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ГУО ДЖИН, МИЯМОТО КАЦУХИРО GUO JIN, MIYAMOTO KATSUHIRO
Анализ устойчивости обменного курса китайского юаня The Analysis of the Equilibrium Exchange Rate of Chinese Yuan
Анализируется обменный курс китайского юаня с точки зрения теории паритета покупательной силы валют (РРР) и поведенческой теории обменного курса равновесия (BEER). Предлагается поведенческая модель обменного курса равновесия для юаня и оценка равновесия реального эффективного обменного курса, основанная на модели BEER.
In this paper, we will study an empirical analysis of the equilibrium exchange rate of China’s Yuan based on two economic theories: The Purchasing Power Parity (PPP) Theory and the Behavioral Equilibrium Exchange Rate (BEER) Theory.
The estimation results show that it is hardly to believe that the Purchasing Power Parity Theory is an appropriate theory to analyze the exchange rate of Yuan/dollar. We also realize when researching the exchange rate of a developing country like China, it is not only have to consider the factor of price but also have to take the fundamentals of the economy into account. Then based on the BEER Theory, we estimate the equilibrium real effective exchange rate (REER) of the Yuan and find the actual REER is very close to its equilibrium level in the long-run. Although, misalignment exists, the magnitude is not extremely serious. Moreover we conclude that either the period of the undervaluation or the overvaluation coincides with the actual behavior of the economy.
1. INTRODUCTION
The decision of revaluating 2% of Yuan/dollar exchange rate in July 21, 2005 must be the most important event in china’s financial fields. The practical fixed exchange rate system taken by china for a long time was abrogated, and a new exchange rate system - currency basket system has been adopted at the same time. The new system makes the Yuan/dollar exchange rate fluctuated within 0.3% of the up-down ranges. Moreover, the adjusting of the exchange rate fluctuation is not only adapt to relationships between Yuan and US$, but also to it with other main currencies such as euro, yen and so on.
In recent years, the GDP of China increases continuously with the astonishing speed of 10% every year. However, on the other hand, the exchange rate of Yuan pegged the US$ constantly until 1994. With the developments of trade after 1978, the Chinese government adopts the dual exchange rate policy: coexistence of official exchange rate and market exchange rate. In order to promote the export, the swap exchange rate (1 dollar = 2.8 yuan) was carried on when trading with the abroad while the official exchange rate was carried on domestic trade transaction. In 1994, Chinese people's bank implemented a reform of exchange rate. The dual exchange rate system was united as a single one; meanwhile, the managed floating system has been adopted for the first time. Nevertheless, the exchange rate of Yuan/dollar floated just only 0.1% scope (1 dollar = 8.27-8.28 yuan) after 1994. Essentially, the exchange rate system in China has become a kind of the fixed exchange rate system which is called the dollar peg system. Giving a glimpse at the development of economy in China recent years, such an exchange rate system played a very important role in the stability of the foreign trade and domestic financial market. However, with the tendency of economic integration and globalization, it is a big challenge for any country to stabilize the economic growth by control the exchange rate.
Recently, an intense dispute about the aptness of the exchange rate system adopted in China has been launched throughout the world. There are mainly two greatest part opinions for the current exchange rate of China. One tends to believe that Yuan is undervalued in view of the economic power of current China. Especially in recent years, with the development of the export-oriented industrialization in China, the trade friction between China and America become more and more violent. Japan also complaint about the Yuan is practically fixed with dollar, therefore China exported deflation toward the peripheral nations at the time of promoting its own export. Furthermore, some scholar considered that with the gradually increase of the trade surplus in China, the People's Bank of China must continuously intervene of buying into the dollar and selling out the Yuan. The aftermath will be that a great deal of money supply flows into the domestic markets and the pressure of high inflation will increase.
The other opinion is to maintain the existing exchange rate system for there is no enough evidence to judge that the Yuan is undervalued. Some scholars consider that the appreciation of the Yuan has a little, even no effect to reduce the trade friction with other country. Although the foreign trade of China is enlarging continuously, it accounts for only 5% of the total amount of international trade. Something more important is that 75% of the total export increase in China is made by the multinational corporations. These multinational corporations transfer production base to China and then export the products to the United States and other countries. Therefore, the increased export sum in China is owing to the increased export sum of the foreign-affiliated company and has no direct relation with the depreciation of the Yuan. Some economists claim that the problem of trade deficit in US is the unbalanced relation of the domestic savings and the investment, and US should not always emphasize the depreciation of currency in other countries.
