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CESifo Area Conference on
Global Economy
10 – 11 December 2004
CESifo Conference Centre, Munich
Chinese Renminbi Revaluation and
the Optimal Exchange Rate
Hui Huang, Yi Wang, Yiming Wang,
John Whalley, Shunming Zhang
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
Chinese Renminbi Revaluation and the Optimal Exchange Rate∗
Hui Huang† Yi Wang‡ Yiming Wang§ John Whalley¶ Shunming Zhang
December 3, 2004
First Rough Draft
Abstract
We present a model of combined interspatial and intertemporal trade between countries recently used by Huang, Whalley and Zhang (2004) to analyze the merits of trade
liberalization in services when goods trade is restricted. We combine this model with a
model of foreign exchange rationing due to Clarete and Whalley (1991) in which there is a
fixed exchange rate with a surrender requirement on foreign exchange generated by exports.
Under either auctioning of foreign exchange by the central bank to importers, or some nonauctioned allocation mechanism with domestic trading trading in foreign exchange, there
will be a premium value on foreign exchange established which is endogenously determined
and operates akin to a tariff on imports. Domestic monetary policy in such a model is nonneutral with respect to trade while trade liberalization (tariff reduction) merely changes the
premium value on foreign exchange, in simple models, leaving trade unchanged. In this combined model, when services remain unliberalized there is some optimal trade intervention,
even in the small open price taking economy case. Given monetary policy and an endogenously determined premium value on foreign exchange, an optimal setting of the exchange
rate will provide the optimal trade intervention. The implication is that in this model a
move to a free float may be welfare worsening if services remain largely unliberalized, the
situation that applies currently in China. We use numerical simulation methods to explore
the properties of the model, which has no closed form solution. These analytics run counter
to those presently advocating a free Renminbi float.
∗
This is an analytical paper drawing on a wider project on Financial Liberalization in China conducted under
the auspices of the Centre for International Governance and Innovation (CIGI), Waterloo, Ontario. The fourth
author acknowledge support form SSHRC (Ottawa).
†
University of Western Ontario
‡
Shanghai University of Finance and Economics and Unicentury Holding Co. Ltd.
§
Peking University
¶
University of Western Ontario, CIGI, NBER, and CES - ifo Munich
University of Western Ontario
1
1
Introduction
This paper is motivated by current debate on financial liberalization in China, and specifi-
cally the issue of Renminbi (RMB) revaluation which China’s OECD trading partners are now
advocating given both the size of the Chinese trade surplus, and their desire for improved access
to Chinese markets. China has long maintained a fixed exchange rate with tight regulation of
domestic banks, and strict limits on entry to the Chinese market for foreign financial institutions. In past, this has reflected a desire for macro stability, but the Chinese banking system
also differs sharply from those in OECD countries with small but growing personal banking,
and state owned banks acting in part as mechanisms for recapitalizing loss making state owned
enterprises. Thus, part of what is at state in debate on financial liberalization in China and
the choice of exchange rate regime is the form and operation of the Chinese banking system
and how this would change with a freely floating fully convertible Renminbi (see the discussion
Zhang and Pan 92004) and Chang and Shao (2004)).
In seeking to contribute to the debates, this paper takes as its point of departure macro
literature on the choice of exchange rate regime. While the choice between a fixed and feasible
exchange rate regime has long been argued and debated in classical monetarist terms (that a
fixed exchange rate implies accommodating monetary policy, and monetary policy determines
the floating rate) as in Friedman’s (1956) classic discussion, little literature suggests that there
may exist an optimal exchange rate. Such a contention is clearly relevant to current policy
debate in China, since with an optimal exchange rate a freely floating rate may be welfare
worsening.
We present a model of combined inter-spatial and inter-temporal trade between countries
recently used by Huang, Whalley and Zhang (2004) to analyze the merits of trade liberalization
in services. In this model, in the presence of tariff on inter-spatial trade, free trade in services,
even for a small open price taking economy, may not be welfare improving, and free trade in
goods if services remain unliberalized may not be Pareto optimal. We combine this with a
related simple model of spatial trade due to Clarete and Whalley (1991) in which there is a
fixed exchange rate accompanied by a surrender requirement for foreign exchange generated
by exportors. Under either auctioning of foreign exchange by the central bank to importers,
or some non auctioned allocation mechanism with domestic trading in foreign exchange, there
will be a premium value on foreign exchange established which is endogenously determined and
operates akin to a tariff on imports. Domestic monetary policy in such a model is non neutral
2
with respect to trade, while trade liberalization (tariff reduction) merely changes the premium
value on foreign exchange, in simple models, leaving trade unchanged.
