Currency Intervention vs. Speculative Sentiment - Analysis of Japanese and US FOREX Markets

Transcription

1 Currency Intervention vs. Speculative Sentiment - Analysis of Japanese and US FOREX Markets Xuxin Mao February 16, 2012 Abstract This paper analyses of the effects of speculative sentiment and currency intervention on the Japanese and US FOREX markets. Japanese Yen s appreciation against USD is a puzzle in international finance even with interventions in April August 2008 period. No previous research addresses the Yen speculation sentiment effects on the interventions and the movements of USD/JPY exchange rate. The paper utilizes a Cointegrated VAR framework (Juselius, 2006) to incorporate suitable international parity conditions and two theoretical influence channels, i.e. the signalling channel and the portfolio balance channel, and to analyze the short- and long-term intervention effects respectively. A speculative sentiment variable is included into the framework to incorporate the empirical speculative effects on different channels.the main findings are: (i) The two theoretical models fail to explain the intervention effects. Currency interventions have both short- and long-run significant counterproductive effects on exchange rate movements through the signalling channel and the portfolio balance channel respectively. (ii) The failure of the theoretical models can be explained by introducing the effects of speculative sentiment, which also suggest a short-term trading strategy. In the short-run, when Japan intervenes with buying 1 billion USD or selling equivalent Yen, the long to short to yen futures will increase by 6.1%, with the result of more than 1 Unit of Yen appreciation against one USD within one month. In the long-run, the Overall Yen selling or USD buying interventions increase Japanese and US interest rate differential, i.e. the risk premium of holding Yen, and make more Yen appreciation through more Yen-buying speculations. There is need for new theoretical models that investigate the effects of interventions by central banks, which also incorporate speculative effects. What is more, to "fade" the spike of a Yen-related intervention is a highly-profitable FOREX trading strategy. JEL classification: E31; E43; F31; F32 Keywords: Cointegrated VAR, Currency Intervention, Portfolio Balance Channel, Risk Premium, Signalling Channel, Speculative Sentiment, Uncovered Interest Parity The author is a PhD student at the University of Glasgow Business School, Department of Economics, Adam Smith Building G12 8RT. Address: x.mao.1@research.gla.ac.uk 1

2 1 Introduction Foreign exchange intervention is defined as purchases and sales of foreign currencies by the monetary authorities with an intention to influence the exchange rates, which dates back to the time when the classical gold standard era was not established. (Bordo et al., 2007) In USA, interventions are conducted by the Federal Reserve Bank of New York and the Treasury after decisions made by the Treasury with consultation of Federal Reserve Board. While in Japan, interventions are imposed by the Bank of Japanthe followed by decisions from the Ministry of Finance. After the meetings at Plaza in 1985 and Louvre in 1987, sterilized exchange rate interventions became regular and sometimes very heavy (Obstfeld, 1990) However, there have been few US interventions since 1997 and Japanese interventions since March (Ito, 2007) Sterilized interventions offset any changes in monetary base caused by interventions through immediate open market operations, while unsterilized interventions changed the monetary base. Most interventions in developed countries are sterilized except some Japanese interventions in (Sarno and Taylor, 2002, Ito, 2007) There are two important channels, i.e. the portfolio balance approach and signalling approach, through which sterilized foreign exchange interventions influence the exchange rates. As a classic influence channel, the portfolio balance approach (Isard,1980, Branson,1984, and Kumhof, 2010) is based on the assumptions that Ricardian condition 1 and bonds in different currencies are not perfect substitutes does not hold true. Frankel (1982), Obstfeld(1983), Rogoff (1984) and Lewis(1988) found the interventions in developed economies are effective at most in the very short term with very small size. Kumhof (2010) showed that the interventions are more effective in developing economies with large fiscal spending volatility and small domestic currency government debt. The signalling approach was proposed by Mussa (1981), Kenen (1988) and Almekinders(1995)and then made influential through works done by Dominguez (1987) and Dominguez and Frankel (1993). Under implicit assumptions that, among all market agents, the monetary authorities obtain most information which will be known to every agent through interventions, exchange rates are affected by the new information associated with the interventions. To be specific, the interventions change the exchange rate expectations of private agents by changing their expectations of the actions of monetary authorities and their effects. The empirical results of the signalling channel in developed countries are mixed. While Dominguez(1987) and Dominguez and Frankel (1993) found sterilized interventions had very substantial effects, Humpage(1989) and Eijffi n- ger and Gruijters (1991) showed they are not effective. Few empirical works on the signalling approach has been done for the developing countries. Since the mid of 1990 s, few theoretical papers have been produced; in addition, many empirical papers focus only the statistical effects of interventions which can be classified into four methodological groups, i.e. low-frequency time 1 Ricardian condition is the condition where expected future tax payments of private agents, served as extra government debt, are offset against the bond holdings in terms of domestic currency. 2

