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Latin American Economic Review

Table 3 PANIC analysis of CPI inflation. Spanish provinces. 1955.1–1978.6

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

4

−3.969***

0.103

0

−3.990***

0.092

0.713

1.808

Albacete

0

−4.315***

0.282*

0

−4.611***

0.110*

0.621

2.513

Alicante

5

−4.327***

0.099

2

−4.582***

0.067

0.566

2.728

Almería

0

−3.904***

0.056

0

−4.115***

0.056

0.604

2.299

Asturias

0

−3.997***

0.072

0

−4.182***

0.068

0.704

2.018

Ávila

0

−3.956***

0.102

0

−4.360***

0.101*

0.713

2.020

Badajoz

8

−4.871***

0.053

0

−4.879***

0.052

0.579

3.554

Balears, Illes

5

−3.026***

0.386**

5

−2.917**

0.190***

0.814

1.452

Barcelona

0

−3.631***

0.092

0

−3.801***

0.085

0.773

2.223

Bizkaia

1

−4.503***

0.187

1

−5.116***

0.072

0.734

2.348

Burgos

1

−2.855***

0.199

1

−3.317***

0.047

0.790

2.568

Cáceres

5

−4.361***

0.284*

5

−4.368***

0.039

0.713

2.504

Cádiz

2

−4.048***

0.100

2

−4.089***

0.077

0.621

2.501

Cantabria

0

−4.841***

0.113

0

−4.861***

0.065

0.796

1.747

Castellón

2

−3.493***

0.403**

2

−3.781***

0.100*

0.647

1.758

Ciudad Real

0

−3.315***

0.226

0

−3.823***

0.064

0.793

1.429

Córdoba

0

−2.263**

0.245*

0

−3.055**

0.062

0.481

2.678

Coruña, A

7

−3.194***

0.601***

7

−3.345***

0.194***

0.679

2.894

Cuenca

3

−3.709***

0.193

2

−4.115***

0.106*

0.476

2.903

Gipuzkoa

6

−4.536***

0.171

6

−4.670***

0.043

0.642

2.732

Girona

1

−3.995***

0.228

1

−4.087***

0.071

0.826

2.256

Granada

0

−4.153***

0.117

0

−4.306***

0.092

0.616

2.984

Guadalajara

1

−4.610***

0.073

1

−4.615***

0.056

0.699

2.496

Huelva

0

−4.262***

0.107

2

−4.252***

0.063

0.692

2.854

Huesca

4

−3.838***

0.216

4

−4.414***

0.114*

0.689

2.441

Jaén

0

−4.883***

0.068

0

−4.876***

0.054

0.639

2.371

León

2

−5.574***

0.142

2

−5.555***

0.052

0.583

2.646

Lleida

0

−3.462***

0.134

0

−3.565***

0.068

0.755

2.075

Lugo

0

−4.357***

0.043

0

−4.586***

0.027

0.706

2.334

Madrid

1

−3.878***

0.467**

1

−4.187***

0.209***

0.545

2.426

Málaga

0

−4.878***

0.276*

0

−4.877***

0.061

0.642

2.531

Murcia

3

−3.824***

0.051

0

−4.072***

0.037

0.478

3.477

Navarra

0

−3.068***

0.073

0

−3.605***

0.035

0.659

2.131

Ourense

5

−5.854***

0.039

5

−5.858***

0.025

0.745

2.371

Palencia

0

−4.587***

0.056

0

−4.587***

0.056

0.581

3.382

Palmas, Las

3

−2.388**

0.755***

3

−3.459***

0.072

0.879

1.259

Pontevedra

2

−3.528***

0.421**

2

−4.335***

0.026

0.742

2.182

Rioja, La

8

−3.044***

0.262*

5

−3.015**

0.121*

0.713

1.947

Salamanca

0

−4.158***

0.079

0

−4.174***

0.081

0.684

1.924

Santa Cruz de Tenerife

2

−3.187***

0.475**

2

−4.164***

0.057

0.947

0.607

Segovia

0

−4.200***

0.069

0

−4.299***

0.052

0.641

3.076

Sevilla

0

−4.951***

0.182

0

−4.991***

0.066

0.632

2.607

Soria

3

−2.820***

0.115

3

−2.792**

0.105*

0.725

2.173

Tarragona

3

−4.006***

0.097

0

−4.002***

0.096

0.645

3.100

Teruel

1

−3.876***

0.199

1

−4.062***

0.147**

0.778

2.225

Toledo

4

−3.443***

0.704***

4

−3.980***

0.062

0.816

1.779

Valencia

0

−5.692***

0.096

0

−5.747***

0.049

0.687

1.853

Valladolid

0

−3.199***

0.107

0

−3.241***

0.081

0.744

1.807

Zamora

0

−2.091**

0.139

0

−2.738**

0.129**

0.751

1.290

Zaragoza

1

−5.986***

0.036

1

−6.000***

0.035

0.581

3.021

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

 

\( P_{{\hat{e}}}^{c} \)

809.457***

N.A.

\( P_{{\hat{e}}}^{\tau } \)

810.675***

N.A.

  
 

\( Z_{{\hat{e}}}^{c} \)

50.166***

N.A.

\( Z_{{\hat{e}}}^{\tau } \)

50.252***

N.A.

  

Bai and Ng (2010) pooled statistics

 

\( P_{a}^{c} \)

−70.372***

 

\( P_{a}^{\tau } \)

−51.347***

   
 

\( P_{b}^{c} \)

−17.300***

 

\( P_{b}^{\tau } \)

−18.592***

   
 

\( {\text{PMSB}}^{c} \)

−4.972***

 

\( {\text{PMSB}}^{\tau } \)

−6.358***

   

Common factor analysis

Statistic

Critical values

 

Statistic

Critical values

1 %

5 %

10 %

1 %

5 %

10 %

\( {\text{ADF}}_{{\hat{F}}}^{c} \)

−2.783*

−3.430

−2.860

−2.570

\( {\text{ADF}}_{{\hat{F}}}^{\tau } \)

−3.427**

−3.960

−3.410

−3.120

\( S_{{\hat{F}}}^{c} \)

1.185***

0.743

0.463

0.343

\( S_{{\hat{F}}}^{\tau } \)

0.371***

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 BIC 3 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
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