BLS WORKING PAPERS

U.S. DEPARTMENT OF LABOR 

Bureau of Labor Statistics 

OFFICE OF PRICES AND LIVING

CONDITIONS 

 

Alternative Consumer Price Index Aggregations: Plutocratic and Democratic Approaches 

Mary Kokoski, U.S. Bureau of Labor Statistics 

 Working Paper 370

 December 2003 

All views expressed in this paper are those of the author and do not necessarily reflect the views or policies of the 

U.S. Bureau of Labor Statistics. 
Alternative Consumer Price Index Aggregations: Plutocratic and 

Democratic Approaches 

April, 2000 

Mary Kokoski 

US Bureau of Labor Statistics 

Division of Price and Index Number Research 

The author would like to thank Rob Cage and Matthew Taylor for supplying data and research 

assistance, respectively. 
 2

Abstract 

Price indices are constructed to represent a population by using a sample of household 

expenditure information as weights. This expenditure information must be aggregated across 

households. In most cases, including the U.S. Consumer Price Index (CPI), the aggregation 

method used corresponds to a plutocratic index. Other types of aggregation, such as the 

democratic index, are also possible, and, in terms of economic theory, equally valid. In practice, 

the plutocratic approach is much more practicable, but it may provide a different measure of price 

change than the democratic index. 

This paper provides an empirical analysis of the differences between the plutocratic and 

democratic price indices, using data from the Consumer Expenditure Survey and the CPI for the 

periods 1987-1997, and for simulated price change scenarios. The results show that there is very 

little difference between the two types of index, and that one index need not always exceed the 

other. In the simulated scenarios, even the extreme cases where prices changed only for 

expenditure-inelastic goods and services, the difference between the democratic and plutocratic 

indices was only about one point for every ten percent increase in the relative prices of these 

goods. 
 3

Introduction: 

 The theory of the cost-of-living index, which underlies the consumer price index, is 

formulated within the context of the preferences and welfare of the individual. To construct an 

aggregate price index for a population requires that some method of aggregation be used to 

“average” the effects of price changes on all households in the population. It is intended that this 

aggregate index be representative of the “average” or “representative” household. 

 In most cases, including the U.S. Consumer Price Index (CPI), the aggregation method 

used corresponds to a plutocratic index. Other types of aggregation, such as the democratic index, 

are also possible, and, in terms of economic theory, equally valid. In practice, the plutocratic 

approach is much more practicable, but it may provide a different measure of price change than 

the democratic index. 

 This paper provides an empirical analysis of the differences between the plutocratic and 

democratic price indices, using data from the Consumer Expenditure Survey and the CPI for the 

periods 1987-1997. The analysis constructs household-specific price indices for the households in 

the CEX Interview sample, using the U.S. national average CPI series for all these households at 

the most detailed level of commodity disaggregation possible for these data sources. Since this 

was a period of low inflation, the analysis was extended to include some hypothetical scenarios of 

price change. While it is impossible to predict what prices will do in future markets, these 

scenarios provide some information on the sensitivity of the differences between the plutocratic 

and democratic indices. 

Theory: 

 The theory of the cost-of-living index, which underlies the consumer price index concept, 

is based on the observed preferences and implied welfare of a single individual- - or a single 

household, if it is assumed to behave as a cohesive decision-making unit. In practice, however, it 

is not possible for a government to produce a separate price index for each household in its 

population. Instead, statistical agencies construct an average, or representative index in order to 

measure the effects of price changes on the average or representative, household. 

 

 In the US, the Consumer Price Index (CPI) is the aggregate, representative measure of 

price change as experienced by households. It is based largely on the Laspeyres index formula, 

and statistical samples of household expenditure, prices, and area population for urban areas. For 

the CPI, information is collected on a representative sample of US urban households to determine 

their expenditure patterns by using the Consumer Expenditure Survey (CEX). Information on 

prices is collected from a sample of outlets and products based on their likelihood of being 

patronized and purchased, respectively. The overall CPI is then constructed by taking a weighted 

average of household information, and the result is a plutocratic Laspeyres price index. 

