Exchange rate dynamics in a Taylor rule framework

J. Int. Financ. Markets Inst. Money xxx (2016) xxx–xxx

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Journal of International Financial Markets, Institutions & Money j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i n t fi n

Exchange rate dynamics in a Taylor rule framework q Chuanglian Chen a,b, Shujie Yao c,d,e,⇑, Jinghua Ou c a

School of Economics and Management, South China Normal University, China China Merchants Group and The Institute of Industrial Economics, Chinese Academy of Social Sciences, China School of Economics and Business Administration, Chongqing University, China d University of Nottingham, UK e Fudan University, China b c

a r t i c l e

i n f o

Article history: Received 20 November 2014 Accepted 20 July 2016 Available online xxxx JEL classification: F830 F822 F820 Keywords: Capital control Foreign exchange intervention Taylor rule China Japan US and UK

a b s t r a c t This paper establishes a dynamic exchange rate determination model incorporating capital control and foreign exchange intervention in a Taylor rule framework. It uses the SVAR model to identify the sources of real exchange rate dynamics for three pairs of currencies: RMB/USD, Yen/USD and GBP/USD. It shows that demand shock, instead of supply shock, plays a dominant role in real exchange determination. Monetary policy has little effect but central bank intervention plays a role in keeping exchange rate persistence for RMB/ USD and Yen/USD. Risk premium shock is almost irrelevant to exchange rate dynamics for Yen/USD and GBP/USD. In the case of China, capital control plays a critical role in exchange rate determination. The results show that social welfare losses of China is the largest, suggesting that capital account liberalization would benefit the country in the long term. Therefore, the central bank of China should gradually open up the capital account, give up the fixed exchange rate or the managed floating exchange rate regime, and reduce central bank intervention to improve the effectiveness of monetary policy and social welfare. Ó 2016 Published by Elsevier B.V.

1. Introduction Exchange rate, monetary policy and inflation are three key economic variables concerned by the central bank in any country. Their relationship is an important issue for economic research. Most studies indicate that exchange rate is an important channel for transmitting monetary policy, affecting interest rate and inflation expectation through the uncovered interest rate parity (UIP) condition of international capital flow. However, there is also a long-term debate on whether monetary policy in exchange rate transmission is effective and whether a stable exchange rate should be considered as a goal of monetary policy. The traditional Taylor rule describes the implementation of monetary policy in a closed economy. Since the world financial crisis starting from the US in 2008, the monetary authorities in most countries have focused their efforts on maintaining q This research is generously supported by the following Grants in China: National Nature Science Foundation (71303081), Postdoctoral Science Foundation (2013M540669), Ministry of Education (12YJC790006), National Social Science Foundation (12BJL057), National Statistics Research Project (2013LY084), Guangdong Soft Sciences Research Project (2014A070704011; 2016A070705046), South China Normal University Policy Project of Philosophy and Social Sciences (JCYJ1507). ⇑ Corresponding author at: School of Economics and Business Administration, Chongqing University, China. E-mail addresses: [email protected] (C. Chen), [email protected] (S. Yao), [email protected] (J. Ou).

http://dx.doi.org/10.1016/j.intfin.2016.07.008 1042-4431/Ó 2016 Published by Elsevier B.V.

Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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financial market stability. More and more central banks recognize and take asset prices or exchange rate stability as main targets for monetary policy in an open economy, which can be seen as a new Taylor-type rule. In the past, the traditional monetary model attempts to explain the effects of monetary factors on the determination and expectation of exchange rate dynamics based on the law of one price and the purchasing power parity (PPP) theory, which are regarded as two identity conditions. Due to the choice of the exchange rate system, trade cost, tariffs and non-perfect capital flow, the PPP theory cannot be held and the traditional monetary model failed to be supported by empirical data (Baillie and Selover, 1987; Flood and Rose, 1995). Bacchetta and van Wincoop (2006), Engel et al. (2007) show that the traditional monetary model of exchange rate determination pays little attention to future market expectation of macroeconomic fundamentals. Thus it is important to build an exchange rate determination model introducing the endogeneity of monetary policy. Kempa and Wilde (2011) show that including monetary policy in exchange rate determination may lead to significant different conclusions in the endogeneity of exchange rate target of Taylor’s rule. In the standard flexible price monetary model, a price rise would lead to exchange rate depreciation, while in a Taylor rule model, a price rise would result in exchange rate appreciation due to the future expectation of tight monetary policy (Clarida and Waldman, 2008). The Taylor rule model has been widely used and recognized. Engel and West (2006) introduce Taylor’s rule into the monetary model to investigate the behavior of exchange rate between deutschemark-dollar in 1978–2001. Following this approach, Beckmanna and Wildeb (2013) build a Taylor rule exchange rate model where exchange rate is determined by the fundamentals. Using an exponential smooth transition regressive model, they show that deutschemark-dollar real exchange rates adjust much faster to their equilibria. Mark (2009) examines Taylor rule fundamentals for real exchange rate determination. His results support that a simple learning model provides plausible understanding of the real deutschemarkdollar exchange rate dynamics in 1973–2005. Recently, Froyen and Guender (2016) support that weight on real exchange rate stability in the loss function of the central bank is sufficient to improve the performance of Taylor-type rules relative to optimal policies, and Taylor rule fundamentals can account for several empirical exchange rate puzzles, including the apparent disconnect from fundamentals (Lansing and Ma, 2015). Engel et al. (2007) and Wilde (2012) use a similar method to make an out-of-sample forecast of real exchange rates. They show that the Taylor rule model has better performance in the expectation of exchange rate determination. Their finding is supported by Molodtsova and Papell (2009). Wang and Wu (2012) use the semi-parametric interval prediction method to study the exchange rate dynamics of twelve OECD countries. The estimated results showed that the Taylor rule model is significantly better in the expectation of exchange rate dynamics than the random walk model, the traditional monetary model or the PPP model. Furthermore, Galimberti and Moura (2013) construct a Taylor rule model to demonstrate the relationship between exchange rate determination and endogenous monetary policy. They use panel data regression to fifteen emerging economies and show that a present-value forward-looking specification has better exchange rate predictability. Ince et al. (2015) use data in 1973–2014 to evaluate the short-run out-of-sample predictability for the exchange rates of eight different currencies against the US dollar. They find strong evidence in favor of the Taylor rule model compared to the random walk model. Wu et al. (2015) conduct an in-sample fitting and out-of-sample prediction of exchange rates applying the forwardlooking, backward-looking and within-quarters non-linear Taylor rule, and find that both the implementation effect and the prediction ability of monetary policies improve. Wang et al. (2016) also use out-of-sample forecasting to show that the Taylor rule-based exchange rate model outperforms the conventional models and the random walk theories for Australia, Sweden, the UK and the USA. Most empirical studies impose a long-run constraint in BQ-SVAR, provided by Blanchard and Quah (1989), to investigate the source of exchange rate dynamics, such as Lastrapes (1992), Clarida and Gali (1994), Enders and Lee (1997). As to the advanced economies, Enders and Lee (1997), Hamori and Hamori (2011), Mirdala (2015), and Gehrke and Yao (2016) show that demand shocks explain much of the real exchange rate dynamics for the Japanese Yen and some European currencies against to the US dollar. Farrant and Peersman (2006), Yilmaz (2012), Huh and Kwon (2015), Grossmann et al. (2014), and Craighead and Tien (2015) show that a nominal shock accounts for much dynamics of the real exchange rates of the US dollar against the British Pound, the Euro, the Japanese Yen and the Canadian dollar by imposing some long run restrictions on a SVAR model. For the emerging economies, several studies show that the exchange rate is determined by real shocks for the Chinese, Indian and Pakistani currencies (Wang, 2005; Inoue and Hamori, 2009). Some studies show that exchange rate dynamics is determined by nominal shocks for the currencies of Poland, Hungary, Ghana and some Asian less developed countries (Dibooglu and Kutan, 2001; Kim and Lee, 2008; Asmah, 2013; Dumrongrittikula and Andersonb, 2016). For the developed countries or the emerging countries, there is no common consensus on the sources of exchange rate dynamics due to different models or different currencies. It is important to be stressed that there is a contradictory relationship among monetary policy, capital flow and a floating exchange rate system. According to Krugman’s trilemma theory, independence of monetary policy, stable exchange rate and free capital flow cannot be achieved at the same time. Monetary authorities can only choose two goals at any one time. In April 2012, China’s central bank relaxed the range of the RMB/USD spot exchange rate up to 1%. This range has been further relaxed up to 2% since March 2014. More importantly, the central bank decided to enhance the marketization of the RMB/ USD exchange rate through improving the intermediated exchange rate quotation system. In fact, the Chinese exchange rate regime experienced two big changes with several minor adjustments in 1985–2015. The two big changes can be considered as two different regimes, a currency peg against the US dollar from 1985 to June 2005 and a currency peg against a basket of currencies with secret weights from July 2005. According to the trilemma theory, the independence of China’s monetary polPlease cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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icy and the exchange rate formation mechanism would be improved under the condition that international capital can flow freely. Capital control is a temporary policy and China’s capital market is expected to be gradually open up in the future. Therefore, we choose three currencies against the US dollar (USD), the Chinese RMB (RMB), the Japanese Yen (Yen), and the British Pound (GBP) to examine how different policy sets may affect the exchange rates in China, Japan and the UK. In China, the policy set includes capital control, foreign exchange intervention and a managed floating exchange rate regime. In Japan, it includes managed capital flow, foreign exchange intervention and a managed floating exchange rate regime. The UK does not control capital flow and has a free floating exchange rate regime. It is relevant and important to make a study further about capital flow control on exchange rate dynamics, not just for China, but also for other countries. This is because China’s monetary policy and exchange policy have had three conflicts since 1994. The contradiction among currency reserves, foreign exchange reserves, domestic interest rate and inflation restricts the independence of monetary policy. If implementing a floating exchange rate system can effectively eliminate the conflict between monetary policy and exchange rate policy to improve the independence of the former, then we should focus more on the advantages of the floating exchange rate system. Therefore, testing the relationship between the managed floating exchange rate regime and the effectiveness of monetary policy is imperative, as it not only gives some insights for China’s progressive reform, but also provides some constructive ideas on how the capital account should be opened up. In order to find out the relationship among the exchange rate system, monetary policy and capital control, three main currencies, RMB, Yen and GBP are used against USD, to build a dynamic exchange rate determination model incorporating capital control and intervention with Taylor rule fundamentals. The BQ-SVAR model is used to identify the sources of exchange rate dynamics in 1985–2015. The results show that demand shock appears to be more important for exchange rate dynamics than supply shock, whereas monetary shock is irrelevant to real exchange rate dynamics for RMB/USD and Yen/ USD. Risk premium shock accounts for less than 10% of exchange rate persistence for Yen/USD and GBP/USD, but it accounts for 16% of the real RMB exchange rate dynamics, meaning that capital control and central bank intervention play an important role in RMB’s exchange rate dynamics. In conclusion, the central bank of China should gradually open up the capital account, give up the fixed exchange rate and the managed floating exchange rate regime, and reduce central bank intervention if the central bank wishes to improve the effectiveness of monetary policy and social welfare. The rest of this paper is organized as follows. Section 2 describes the theoretical model incorporating capital control and foreign exchange intervention with Taylor rule fundamentals. Section 3 presents the methodology and long-run conditions. Section 4 discusses the data. Section 5 reports and discusses the empirical results. Section 6 presents some policy simulations and discusses their implications on social welfare. Section 7 concludes. 2. The theoretical model We start with an open economy model of Taylor’s rule with capital control and foreign exchange intervention, and use it to analyze the sources of real exchange rate dynamics. Following Besancenot and Vranceanu (2003), we assume that the aggregate demand curve of output gap in an open economy is given in Eq. (1).1