When we combine these two models we create a world in which monetary policy is non
- neutral, and when services remain unliberalized there is some optimal trade intervention.
Given monetary policy and an endogenously determined premium value on foreign exchange,
an optimal setting of the exchange rate will provide the optimal trade intervention. By allowing
for a freely floating exchange rate any departure from this optimal rate will typically inflict
welfare losses. We present such a combined model, and illustrate these possible outcomes using
numerical simulation.
We would not pretend that this model realistically captures all of the relevant features of
the financial and real sides of the Chinese economy, and hence may only be suggestive in its
implication for current policy. But the implication that a more to a free float if services remain
largely unliberalized (as in China today) seems clear and relevant, and should perhaps be kept
in mind by those advocating a free Renminbi float.
3
2
A Simple Single-Country Model of Spatial and Inter-Temporal
Trade
We begin by presenting a single country version of the two country model presented by
Huang, Whalley and Zhang (2004) which incorporates both spatial and inter-temporal trade.
In this model monetary policy in its conventional form reflecting money as a means of exchange
is absent, but there is inter-temporal trade possible in the sense of Duffie and Sharfer (1985)
through established lines of credit.
We can present the 2 period (t = 0, 1) 1 country 2 good (l = 1, 2) pure exchange international
trade case of a small open price taking economy as follows. The country has a single representative consumer, with endowments of the two goods in each period (Elt ; t = 0, 1, l = 1, 2). For
simplicity, a time-additive Cobb-Douglas utility function of the form
U=
1
t=0
1
1
ut (X1t , X2t ) = u0 (X10 , X20 ) +
u1 (X11 , X21 )
t
(1 + ρ)
1+ρ
t
(1)
t
is used where ut (X1t , X2t ) = [X1t ]α1 [X2t ]α2 for t = 0, 1. This can be represented more explicitly
as
0
0
U = [X10 ]α1 [X20 ]α2 +
1
1
1
[X 1 ]α1 [X21 ]α2
1+ρ 1
(2)
where ρ is inter-temporal discount factor, Xlt denotes consumption of good l at date t, and αlt
is share parameter for good l at date t ( 2l=1 αlt = 1).
For any good l, in any period t, the exogenous world price is Πtl and we can allow the
country to impose tariffs at rate Tlt on each imported good l (i.e. if Xlt ≥ Elt , then Tlt ≥ 0).
Tariffs are set to zero for any export (i.e. if Xlt ≤ Elt , then Tlt = 0). Internal (gross of tariff)
prices for good l at date t are thus
Plt = Πtl (1 + Tlt ),
t = 0, 1,
l = 1, 2.
(3)
t = 0, 1
(4)
These are also sellers prices of good l.
Tariff revenues collected in period t are
t
R =
2
Πtl Tlt (Xlt − Elt )+ ,
l=1
where Elt denotes the initial endowment of good l, and the total income in period t is given by
It =
2
Plt Elt + Rt ,
l=1
4
t = 0, 1.
(5)
To simplify matters, we assume that there is service autarky and that in this case as a
strong assumption there are no intermediation services provided by domestic service providers.
1
This enables us to appeal directly to literature on multi-commodity inter-temporal mod-
els from Radner(1972), Hart (1975), Duffie and Shafer (1985), Werner (1985), Duffie (1987),
Geanakopolos (1990), Magill and Shafer (1991), and Magill and Quinzii (1996) in analyzing the
effects of service liberalization in this model in a simple way. We do this without the added
complication of uncertainty which is in practice central to this liberalization. Most of this
literature is concerned with existence issues; our focus here is comparative statics.
In the services autarky case, period by period budget constraints apply in each period t, i.e.