 To see this more formally, one would first define the Laspeyres price index for each 

individual household, h, as follows: 

(1) n n

h Lh = ∑ Sn P , 
 4

where: Lh is the index value for household h, h

n S is the share of household h’s total expenditures 

devoted to good n, and Pn is the market price relative for good n. It is assumed that all 

households face the same market prices for goods and services. An aggregate Laspeyres index for 

a population is, therefore, a weighted average of the price index values for all households in the 

population. If there are H households in the population, the aggregate index would look like (2), 

below: 

(2) n n

h

n

H

h

LH ∑ wh∑ S P = = 1 , 

where: wh represents the weight given to the individual index for household h in computing the 

average. 

 The choice of the weighting scheme used to derive the aggregate price index is not 

prescribed specifically by economic theory. It depends upon the assumptions adopted about the 

social welfare function for the society whose index it is to represent. (See Pollak (1981) for more 

detail on this general issue.) If we decide to accord equal weight to each household in its 

representation in the aggregate index, then wh = 1/H for all households h and the aggregate price 

index follows the democratic formula. If we decide to weight each household in accordance to its 

total household expenditure, then the weights are determined by equation (3) below: 

(3) ∑ =

h h

h

h E

E

w , 

where: Eh is the total expenditure of household h. Using this weighting scheme equation (2) 

becomes the plutocratic formula. 

 The advantage of the plutocratic formula is that the expenditure shares for each good by 

all households are treated as if they were those of one, aggregate “super-household” (Diewert 

(1983)). This means that the index can be constructed from information just on the prices and 

aggregated mean expenditure shares of all households. To produce a democratic index, one must 

first construct the price indices for each individual household first, then average them to produce 

an aggregate index. This is far less practicable. 

 

 In the democratic index, the expenditure pattern of each household counts in 

equal measure in determining the population index; in essence, it is a case of “one household- one 

vote”. In the plutocratic case, the contribution of each household’s expenditure pattern is 

positively related to the total expenditure of that household relative to other households- in 

essence, “one dollar, one vote”. If all households, regardless of how much they spend in total, 

have the same expenditure pattern, then both formulas would give the same index number as a 

result. Also, if all prices change by the same amount, the two index formulas will give the same 

result (a trivial case). However, if expenditure patterns differ across households, then there is no 

reason to expect the democratic and plutocratic indices to provide the same numbers. Most 

importantly, if the expenditure patterns of households differs systematically according to how 

much they spend in total, then the differences between the democratic and plutocratic formulas is 

of more than academic interest. 

It is reasonable to assume that household expenditure is strongly related to household 

income, at least relative to other households. Richer households are likely to spend more in any 

given time period than poorer households. They are also more likely to spend a higher proportion 
 5

of their total expenditure on different goods and services than are poorer households, specifically 

those goods which are not income-elastic or “necessities” (e.g. food and shelter, as opposed to 

entertainment and travel). In this situation, the democratic index may be more representative of 

the inflation experience of the less rich households, while the plutocratic index may be more 

representative of richer households. 

Empirical Experience:

 To assess the importance of the choice of a plutocratic versus a democratic approach for 

the CPI, we start with an historical empirical analysis. We use the same data as for the CPI, 

specifically the Consumer Expenditure Survey to provide the household expenditure weights and 

CPI item price indices for the price changes in goods and services. The CEX sample comprises 

the 1982/84 households in the Interview Survey. For the CPI, both an Interview and a Diary 

survey are undertaken to provide the expenditure weights. Households participating in the 

Interview survey provide information on their expenditures on various goods and services in four 

separate quarterly interviews. The Diary survey complements the Interview by collecting 

expenditure information on more detailed categories of goods and services, those which are 

purchased frequently such as food. This survey comprises a different sample of households than 

the Interview participants and is administered in two weekly installments. For the CPI, 

information from the Diary is statistically raked into the expenditure share information from the 

Interview. For example, while the Interview provides the expenditure share for all food at home, 

the Diary allows this share to be further disaggregated into the various categories of food items. 

While this works well for the CPI, a plutocratic method, the construction of an alternative, 

democratic index requires constructing household level price indices and thus limits the analysis 

to the Interview sample and level of detail. The total number of households in this analysis is 18, 

984. 

 The time period encompassed by the analysis is 1987-1997. By choosing 1987 as the 

reference period a few more detailed expenditure categories could be included which did not have 

separate item price indices in 1984. Beyond 1997, some item category definitions changed, which 

would have limited the level of detail as well. The total number of expenditure categories is 146. 

