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Biggeri L*., Brunetti* A. and. Laureti° T *Italian National Statistical Institute (Istat), Rome, Italy;

° University of Tuscia, Viterbo, Italy

Geneva, 8-9 May 2008

The interpretation of the divergences between CPIs at territorial level:

Evidence from Italy

Joint UNECE/ILO Meeting on Consumer Price Indices

2

Structure of the paper

Joint UNECE/ILO Meeting on

Consumer Price Indices

Geneva, 8-9 May 2008

1. Introduction

2. The divergence between CPIs at territorial level: a method for decomposing and interpreting it 2. The divergence between CPIs at territorial level: a method for decomposing and interpreting it

3. The organisation of the decomposition analyses on Italian data3. The organisation of the decomposition analyses on Italian data

4. Analysis of the results4. Analysis of the results

5. Concluding remarks5. Concluding remarks

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Joint UNECE/ILO Meeting on

Consumer Price Indices

Geneva, 8-9 May 2008

1. Introduction

The aim of the paper is twofold

Empirical analyses to show the usefulness of the method Empirical analyses to show the usefulness of the method

Method for the decomposition CPIs divergences Method for the decomposition CPIs divergences

For the construction of CPIs most NSIs make use of the Laspeyres formula

,1 1

n ntk

r t r k r k t r kk krk

pw P w

p

P

, ,1 1

n nj l j j l l

r t r t r k t r k r k t r kk k

P w P w

P P

Considering the same basket of products and services, the divergence between two CPIs in different areas l and j

[1]

[2]

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Joint UNECE/ILO Meeting on

Consumer Price Indices

Geneva, 8-9 May 2008

From a different point of view, by considering area j as reference area:

, ,1 1

n nl j l l j j

r t r t r k t r k r k t r kk k

P w P w

P P

A comparison between two local CPIs depends on• Elementary indices• Weighting system

[5]

Examine and decompose these divergencesUnderstand which are the factors that cause them

Four equivalent decomposition formulae

2. The divergence between CPIs at territorial level

5Geneva, 8-9 May 2008

[3]

Factors influencing the Elementary Price Index Effect

Factors influencing the Weight Effect

, , , ,

1 1 1 1

, , ,

Weight EfElementary Price Index E fect ffect

n n n nj l j j l l j l j l

r t r t r k t r k r k t r k r k t r k r k t r kk k k k

l j l j j lr k r k t r k t r k t r k r k

k k

P w P w P w P w

w P P P w w

P P

, ,l l j j

j lr t r t dw w P P d

n s s R n s s R P P

, ,j l

k r k t r k tP P

Joint UNECE/ILO Meeting on

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2. A method for decomposing and interpreting the differences (a)

j lk r k r kd w w

[3bis]

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The factors can give different results since they are defined relating to different distributions of elementary price indices and weights

Joint UNECE/ILO Meeting on Consumer Price Indices

2. A method for decomposing and interpreting the differences (b)

, , , ,1 1 1 1

, , ,

, ,j j l l

n n n nl j l l j j l j l j

r t r t r k t r k r k t r k r k t r k r k t r kk k k k

j l j l l jr k r k t r k t r k t r k r k

k k

dw w P P d

P w P w P w P w

w P P P w w

n s s R n s s R

P P

[6]

1 1 j lj lr t r tr tk r tk

k k

P P P Pn n

Geneva, 8-9 May 2008

interesting interpretation from an economic point of view determining the “price effect” influencing the overall difference between the two CPIs considered.

difference between the two arithmetic means of elementary price index distributions

difference between the two arithmetic means of elementary price index distributions

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Joint UNECE/ILO Meeting on

Consumer Price Indices

Geneva, 8-9 May 2008

3. Data set description and organisation of analyses on Italian data

DATA DESCRIPTION: Monthly CPIs for the whole nation for elementary aggregates

• 40,000 outlets;• 85 municipalities;•400,000 elementary prices;•540 representative products

System of weights for 85 municipalities using household expenditure shares Period: January 2002-December 2007

DATA DESCRIPTION: Monthly CPIs for the whole nation for elementary aggregates

• 40,000 outlets;• 85 municipalities;•400,000 elementary prices;•540 representative products

System of weights for 85 municipalities using household expenditure shares Period: January 2002-December 2007

CALCULATIONS:analysis limited to December of the years 2002 and 2007 Similar basket of products and servicesSelection of 9 chief regional towns

CALCULATIONS:analysis limited to December of the years 2002 and 2007 Similar basket of products and servicesSelection of 9 chief regional towns

