As an alternative modelling approach to the factor model presented in Section 3, regional inflation could be made dependent on area wide, national and regional macroeconomic vari-ables. Let us consider for simplicity the case where regional inflation depends on area wide variables only, zt, so that
xijt = λijzt+ eijt. (8)
In this model, the regional variables are linked together by the area wide variables zt, as for example in the Global VAR models of Peseran et al. (2004) at a national level.
To analyse whether our results for regional inflation obtained with the factor based regres-sions are robust in comparison with those obtained in a macro variable based approach, we have estimated an extended version of the model in (8) using money, interest rates, exchange rate and oil prices as euro area macroeconomic variables to capture area wide determinants of inflation, including common monetary policy within the euro area and common external developments such as oil price and exchange rate changes. We have also added the un-employment rate, the growth rate in wages, unit labour cost and industrial production as country-specific variables, since their heterogeneous behaviour in the countries under anal-ysis can have different effects on regional inflation. The results of the regressions on the macroeconomic variables are available from the authors upon request.
The macroeconomic variables are strongly significant. However, the values of the adjusted R2 are systematically lower than the corresponding numbers for the factor based regressions, the losses are around 10 %.
Another interesting feature which can be evaluated is whether the rejection of homogene-ity of the coefficients of the area wide factors detected within the factor based approach holds also in this variable based framework.
The p-values of the test for the null hypothesis of homogeneity do not reject in this case, except for money M3 and oil prices in Italy and short-term interest rates in Portugal. In particular, the impact of a short-term interest rate and area wide M3 does differ significantly across regions, which is of importance from a monetary policy point of view. However, this finding appears to be due to the substantially higher estimation uncertainty of the coefficients of the macro variables compared with those of the factors.
A final important question is to evaluate whether the factors have additional explanatory power if included in the macro variable based regression.
Therefore, we have regressed regional inflation series on both the factors and the macro variables, i.e.
πijtreg = νij + λijft+ ηijgjt+ aijzt+ bijyjt+ eijt, (9) where ft and gjt are the area wide and national factors and zt and yjt are the area wide and national variables. In the final two columns of Table 6 we report, for each region, an F-test (F-test 1) for the non-significance of, respectively, the area wide and national factors, i.e. testing H0 : λij = 0 and ηij = 0, in equation (9). Furthermore, we report an F-test for the non-significance of the area wide and national macro variables (F-test 2), i.e. testing H0 : aij = 0 and bij = 0 in equation (9). The zero effect of the factors is rejected in each region at a 5% significance level, while the zero effect of the macroeconomic variables is only rejected in 25 out of 70 regions. Therefore, macro variables might be excluded from the model in many regions, but factors always have to be included.
On the basis of these results and of the previous finding on the improved goodness of fit, we conclude that the factor model provides a better representation for our regional inflation data set.
