Is the PPP valid for the EA-11 countries? New evidence from nonlinear unit root tests

Figures & data

Table 1. Results of unit root test for US dollar rates.

Country	Trendp-value	Intercept			Intercept and time trend
		No. of lags	KSS	ADF	No. of lags	KSS	ADF
Austria	0.000	1	−1.838	−1.241	1	−2.390	−2.332
Belgium	0.000	6	−1.799	−1.318	6	−2.181	−2.344
Finland	0.000	1	−1.827	−1.207	1	−2.338	−2.239
France	0.000	1	−1.912	−1.235	1	−2.499	−2.469
Germany	0.000	1	−1.834	−1.200	1	−2.379	−2.397
Ireland	0.000	1	−1.803	−1.228	1	−2.054	−2.621
Italy	0.000	1	−1.905	−1.321	1	−2.466	−2.505
Luxembourg	0.000	1	−1.852	−1.451	1	−2.486	−2.354
Netherlands	0.000	1	−1.811	−1.225	1	−2.130	−2.450
Portugal	0.000	1	−1.873	−1.343	1	−2.278	−2.576
Spain	0.000	1	−1.840	−1.442	1	−2.371	−2.554

Notes: The number of lags in the auxiliary regression is defined as the minimal number that removes residual autocorrelation. The 1, 5 and 10% asymptotic critical values for ADF with intercept are –3.46, –2.88 and –2.57, respectively. The 1, 5 and 10% asymptotic critical values for ADF with intercept and trend are –4.01, –3.43 and –3.14, respectively. The 1, 5 and 10% asymptotic critical values for KSS with intercept are –3.48, –2.93 and –2.66, respectively. The 1, 5 and 10% asymptotic critical values for KSS with intercept and trend are –3.93, –3.40 and –3.13, respectively. The critical values for KSS are taken from Kapetanios et al. (2003).

Table 2. Results of unit root test for Japanese yen rates.

Country	Trendp-value	Intercept			Intercept and time trend
		No. of lags	KSS	ADF	No. of lags	KSS	ADF
Austria	0.000	1	−0.426	−0.753	1	−2.167	−1.443
Belgium	0.000	4	0.102	−0.258	4	−1.983	−1.035
Finland	0.000	1	−0.466	−0.723	1	−2.153	−1.328
France	0.000	1	−0.516	−0.820	1	−2.256	−1.512
Germany	0.000	1	−0.639	−0.846	1	−2.073	−1.448
Ireland	0.000	1	−0.895	−0.965	1	−2.598	−1.869
Italy	0.000	1	−0.486	−0.756	1	−2.316	−1.566
Luxembourg	0.000	4	0.392	−0.056	4	−1.996	−1.078
Netherlands	0.000	1	−0.645	−0.832	1	−2.492	−1.572
Portugal	0.000	1	−0.263	−0.632	1	−2.346	−1.560
Spain	0.000	1	−0.366	−0.645	1	−2.397	−1.667

Notes: The number of lags in the auxiliary regression is defined as the minimal number that removes residual autocorrelation. The 1%, 5% and 10% asymptotic critical values for ADF with intercept are –3.46, –2.88 and –2.57, respectively. The 1%, 5% and 10% asymptotic critical values for ADF with intercept and trend are –4.01, –3.43 and –3.14, respectively. The 1%, 5% and 10% asymptotic critical values for KSS with intercept are –3.48, –2.93 and –2.66, respectively. The 1%, 5% and 10% asymptotic critical values for KSS with intercept and trend are –3.93, –3.40 and –3.13, respectively. The critical values for KSS are taken from Kapetanios et al. (2003).

Table

	AT_USD	BE_USD	DE_USD	ES_USD	FI_USD	FR_USD	IE_USD	IT_USD	LU_USD	NL_USD	PT_USD
Mean	0.163812	0.162578	0.161686	0.179019	0.152618	0.169824	0.197911	0.172500	0.175009	0.181082	0.183485
Median	0.197774	0.200057	0.197595	0.199073	0.189578	0.196560	0.213375	0.194628	0.201424	0.195978	0.197598
Max	0.508154	0.494964	0.504447	0.470881	0.513180	0.510106	0.491579	0.502598	0.475364	0.525764	0.495789
Min	−0.179245	−0.180007	−0.190551	−0.122313	−0.211162	−0.170942	−0.132735	−0.153948	−0.143244	−0.173726	−0.137607
Std. Dev.	0.185549	0.178332	0.193273	0.150557	0.195774	0.184691	0.166520	0.171786	0.156353	0.181510	0.164202
Skewness	−0.292760	−0.347120	−0.271234	−0.419035	−0.307485	−0.252556	−0.313543	−0.299953	−0.413041	−0.276773	−0.321523
Kurtosis	1.949599	2.054325	1.880635	2.310424	1.945795	1.933170	2.185696	2.077193	2.265751	2.079748	2.181856

Table

	AT_YEN	BE_YEN	DE_YEN	ES_YEN	FI_YEN	FR_YEN	IE_YEN	IT_YEN	LU_YEN	NL_YEN	PT_YEN
Mean	4.896205	4.897887	4.892043	4.923217	4.886271	4.902149	4.943409	4.911372	4.915072	4.920922	4.926767
Median	4.923701	4.927598	4.919582	4.932254	4.912400	4.924481	4.925670	4.923708	4.934621	4.922301	4.927560
Max	5.218921	5.234801	5.196223	5.309191	5.209846	5.224337	5.340339	5.262156	5.284495	5.287022	5.302806
Min	4.462798	4.450512	4.482004	4.447832	4.446623	4.478970	4.530526	4.461659	4.429349	4.493599	4.459996
Std. Dev.	0.163804	0.171894	0.157177	0.191247	0.169465	0.160866	0.182767	0.175885	0.184635	0.174447	0.182418
Skewness	−0.437468	−0.433336	−0.416966	−0.232825	−0.357334	−0.393090	0.194355	−0.308005	−0.404806	−0.101648	−0.119666
Kurtosis	2.509661	2.559432	2.386007	2.709038	2.304845	2.490800	2.455292	2.573954	2.773989	2.383257	2.630954

Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112, 359–379. 10.1016/S0304-4076(02)00202-6

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