3 series, event studies, high-frequency, and identified models. The low frequency time series analysis is a standard approach which measures the effects of exchange rate interventions on the daily, monthly or quarterly changes of the exchange rates. Since the influential work of Rogoff (1984), the method has been continually used to analyze the interventions with new attempts. Taylor (2004, 2005) examines the effectiveness of interventions using a Makov-switching model on real exchange rates, while Frenkel, et al. (2005) introduces interventions as dummy variables into the exchange rate volatility equation to testify the validity of the signaling approach. Followed by Ramaswamy and Samiei (2000) using cointegrated VAR and GARCH(1,1) model, Hillebrand and Schnabl (2008), through a new GARCH framework, analyze the differences of Japanese intervention effects of sterilized interventions in most periods, and unsterilized ones in Although the low-frequency time series studies have the merits of being able to measure the exact intervention effects, they do have the following demerits. Since interventions happen at only a small part of an economic year, the intervention data is nearly zero in most periods, which makes the intervention effects measurement harder to interpret. Some variables are diffi cult to be justified as there is little consensus on exchange rate determination models. (Obstfeld and Rogoff, 1995) There may be endogenous relations between the variables in the model and the sample selection also matters. The intervention effects which often happen high-frequently in clusters are hard to be estimated. The event studies approach is introduced for the analysis of German and US interventions, then for the Japanese interventions. (Fatum and Hutchison, 2003, 2006) Starting with definition of the events, the approach identifies the periods during which the exchange rates are examined with definition of the measures of intervention effectiveness.this approach focuses on the structure of intervention data, stresses on the non-zero observations and does not require exchange rate determination models as the basis of data analysis. Nevertheless, this methodology is not devoid of problems. The definition of an event is arbitrary and not formalized among researchers, which means one may have different number of events in the same time zone with different criteria. It is also diffi cult to construct comparable events, both temporally and quantitatively. The longeval events with large number of continuous interventions are diffi cult to compare with ephemeral events with smaller number of interventions.there is also risk of endogenous problems among the variables in the event studies approach and selecting a proper sample and specify the exact intervention effects are diffi cult. The high-frequency time series method uses high-frequency exchange rate and intervention data to explain the intermediate intervention effects with more specific information diffi cult to grasp by low-frequency time series and event studies approaches.(vitale, 2007) However, one problem vis-a-vis this approach is the limited availability of high-frequency intervention data. Although Dominguez (2003) analyzes the US and Japanese interventions with news report data, it is very unlikely to get satisfactory results without real intervention data as Fisher (2006) shows that Reuters news reports have a serious time delay and sometimes are not correct. Another problem is the lack of identification of foreign exchange interventions and dynamics. Simple linear regressions estimated by Payne and 3

4 Vitale (2003) can not insulate the unexpected intervention effects from other exchange rate innovations. And the high-frequency event studies approach proposed by Fatum and King (2005) is not free of the endogeneity problem and other problems that low frequency event studies approach encounters. There is also an inference problem caused by the paucity of exact intervention timing. (Neely, 2005a) In contrast, the identified model apporach models structural economic relations to identify the intervention impacts on exchange rate behaviors. Kim (2003) adopts a structural VAR model combining exchange rate interventions with multiple monetary variables based on the monetary literature. He estimates the effects of both interventions and monetary policies on weighted US exchange rates. The included macro variables and monetary policy measures, such as federal funds rates, the monetary aggregates, and commodity prices, permit his approach to overcome the problem of omitted variables. The rich set of macroeconomic relations and policy interactions is also an achievement of his approach. Furthermore, his model analyzes the joint interaction between monetary and intervention policy. However, Neely (2005b) shows that some parameters in his VAR model are not identified and in the wrong rank condition according to Hamilton (1994), which makes the estimation results questionable. Kearns and Rigobon (2005) estimate the structural breaks of Japanese and Australian reaction functions to analyze a nonlinear intervention model with simulated method of moments. Similarly, based on a friction of model of foreign exchange interventions, Neely (2005c) estimates a system of equations to identify the cross-effects of intervention with the level and volatility of exchange rates. However, none of the above identified models has market microstructure components nor clear theoretical foundations of the exchange rate intervention effects. (Vitale, 2007) All the four approaches mentioned above have both advantages and disadvantages. In my paper, a Cointegrated VAR model will be built to incorporate both theoretical influence channels and suitable international parity conditions to analyze the short- and long-term intervention effects. In order to understand why neither channel works, I will include speculation variable into my model to emphasize the empirical speculative effects on different channels, which also provide possibility to develop more plausible theoretical models. 2 The International Parities and Hypothesis of The Channels of Influence 2.1 The International Parities The researches of intervention impacts on the economic parity relations are still sparse in spite of the importance of long run relations of price adjustments, interest and exchange rates fluctuations although Juselius and MacDonald (2004) have provided a framework to analyze the international parity conditions. I will present the parity conditions in this section, and test them as hypotheses in 4