Table 1: Countries and Regions Included in our Study
Germany (12 NUTS-I Regions)
Regions: Baden-W¨urttemberg, Bayern, Berlin, Brandenburg, Hessen,
Mecklenburg-Vorpommern, Niedersachen, Nordrhein-Westfalen, Saarland, Sachsen, Sachsen-Anhalt, Th¨uringen
Data Source: Statistical offices of the individual German states Austria (9 NUTS II Regions)
Regions: Burgenland, K¨arnten, Nieder¨osterreich, Ober¨osterreich, Salzburg, Steier-mark, Tirol, Vorarlberg, Wien
Data Source: Statistics Austria
Finland (5 NUTS-II Regions)
Regions: Ita-Suomi, Etela-Suomi, Lansi-Suomi, Pohjois-Suomi, Aland Data Source: Statistics Finland
Italy (20 Major Cities of NUTS-II Regions)
Regions: Ancona, Aosta, Bari, Bologna, Cagliari, Campobasso, Firenze, Gen-ova, L’Aquila, Milano, Napoli, Palermo, Perugia, Potenza, Reggio Calabria, Roma, Toino, Trento, Trieste, Venezia
Data Source: Istituto Nazionale di Statistica (ISTAT) Spain (18 NUTS-II Regions)
Regions: Andalucia, Aragon, Principado de Asturias, Baleares, Canarias, Caabria, Castilla y Leon, Castilla La Mancha, Cataluna, Ceuta y Melilla, Extremadura, Galicia, Communidad Madrid, Cummunidad Murcia, Navarra, Pais Vasco, La Rioja, Communidad Valenicana
Data Source: Instituto Nacional de Estadistica (INE) Portugal (7 NUTS-II Regions)
Regions: Acores, Algarve, Altenejo, Centro, Lisbon, Madeira, Norte Data Source: Instituto Nacional de Estatistica (INE)
U.S.A. (11 Metropolitan Areas)
Regions: Boston-Brockton-Nashua, Chicago-Gary-Kenosha, Cleveland-Akron,
Dallas-Fort Worth, Detroit-Ann Arbor-Flint, Houston-Galveston-Brazoria, Los Angeles-Riverside-Orange County, Miami-Fort Lauderdale, New York-Northern New Jersey-Long Island, Philadelphia-Wilmington-Atlantic City, San Francisco-Oakland-San Jose
Data Source: Bureau of Labor Statistics (BLS)
Table 2: Country/Region Short Names
Sardegna cagl Molise camp Ceuta e Melilla ceut
Norte coim Algarve evor Centro faro
Pais Vasco sans Cantabria sant Aragon sara
Andalucia sevi Steiermark stei Aland tamp
Th¨uringen thue Tirol tiro Piemonte tori
Trento tren Friuli-Venezia trie Valencia vale
Castilla Leon vall Veneto vene Vorarlberg vora
Wien wien
Table 3: Descriptive Statistics for Euro Area and US Regional Inflation Rates (1995.01 -2004.10, 1995.01 - 1998.12, 1999.01 - 2004.10))
Euro Area
All Regions 2.18 0.63 1.89 0.61 2.26 0.70
Germany 1.35 0.15 1.21 0.21 1.31 0.20
Austria 1.62 0.10 1.19 0.17 1.73 0.11
Finland 1.41 0.09 1.07 0.05 1.60 0.13
Italy 2.26 0.22 2.13 0.33 2.22 0.22
Spain 2.87 0.22 2.45 0.25 3.06 0.24
Portugal 2.85 0.15 2.41 0.28 3.09 0.12
U.S.A.
All Regions 2.50 0.29 2.28 0.43 2.68 0.35
Notes:
The mean year on year CPI inflation rate (mean) is computed as the cross-sectional mean of all regional mean inflation rates (geometric mean) included in the respective sample. The computation of the standard deviation (std. dvt.) is likewise based on the cross-section of the geometric means of all regional mean inflation rates included in the respective sample.
Table 4: : ADF Unit Root Tests on euro area regional inflation series, 1995-2004 Total Number of
Re-gions
Number of Rejections (5% Significance Level)
All Regions 70 17
Germany 12 8
Austria 9 0
Finland 5 0
Italy 19 8
Spain 18 1
Portugal 7 0
Notes:
1) Results are based on regressions including a constant and lagged differences up to the highest significant lag with a maximum of 12 lags.
2) Critical values are taken from MacKinnon (1991).