Unfortunately, there are no data available to determine whether there are differences in the prices 

paid for any goods and services across households. It is assumed that the same U.S. national 

urban average CPI prices apply to all the households in the sample. 

 While the household indices were constructed from 146 expenditure categories, it is 

difficult to get a sense of price change patterns from such a detailed list of item price indices. 

Thus, to provide a setting for the analysis, Table 1 presents an overview of the price changes for 

the period 1987-1997 (1987=100) by general expenditure category. As this table shows, the 

relative prices for fuels and utilities and housefurnishings increased most slowly, while those of 

medical care and other goods and services increased most rapidly. Overall, however, inflation 

rates were lower than in other periods such as the 1970s and early 1980s. 
 6

Table 1: Price Indices by Major Expenditure Category, 1987=100 

Year Food Housing Fuel/Util Housfurn Apparel Transport Medical Entertnmt Other 

1987 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 

1988 104.1 103.8 101.4 102.2 104.3 103.1 106.5 104.3 106.6 

1989 110.0 107.7 104.7 103.8 107.2 108.3 114.8 109.7 114.9 

1990 116.4 112.5 108.3 105.8 112.2 114.3 125.1 114.9 123.7 

1991 120.5 117.0 111.9 108.3 116.4 117.5 136.1 120.0 133.5 

1992 122.2 120.4 114.4 110.2 119.3 120.0 146.1 123.4 142.7 

1993 124.8 123.6 117.8 111.4 120.9 123.7 154.8 126.5 150.1 

1994 127.7 126.8 119.2 113.0 120.6 127.4 162.9 130.2 154.5 

1995 131.2 130.0 120.1 114.8 119.4 132.0 169.5 132.7 161.0 

1996 135.4 133.8 123.8 116.4 119.1 135.7 175.4 136.8 167.6 

1997 138.9 137.3 127.0 117.1 120.2 136.9 180.3 139.9 174.9 
 7

 Household-specific price indices were constructed for each household in the 1982/84 

CEX sample. These indices were then aggregated by both the plutocratic method and the 

democratic method, following the formulae in the previous section. The resulting aggregate index 

values are presented in Table 2, below, along with the percentage difference between the 

plutocratic index value and its corresponding democratic index counterpart by year. 

Table 2: Index Values, Plutocratic and Democratic, (whole sample), base=1987 

Year Plutocratic (P) Democratic (D) Percentage Difference 

1987 100.00 100.00 0

1988 103.76 103.84 -0.077

1989 108.38 108.90 -0.480

1990 113.71 114.93 -1.073

1991 117.95 119.14 -1.009

1992 121.27 122.22 -0.783

1993 124.95 125.57 -0.496

1994 128.30 128.59 -0.226

1995 132.05 132.03 0.015

1996 135.61 135.92 -0.229

1997 138.01 138.70 -0.500

 Generally, it appears that there is very little difference between the two types of indices 

over this study period, with the democratic index usually slightly higher in value. The largest 

differences are about one index point, and occur in years 1990 through 1992. The inflation rates 

for most commodities appear to be somewhat higher during this three-year period within the 

study period. In one year, 1995, it appears that the plutocratic index value exceeds its democratic 

counterpart. There is no overall trend or divergence between the two index series. Since the 

statistical significance of these results are not known, it is difficult to draw quantitative, rather 

than qualitative conclusions from the index values. 

 The practical implications of using the plutocratic versus the democratic price index 

formula depend upon the extent of systematic differences in expenditure patterns across 

households and the patterns of price changes experienced by these households. Since the 

plutocratic index will likely be more representative of those households with higher total 

expenditures, it would be of interest to examine the differences between the plutocratic and 

democratic aggregations by population subgroups defined by different levels of total expenditure. 