IS curv e : yt ¼ /st  brt þ eyt

/ < 0; b > 0

ð1Þ

where yt is the output gap, st the log-form of real exchange rate, rt real interest rate which can be denoted as nominal interest rate minus inflation based on Fisher’s theorem, eyt supply shock. The new Keynesian–Phillips curve (NKPC) comes from the staggered price adjustment model. Choudhri and Hakura (2006) and McCarthy (2007) stress that domestic inflation is affected by exchange rate dynamics. Then, the NKPC is presented in Eq. (2). 2

NKPC :

pt ¼ bEt ptþ1 þ jyt  uDet j > 0; u > 0

ð2Þ

Many empirical studies have shown that the uncovered interest rate parity (UIP) condition is rather weak (McCallum, 1994; Lewis, 1995; Engel, 1996) as most economies implement capital regulation, hence UIP needs to be modified in Eq. (3). 3 f

Modified UIP : it  it ¼ sðEDetþ1 Þ þ eCt

ð3Þ

1 St ¼ Et P tf =P t , whose log-form is st ¼ et þ ptf  pt . St is real exchange rate, Et nominal exchange rate, Ptf and Pt respectively foreign and domestic inflation rates, et log-form of nominal exchange rate under direct quotation. / < 0 denotes output increase (decrease) if exchange rate depreciates (appreciates). According to the Keynesian theory, a rise of interest rate will reduce investment and output, or vice versa, so b > 0. 2 The looking-forward NKPC is pt ¼ bEt ptþ1 þ kmct , where b is a subjective discount factor, k denotes the influence of marginal cost (mct ) on inflation p. Galí and Monacelli (2005) show a linear relationship between marginal cost and output gap mct ¼ ðra þ dÞyt . Therefore, j ¼ kðra þ dÞ, and j > 0 denotes that domestic inflation will increase (decrease) if the output gap is positive (negative). u > 0 shows that exchange rate appreciation (depreciation) would lead to a rise (decrease) in domestic inflation. 3 EDet > 0 denotes exchange rate depreciation expectation, EDet < 0 means the opposite. In the perfect control case, UIP can be written as it  itf ¼ eCt , meaning that interest rate is only related to the risk premium and has nothing to do with exchange rate.

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where it and it are respectively domestic and foreign nominal interest rates, s is tax rate on capital flow, measuring the degree of capital control. s ¼ 1 means no control at all, s ¼ 0 means perfect control. eCt is time varying risk premium shock denoting risk compensation to the expectation of exchange rate variation. Following Olivo (2003) and considering the managed floating exchange rate regime, we assume that the change in exchange rate expectation depends on the change in exchange rate and central bank intervention in Eq. (4).

EDetþ1 ¼ et  et1 þ cf t þ eIt

ð4Þ

where f t is a foreign exchange market intervention index, eIt a monetary authority intervention shock. If c = 0, the model degenerates into a free floating exchange rate regime without government intervention. Substituting (4) into (3), and using Fisher’s theorem yields Eq. (5). f

it  it ¼ sðst  st1 Þ þ csf t þ sðpt  ptf Þ þ seIt þ eCt

ð5Þ

The expectation of exchange rate appreciation (depreciation) leads to a larger (smaller) spread of interest rate and foreign capital inflows (outflows), and finally resulting in foreign exchange supply more (less) than demand and real exchange rate appreciation (depreciation). The range of exchange rate appreciation and depreciation depends on the degree of capital control. The Fisher effect indicates that a higher interest rate will lead to higher inflation and domestic currency depreciation. To analyze the transmission mechanism of monetary policy on exchange rate fluctuations, we need to define the objective loss function of monetary policy. The loss minimization function is defined over the output gap variance and the inflation variance in Eq. (6).

L ¼ Min Et

1 h X

ay2tþi þ ðptþi  p Þ2

i

ð6Þ

i¼0

where a is the preference of monetary policy with respect to central bank’s ultimate goal, keeping inflation stable around its target p and output around its potential level. a ¼ 0 means that monetary authorities prefer to restrict inflation target. Using Eqs. (1), (2) and (5), minimizing L in Eq. (6) with respect to it leads to, 4

it  it ¼ r t þ Et ptþ1 þ qyt þ hðpt  p Þ þ #st1 þ tcf t þ eMt f

ð7Þ

Eq. (7) denotes the modified Taylor rule of monetary policy. In the traditional Taylor rule, interest rate only reacts to the output gap and inflation target. However, in an open economy, Taylor’s rule cannot combine all of the core variables of monetary policy. Therefore, neglecting the exchange rate target cannot describe the rule of monetary policy. Whereas, in our model, besides the output gap and inflation target, interest rate not only reacts to the lagged exchange rate variable, but also is affected by central bank’s intervention in the foreign exchange market. Furthermore, the reaction of interest rate to inflation and output gap depends on the signs of q and h. If q and h are positive, there would be a cyclical adjustment of interest rate in response to inflation and output. If q and h are negative, there would be a countercyclical adjustment. The implication of Taylor’s rule is that only if real interest rate equals the long term equilibrium interest rate and real output equals the potential output, the whole economy would keep on developing steadily and sustainably. To characterize the dynamic system of real exchange rate and inflation, we first construct and derive the following two equations. Combining Eqs. (1), (5) and (7) yields the dynamics of difference for real exchange rate in Eq. (8).