Table 5: Euro Area Wide and National Factors
Comp. 1 Comp. 2 Comp. 3 Comp. 4 Comp. 5 Comp. 6
All Regions
Eigenvalue 33.499 11.384 7.381 3.732 2.964 1.876
Variance Prop. 0.483 0.164 0.106 0.054 0.043 0.027
Cumulative Prop. 0.483 0.647 0.754 0.808 0.850 0.877
Austria
Eigenvalue 1.343 0.513 0.238 0.195 0.163 0.128
Variance Prop. 0.501 0.192 0.089 0.073 0.061 0.048
Cumulative Prop. 0.501 0.693 0.782 0.854 0.915 0.963
Germany
Eigenvalue 0.701 0.501 0.385 0.328 0.160 0.100
Variance Prop. 0.291 0.208 0.160 0.136 0.066 0.042
Cumulative Prop. 0.291 0.500 0.659 0.796 0.862 0.904
Spain
Eigenvalue 1.195 0.604 0.491 0.186 0.155 0.144
Variance Prop. 0.380 0.192 0.156 0.059 0.049 0.046
Cumulative Prop. 0.380 0.572 0.728 0.787 0.836 0.882
Finland
Eigenvalue 1.468 0.072 0.062 0.018 0.008
Variance Prop. 0.901 0.044 0.038 0.011 0.005
Cumulative Prop. 0.901 0.945 0.984 0.995 1.000
Italy
Eigenvalue 1.283 0.860 0.451 0.350 0.320 0.288
Variance Prop. 0.299 0.201 0.105 0.082 0.075 0.067
Cumulative Prop. 0.299 0.500 0.606 0.687 0.762 0.829
Portugal
Eigenvalue 1.341 0.778 0.440 0.155 0.105 0.102
Variance Prop. 0.453 0.263 0.149 0.052 0.035 0.035
Cumulative Prop. 0.453 0.716 0.864 0.917 0.952 0.987
Notes:
1) The area wide factors (‘All Regions’) are estimated as the principal components extracted from a dataset with all the regions of all countries and the sample period 1995-2004.
2) The national factors are estimated as the principal components, extracted for each country from the residuals of a regression of regional inflation rates on area wide components over the same sample period.
We report eigenvalues associated with the first 6 principal components, the proportion of variance explained by each component, and the cumulative proportion of explained variance.
Table6:Explainingregionalinflationintheeuroarea RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 auburg-0.0990.1110.0550.364-0.9330.1570.9200.9940.2680.2220.2160.0000.835 0.0060.0100.0110.0110.0270.0240.044 aukaer-0.1290.077-0.0240.306-0.0360.1400.6120.9130.5280.3640.3880.0000.488 0.0120.0230.0270.0380.0780.0870.083 aunied-0.1640.094-0.0190.1880.2820.6130.8280.9600.1050.6250.6040.0000.074 0.0150.0250.0280.0280.0680.0630.060 auober-0.1450.1070.0380.2900.0970.1250.8200.9650.0060.0990.9890.0000.067 0.0130.0240.0270.0260.0630.0590.064 ausalz-0.1300.089-0.0230.4810.145-0.4600.6740.9940.0300.1440.6880.0000.131 0.0040.0070.0080.0100.0220.0230.078 austei-0.158-0.0020.0610.299-0.1350.2480.5860.8720.8010.2130.0050.0000.481 0.0150.0260.0310.0450.0920.1030.079 autiro-0.1120.144-0.0480.2060.1250.1560.8720.9630.7340.8270.5710.0000.019 0.0150.0240.0280.0270.0670.0600.046 auvora-0.1150.161-0.0670.2930.2230.3410.8100.9570.0200.0290.5500.0000.000 0.0140.0250.0290.0290.0700.0660.062 auwien-0.1250.123-0.0490.3040.0640.1930.7120.9610.0220.9210.7480.0000.001 0.0110.0200.0230.0270.0650.0610.087 Mean-0.1310.100-0.0090.303-0.0190.1680.759 