There are great divergences between these opinions, so the problem of the actual value of the Chinese Yuan needs to be studied further. There are large quantities of early studies to analyze the exchange rate of the China’s Yuan. The Purchasing Power Parity approach is a traditional theory which is used to judge whether the exchange rate is appropriate or not. Based on the PPP Theory, Bosworth (2004) and Overholt (2003), Frankel (2004) and Chou and Shih (1998) demonstrated that the Yuan has been apparently undervalued in recent years. However, based on the same theory, Zhang (2002), Shirai (1999), Thacker (1995), and Dowla (1993) found that the long-run PPP does not hold for exchange rate of Yuan. Some economists analyze the Yuan based on the equilibrium exchange rate theories. The results indicate that the Yuan is not being undervalued (see Zhang, 2002, Zhichao Zhang, 2000).
In this paper, we will do an empirical analysis about the exchange rate of Yuan based on the Purchasing Power Parity Theory and Behavioral Equilibrium Exchange Rate Theory. We attempt to estimate the equilibrium exchange rate of the Yuan and investigate whether the Yuan is undervalued or not by comparing the actual rate with its equilibrium level. The organization of the paper is as follows. In Section 2, we will examine whether the Purchasing Power Parity Theory does hold for the exchange rate of Yuan/dollar at first. Subsequently, the misalignment of the Yuan/dollar nominal exchange rate will also be estimated. In section 3, we firstly construct a behavioral equilibrium exchange rate model for the Yuan. Secondly, the estimation of the equilibrium real effective exchange rate will be carried out and we also discuss the misalignment in the end. Section 4 contains conclusions.
2. AN ANALSIS BASED ON THE PURCHASING POWER PARITY THEORY
2.1 Model and data
A more traditional, but still popular, definition of the real exchange rate relies on the Purchasing Power Parity (PPP) Theory. The PPP real exchange rate (errr) is equal to the nominal exchange rate (£) corrected by the ratio of the foreign price level ^*) to the domestic price level, we express this relation as:
RER = e PPP = EP */P . (1)
Where RER is the real exchange rate. Depending on whether Р and Р* are consumer prices indexed or producers price indexed, ep„ will be the relative price of foreign to domestic consumption or production baskets. Although this definition of real exchange rates is still widely used, it is difficult to measure the relative price of tradable goods to non-tradable goods. Here we assume that goods of one country are composed by tradable goods and non-tradable goods simply. Assuming the PPP hold for the tradable goods for it is transacted beyond the border. Furthermore, we suppose that the price of tradable goods and non-tradable goods of domestic and foreign country occupy the similar weight (w) in the synthetic price. Then equation (1) can be transform into equation (2) below (Appendix):
RER = errr =
P / P
T N
P 7 P*
TN
(2)
w
Where PT,P* indicate the price of domestic and foreign tradable goods. PN,P'N indicate the price of domestic and foreign non-tradable goods. According to equation (2), we know that the real exchange rate depends on the tradable goods - non-tradable goods relative price of domestic and foreign country. In most modern theoretical works, the price of foreign goods is assumed to be unchangeable. Eventually, the real exchange rate is defined as the domestic relative price of tradable goods to non-tradable goods. It can be written as:
RER = Pt / Pn . (3)
In Hinkle and Montiel (1999) called the two-goods internal real exchange rate for tradable goods and not-tradable goods. Note that a decline in the RER denotes appreciation, while an increase in the RER indicates depreciation. Assuming that the country is small, and the law of one price holds for tradable goods, we have:
E = PT / P* . (4)
We substitute equation (3) by equation (4) then the RER indexes invariably take the following form:
RER = EPT'/ PN . (5)
In our analysis we choose the wholesale price indexes (WPI) of America as the proxy variable forpt*. Since America is the major trade partner of China, and the WPI contains mainly tradable goods. With respect to the proxy variable of domestic price of non-tradable goods, Chinese consumer price index (CPI) is chosen. Although CPI contains some tradable goods, in available data of China we can not find a better proxy than it.