Dst ¼ ½h  sð1 þ qbÞk1 ðpt  p Þ þ sk1 ð1 þ qbÞðptf  p Þ þ ð# þ q/Þk1 st1 þ ½tc  csð1 þ qbÞk1 f t þ ½k1rt  k1 ð1 þ qbÞr tf  þ k1 eMt þ qk1 eyt  sk1 ð1 þ qbÞeIt  k1 ð1 þ qbÞeCt

ð8Þ

1

where k1 ¼ ½sð1 þ qbÞ  q/ . While substituting equations (1) and (2) into (7) and using (8) yields the dynamics of difference for inflation in Eq. (9).

Dpt ¼ ½k1 l2 ðh  s  sqbÞ  hl1 l3 ðpt  p Þ þ sk1 l2 l3 ð1 þ qbÞðptf  p Þ  ½q/l1  j/ þ #l1  ð# þ q/Þk1 l2 l3 st1 n o þ ½ðtc  cs  csqbÞk1 l2  tcl1 l3 f t þ ½k1r t  k1 ð1 þ qbÞr tf l2  l1r t þ bEt ptþ1  pt1 l3  ðl1  k1 l2 Þl3 eMt þ ðqk1 l2  ql1 þ jÞl3 eyt  sk1 l2 ð1 þ qbÞl3 eIt  k1 l2 ð1 þ qbÞl3 eCt

ð9Þ

  Using Fisher’s theorem and then combine Eqs. (1) and (5), it yields yt ¼ /s  b it þ /et1  /s itf  /cf t þ ðb  /Þpt þ/ptf  /s ect þ eyt  /eIt . Substituting Eq. f 1 1 (5) to Eq. (2) yields pt ¼ bEt ptþ1 þ jyt  u½s ðit  it Þ  cf t  s eCt  eIt . Substituting the above two equations into the loss function, and minimizing L in Eq. (6)   1     2   2 , q ¼ jus r, with respect to it yields Eq. (7). Where r t ¼ abr /s  b itf þ h  usr p þ #pt1  ar /s  b /ptf , the parameters satisfy bus r ¼ 1, r ¼ a /s  b þ us2   2 # ¼ a/rðb  /s Þ, h ¼ arðb  /s Þðb  /Þ, t ¼ a/r /s  b  us r, denotes the long term equilibrium of real interest rate. eMt is a monetary policy shock, defined as h   i    h i 2 1 þ abr /s  b þ ect  ar /s  b eyt þ /s  b a/ þ us reIt . 4

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1

where l1 ¼ jbð1 þ qbÞ , l2 ¼ j/  q/l1  u, l3 ¼ ðu þ 1Þ1 . Setting Dst ¼ 0 and Dpt ¼ 0 in Eqs. (8) and (9), and combining the two simultaneous equations, we can make the following propositions. Proposition 1. In the managed floating exchange rate regime with capital control, monetary shock, such as the Taylor rule shock, there is only a short term effect on real exchange rate fluctuations. Proposition 2. In the managed floating exchange rate regime with capital control, both supply and demand shocks have a short term and a long term effect on real exchange rate fluctuations. A one unit negative supply shock or a one unit positive demand shock would lead to real exchange rate depreciation by j1=/j units. Proposition 3. In the managed floating exchange rate regime with capital control, a risk premium shock has a short term and a long term effect on real exchange rate fluctuations. A one unit positive risk premium shock would lead to real exchange rate appreciation by jb=/j units. Proposition 4. In the managed floating exchange rate regime with capital control, a central bank intervention shock has a short term and a long term effect on real exchange rate fluctuations. A one unit positive intervention shock would lead to real exchange rate depreciation by jsb=/j units. 3. Research methodology Eqs. (8) and (9) can be seen as a dynamic economic system where there is a steady state path. Setting Ds ¼ 0 and Dp ¼ 0, a steady equilibrium, which is the steady-state of the system, can be derived. In this system, the impact of five different shocks on the endogenous variables can be expressed in Eq. (10).

2

 dy

6 6 df 6 6 dr 6 6 4 ds

dðp  p Þ

3

2

deS

7 6 7 6 deI 7 6 7 ¼ B6 deC 7 6 7 6 5 4 deD

3 7 7 7 7 7 7 5

ð10Þ

deM

t , where xt is real demand and y t real supply. Output can be decomposed into both The output gap is defined as yt ¼ xt  y demand and supply shocks. Following the above model, a supply shock is derived from relative output, an intervention shock is decomposed from a central bank intervention index and a risk premium shock, a demand shock and a monetary shock are respectively derived from the relative interest rate, real exchange rate and relative inflation. Following BQ-SVAR, we impose the identification restrictions of the B matrix on a reduced form SVAR model in t ; f t ; rt ; Dst ; pt  p Þ0 . 5 X t ¼ ðy Consider a p-order structural VAR model in Eq. (11).

X t ¼ C0 X t þ C1 X t1 þ C2 X t2 þ    þ Cp X tp þ nt

ð11Þ

where p is the lag order, Ci is a coefficient vector, nt denotes structural shocks. Eq. (11) can be rewritten as a vector moving average representation as in (14).

X t ¼ CðLÞut

ð12Þ

To recover the structural parameters, we estimate the reduced form of SVAR (13).

X t ¼ AðjÞet

ð13Þ

Relating (12) and (13), if there is a matrix Bð0Þ satisfying u ¼ Bð0Þe for any L (L = 0, 1, 2, . . .), then AðLÞ ¼ CðLÞBð0Þ strongly holds. We need to find Bð0Þ, and then decompose structural shocks et for each period from ut . Following BQ, to identify the model, we need twenty-five constricted conditions for the model including five endogenous variables. If X ¼ Bð0ÞBð0Þ0 , we can get fifteen constricted conditions. We also need to derive ten more long term constricted conditions. Based on (8), (9) and the above-mentioned four propositions, we can get the B matrix which is equal to the following long term constricted conditions (LTC) for RMB/USD. 6

5 6

Since in BQ-SVAR model, the series should be stationary, see the unit root test in Table 1. Appendix B gives the long term constricted conditions for Yen/USD and GBP/USD.

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2

1

0

6 1 60 6 6 s LTC ¼ 6 0 6 1 sb 6/ / 4 j/sð1þqbÞ #  ½l1 ð#þq/Þ h/ j/h

0

0

0

0

1

0

 /b

1 /

j/ð1þqbÞ #  ½l1 ð#þq/Þ  h/ j/h

0

3

7 0 7 7 1 7 7 7 0 7 5  1h

ð14Þ

In a stable economic system, a monetary shock has no long term effect on real interest rate and real exchange rate. A demand shock only has a short term effect, but no long term effect on real interest rate. Central bank intervention is only affected by the intervention shock. Following Blanchard and Quah (1989) and the LTC, we know that the dynamics of output only depend on the supply shock, but not on any other shock.