5 later sections. As the most well-known international parity, purchasing power parity (PPP) is a theory about exchange rate determination based on the idea that two currencies have the same purchasing power for the same goods. The logarithm version of the absolute PPP is: ppp t = p t p t s t (1) Here, ppp t = ln(p P P t ), p t = ln(p t ), p t = ln(pt ) and s t = ln(s t ), where P P P t is often denoted as real exchange rate, Pt is the price for the same goods or basket of goods in the foreign country and S t is the norminal exchange rate expressed as the units of the domestic currency per unit of foreign currency. With a error term ε t, the relative PPP can be defined as: p t p t s t = ε t (2) When PPP holds, the change of the nominal exchange rate should have the same sign with the change of the relative price and the real exchange rate should be mean-reverted. Although great efforts have been made over the past decades on empirical tests of PPP, the results are still questionable. One explanation of the persistence of PPP deviations is the existence of current account imbalance which is financed by capital accounts. Hence a new parity condition, namely uncovered interest rate parity (UIP), is used to explain the PPP deviation. The logarithm version of UIP can be represented as: E t ( s t+l ) (i l t i l t ) = 0 (3) l where E t s t+l is the expected nominal exchange rate conditional on the the information from time period t, i l t is the domestic interest rate at time t with maturity t + l and i l t is its foreign counterpart. If rational expectations hypothesis (REH) exists, I have: and a testable parity: E t ( s t+l ) = s t+l + ε t+l (4) l s t (i l t i l t ) = ε t (5) where ε t+l is a white noise error, which means agents do not make systematic forecasting error. However, many empirical tests, e.g. Cumby and Obstfeld (1981), have shown UIP is not stationary. One explanations is that there exists a risk premium µ t. With the consideration of the risk premium and PPP, (5) can be transformed into i l t i l t = s t + µ t + ε t (6) = (p t p t ) + µ t (7) 5

6 In the above UIP condition, the differential of long term interests sometimes can be replaced by short term interests. Then term structure of interest rates can be adopted to link the long term with short term interests, named as term spread parity: i b,t i m,t = ν t (8) where i b,t and i m,t are the nominal long term bond and short term libor rates respectively and ν t is the random error term. Although Campell and Shiller (1987) propose that the term spread should be stationary, empirical results from Campell (1995) show the existence of nonstationarity. The interest rates can also be illustrated by Fisher parity, a composition of real interests and expected price change, as follows: r b,t = i b,t E t ( p t+l ) (9) l r m,t = i m,t E t ( p t+s ) (10) s where r b,t and r m,t are real long term and short term interest rates respectively, and E t ( p t+l l ) and E t ( pt+s s ) are expected price changes in the long run and short run respectively. Based on rational expectations, the two above functions can be transformed into the real interest parity (RIP): r b,t r m,t = (i b,t E t ( p t+l l )) (i m,t E t ( p t+s )) = ε s t (11) If sticky goods prices hold, the real interest rate differentials are widely treated as stationary as the short term interest rates are set by monetary authorities. If the expected inflation differential item is not stationary, the term spread should not be stationary to possibly make the real rates stationary. However, real interest rate parity does not hold in most cases. (Hallwood and MacDonald, 1999) 2.2 The Channels of Influence and Hypothesis Most foreign exchange intervention researches focus the intervention effects on exchange rate movements without being able to indentify the ditinctive effects from different channels jointly in one coherent framework. A new way to test them with variables with a mothly frequency will be proposed in my paper as follows: The influence of signalling channel will be tested as short-term effects with interventions of that specific month as the regressor, while the influence of the portfolio balance channel will be tested as long-term effects with cumulative interventions of the whole priod as major regressor. The signalling approach is based on the implicit assumptions that the monetary authorities have superior information among all market agents. However, 6

7 this assumption can only hold true in the short-term as all FOREX participants will know more and more information with respect to the interventions within that specific month. What is more,only the interventions within the specific month, not the cumulative interventions of all periods, are important to reflect the signals sent by the central banks. Based on the the above assumptions, a testable hypothesis is proposed with the null hypothesis H 0: I > 0 = s t < 0 and H 1: I > 0 = s t > 0 where I stand for interventions to appreciate the domestic currency and s t means the spot exchange rate at which one unit of foreign currency can be exchanged for domestic currency. If we take Japanese and US FOREX markets as example, I is positive if selling US Dollar or buying Japanese Yen and s t < 0 when Janpanese Yen appreciates agaisnt US dollar. The core of the portpolio balance channel is the imperfect substitutability of domestic and foreign assets, which means there exsists risk premium µ t measured by deviations from uncovered interest parity: µ t = (i t i t ) s t + ε t where (i t i t ) is the domestic and foreign interest rate differential on securities. If (i t i t ) I(1) and s t I(0), then (i t i t ) s t I(1), which means there exists risk premium which make the infuence of interventions through the portfolio balance channel become possible. As the risk premium depends on the relative stock supplies of outside assets denominated in domestic and foreign currencies, the cumulated interventions of whole sample period are used. Hence the portfolio balance channel is tested in the form of the long-term relationships. Therefore the following tests on (i t i t ) and s t will be conducted later together with other long-run parity tests to find whether the portpolio balance channel is valid and,if yes, what effects the interventions have on long-term exchange rate movements and possible international parities. 3 Data Description and Parity Illustration 3.1 Data Description and Dummies In order to get optimal empirical results, the choice of "right" data and variables is the first important thing to be taken care of. Most of the varialbes are from the EconWin database except Japanese and US Intervention data are from Bank of Japan and Federal Reserve Economic Data respectively, and COT data is from the Commodity Futures Trading Commission. The variables are with duration of April 1991 to August 2008 with Japan and USA are labelled as home and foreign country respectively. I choose the specific period out of two reasons. Firstly, the offi cial Japanese and US foreign intervention data are jointly available only from April Secondly, the choice is economically meaningful, which covers the lost years of Japanese economy and ends at the eve before the current global economic recession started from September The vairalbe illustrations are with introductions of possible dummies if the standard error of the variable residuals at spefic period is larger than 3. To illustrate the international parities in the same time analyzing the short term intervention 7