Based on equation (5) we will investigate whether the PPP theory is appropriate to exchange rates of Yuan/dollar. In this paper three versions of the PPP, which is the univariate, bivariate, and trivariate PPP theory will be applied. Our sample is from 1987:1 to 2005:5, and all data are monthly, most data sets root in the International Finance Statistics published by IMF and China Monthly Economic Indicators.
2.2 The analysis based on univariate PPP Theory
In order to test whether the univariate PPP holds for the exchange rate
of Yuan/Dollar, we will test whether the real exchange rate behaves as a unit
root process. The logarithm of real exchange rate qt is defined as:
qt = St + wpi US - cpi . (6)
Where st is the logarithm of the nominal exchange rate in terms of the Yuan against the U.S. dollar, wpi'f and cpi™ are the logarithms of the America and China’s price index. The univariate PPP Theory is a comparatively strict form of the PPP Theory, for it is not only have to maintain the symmetry of the domestic price and the foreign price but also require the price indexes are in proportion to the nominal exchange rate. Basing on equation (6) we can compute the real exchange rate of Yuan/dollar, and the diagram of it is shown in Figure 1.
It is difficult to judge whether the RER is a stationary series only by the figure. So we apply a statistical method to test whether the RER has a unit root. The standard approach to test whether a series have a unit root process is the Augmented Dickey-Fuller (ADF) and the Phillips-Perron unit root test. Table 1 reports the result of the unit root test.
Table 1
Unit root test for real exchange rate
Test Statistic P-value
ADF test 0.2354 0.75694
Phillips-Perron test 0.04946 0.70097
From Table 1, we can verify that the null hypothesis which unit root existed in can not be rejected either in the ADF test or the P-P test. This indicates that the real exchange rate qt is not a stationary series. Strictly speaking, the univariate PPP Theory does not hold for the real exchange rate of Yuan/dollar.
2.2 The analysis based on the bivariate PPP
In comparison with the univariate specification, the bivariate PPP is a relatively relaxed version. In the bivariate version of PPP the cointegration relationship between the nominal exchange rate and the difference in price of China and America which described in equation (7) will be tested. The bivari-ate PPP can be written as:
st = a + P (cpi CH - wpi tUS ) + /Ut . (7)
If st and (cpifH - wpiU) are found to be cointegrated, deviations from a liner combination of the variables are mean-reverting and it suggests that these variables have a long-run relationship. Basing on the method of Engle and Granger, the cointegration analysis begins with examining the order of integration of the nominal exchange rate (st) and the difference in price of China and America in equation (7). Table 2 shows the result.
Table 2
Variables Test specification Test Statistic P-value
St (C,T) -1.17523 0.91546
Ast (0,0) -8.20109** 0.00000
cpi - wpi US (C,T) -1.65050 0.77204
A ( cpi C - wpi U ) (0,0) -1.65337* 0.092867
Note. C and T denote the constant and trend term in the unit root test.
* Denotes rejection at the 10% significance level.
** Denotes rejection the null hypothesis at the 1% significance level.
The results of unit root tests indicate that the st, and (cpi™ - wpi'U ) are both I(1), where I(1) denotes integrated of order one. Johansen (1991) and Juselius (1990) developed the maximum likelihood estimator for cointegration analysis. Since the st and ( api™ - wpiU ) are found to be integrated of the same order, the long-run PPP relation will be tested using Johansen’s trace cointer-gration test. The result shows that there is no cointegration relationship between st and (apt r - wpiD. So the bivariate PPP is also not appropriate to the exchange rate of Yuan.
2.3 The analysis based on trivariate PPP
In the version of trivariate PPP Theory, the restriction is more relaxed. In order to verify whether the trivariate PPP is appropriate to the Yuan, it has to test whether the nominal exchange rate, the domestic price, and the foreign price are cointegrated. We write the trivariate PPP relationship as
st = a + Picpi r - Piwpi U M . (8)
We also use the ADF and P-P unit root test to examine the order of integration of the cpi™ and wpi'U .The result indicate that the both cpi™ and wpi'U are I (1), since st, cpi™ and wpiU are all I (1), Johansen’s trace test is also used to test the cointegration of them. The test results are listed in Table 3.
