PLUTOCRATIC AND DEMOCRATIC CONSUMER PRICE INDEXES: Francesco Chelli and Elvio Mattioli

Transcription

1 LUTORATI AND DEMORATI ONSUMER RIE INDEXES: AN ESTIMATION OF A DEMORATI INDEX FOR ITALY Francesco helli and Elvio Mattioli We thank. Ercolani for helful discussion and comments. All errors are ours. Diartimento di Economia, Università olitecnica delle Marche.

2 ABSTRAT The consumer rice indexes for the entire country and those for individual households are weighted arithmetic averages of relative rices, and they differ essentially in terms of their weighting systems. Whereas the former use the roortions of total exenditure on goods and services, the latter use the roortions of exenditure by each household. In the usual calculation of the index for the entire country, each household contributes to determining the national index with a weight roortional to its exenditure. In other words, the households that send more that is, the wealthier ones are reresented in calculation of the national index to a greater extent, and this exlains why the latter is termed the lutocratic index. In contraosition to lutocratic indexes are the democratic ones in which the same weight is assigned to each household. The aer resents a first estimation of the democratic rice indexes for Italy in the eriod The results show significant differences between the two calculation methods. JEL lass.: 43, E3, E64. Keywords: onsumer rice indexes; lutocratic and democratic indexes; inflation; rice olicy. Indirizzo: Diartimento di Economia Facoltà di Economia Giorgio Fuà Università olitecnica delle Marche.le Martelli, Ancona f.chelli@univm.it; e.mattioli@univm.it;

3 LUTORATI AND DEMORATI ONSUMER RIE INDEXES: AN ESTIMATION OF A DEMORATI INDEX FOR ITALY Francesco helli and Elvio Mattioli. Introduction When a national consumer rice index is used, the shoing basket to be riced corresonds to the total urchases of each good or service by all the consumers resent in the country. But it also ossible to refer the shoing basket urchased to a articular section of the oulation. One can think, for examle, of a regional rice index or a rice index for the elderly, for the oor, and so on 2. In theory, a consumer rice index can also be constructed for a household. Every household, in fact, has its own sending attern on which rice variations have an entirely secific imact. Two imortant issues arise from reflection on rice indexes for grous or for individual households. Firstly, households differ with resect to both the shoing basket of goods urchased and the rices aid, which in general may differ even for the same good. Secondly, one should inquire whether and how it is ossible to relate the single national index to the lurality of indexes calculated at the level of the individual household. The roblem of aggregating household rice indexes into a national rice index can be more easily addressed by assuming that each household ays the same rice for each of We thank. Ercolani for helful discussion and comments. All errors are ours. Diartimento di Economia, Università olitecnica delle Marche. This study has been roduced as art of the research roject onsumer rice Indexes and Measures of Inflation financed by the Università olitecnica delle Marche Year See Istat (2007) for a recent research on this toic.

4 the goods considered. By contrast, if households ay different rices to urchase the same roduct, it becomes much more difficult to analyse the aggregation of household indexes. In a well-integrated economy with moderate transort costs like Italy s, the assumtion that all households ay the same rices for the same goods is generally accetable, although there are obvious excetions: sending on healthcare and housing, for examle. Let us therefore imagine an economy in which the first of the two above hyotheses holds. In the indexes normally used by the national statistical institutes, rices are weighted in roortion to household exenditure in the index relative to the individual household, and they are weighted in roortion to aggregate exenditure in the national index. These indexes, in fact, are calculated as weighted averages of relative rices. The weights are therefore the shares of each good in total exenditure at both the household and the national level. onsequently, under the above-stated hyothesis regarding rices, the two indexes differ only in the weights used: for the national index, the weights corresond to the shares of each good in total exenditure by the country as a whole; for the family index, they corresond to the shares of each good in total exenditure by each household. Given that the national rice index is a weighted average of the indexes of individual households, those of the latter that send more obviously have a greater imact on the country s sending. Wealthier households therefore count for more in determination of the national index. This weighting is ointedly called lutocratic. 3 The alternative, where the contribution of each individual household corresonds to its own rice index, is termed a democratic rice index, which must be calculated as the unweighted average of the household rice indexes. In general, democratic and lutocratic rice indexes seem to differ not only in their amounts but also in their dynamics. For examle, an increase in the rice of cigarettes imacts, consumtion remaining equal, more on low-income households; and this increases the democratic index to a greater extent than it does the lutocratic index. 3 It should be borne in mind that, for various reasons, the rice indexes roduced by national statistical institutes are always calculated using the lutocratic method. 4

