Econ616 – Spring 2006

The Spillover Effects of Deposit Rate between Japan and the United States: a Bivariate GARCH Model

Yan Hu

Objective

To employ the bivariate GARCH methodology to investigate the deposit rate transmission and its volatility spillover effects between the United States and Japan.

Motivation Japan and the United States have strong

economies and different banking systems. The deposit rate transmission and spillover

effects are generally overlooked in the existing literature.

To examine the spillover effects of variables with time-varying conditional variances as well as covariance, academicians use the multivariate GARCH model.

Literature Review (1)

International linkages of interest rate among financial markets

--- Kirchgassner and Wolter(1987, 1993), Karfakis and Moschos (1990) and Fung and Lo (1995): examine international interest rate transmission primarily on conditional mean values, and find strong contemporaneous correlations and/or transmission of various interest rates.

Literature Review (2) Using Multivariate GARCH model to examine the spillover

effects of variables with time-varying conditional variances as well as covariance: --- Bollerslev (1990): the conditional volatility is lower and the coherence among exchange rates is higher in the post-EMS period. --- Hu, Jiang and Tsoukalas (2004): the volatility of log returns of European currencies had generally decreased.

Volatility spillover of economic variables --- Ross (1989): information transmission speed is more relevant to the conditional variance of an asset’s price changes.--- Kearney and Patton (2000): German mark plays a leading role in the transmission of volatility.

Multivariate Model Y=βX

Hij(t)=cij+AijHij(t-1)+Bijui(t)uj(t)

For bivariate, constant correlation:

BEK formulation (Engle and Kroner (1995)) directly imposes positive definiteness on the variance matrix:H(t)=C’C+B’u(t)u’(t)B+A’H(t-1)A

)()()( 221112 tHtHtH

Model

ttttttttt MMMMBYBYRRRR ,11,117,1161,115,1141,213,2121,11110,1

ttttttttt MMMMBYBYRRRR ,21,227,2261,225,2241,123,1221,22120,2

1,21321,1121,111110,11 tttt VOLhh

1,1232

1,2221,222120,22 tttt VOLhh

221112,12 hhh t

1,

,, log

ti

titi BYR

BYRBY

1,

,, log

ti

titi d

dR

1,

,, log

ti

titi MMR

MMRMM

DATA International Financial Statistics (IFS): 1. monthly deposit rate2. money market rate 3. long-term government bond yield

The sample period is from January, 1982 to June, 2003.

Sample DescriptionJapan United States

No. of Observations 257 257Mean -0.015222 -0.010345Variance 0.033900 0.002972Skewness -0.80832*** -0.88139***Kurtosis 20.69253*** 2.38460*** Jarque-Bera 4613.08790*** 94.16577***LM(χ2) 10.006345** 24.390088***Q(8) 23.4962*** 7.7818Q(16) 65.6287*** 13.0858Q(24) 91.9187*** 16.7850

Empirical ResultsR1,t = 0.0003 - 0.0316 R1,t-1 - 0.0634 R2,t - 0.0237 R2,t-1 + 0.1136 BY1,t (0.257) (-1.752)* (-2.775)*** (-1.106) (6.142)***

+0.0981 BY1,t-1 + 0.4310 MM1,t + 0.1596 MM1,t-1 (6.402)*** (40.640)*** (10.036)***

R2,t = 0.0006 - 0.1062 R2,t-1 -0.0049 R1,t + 0.0015 R1,t-1 + 0.4301 BY2,t (0.337) (-1.477) (-0.498) (0.166) (8.101)***- 0.003 BY2,t-1 + 0.6149 MM2,t + 0.3199 MM2,t-1 (-0.049) (14.380)*** (4.660)***

H11 = 0.0013 - 0.0012 h11,t-1 + 4.1837 ε21,t-1 - 0.000124 VOL2,t-1 (3.85)*** (-1.16) (6.08)*** (-3.95)***

H22 = 0.0004 + 0.3849 h22,t-1 + 0.3118 ε22,t-1 - 0.000002 VOL1,t-1 (3.08)*** ( 2.58)*** (2.62)*** (-0.13)

Hypothesis Test (1) 1. The basic bivariate GARCH

(1,1) model is appropriate:1. The basic bivariate GARCH

model is appropriate:H1: β11 = β12 = β13 = β14 = β15 = β16 = β17 = β21 = β22 = β23 = β24 = β25 = β26 = β27 = α11 = α12 = α13 = α21 = α22 = α23 = 0

2. The variance is constant for Japan and the United States, respectively:1. H2: α11 = α12 = α13 = 02. H3: α21 = α22 = α23 = 0

***51.3091220

***75.10023

***97.4223

Hypothesis Test (2) 2. Log difference of deposit

rate is transmitted at the mean level:

1. There are no spillover effects in the mean level between Japan and the United States:H10: β12 = β13 = β22 = β23 = 0

2. There is no spillover effect in the mean level from the United states to Japan:H11: β12 = β13 = 0

3. There is no spillover effect in the mean level from Japan to the United States:H12: β22 = β23 = 0;

*12.824

**10.822

28.022

Hypothesis Test (3) 3. There are deposit rate

volatility spillover effects:1. There is no deposit rate

volatility spillover between Japan and the United States:H13: α13 = α23 = 0

2. There is no deposit rate volatility spillover from the United States to Japan:H14: α13 = 0

3. There is no deposit rate volatility spillover from Japan to the United States:H15: α23 = 0

***59.1522

T-stat = -3.95***

T-stat = -0.13

Conclusion Bivariate GARCH (1,1) is appropriate for

analyzing the deposit rate transmission and volatility spillover effects.

The deposit rate of one country is affected by domestic long-term government bond yield and money market rate.

Both at the mean level and the volatility level, the deposit rate transmission is from the United States to Japan.

Future Research

Include more countries into the model: multivariate GARCH model.

Compare the deposit rate transmission with other interest rate transmission.