Table 3
Null Alternative A^trace P-value
Test for cointegration relationship between st, cpi™ and wpi'f
H0:r=0 H1: r=1 41.99247 * 0.00676
H0:r<=1 H1: r=2 8.71513 0.58534
* Denotes rejection of the null hypothesis at the 1% significance level.
The hypothesis of a non-cointegrated relationship is rejected, so it confirms that there is one cointegration relationship between the nominal exchange rate of Yuan/dollar, the Chinese CPI index and American WPI index. So we conclude that the trivariate PPP Theory does hold for the exchange rate of Yuan/dollar. In the end, we can derive a cointegration equation based on the cointegration vector, Equation (9) express the cointegration relationship of st,cpi™ and wpi'f with constant and trend term.
st = -0.9457 + 0.89915cpitCH - 0.01339wpi“ - 0.00021916Trend . (9)
We can observe that the signs of cpic;H and wpiUS in equation (9) are correspond to the signs in equation (8). According to the basic principles of PPP, the nominal Yuan/dollar exchange rate should depreciate (namely, st should go up) when consumer price index of China goes up; and it should appreciate (namely, st should go down) when the US wholesale price go up. This is the reason which in equation (9) the sign of cpiCH is positive; and the sign of wpiU is negative. So we conclude that a reasonable cointegration relationship does exist among st, cpi™ and wpiU .
2.4 The misalignment of the nominal exchange rate of the Yuan/dollar
Since real exchange rate misalignment is defined as sustained departures of the actual exchange rate from its equilibrium value, estimating of equilibrium exchange rates is the first step in any attempt to understand real exchange rate misalignment and overvaluation or undervaluation. Here we define the exchange rate which is derived by cointegration equation (9) as the equilibrium exchange rate. The movement of the actual exchange rate and the equilibrium exchange rate based on PPP Theory in China from 1987 to 2005 are graphed in Figure 2.
-----equilibrium rate -------------actual NER
Figure 2
We know if the actual real exchange rate is below the equilibrium exchange rate value, we say that there is an overvaluation. On the other hand, if the actual exchange rate exceeds the equilibrium exchange rate, we say that there is an undervaluation.
Moreover, in order to identify the degree of misalignment we compare the equilibrium exchange rate with the actual exchange rate in Table
4. Here, we take the average value of the equilibrium rate and the actual rate of every year from 1987 to 2005. In Table 4, the fourth column is computed as [(Actual rate - Equilibrium rate)/Equilibrium rate] x 100 x (-1), and a positive sign refers to an overvaluation and a negative sign refers to an undervaluation.
Table 4
Year Equilibrium exchange rate Actual exchange rate % Deviations from equilibrium exchange rate
1987 0.544491 0.570776 -4.83
1988 0.610616 0.570776 6.52
1989 0.676607 0.570776 15.64
1990 0.688322 0.679512 1.28
1991 0.701927 0.726161 -3.45
1992 0.725864 0.741453 -2.15
1993 0.778762 0.760561 2.34
1994 0.863168 0.935426 -8.37
1995 0.924388 0.921763 0.28
1996 0.955495 0.919823 3.73
1997 0.966263 0.918546 4.94
1998 0.963067 0.917978 4.68
1999 0.957483 0.917934 4.13
2000 0.95816 0.917947 4.20
2001 0.959906 0.917882 4.38
2002 0.964426 0.917873 4.83
2003 0.96515 0.917873 4.90
2004 0.965545 0.917873 4.94
2005 0.965647 0.917873 4.95
According to Table 4, we know that since 1987 the Yuan has been undervalued four times. It is undervalued by 4.83% in 1987, 3.45% in 1991, 2.15% in 1992, and 8.37% in 1994, respectively. As for the other left period the Yuan is overvalued. Furthermore, it is interesting to observe that instead of the undervaluation by contraries it is an overvaluation of the Yuan in recent year. The degree of overvaluation is 3%~5% roughly in the period from 1996 to 2005.
According to the analysis result in section 2, honestly speaking, it is hardly to consider that the PPP Theory is an appropriate theory to the exchange rate of Yuan/dollar. Since the results are almost unrealistic.