4. Data This paper uses quarterly data during 1985Q1-2015Q2 (122 observations) for China, Japan, the UK and the US, and five variables, including output growth rate, interest rate, exchange rate, inflation and foreign exchange intervention.7 We use real GDP (gross domestic product) growth to represent real output supply. Quarterly GDP data during 1992–2015 are available from the China Statistical Yearbook (NBS, various issues). Data in 1985–91 are available on an annual basis. We use the Chow-Lin series technology as discussed in Abeysinghe and Rajaguru (2004) to convert annual data into quarterly data. Quarterly nominal GDP growth rates for Japan, the UK and the US are derived from the International Monetary Fund (IMF). Then, we estimate the nominal value of the quarterly GDP, and use the Seats-Tramo method to make a seasonal adjustment of GDP data. Finally, we calculate the real GDP through yt ¼ 100  log GDP t . We also use the HP filter de-trended . method to estimate the output gap y In the US, the federal government regulates the interbank interest rate to influence the capital cost of commercial banks, and takes the federal fund rate as a preferred policy tool to regulate money supply and demand. Compared to other interest rate indexes, such as the repo rate and banks’ lending rate, interbank lending rate can well reflect the real cost of capital. We use the federal fund rate and the interbank lending rate as two instruments of monetary policy for the US. China’s interbank market was established in 1984, and has developed quickly since then. Despite some chaotic interbank lending activities between national financial institutions in 1993, the Shanghai interbank offered rate could well reflect the interbank lending market before 1996 when the national network was not connected. Interbank offered rates before 1996 are provided by the Shanghai Financial Center, while data during 1997–2015 are replaced by the seven days interbank lending rate. All the data are collected from Bank of China’s Quarterly Reports. The US and UK’s interest rates are measured by the seven days London interbank offered rate, and then calculated quarterly data by using the three-days moving average method. Japan’s nominal interest rate is substituted by the treasuries bill rate of government securities. Real interest rate is defined as the nominal interest rate minus inflation. Nominal interest rates of Japan, the UK and the US come from the IMF. We use the three-periods moving average method to calculate quarterly CPI from monthly data, all of which are collected from China Economic Reports and China Statistical Monthly Reports (NBS website). Quarterly CPI of the US is derived from the IMF. We use the HP filter de-trended method to estimate the inflation gap ðpt  p Þ. Inflation rates of Japan, the UK and the US come from the IMF. The bilateral real exchange rate (RER) is derived by S ¼ E  CPI =CPI, where S denotes bilateral nominal exchange rate, CPI is consumer price index (with 2010 as the base year) and CPI is CPI of the US (with 2010 as the base year). As China has not yet published quarterly CPI based on a fixed year, this paper uses the current quarterly CPI index and seasonally adjusted index to construct the quarterly CPI with 2010 as the base year. The three-periods moving average method is used to calculate quarterly CPI using monthly data. The quarterly CPI for other countries is derived from IMF. The nominal exchange rates of RMB/USD, Yen/USD and BGP/USD are also derived from IMF. Monetary authorities intervene the foreign exchange market through buying and selling foreign currencies. According to Weymark (1997), we define the foreign exchange intervention index as -t ¼ gDRt =ðDet þ gDRt Þ, where DRt is the change in foreign exchange reserves, g ¼ @ Det =@ DRt . We can see Det ¼ 0 when -t ¼ 1, indicating that policy authorities hold the exchange rate fixed. In contrast, -t ¼ 0 allows the exchange rate to float freely. The value of -t lies between 0 and 1. Monetary authorities intervene the foreign exchange market through removing excess demand for a currency using different policy instruments such as exchange rate control and foreign exchange reserves control. We can rewrite the intervention index as Det ¼ gDRt =-t  gDRt , where the first term on right hand side denotes the exchange rate change through foreign exchange market intervention, and the second term is the observed changes in the exchange rate relieved by foreign market pressure. Therefore, we set f t ¼ gDRt =-t to investigate the effect of foreign exchange intervention on exchange rate dynamics. Following Weymark (1997), Fiess and Shankar (2009), we set g equal to the standard deviation of exchange rate divided by the standard deviation of foreign exchange reserves (g ¼ rDe =rDR ), and then the foreign exchange rate intervention index 7 Appendix C plots the relative GDP and interest rates of China, Japan and the UK against those of the US, the relative inflation rates of China, Japan and the UK against the US and the foreign exchange intervention index of China and Japan.

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7

is -t ¼ ðDRt rDe =rDR Þ=ðDet þ DRt rDe =rDR Þ. Foreign exchange reserves data for China are collected from China’s Financial Yearbook and the Bank of China. While the foreign exchange reserves for other countries are collected from the IMF.

5. Empirical results Table 1 presents the estimated results of unit root test. The critical values for ADF and PP tests are given by MacKinnon (1996), while the unit root test using GLS de-trended data are given by Ng and Perron (2001). The traditional ADF and PP tests have low power when the root of the auto-regressive polynomial is less than unity and often suffer from severe size distortions. To overcome these defects, Ng and Perron (2001) provide a unit root test under GLS de-trending, where a constant term is included in the level equation but none in the first difference one in all of the tests. The lag order for the ADF test is selected by the SC criterion, bandwidth for the PP test is selected by Newey and West (1994), while the lag order for unit root test under GLS de-trending is selected by the modified Information Criteria (MIC). The results suggest that the null hypothesis of a unit root cannot be rejected at the 5% critical level. The results of Tradi, f, r and p  p are I(0), while s are I(1). tional Test and Test under GLS De-trending suggest that y The purpose of the co-integration test is to determine whether there is a linear co-integration relationship between two or more than two non-stationary time series, which represents a long-term equilibrium relationship. The test results in , f, r, p  p and Ds for China and Japan, Table 2 show that there exist five co-integration relationships among the variables y , r, p  p and Ds for the UK. Then we can use stationary series and four co-integration relationships among the variables y t ; f t ; rt ; Dst ; pt  p Þ0 to construct a SVAR model based on the theoretical model. ðy t ; f t ; r t ; Dst ; pt  p Þ0 , and conBased on the unit root test and Johansen’s co-integration test, we use five stationary series ðy struct ten long term constricted conditions in Eq. (14) to estimate Bð0Þ in the BQ-SVAR model for RMB/USD, while we also construct long term constricted conditions in Appendix B to estimate Bð0Þ for Yen/USD and GBP/USD. As the inverse of the matrix eigenvalues of the two orders lag operators are located inside the unit circle, it indicates that the estimated results of the SVAR model are stable. Finally, et ¼ Bð0Þ1 ut is used to derive five types of structural shocks. Fig. 1 displays the cumulative impulse responses of real exchange rate dynamics to one unit structural shock of five different kinds. As the empirical results show that the impact of one positive unit of supply shock, intervention shock, risk premium shock and demand shock on real exchange rate dynamics all have a long run effect and converge after 12 quarters, while a monetary shock only has a short term effect on real exchange rate dynamics, which supports proposition 1. 8 To confirm the dynamic effect of a monetary shock on exchange rate dynamics, we construct two curves Ds ¼ 0 (exchange rate change) and Dp ¼ 0 (interest rate change) in Fig. 2–5, based on the results of the theoretical model. As shown in Fig. 2 and Eq. (5), one unit of positive monetary shock leads to a rise in the nominal interest rate in the short run, resulting in nominal exchange rate depreciation as to the modified uncovered interest rate parity (UIP) condition, where the degree of depreciation depends on the level of capital control. The real exchange rate would depreciate due to the short term inflation rate remaining unchanged. Taking partial derivatives from Eq. (8), we can see that one unit of monetary shock would bring the Ds ¼ 0 cure downward to the right by 1=ð# þ q/Þ units, from point A to point B. However, a positive monetary shock would depress domestic inflation, and lead to real exchange rate appreciation in the long run. Finally, going back to the initial equilibrium point C, one unit of monetary shock would bring the Dp ¼ 0 curve downward to the left by ðl1  k1 l2 Þ=½q/l1  j/ þ #l1  ð# þ q/Þk1 l2  units. The cumulative impulse responses also show that one unit of demand shock leads to a permanent real exchange rate appreciation in both the long run and the short run, and after 12 quarters, RMB/USD, Yen/USD and GBP/USD would respectively appreciate by 0.626, 0.051 and 10.009 percent. The results are consistent with the IS-LM theory that the expansion of demand would make exchange rate appreciate. Meanwhile, one unit of supply shock leads to a modest real exchange rate appreciation, and after 12 quarters, RMB/USD would appreciate by 0.0401 percent, while Yen/USD and GBP/USD would respectively depreciate by 0.0017% and 2.049%. However, the effect of supply shock on real exchange rate is insignificant as shown by the cumulative impulse response function in the 90% confidence interval for Yen/USD and GBP/USD. The conclusions of a demand shock for the three currencies pairs and a supply shock for the Yen/USD and GBP/USD exchange rates support proposition 2. Fig. 3 (p = inflation, s = log of real exchange rate) shows that a positive demand shock or a negative supply shock would enlarge the output gap and raise the domestic price and inflation in the open commodity market. To keep the real money supply unchanged and maintain an equilibrium of the money market, the nominal money supply should be increased in the same growth ratio, causing the corresponding expansion of base currency and money supply through the multiplier effect (from point A to point C). Based on Eqs. (8) and (9), one unit of positive demand shock or one unit of negative supply shock would bring about real exchange rate depreciation by j1=/j units. The cumulative impulse responses also show that one unit of risk premium shock can lead to real exchange rate depreciation in the short run, and after 12 quarters, RMB/USD and GBP/USD would respectively depreciate by 0.264 and 8 Although endogenous variable responses to the shocks impose a long-term constraint, imposing a Taylor’s rule shock has no long term effect on the estimated results. This implies that the responses of endogenous variables to the shocks are consistent with the expected results of the theoretical model, supporting propositions 2-4.

Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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C. Chen et al. / J. Int. Financ. Markets Inst. Money xxx (2016) xxx–xxx

Table 1 Results of unit root test. Variables

Traditional test

 y f r

China

p  p s Ds  y f r

Japan

p  p s Ds  y r

UK

p  p s Ds 5% critical value for levels 5% critical value for 1st difference

Test under GLS de-trending

ADF

PP GLS

MZ GLS a

MZ GLS t

MSBGLS

MPGLS T

4.305*** 10.343*** 4.566*** 4.691*** 2.522 8.277***

4.762*** 10.360*** 4.575*** 11.577*** 2.526 8.285***

31.664*** 34.206*** 40.019*** 258.143*** 8.724 55.486***

3.979*** 4.127*** 4.473*** 11.361*** 1.986 5.266***

0.126*** 0.121*** 0.112*** 0.044*** 0.228 0.095***

2.880*** 2.712*** 2.278*** 0.353*** 10.823 0.445***

3.390* 4.825*** 3.361* 5.981*** 3.228* 4.783***

3.256* 8.481*** 2.657* 4.074*** 3.409* 8.935***

26.628*** 50.233*** 6.524* 22.294*** 7.287 53.664***

3.646*** 5.011*** 1.772* 3.314*** 1.796 5.174***

0.137*** 0.099*** 0.272* 0.149*** 0.247 0.096***

0.929*** 0.490*** 3.873* 1.185*** 12.719 0.472***

5.353*** 4.286*** 3.398* 3.760** 8.518*** 3.448 2.889

4.590*** 4.313*** 4.306*** 3.541** 9.142*** 3.447 2.890

9.012** 7.323* 3.317* 12.195 9.494** 17.300 8.100

2.114** 1.911* 1.722* 2.435 2.158** 2.910 1.980

0.235* 0.261* 0.273* 0.199 0.227** 0.168 0.233

2.752** 3.355* 4.067* 7.662 2.662** 5.480 3.170

, f, r, p  p , s respectively denote output gap, intervention index, real interest rate, inflation gap and real exchange rate against USD. D denotes the Notes: y 1st difference of variables. * Significant at 10%. ** Significant at 5%. *** Significant at 1%.

Table 2 Results of the Johansen co-integration test. Eigenvalue 0.4602 0.4003 0.2641 0.1953 0.0349

(0.4254) (0.2456) (0.2014) (0.1688) (0.0381)

H0 [0.4506] [0.1944] [0.1591] [0.0337]

r r r r r

¼0 61 62 63 64

H1 r r r r r

¼1 ¼2 ¼3 ¼4 ¼5

Trace statistic

5% critical value

183.974 (152.889) [121.739] 116.753 (86.936) [50.445] 61.010 (53.391) [24.710] 27.5718 (26.625) [4.089] 3.8759 (4.617)

69.818 (69.818) 47.856 (47.856) 29.797 (29.797) 15.495 (15.494) 3.841 (3.841)

Prob. [47.856] [29.797] [15.494] [ 3.841]

0.0000 0.0000 0.0000 0.0005 0.0490

(0.0000) [0.0000] (0.0000) [0.0001] (0.0000) [0.0016] (0.0007) [0.0431] (0.0317)

Notes: (1) The deterministic trend assumption of the test allows for an intercept and a trend. (2) The optimal VAR model is based on the BC Criterion. (3) Values without brackets, in brackets and in square brackets represent China, Japan and the UK, respectively. (4) MacKinnon–Haug-Michelis (1999) p-values.

0.922 percent. The results support that both risk premium and capital control play a critical role in exchange rate persistence. Fig. 4 shows that a risk premium shock causes nominal interest rate to rise. Since inflation keeps unchanged in the short run, real interest rate increases and real money demand declines. If nominal money supply remains unchanged, to maintain equilibrium in the money market, domestic price should be raised to reduce real money supply, leading to real exchange rate appreciation. Based on Eqs. (8) and (9), one unit of positive risk premium shock would cause real exchange rate depreciation by jb=/j units in the long run, supporting proposition 3. 9 One unit of intervention shock leads to real exchange rate deprecation in both the short and long runs, and after 12 quarters, RMB/USD and Yen/USD would respectively depreciate by 0.724 and 0.049 percent, and both are significant at the 90% confidence level. The results support that intervention is an effective instrument for the central bank to keep exchange rate persistent. Fig. 5 shows that current account surplus raises the level of foreign exchange reserves and domestic currency appreciation pressure. Monetary authorities would intervene to stabilize the exchange rate through purchasing and selling foreign currencies, leading to base money expansion, domestic inflation and real exchange rate depreciation. Based on Eqs. (8) and (9), one unit of positive intervention shock would bring about real exchange rate depreciation by jsb=/j units in the long run, supporting proposition 4. Now we use a more formal statistical assessment method to decompose the variance of real exchange rate volatilities. Notice that the estimated results are also based on BQ-SVAR (Table 3).

9 The effect of risk premium on real exchange rate is insignificant as shown by the cumulative impulse response function in the 90% confidence for RMB/USD and BGP/USD.

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9

Fig. 1. Cumulative impulse response function of real exchange rate. The solid line is the cumulative impulse response function, and the dotted line is the cumulative impulse response of the 90% confidence interval using 10,000 bootstrap simulations.

π

π=0 B

A

Δπ’=0

Δs=0

C

Δs’=0 s Fig. 2. Monetary shock.

The relative contribution of a demand shock to real exchange rate dynamics is 22, 65 and 79 percent respectively for RMB/USD, Yen/USD and GBP/USD at a 20 quarters horizon. Supply shock is almost irrelevant to real exchange rate dynamics, which explains 1–4% of its variations in the long run. The results show that demand shock appears to be important for exchange rate dynamics, which is consistent with the cumulative impulse responses and those found in Enders and Lee (1997). Intervention shock explains respectively 53% and 14% of the variations in RMB/USD and Yen/USD, indicating that central bank intervention is one important policy instrument to maintain exchange persistence. Monetary shock explains 27–68% of the inflation dynamics at the 20 quarters horizon for China and Japan, indicating that targeting inflation of interest rate policy is effective. Monetary shock explains 16–19% of interest rate dynamics for China and Japan, showing that the transmission of monetary policy is effective. Combined with the previous analysis, we can conclude that although monetary shock increases interest rate and depreciates real exchange rate through the modified uncovered interest rate parity (UIP) in the short run, domestic inflation would decline to make real exchange rate appreciate slowly in the long run, and finally return to the initial equilibrium point. The results show that monetary shock is almost irrelevant to real exchange rate dynamics for RMB/USD and Yen/USD. Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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Δπ’=0

π

Δπ=0

C

A

B

Δs=0

s

Δs’=0 Fig. 3. Demand and supply shocks.

π C

A

Δπ=0

B

Δs’=0

Δs=0 s Fig. 4. Risk premium shock.