2
Plt Xlt = I t ,
t = 0, 1.
l=1
These imply that
2
Πtl (1 + Tlt )Xlt =
l=1
2
Πtl (1 + Tlt )Elt + Rt ,
t = 0, 1.
(6)
l=1
The combined budget constraint over the two periods is
2
1 t=0 l=1
which implies
2
1 t=0 l=1
Πtl (1 + Tlt )Xlt =
Plt Xlt
=
2
1 t=0 l=1
1
It
t=0
Πtl (1 + Tlt )Elt +
1
Rt .
(7)
t=0
This simple treatment of services allows us to consider two different single country equilibria, one with period by period budget constraints, and the other only with across period budget
constraints which reflects international liberalization of banking services with such services being supplied by foreign service providers. Moving from period by period budget constraints
to an across period budget constraint can thus be thought of as allowing for inter-temporal
intermediation in consumption activities across periods where non previously occurred. The
interpretation is that initially there is autarky in trade in intermediation services since none
can be provided domestically. We can then open up the economy to international trade in intermediation services, which are costlessly provided, as a simple form of trade liberalization in
inter-temporal intermediation services. In this model, we can thus consider goods trade liberalization as a reduction in tariffs where no service liberalization occurs, or service liberalization
1
See the discussion of barriers to trade in intermediation services in practice in the Chen and Schembri (2002),
Francois and Schuknecht (2000), Kalirajan, McHuire, Nguyen and Schuele (2001), and Mattoo (1999).
5
where no tariff liberalization occurs. We can also consider services liberalization in a tariff-free
world, and tariff liberalization in a world either with or without service restrictions. Finally,
we can consider joint tariff and services liberalization.
This joint spatial inter-temporal economy can be thought of as one in which there are a
series of spot markets in goods, and in the presence of services liberalization a system of asset
markets which permit the transfer of income among spot markets in the sense first analyzed
by Arrow (1964) and later by Hart (1975), Werner (1985), and Magill and Shafer (1991).
It contrasts with earlier inter-temporal equilibrium formalizations of a set of Arrow-Debreu
contingent commodity markets as in Debreu (1959).
2
The one single country equilibria we consider for this structure can be stated as follows.
Definition 1 Country Equilibrium with Period by Period Budget Constraints
(Service Autarky) A general equilibrium for this economy with period by period budget constraints is characterized by consumption of goods (Xlt : t = 0, 1; l = 1, 2) such that (Xlt ; t =
0, 1, l = 1, 2) solve the utility maximization problem subject to the period by period budget constraints (6),
1
u1 (X11 , X21 )
1+ρ
2
2
Πtl (1 + Tlt )Xlt =
Πtl (1 + Tlt )Elt + Rt ,
max U = u0 (X10 , X20 ) +
s.t.
l=1
t = 0, 1
l=1
Definition 2 Country Equilibrium with Across Period Budget Constraints
(Service Liberalization) A general equilibrium for this economy with combined budget constraints over periods is characterized by consumption of goods (Xilt : t = 0, 1; l = 1, 2) such that
(Xlt ; t = 0, 1, l = 1, 2) solves the utility maximization problem subject to the combined across
period budget constraint (7),
1
u1 (X11 , X21 )
1+ρ
2
2
1 1 1
Πtl (1 + Tlt )Xlt =
Πtl (1 + Tlt )Elt +
Rt
max U = u0 (X10 , X20 ) +
s.t.
t=0 l=1
2
t=0 l=1
t=0
Hart (1975) showed that with uncertainty and hence incomplete markets an equilibrium may not exist, or
an inefficient equilibrium may result. Werner (1985) discusses the general issue of existence for such economies;
Magill and Shafer (1991) show among others results how in the certainty case the multi-commodity inter-temporal
equilibrium is equivalent to one in which an interest rate is endogenously determined and equals the ratio of the
shadow prices of period by period budget constraints for each of the individuals in the economy.
6
The combined across periods budget constraint (7) for can also be written as
2
Π0l (1 + Tl0 )Xl0 + F =
2
Π0l (1 + Tl0 )El0 + R0
(8)
Π1l (1 + Tl1 )El1 + R1 + F
(9)
l=1
2
l=1
Π1l (1 + Tl1 )Xl1 =
2
l=1
l=1
where F represents the amount of lending (borrowing) by (from) one period to (by) another.