3. AN ANALYSIS BASED ON THE BEHAVIORAL EQUILIBRIUM EXCHANGE RATE THEORY
3.1 The Theory of the Equilibrium Exchange Rate
Recent years, in order to appreciate the rationality of an exchange rate, the Equilibrium Exchange Rate Theory has been extensively used. However the definition of the equilibrium exchange rate is not unique. From the viewpoint of early stage, the equilibrium exchange rate is regarded as the real exchange rate when the PPP hold. However, at the reality, the structural change occurs in the real exchange frequently. In other words the equilibrium real exchange rate reacts to some economic fundamentals, such as terms of trade shocks, changes in the tax system, and technological progress, and so on. So we realize when researching the exchange rate of a developing country like China, it is not only have to consider the factor of price but also take the fundamentals of the economy into account.
In this section we estimate the equilibrium exchange rate based on the Behavioral Equilibrium Exchange Rate (BEER) model which developed by
Clark and MacDonald (1998).In this approach, the relevant notion of equilibrium is not derived from macroeconomic balance; rather it is determined by an appropriate set of explanatory variables. The actual real exchange rate is said to be in equilibrium in a behavioral sense when its movements reflect changes in the economic fundamentals that are found to be related to the actual real exchange rate in a well-defined statistical manner. The systematic relationship between the actual real exchange rate and its fundamental determinants can be estimated directly.
3.2 The BEER model for the Yuan
Since the core of the BEER model is a behavioral model, and the behavioral model can be derived from various exchange rate model. Here we follow the method of Clark and MacDonald (1998), and construct our model based on the familiar risk-adjusted interest parity condition:
Et [Ast+*] = i, - i, *. (10)
Where st is the logarithm of the nominal exchange rate. it and it * is the nominal interest rate of domestic and foreign country. Et is the conditional expectations operator, t + k defines the maturity horizon of the bonds. Equation (10) can be converted into a real relationship by subtraction the expected inflation differential, Et [Apt+* -Apt+* *], from the exchange rate and interest differential. After rearrangement equation (10) we have:
q, = E, [q,+t ] + (rt- r *)t. (11)
Where rt = it - Et (Apt+t) is the ex ante real interest rate, qt = S - Et [APt+*]
is the ex ante real exchange rate. Equation (11) describes the current equilib-
rium exchange rate as being determined by two components: the expectation of the real exchange rate in period t + k, the real interest differential with a maturity t + k.
The unobservable expectation of the exchange rate Et [qt+* ] is determined solely by the long-run economic fundamentals. We denote unobservable expectation of the exchange rate as € In order to make a different with €, we denote the current long-run equilibrium exchange rate as q *. So instead of equation (11), we have:
q* = € + (rt - rt *). (12)
From equation (12), we can conclude that the current equilibrium exchange rate is made up by two part: one is the economic fundamentals expressed by <€, and the other one is the difference of the real interest of domestic and foreign country. In our analysis we will not take the interest rate factor into account for the interest rate isn't liberalized in China. So we consider that it isn't suitable to adopt the interest rate as the variable which influent the equilibrium exchange rate.
In equation (12), the current equilibrium exchange rate is influenced by the sole factor: the economic fundamentals with the expression of <£. Further-
more we assume that q = Et[qt+*] = Et[P'Ft] = p'Ft ,where Ft is the vector of fundamentals, and p is a vector of coefficients for the long-run fundamentals.
Next, in order to make this model operational, as a first step we assume that the long-run relationship delivered by theory is linear in logarithmic transformation of the variables. The BEER Theory can be expressed in a general form,
ln q* =pFtP, (13)
where q* is the equilibrium real exchange rate, Ftp is the vector of permanent values for economic fundamentals that are identified by theory, and p is a vector of coefficients for the long-run fundamentals. At a conceptual level, the task of estimating the equilibrium real exchange rate breaks into two pieces. The first is to estimate the vector ofp ; the second is to choose a set of permanent values for the fundamentals.
The estimation of p requires the specification of an empirical model which is consistent with equation (13) but relates observable variables since the equilibrium real exchange rate is not observable, is specified. This relationship can be captured in a cointegration equation of the form
ln qt =pFtP + Ml, (14)
where nt is a stationary random variable with zero mean. Then, our task is to determine whether there is a cointegration relationship exists. If so the cointegration parameters can be used to estimate the parameter vector p in equation (14) and the equilibrium real exchange rate can be derived.