5 It should also be ointed out that, in terms of economic theory, democratic indexes are just as valid as lutocratic ones (Kokoski, 2000). In what follows, starting from the hyothesis that households ay the same rices for the same goods, we construct the democratic rice indexes for Italy in the eriod lutocratic and democratic indexes: formal asects Indicating with 4 : [... ] = t t kt t = 0, ; () the vector (column) of the rices of the k goods and services considered with regard to the base situation (t=0) and the reference situation (t=), and with the same notation for the corresonding vector of quantities: [ q... q ] q = t t kt t = 0, ; (2) we can define the Laseyres rice index 5 as follows: L (,,q ) 'q S = = (3) 'q S Moreover, as well known, this index can be written as a function of the k relative rices and of the shares of sending s it defined as: itqit itqit s it = = ; i =,, k; t = 0,. (4) ' q S t t tt Using (4), we can rewrite the index defined by (3) as: S k ( ) 0,,q = = i L si0. (5) 0 0 S00 i0 The shoing baskets of goods and services q t considered thus far refer to the total quantities consumed by the H households of the country for which the rice index is 4 The quote character defines the transosition oeration. 5 To be stressed is that entirely similar relations between the various tyes of indexes hold for aasche indexes as well. 5

6 calculated. onsequently, using q th to denote the shoing basket relative to the generic h- th household, we have: H q = q. (6) t th h = Suosing that on each occasion (t = 0, ) households exerience the same configuration of rices t, the above exressions can be used to construct a rice index for each household. The rice index for the generic h-th household is: Lh k i (,,q ) si0h 0 0h =,, H, (7) i0 k where S 00h = i0qi0h is total sending by the h-th household in the base eriod, while s = q / S reresents to roortion of sending on the i-th good. i0h i0 i0h 00h Both the rice index (3) for the entire country and the rice indexes (7) calculated for individual households are weighted arithmetic averages for the same relative rices i / i0, and they differ only in their weighting systems. In fact, while the aggregate index (5) uses the roortions s i0 of total exenditure, the individual index (7) uses the roortion s i0h of exenditure by the h-th household. These two systems of weights are tied by the following relation: H i0qi0 S00h s i0 = = si0h,, k. (8) S00 S h = 00 Relation (8) shows that the shares of national exenditure for each good or service are the weighted averages of the shares of individual household budgets, where the weights are the roortions of exenditure by each household in national exenditure. Taking account of (5), (7) and (8), we can secify the national index in terms of the individual household indexes by means of the relation: L (,, q )= H S00h (,,q ) 0 0 S h = 00 Lh 0. (9) 0h 6

7 It is evident from (9) that each household contributes to determination of the national index with a weight roortional to its exenditure; and this justifies, as said, the definition of the lutocratic index. ontraosed to lutocratic indexes are the democratic indexes in which the same weight is assigned to each household. Hence the democratic index oosable to the lutocratic index (9) is: H (,,q ) = (,, q ) * L Lh. (0) 0 0 H 0 0h h = On comaring (9) and (0), one may ascertain that lutocratic indexes coincide with democratic ones if: each household sustains the same amount of exenditure (S 0h = constant,,, H); the roortions of the various goods and services urchased by households are the same (q i0h = q i0 /H;,,k;,, H); the relative rice variation is the same for each good or service ( i / i0 = r 0,,,k). Vice versa, the more the actual situation differs from that described by these conditions, the greater the differences between the values assumed by the two tyes of index will be. The choice of adoting a democratic or a lutocratic index is determined, not by formal considerations, but by the use that is to be made of the consumer rice index. It is referable to choose democratic indexes when addressing welfare olicy roblems where each household should have the same imortance. Vice versa, for the uroses of national accounting, it is referable that the same weight be assigned to each monetary unit, so that in this case lutocratic indexes are better. 3. The democratic index: a first attemt at estimation 6 Now described is a first attemt to calculate democratic indexes using Istat data on household consumtion and regional economic accounts. The calculation was based on the 6 For further details, see the Aendix. 7

