Download The Sequence of Capital Account Liberalization: a Microcosmic Model

The Sequence of Capital Account Liberalization: a Microcosmic
Model*
XIONG Fang1,2 HUANG Xian1
1 Economics and Management School, Wuhan University, P.R.China, 430072
2 Economy school, S.Cent.Univ.Nationalities, P.R.China, 430074
Abstract: This paper is to explore the sequence of the capital account liberalization by establishing a
microcosmic model of non-cooperation game among the government, the domestic firm borrowing from
abroad, and the foreign exchange short seller. We prove again that to ensure the financial stability and
sustainability, a country should launch its reform of economy liberalization, especially the capital
account liberalization with strong macroeconomic environments. Meanwhile, the proper sequence
should be: the interest liberalization is in the first order, second is to reform foreign exchange rate
system, and the capital account liberalization is in the end.
Key Words: capital account liberalization, finance stability, sequence interest rate liberalization
foreign exchange rate
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1. Introduction
Since the early of the 20 century 80s, the financial crises owing to the incorrect sequence of the
capital account liberalization have swept the world. So, McKinnon (1984) and Edwards (1994) argue
that according to the general theory of the second best and the theory of hysteresis the economy reform
should have an optimal sequence, and persist that the capital account must be the last to liberalize. Also,
Edwards (2001) states that on the issue of liberalization sequencing, the first and also the only one to be
generally agreed is that release of capital control should be after the reform of domestic financial market
and interest rate, and the interest rate liberalization should not be implemented until the financial deficit
is controlled. Meanwhile, Lshii and Habermeier (2002) argue that the general principle of the correct
sequence of the capital account liberalization and other economy reforms is, stressing the importance of
the macroeconomic stability, selecting proper exchange rate system and developing the financial sector
to support macroeconomic stability. In the same vein, domestic researchers Yin Jian Feng and Li Yang
(2000) certify that considering the capacity of an open economy to defend outside shocks, the rational
order for a completed controlled economy translating to an all-around open one should be: adopting
floating foreign exchange rate should precede to capital account liberalization; and the abolish of the
fixed exchange rate system should be after the development of domestic financial sector.
The evolution of the theory demonstrates that to keep stability and sustainability, there is an
optimal sequence among the capital account liberalization and other economy reforms. Bhattacharya
2003 establishes a dynamic model including the government, a domestic firm borrowing abroad and
a foreign exchange short seller covering time 0 and time 1 to certify that when the capital controls are
released to a certain degree, the free flow of capital and the fixed exchange rate system is incompatible.
This paper perfects the model in Bhattacharya (2003) by bringing the foreign exchange short seller into
the scope of the capital controls as well as considering the influence of domestic interest rate on the
costs of safeguarding the exchange rate to explain the optimal order of capital account liberalization.
The following paper organized as follows. In section 2, we lay out the hypotheses and rules of the model.
In section 3 are the analysis of the model. And in section 4 are conclusions and remarks.
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*
Fund: Financial development and China’s income distribution: the theory, empirical analysis, and policies selection,
Sponsored by Ministry of Education of the People’s Republic of China (Fund Number: 06JA790116).
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2. The model
There are four participants in this model: the government, the foreign exchange short seller, the
domestic firm borrowing abroad and the foreign bank, and two times: 0 and 1. Meanwhile, the economy
is a small developing country in the process of economy liberalization. Besides, there are some other
hypotheses as follows.
H1: The participants are all rational and risk neutral;
H2: The information of the foreign exchange short seller and domestic lender is independent;
H3: The participants invoke no-arbitrage on their foreign exchange;
H4: The government can observe the macroeconomic fundamentals a and the quantity S exchanged by
the foreign exchange short seller. Here, a is a summary statistic of every macroeconomic variable that
has been known to help the government defend its currency, such as current account surpluses, foreign
exchange reserves, low foreign loan and fiscal deficits, and low inflation. A is assumed to be
independently drawn from a uniform distribution;
H5: All control measures implemented by government on capital account can be replaced by a relevant
tax rate T, and the number of T indicates the degree of the capital account liberalization;
H6: At time 0, a is strong relative to the world economy, which means the economy is in equilibrium,
and the fixed exchange rate is e0. In this paper, the exchange rate is defined as the price of one unit of
domestic currency in units of foreign currency.
