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Table 4 PANIC analysis of CPI inflation. Spanish Provinces. 1978.7–2014.4

From: The economic integration of Spain: a change in the inflation pattern

  No trend specification Trend specification
\( k \) \( {\text{ADF}}_{{\hat{e}}}^{c} (i) \) \( S_{{\hat{e}_{1} }}^{c} (i) \) \( k \) \( {\text{ADF}}_{{\hat{e}}}^{\tau } (i) \) \( S_{{\hat{e}_{1} }}^{\tau } (i) \) \( \frac{{\sigma (\Delta \hat{e}_{it} )}}{{\sigma (\Delta \pi_{it} )}} \) \( \frac{{\sigma (\lambda^{{\prime }}_{i} F_{t} )}}{{\sigma (\hat{e}_{it} )}} \)
Álava 5 −4.337*** 0.148 5 −5.455*** 0.057 0.523 3.665
Albacete 7 −3.058*** 0.293* 7 −4.592*** 0.109* 0.478 4.393
Alicante 8 −5.769*** 0.068 8 −5.884*** 0.042 0.425 4.434
Almería 4 −3.722*** 0.115 4 −4.311*** 0.087 0.607 3.418
Asturias 4 −2.763*** 0.091 4 −3.964*** 0.063 0.498 2.880
Ávila 1 −5.079*** 0.057 0 −5.082*** 0.042 0.556 3.218
Badajoz 0 −4.082*** 0.073 0 −4.335*** 0.062 0.426 4.715
Balears, Illes 5 −7.753*** 0.067 3 −8.751*** 0.061 0.521 4.964
Barcelona 0 −4.111*** 0.420** 1 −4.638*** 0.166** 0.538 4.125
Bizkaia 1 −1.824* 0.447** 3 −2.959** 0.159** 0.503 3.543
Burgos 2 −7.806*** 0.130 2 −8.060*** 0.063 0.529 5.359
Cáceres 1 −3.972*** 0.083 2 −4.041*** 0.064 0.485 3.707
Cádiz 5 −3.923*** 0.068 5 −4.791*** 0.068 0.531 5.720
Cantabria 7 −7.205*** 0.192 3 −7.666*** 0.124** 0.412 4.703
Castellón 2 −6.442*** 0.219 2 −6.403*** 0.062 0.591 4.561
Ciudad Real 0 −6.191*** 0.283* 0 −6.725*** 0.089 0.478 4.737
Córdoba 8 −5.243*** 0.186 0 −5.127*** 0.160** 0.375 4.572
Coruña, A 1 −2.781*** 0.122 1 −4.841*** 0.078 0.619 2.706
Cuenca 0 −4.685*** 0.101 0 −6.507*** 0.038 0.346 3.451
Gipuzkoa 2 −3.642*** 0.386** 2 −6.034*** 0.062 0.616 2.587
Girona 8 −4.414*** 0.119 8 −4.848*** 0.070 0.426 5.012
Granada 2 −5.377*** 0.046 5 −5.370*** 0.046 0.476 4.820
Guadalajara 4 −5.199*** 0.101 3 −5.132*** 0.083 0.455 4.684
Huelva 0 −3.011*** 0.073 3 −4.153*** 0.046 0.423 4.205
Huesca 8 −4.032*** 0.089 8 −5.438*** 0.029 0.615 3.869
Jaén 2 −6.002*** 0.059 2 −7.693*** 0.044 0.559 4.025
León 3 −5.093*** 0.268* 3 −5.593*** 0.101* 0.418 6.499
Lleida 3 −4.560*** 0.088 3 −5.276*** 0.089 0.659 3.487
Lugo 4 −9.404*** 0.042 4 −9.433*** 0.020 0.608 3.319
Madrid 0 −3.535*** 0.074 0 −3.926*** 0.051 0.431 4.052
Málaga 8 −3.856*** 0.087 8 −4.861*** 0.075 0.702 3.213
Murcia 3 −6.596*** 0.102 3 −6.677*** 0.076 0.492 4.704
Navarra 0 −4.801*** 0.523** 0 −4.900*** 0.318*** 0.340 6.899
Ourense 2 −3.564*** 0.107 7 −4.056*** 0.097 0.776 1.141
Palencia 7 −5.147*** 0.157 7 −5.186*** 0.115* 0.469 4.851
Palmas, Las 1 −2.821*** 0.082 3 −3.881*** 0.085 0.792 1.305
Pontevedra 7 −2.664*** 0.096 7 −3.117** 0.064 0.624 3.713
Rioja, La 0 −4.420*** 0.174 0 −4.708*** 0.100* 0.527 4.309
Salamanca 2 −3.539*** 0.058 2 −4.897*** 0.049 0.542 5.490
Santa Cruz de Tenerife 3 −2.825*** 0.043 8 −4.731*** 0.043 0.819 1.249
Segovia 0 −3.453*** 0.358** 0 −3.815*** 0.186*** 0.535 3.487
Sevilla 3 −5.055*** 0.231 3 −5.054*** 0.178** 0.309 7.085
Soria 1 −5.262*** 0.078 1 −5.177*** 0.082 0.590 5.611