The across period budget constraint equilibrium is the same as an equilibrium characterized
by consumption of goods (Xlt : t = 0, 1; l = 1, 2) such that (Xlt ; t = 0, 1, l = 1, 2) solve the utility
maximization problem subject to the budget constraints (8) - (9)
1
u1 (X11 , X21 )
1+ρ
2
2
Π0l (1 + Tl0 )Xl0 + F =
Π0l (1 + Tl0 )El0 + R0
max U = u0 (X10 , X20 ) +
s.t.
l=1
2
l=1
2
Π1l (1 + Tl1 )Xl1 =
l=1
Π1l (1 + Tl1 )El1 + R1 + F
l=1
Setting the interest rate for lending and borrowing equal to r, the combined budget constraints become
2
Pl0 (1 + Tl0 )Xl0 + F =
l=1
2
2
Pl0 (1 + Tl0 )El0 + R0
(10)
l=1
Pl1 (1 + Tl1 )Xl1 =
l=1
2
Pl1 (1 + Tl1 )El1 + R1 + [1 + r]F
(11)
l=1
Thus, the across period equilibrium (service liberalization) is equivalent to an equilibrium
with the same lending and borrowing interest rate, characterized by consumption of goods
(Xlt : t = 0, 1; l = 1, 2) such that (Xlt ; t = 0, 1, l = 1, 2) solve the utility maximization problem
subject to the budget constraints (10) - (11)
1
u1 (X11 , X21 )
1+ρ
2
2
0
0
0
Pl (1 + Tl )Xl + F =
Pl0 (1 + Tl0 )El0 + R0
max U = u0 (X10 , X20 ) +
s.t.
l=1
2
l=1
l=1
Pl1 (1 + Tl1 )Xl1 =
2
Pl1 (1 + Tl1 )El1 + R1 + [1 + r]F
l=1
If tariff rates are zero on both products at both dates (Tlt = 0 for t = 0, 1 and l = 1, 2),
then these equilibria are also free trade competitive equilibria.
7
Comparing across these equilibria in this simplified world enables the effects of services
liberalization (in the sense assumed here) in the presence of restrictions on goods trade to be
evaluated. Huang, Whalley and Zhang (2004) analyze a 2 country version of this structure
and show examples where services liberalization in the presence of preexisting tariffs can be
welfare worsening. They use this structure to raise the wider policy issue of whether service
trade liberalization in GATS can be defended if goods trade is not free of restrictions.
8
3
A Model of Spatial and Inter-temporal Trade with Exchange
Rates and Monetary Policy
We now consider an extension of the simple 1 country 2 period (t = 0, 1) 2 good (l = 1, 2)
trade model from previous section which now also captures exchange rate policy in a world
with both services and goods and monetary non-neutralities. In this model domestic currency
is needed to execute domestic transactions and foreign currency is needed for purchase of
imports and yielded by sale if exports. We assume services remains unliberalized in the sense
that budget constraints within period apply and consider changes in exogenous exchange rates,
We again assume this country also has a single representative consumer with a time-additive
Cobb-Douglas utility function of the form (1) and (2), and endowments of the two goods in
each period (Wlt ; t = 0, 1 and l = 1, 2).
To represent an equilibrium in the presence of foreign exchange rationing, we consider the
case of a small open price-taking economy in which there is no production and all goods are
traded. The world prices for 2 goods are given as Πtl for t = 0, 1 and l = 1, 2. The domestic
(gross of tariff and gross of foreign exchange premia for imports) prices for 2 goods are denoted
as Plt for t = 0, 1 and l = 1, 2.
We assume that the government fixes the exchange rate at et , and requires all foreign
exchange earned by exporters to be surrendered to the Central Bank at the rate et . It then
allocates rights to purchase available foreign exchange at the same rate et to importers. We
assume that exporters comply with this policy and fully meet the surrender requirement, even
though there are obvious incentives for exporters to conceal foreign exchange and attempt to
sell it on parallel (black) markets rather than surrender it at lower fixed rate.
