The long-run validity of PPP in some major advanced and emerging countries using alternative models

Figures & data

Table 1. Coefficient of variation of the variables

Country	RER	EXR	Pd	Pd/Pf	Skewness	Kurtosis	Jarque-Bera
PANEL A
Canada	0.6580	0.5470	0.0656	0.0114	0.2049^a	2.2266^z	14.9706^a
Denmark	0.0865	0.0950	0.0657	0.0117	0.9010^a	3.3242^z	65.5132^a
Euro	0.0922	0.1119	0.0187	0.0091	0.3213^a	1.9294^a	15.6566^a
Japan	0.0418	0.0630	0.0171	0.0601	−0.0091	2.3975^a	7.0995^b
Norway	0.0728	0.0781	0.0779	0.0160	0.4158^a	2.2056^a	25.8487^a
Sweden Switzerland	0.0963 0.9638	0.0907 0.8917	0.0741 0.0402	0.0214 0.0361	−0.1004 0.7819^a	2.4059^a 3.5135^a	7.6867^b 52.9365^a
UK	0.1150	0.1031	0.0787	0.0112	0.7956^a	4.0781^a	72.1926^a
Algeria	0.1203	0.3463	0.2754	0.2190	−0.8213^a	2.0561^a	70.1427^a
Cote d’Ivoire	0.0328	0.0520	0.1133	0.0444	−0.1230	2.6965^a	2.9834
Egypt	0.1211	0.4513	0.3110	0.2532	0.5109^a	2.5633^a	24.1311^a
Mauritius	0.0363	0.1373	0.1758	0.1068	−0.6600^a	4.1884^a	61.6500^a
Morocco	0.0609	0.0889	0.0877	0.0239	−1.2714^a	6.9731^a	434.8390^a
Nigeria	0.1166	0.5029	0.5740	0.5370	−0.6492^a	2.2403^a	44.2192^a
South Africa	0.0711	0.3459	0.2391	0.1787	0.4282^z	2.8655^a	14.6873^a
PANEL B
Canada	0.0996	0.0658	0.0655	0.0514	1.1076^a	3.0469^a	95.9352^a
Denmark	0.1273	0.0751	0.0657	0.0517	1.0158^a	3.8799^a	95.7810^a
Euro area	0.0367	0.0273	0.0187	0.0181	−0.6441^a	2.6367^a	17.9882^a
Norway	0.1777	0.1103	0.0779	0.0637	1.0959^a	3.5012^a	98.7860^a
Sweden	0.2007	0.1346	0.0741	0.0591	1.1964^a	3.5235^a	117.2370^a
Switzerland	0.0470	0.0371	0.0402	0.0250	0.5637^a	2.9970^a	24.8384^a
UK	0.1211	0.0716	0.0787	0.0643	0.7882^a	2.7340^a	49.9475^a
Algeria	1.0885	1.0512	0.2754	0.2646	0.7235^a	1.8824^a	65.3253^a
Cote d’Ivoire	−1.0779	−0.4237	0.1133	0.1000	0.6768^a	1.9584^a	57.0077^a
Egypt	0.4554	0.2750	0.3110	0.3010	0.3704^b	2.1963^a	23.3477^a
Mauritius	0.5226	0.3795	0.1758	0.1636	0.4957^a	2.0175^a	38.0711^a
Morocco	0.2366	0.1580	0.0877	0.0733	1.4005^a	4.1074^a	177.2750^a
Nigeria	1.2377	1.5070	0.5740	0.5695	0.4406^a	1.7487^a	45.7717^a
South Africa	0.4407	0.2801	0.2391	0.2278	0.6243^a	2.2468^a	41.5484^a

Note: a, b and c indicate statistical significance at 1%, 5% and 10% respectively. Columns RER, EXR, Pd, and Pd/Pf are in logged terms and relate to the real exchange rate, the nominal exchange rate, the domestic prices, and the price ratio respectively.

