International Parity Conditions and Market Risk

Chiang, Thomas C.

doi:10.1007/978-1-4614-5360-4_7

Table A.1 Estimates of international parity conditions

From: International Parity Conditions and Market Risk

Country	β ₀	β ₁	R ²	DW	Joint test
A. Efficient interest-rate parity: \( {{s}_{{t + 1}}} - \left( {{{r}_t} - r_t^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0315	0.933^***	0.858	1.692	2.556
	(1.553)	(20.87)			(0.279)
FR	0.0452	0.975^***	0.934	1.848	1.558
	(1.128)	(43.14)			(0.459)
GM	0.0123	0.980^***	0.941	1.774	1.153
	(1.027)	(45.83)			(0.562)
SW	0.0162	0.958^***	0.993	1.721	3.065
	(1.678)	(40.19)			(0.216)
B. Efficient international-stock parity: \( {{s}_{{t + 1}}}\left( {{{R}_{{m,t + 1}}} - R_{{m,t + 1}}^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0281	0.943^***	0.857	1.716	3.100
	(1.359)	(20.68)			(0.212)
FR	0.0316	0.982^***	0.932	1.800	0.594
	(0.770)	(42.42)			(0.743)
GM	0.0097	0.984^***	0.939	1.747	0.667
	(0.800)	(45.37)			(0.716)
SW	0.0167	0.958^***	0.912	1.679	3.026
	(1.706)	(39.35)			(0.220)
C. Efficient purchasing power parity: \( {{s}_{{t + 1}}} - \left( {\Delta {{p}_{{t + 1}}} - \Delta p_{{t + 1}}^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0357^**	0.918^***	0.789	2.095	6.127
	(2.221)	(26.52)			(0.047)
FR	0.1003^*	0.945^***	0.853	2.317	3.677
	(1.833)	(30.59)			(0.159)
GM	0.0226	0.961^***	0.841	2.207	1.879
	(1.365)	(31.36)			(0.391)
SW	0.0160	0.954^***	0.857	2.088	1.823
	(1.264)	(28.22)			(0.402)
D. International Fama parity: \( \left( {\Delta {{p}_{{t + 1}}} - \Delta p_{{t + 1}}^{}} \right) = {{\beta }_0} + {{\beta }_1}\left( {{{r}_1} - r_t^{}} \right) + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0003	0.339	0.021	1.898	20.754
	(0.587)	(1.517)			(0.000)
FR	−0.0009^***	0.070	0.007	2.103	335.354
	(5.056)	(1.055)			(0.000)
GM	−0.0005^**	0.384^***	0.081	1.760	25.218
	(2.040)	(3.106)			(0.000)
SW	−0.0004	0.311^***	0.058	2.057	57.229
	(1.357)	(3.015)			(0.000)
E. Real interest-rate parity: \( {{\bar{r}}_{{t + 1}}} = {{\beta }_0} + {{\beta }_1}\bar{r}_{{t + 1}}^{*} + {{\varepsilon }_{{t + 1}}} \)
UK	0.0032^***	0.249	0.013	1.660	28.741
	(5.267)	(1.478)			(0.000)
FR	0.0032^***	0.217^**	0.028	1.014	91.299
	(9.547)	(2.092)			(0.000)
GM	0.0021^***	0.253^**	0.032	1.570	42.080
	(5.404)	(2.192)			(0.000)
SW	0.0012^***	0.263^***	0.035	1.869	57.168
	(3.958)	(2.672)			(0.000)
F. Equity-premium parity: \( {{R}_{{m,t + 1}}} - {{r}_t} = {{\beta }_0} + {{\beta }_1}\left( {R_{{m,t + 1}}^{} - r_t^{}} \right) + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0038^***	0.793^***	0.525	2.028	32.905
	(2.579)	(13.78)			(0.000)
FR	−0.0024	0.907^***	0.401	2.092	2.010
	(0.667)	(10.75)			(0.366)
GM	−0.0000	0.921^***	0.357	2.051	0.495
	(0.001)	(7.827)			(0.781)
SW	0.0021	0.937^***	0.477	1.957	0.639
	(0.650)	(9.600)			(0.726)
G. Covered interest rate parity: \( {{r}_t} - r_t^{*} = {{\beta }_0} + {{\beta }_1}\left( {{{f}_t} - {{s}_t}} \right) + {{\varepsilon }_t} \)
UK	0.0002	1.018^***	0.810	1.847	11.045
	(1.300)	(28.52)			(0.004)
FR	0.0001	1.025^***	0.887	2.015	8.607
	(0.997)	(56.17)			(0.014)
GM	0.0000	1.004^***	0.854	2.001	0.075
	(0.161)	(28.24)			(0.963)
SW	0.0000	0.988^***	0.830	1.679	0.144
	(0.124)	(25.63)			(0.931)
H. Unbiased forward-rate hypothesis I: \( {{f}_1} - {{s}_{{t + 1}}} = {{\beta }_0} + {{\beta }_1}\left( {{{f}_t} - {{s}_t}} \right) + {{\varepsilon }_{{t + 1}}} \)
UK	0.0007	0.510	0.001	1.737	0.127
	(0.217)	(0.369)			(0.938)
FR	0.0007	1.057	0.008	1.902	0.065
	(0.219)	(0.875)			(0.968)
GM	0.0005	1.210	0.010	1.818	0.064
	(0.184)	(1.007)			(0.969)
SW	0.0017	2.182^*	0.026	1.742	6.455
	(0.486)	(1.704)			(0.040)
I. Unbiased forward-rate hypothesis II: \( {{s}_{{t + 1}}} - {{s}_t} = {{\beta \prime}_0} + {{\beta \prime}_1}\left( {{{f}_t} - {{s}_t}} \right) + {{\varepsilon }_{{t + 1}}} \)
UK	−0.0007	0.490	0.001	1.737	0.881
	(0.287)	(0.372)			(0.644)
FR	−0.0007	−0.057	0.000	1.902	1.074
	(0.219)	(0.047)			(0.584)
GM	−0.0005	−0.210	0.000	1.818	1.042
	(0.184)	(0.175)			(0.594)
SW	−0.0017	−1.182	0.008	1.742	2.942
	(0.486)	(0.923)			(0.230)

a. The numbers in parentheses are absolute values of the t-statistics
b. The ^***, ^**, and ^*indicate statistically significant difference from zero at the 1%, 5%, and 10% levels for the t-ratios, respectively
c. DW denotes the Durbin-Watson statistic
d. The joint test is to test (β ₀ β ₁)′ = (0 1)′; the joint test is the statistics of the χ ² (2) distribution with 2 degrees of freedom and the numbers in parentheses are the significance levels

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