Tarragona 0 −4.923*** 0.289* 0 −6.262*** 0.101* 0.555 3.805
Teruel 7 −3.801*** 0.188 7 −5.345*** 0.074 0.534 3.539
Toledo 3 −4.922*** 0.029 3 −6.685*** 0.029 0.412 4.731
Valencia 1 −4.421*** 0.079 1 −5.820*** 0.044 0.465 3.675
Valladolid 0 −5.908*** 0.106 0 −6.246*** 0.065 0.377 7.411
Zamora 0 −6.451*** 0.160 0 −6.497*** 0.072 0.537 4.501
Zaragoza 1 −7.648*** 0.052 0 −8.372*** 0.034 0.480 4.665
Critical values
  1 % −2.580 0.536   −3.167 0.185   
  5 % −1.950 0.324   −2.577 0.122   
  10 % −1.620 0.235   −2.314 0.098   
Bai and Ng (2004a) pooled statistics
   \( P_{{\hat{e}}}^{c} \) 835.432*** N.A. \( P_{{\hat{e}}}^{\tau } \) 895.914*** N.A.  
   \( Z_{{\hat{e}}}^{c} \) 52.003*** N.A. \( Z_{{\hat{e}}}^{\tau } \) 56.280*** N.A.  
Bai and Ng (2010) pooled statistics
   \( P_{a}^{c} \) −8.448***   \( P_{a}^{\tau } \) −15.370***   
   \( P_{b}^{c} \) −5.343***   \( P_{b}^{\tau } \) −8.698***   
   \( {\text{PMSB}}^{c} \) −3.231***   \( {\text{PMSB}}^{\tau } \) −4.722***   
  1. The augmented autoregressions employed in the ADF analysis select the optimal lag-order with the t-sig criterion of Ng and Perron (1995), setting a maximum lag-order equal to \( p = 4(T/100)^{1/4} \). The stationarity tests are based on 12 lags of the Quadratic spectral kernel. The information criterion BIC3 has chosen an optimal rank equal to 1. \( P_{{\hat{e}}} \) is distributed as \( \chi_{100}^{2} \), with 1, 5 and 10 % critical values of 135.807, 124.342 and 118.498, respectively. \( Z_{{\hat{e}}} \) is distributed as N(0,1) with 1, 5 and 10 % critical values equal to 2.326, 1.645 and 1.282, respectively. \( P_{a} \), \( P_{b} \) and \( {\text{PMSB}} \) are distributed as N(0,1) with 1, 5 and 10 % critical values of −2.326, −1.645 and 1.282, respectively. ***, ** and * imply rejection of the null hypothesis at 1, 5 and 10 %, respectively
Common factor analysis Statistic Critical values   Statistic Critical values
1 % 5 % 10 % 1 % 5 % 10 %
\( {\text{ADF}}_{{\hat{F}}}^{c} \) −2.022 −3.430 −2.860 −2.570 \( {\text{ADF}}_{{\hat{F}}}^{\tau } \) −2.408 −3.960 −3.410 −3.120
\( S_{{\hat{F}}}^{c} \) 3.608*** 0.743 0.463 0.343 \( S_{{\hat{F}}}^{\tau } \) 0.859*** 0.215 0.149 0 .120
  1. The augmented autoregressions employed in the ADF analysis select the optimal lag-order with the t-sig criterion of Ng and Perron (1995), setting a maximum lag-order equal to \( p = 4(T/100)^{1/4} \). The stationarity tests are based on 12 lags of the Quadratic spectral kernel. The information criterion BIC3 has chosen an optimal rank equal to 1. \( P_{{\hat{e}}} \) is distributed as \( \chi_{100}^{2} \), with 1, 5 and 10 % critical values of 135.807, 124.342 and 118.498, respectively. \( Z_{{\hat{e}}} \) is distributed as N(0,1) with 1, 5 and 10 % critical values equal to 2.326, 1.645 and 1.282, respectively. \( P_{a} \), \( P_{b} \) and \( {\text{PMSB}} \) are distributed as N(0,1) with 1, 5 and 10 % critical values of −2.326, −1.645 and 1.282, respectively. ***, ** and * imply rejection of the null hypothesis at 1, 5 and 10 %, respectively