Table 2. ADF and PP Unit Root Test for Mean stationery of RERs of 468 Obs

Country	ADF Constant and Constant and Trend		PP Constant and Constant and Trend
	Constant	Constant and Trend	Constant	Constant and Trend
PANEL A
Canada	−1.5022	−1.5346	−1.4265	−1.4574
Denmark	−2.1721	−2.3901	−2.3251	−2.5750
Euro	−1.9482	−1.9805	−1.9505	−1.9833
Japan	−1.7129	−1.7890	−1.8766	−1.9850
Norway	−2.2488	−2.2511	−2.3683	−2.3701
Sweden	−2.0918	−2.2915	−2.3242	−2.5811
Switzerland	−2.2523	−2.7821	−2.2523	−2.8500
UK	−2.1663	−2.1168	−2.2903	−2.2406
Algeria	−1.5079	−1.4813	−1.5162	−1.6045
Cote d’Ivoire	−2.9591^b	−2.8785	−2.9598^b	−2.8806
Egypt	−2.5739^c	−2.5215	−2.5061	−2.4029
Mauritius	−3.2431^b	−3.0703	−3.2424^b	−3.0682
Morocco	−4.3219^a	−4.0658^a	−4.3100^a	−4.0789^a
Nigeria	−2.1845	−1.9405	−2.2457	−2.0601
South Africa	−2.3991	−2.4510	−2.4792	−2.5244
Stationary #	4	1	2	1
PANEL B
Canada	−2.2645	−2.2947	−2.2513	−2.3353
Denmark	−3.6805^a	−3.6192^b	−3.6127^a	−3.6309^b
Euro	−1.8194	−1.7652	−1.8803	−1.9128
Norway	−3.1027^b	−3.0357	−2.9939^b	−3.0439
Sweden	−3.6231^a	−2.7230	−3.3894^b	−2.7222
Switzerland	−2.9621^b	−2.3859	−2.9735^b	−2.4149
UK	−2.5526	−1.9662	−2.4474	−2.0297
Algeria	−2.2141	−0.3691	−2.2361	−0.2900
Cote d’Ivoire	−2.5880^c	−1.7730	−2.5195	−1.8480
Egypt	−0.4794	−1.5331	−0.4867	−1.4455
Mauritius	−3.4015^b	−1.1017	−3.5385^a	−1.0490
Morocco	−4.8054^a	−3.0267	−4.6831^a	−2.9934
Nigeria	−1.2685	−0.6159	−1.1854	−0.8386
South Africa	−2.6023^c	−1.3289	−2.6357^c	−1.3219
Stationary #	8	1	7	1

Note: a, b and c indicate statistical significance at the 1%, 5% and 10%, respectively.

Table 3. Estimation results of Time Varying-Cointegration Coefficients for CPI

Country	Coefficients results of TVC	$R^2/adj{R}^2$ of CCC cointegration estimation
Panel A
Canada	84.604	0.997/0.997
Denmark	11.083	0.984/0.983
Euro	91.889	0.988/0.987
Japan	15.506	0.994/0.994
Norway	38.029	0.996/0.996
Sweden	38.337	0.991/0.991
Switzerland	29.973	0.998/0.998
United Kingdom	24.671	0.998/0.995
Algeria	.071	0.987/0.986
Cote d’Ivoire	32.480	0.960/0.959
Egypt	64.557	0.971/0.971
Mauritius	74.731	0.973/0.972
Morocco	22.818	0.945/0.943
Nigeria	16.917	0.969/0.967
South Africa	36.213	0.985/0.985
Panel B
Canada	97.138	0.996/0.995
Denmark	38.024	0.881/0.879
Euro	28.962	0.987/0.986
Japan	n/a	n/a
Norway	35.695	0.996/0.996
Sweden	69.175	0.985/0.984
Switzerland	19.323	0.995/0.995
United Kingdom	25.795	0.998/0.998
Algeria	42.640	0.984/0.983
Cote d’Ivoire	21.544	0.987/0.984
Egypt	81.254	0.825/0.824
Mauritius	78.571	0.916/0.915
Morocco	37.454	0.949/0.948
Nigeria	17.782	0.955/0.954
South Africa	13.196	0.980/0.980

Table 4. Estimation results of Time Varying-Cointegration Coefficients

Country	Coefficients results of TVC	$R^2/adj.R^2$of CC cointegration estimation
Panel A
Canada	. 938	−1.183/-1.197
Denmark	−11.444	0.044/0. 038
Euro	−27.437	0.397/0. 390
Japan	−17.286	0.736/0.734
Norway	43.412	−0.244/-0.252
Sweden	−42.065	0.025/0.018
Switzerland	44.511	0.753/0.752
United Kingdom	20.621	−0.447/-0.457
Algeria	3.813	0.982/0.982
Cote d’Ivoire	−7.311	0.657/0.655
Egypt	8.141	0.837/0.836
Mauritius	4.757	0.935/0.935
Morocco	56.404	0.544/0.541
Nigeria	0.960/0.959	−12.101
South Africa	12.375	0.927/0.927
Panel B
Canada	105.962	0.741/0.740
Denmark	107.883	0.649/0.647
Euro	.835	−0.058/-0.071
Japan	n/a	n/a
Norway	66.203	0.844/0.843
Sweden	138.479	0.784/0.783
Switzerland	469.357	0.255/0.250
United Kingdom	150.753	0.786/0.785
Algeria	40.101	0.970/0.970
Cote d’Ivoire	93.721	0.754/0.753
Egypt	8.559	0.949/0.949
Mauritius	94.710	0.954/0.953
Morocco	163.846	0.896/0.895
Nigeria	60.146	0.904/0.904
South Africa	17.161	0.975/0.975