8 effects, the initial data set consists of the following variables 2 : s t =the logarithm of the logarithm of the spot exchange rate USD/JPY (the rate at which one US Dollar can be exchanged for Yen) p t =the logarithm of the Japanese consumer price index p t =the logarithm of the US consumer price index r b,t =the Japanese 10 years bond rate/1200 rb,t =the US 10 years bond rate/1200 r m,t =the Japanese 3 months libor rate/1200 rm,t =the US 3 months libor rate/1200 CI =Cumulated Japanese currency interventions defined as total net purchase of Japanese Yen or sales of US Dollar in unit of billion US Dollar CI =Cumulated US currency interventions defined as total net purchase of Japanese Yen or sales of US Dollar in unit of billion US Dollar COT =Long to short ratio of speculators postions on Yen futures from Commitments of Traders reports of the Chicago Mercantile Exchange An increase in the value of exchange rate s t reflects an depreciation of Japanese Jen. The graphs of exchange rate with its levels and differences are shown in the above part of the Figure 1. From the levels graph, a steady Jen appreciation in the early1990s was followed by a depreciation period until late While the first change might be caused by coordinated foreign exchange interventions, speculations and the Kobe earthquake in the early 1995, the second might be the result of continued injection from Bank of Japan to keep the stability of the financial markets to accommodate the expansion of money supply. Accordingly, in the difference graph, there were two impulse changes happened in August 1995 and October 1998, which could be counted as impulse dummies for the later data analysis. The1995:08 dummy is related to a series of coordinated Japanese and US interventions. Except the dummy effects, the differenced exchange rate variable seems quite stationary which suggests s t I(1). The differenced price variables p t and p t reflect the inflation levels of Japan and USA respectively. There was a trend break in April 1997 which corresponds to the sharp slowdown of Japanese economy caused by an inappropriate fiscal policy: An increase of consumption tax rate from 3% to 5%, combined with the end of a temporary tax cut, amounted to a 9 trillion yen increase of tax, which ended short-lived economy recovery with credit crunch and sharp decline. There is a blip dummy in the US inflation rate which happened in September 2006 and was probably related to the real estate bubbles in US, and transitory dummies between the September and November of Transitory dummies are not used in the cointergrated VAR system as they are not statistically significant. From the inflation graphs of the Figure 1, both the levels and differences of price variables are not stationary, which may suggest p t, p t I(2). r b,t and r b,t reflect the long-term interest rates, i.e. bond rates with the 2 All original annual interest rate variables (in %) have been devided by 1200 to be comparable with the price variables in logarithm. 8

9 5.00 Norminal Exchange Rate Change in Norminal Exchange Rate Japanese Price US Price Japanese Inflation (Change in Japanese Price) US Inflation (Change in US Price) Yen Speculative Long to Short Position Difference of Yen Speculative Position 10 Norminal Exchange rate Relative price 0.25 PPP Figure 1: Exchange Rates, Prices, Speculative Sentiment and PPP maturity of 10 years. There was a relatively steady downward trend in Japanese bond rate from 1991 to the end of Followed by a short mean shift period, the level became relatively stable. In Figure 2, two impulse dummies appeared in the differenced Japanese bond rate in December 1998 and July 2007 to account for the sharp increases of bond rate from 0.85% to 1.97% and from 0.94% to 1.46% respectively. Except for the innovation effects, the differenced Japanese and US bond rate variables are fairly stationary, which reflect both r b,t and rb,t were I(1). r m,t and rm,t are the the short-term interest rates, i.e. libor rates with the maturity of 3 months. 3 After decreasing steadily in the first half of 1990s and then slowly in the second half with some minor shift effects, the Japanese libor 3 The libor rate is usually called federal funds rate in the USA. However, in my paper I used the term of libor rate in both Japanese and US cases. 9

10 Long term Bond Rate, Japan Long term Bond Rate, US Change in Long term Bond Rate, Japan Change in Long term Bond Rate, US Months libor Rate, Japan Months libor Rate, US Change in 3 Months libor Rate, Japan Change in 3 Months libor Rate, US Cumulative Foreign Exchange Interventions, Japan Cumulative Foreign Exchange Interventions, US Foreign Exchange Interventions, Japan Foreign Exchange Interventions, US Figure 2: Interest Rates and Foreign Exchange Interventions rate came into a steady zero interest condition until The unusual phenomenon reflects the strong stimulative monetary policies from Bank of Japan to promote investments and to prevent further deterioration of economic conditions. However, this granted little space for Japanese monetary authorities to impose further stimulative monetary policies. In the differenced US libor rate, there was one impulse dummy in February 2008, which reflected a sharp drop of libor rate from 3.94% to 2.98% to fight for the economic recession. Except for this dummy, the differences of the Japanese and US interest rates in Figure 2 look quite stationary, which suggests that the libor rate variables r m,t and rm,t may also be I(1). CumInt and CumInt are set as weak exogenous variables 4 in the coin- 4 In the cointergrated VAR model, a weak exogenous variable is a variable which affects long-run relations of other variables, without being influenced by them. (Juselius, 2006) 10

