence of single period decision
problems of monetary authorities. As the single period decision problems are independent,
the central bank’s optimisation problem consists simply of minimising the one-period loss
function, L , in (7). The first order condition of the central bank’s minimisation problem (7),
following Walsh (2002), is:
∂L / ∂π = 0 ⇒ λ
∂y
( y − y ∗ ) + κ (π − π T ) = 0 .
∂π
Using then equation (3) and the result
(A.1)
∂y 1
obtained from equation (2), we obtain:
=
∂π α
{
}
λ
− β (i − π e ) + γ s − y ∗ + ε d + κ (π − π T ) = 0 .
α
(A.2)
Equation (A.2) gives the following central bank’s optimal monetary policy rule:
i =πe +
1
κα

(π − π T ) − y ∗ + ε d 
γ s +
λ
β

(A.3)
Replacing the expected real interest rate drawn from (A.3) in equation (2), one has:
y = y* −
κα
(π − π T ) .
λ
(A 4)
Using equations (2) and (A.4), one obtains:
 e

λ
κα 2 T
e
e
&
π=
ρπ
+
(
1
−
ρ
)(
π
+
e
)
+
π
+
ε


π
f
λ
(λ + κα 2 ) 

y = y* +
[− ρπ
(λ + κα )
κα
2
e
− (1 − ρ)(π ef + e& e ) + πT − ε π
(A.5)
]
.
Appendix B. Dynamics of expected inflation rate and real exchange rate
i) The differential equation for inflation rate ( π& ):
Deriving equation (5) in relation to time leads to:
26
(A.6)
m& − p& = l1 y& − l 2 i& + ε&m , l1 , l 2 > 0 .
(B.1)
& = µ , and ε& m = 0 (in the same way one assumes also ε&d = 0 , ε&π = 0 , i.e. shocks
Noting m
without tendency), that returns to:
µ − π = l1 y& − l 2 i& .
(B.2)
Given π , y& and i& , the equation (B.2) can be used to determine the growth rate of money
supply, with µ = π + l1 y& − l 2 i& . The mathematical expectation of (B.2) gives to
µ e = π e + l1 y& e − l 2 i&e .
(B.3)
The equations (B.2) and (B.3) imply that at the stationary state π e = π = µ . Once µ is
published, economic agents can recalculate their expectations of inflation rate using (B.3) in
using a simple learning rule about µ . Knowing that at every moment the information on the
growth rate of money supply ( µ ) is available through the announcements of the central bank,
the private agents adjust simply their expectations to the announced rate so that µ e = µ and
thus:
π e = µ − l1 y& e + l 2 i&e .
(B.4)
According to (B.4), the private agents can use the whole set of information concerning
the conditions of supply and demand on goods market, and financial and monetary markets.
Combining (B.2) and (B.4), one has:
π e = π + l1 y& − l 2 i& − l1 y& e + l 2 i&e .
According to the equation (1), one has y& =
y& e =
β
π& =
1
[π& − ρπ& e − (1 − ρ)(π& ef + e&&e ) − ε& π ] + y& ∗ and
α
1 e
[π& − ρπ& e − (1 − ρ)(π& ef + e&&e ) − ε& π ] + y& ∗ .
α
1
κα
i& = (γs& +
π& ) + π& e
λ
[ρπ&
(λ + κα )
λ
2
e
and
According
1
κα e
i&e = (γs& e +
π& ) + π& e .
β
(B.5)
λ
to
Using
(A.3),
one
(A.5),
obtains
one
has
]
+ (1 − ρ)(π& ef + e&&e ) . Taking account of these results and the assumption
s& = s& e , one can rewrite the equation (B.5) as follows:
π& e =
 λ (1 − ρ) e
(λ + κα 2 ) e
λ  e
κα 2 T
e
e
&
π −
ρπ
+
(
1
−
ρ
)(
π
+
e
)
+
π + επ  −
(π& f + &e&e ) , (B.6)

f
ΩΨ
ΩΨ 
λ
Ψ

27
where Ω = (
l1 l 2 κα
−
) , Ψ = −λ (1 − ρ) − κα 2 . Under fixed exchange rate regime, one has at
α
βλ
the stationary state π e =
λ
λ (1 − ρ) + κα
[(1 − ρ)π ef +
2
κα 2 T
π + ε π ]. .
λ
ii) The differential equation for real exchange rate ( s& )
By definition, one has e& e = s& e − p& ef + p& e = s& e − π ef + π e . Under rational expectations, we
assume that s& e = s& . As e& = 0 under the fixed exchange rate regime, when this regime is
sustainable, i.e. when the balance of payment is in equilibrium, the market expects that
e& e = 0 . The market may expect a revaluation (or devaluation) of national currency when the
balance of payment is in surplus (or deficit respectively). This eventuality is not considered
here. As in the article we consider only the stationary equilibrium, it is assumed that R& = 0 ,
i.e. that foreign exchange reserve remains unchanged, so there is no reason for e& e ≠ 0 . In that
case, the dynamics of the real exchange rate is governed by the following equation
s& = π ef − π e .
(B.7)
28
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