Choice of Main Variables

The relevant variables is chosen through Nominal-To-Real transformations, and misspeci…cation and rank tests. The software package, Cats in Rats (Dennis et al. 2005) is used to analyse our data.

Basic Model Setup

Based on the ‘speci…c-to-general’ principle of choosing variables, we start with a basic variable vector ^st, ^pt, ^p?_t,ⁱb;t,ⁱ_b;t,^CIt,^CI_t . The price variables are 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 intervention variables^CItand^CI_t are tested to be weakly exogenous with probability 0.64, which support the idea that interventions are set by the monetary authorities and not pushed by other macroeconomic variables.

There are some I(2) signals in the model related to price variables. Hence, Nominal-To-Real transformations are conducted by …rst testing whether rel-ative price ^(p_t ^p?_t⁾, and real exchange rate ^(p_t ^p?_t ^st)¹³ are I(1). A necessary condition for ppp_t I(1) is that s_t is I(2) and cointegrated with pp_t. We test whether the condition holds true given its theoretical and empirical impor-tance.

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, we test whether the PPP condition is acceptable in all cointegration relations of the I(2) model based on Johansen and Luetkepohl (2005). The results are mixed: the relative price ^pp_t ^I(1) was not rejected with a p-value of 0.09, but ppp_t I(1) was clearly rejected with a p-value of 0.00.

13Later pp_tand ppp_twill be used to stand for (p_t p^?_t) and (p_t p^?_t s_t) respectively.

Hence my empirical analysis after Nominal-To-Real transformations is based on the following variable vector

pp_t;4pt; s_t; i_b;t; i_b;t; CI_t; CI_t I(1); (3.34)

where _4pt I(1) is also included to consider the intervention e¤ects on the domestic in‡ation levels. Based on the ML function with an additional pe-nalising factor related to the number of estimated parameters, the Schwartz and the Hannan-Quinn information criteria suggest the number of lags k = 2, which is enough for a quite rich dynamic structure even in a small dimensional system (Juselius, 2006).

Let vector X_t = fX^1;t; X_2;tg where X_1;t= pp_t;4pt; s_t; i_b;t; i_b;t , and sub-vector of weakly exogenous foreign intervention variables, X2;t = fCI^t; CI_tg. Then our partial error correction representation of V AR(2) model becomes

4X1;t = _1;14Xt 1+ ₁ ⁰X_{t 1}+A₀4X2;t+ ₀+ D_t+"_1;t;

"_1;t N (0; ); t = 1991 : 04 2008 : 08:

Based on the standard residual errors, there are impulse dummies in Au-gust 1995, April 1997, October 1998, December 1998, July 2003 and Sep-tember 2005, which are ...,0,1,0,...dummies measuring permanent shocks. To take account of the trend-break e¤ects of the consumption tax hike in April 1997, a shift dummy is added into the cointegration relations ⁰X_{t 1}, which is a ...,0,1,1,1,...dummy measuring a mean shift of the cointegration relations.

To check the statistical adequacy of the small model, some important misspeci…cation test statistics are presented in Table 3.1¹⁴. We …nd that the normality¹⁵ and no autocorrelation are rejected at the multivariate level with

p-values smaller than 0.05. Given a cointegrated VAR model is robust to moderate AR e¤ects and excess kurtosis, we continue with the current model speci…cation.

14The signi…cant test statistics are in bold face.

15The non-normality is mostly due to excess kurtosis in the interest rate equations.

Table 3.1: Misspeci…cation and Rank Tests for the Basic Model Multivariate Test Results

Autocorrelation: LM1: ²(25) = 43:16 with p-value 0.01 LM2: ²(25) = 41:55 with p-value 0.02 Normality: ²(10) = 20:30 with p-value 0:03

Univariate Test Results

4pp^t 4²p_t 4s^t 4i^b;t 4ib;t

ARCH(2) 0:27 8:18 2:84 10:02 0:41 Normality 3:38 9:38 0:87 6:24 2:16 Skewness 0:04 0:50 0:04 0:00 0:24 Kurtosis 3:50 3:93 3:17 3:75 2:94 Trace tests r = 0 r = 1 r = 2 r = 3 r = 4

p-value 0:00 0:00 0:00 0:02 0:22 Modulus of Five Largest Roots

r = 4 1 0:85 0:85 0:62 0:31

r = 3 1 1 0:86 0:61 0:30

r = 2 1 1 1 0:63 0:28

The cointegration rank divides the variables into r relations towards which the system is adjusting and ^{p r} relations which are pushing the system. In order to determine the cointegration rank, the trace test statistics and the

…ve largest roots of the characteristic polynomial are reported in Table 3.1.