11 tegrated VAR system as it is the changes of them, the original intervention variables, that influence the changes of exchange rate, interest rate and inflation variables. Both of them are in the unit of billion US dollar (adjusted with the spot offi cial exchange rate in Japanese case) and positive if the authorities sell US dollar or buy Jen and vice versa. It can be found that the Japanese interventions were quite frequent, normally in the form of separate clusters, while the US interventions were active until mid of the 1990s. 3.2 Illustration of International Parity Conditions In this section, I illustrate the parities and differentials vis-a-vis exchange rates, prices and interest rates. In comparison of mean-adjusted price differential and nominal exchange rate, there are three main features: Firstly, the stochastic trend in the relative price between Japan and US is downward sloping. Secondly, the nominal exchange rate evolves, with large persistent swings, around a similar trend as price differential. Thirdly, there was a trend break happened in April 1997 in the price differentials. Therefore, the PPP in the lower panel of first graph shows no sloping trend. This break has dynamic effects on prices and interest rates, which is modeled in the cointegration relations of the contegrated VAR model. In Figure 3 the forward premiums, the bond rate differential i b,t i b,t and libor rate differential i m,t i m,t, are not stationary. According to the UIP parity condition, this might be due to the nonstationarity of risk premium µ t or depreciation rate s t. Suggested in the previous section, s t I(1), and s t I(0), which means the nonstationarity of risk premium may play a central role. The term spreads i b,t i m,t and i b,t i m,t are also not stationary. In Figure 4, while the real interest rate parity conditions (real term spread) in Japan and US seem not stationary, the stationarity of the Japanese and US real rates suggests that Fisher parities (9) and (10) might possibly hold true. The graphical analysis reflects the nonstationarity of most parity conditions except the Fisher parity condition, 5 which suggest that the standard economic conditions may not be good fits of the data. Frydman and Goldberg (2007) and Frydman, et al. (2008) develop an imperfect knowledge economics (IKE) representation model which suggests that risk averse and myopic agents, although rational, make forecasts or decisions based on their imperfect knowledge. Their behaviors, especially speculations in the foreign exchange markets, drive the international parity conditions out of stationarity. Johansen, et al. (2010) provides an empirical support for a IKE model with I(2) cointegration tests on PPP and long swings puzzles. 5 The stationarity tests of some parity conditions in the later sections further justifies the conclusion. 11

12 0.001 Bond Rate Differential month Interest Rate Differential Term Spread in Japan Term Spread in US Inflation Rate Differential Change in Norminal Exchange Rate Figure 3: Interest Rate Differentials Real Long term Bond Rate, Japan 0.01 Real 3 Months Libor Rate, Japan Real Long term Interest Rate, US 0.01 Real 3 Months Libor Rate, US Real Long run Term Spread Real Short run Term Spread 0.01 Figure 4: Real Interest Rates and Spreads 12

13 4 The Cointegrated VAR Methodology 4.1 Cointegrated VAR I(1) model Introduction Engle and Granger (1987) initiates cointegration and Error Correction Models (ECM). A VAR model in levels can be reparameterized in a multivariate ECM form: X t = ΠX t 1 + ΣΓ i X t i + ΦD t + ɛ t (12) With the assumption that the errors are Gaussian, I start with a baseline VAR(2) model for the purpose of simplicity: X t = π 1 X t 1 + π 2 X t 2 + ε t (13) where X t is a p vectors are I(1) variables and ε t is a p vector of white noises. The equation can be formulated into: X t = ΠX t 1 + ΣΓ i X t i + ΦD t + ɛ t (14) where Π = π 1 + π 2 1 and Γ = π 2. If X t is I(1), which means X t is stationary, Π should not be of full rank to guarantee this equation is consistent. Hence, either Π = 0, or it has reduced rank: Π = αβ where α and β are p r matrixes, r < p. Thus, under the I(1) hypothesis, the cointegrated VAR model is given by: X t = αβ X t 1 + Γ X t 1 + ε t (15) where β X t 1 is an r 1 vector of stationary cointegration relations and ε t N p (0, Ω ), t = 1,..., T. Johansen (1996) states, A(z) = 0 implies that z > 1 or z = 1 and rank(π) = r < p, there exist p r matrices with rank r such that Π = αβ. A necessary and suffi cient condition to make sure X t E( X t ) and β X t E(β X t ) are stationary is that α (I ΣΓ i)β has full rank with β β = 0. The individual columns of β define the individual cointegration vectors, i.e. the linear combinations of the variables with reduced order of integration, which can be interpreted as the steady state relations in the system. On the other hand, the rows of α determine the way in which the deviations from the steady state relations influence the short run dynamics in the dependent variables of each equation Rank Determination: Cointegrating Vector Estimation The method to determine the rank of my model is based on Johansen (1988, 1991). By eliminating the short-run effects first, a clean long-run adjustment model is obtained to estimate the coeffi cient vectors α and β. After concentrating out the short-run effects, a regression of reduced rank is performed. With eigenvalues which determine the likelihood values, the number of eigenvalues different from zero equals to the number of cointegrating relations. 13