3.3 Data Sources and Definitions
Estimation of the BEER model is dependent on theoretical guidance for the choice of an appropriate set of economic fundamentals. In a recent study, Montiel (1999b) develops a model that synthesizes previous models of the
equilibrium real exchange rate. Following Montiel’s theory and considering
the practice of China and data availability, we specify the model as using the following fundamentals:
BEER = (TOT, OPEN, FDI, FCR, GCON, FINVEST). (15)
Where TOT is the terms of trade which is denoted the ratio of export price index to import price index. OPEN is the degree of economic openness. The variable OPEN is the national degree of opening measured as the ratio of the sum of imports plus exports to GDP in domestic currency. FDI is the foreign directly investment flows into China. In the model of Clark and MacDonald (1998), they adopt the net foreign assets as the fundamental variable. However, if run our eye down the balance of payments of China in recent years, we discover that FDI is the most important influence element of the net foreign assets, so we consider the FDI is an important fundamental of the equilibrium exchange rate. FCR is the foreign currency reserves. Until 2005, the foreign currency reserve of China exceeds 700 billion dollars. So we also regard the foreign currency reserves as very important factor to the equilibrium exchange rate. In our analysis, FDI and FCR are expressed as a ratio to GDP.
GCON is the government consumption. FINVEST is the gross fixed capital formation, which can be viewed as a proxy for technological progress.
Since the equilibrium exchange rate can not be observed in the reality, so we have to choose a proxy variable for it. Here we use the real effective exchange rates (REER) of China which is calculated by IMF. The REER is defined as the ratio that a Chinese price to the trade dealing country’s price which was weighted average the trade value. When we use the REER from IMF, one thing have to explain here. The real exchange rate which defined by IMF is expressed as RER = P/EP * . Comparing with equation (1), we can find the numerator and denominator is reverse in right-hand-side. Hence, When the real exchange rate is defined as the domestic relative price of tradable goods to non-tradable goods, in accordance with the definition of the IMF, It can be written as: RER = PN /PT. So according to the definition of IMF a decline in the REER denotes depreciation, while an increase in the REER indicates appreciation. In the end, we take the logarithm of all variables.
Our sample is from 1980 to 2002 and all the data are annual. Almost of the data is taken from United Nations Conference on Trade and Development (UNCTAD), China Statistical Yearbook and International Financial Statistics Yearbook published by IMF.
3.4 The unit root test and cointegration analysis
According to the BEER Theory, once the fundamentals are identified the cointegration relationship between the real effect exchange rate and these long-run fundamental determinants can be estimated directly
We apply the similar method as well as the previous section, firstly we apply the ADF and P-P unit root test to test the stationary of all variables.
Table 5 shows the results of unit roots test.
Table 5
Variables Test specification ADF test statistics P-value PP test statistics P-value
REER (C,T) -1.02931 0.94004 -1.27561 0.98478
Д REER (0,0) -1.75815* 0.07473 -9.40022** 0.033617
TOT (0,0) -0.65230 0.43269 -0.031535 0.68120
Д TOT (0,0) -2.51744*** 0.01100 -22.20111*** 0.00098
OPEN (C,0) -1.13740 0.69993 -2.04209 0.77516
Д OPEN (0,0) -2.79558*** 0.00500 -17.652 *** 0.00333
FDI (C,T) -1.52641 0.81990 -2.72594 0.94764
Д FDI (0,0) -2.09259** 0.03490 -8.27870** 0.04657
FCR (C,T) -2.87957 0.16925 -8.91402 0.51327
Д FCR (0,0) -3.50584*** 0.00047 -13.21991*** 0.01136
GEXP (C,0) -1.57823 0.49452 -4.39545 0.49480
Д GEXP (0,0) -2.75641*** 0.00570 -10.81978** 0.022371
FINVEST (C,0) -2.05608 0.26254 -3.17998 0.63540
Д FINVEST (0,0) -3.37058*** 0.00077 -16.49454*** 0.00459
Note. C and T denote the constant and trend in unit root test.
* Denotes rejection at the 10% significance level.