A simple modeling of the allocation process of foreign exchange among importers is to
assume that the government auctions (or sells) foreign exchange. In practice, allocation schemes
actually followed are more complex than this involving priority allocation of various forms, but
we abstract from these. Under a simple auction scheme, if desired imports require more foreign
exchange then the government offers for sale, the price of foreign exchange paid by importers
will be bid up. This price will thus include a foreign exchange premium above the fixed rate
et , which we designate as λt . This premium acts as a surcharge on foreign exchange bought by
importers, and adjusts so as to clear the foreign market.
The net effect of foreign exchange rationing in this case is akin to a general tariff on all
9
imports, since the exchange rate received by exporters differs from the gross of premium value
exchange rate paid by importers. As modeled above, the foreign exchange premium accrues to
the government, but if rights to purchase foreign exchange at the rate et are allocated by the
government without charge, the premium would instead go directly to importers.
t at date t is given by the value of domestic demands in
The domestic demand for RMB MD
domestic currency
t
MD
=
2
Plt Xlt ,
t = 0, 1
(12)
l=1
where r is interest rate. The domestic supply of RMB at date t is assumed set by the monetary
authorities and is given by MSt .
Because of the foreign exchange premium, relative domestic prices of the 2 traded goods will
now differ from world prices, depending upon whether they are imported or exported. Domestic
prices Plt are given by
Plt =


et Πt ,
l
if Xlt − Wlt ≤ 0

(1 + λt )et Πt ,
l
if
Xlt
−
Wlt
(13)
≥0
where Xlt − Wlt denotes the net import of goods l, and λt is the premium value over the official
exchange rate paid by purchasers of imports.
t at date t is given by the value of import
The demand for foreign currency (US dollar) ND
of goods
t
ND
=
2
Πtl [Xlt − Wlt ]+ ,
t = 0, 1.
(14)
l=1
The supply of foreign currency (US dollar) NSt at date t is given by the value of export of goods
NSt
=
2
Πtl [Xlt − Wlt ]− ,
t = 0, 1.
(15)
l=1
The total demand for foreign currency is ND =
currency is NS =
1
NSt
1
t=0
t
ND
. The total supply of foreign
(1 + r)t
.
(1 + r)t
The trade balance implies that the total value of import of goods is equal to the total value
t=0
of export of goods, ND = NS ,
1
t=0
2
2
2
1
1 1 1
t
t
t
0
0
0
Πl [Xl − Wl ] =
Πl [Xl − Wl ] +
Πl [Xl − Wl1 ] = 0.
(1 + r)t
1+r
l=1
l=1
l=1
10
(16)
Total revenues accruing to sellers of rights to purchase foreign exchange at the rate et are
t
t t
R =λe
2
Πtl [Xlt − Wlt ]+ ,
t = 0, 1
(17)
l=1
These rents accrue either directly to the household sector as additional revenues of importers
who are given allocations of foreign exchange by the government which they resell on premium
markets, or indirectly as recycled government revenues.
Because anticipated revenues Lt from rights of access to foreign exchange affect commodity
demands and are a component of income for at least one of the agents in the model, market
demand functions have to be rewritten to reflect this. Both Lt and Rt are each endogenously
determined, and only in equilibrium Lt = Rt .