However, monetary shock explains 16% of real exchange rate dynamics for GBP/USD. One possible reason is that although monetary shock accounts for 51% of inflation dynamics, it explains only 9% of interest rate dynamics in the UK, indicating that monetary policy has no significant effect on inflation. Monetary shock depreciates exchange rate in the short run, while domestic inflation would not decline simultaneously, causing monetary policy to have a significant effect on real exchange rate dynamics for GBP/USD. This may be due to the fact that the UK allows free capital flow and adopts a free floating exchange rate regime without foreign exchange intervention. Risk premium, caused by capital control, explains 16 percent of the real exchange rate dynamics for RMB/USD, but less than 10% for Yen/USD and GBP/USD. Since China imposes capital control, Japan and the UK allow free capital flow (Fig. 6), the results imply that capital control plays an important role in exchange rate dynamics. The exogeneity of monetary policy and the huge effect of capital control on real exchange rate indicate that the adjustment of interest rate has no significant effect on exchange rate determination. Because many developed countries implement a free floating exchange rate system, such as the US, the UK and Japan, the exchange rate is an endogenous variable of interest rate. Exchange rate affects more on interest rate through output and inflation. The Chinese government has promulgated a series of policies to liberalize the foreign exchange and interest rate markets in recent years, including reform of the exchange rate system from 1994, the connection of the interbank funding market network from 1996, and the removal of interest rate ceiling as well as the implementation of a managed floating exchange rate system from 2005. However, despite the policy changes, exchange rate is not an endogenous variable of interest rate. There exists a single relationship between the interest rate and foreign exchange rate, which is relatively small due to the amplitude of exchange rate volatilities. As China still implements capital control, any monetary policy may be irrelevant to exchange rate determination in the short run. We use recursive forecast variance decomposition to check the robustness of our results. Unlike the rolling analysis, the window length is increased by one period forward at a time in the recursive analysis. The regression process is as follows. We use an eighty-three period sample and conduct the first variance decomposition. The second variance decomposition is based on the eighty-four period sample. The sample size is increased by one period at a time, and respective variance decompositions are conducted until the entire sample is included. The results of all the variance decompositions (with twenty prediction periods) are presented in Fig. 7. The recursive forecast variance decomposition is also based on BQ-SVAR.

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π

Δπ’=0 C

Δπ=0

A B

Δs=0

Δs’=0 s Fig. 5. Foreign exchange intervention shock.

Table 3 Forecast error variance decompositions of RER based on BQ-SVAR. Period (quarter)

Supply shock

Monetary policy shock

Risk premium shock

Demand shock

Intervention shock

RMB/USD 1 2 8 20 40

0.0076 0.8741 1.1705 2.3644 2.4008

4.6671 5.3763 6.2541 6.4511 6.4713

13.1252 12.3072 15.0116 16.0917 16.2496

20.4243 22.7752 22.2035 21.5306 21.4745

61.7759 58.6672 55.3603 53.5623 53.4039

Yen/USD 1 2 8 20 40

0.4150 0.5441 0.8725 0.9788 1.0276

10.2238 9.7159 10.3128 10.3663 10.3593

7.6358 7.4638 9.4816 9.5063 9.5205

77.4571 69.4766 64.9384 64.7466 64.6978

4.2683 12.7996 14.3948 14.4020 14.3948

GBP/USD 1 2 8 20 40

3.8687 3.9257 3.8541 3.8548 3.8548

14.9386 14.7962 15.9343 15.9555 15.9555

0.6361 0.9251 1.3679 1.3698 1.3698

80.5565 80.3530 78.8437 78.8199 78.8199

– – – – –

Fig. 7 shows that 20–50% of the RMB/USD real exchange rate dynamics are explained by exchange rate intervention, demand and risk premium shocks. Supply and monetary shocks are almost independent of the exchange rate dynamics. The effect of risk premium shocks on exchange rate dynamics declined over time. As for the Yen/USD exchange dynamics, demand and intervention shocks respectively explain 60% and 10%, while the other three shocks have limited effect. A recursive forecast variance decomposition of GBP/USD shows that demand shock is still the most important factor responsible for exchange rate determination, but different from the other two bilateral exchange rates. Monetary shock plays an important role in explaining the GBP/USD dynamics (about 10–18%). The recursive analysis shows that the estimated results of variance decomposition are consistent based on different sample periods, indicating that the above conclusions are robust. 6. Policy simulations and implications To assess the social welfare losses of China, Japan and the UK induced by monetary policy, we use three methods, HP Filter, CF Filter and BK Filter, to measure the output and inflation gaps, and then derive the loss functions of the three countries under different inflation targets. HP filter is a high-pass linear filter that calculates the smoothed series (st ) of yt by minimizing the variance of yt , subject to a penalty constraining the second difference of the smoothed series (Hodrick and Prescott, 1997). HP filter minimizes the variance by choosing an optimal st ,

Min

T T1 X X ðyt  st Þ2 þ k ½ðstþ1  st Þ  ðst  st1 Þ2 t¼1

ð15Þ

t¼2

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Fig. 6. Financial openness index. Source: Chinn and Ito (2015).

Fig. 7. Recursive forecast variance decomposition.

where k > 0 is the smoothed parameter. The larger the value of k, the smoother is st . For k ¼ 1, st approaches a linear trend. Generally, k is set to 1600 for the quarterly data. However, many studies show that BK filter has significant better advantages over HP filter for dealing with the quarterly or higher frequency data. BK filter is provided by Baxter and King (1999) to derive a moving average based on band-pass filter, which is symmetric. We can isolate the smoothed, cyclical and irregular series from a seasonally adjusted series, where smoothed and irregular respectively denotes the lower and the upper frequency bands. Then we can derive the intermediate frequency corresponding to an economic cycle.

bt ¼

T X

-i yti

ð16Þ

i¼1

where -i is calculated through the frequency response function of Fourier transform. Generally, T is equal to twelve for the quarterly data. To calculate the smoothed trends of stationary and non-stationary series, Christiano and Fitzgerald (2003) propose a random walk filter, which can be seen as a non-symmetric band-pass filter. The weight of filter varies with times and is asymmetric besides the point in the sample, and then can isolate the smoothed trend. In comparison, BK filter is a special case of CF filter. Furthermore, CF filter not only uses different filtering formula for different kinds of time series, but also chooses different truncations and weights for different points in the same time series. To be robust, we use the above three filters to calculate social welfare losses. The results are presented in Table 4. The social welfare loss of China is the largest, and that of Japan the smallest, meseared by all the three methods, indicating that the implementation of Japan’s monetary policy is the best among the three countries. The reasons are as follow. Firstly, to deal with the long term economic recession, the Bank of Japan implements zero interest rate and quantitative easing policy, whereas, the UK has implemented the great moderation economic cycle strategy during 1980–2007, making the monetary policy have little effect on the output gap and inflation target, and little social welfare loss. During the data periods, China has carried out the reform of economic structure and policy, leading to higher economic growth and inflation dynamics, and greater social welfare losses. Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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C. Chen et al. / J. Int. Financ. Markets Inst. Money xxx (2016) xxx–xxx Table 4 Welfare comparisons. Country

Method

a¼0

a ¼ 0:2

a ¼ 0:5

a ¼ 0:8

a¼1

China

HP CF BK

2386.702 2477.827 2177.886

2905.65 3028.33 2660.378

3684.073 3854.084 3384.115

4462.496 4679.838 4107.853

4981.444 5230.34 4590.345

Japan

HP CF BK

113.4833 110.3428 113.7846

130.5509 126.0002 130.8014

156.1522 149.4863 156.3266

181.7536 172.9724 181.8518

198.8212 188.6299 198.8686

United Kingdom

HP CF BK

129.9186 120.2908 123.3194

161.684 144.5622 155.4926

209.3321 180.9693 203.7523

256.9803 217.3764 252.0121

288.7457 241.6478 284.1853

Secondly, as China has exercised capital control, foreign exchange inflows would inevitably increase money supply, causing high inflation and social welfare losses. Thirdly, as in the managed exchange rate system, to keep the exchange rate stable, the independence of monetary policy would be undermined with embedded welfare losses. Therefore, China’s capital market should be gradually opened up to the outside world, and adapt a free floating exchange rate regime if the cental bank wishes to improve the effectiveness of monetary policy and reduce welfare losses.