Table 5. Hurst exponents of the real exchange rate in absolute form

Country	Hurst exponents US as base	Hurst exponents Japan as base
Canada	0.8122	0.8409
Denmark	0.7832	0.8225
Euro	0.8052	0.8346
Japan	0.8330	n/a
Norway	0.7707	0.8394
Sweden	0.7952	0.8341
Switzerland	0.7727	0.8264
United Kingdom	0.8196	0.8451
Algeria	0.8620	0.8575
Cote d’Ivoire	0.7904	0.8402
Egypt	0.7765	0.8578
Mauritius	0.8004	0.8446
Morocco	0.7204	0.8356
Nigeria	0.8064	0.8488
South Africa	0.7943	0.8457

Table 6. Johansen’s trace and maximal eigenvalue test statistics for the cointegration of countries in the study using the US as a base

Unrestricted cointegration rank test (trace) Null hypothesis: the number of cointegrating vectors is less than or equal to r Alternative hypothesis: there are more than r cointegrating vectors Panel A						Unrestricted cointegration rank test (maximum eigenvalue) Null hypothesis: the number of cointegrating vectors is r Alternative hypothesis: there are (r + 1) cointegrating vectors Panel B
Country	Hypothesised Null Alternative	Eigenvalue	Trace Statistics	0.05 Critical val.	VAR	Hypothesised Null Alternative	Eigenvalue	Max-eigenvalue Statistics	0.05 Critical value	VAR
Canada	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.155 0.008 0.005	85.015^a 6.443 2.480	29.797 15.495 3.841	2	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.155 0.008 0.005	78.573^a 3.963 2.480	21.132 14.265 3.841	2
Denmark	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.185 0.031 0.013	115.847^a 20.857^b 5.988^c	29.797 15.495 3.841	3	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.185 0.031 0.013	94.989^a 14.869^b 5.988^c	21.132 14.265 3.841	3
Euro Area	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.124 0.024 0.012	40.175^a 8.719 2.894	29.797 15.495 3.841	2	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.124 0.024 0.012	31.455^a 5.825 2.894	21.132 14.265 3.841	2
Japan	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.075 0.029 0.005	52.099^a 15.999^b 2.128	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.075 0.029 0.005	36.100^a 13.871 2.128	21.132 14.265 3.841	4
Norway	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.092 0.027 0.010	61.761^a 17.352^b 4.795^c	29.797 15.495 3.841	7	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.092 0.027 0.010	44.409^a 12.557 4.795	21.132 14.265 3.841	7
Sweden	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.071 0.024 0.003	46.655^a 12.647 1.278	29.797 15.495 3.841	7	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.071 0.024 0.003	34.008^a 11.369 1.278	21.132 14.265 3.841	7
Switzerland	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.053 0.019 6.25E–05	34.050^a 8.704 0.029	29.797 15.495 3.841	7	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.053 0.019 6.25E–05	25.346^a 8.675 0.029	21.132 14.265 3.841	7
UK	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.064 0.018 0.003	40.351^a 9.952 1.613	29.797 15.495 3.841	7	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.064 0.018 0.003	30.398^a 8.339 1.613	21.132 14.265 3.841	7
Algeria	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.067 0.031 0.004	48.756^a 16.614^b 1.913	29.797 15.495 3.841	2	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.067 0.031 0.004	32.142^a 14.701^b 1.913	21.132 14.265 3.841	2
Cote d’Ivoire	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.068 0.020 0.009	46.208^a 13.602 4.268^c	29.797 15.495 3.841	2	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.068 0.020 0.009	32.607^a 9.334 4.268^c	21.132 14.265 3.841	2
Egypt	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.057 0.012 8.98E–05	32.932^a 5.799 0.042	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.057 0.012 8.98E–05	27.133^a 5.758 0.042	21.132 14.265 3.841	4
Mauritius	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.077 0.022 0.014	54.444^a 16.975^b 6.558^c	29.797 15.495 3.841	3	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.077 0.022 0.014	37.469^a 10.418 6.558^c	21.132 14.265 3.841	3
Morocco	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.092 0.034 0.006	63.024^a 18.780^b 2.821	29.797 15.495 3.841	8	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.092 0.034 0.006	44.244^a 15.959^b 2.821	21.132 14.265 3.841	8
Nigeria	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.069 0.020 0.012	47.667^a 14.617 5.421^c	29.797 15.495 3.841	3	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.069 0.020 0.012	33.051^a 9.196 5.421^c	21.132 14.265 3.841	3
South Africa	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.091 0.016 0.006	54.108^a 10.187 2.613	29.797 15.495 3.841	5	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.091 0.016 0.006	43.921^a 7.573 2.613	21.132 14.265 3.841	5