The rationale for the homogeneity property assumed for demand functions can be seen
from the budget constraint for the household sector, which includes initial holdings of money
balances, and is given by
It =
2
Plt Wlt + MSt + Lt ,
t = 0, 1
(18)
l=1
If two periods are considered for this model with no trading allowed across periods, as in the
earlier section, to represent unliberalized services trade in financial intermediation services, the
total value of expenditures must satisfy the household budget constraint in each period, i.e.,

2

0 0
0
0

l=1 Pl Xl + MD + F = I
(19)

 2 P 1 X 1 + M 1 = I 1 + (1 + r)F
l=1 l
D
l
where as in the earlier section F is the amount deposited to Central Bank, in this case,

2
2

0 0
0
0
0
0
0

l=1 Pl Xl + MD + F =
l=1 Pl Wl + MS + L

 2 P 1 X 1 + M 1 = 2 P 1 W 1 + M 1 + L1 + (1 + r)F
l=1 l
l=1 l
D
S
l
l


 e0 2 Π0 [X 0 − W 0 ] + (M 0 − M 0 ) + (R0 − L0 ) + F = 0
l=1 l
D
S
l
l

 e1 2 Π1 [X 1 − W 1 ] + (M 1 − M 1 ) + (R1 − L1 ) = (1 + r)F
l=1 l
D
S
l
l
and
e0
2
l=1
Π0l [Xl0 − Wl0 ] +
(20)
(21)
2
1 1 1 1
Πl [Xl − Wl1 ] + (MD − MS ) + (R − L) = 0
e
1+r
l=1
11
(22)
1
1 is total domestic demand for RMB, M = M 0 + 1 M 1 is total
MD
S
S
1+r
1+r S
1
domestic supply for RMB, R = R0 +
R1 is total revenues accruing to sellers of rights to
1+r
1
L1 is total anticipated revenues.
purchase foreign exchange, and L = L0 +
1+r
A country general equilibrium for this model is given by values of (λt , Lt ) which satisfy the
0 +
where MD = MD
conditions:
[1] (Xlt : t = 0, 1; l = 1, 2) solves
max
s.t.
U
(23)
2
2
0 +F =
0
0
0
0
+ MD
l=1 Pl Wl + MS + L
2
2
1 1
1
1
1
1
1
l=1 Pl Xl + MD =
l=1 Pl Wl + MS + L + (1 + r)F
0 0
l=1 Pl Xl
[2]
1
t=0
2
1
et
Πtl [Xlt − Wlt ] = 0
t
(1 + r)
and
Rt − Lt = 0 f or t = 0, 1
(24)
l=1
[3]
t
MD
− MSt = 0 f or t = 0, 1
(25)
In this model reflecting a model of foreign exchange rationing combined with the service
and goods flow structure of the previous section, if services trade remains unliberalized there
is an optimal trade intervention even for a small open economy. If tariffs are bound under
WTO / GATT (as in China) monetary policy provides an instrument for achieving this optimal
intervention. If monetary policy is given, an optimal exchange rate will exist, and any departure
from this via a free float will impose welfare losses.
12
4
Some Numerical Simulation Results Yielding an Optimal Exchange Rate
We have used the structure set out in Section 3 in numerical simulations which show how
in the presence of given monetary policy (in the form of a setting on the size of the money
supply), WTO bound tariffs on goods flows, and service trade remaining unliberalized, there
will be an optimal exchange rate. In such cases welfare losses will occur with any move to a
freely floating exchange rate, raising questions as to the desirability of a free Reminbi float in
China.
In our simulations we assume Cobb-Douglas preferences and consider a case where period by
period budget constraints apply reflecting unliberalized services trade. The model parameter
settings we use are given in Table 1.
Table 1: Parameters Values Used in A 1 Country 2 Period 2 Good CD Model
1.1 Model Characteristics
• Small Open Price Taking Economy
• 1 Country 2 Period 2 Good
• Cobb-Douglas utility function
1.2 Model Parameterization
Utility Discount Rate
ρ = 0.10
Share Parameters
Good 1
Good 2
Period 1
0.50
0.50
Period 2
0.60
0.40
Initial Endowments
Good 1
Good 2
Period 1
20
80
Period 2
25
75
World Prices
Good 1
Good 2
Period 1
1.00
1.00
Period 2
1.00
1.00
Exchange Rates
e0 = e1 = 1.50
Domestic Supply of Renminbi
13
MS0 = 120 and MS1 = 200
Table 2: An Equilibrium for the Model Parametrization Set Out in Table 1
Interest Rate
Premium Rate
r = 0.08871442
λ0 = λ1 = 0.10321541
Domestic Prices
Good 1
Good 2
Period 1
1.65482311
1.50000000
Period 2
1.65482311
1.50000000
Utility Value
U = 96.38235433
Consumptions
Good 1
Good 2
Period 1
36.25765176
40.00000000
Period 2
72.51530352
53.33333333
Imports of Good 1
Exports of Good 2
Period 1
16.25765176
40.00000000
Period 2
47.51530352
21.66666667
Demand
Supply
Period 1
16.25765176
40.00000000
Period 2
47.51530352
21.66666667
Total
59.90114791
59.90114791
Imports and Exports
US Dollar
Total Revenue
Income
R0 =2.51706019 and R1 =7.35646700; R = 9.27408193
I 0 =275.6135 and I 1 =361.2270
Money Deposit
F = 35.61352236
14
For this parametrization, we take monetary policy as given and then compute equilibrium
solutions for alternative settings of the exchange rate to explore the behaviour of the optimal
exchange rate. Table 2 presents an equilibrium solution for this model, given the exchange rate
and monetary policy in Table 1.