14 Firstly the residuals R 0t and R 1t are obtained from auxiliary regressions of X t on X t 1 and X t 1 on X t 1, which is defined according to the Frisch- Waugh theorem: X t = ˆB 1 X t 1 + R ot (16) X t 1 = ˆB 2 X t 1 + R 1t (17) where ˆB 1 = S 02S22 1, ˆB 2 = S 12 S22 1 and S ij are covariance expressed as S ij = T 1 ΣR it R jt for i, j = 0, 1. Hence, the concentrated model can be expressed as: R 0t = αβ R 1t + error terms (18) which is important for understanding both the statistical and economic properties of the VAR model. The "messy" empirical model has been transformed into not only a clean statistical model, but also into a more interpretable economic form. The Maximum-likelihood (ML) estimator is derived with two steps. The first step is to derive an estimator of α under the assumption that β and β R 1t are known. Then α = ˆα(β) is inserted into the ML function to become a function of β to obtain the maximizer ˆβ and then ˆα = α(ˆβ). The second step is to solve the likelihood problem by calculating the eigenvalue function λs 11 S 10 S00 1 S 01 = 0. A solution of β can be found to minimize ˆΩ(β), from which the eigenvalues 1 > ˆλ 1 > > ˆλ p > 0 can be calculated. The r - dimensional cointegrating space corresponds to the space spanned by the r largest eigenvalues. For a given choice of r, the maximum of the likelihood function equals L 2/T max = S 00 Π r i=1 (1 ˆλ i ). A likelihood test of the hypothesis H(r ) : r r for some number r against the general unrestricted model H(p) : r p is given by: T (r ) = 2lnQ[H(r ) H(p)] = T Σln(1 ˆλ i ) (19) where T (r ) is asymptotically distributed as a multivariate type of a Dickey- Fuller test statistic. (Juselius, 2006) Identification of the Long-run Structure Structural tests on the cointegration space are performed to identify the estimated cointegration vectors by imposing restrictions on the whole space of β, calculating the likelihood value once more with the restricted vectors, and comparing whether the new likelihood value is statistically equal to the original likelihood value of a likelihood ratio test which is asymptotically χ 2 distributed. There are several types of tests on the long-run structure. One type is to test whether some rows of β are in a specified form, i.e. whether some long-run economic parity condition is present in all cointegration vectors. Another type is based on the hypothesis of β = (b, η), where b is some known vector and η is the matrix of unrestricted vectors. The two tests can also be combined 14

15 so that the hypothesis of some known vectors is tested in combination with imposed restrictions on the other parameters. Finally, hypothesis on α can alos be tested to find whether the deviations from one cointegration relation affect the short run changes of one specific variable Identification of the Short-Run structure After the determination of long run relations, parsimonious short-run adjustment structure can be presented by using the following transformation: A 0 x t = A 1 x t 1 + a(ˆβ c ) x t 1 + µ 0,a + µ 1,a t + v t (20) where A 1 = A 0 Γ 1, a = A 0 α, µ 0,a = A 0 µ 0, µ 1,a = A 0 µ 1 and v t = A 0 ε t IN p (0, Σ). The parsimonious model is estimated by keeping the cointegrating relations fixed with their estimated values since the estimated β is super consistent.the system is first estimated by imposing p 1 just-identifying restrictions on each equation. Then zero restrictions are imposed on the off-diagonal elements of the A 0 matrix, i.e. A 0 = I to disregard the simultaneous effects among variables. By removing insignificant lagged variables from the system based on F - test and then insignificant coeffi cients from the equations based on the likelihood ratio test, a parsimonious shor-run dynamics representation can be achieved. 4.2 Links between the I(1) and I(2) model It is not unusual that I(2) data is analyzed in a cointegrated VAR I(1) model either because the author has not yet checked the existence of I(2) features of the data or because I(2) properties are ignored for the reason of simplicity. Therefore, to check whether a proposed I(1) analysis is still credible under the I(2) condition becomes one important issue at the beginning stage. As an illustration purpose, a transformed baseline VAR(2) model (15), and its corresponding R-form (18) based on auxiliary regressions (16) and (17) are used here. If X t I(2), both X t and X t 1 have a common I(1) trend which can be eliminated. Therefore, under the condition that X t are I(1) variables, R 0t can be treated as stationary I(0). However, in equation (17), X t 1 has a I(2) trend while X t 1 contains an I(1) trend. Hence it is not possible to cancel the I(2) trend and consequently R 1t has a I(2) trend. Therefore the equation (18) can only hold true under the condition that β = 0 or β R 1t I(0) given that R 0t I(0) and ε t I(0). The linear combination β R 1t transforms the process from I(2) to I(0) unless the rank is zero. Juselius (2006) inserted equation (17) into equation (18) to find the connection between β X t 1 and β R 1t : 15

