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Testing on Unbiased Expectation Hypothesis with Panel-VEC Model Fang Liu May 30,2003

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Unbiased Expectation Hypothesis Forward rate of asset is an unbiased predictor of expected future spot rate of this asset. general model: (1) Assumption risk-neutral investors rational Market behavior

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Literature Review: Group 1 Level model of UEH (2) VECM: cointegration model for and Hakkio and Rush (1998) Barnhart and Szakmary (1991) Hai, Mark and Yu (1997) VECM: cointegration model for and, and. Eric (1999)

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Literature Review: Group 2 Difference model of UEH (3) Panel approach: Frankel and Froot (1991) Some stylized results return of spot rate Forward premium

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Testing models Asset price VECM

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Case to illustrate Panel-VEC model JPY USD ITL

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Assumption of model Independent Long-run relationship Dependency in short-run relationship: adjustment speeds short-run relationships---lags

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Panel-VEC model General model

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Restricted model Panel-VEC model for testing UEH = +

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Panel cointegration test Johansen Likelihood Ratio (JLR) matrices are residual moment matrices from the VECM

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Empirical Result of JLR test Eigenvalue and JLR No. of CE(s)eigenvalueTrace statistic5% critical value 1% critical value None0.428167736.0218NA At most 1 0.401878 603.5603 NA At most 2 0.333064 481.7515 NA At most 3** 0.301078 385.7519277.71293.44 At most 4** 0.250177 300.8545233.13247.18 At most 5** 0.234673 232.6180192.89204.95 At most 6** 0.198578 169.2319156.00168.36 At most 7 0.176621 116.7679124.24133.57 JLRCritical valueAdjusted critical value -60.433363.544.014

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Decomposition of coefficient matrix of cointegration error term Decompose into two part: –Adjustment speed of deviation from long-run relationship = –Cointegration coefficients matrix

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Error term matrix Error term

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Cointegration vector Cointegration relationships Country1979.01-1998.121979.01-1988.121989.01-1998.12 Belgium (S.D) Canada (S.D) Germany (S.D) France (S.D) Italy (S.D) Japan (S.D) the United States (S.D) (1, -1.0018) (0.0021) (1, -0.9906) (0.0030) (1, -0.9909) (0.0017) (1, -1.0017) (0.0019) (1, -0.9962) (0.0024) (1, -0.9992) (0.0008) (1, -0.9919) (0.0025) (1, -0.9856) (0.0043) (1, -0.9952) (0.0031) (1, -1.0004) (0.0032) (1, -1.0062) (0.0034) (1, -0.9946) (0.0039) (1, -0.9975) (0.0013) (1, -0.9972) (0.0021) (1, -0.9895) (0.0034) (1, -0.9742) (0.0040) (1, -0.9873) (0.0050) (1, -0.9898) (0.0030) (1, -1.0141) (0.0029) (1, -1.0021) (0.0017) (1, -0.9831) (0.0055)

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Restricted model Panel-VEC model for testing UEH = +

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Empirical Result of Panel-VEC model Estimate of intercepts 1979.01-1998.121979.01-1988.121989.01-1998.12 Belgium (S.D) Canada (S.D) German (S.D) France (S.D) Italy (S.D) Japan (S.D) The United States (S.D) -0.000464 (0.00179) 0.000533 (0.00231) -0.001366 (0.00183) 0.0000232 (0.00179) 0.0013640 (0.00179) -0.002367 (0.00248) -0.001226 (0.00232) -0.000634 (0.00349) -0.000311 (0.00373) -0.001352 (0.00435) -0.01235 (0.00440) -0.003469 (0.00386) -0.003614 (0.00380) 0.000502 (0.00363) -0.000728 (0.00212) -0.000734 (0.00211) 0.002560 (0.00328) 0.002908 (0.00326) -0.000908 (0.00226) -0.000803 (0.00211) -0.001010 (0.00205)

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Slope Coefficients Estimate of slope coefficients 1989.01-1998.12 1979.01-1998.121979.01-1988.12 Belgium (S.D) Canada (S.D) Germany (S.D) France (S.D) Italy (S.D) Japan (S.D) The United States (S.D) 1.401537 (0.89853) 0.717169 (0.94798) 0.366510 (0.67193) -0.175033 (1.05144) 0.601968 (0.75359) 1.355498 (0.79537) -0.714788 (1.04414) 0.449535 (1.22496) 2.483825 (1.88851) 0.976440 (0.98098) 1.631622 (1.53168) 0.276975 (1.35159) 1.035106 (1.37280) -3.114742 (2.28451) -0.98531 0.0627 (1.66353) -1.478852 0.0335 (1.56252) 2.738813 0.0409 (1.40639) -4.964997 0.0424 (2.08171) 1.857054 0.0140 (0.77552) 2.787613 0.0559 (1.40052) 1.83016 0.0281 (1.58603)

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Cross-sectional dependency of adjustment speeds Two groups { BF, DMK, FRF, ITL} {USD, CAD, JPY} Significant relationship FRF BF, DMK, ITY DMK CAD, USD JPY CAD

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Dependency of short-run relationship Significant relationships JPY: BF DMK FRF ITY

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Conclusion Estimate of slope coefficient are not equal to unity although error terms are white noise. Therefore, forward rate is not unbiased predictor of expected spot rate, and UEH breaks down.

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