** Denotes rejection at the 5% significance level.
*** Denotes rejection of the null hypothesis at the 1% significance level.
The result of unit root test indicates that all of the variables are found to be I(1), where I(1) denotes integrated of order one. Since all the variables are found to be integrated of the same order, the Johansen’s cointegration test is applied to test the cointegration relationship between the real effect exchange rate and the economic fundamentals. Table 6 reports the result.
Table 6
Null Alternative Âjrace P-value
Test for cointegration of REER, TOT, OPEN, FDI, FCR, GCON, FINVEST
H0:r=0 H1: r=1 149.79663* 0.0062077
H0:r<=1 H1: r=2 92.35226 0.25103
* Denotes rejection of the null hypothesis at the 1% significance level.
The result shows that there is a cointegration relationship exists. Since Johansen’s cointegration test provides the estimates of all possible coingetra-tion vectors, the following cointegration equation with constant and trend term is derived:
LREER = 2.14243 + 0.04288TOT - 0.74857LOPEN - 0.17LFDI +
+ 0.149LFCR + 0.4LGCON + 0.71LFINVEST - 0.0013775 Trend. (16)
From equation (16), we can observe that the openness and the gross fixed capital formation give a relatively great influence to the REER, and the impact from the terms of trade is thought to be small. The variables of TOT, FCR, FINVEST, GCON have a positive sign suggests that the increase of these variables will cause the real effective exchange rate to appreciate. The negative sign of OPEN variable suggests that a more liberalized and open economy will cause the real effective exchange rate to depreciate. The negative sign of FDI suggests that the increase of the foreign directly investment flows into China will also cause the real effective exchange rate to depreciate. Then we can rewrite the equation (15) as:
BEER = (TOT, OPEN , FDI, fCr , GCON , FInVeST ). (17)
3.5 The misalignment of the real effective exchange rate of the Yuan
Basing on the cointegration equation (16), we can capture a steady-state relationship between actual values of the real effect exchange rate and economic fundamentals. The estimated cointegration equation can be used to approximate the equilibrium real exchange rate and to gauge the misalignment. The movements of the actual and the equilibrium real exchange rate in China from 1980 to 2002 are graphed in Figure 3.
In figure 3, if the actual real effective exchange rate below the equilibrium exchange rate, we consider it indicates an undervaluation and if the actual real effective exchange rate exceeds the equilibrium exchange rate, we define it as an overvaluation.
Figure 3
Moreover, in order to identify the degree of misalignment, as the same way in section 2, we compute the level of undervaluation and overvaluation and present the results in Table 7.
Table 7
Year Equilibrium exchange rate based on BEER Actual REER % Deviations from BEER *
1980 2.46747 2.46234 -0.2
1981 2.36030 2.40973 2.1
1982 2.41726 2.38971 -1.1
1983 2.42196 2.38231 -1.6
1984 2.33639 2.33243 -0.2
1985 2.13747 2.26115 5.8
1986 2.09256 2.12338 1.5
1987 2.08643 2.06382 -1.1
1988 2.05065 1.98435 -3.2
1989 2.04041 2.04637 0.3
1990 2.03908 1.99538 -2.1
1991 2.04001 1.94325 -4.7
1992 1.98070 1.89708 -4.2
1993 1.96800 1.84394 -6.3
1994 1.88399 1.88024 -0.2
1995 1.90228 1.92722 1.3
1996 1.95309 1.96734 0.7
1997 1.96533 1.99492 1.5
1998 2.01495 2.00352 -0.6
1999 2.03895 1.98904 -2.4
2000 2.00757 2.00000 -0.4
2001 2.03776 2.01837 -1.0
2002 2.03300 2.01132 -1.1
* Computed as (Actual rate/Equilibrium rate - 1)*100*(-1). A positive sign refers to an overvaluation and a negative sign refers to an undervaluation.
According to figure 3 and table 7, we can find that the Yuan experienced both overvaluation and undervaluation from 1980 to 2002, and since 1998, the real effective exchange rate of Yuan is trend to be undervalued. Moreover, we fail to observe that the actual REER deviate from its equilibrium level greatly in the long-run.