16 R 0t }{{} I(0) = αβ (X t 1 B 2 X t 1 ) + ε t (21) }{{}}{{} I(2) I(1) = α(β X t 1 β B 2 X t 1 ) + ε t }{{}}{{} I(1) I(1) = α(β X t 1 ω X t 1 ) + ε t }{{} I(0) where ω = β B 2. Therefore, β ir 1t = β ix t 1 + ω x t 1,where i = 1,..., r. There are two cases of relations β ir 1t I(0). One case is that ω i = 0 and β ix t 1 I(0), which means directly stationary long run relations can be achieved. The other case is that β ix t I(1) and cointegrates with ω i x t 1 I(1), which means polynomially cointegrated relations instead of direct relations can be found. There might be a mixed case where for some relations β x t I(1) with other cointegration relations β x t I(0). R 0t I(0) and β R 1t I(0) have been showed in (18), which allows the estimations and tests of I(2) data to be done in the I(1) model. Roughly speaking, a number of hypotheses can be tested in the I(1) model even if x t is I(2). However, as Juselius (2006) pointed out, the interpretation of the results has to be modified to some extent as compared to the I(1) case because of the following limitations: 1. The I(1) rank test cannot say anything about the reduced rank of the Γ matrix, i.e. about the number of I(2) trends. The determination of the reduced rank of the Π matrix, though asymptotically unbiased, might have poor small sample properties. (Nielsen and Rahbek, 2007) 2. The ˆβ coeffi cients relating I(2) variables are T 2 consistent and, thus, very precisely estimated. This means that the estimate ˆβ is super-super consistent. 3. The tests of hypotheses on β are not tests of cointegration from I(1) to I(0), but instead from I(2) to I(1) and a cointegration relation should in general be considered I(1), albeit recalling that a cointegration relation β ix t can be CI(2, 2), i.e. be cointegrating from I(2) to I(0). 4.3 Nominal-to-real transformation Nominal variables are often modelled as being I(2). A Nominal-to-real transformation is to reduce the integration order of nominal variables and transform them into empirically valid real variables in accordance with long-run price homogeneity while preserving the (polynomially) cointegrating relations among the variables. After the transformation, I(1) model can be adopted directly in stead of more complicated I(2) analysis. Here I take the PPP related variables p t, p t and s t as example. The price level variables p t, p t are I(2) and therefore their differences, inflation variables p t, p t are I(1). Given all other initial variables are I(1), a common stochastic trend of the price variables and possibly with combination of other variables are needed to make them cointegrated into I(1). Based on economic theories and long-run price homogeneity, the relative 16

17 prices (p t p t ) I(1) and purchasing power parity (p t p t s t ) I(1) are needed to be tested. 5 Data Analysis in A Cointegrated VAR Model In this section, I start the cointegration analysis, first with 5 main variables to find the basic information of long-run parities, then with 7 main variables to explore more detailed information of short-run and long-run intervention effects and finally with one more variable to analyze specualtive sentiment effects. The choice of relevant variables is verified in the I(2) model through nominal-to-real transformations where PPP is rejected but PP not. With the consideration of weak exogeneity of nominal exchange rate variable, I present the long-run structure based on the information from the parity tests and unrestricted Π information. Furthermore, a short-run adjustment model is provided. In the end, the results of the cointegration analysis are interpreted with focuses on the foreign interventions. The software packages, Cats in Rats (Dennis et al. 2005) and PcGive are used to analyze the data. 5.1 Data Analysis in the Intervention Model Based on the specific-to-general principle of choosing } variables, I start with the variable vector {s t, p t, p t, i b,t, i b,t, CI, CI. The price variables are also included because of their close relationship with the nominal exchange rate. The long-term interest rates, instead of short-term interest rates, are chosen because they are more informative in terms of long-run movements of exchange rates. The relations relevant with the long-term movements in the exchange rates are investigated first with further short-term information added through short-term interest rates. The intervention variables CI and CI are assumed to be weakly exogenous because they are set by the monetary authorities and not pushed by other macroeconomic variables. There are some I(2) signals in the model in line with the data illustration of price variables. Hence nominal-to-real transformations are conducted by first testing whether relative price, (p t p t ), and PPP, (p t p t s t ), are I(1). Although a necessary condition for (p t p t s t ) I(1) is that s t is I(2) and cointegrated with (p t p t ), I test whether it holds true given its theoretical and empirical importance. Based on a rank test of the I(2) model, the number of rank is set to be 3 with one I(1) stochastic trend and one I(2) stochastic trend. After imposing the rank condition, I test whether the parity conditions are acceptable in all cointegrating relations in the I(2) model based on Johansen and Luetkepohl (2005). The results are mixed: the relative price (p t p t ) 6 I(1) is not rejected with p-value 0.09, but (p t p t s t ) I(1) is clearly rejected with p-value In order to consider the intervention effects on the domestic inflation levels, p t I(1) is also included. Hence my empirical analysis after 6 Later pp t will be used to stand for (p t p t ). 17

18 Table 1: Estimated Effects of Outliers and Weakly Exogenous Interventions Dp 95:08 Dp 97:04 Dp 98:10 Dp 98:12 Dp 03:07 Dp 05:09 Ds 97:04 I I pp t 0.01 [4.74] 0.01 [2.17] 0.01 [ 4.21] 0.01 [3.80] 2 p t 0.02 [6.34] s t 0.12 [4.75] 0.01 [3.09] 0.14 [ 5.71] 0.00 [2.26] 0.07 [ 2.78] i b,t 0.00 [6.04] [3.84] i b,t [3.82] [ 2.00] [3.72] t-values in brackets, indicates a t-value 2.0. Only significant values are shown here [2.69] nominal-to-real transformations is based on the following variable vector: { ppt, p t, s t, i b,t, i b,t, CI, CI } I(1) (22) Based on the maximal value of the likelihood function with an additional penalizing factor related to the number of estimated parameters, the Schwartz and the Hannan-Quinn information criteria suggest the number of lags to be k = 2, which is enough for a quite rich dynamic structure even in a small dimensional { system. (Juselius, } 2006) Let vector X t = {X 1,t, X 2,t } where X 1,t = pp t, p t, s t, i b,t, i b,t, and sub-vector of weakly exogenous foreign intervention variables, X 2,t = {CI, CI }. My partial error correction representation of V AR(2) model becomes: X 1,t = Γ 1,1 X t 1 + α 1 β X t 1 + A 0 X 2,t + µ 0 + ΦD t + ε 1,t ε 1,t N 5 (0, Σ), t = 1991 : : 08 From the standard errors of five variable residuals, there are impulse dummies in 1995:08, 1997:04, 1998:10, 1998:12, 2003:07 and 2005:09, which are...,0,1,0,...dummies measuring permanent intervention shocks. In order to take account of the trend break in 1997:04, a new shift dummy is added in the cointegrating relations β X t 1, which is a...,0,1,1,1,...dummy restricted to be in the cointegration space measuring a shift of the cointegration mean. From the statistics of the Table 1, all the dummy variables significantly affect at least one main variable, which means all of them should be included in the model. And the exchange interventions in Japan and US both significantly influence the nominal exchange rate. The effects of US foreign exchange interventions are modest while the effects of Japanese ones are relatively small. To check the statistical adequacy of the small model, some important multivariate and univariate misspecification test statistics are presented in the Table 2 with significant test statistics in bold face. Normality and no autocorrelation 18