While the trace test statistics suggest borderlinely accepting the rank number to be 4, we set the rank number as 3, considering estimated characteristic roots.

I(2) Analysis and Nominal-To-Real Transformation

We examine potential I(2) features with the variable vector ^st; p_t; p^?_t; i_b;t; i_b;t; i_m;t; i_m;t; CI_t; CI_t

before conducting a cointegrated I(1) analysis. The I(1) trace tests of Ta-ble 3.2 suggest that the rank of the I(1) model can be either 3 or 4 with

Table 3.2: Rank Test Statistics under the I(1) Model Setup

I(1):Rank 0 1 2 3 4 5 6

p-value 0:00 0:00 0:00 0:06 0:17 0:23 0:26 Modulus of Five Largest Roots

r = 5 1 1 0:97 0:93 0:84 0:80 0:52

r = 4 1 1 1 0:97 0:89 0:83 0:50

r = 3 1 1 1 1 0:95 0:88 0:53

Table 3.3: Rank Test Statistics under the I(2) Model Setup

p r r s2 = 7 6 5 4 3 2 1 0

p-values in brackets. Only p-values 0.05 are shown here.

probability 0.06 and 0.17 respectively. However, based on the modulus of the largest roots, there exist two large roots for both rank r = 3or 4, which means that there might be some I(2) features in the model. In order to con…rm the existence of the I(2) features, we implement further rank tests for the I(2) model and present the test statistics in Table 3.3. With a p-value of 0.11, we can not reject the I(2) set-up of rank r = 4 with one I(1) trend and two I(2) trends.

As the price variables are I(2) processes, Nominal-To-Real transformations are needed to reduce their integration order. By imposing restrictions on all vectors, we …nd that the relative price pp_t I(1) is not rejected with a p-value

Table 3.4: Misspeci…cation and Rank Tests for the Extended Model Multivariate Test Results

Autocorrelation: LM1: ²(49) = 73:01 with p-value 0.02 LM2: ²(49) = 61:01 with p-value 0.12 Normality: ²(10) = 150:91 with p-value 0:00

Univariate Test Results

4pp^t 4²p_t 4s^t 4i^b;t 4ib;t 4i^m;t 4im;t

ARCH(2) 0:06 8:05 5:60 10:22 0:75 1:19 11:63 Normality 2:26 5:32 2:80 6:07 1:91 108:2 20:9

Skewness 0:01 0:36 0:15 0:03 0:23 0:22 0:85 Kurtosis 3:38 3:53 3:41 3:74 3:02 8:29 4:26 Trace tests r = 0 r = 1 r = 2 r = 3 r = 4 r = 5 r = 6

p-value 0:00 0:00 0:00 0:00 0:18 0:29 0:18 Modulus of Five Largest Roots

r = 5 1 1 0:94 0:94 0:82 0:55 0:34

r = 4 1 1 1 0:95 0:88 0:56 0:37

r = 3 1 1 1 1 0:91 0:60 0:33

of 0.052, while ^ppp_t ^I(1) is rejected with a p-value of 0.00. Therefore, we include the domestic in‡ation level _4pt I(1) in the variable vector, which becomes

pp_t;4pt; s_t; i_b;t; i_b;t; i_m;t; i_m;t; CI; CI I(1): (3.35)

The Unrestricted Extended I(1) Model and Rank Tests

After de…ning the main variables, we conduct the misspeci…cation and rank tests for the structure of the extended model and summarise the related results in Table 3.4.

At the multivariate level, the p-values of the LM tests with respect to the second order residual autocorrelations is 0.30, which indicates no signi…cant second autocorrelation in my model. However, at the univariate level, there are some ARCH e¤ects in the variables of the Japanese in‡ation and bond rates, and the US libor rate. From the results of normality tests, there is no normality at the multivariate level with a p-value of 0.0. The …nding is supported by the …ndings at the univariate level that there are signi…cant non-normality in the variables of the Japanese bond rate and US interest rate variables, and excess kurtosis in the libor rate variables. Nevertheless, the extended model shows much better validity than the basic model and is adopted given the robustness of the cointegrated VAR model.

From the rank test statistics and modulus of seven largest roots, the rank of my model is set as 4 with a p-value of 0.18. This means the inclusion of libor rates adds one more long-run stationary relation into the extended model.

Summary

This section sets up our main model. In the following sections, we will test the e¤ects of currency intervention and speculation on the long-term parity conditions and the e¤ectiveness of speci…c transmission channels.