Therefore, we have divided the household sample into expenditure quintiles and constructed 

separate plutocratic and democratic indices by quintile. The lowest quintile (Q1) includes those 

households which are in the lowest 20% of the CEX sample, as ranked by total household 

expenditure. The highest quintile (Q5) is, therefore the highest 20% of households in terms of 

expenditure. While each quintile includes the same number of households, the range and mean of 

total expenditures by quintile varies, as described in Table 3, below: 
 8

Table 3. Mean and Range of Total Expenditures by Expenditure Quintile 

Quintile Mean Expenditure Range of Expenditure Amounts

Q1 $1066.57 $6.00- $1737.13 

Q2 $2389.00 $1737.14- $3069.69 

Q3 $3863.32 $3069.80- $4730.88 

Q4 $5933.02 $4730.99- $7522.17 

Q5 $13195.87 $7522.20- $89561.12 

As Table 3 shows, the range of total expenditure values encompassed by each quintile 

varies from about $1600 (Q1 through Q3) to a high of over $80,000 in Q5. Doubtless there are a 

few “outlier” households in the highest quintile. However, since they are legitimate members of 

the sample and represent the very high-expenditure households in the population, they are not 

eliminated from this study. 

 The plutocratic and democratic index values by expenditure quintile are presented in 

Table 4A., where P= the plutocratic index and D= the democratic index. Table 4B. provides the 

percentage difference between the plutocratic value and its democratic counterpart, based on the 

values in Table 4A. 

Table 4A: Index Values by Expenditure Quintile, base=1987 

 Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Year P D P D P D P D P D

1987 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 

1988 103.74 103.73 103.86 103.86 103.89 103.89 103.97 103.97 103.62 103.74 

1989 109.32 109.35 109.19 109.19 108.99 109.00 108.90 108.90 107.74 168.04 

1990 116.11 116.19 115.63 115.65 115.15 115.16 114.79 114.81 112.26 112.82 

1991 120.06 120.09 119.90 119.91 119.51 119.52 119.14 119.17 116.41 117.02 

1992 122.62 122.54 122.96 122.96 122.73 122.74 122.50 122.52 119.87 120.48 

1993 125.28 125.12 126.08 126.06 126.05 126.05 126.08 126.09 123.89 124.52 

1994 127.85 127.64 128.93 128.90 129.02 129.01 129.24 129.24 127.59 128.15 

1995 130.84 130.60 132.14 132.11 132.37 132.36 132.87 132.85 131.68 132.27 

1996 135.05 134.85 136.26 136.23 136.30 136.30 136.66 136.65 134.85 135.56 

1997 138.09 137.82 139.36 139.34 139.31 139.31 139.47 139.47 136.72 137.58 
 9

Table 4B: Percentage Difference between Plutocratic and Democratic Index, by Year and 

Quintile 

Year Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 

1987 0 0 0 0 0

1988 9.64E-03 0 0 0 -0.116

1989 -0.027 0 -9.2E-03 0 -55.968

1990 -0.069 -0.017 -8.7E-03 -0.017 -0.499

1991 -0.025 -8.3E-03 -8.4E-03 -0.025 -0.524

1992 0.0652 0 -8.1E-03 -0.016 -0.509

1993 0.1277 0.0159 0 -7.9E-03 -0.509

1994 0.1643 0.0233 7.75E-03 0 -0.439

1995 0.1834 0.0227 7.55E-03 0.0151 -0.448

1996 0.1481 0.022 0 7.32E-03 -0.527

1997 0.1955 0.0144 0 0 -0.629

As for the sample taken as a whole, the differences between the two types of index within 

each quintile are generally quite small. The largest differences appear in the first and fifth 

quintiles, not unexpected in the latter case. In Q5 there are a very few households with very high 

expenditures which therefore have a larger effect on the plutocratic index, while the democratic 

index diminishes their disproportionate contribution to the index value. Still, while the democratic 

index for Q5 rises more quickly than its plutocratic counterpart, the differences are generally less 

than an index point. In other quintiles there is no consistent pattern; the plutocratic index value 

often exceeds the democratic index value. Comparing index values by index type across quintiles 

an interesting pattern emerges. For the plutocratic index there is a general inverted U-shaped 

pattern, with higher index values in the middle three quintiles and lower values in Q1 and Q5. 

The cross-quintile pattern for the democratic index is different, with generally the lowest index 

values in the highest quintile, Q5. Again, the differences are quite small. 

 Past empirical studies have shown that differences in expenditure patterns based on 

household demographic attributes are generally not statistically significant (Michael (1979), 

Hagemann (1982)) and separate indices for different demographic groups do not necessarily 

better represent subgroups within larger groups (Kokoski (1987)). For most a priori definitions of 

demographic groups, there is generally more variation across households within each group than 

there is across groups. Since the statistical significance of any differences observed here between 

quintile indices is unknown, one should not draw quantitative conclusions from these results. 