As Bhattacharya, capital account liberalization is defined as the freedom degree for the domestic
firm to borrow from foreign countries and denoted by the tax rate levied upon the profits of domestic
firm from borrowing abroad. However, Bhattacharya (2003) does not incorporate the foreign exchange
short seller into the scope of the capital control, so the decrease of T does not affect the foreign
exchange short seller. Thus, Bhattacharya concludes that the excessive lending is the only reason to lead
to the instability of the foreign exchange rate. But in this paper, Tobin Tax levies also on the foreign
exchange short seller, so, both excessive lending by domestic lenders and the speculative attacks by
foreign exchange short sellers will result in exchange rate instability.
2.1 The government
The objective of the government is to keep financial stability through the process of the economy
liberalization. So, when liberalizing their capital account, government needs to safeguard its foreign
exchange rate system. While whether the government can achieve this objective depends on the benefits
and costs to do this. Now supposing the costs to maintain the exchange rate C, is the function of
domestic interest rate r, the quantity of local currency m purchased by the government to defend the
exchange rate, and the domestic fundamentals a. Therefore, it can be denoted as C=c (r,m,a). Obviously,
C is monotonically increasing with r and m but decreasing with a. Let function m (a1) means the relation
of m varying with a1, which is interpreted as the maximum currency the government purchases to
defend the exchange rate, or equivalently, the minimum currency needed by the foreign exchange short
seller to defeat the government. Here, a1 is the fundamentals at time=1. Additionally, supposing the
benefits for the government to defend its currency are B. Thereby, the necessary condition for the
government to fix the foreign exchange rate is:
B≥c(r,m,a )
1
Considering the signaling function of the interest rate, namely, a relative high interest rate means
better economic fundamentals. So, when the interest rate is in a relative high level, the public will deem
the economy too strong to be attacked, the exchange rate thus keeps stability. Contrarily, when the
interest rate is below a certain number, the public think the fundamentals weak and speculate. Hence, the
condition for the government to defend its currency can be rewritten as:
B≥c(m,a)
2
2.2 The domestic firm
The domestic firm has a project that requires an investment of one unit local currency at t=0 and
returns R in local currency at t=1. The needed fund, the domestic firm may borrow from domestic banks
at rd or from foreign banks at r f. The objective of domestic firm is to maximize its expected profits at
t=1, so he needs the exchange rate to be stabile and will not speculate in local currency.
If the domestic firm borrows from domestic banks, then, under a competition condition, the lending
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interest rate will equal the risk-free interest rate. So, the expected profits of the domestic firm will be:
Rrd
Rr
3
And if the domestic firm borrows e0 units of foreign currency from abroad, he will need e0 1+ rf /
e1(a1) units local currency to payoff its loan at t=1. Here, e0 and e1 (a1) denote the exchange rate at t=0
and t=1 respectively. Then, at t=1, when government defends its currency successfully, this probability
＊ a＊ is the threshold number to make C equate to B , the profits of the domestic in local
is
-a
currency are R- e0 1+ rf / e1 1-T
Rrf
1-T ; otherwise the domestic firm will
pay its return R back to the foreign banks, and the government may no longer levy upon the domestic
firm because it gains nothing from borrowing abroad. So, the expected profits of the domestic firm from
borrowing abroad will be:
Rrf
-a＊ 1-T
4
If it is indifferent for the domestic firm to borrow from domestic and abroad, then, the following
equation must occur
＊ 1-T
Rr
Rrf
-a
5
2.3 The foreign exchange short seller
The foreign exchange short seller gains from the spreads of the exchange rate between t=0 and t=1,
so he needs to defeat the current exchange rate. However, whether the foreign exchange short seller will
short sell the domestic currency depends on its expected profits, which lies on his information on the