Considering the cities where it is reasonable to assume a different behaviour of the sellers and consumers and a different evolution of attitude regarding sale and purchase. The territorial location of the cities in the north, centre and south Italy

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4. Analysis of the results (a)

TURIN TRENTO VENICE TRIESTE FLORENCE ROME NAPLES POTENZA PALERMO

Nic dic_02 102.940 102.726 103.334 102.815 102.134 103.003 103.825 102.222 102.839

TURIN 102.940 0.214 -0.394 0.125 0.806 -0.064 -0.885 0.718 0.101

TRENTO 102.726 -0.214 -0.608 -0.089 0.592 -0.278 -1.099 0.504 -0.113

VENICE 103.334 0.394 0.608 0.519 1.200 0.331 -0.491 1.112 0.495

TRIESTE 102.815 -0.125 0.089 -0.519 0.681 -0.189 -1.01 0.593 -0.024

FLORENCE 102.134 -0.806 -0.592 -1.2 -0.681 -0.87 -1.691 -0.088 -0.705

ROME 103.003 0.064 0.278 -0.331 0.189 0.870 -0.822 0.781 0.165

NAPLES 103.825 0.885 1.099 0.491 1.010 1.691 0.822 1.603 0.986

POTENZA 102.222 -0.718 -0.504 -1.112 -0.593 0.088 -0.781 -1.603 -0.617

PALERMO 102.839 -0.101 0.113 -0.495 0.024 0.705 -0.165 -0.986 0.617

Table 2 Overall Differences between pairs of cities

Comparing Naples with the other cities the differences

(all positive but with different values) have a “hidden meaning” concerning the degree of importance of the various factors

1,12 1,12j l

t t m t t m P P

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4. Analysis of the results (b)

Naples (j) –Turin (l)

Price change distribution

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CPI difference 0.885

Price Effect 0.516

Weight Effect 0.369

factors

factors12.335

0.002

0.034

-0.639

0.0035

13.029

0.0441

,jP dR

ds

lws

s

,lwR

jPs

Correlation coefficient between elementary indices and weights

NAPLES TURIN Mean 102.40 103.03 Standard Deviation 12.34 5.25 Skewness -6.900 2.252 Kurtosis 58.908 16.616

Turin -0.01Naples 0.056

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Geneva, 8-9 May 2008

4. Analysis of the results (c)

Naples (j) –Florence (l)

Price change distribution

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CPI difference 1.691

Price Effect 1.396

Weight Effect 0.295

factors

factors12.335

0.0018

0.0240

0.596

0.0037

12.131

0.031

,jP dR

ds

lws

s

,lwR

jPs

Correlation coefficient between elementary indices and weights

Florence 0.026Naples 0.056

NAPLES FLORENCE Mean 102.40 101.80 Standard Deviation 12.34 6.07

Skewness -6.900 -7.541 Kurtosis 58.908 144.262

11Geneva, 8-9 May 2008

4. Analysis of the results (d)

The evolutions of local CPIs is quite different across Italy and influence the divergences between the CPIs in different ways and degrees.

The evolutions of local CPIs is quite different across Italy and influence the divergences between the CPIs in different ways and degrees.

The divergences in the evolution of the CPIs depend:

mostly on the price effects.

in same cases on the different share of expenditures (two southern cities with all the other cities)

on the characteristics of the corresponding distribution of the elementary price indices and on the value of the correlation between elementary indices and weights

The divergences in the evolution of the CPIs depend:

mostly on the price effects.

in same cases on the different share of expenditures (two southern cities with all the other cities)

on the characteristics of the corresponding distribution of the elementary price indices and on the value of the correlation between elementary indices and weights

Similar results from the comparisons for December 2007 Similar results from the comparisons for December 2007

Joint UNECE/ILO Meeting on

Consumer Price Indices

12Geneva, 8-9 May 2008

5. Concluding remarks

A simple method for calculating the decomposition of the divergence between two CPIs to obtain a measure of the importance of the factors that affect it.

A simple method for calculating the decomposition of the divergence between two CPIs to obtain a measure of the importance of the factors that affect it.

Very interesting results

Further researchFurther research

improve the method of the decomposition of the divergences between the CPIs

Analysis for CPIs by classes and groups of products to understand the importance of the different products in affecting the price and weights effects

analyse the degree of the price and weights effects during periods with different inflation rates.

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Understanding why the local CPIs often differ among one another

Understanding why the local CPIs often differ among one another

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Joint UNECE/ILO Meeting on

Consumer Price Indices

Joint UNECE/ILO Meeting on

Consumer Price Indices

Thank you for your kind attention!