1. Econ616 – Spring 2006 The Spillover Effects of Deposit Rate between Japan and the United States: a Bivariate GARCH Model Yan Hu

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

3. 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.

4. 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.

5. 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.

6. Multivariate Model  Y=βX H ij (t)=c ij +A ij H ij (t-1)+B ij u i (t)u j (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

7. Model

8. DATA  International Financial Statistics (IFS): 1.monthly deposit rate 2.money market rate 3.long-term government bond yield  The sample period is from January, 1982 to June, 2003.

9. Sample Description JapanUnited States No. of Observations257257 Mean-0.015222-0.010345 Variance0.0339000.002972 Skewness-0.80832*** -0.88139*** Kurtosis20.69253*** 2.38460*** Jarque-Bera 4613.08790***94.16577*** LM(χ2)10.006345**24.390088*** Q(8)23.4962***7.7818 Q(16)65.6287***13.0858 Q(24)91.9187***16.7850

10. Empirical Results R1,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)

11. 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 = 0 2.H3: α21 = α22 = α23 = 0

12. 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;

13. 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 T-stat = -3.95*** T-stat = -0.13

14. 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.

15. Future Research  Include more countries into the model: multivariate GARCH model.  Compare the deposit rate transmission with other interest rate transmission.