economic fundamentals. At t=0, if he conjectures a1≤a＊ he will participate the financial market: he will
borrow one unit of domestic currency and convert it to foreign currency, invest in foreign risk-free bond,
and pay back equivalent value at t=1. Suppose the tax rate the government levies upon the profits of
currency transaction, then, the benefits the foreign exchange short seller reaps at t=1 will be e0 1-T 1+
r* units of foreign currency. r* is the risk-free interest rate for the foreign country. So, if the foreign
exchange rate keeps stability, that is e1(a1)
e0 the final profits of the foreign exchange short seller
will be [e0 1-T 1+ r* - e0 1+ r / 1-T ] units of foreign currency; but if the government fails to
defend its currency, then the final profits of the foreign exchange short seller will be [e0 1-T 1+ r* e1 1+ r / 1-T ] units of foreign currency. Let the expected profits be 0, we can get:
＊
[e0 1-T 1+ r* - e0 1+ r / 1-T ]
-a +[e0 1-T 1+ r* - e1 1+ r / 1-T ]
＊
a =0
Namely, E(e1) =e0 1-T 2 1+ r* / 1+ r
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So, the foreign exchange short seller will short sell domestic currency only when:
E(e1) <e0 1-T 2 1+ r* / 1+ r
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2.4 The foreign bank
The foreign bank can either provide loans in the foreign markets at risk-free interest rate r* at t=0,
and gains e0
r*
units of foreign currency, or, it can offer an interest rate rf to the domestic firm
and gains e0
rf
-a＊
e1 a１ Ra＊ units in foreign currency. So the foreign bank will provide
loans to domestic only when
e0
r*
e0
rf
-a＊
e1 a１ Ra＊
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According to equation (5) and (8), we substitute rf and get
＊
＊ 1-T
Rr
R/ e0
e0 ( -a
e1 a１ a
r*
Rr
*
[R E(e1) e0r ]
9
Moreover, let T 0, we can get another equation
r
R- R e0 / E(e1)+ r*
10
It deserves to note that equation (10) deviates away from the traditional uncovered interest rate
parity (UIRP). According to Francis et al. 2002 , in emerging countries, even if the capital market
integrates with the international capital market after capital account liberalization, the UIRP will no
longer hold owing to the existence of a time-varying risk premium as a compensation for the speculative
position in the foreign currency.
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3. Analysis on the model
，
，
（ ＝，
：
According to equation (2), we know that there exist aL and aH assuming aL<aH where C m 0
a1 aL =B and C m→∞ a1 aH
B. Therefore, fundamentals can be classified into three zones
[0 aL , [aL aH ] and (aH 1]. The first zone [0 aL means a country is weak relative to the world
economy and the fixed exchange system is either abandoned by the government or collapsed by the
speculative attack; the zone aH 1] means a country with respect to the world economy is strong and no
matter what the attack will be, the government can defend its currency successfully. While in zone [aL
aH ] whether the current exchange rate can be maintained mainly relies on the real economic
fundamentals and the beliefs for the government to defend its currency. If a１≥a＊ then it is easy for the
government to keep the exchange rate, or , the government will find it difficult to keep the exchange rate.
Following we will analyze different situations when a belongs to [aL aH ].
3.1 The situation with either the domestic firm or the foreign exchange short seller
First of all, we consider the situation with only the domestic firm participating in the financial
＊
market. As regards to a set tax rate, the domestic firm conjectures that if a1>a the government can
defend its currency, then it will borrow from a foreign bank the mount of equivalent to b* in domestic
currency at t=0 and repay back at t=1. Otherwise, the domestic firm will not borrow from the foreign
＊
＊
bank. b* is the point of intersection of vertical line a b and m(a1) in fig.1. We may first solve a b from
equation (9). If the government conjectures that the above is the strategy of the domestic firm, his
＊
optimal choice is to fight and win when a1>a while not fight and the domestic currency depreciate
＊
when a1≤a . This is because the maximum currency M, that the government can purchase to defend the
local currency is more or less than b * respectively.