7. Conclusions Monetary and exchange rate policies are two important tools to achieve internal and external economic balances. In July 2005, the Chinese government abandoned the fixed exchange rate system, replacing it with a managed floating one. In 2014, the central bank further relaxed the range of RMB/USD spot exchange rate up to 2%. According to the trilemma theory, the independence of China’s monetary policy and exchange rate formation mechanism would be improved if international capital were allowed to flow freely. Capital control is a temporary policy, and China’s capital market would gradually be open up in the long term. Based on economic theory, foreign exchange intervention and capital control on exchange rate have significant and academic value. We choose three currency pairs, RMB/USD, Yen/USD, GBP/USD to make a comparison. As China, the UK and Japan have implemented different sets of monetary, capital control and exchange rate policies, it is possible to investigate the different effects of such policies on exchange rate persistence and social welfare losses. This paper makes a useful contribution to the literature. It builds a dynamic exchange rate determination model of capital control and intervention with Taylor rule fundamentals, and derives the dynamics of the difference for exchange rate and inflation equations. Based on the theoretical model, it uses BQ-SVAR to identify the sources of exchange rate dynamics in 1985–2015 for RMB/USD, Yen/USD and GBP/USD. The estimated results show that compared to a supply shock, a demand shock appears to be more important for exchange rate dynamics. Furthermore, a monetary shock increases interest rate and depreciates real exchange rate through the modified uncovered interest rate parity (UIP) in the short run. However, domestic inflation would decline to make real exchange rate appreciate slowly in the long run, and return to its initial equilibrium point. These empirical results show that a monetary shock is almost irrelevant to real exchange rate dynamics for RMB/USD and Yen/USD. As Japan and the UK have opened their capital accounts, such that the risk premium accounts for less than 10 percent of exchange rate persistence for Yen/USD and GBP/USD. In contrast, as China has implemented capital control, the risk premium shock explains 16 percent of the real RMB exchange rate dynamics. The exogeneity of monetary policy and the huge effect of capital control on the equilibrium of real exchange rate show that the adjustment of interest rate has no significant effect on exchange rate determination. This is mainly because the Chinese currency is not an endogenous variable of its interest rate. There only exists a single relationship between interest rate and exchange rate, which is relatively small due to the amplitude of exchange rate dynamics. Furthermore, as China is still implementing capital control, monetary policy is irrelevant to exchange rate determination. Intervention shock explains respectively about 53% and 14% of the dynamics of RMB/USD and Yen/USD, showing that central bank intervention is still an important policy instrument to keep exchange rate persistent. However, the higher degree of foreign exchange intervention, the greater conflict of the internal and external equilibria, and then the independence of central bank monetary policy will be less relevant. In contrast, the lesser degree of foreign exchange intervention, the smaller conflict of internal and external policies, and the stronger of the independence of monetary policy. The recursive forecast variance decomposition analysis shows that a monetary shock is almost irrelevant to real exchange rate dynamics for RMB/USD and Yen/USD, but explains more real exchange rate dynamics for GBP/USD from 2008, meaning that the transmission of monetary policy onto exchange rate dynamics is relatively more effective in a free floating exchange rate system than in a managed floating exchange rate one. Moreover, intervention shock accounts for much of the RMB/USD exchange rate dynamics, but is almost independent of the GBP/USD exchange rate dynamics, indicating that the independence of monetary policy is contradictory to a free floating foreign exchange regime. Most strikingly, risk premium shock Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

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explains much of the RMB exchange rate dynamics but the effect appears to have diminished recently due to a certain degree of capital account liberalization. As expected, the same shock is almost irrelevant to the GBP/USD real exchange rate dynamics, implying that capital control is in conflict with a free floating exchange rate system. As to the policy set that monetary authorities implement, including capital control, foreign exchange intervention and managed floating exchange rate, we can conclude that the independence of monetary policy, stable exchange rate and free capital flow cannot be achieved at the same time. The authorities can only choose two goals at best. Therefore, reducing foreign exchange intervention by the central bank is helpful to realize the independence of monetary policy. Furthermore, the estimated results show that the social welfare loss of China is the largest, and that of Japan the smallest, indicating that the implementation of Japan’s monetary policy is the best among the three countries in our study. In conclusion, the central bank of China should gradually open up the capital account, giving up the fixed exchange rate or the managed floating exchange rate regime, and reducing central bank intervention to improve the effectiveness of monetary policy and social welfare. Finally, as there is no good method to measure the independence of monetary policy, we cannot figure out the devolution of the independence of monetary policy for China, Japan and the UK. Therefore, future research can extend our model by incorporating two time-varying variables representing the independence of monetary policy and time-varying central bank intervention index into a time-varying parameters vector autoregressive (TVP-VAR) model, which can be seen as a feasible idea and interesting to identify whether there is a trilemma theory in other emerging economies and/or developed countries. Appendix A Using matrix form, Eqs. (8) and (9) can be expressed as a following economic system,

h i)3 sk1 ð1 þ qbÞðpt1  p Þ þ ½tc  csð1 þ qbÞk1 f t þ k1rt  k1 ð1 þ qbÞrtf 7 6 7 6 7     6 þk1 eMt þ qk1 eyt  sk1 ð1 þ qbÞeIt  k1 ð1 þ qbÞeCt 68 9 7 st1 Ds t  7 6 ¼A þ s k l l ð1 þ q bÞð p  p Þ þ ½ð t c  c s  c s q bÞk l  t c l l f > > 1 2 3 t1 1 2 1 3 t 6> > = 7 i o Dp t pt  p 7 6 < nh 7 6 þ k1r t  k1 ð1 þ qbÞr f l2  l1rt þ bEt ptþ1  pt1 l3  ðl1  k1 l2 Þl3 eMt t 5 4> > > > : ; þðqk1 l2  ql1 þ jÞl3 eyt  sk1 l2 ð1 þ qbÞl3 eIt  k1 l2 ð1 þ qbÞl3 eCt 2(



 ½h  sð1 þ qbÞk1 ð# þ q/Þk1 . According to the optimal dynamic theory, the ½k1 l2 ðh  s  sqbÞ  hl1 l3 ½q/l1  j/ þ #l1  ð# þ q/Þk1 l2 l3 model satisfies the two following conditions, where A ¼

detðAÞ < 0 and DðAÞ ¼ trðAÞ2  4 detðAÞ > 0 Therefore, matrix A has two real eigenvalues, one is positive and another is negative. Then there is a steady equilibrium in the economic system. In the certain point satisfies Ds ¼ 0 and Dp ¼ 0 is a steady state of the model, which is named as steady equilibrium. Appendix B Firstly, based on the Eqs. (8), (9) and four Propositions, considering Japan has implemented free capital flow, foreign exchange intervention and free floating exchange rate regime, then s ¼ 1, we can derive the long term constricted conditions (LTC) for Yen/USD as follow,

2

1 0 6 1 60 6 6 1 LTC ¼ 6 0 6 1 b 6/ / 4 j/sð1þqbÞ #  ½l1 ð#þq/Þ j/h h/

0

0

0

0

1

0

 /b

1 /

j/ð1þqbÞ #  ½l1 ð#þq/Þ  h/ j/h

0

3

7 0 7 7 0 7 7 7 0 7 5  1h

Secondly, based on the Eqs. (8), (9) and four Propositions, considering United Kingdom has implemented free capital flow, non-foreign exchange intervention and free floating exchange rate regime, then s ¼ 1, f t ¼ 0 and c ¼ 0, we can derive the long term constricted conditions (LTC) for GBP/USD as follow,

2

1

0

0

0

3

60 1 0 0 7 7 6 7 LTC ¼ 6 1 7 6  /1  /b 0 / 5 4 j/ð1þqbÞ # #  ½l1 ð#þq/Þ  h/  1h j/h h/

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Appendix C The figure for five variables is described as follow (see Figs. C-1–C-3).

China to USA

Japan to USA

United Kingdom to USA

Fig. C-1. GDP growth and nominal interest rate ratios.

China to USA

Japan to USA

United Kingdom to USA

Fig. C-2. Relative inflation and real exchange rate.

China

Japan

Fig. C-3. Foreign exchange intervention index.

Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008

16

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References Abeysinghe, Tilak., Rajaguru, Gulasekaran., 2004. Quarterly real GDP estimates for China and ASEAN 4 with a forecast evaluation. J. Forecasting 23, 431–447. Asmah, Emmanuel E., 2013. Sources of real exchange rate fluctuations in Ghana. Am. J. Econ. 3, 291–302. Bacchetta, P., van Wincoop, E., 2006. Can information heterogeneity explain the exchange rate determination puzzle? Am. Econ. Rev. 96, 552–576. Baillie, Richard T., Selover, David D., 1987. Cointegration and models of exchange rate determination. Int. J. Forecast. 3, 43–51. Baxter, King, 1999. Measuring business cycles: approximate band-pass filters for economic time series. Rev. Econ. Stat. 81, 575–593. Beckmanna, Joscha, Wildeb, Wolfram, 2013. Taylor rule equilibrium exchange rates and nonlinear mean reversion. Appl. Finance Econ. 23 (13), 1097–1107. Besancenot, D., Vranceanu, R., 2003. Credibility costs in the monetary integration game. Econ. Transitions 11, 727–741. Blanchard, O., Quah, D., 1989. The dynamic effects of aggregate demand and supply disturbances. Am. Econ. Rev. 79, 655–673. Chinn, Menzie D., Ito, Hiro, 2008. A new measure of financial openness. J. Comp. Policy Anal. 10, 309–322. Choudhri, Ehasn U., Hakura, Dalia S., 2006. Exchange rate pass-through to domestic prices: does the inflationary environment matter? J. Int. Money Finance 25 (4), 614–639. Christiano and Fitzgerald, 2003. The band pass filter. Int. Econ. Rev. 44, 435–465. Clarida, R., Gali, J., 1994. Sources of real exchange rate fluctuations: how important are nominal shocks?. NBER Working Paper. 4658. . Clarida, R., Waldman, D., 2008. Is bad news about inflation good news for the exchange rate. In: Campbell, John Y. (Ed.), Asset Prices and Monetary Policy. University of Chicago Press, pp. 371–396. Craighead, William D., Tien, Pao-Lin, 2015. Nominal shocks and real exchange rates: evidence from two centuries. J. Int. Money Finance 56, 135–157. Dibooglu, S., Kutan, A., 2001. Sources of real exchange rate fluctuations in transition economies: the case of Poland and hungry. J. Comp. Econ. 29, 257–275. Dumrongrittikula, Takeshi Taya, Andersonb, Heather M., 2016. How do shocks to domestic factors affect real exchange rates of Asian developing countries? J. Dev. Econ. 119, 67–85. Enders, W., Lee, B.S., 1997. Accounting for real and nominal exchange rate movements in the post-bretton woods period. J. Int. Money Finance 16, 233–254. Engel, C., 1996. The forward discount anomaly and the risk premium: a survey of recent evidence. J. Empirical Finance 3, 123–192. Engel, C., West, K.D., 2006. Taylor rules and the deutschmark-dollar real exchange rate. J. Money Credit Banking 38, 1175–1194. Engel, C., Mark, N.C., West, K.D., 2007. Exchange rate models are not as bad as you think. NBER Macroecon. Ann. 22, 381–441. Farrant, K., Peersman, G., 2006. Is the exchange rate a shock absorber or source of shocks?: New empirical evidence. J. Money Credit Banking 38, 939–962. Fiess, Shankar, 2009. Determinants of exchange rate regime switching. J. Int. Money Finance 28, 68–98. Flood, R.P., Rose, A.K., 1995. Fixing exchange rates: a virtual quest for fundamentals. J. Monetary Econ. 36, 3–37. Froyen, Richard T., Guender, Alfred V., 2016. The real exchange rate in open-economy Taylor rules: a re-assessment. University of Canterbury Working Paper, No. 10. . Galí, Monacelli, 2005. Monetary policy and exchange rate volatility in a small open economy. Rev. Econ. Stud. 72, 707–734. Galimberti, Jaqueson K., Moura, Marcelo L., 2013. Taylor rules and exchange rate predictability in emerging economies. J. Int. Money Finance 32, 1008–1031. Gehrke, Britta, Yao, Fang, 2016. Persistence and volatility of real exchange rate: the role of supply shocks revisited. Reserve Bank of New Zealand. 2016/02. . Grossmann, A., Love, I., Orlov, R.G., 2014. The dynamics of exchange rate volatility: a panel VAR approach. J. Int Financial Markets Inst. Money 33, 1–27. Hamori, Shigeyuki, Hamori, Naoko, 2011. An empirical analysis of real exchange rate movements in the euro. Appl. Econ. 43, 1187–1191. Hodrick, R., Prescott, E.C., 1997. Post-war U.S. business cycles: an empirical investigation. J. Money Credit Banking 29 (1), 1–16. Huh, Hyeon-seung, Kwon, Won Soon, 2015. Sources of fluctuations in the real exchange rates and trade balances of the G-7: a sign restriction VAR approach. Rev. Int. Econ. 23, 715–737. Ince, Onur, Molodtsova, Tanya, Papell, David H., 2015. Taylor rule deviations and out-of-sample exchange rate predictability. April 30. http://dx.doi.org/10. 2139/ssrn.2601193. Inoue, Takeshi., Hamori, Shigeyuki., 2009. What explains real and nominal exchange rate fluctuations?: evidence from SVAR analysis for India. Econ. Bull. 29, 2803–2815. International Monetary Fund (http://www.imf.org). Kempa, Bernd, Wilde, Wolfram, 2011. Sources of exchange rate dynamics with Taylor rule fundamentals. Econ. Model. 28, 2622–2627. Kim, S., Lee, S., 2008. The role of the exchange rate in Korean economy: a shock absorber or a source of shocks. J. Econ. Res. 13, 303–324. Lansing, Kevin J., Ma, Jun, 2015. Explaining exchange rate anomalies in a model with Taylor-rule fundamentals and consistent expectations. Federal Reserve Bank of San Francisco Working Paper. No. 2014–22. . Lastrapes, W.D., 1992. Sources of fluctuations in real and nominal exchange rates. Rev. Econ. Stat. 74, 530–539. Lewis, K.K., 1995. Puzzles in international financial markets. In: Grossman, G.M., Rogoff, K. (Eds.), Handbook of International Economics, vol. 3. Elsevier, North-Holland, Amsterdam, New York and Oxford, pp. 1913–1971. MacKinnon, J.G., 1996. Numerical distribution functions for unit root and co-integration tests. J. Appl. Econ. 11, 601–618. Mark, N., 2009. Changing monetary policy rules, learning, and real exchange rate dynamics. J. Money Credit Banking 41, 1047–1070. McCallum, B.T., 1994. A reconsideration of the uncovered interest parity relationship. J. Monetary Econ. 33, 105–132. McCarthy, J., 2007. Pass-through of exchange rates and import prices to domestic inflation in some industrialized economies. Eastern Econ. J. 33 (4), 511– 537. Mirdala, Rajmund, 2015. Source of real exchange rate fluctuations in new EU member countries. FIW Working Paper. 160. . Molodtsova, Tanya, Papell, David H., 2009. Out-of-sample exchange rate predictability with Taylor rule fundamentals. J. Int. Econ. 77, 167–180. National Bureau of Statistics (NBS website), China Economic Reports and China Statistical Monthly Reports (http://www.stats.gov.cn/). National Bureau of Statistics (NBS, 1993–2015), China Statistical Yearbook (various issues), Statistical Press, Beijing, China. Newey, W., West, K., 1994. Automatic lag selection in covariance matrix estimation. Rev. Econ. Stud. 61, 631–653. Ng, S., Perron, P., 2001. Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1529–1554. Olivo, Víctor Tiberio, 2003. Taylor rules and inflation targeting do not work with systematic foreign exchange market intervention. Money Affairs 14 (1), 51– 67. Wang, Tao, 2005. Sources of real exchange rate fluctuations in China. J. Comp. Econ. 33, 753–771. Wang, Jian, Wu, Jason J., 2012. The Taylor rule and forecast intervals for exchange rates. J. Money Credit Banking 44, 103–144. Wang, Rudan, Morley, Bruce, Ordóñez, Javier, 2016. The Taylor rule, wealth effects and the exchange rate. Rev. Int. Econ. 24 (2), 282–301. Weymark, D., 1997. Measuring the degree of exchange market intervention in a small open economy. J. Int. Money Finance 16, 55–79. Wilde, Wolfram, 2012. The influence of Taylor rule deviations on the real exchange rate. Int. Rev. Econ. Finance 24, 51–61. Wu, Guobing, Zhang, Hao, Chen, Ping, 2015. Fitting and forecasting of nonlinear Taylor rule in China: review on the roles of foreign exchange in monetary policies. China Finance Rev. Int. 5 (4), 402–420. Yilmaz, Ensar, 2012. The exchange rate: a shock absorber or source of shocks in Turkey? Int. Econ. J. 26, 175–188.

Please cite this article in press as: Chen, C., et al. Exchange rate dynamics in a Taylor rule framework. J. Int. Financ. Markets Inst. Money (2016), http://dx.doi.org/10.1016/j.intfin.2016.07.008