 

 Empirical analysis relies upon observed information. In recent years (the study period), 

both overall inflation and variability of price changes relative to each other have been smaller 

than in other historical periods. Thus price index values have exhibited very little change. If 

plutocratic and democratic indices do not differ much over the period of empirical observation, 

conclusions from an empirical analysis cannot be easily generalized and the sensitivity of the 

issue to more extreme experiences of price change has not been tested. In the context of the 

Laspeyres index, because of its fixed weight property, it is fairly straightforward to perform a 

simple sensitivity test of this issue. This is done by posing hypothetical scenarios of price change 

and assessing the resulting effects on the comparison of plutocratic and democratic index 

formulations. 
 10

Hypothetical Scenarios:

 If the historical period of study does not provide much evidence of a difference between 

the plutocratic and democratic index alternatives, then one might ask what price change scenarios 

would make this issue of practical importance. It is impossible to predict what specific price 

regimes might occur in the future, or how consumer behavior might change and make the fixedweight Laspeyres assumption untenable. It is also impractical to simulate large numbers of 

hypothetical price change scenarios and attempt to summarize them in a meaningful way. 

Nevertheless, it may be illuminating to simulate a few scenarios for price change, including a few 

extremes, and make a qualitative assessment of their effects. 

 Since the issue of plutocratic and democratic index differences is driven by differences in 

expenditure patterns among households which are correlated with total expenditure (and, thus, 

likely income) we have framed this hypothetical analysis within this context. First, we pose 

several degrees of price change, from a decline of 10% to an increase of 500%. Using the 

observed relative prices for 1987 as the reference, we pose these hypothetical price change 

scenarios on the CEX sample in the previous analysis for two different groups of commodities 

and services, while all other prices are held the same (i.e. at the 1987 level). 

 Based on a survey of the empirical literature, and the observed expenditure shares by 

quintile in our CEX sample, we identify a set of commodities and services as “necessities” and 

“luxuries”. Necessities are those goods and service categories which are expenditure (or income) 

inelastic. “Luxuries” are expenditure (and income) elastic goods. This is not a finely detailed, or 

by any means a definitive categorization, but we have included in necessities the following: food 

at home, shelter, fuels and utilities, motor fuel, vehicle maintenance and repair, tobacco products, 

and personal care. Among luxuries we include alcoholic beverages, food away from home, 

housefurnishings, and entertainment. These two groups are not mutually exhaustive since several 

categories of goods and services appeared to be ambiguous or their elasticities unknown , based 

on the existing literature. Any number of groupings of item categories is possible, even given this 

elasticity criterion, and this is intended to be illustrative. 

While it may not be informative to provide the expenditure shares by 146 detailed 

categories, Table 5 presents a summary for more aggregate categories by expenditure quintile. 

These shares generally corroborate the economic literature, with lower quintiles having higher 

shares for food, housing, and fuels and utilities. Private transportation, because it includes not 

only motor fuels, and maintenance and repair, but also vehicle purchases themselves, has a higher 

relative share for higher quintile groups. Higher quintile groups also spend relatively more on 

entertainment and housefurnishings. 
 11

Table 5: Expenditure Shares, Average, by Expenditure Quintile 

Commodity Quintile 1 Quintile 2 Quintile3 Quintile 4 Quintile 5 

Food 0.302 0.294 0.271 0.268 0.241 

Housing 0.170 0.185 0.181 0.157 0.103 

Fuels/Utilities 0.168 0.170 0.156 0.156 0.116 

Furnishings 0.033 0.044 0.049 0.055 0.073 

Apparel 0.057 0.049 0.053 0.055 0.069 

Private Trans. 0.069 0.105 0.129 0.150 0.229 

Medical Care 0.108 0.072 0.072 0.071 0.060 

Entertainment 0.025 0.027 0.031 0.033 0.050 

Other 0.067 0.055 0.057 0.055 0.059 

The index values for the hypothetical scenarios are presented in Table 6 for the aggregate 

sample of households. In Tables 7A and 8A we provide the index values for the same scenarios 

by expenditure quintile. Tables 7B and 8B provide the corresponding differences between the 