8 hyothesis that households are homogeneous within 44 grous created on the basis of territorial districts (4 classes) and household tye ( classes). These indexes are reorted in the first section of Table. In order to calculate the democratic indexes of the four geograhic areas considered, we aggregated the indexes of each row in this section with a weight equal to the frequency of households in the various tyes (second section of Table ). In other words, assuming that all households in the same grou exerienced exactly the same value of the rice index, the latter contributed to determination of the national index with a weight roortional to the numerical size of the grou. This determined the democraticness of the index calculated, which was no longer based on the grou s total exenditure, as in lutocratic indexes, but on its numerical size. omarison between these two indexes (Table 2) clearly shows that the lutocratic index always assumes values lower than those of the democratic index. onsequently, comared with the latter, it tends to furnish a more attenuated icture of inflation for both the four geograhic areas and the country as a whole. The difference between the values of the lutocratic and democratic rice indexes is known as the lutocratic bias, and it can be interreted as a synthetic index exressing the extent to which rice rises differentially affect households. One deduces from the data that the lutocratic bias is just under one half ercentage oints for Italy as a whole and 8

9 Table onsumer rice indexes and number of households by geograhic area and household tye, Democratic consumer rice indexes by tye of household, HZ TYE TERRITORIAL DISTRITS Single erson aged under 35 Single erson aged Single erson aged over 65 hildless coule with householder aged under 35 hildless coule with householder aged hildless coule with householder aged over 65 oule with child oule with 2 children oule with 3 or more children Single arent Other ONSUMER RIE INDEXES (995=) NORTH- WEST NORTH EAST ENTRE SOUTH NUMBER OF HOUSEHOLDS NORD-WEST 200,23 689,685,00,56 55, , ,438,290, ,43 55, , ,975 NORD-EAST., ,25 622,942 33, , , ,42 667,438 33, ,223 3,47 ENTRE 33, ,70 578,446 88, , , , ,429 33,488 3,47 378,25 SOUTH. 33, , ,908, ,25 689,685,79,40,757, , , ,79 ITALY 578,446,935,569 3,8, ,454,535,06 2,29,535 4,093,67 4,5,865,090,48,668,594,290,379 DEMORATI ONSUMER RIES INDEXES (995=) ITALY % WITH RESET TO NAT. DEMO. I

10 Table 2 Democratic and lutocratic consumer rice indexes, ONSUMER RIE INDEXES (995=) GEOGRAHI AREA Democratic lutocratic [(a)-(b)]% indexes (a) indexes (b) NORD-WEST NORTH-EAST ENTRE SOUTH ITALIA eaks at around 3 oints for the North-West. To rovide more detail, it is ossible to disaggregate the national democratic index by the various household tyes. In this case, too, the results seem to reflect an oinion widely held by the ublic but which to date has been merely a ercetion: namely that rice increases imact to different extents on sending by the distinct household tyes. In articular, the bottom row of Table shows values consistently above the average for single-erson households, while the values for households with two or more children are below the national average. 4. onclusions The consumer rice indexes for the entire country and those for individual households are weighted arithmetic averages of relative rices, and they differ essentially in terms of their weighting systems. Whereas the former use the roortions of total exenditure on goods and services, the latter use the roortions of exenditure by each household. In the usual calculation of the index for the entire country, each household contributes to determining the national index with a weight roortional to its exenditure. In other words, the households that send more that is, the wealthier ones are reresented in calculation of the national index to a greater extent, and this exlains why the latter is termed the lutocratic index. In 0

11 contraosition to lutocratic indexes are the democratic ones in which the same weight is assigned to each household. The aer has resented a first estimation of the democratic rice indexes for Italy in the eriod The results are extremely interesting, in that they highlight significant differences between the two calculation methods. onsidering the imortance of the toic addressed, these reliminary findings on the one hand induce the authors to recommend that Istat should conduct targeted surveys on the matter, and on the other, to continue with more detailed inquiry. Aendix A. aasche democratic index. Using the notation followed in the text, the aasche lutocratic index ( ) is defined as follows: where iq i ( ) i,,q = = = 0 k q i0 i0qi S0 k i0 i S S 0 = s = is the roortion of sending on the i-th good, valued at base k i i0 s i0 (a.) eriod rices while the quantities relate to the reference eriod. Suosing that on every occasion (t = 0, ) families exerience the same configuration of rices, for the generic h-th family, the aasche rice index is: t k (,, q ) = i h s 0 h i0h,,, H, (a.2) i0 k Where i0q s ih i0h = i0qih i0qih = reresents the roortion of sending S 0h for the i-th good sustained by the h-th family, at the base eriod rices.