Std.dev.0.0210.0470.0480.0850.3650.2810.118 Min-0.164-0.002-0.0670.188-0.933-0.4600.586 Max-0.0990.1610.0610.4810.2820.6130.920 debade-0.0930.1640.093-0.1440.3270.1690.8580.9690.6980.4340.2110.0000.142 0.0130.0220.0270.0540.0440.0470.051 debaye-0.0930.1750.107-0.6140.163-0.1340.6190.9640.4180.2670.8890.0000.004 0.0080.0150.0180.0450.0420.0470.081 deberl-0.0850.1950.061-0.1920.2400.4380.9090.9530.9590.9740.0220.0000.123 0.0170.0280.0340.0680.0550.0570.042 ...tobecontinued
Table6:...continued RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 debran-0.0880.1090.240-0.4570.117-0.4220.8560.9700.0080.6050.0370.0000.001 0.0140.0220.0270.0530.0430.0460.055 dehess-0.0410.229-0.0040.2000.6130.4980.5470.9850.4170.0470.9400.0000.492 0.0040.0080.0100.0260.0250.0290.082 demeck-0.0740.1310.2630.6090.492-0.5910.9240.9470.8850.7660.0000.0000.094 0.0190.0290.0350.0720.0580.0600.046 denied-0.1090.1630.1510.0800.2740.1170.6620.9790.7290.9160.4540.0000.191 0.0070.0120.0150.0370.0330.0370.074 denord-0.1010.1900.103-0.0020.2460.1720.8690.9710.1090.3180.4140.0000.507 0.0140.0220.0270.0530.0430.0460.059 desaan-0.0760.1200.267-0.2830.140-0.3770.6660.9650.0110.8870.0250.0000.000 0.0090.0160.0190.0510.0420.0470.083 desaar-0.0960.1910.141-0.2080.2260.1450.5080.9560.2000.5950.0020.0000.764 0.0070.0130.0160.0430.0430.0490.090 desach-0.0780.1600.1590.0910.246-0.2030.8170.9701.0000.2950.0000.0000.072 0.0120.0200.0250.0500.0420.0450.056 dethue-0.0770.1810.0950.0230.307-0.1660.9060.9680.4160.6280.0000.0000.143 0.0150.0230.0280.0560.0450.0470.045 Mean-0.0840.1670.140-0.0750.283-0.0300.762 Std.dev.0.0170.0340.0830.3200.1430.3410.151 Min-0.1090.109-0.004-0.6140.117-0.5910.508 Max-0.0410.2290.2670.6090.6130.4980.924 esalba-0.156-0.012-0.0430.253-0.1690.0190.6500.9900.1910.8910.6030.0000.009 0.0050.0080.0100.0150.0280.0240.075 esbada-0.135-0.012-0.0960.136-0.1570.0270.9430.9760.9960.3580.9710.0000.339 0.0130.0190.0220.0270.0610.0380.034 esbarc-0.138-0.007-0.0880.291-0.050-0.0100.9170.9870.6040.7810.3610.0000.124 0.0090.0140.0170.0190.0450.0280.041 ...tobecontinued
Table6:...continued RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 esceut-0.135-0.020-0.091-0.056-0.775-0.4990.8500.9640.5630.0300.6330.0000.183 0.0150.0240.0280.0330.0770.0480.064 eslaco-0.158-0.049-0.0840.284-0.007-0.0490.8400.9790.4030.3230.7740.0000.478 0.0110.0180.0210.0240.0550.0360.059 eslapa-0.1170.060-0.0500.0140.444-0.8870.6800.9960.9770.9800.9480.0000.007 0.0030.0060.0070.0100.0210.0160.070 eslogr-0.146-0.046-0.0770.3260.3110.0640.7060.9571.0000.0380.6810.0000.185 0.0110.0200.0230.0320.0650.0510.077 esmadr-0.153-0.017-0.0420.213-0.160-0.0450.8710.9820.1980.0220.3890.0000.006 0.0110.0180.0200.0240.0530.0340.049 esmurc-0.153-0.032-0.1310.186-0.352-0.0920.8530.9740.5170.5480.4110.0000.105 0.0120.0210.0240.0270.0610.0400.055 esovie-0.148-0.008-0.1040.277-0.085-0.0560.7690.9650.2300.0050.0020.0000.233 0.0120.0210.0240.0300.0650.0460.066 