Furthermore, according to Table 7, we can observe the real effective exchange rate of Yuan is close to the equilibrium level from 1980 to 1984. The result of this can be thought that after 1979, the pattern changed as economic reform was launched in China, and the actual REER fluctuated closely around its equilibrium level in the initial years. We also find the real effective exchange rate of Yuan is also close to the equilibrium level in 1994. This is associated with the foreign exchange system reform of China in 1994. Thus, the exchange rate in 1994 can reflect the supply and demand of the market, and close to the equilibrium exchange rate.
Since 1980, the Yuan has been undervalued in two major periods. The first devaluation took place during the period of 1988~1993. The Yuan was undervalued by 3.2% in 1988, 2.1% in 1990, 4.7% in 1991, 4.2% in 1992, and 6.3% in 1993, respectively. This is primarily because that the foreign exchange swap market is expanded in 1988. This factor leads to the rapid depreciation of actual REER of Yuan from 182.451 in 1985 to 96.46 in 1988. However, during the same period the equilibrium rate does not depreciate significantly. The second undervaluation took place during the period of 1998~2002 as a result of the minor deflation occur in China during 1998~2002. The price of domestic non-trade goods decline and the real effective exchange rate of Yuan is trend to depreciate.
The first overvaluation occurred during the period of 1985~1986. The Yuan was overvalued by about 5.8% in 1985, and 1.5% in 1986. This can be attributed primarily to the fact that the openness of China is improved from 7% to 13.8% in this period. Since we know a more liberalized and open economy will cause the real effective exchange rate to depreciate. The second overvaluation occurred during the period of 1995~1997, Therefore, the Yuan slightly overvalued in 1996 and then more overvalued to 1.5% in 1997. The overvaluation in 1997 was associated with the Asian financial crisis, which resulted in an appreciation of the actual real effective change rate of Yuan.
4. CONCLUSION
This paper has done an empirical analysis of the exchange rate of Chinese Yuan, based on the Purchasing Power Parity Theory and the Behavioral Equilibrium Exchange Rate Theory. According to the analysis we obtained some major conclusion below.
It is hardly to believe that the Purchasing Power Parity Theory is an appropriate theory to analyze the exchange rate of Yuan/dollar. In section 2, we adopted three versions of the PPP model to estimate the equilibrium exchange rate of Yuan. However the results indicated that either the univariate PPP or the bivariate PPP is not appropriate to the exchange rate of Yuan/dollar. In the end we demonstrated that the trivariate PPP Theory does hold for the real exchange rate of Yuan/dollar, after comparing the actual exchange rate with the equilibrium exchange rate which derived from the cointegration equation, we find the Yuan was overvalued by roughly 3%~5% in the period from 1996 to 2005.
Moreover, we realize that in researching the exchange rate of a developing country like China, it is not only have to consider the factor of price but also have to take the fundamentals of the economy into account. In section 2, we constructed a behavioral equilibrium exchange rate model for the Yuan and estimate the equilibrium real effective exchange rate based on the BEER model. According to the analysis, we find the actual real effective exchange rate of Yuan is very close to its equilibrium level in the long-run. Although the misalignment exists, the magnitude is not extremely serious. Furthermore we observe that either the period of the undervaluation or the overvaluation is thought to be coincided with the actual behavior of the economy.
APPENDIX
We redefine the domestic price P and foreign price P* as:
P = P^x P^-a, (A-l)
P* = P/x p;m) , (A-2)
where a - the weight of domestic non-tradable goods, l-a - the weight of domestic tradable goods, PT - the price of domestic tradable goods, PN - the price of domestic non-tradable goods, ( - the weight of foreign non-tradable goods, 1-( - the weight of foreign tradable goods, P* - the price of foreign tradable goods, p* - the price of foreign non-tradable goods.
We substitute equation (1) by equation(A-l) and (A-2), then we have:
RER = e„ = EP*( x P*(i-p) / P^ x Pl;a . (A-3)
Assuming that the country in question is small, and the law of one price holds for tradable goods, we have:
E = PT / P*. (A-4)
Furthermore, we assume that the weight of the tradable goods and nontradable goods are similar in foreign and domestic country which expressed as a = ( = w, then after substituting (A-3) by (A-5) using (3-4) we have:
RER = e,„ =
P / P
■L T 1 1 Af
P / P
_ T ' N
This equation is similar to equation (2).
(A-5)
w
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© ryo 3®hh, Mhhmoto Ka^xnpo, 2006 r.