12 Taking account that the weights that aear in (a.) and (a.2) are tied by the relationshi: H = i0qi S s = 0h i0 si0h i =,, k, (a.3) S0 S0 we can exress the national index (a.) in terms of the single family indexes (a.2) through the exression: H (,, q ) = (,, q ) 0 S (a.4) 0h h 0 h S 0 To obtain the aasche democratic index (* ) we assign the same weight to each family: * H (,, q ) = (,, q ). (a.5) 0 H 0 h h A2. rocedure followed in the emirical alication. As already said in the main text, the two sources of data used are derived from the Regional Economic Accounts (Istat, 2004a) and the Household Exenditure Survey (Istat, 2004b) conducted by Istat. To obtain comarable data 7, the sending items (Regional Economic Accounts) and the consumtion grous (Household Exenditure Survey) have been aggregated into the following 0 items (denoted in the formulas with the subscrit i ): )Food, beverages and tobacco, 2) lothing and footwear, 3) Housing, water, electricity, gas and other fuels, 4)Furnishing, household equiment, routine maintenance of the house, 5) Health, 6) Transort, 7) ommunication, 8) Recreation and culture, 9) Education 0) Miscellaneous goods and services. Again for comarability, we choose as geograhical level of detail the following territorial districts (denoted in the formulas with the subscrit r): ) North West, 2) North East, 3) entre and 4) South. 7 For further details on inconsistencies between Household Exenditure Survey and National Accounts estimates see Istat (2000). 2

13 Let: 2002 ir2002 and 995 ir2002,, 0; r=,, 4, be the sending, from the Regional Accounts, of families resident in the r-th district to urchase the i-th category of good and services, valued, resectively, at current rices and at 995 rices. The rice indexes are calculated through the relationshis: 995 ir2002 = ir2002 ir2002,, 0; r=,, 4. Likewise, drawn from the Household Exenditure Survey is 2002 irh2002, which exresses sending to urchase the i-th category of good and services, in the r-th district, by the h-th family tye 8, valued at current rices. The same sending, valued at 995 rices: 995 irh2002, can be calculated under the hyothesis that in each district rices do not deend on the tye of family considered, through the following relationshi: 995 irh2002 = irh2002 ir2002,, 0; r=,, 4;,,. From this information it is ossible to obtain the rice indexes by district and family tye: 995 rh2002 = = rh2002 irh2002 irh2002 = rh2002 r =,.., 4; h =,,. (b.) 8 Refer to the tables in the text for a detailed descrition of the family items considered. 3

14 rice indexes (b.) reresent the basic comonents to build lutocratic or democratic tye consumtion rice indexes for the higher levels of aggregation. In articular, the lutocratic consumtion rice index for the r-th district is: 995 r2002 = irh2002 irh2002 = rh2002 rh2002 and substituting (b.): 995 r2002 = 995 rh rh2002 rh2002. (b.2) To obtain the corresonding democratic index, it is necessary to modify the weighting system of (b.2) relacing the sending on consumtion by the h-th family tye, resident in the r-th district, ( 995 rh2002 ) with the corresonding number of families (n rh ): * 995 r2002 = 995 rh2002 n rh n rh, (b.3) Likewise, the lutocratic consumtion rice index for the h-th family tye is: rh rh h2002 = r= rh2002 r= while the corresonding democratic index is: (b.4) 4

15 * 995 h2002 = rh2002 r= 4 r= n rh n rh. (b.5) 5

16 References Diewert W.E. (200). The onsumer rice Index and Index Number urose, Journal of Economic and Social Measurement. Diewert W.E. (2002). Harmonized Index of onsumer rices: Their oncetual Foundations, Working aer n. 30, Euroean entral Bank. Fisher M.F (2003). rice Index Aggregation: lutocratic Weights, Democratic Weights and Value Judgments, Relazione resentata al onvegno: R&D, Education and roductivity. An international conference in memory of Zvi Griliches ( ), aris, France. Istat (994). Numeri indici dei rezzi al consumo, in Metodi e Norme n. 30, Istat. Istat, (2000), Le nuove stime dei consumi finali delle famiglie secondo il Sistema euroeo dei conti SE95, Metodi e Norme, n.7. Istat (2004a). onti economici regionali; Anni Istat (2004b). I consumi delle famiglie; Anno Istat, (2007), Indicatori della dinamica dei rezzi al consumo er alcune tiologie di famiglie. Anni , Arofondimenti. Kokoski, M. (2000). Alternative I aggregations: two aroaches, BLS Montly Labor Review. Kokoski, M. (2003). Alternative onsumer rice Index Aggregations: lutocratic and Deocratic Aroaches, BLS Working aer No