Second, we come to the situation with only the foreign exchange short seller participating in the
financial market. Suppose at t=0, the foreign exchange short seller conjectures that the government can
not defend successfully its currency at t=1 if a1≤a＊ then he will short sell a quantity s. On the other hand,
the foreign exchange short seller will not short sell if a1>a＊. The same, when the government observes
＊
the strategy of the foreign exchange short seller, his best strategy is to give up fighting if a1≤a or fight
＊
and win otherwise. Hence, a s , the corresponding point to the intersection of the horizontal line s and m
(a1) in fig.1 is the threshold point for the government to give up intervention.
＝ ）
（
， ） ，
，
， ＝ ）＝
，
（ ，
， ）
，
，
，
，
，
m
M
m (a1)
S
a
b*
0
aL
a＊b
a ＊s
aH
1
Figure.1. The broken line indicates the situation with only foreign exchange short seller
The real line indicates the situation with only domestic firm
3.2 The situation with both the domestic firm and the foreign exchange short seller participating
in the financial market
What the situation will be when both the domestic firm and the foreign exchange short seller
＊
participate in the financial market. According to equation (9), we can first solve a , which is the
threshold point for the government to maintain the exchange rate stability. Meanwhile, the point of
intersection of a ＊ and m (a1) determines Q* in fig.2. Since we have already solved a ＊s and a ＊b
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respectively with either the domestic firm or the foreign exchange short seller participating in the market,
then, there must be a T* that will make a＊s a＊b. Following, we will analyze the equilibrium according
to the relationship of T and T*.
＊ ＊ ＊
＊
Given T>T*, we know that there exists a a s>a b . Because a b is the point to make the
＊
domestic firm indifferent to borrow from domestic and abroad, so a a＊s>a＊ b demonstrates that the
probability for the government to maintain the exchange rate is less than the probability required for the
domestic firm to borrow from abroad. Therefore, the dominate strategy for the domestic firm is
borrowing only from domestic market. The situation is tantamount to the equilibrium with only foreign
exchange short seller participating in the market in fig.1.
＊ ＊
＊
＊
Given T< T*, we know that there is a a b>a s. According to fig.2, if a1<a , the foreign exchange
＊
short seller will short sell a quantity of local currency S at t=0. While if a1≥a , the foreign exchange
short seller will not participate in the market, namely S=0. The domestic firm observes the strategy of
the foreign exchange short seller and will borrow a quantity of local currency b*at t=0. b* is subtracted S
from Q*. As our previous discussion, the dominate strategy of a rational government is to abandon its
＊
＊
current exchange rate if a1<a , while abandon its intervening in the current exchange rate if a1 >a when
observing the strategies of the foreign exchange short seller and the domestic firm.
Additionally, we may know that when T is gradually decreasing, that is to say, when it becomes
easier and easier for the domestic firm to borrow from abroad, it will arouse at least three effects. First,
the decrease of T indicates that the government will levy less on the profits of domestic firm from
borrowing abroad, so even if the spreads between the foreign interest rate and domestic interest rate
shrinks, the domestic firm will still borrow from abroad, which thus stimulates excessive lending.
Second, according to equation (6) and (7), when T decreases, a tiny change of exchange rate will
increase the expected returns of the foreign exchange short seller for short selling. So the probability for
the foreign exchange short seller to attack will augment. Last but not least, a＊ will increase as T
decrease, which indicates that in the process of capital account liberalization, the probability for the
government to fix the exchange rate diminishes, and corresponding, the probability for the exchange rate
to be instable increases.
＝
＝
＝
＝
m
m (a1)
M
Q*
a
S
＊
＝＊
＊
0
aL
a＊s a＊ a＊b aH
1
Figure.2. The situation with both domestic firm and foreign exchange short seller
4. Conclusions and discussions
This paper is to explore the sequence of capital account liberalization by establishing a
microcosmic model of non-cooperation game among the domestic firm borrowing from abroad, the
foreign exchange short seller and the government. According to the previous analysis and our hypothesis,
we may conclude that to ensure the financial stability and sustainability, a country should launch its
reform of economy liberalization, especially the capital account liberalization in a proper sequence.