Figure 1 shows the optimal exchange rate for this case, and the welfare costs which would
follow with a move to a freely floating exchange rate under which the premium value on foreign
exchange is eliminated. Concave utility first increases then decreases when the exchange rate
increases. It reaches a maximal value when the exchange rate e0 = e1 = 1.540198.
Table 3 reports the utility loss when a freely floating exchange rate preruids. In this case the
loss is relative small, but this emphasizes the presumption in favour of a fixed over a floating
exchange rate in this case.
Table 3: Maximum Utility when Exchange Rate Changes
Exchange Rate (e0 = e1 )
Total Utility Value
λ’s are endogenously determined
1.540198
96.40979619
λ0 = λ1 = 0
1.58497214323959
96.3790727500288
Table 4 and Figure 2 show the relation between utility and domestic money supply changes,
since changed monetary policy provides a substitute instrument for exchange rate policy in this
case. Concave utility first increases then decreases when RMB supply increases. It reaches a
maximal value when RMB supply MS0 equals 112.
Table 4: Utility when Domestic Supply of RMB Changes
Domestic Supply of RMB MS0
Total Utility Value
λ’s are endogenously determined
112.0000
96.41771120
λ0 = λ1 = 0
103.620927249971
96.3790727500288
Figures 3 - 6 report the behaviour of interest rate and premium values, when exchange rates
and monetary policy vary.
15
Figure 1: Concave Utility form the Model in Table 1 when Exchange Rate Increases
96
94
92
90
1
1.2
1.4
1.6
Exchange Rate
Exchange Rate --- Equilibrium Utility Value
Figure 2: Concave Utility form the Model in Table 1 when RMB Supply Increases
97
96
95
94
93
100
150
RMB Supply
RMB Supply --- Equilibrium Utility Value
16
200
Figure 3: Equilibrium Interest Rate Decreases when Exchange Rate Increases
.2
.15
.1
.05
1
1.2
1.4
1.6
Exchange Rate
Exchange Rate --- Equilibrium Interest Rate
Figure 4: Equilibrium Premium Value Decreases when Exchange Rate Increases
1.5
1
.5
0
1
1.2
1.4
Exchange Rate
Exchange Rate --- Equilibrium Premium Value
17
1.6
Figure 5: Equilibrium Interest Rate Increases when RMB Supply Increases
.14
.12
.1
.08
100
150
RMB Supply
200
RMB Supply --- Equilibrium Interest Rate
Figure 6: Equilibrium Premium Value Increases when RMB Supply Increases
.8
.6
.4
.2
0
100
150
RMB Supply
RMB Supply --- Equilibrium Premium Value
18
200
5
Concluding Remarks
This paper presents a model of international trade with both inter-temporal and spatial
trade motivatedly by current debate on Reminbi revaluation in China. In this model if intertemporal trade is restricted by service regulation, even for a small open price taking economy
free trade in goods will typically not be the best policy. A fixed exchange rate policy with a
surrender requirement on exporters and rationing (or auctioning) of foreign exchange among
importers can then be a welfare improving intervention compared to a free floating exchange
rate. In China with services unliberalized until 2007 when the terms of China, WTO accession
apply (see Whalley (2003)) and tariff rates bound under WTO accession terms this analysis
seems relavant to the present debate.
While this analysis may not be fully realistic of the situation in economies such as China
under international pressure to liberalize the exchange rate regime, it does provide possible
inter-lectural coherence to a position opposed to seeming international conventional wisdom
that China’s best policy is to move to a free float.
19
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NBER Working Paper