plutocratic and democratic index values by expenditure quintile and price change scenario. The 

results in Table 6 show the expected result that the democratic index will increase more rapidly 

than the plutocratic as the relative prices of necessities increase. It appears that the democratic 

index will exceed its plutocratic counterpart by one index point for every 10% change in 

necessities prices. Thus, if necessities prices should rise by 100%, the democratic index will be 10 

points higher, or 14% higher, than the plutocratic. The designated luxury goods group represents 

a smaller proportion of the average household’s total expenditures than necessities, so the impact 

of radically changing its prices is much less. As expected, under these scenarios the plutocratic 

index will rise more quickly than its democratic counterpart. The maximum difference, however, 

is less than one index point, or 0.4%, when luxury prices rise by the extreme of 500%. 
 12

Table 6: Simulated Price Change Scenarios 

 Necessities Luxuries

Price Change P D % Change P D % Change

0% 100 100 0 100 100 0

-10% 96.17 94.18 2.0692524 98.04 98.06 -0.0204

-5% 97.58 97.09 0.5021521 99.02 99.03 -0.010099

-1% 99.51 99.42 0.0904432 99.8 99.81 -0.01002

1% 100.48 100.58 -0.0995223 100.2 100.19 9.98004E-03

5% 102.42 102.91 -0.4784222 100.98 100.97 9.90295E-03

10% 104.83 105.82 -0.9443861 101.96 101.94 0.0196155

15% 107.25 108.73 -1.3799534 102.93 102.91 0.0194307

20% 109.67 111.64 -1.796298 103.91 103.88 0.0288711

50% 124.17 129.11 -3.9784167 109.78 109.7 0.072873

100% 148.34 158.21 -6.6536335 119.56 120.22 -0.552024

120% 158.01 169.85 -7.4931966 123.47 123.27 0.1619827

130% 162.84 175.67 -7.8788995 125.42 125.21 0.1674374

50% 172.51 187.31 -8.5792128 129.38 129.09 0.2241459

200% 196.68 216.42 -10.0366077 139.11 138.78 0.2372223

250% 220.85 245.52 -11.1704777 148.89 148.48 0.2753711

300% 245.02 274.63 -12.0847278 158.67 158.18 0.308817

350% 269.19 303.73 -12.8310859 168.44 167.87 0.3383994

400% 293.36 332.84 -13.4578675 178.22 177.57 0.3647178

450% 317.53 361.94 -13.9860801 188 187.26 0.393617

500% 341.7 391.05 -14.4424934 197.78 196.96 0.4146021
 13

Table 7A: Simulated Price Changes, Necessities, by Quintile 

Price Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Change P D P D P D P D P D

0% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 

-10% 93.35 93.41 93.47 93.46 93.76 93.74 94.31 94.29 96.42 96.01 

-5% 96.68 96.70 96.73 96.73 96.88 96.87 97.16 97.14 98.21 98.00 

-1% 99.34 99.34 99.35 99.35 99.38 99.37 99.43 99.43 99.64 99.60 

+1% 100.67 100.66 100.65 100.65 100.62 100.63 100.57 100.57 100.36 100.40 

+5% 103.33 103.30 103.27 103.27 103.12 103.13 102.84 102.85 101.79 102.00 

+10% 106.65 106.59 106.53 106.54 106.24 106.26 105.69 105.72 103.58 104.00 

+15% 109.98 109.89 109.80 109.81 109.37 109.39 108.53 108.57 105.38 105.99 

+20% 113.30 113.18 113.06 113.08 112.49 112.52 111.37 111.43 107.17 107.99 

+50% 133.25 132.96 132.66 132.71 131.22 131.31 128.44 128.57 117.92 119.97 

+100% 166.50 165.91 165.31 165.42 162.44 162.81 156.87 157.15 135.83 139.95 

+120% 179.80 179.10 178.38 178.50 174.92 175.13 168.25 168.58 143.00 147.94 

+130% 186.45 185.67 184.91 185.05 181.17 181.39 173.93 174.29 146.58 151.93 

+150% 199.75 198.87 197.97 198.13 193.65 193.91 185.31 185.72 153.75 159.92 

+200% 233.00 231.83 230.62 230.84 224.87 225.22 213.74 214.29 171.66 179.89 

+200% 266.25 264.79 263.28 263.55 256.09 256.52 242.18 242.87 189.58 199.87 

+300% 299.50 297.74 295.94 296.26 287.31 287.83 270.62 271.44 207.49 219.84 

+350% 332.75 330.70 328.59 328.97 318.53 319.13 299.05 300.00 225.41 239.81 

+400% 366.00 363.66 361.25 361.28 349.74 350.44 327.49 328.59 243.32 259.79 

+450% 399.25 396.61 393.91 394.39 380.96 381.74 355.92 357.16 261.24 279.76 

+500% 432.50 429.57 426.56 427.10 412.18 413.05 384.36 385.74 279.15 299.73 

Table 7B: Percentage Differences Between Plutocratic and Democratic Index, by Scenario and Quintile, 

Necessities 

Price Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Change

0% 0 0 0 0 0

-10% -0.064 0.0107 0.0213 0.0212 0.4252

-5% -0.021 0 0.0103 0.0206 0.2138

-1% 0 0 0.0101 0 0.0401

1% 9.93E-03 0 -9.9E-03 0 -0.04

5% 0.029 0 -9.7E-03 -9.7E-03 -0.206

10% 0.0563 -9.4E-03 -0.019 -0.028 -0.405

15% 0.0818 -9.1E-03 -0.018 -0.037 -0.579

20% 0.1059 -0.018 -0.027 -0.054 -0.765

50% 0.2176 -0.038 -0.069 -0.101 -1.738

100% 0.3544 -0.067 -0.228 -0.178 -3.033

120% 0.3893 -0.067 -0.12 -0.196 -3.455

130% 0.4183 -0.076 -0.121 -0.207 -3.65

150% 0.4406 -0.081 -0.134 -0.221 -4.013

200% 0.5021 -0.095 -0.156 -0.257 -4.794

250% 0.5484 -0.103 -0.168 -0.285 -5.428

300% 0.5876 -0.108 -0.181 -0.303 -5.952

350% 0.6161 -0.116 -0.188 -0.318 -6.388

400% 0.6393 -8.3E-03 -0.2 -0.336 -6.769

450% 0.6612 -0.122 -0.205 -0.348 -7.089

500% 0.6775 -0.127 -0.211 -0.359 -7.372
 14

Table 8A: Simulated Price Change, Luxuries, by Quintile 

Price Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Change P D P D P D P D P D

0% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 

-10% 98.23 98.17 98.23 98.23 98.06 98.07 97.85 97.86 98.08 97.98 

-5% 99.11 99.09 99.11 99.12 99.03 99.03 98.93 98.93 99.04 98.99 

-1% 99.82 99.82 99.82 99.82 99.81 99.81 99.79 99.79 99.81 99.80 

+1% 100.18 100.18 100.18 100.18 100.19 100.19 100.22 100.21 100.19 100.20 

+5% 100.89 100.92 100.89 100.88 100.97 100.97 101.08 101.07 100.96 101.01 

+10% 101.77 101.83 101.77 101.76 101.94 101.93 102.15 102.14 101.92 102.02 

+15% 102.66 102.75 102.66 102.65 102.91 102.90 103.22 103.21 102.88 103.03 

+20% 103.55 103.66 103.55 103.54 103.89 103.87 104.30 104.28 103.84 104.04 

+50% 108.87 109.16 108.87 108.84 109.71 109.67 110.75 110.70 109.60 110.11 

+100% 117.74 118.31 117.73 117.68 119.43 119.34 121.49 121.41 119.20 120.22 

+120% 121.29 121.97 121.28 121.22 123.31 123.21 125.79 125.69 123.04 124.27 

+130% 123.07 123.80 123.05 122.99 125.25 125.14 127.94 127.83 124.96 126.29 

+150% 126.61 127.46 126.59 126.53 129.14 129.01 132.24 132.11 128.80 130.33 

+200% 135.49 136.62 135.46 135.37 138.85 138.67 142.98 142.81 138.40 140.45 

+250% 144.36 145.77 144.32 144.21 148.56 148.34 153.73 153.52 148.00 150.56 

+300% 153.23 154.93 153.19 153.05 158.28 158.01 164.47 164.22 157.60 160.67 

+350% 162.10 164.08 162.05 161.89 167.99 167.68 175.22 174.92 167.20 170.78 

+400% 170.97 173.24 170.92 170.73 177.70 177.35 185.96 185.62 176.80 180.89 

+450% 179.84 182.39 179.78 179.58 187.42 187.02 196.71 196.33 186.40 191.00 

+500% 188.71 191.55 188.65 188.42 197.13 196.69 207.45 207.03 196.00 201.11 

Table 8B: Percentage Differences Between Plutocratic and Democratic Index, by Scenario and Quintile, 