19 are rejected in the multivariate level with p-values smaller than the critical value The former is mostly due to excess kurtosis in the interest rate equations. Given the cointegrated VAR model is robust to moderate AR effects and excess kurtosis, I continue with current model specification. The cointegration rank divides the variables into r relations towards which the system is adjusting (equilibrium errors which are the deviations from the steady state) and p r relations which are pushing the system (common driving trends in the model). Therefore, the conitegration rank indicates the effectiveness of adjustment of system. In order to determine the cointegration rank, the trace test statistics and the five largest roots of the characteristic polynomial are also reported in the Table 2. Trace test statistics suggest borderlinely accepting the rank number to be 4. However, combined with the above estimated characteristic roots and three stationary cointegration relations, the rank numberis set to be 3 although there is a big root left in the system. With the assistance of Cats mining procedure in Cats in Rats, the cointegrating structure in the Table 3 is not rejected with probability The first one representing a relative price relationship is given by: pp t = 0.92i b,t 0.00T 97: T rend + error term (23) The interpretation is that the relative price is nearly one-to-one positively related to the US bond rate with a long-run negative trend and some additional small but significant effects from the trend break in And the short-run adjustment of (5.3) is from the changes in the Japanese and US bond rates. The second cointegrating relation is about Japanese inflation rate: p t = 0.16pp t 0.00CI 0.00T rend + error term (24) where the domestic inflation rate is negatively related to the relative price with a small but significant trend and influences from the US interventions. The short-run adjustments come from the change of Japanese inflation rate with self-adjustment effects. The third vector, representing long-term bond rate differential, is given by: i b,t i b,t = 0.51pp t 0.00T 97: T rend + error term (25) The bond rate differential is negatively related to the relative price with a small but significant trend and trend break. From the information of relevant α vector, there is also self-adjustment of the bond rate differential. 5.2 The Extended Intervention Model In this section, after a I(2) cointegration test to find I(2) signals in the variables, I continue with a nominal-to-real transformation followed by the tests of the relative price and PPP conditions. In the I(1) analysis section, after misspecification tests and rank determination, a detailed long-run structure and short-run dynamics are presented. 19

20 Table 2: Tests for The Small Model Multivariate tests: Autocorrelation: LM 1 : χ 2 (25) = with p-value 0.01 LM 2 : χ 2 (25) = with p-value 0.02 Normality: χ 2 (10) = with p-value 0.03 Univariate tests: pp t 2 p t s t i b,t i b,t ARCH(2) Normality Skewness Kurtosis Trace tests r = 0 r = 1 r = 2 r = 3 r = 4 p-value Modulus of five largest roots r = r = r = I(2) Analysis and Nominal-to-real Transformation } Within the variable vector {s t, p t, p t, i b,t, i b,t, i m,t, i m,t, CI, CI, there exist I(2) signals in some variables, i.e. the price variables. After I(1) trace tests, the rank number can be either 3 or 4. When Xt I(2) and hence Xt I(1), it is not possible to remove all (near) unit roots from the model by reducing rank restriction on the matrix αβ. (Juselius, 2006) Therefore, when there are more than (p r) big roots, there is strong sign of I(2) features in the I(1) model. With two extra big roots in the Table 4 and rank test statistics in the Table 5, the I(2) model have four ranks, one I(1) trend and two I(2) trends. Furthermore, from the Table 6, the I(2) trends of the unrestricted I(2) model are as follows: In the long-run respective, the twice accumulated US short-term libor rate and long-term bond rate shocks are the main driving trends of the nominal exchange rates and the US price levels. This is to say that US central bank held the key of swings of real exchange rate between US and Japan. After imposing the rank condition, I continue with nominal-to-real transformations by testing whether the parity conditions with respect to price variables were acceptable in the I(2) model. By imposing restrictions into all vectors, I get similar mixed results as in the small model: Relative prices (p t p t ) I(1) are not rejected with p-value 0.052, while PPP (p t p t s t ) I(1) is rejected with p-value With the domestic inflation level p t I(1) included in the variable vector, my further empirical analysis after nominal-to-real transformation is based on the following vector: { ppt, p t, s t, i b,t, i b,t, i m,t, i m,t, CI, CI } I(1) (26) 20