espalm-0.1570.001-0.0840.1160.1100.1380.4320.9600.4730.7500.9750.0000.003 0.0060.0110.0130.0250.0420.0420.092 espamp-0.1170.023-0.0950.3080.048-0.0220.8390.9670.1710.0360.1240.0000.116 0.0130.0220.0270.0300.0670.0450.037 essans-0.149-0.007-0.1120.2760.0480.0320.8890.9820.4970.9970.6990.0000.425 0.0110.0170.0200.0230.0540.0340.049 essant-0.154-0.047-0.0750.2890.094-0.0320.6360.9450.9190.3010.8220.0000.974 0.0100.0190.0230.0350.0660.0560.081 essara-0.162-0.070-0.0380.2940.0950.0520.7420.9830.3090.3190.8740.0000.632 0.0080.0140.0160.0210.0440.0320.054 essevi-0.159-0.043-0.0730.189-0.191-0.0080.7990.9900.5480.1810.6490.0000.006 0.0070.0120.0140.0170.0360.0250.061 esvale-0.159-0.027-0.0750.208-0.183-0.0120.7520.9880.9910.2860.3490.0000.198 0.0060.0120.0140.0180.0360.0270.072 ...tobecontinued
Table6:...continued RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 esvall-0.161-0.021-0.0420.2530.039-0.0040.7520.9910.2200.2120.8140.0000.358 0.0060.0110.0120.0150.0330.0240.060 Mean-0.148-0.019-0.0780.214-0.052-0.0770.773 Std.dev.0.0140.0290.0260.1040.2620.2400.124 Min-0.162-0.070-0.131-0.056-0.775-0.8870.432 Max-0.1170.060-0.0380.3260.4440.1380.943 fihels-0.0530.126-0.1080.3470.9060.9830.0140.0900.7330.0000.000 0.0100.0170.0190.0280.037 fijoen-0.0780.187-0.1040.4510.6350.9860.0810.4540.3720.0000.318 0.0050.0100.0110.0200.079 fikokk-0.0820.184-0.0710.4640.7250.9840.1270.0620.0000.0000.911 0.0070.0120.0140.0240.068 fioulu-0.0740.220-0.1280.4860.8500.9750.0190.4020.8780.0000.022 0.0120.0200.0230.0330.052 fitamp-0.0670.195-0.1010.4600.5900.9900.0000.125 0.0040.0070.0090.0160.081 Mean-0.0710.182-0.1020.4420.741 Std.dev.0.0120.0350.0200.0550.136 Min-0.0820.126-0.1280.3470.590 Max-0.0530.220-0.0710.4860.906 itanco-0.072-0.0750.0330.229-0.0660.1280.9290.9581.0000.5590.0990.0000.212 0.0140.0250.0330.0520.0760.0640.034 itbari-0.084-0.0760.0880.0080.066-0.0620.9530.9700.1450.9000.1920.0000.086 0.0130.0220.0290.0460.0680.0560.031 itbolo-0.101-0.1380.0930.3130.3470.1360.5660.9480.0000.0010.0010.0000.166 0.0080.0140.0170.0350.0440.0540.083 itcagl-0.105-0.2170.2380.0890.1150.4460.8800.9361.0000.0830.0070.0000.323 0.0180.0300.0390.0610.0890.0770.048 ...tobecontinued
Table6:...continued RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 itcamp-0.096-0.1330.223-0.153-0.068-0.4550.8270.8940.0800.1340.0600.0000.159 0.0220.0370.0450.0780.1040.0980.065 itfire-0.112-0.1240.0690.3820.0040.0650.5730.9370.0190.2370.6800.0000.058 0.0090.0150.0190.0380.0470.0570.081 itgeno-0.097-0.115-0.0030.171-0.241-0.0200.8590.9711.0000.5010.6740.0000.235 0.0120.0210.0250.0400.0600.0520.053 itlaqu-0.137-0.0770.0710.065-0.5620.0420.4330.9610.1410.2070.0560.0000.001 0.0060.0110.0130.0280.0330.0440.091 itmila-0.097-0.1610.0830.1740.0790.0570.9370.9770.3610.1650.2580.0000.611 0.0110.0190.0240.0380.0570.0470.038 itnapo-0.091-0.1320.117-0.053-0.2150.1850.8740.9600.6780.0570.6130.0000.740 