Note: **MacKinnon-Haug-Michelis (1999) p-values

Table 7. Johansen’s trace and maximal eigenvalue test statistics for the cointegration of countries in the study using Japan as a base

Unrestricted cointegration rank test (trace) Null hypothesis: the number of cointegrating vectors is less than or equal to r Alternative hypothesis: there are more than r cointegrating vectors Panel A						Unrestricted cointegration rank test (maximum eigenvalue) Null hypothesis: the number of cointegrating vectors is r Alternative hypothesis: there are (r + 1) cointegrating vectors Panel B
Country	Hypothesised Null Alternative	Eigenvalue	Trace Statistics	0.05 Critical val.	VAR	Hypothesised Null Alternative	Eigenvalue	Max-eigenvalue Statistics	0.05 Critical value	VAR
Canada	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.102 0.054 0.002	76.761^a 26.674^b 0.994	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.102 0.054 0.002	50.087^a 25.680^b 0.994	21.132 14.265 3.841	4
Denmark	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.192 0.041 0.003	119.612^a 20.846^b 1.302	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.192 0.041 0.003	98.765^a 19.544^b 1.302	21.132 14.265 3.841	4
Euro Area	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.112 0.025 0.008	36.074^a 8.005 1.937	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.112 0.025 0.008	28.069^a 6.068 1.937	21.132 14.265 3.841	4
Norway	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.095 0.034 0.002	62.669^a 16.866^b 0.828	29.797 15.495 3.841	8	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.095 0.034 0.002	45.803^a 16.038^b 0.828	21.132 14.265 3.841	8
Sweden	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.159 0.060 0.010	113.982^a 33.491^b 4.619^c	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.159 0.060 0.010	80.491^a 28.872^b 4.619^c	21.132 14.265 3.841	4
Switzerland	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.048 0.033 0.008	42.068^a 19.522^b 3.894^c	29.797 15.495 3.841	7	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.048 0.033 0.008	22.546^a 15.628^b 3.894^c	21.132 14.265 3.841	7
UK	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.057 0.024 0.002	39.539^a 12.359 1.051	29.797 15.495 3.841	8	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.057 0.024 0.002	27.180^a 11.309 1.051	21.132 14.265 3.841	8
Algeria	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.056 0.054 0.031	67.038^a 40.191^b 14.513^c	29.797 15.495 3.841	5	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.056 0.054 0.031	26.847^a 25.678^b 14.513^c	21.132 14.265 3.841	5
Cote d’Ivoire	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.116 0.022 0.014	73.775^a 16.734^b 6.394^c	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.116 0.022 0.014	57.041^a 10.340 6.394^c	21.132 14.265 3.841	4
Egypt	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.081 0.020 0.003	49.970^a 10.831 1.349	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.081 0.020 0.003	39.139^a 9.483 1.349	21.132 14.265 3.841	4
Mauritius	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.100 0.030 0.011	68.230^a 19.295^b 5.297^c	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.100 0.030 0.011	48.935^a 13.998 5.297^c	21.132 14.265 3.841	4
Morocco	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.066 0.016 0.007	42.138^a 10.762 3.244	29.797 15.495 3.841	8	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.066 0.016 0.007	31.376^a 7.518 3.244	21.132 14.265 3.841	8
Nigeria	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.043 0.027 0.016	40.404^a 20.166^b 7.587^c	29.797 15.495 3.841	8	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.043 0.027 0.016	20.238 12.578 7.587^c	21.132 14.265 3.841	8
South Africa	r = 0 r ≥ 1 r ≤1 r ≥ 2 r ≤2 r ≥ 3	0.091 0.074 0.014	86.456^a 42.112^b 6.591^c	29.797 15.495 3.841	4	r = 0 r = 1 r = 1 r = 2 r = 2 r = 3	0.091 0.074 0.014	44.344^a 35.521^b 6.591^c	21.132 14.265 3.841	4

Note: **MacKinnon-Haug-Michelis (1999) p-value

Figure 1. Time-varying cointegration coefficient on the CPI using the US as a base country.

Figure 2. Time-varying cointegration coefficient on a foreign exchange using the US as a base country.

Figure 3. Time-varying cointegration coefficient on the CPI using Japan as a base country.

Figure 4. Time-varying cointegration coefficient on a foreign exchange using Japan as a base country.