First, a stable and strength macroeconomic fundamentals are pre-conditions for the capital account
liberalization. Under the hypothesis of complete information theory, whether the foreign exchange short
seller will attack mainly depends on the economic fundamentals and the beliefs of the government to
maintain exchange rate. Hence, strong fundamentals may decrease the probability for the foreign
exchange short seller to speculate, and even the speculator attack, the strong fundamentals will help to
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keep stability. Because according to the relationship of parameters in function C=c(r, m, a), when facing
the speculative attack, the government can keep the exchange rate stability by increasing the domestic
interest rate if the fundamentals are energetic and strong, otherwise, increasing interest rate can neither
keep the exchange rate, and a high interest rate is most likely to restrain the fundamentals and cause
economy crises.
Second, interest rate liberalization should proceed to the capital account liberalization and foreign
exchange rate reform. The equation (4) is the restricted conditions for the domestic firm to participate in
the financial market. Because there exists
-a＊ 1-T
1, so there must be r> rf to satisfy this
equation. This result indicates that when the degree of capital control is high, the domestic firm will
borrow from abroad only with interest rate compensation. Furthermore, the higher degree of capital
control is, the more interest rate compensation should be. Namely, the spreads of r and rf should increase
with the value of T to induce the domestic firm to borrow from abroad. Meanwhile, the analysis also
indicates that it will introduce excessive lending of the domestic firm if it is too early to release the
capital control. Besides, all kinds of capital control will signal some information. For example, levying
upon the domestic firm for the profits gaining from borrowing abroad will means something like more
instability of macroeconomic fundamentals than expected or a tight policy for the government to reduce
the profits of investment. The public will consider it as a signal and thus change their investment
decisions. Therefore, for those countries in lack of capital should liberalize their domestic interest rate
first so as to mitigate the low interest rate caused by financial restraint, and induce the domestic firm
utilize the foreign capital. Also, they should retain a certain degree of capital control to isolate the
financial risks owing to the speculative attacks by the foreign exchange short seller and excessive
lending by the domestic firm during the process of interest rate liberalization.
Finally, Capital account liberalization should be subsequent with the reform of foreign exchange
rate. We know from equation (9) that a＊ will increase as the decrease of T, which means that the more
the capital account is open, the less probability for the government to fix the exchange rate, and
corresponding the more probability for the foreign exchange short seller to attack on the local currency.
Moreover, once the speculative attack begins, the expected return of the foreign bank will diminish
according to equation (6). So the foreign bank will require the domestic firm to repay their loan before
the mature date, which will exacerbate the stability of the foreign exchange system. Otherwise, even
only one debtor can not repay their loan, then few creditors will to provide a loan any longer. As a result,
even a slight shock may make the capital inflow suddenly reverse and finally trigger a financial crisis.
Moreover, if a country abolishes the fixed exchange rate system at the time that the market is conscious
about the fragile of the system and the speculator considers it is the time to launch an attack on the
currency. Therefore, the time opportunity for a country to retreat from a fixed exchange rate system is
when this country has no deprecation pressure on its currency and has a net capital inflow.
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References
[1] Bhattacharya. Financial liberalization and the stability of currency pegs. Journal of Corporate Finance, 2005,
11(1-2): 351-374
[2] Francis, Hasan, Hunter. Emerging market liberalization and the impact on uncovered interest rate parity. Journal of
International Money and Finance, 2002, 21(6): 931-956
[3] Ogawa, E. and Sun Lijian. How were capital inflows stimulated under dollar peg system?. 2001, in Sun Lijian et
al. The efficiency of capital controls and the matchup of policies. Journal of Finance, 2003(1):19 (In Chinese)
[4] Wang Luo-lin, Li Yang. Financial structure and financial crises. Beijing: Economic and Management Press, 2002. 230-255
(In Chinese)
[5] Ishii, Shogo. Habermeier, Karl et al. Capital account liberalization and financial sector stability. IMF Occasional
Paper No.211, 2002
[6] Qi Qi-bu. Comment on the selection of the exchange rate system. Journal of Finance, 2004(2):30-42 (In Chinese)
The author can be contacted from e-mail : Woxf99@163.com
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