0.0140.0240.0320.0500.0690.0620.053 itpale-0.125-0.1890.0420.049-0.2820.0850.8280.9270.2600.0860.3060.0000.562 0.0180.0320.0380.0620.0940.0850.067 itperu-0.129-0.1760.1150.0780.1050.1400.6740.9330.8610.0900.0000.0000.008 0.0120.0220.0260.0500.0660.0750.075 itpote-0.110-0.1200.076-0.062-0.337-0.1820.7520.9500.6410.2510.8500.0000.098 0.0130.0210.0260.0470.0620.0660.073 itregg-0.124-0.1190.1790.0330.213-0.5350.5890.9460.4800.3020.0400.0000.407 0.0090.0160.0200.0410.0490.0620.085 itroma-0.122-0.1560.1520.0790.127-0.0090.6330.9660.2160.2530.4440.0000.030 0.0080.0140.0160.0340.0410.0500.083 ittori-0.102-0.0500.0500.203-0.014-0.4200.8500.9370.6150.3670.0000.0000.118 0.0170.0300.0370.0600.0850.0780.053 ittren-0.105-0.057-0.0380.635-0.345-0.0510.8840.9590.1610.3360.0340.0000.010 0.0150.0250.0320.0510.0720.0640.054 ittrie-0.139-0.1360.0680.3520.069-0.2230.5880.9570.6500.2550.0000.0000.000 0.0080.0140.0180.0350.0440.0520.081 ...tobecontinued
Table6:...continued RegionPC1ALLPC2ALLPC3ALLPC1CSPC2CSPC3CSAR(1)Adj.R2LMWhiteJBF-Test1F-Test2 itvene-0.108-0.1420.0640.3010.222-0.0460.7560.9720.4640.0100.2410.0000.425 0.0100.0180.0200.0350.0480.0480.074 Mean-0.108-0.1260.0900.152-0.041-0.0380.757 Std.dev.0.0180.0440.0700.1870.2330.2400.154 Min-0.139-0.217-0.038-0.153-0.562-0.5350.433 Max-0.072-0.0500.2380.6350.3470.4460.953 pocoim-0.110-0.058-0.2070.4670.164-0.0890.7990.9630.1130.0850.2630.0000.836 0.0140.0230.0260.0310.0430.0500.063 poevor-0.094-0.020-0.2020.3720.1780.1190.7480.9620.8800.8390.7320.0000.229 0.0110.0200.0240.0310.0420.0500.070 pofaro-0.089-0.033-0.2220.4300.304-0.2410.6040.9410.0440.3920.6760.0000.190 0.0100.0190.0230.0350.0490.0580.081 pofunc-0.068-0.077-0.1280.398-0.5720.6730.7180.9930.9460.8000.7190.0000.536 0.0050.0080.0100.0130.0180.0210.073 polisb-0.110-0.037-0.1640.2930.2780.0080.8070.9560.0100.7930.0150.0000.375 0.0140.0250.0300.0340.0470.0540.062 popont-0.004-0.046-0.2050.311-0.641-0.6810.6520.9950.8510.5470.7370.0000.724 0.0030.0060.0070.0100.0140.0170.081 poport-0.1090.024-0.1630.3470.1750.1450.7140.9740.9740.8180.9820.0000.320 0.0090.0160.0190.0250.0340.0410.080 Mean-0.084-0.035-0.1850.374-0.016-0.0090.720 Std.dev.0.0380.0320.0340.0630.4070.4120.074 Min-0.110-0.077-0.2220.293-0.641-0.6810.604 Max-0.0040.024-0.1280.4670.3040.6730.807 Notes: 1)Thetablereportstheestimatedcoefficientsandstandarderrors(2ndline)forregressionsofregionalinflationratesonareawidefactors(PCiALL) andcountry-specificfactors(PCiCS),overtheperiod1995-2004,allowingforAR(1)errors.ThenextfourcolumnsreporttheadjusetdR2ofeach regressionandthep-valuesoftestsfornocorrelation(LM),homoskedasticity(White)andNormality(JB)oftheresiduals.Thefinaltwocolumns report,respectively,F-testsforthenon-significanceofthefactors(F-test1)andofthemacrovariables(F-test2)inanestingmodelwheneachseries isregressedonthefactorsandonthemacrovariables,asdescribedintheAppendix.Foreachcountry,wealsoreportsomesummarystatistics.
Table 7: US area wide factors
Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6
Eigenvalue 7.167 1.663 1.209 0.792 0.701 0.432
Variance Prop.
0.568 0.132 0.096 0.063 0.055 0.034
Cumulative Prop.
0.568 0.699 0.795 0.858 0.913 0.947
Notes:
1) The area wide factors are estimated as the principal components extracted from the inflation series for the metropolitan areas. 2)See notes to Tables 5.
Table8:ExplainingregionalinflationintheUS USPC1USPC2USPC3AR(1)AdjR2LMWhiteJB USBOST-0.234-0.058-0.0620.6210.7050.1670.0150.010 0.0520.1120.1140.144 USCHIC-0.279-0.3130.1140.1020.7120.3110.7270.325 0.0300.0650.0750.146 USCLEV-0.203-0.2410.1200.8190.8130.7860.1930.816 0.0460.0980.0980.087 USDALL-0.3630.2420.1710.7600.9870.4560.0610.732 0.0120.0260.0250.097 USDETR-0.165-0.524-0.0980.3340.6480.1300.2560.946 0.0420.0900.1000.133 USHOUS-0.264-0.071-0.2670.4260.7130.0610.0580.641 0.0430.0890.0980.135 USLOSA-0.186-0.165-0.5130.4780.8010.4410.1140.888 0.0370.0750.0830.127 USMIAM-0.6920.4610.3270.7600.9870.4560.0610.732 0.0220.0490.0480.097 USNEWY-0.1180.089-0.1870.2840.7850.1200.3210.855 0.0150.0310.0360.141 USPHIL-0.2300.170-0.7270.6490.7800.0160.1470.140 0.0450.0980.1040.121 USSANF-0.099-0.4730.2930.7250.9020.8730.6800.584 0.0320.0670.0680.100 Notes: 1)Thetablereportstheestimatedcoefficientsandstandarderrors(2ndline)forregressionsofregionalinflationratesonareawidefactors(PCiALL), overtheperiod1995-2004,allowingforAR(1)errors.ThenextfourcolumnsreporttheadjusetdR2ofeachregressionandthep-valuesoftestsfor nocorrelation(LM),homoskedasticity(White)andNormality(JB)oftheresiduals.
Table9:Explainingeuroareainflationwithareawidefactors CorrelationMatrix:LevelofInflation HICP euroPC1 ALLPC2 ALLPC3 ALL HICPeuro1.000-0.9040.0420.087 PC1ALL-0.9041.0000.0000.000 PC2ALL0.0420.0001.0000.000 PC3ALL0.0870.0000.0001.000 RegressionResults:LevelofInflation CPC1 ALLPC2 ALLPC3 ALLM3 euroIS euroEXR euroPOIL euroULC euroUR euroIP euroAR(1) HICPeuro2.261-0.0980.016-0.0040.0060.1060.029-0.0240.940 0.4960.0340.1010.0080.0020.1000.0210.0120.044 AdjR20.889LM0.357White0.442JB0.510 HICPeuro2.399-0.0740.0430.038-0.023-0.109-0.0020.0010.0740.029-0.0120.574 0.2250.0070.0110.0120.0180.0420.0050.0010.0420.0060.0090.093 AdjR20.955LM0.213White0.205JB0.066 HICPeuro2.281-0.0670.0550.0170.011-0.104-0.0030.0020.0090.033-0.0250.506 TSLS0.3410.0130.0260.0170.0250.0620.0110.0020.0600.0080.0160.123 AdjR20.951LM0.001White0.04JB0.29 Notes: Sampleperiod:1996(1)-2004(10);Model:ADL(1,1),regressors:euroareanominalinterestrate(IR),unemployment(UR)andthegrowthrate ofoilprices(POIL),euroareamoneysupply(M3),nominaleffectiveexchangerate(EXR),unitlabourcosts(ULC)andindustrialproduction (IP),possiblyaddingthreeareawidefactors;Estimationmethod:OLSandtwostageleastsquares(TSLS)withthesecondlagofdependentand independentvariablesasinstruments;reportedvaluesareestimatedparameters(1strow)andstandarderrors(2ndrow);p-valuesoftestsforno correlation(LM),homoskedasticity(White)andNormality(JB)oftheresiduals
Table10:ExplainingUSinflationwithareawidefactors CorrelationMatrix US CPIUS PC1US PC2US PC3 USCPI1.000-0.897-0.179-0.082 USPC1-0.8971.0000.0000.000 USPC2-0.1790.0001.0000.000 USPC3-0.0820.0000.0001.000 ExplainingUSinflation CUS PC1US PC2US PC3US M3USISUS EXRUS POILUS ULCUS URUSIPAR(2)AR(3) USCPI0.0150.1360.010-0.0040.0120.034-0.010-0.1060.3820.275 0.0060.0600.0050.0170.0030.0440.0430.0430.1730.172 ADJR20.689LM0.239White0.518JB0.776 USCPI0.016-0.002-0.001-0.0010.0960.004-0.0200.0030.014-0.004-0.0090.2930.293 0.0030.0000.0000.0010.0350.0030.0100.0020.0300.0080.0290.1550.150 ADJR20.923LM0.35White0.48JB0.71 USCPI0.017-0.002-0.001-0.0010.0810.004-0.0150.0020.0110.004-0.0080.1670.205 (TSLS)0.0460.0000.0000.0010.0480.0030.0130.0020.0390.0090.0340.2260.205 ADJR20.923LM0.35White0.48JB0.71 Notes: Sampleperiod:1995-2004;Model:ADL(3,3),regressors:USnominalinterestrate(IR),unemployment(UR)andthegrowthrateofoilprices (POIL),moneysupply(M3),nominaleffectiveexchangerate(EXR),unitlabourcosts(ULC)andindustrialproduction(IP),possiblyaddingthree areawidefactors;Estimationmethod:OLSandtwostageleastsquares(TSLS)withfivelagsofdependentandindependentvariablesasinstruments; reportedvaluesareestimatedparameters(1strow)andstandarderrors(2ndrow);p-valuesoftestsfornocorrelation(LM),homoskedasticity(White) andNormality(JB)oftheresiduals
Figure 1: Regional European Inflation Rates: 1995 - 2004
Note: Figure 1 plots cross-sectional inflation rates for Germany, Austria, Finland, Italy, Spain, and Portugal. Inflation rates are computed as year-on-year percentage changes in the underlying consumer price index.
Figure 2: Regional European Inflation Rates: Grouped by Countries
(a) Germany (b) Austria
(c) Finland (d) Italy
(e) Spain (f) Portugal
Notes: Figure 2 plots cross-sectional inflation rates for Germany, Austria, Finland, Italy, Spain, and Portugal. Inflation rates are computed as year-on-year percentage changes in the underlying consumer price index.