Luxuries 

Price Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Change

0% 0 0 0 0 0

-10% 0.0611 0 -0.01 -0.01 0.102

-5% 0.0202 -0.01 0 0 0.0505

-1% 0 0 0 0 0.01

1% 0 0 0 9.98E-03 -1E-02

5% -0.03 9.91E-03 0 9.89E-03 -0.05

10% -0.059 9.83E-03 9.81E-03 9.79E-03 -0.098

15% -0.088 9.74E-03 9.72E-03 9.69E-03 -0.146

20% -0.106 9.66E-03 0.0193 0.0192 -0.193

50% -0.266 0.0276 0.0365 0.0451 -0.465

100% -0.484 0.0425 0.0754 0.0658 -0.856

120% -0.561 0.0495 0.0811 0.0795 -1.00

130% -0.593 0.0488 0.0878 0.086 -1.064

150% -0.671 0.0474 0.1007 0.0983 -1.188

200% -0.834 0.0664 0.1296 0.1189 -1.481

250% -0.977 0.0762 0.1481 0.1366 -1.73

300% -1.109 0.0914 0.1706 0.152 -1.948

350% -1.221 0.0987 0.1845 0.1712 -2.141

400% -1.328 0.1112 0.197 0.1828 -2.313

450% -1.418 0.1112 0.2134 0.1932 -2.468

500% -1.505 0.1219 0.2232 0.2025 -2.607
 15

In Table 7 the pattern of differences between index types across quintiles is somewhat 

more interesting. In the lowest quintile the plutocratic index exceeds the democratic, but by a 

very small amount. In the other quintiles the democratic index exceeds the plutocratic when 

necessities prices rise, but, again the differences are very small. The largest divergence between 

index types is, as expected, within the highest quintile, Q5, but, still, only 4 index points with a 

doubling of necessities prices. In Table 8, the pattern comparing index types across quintiles is 

the opposite of Table 7. The largest divergence is, again, in quintile 5, at about one index point 

for a doubling of luxuries prices. 

While in some cases extreme, these scenarios give some indication of the maximum 

effects that price changes could impose on the comparison of plutocratic and democratic indices. 

It is the pattern of price changes, not the general level of inflation, which matters for this issue. In 

the empirical analysis of the previous section, the democratic index exceeded the plutocratic by 

about 0.6 points in 1997, when prices were less than 40% higher than the reference period. If the 

prices of only necessities were to increase by 50% the simulated democratic index exceeded the 

simulated plutocratic index by 5 points. Since patterns of price change cannot be predicted, this 

leaves the issue as an empirical matter. 

Conclusions: 

 The foregoing analysis examines the issue of the choice between the plutocratic (“one 

dollar-one vote”) approach and the democratic (“one household-one vote”) approach to 

constructing an aggregate price index for a society. Neither is favored by economic theory, but 

each incorporates different normative assumptions about the social welfare function. The extent 

to which the two types of index formulation will give different index values is an empirical issue 

and depends upon systematic difference in household expenditure patterns, the patterns of price 

changes which occur, and the assumptions about household behavior which underlie the index 

formula used to construct a household-level index. This empirical and hypothetical analysis used 

data from the Consumer Expenditure Survey and the CPI, at the greatest level of commodity 

disaggregation possible. The results show that there is little difference between the democratic 

and plutocratic index values for the period 1987-1997, and that the one index type need not 

always exceed the other. Extreme scenarios for price changes for only expenditure-inelastic 

goods showed a difference between the democratic and plutocratic index values of about 1 index 

point for every 10% increase in the relative prices of these goods. 

 A complete examination of this issue would take into consideration other aspects for 

which empirical information are not, at present, available: 

 

(1) Differences in price changes faced by different households, or different demographic 

groups of households, remains an empirically elusive issue. Unfortunately, data collected for the 

CPI do not identify the prices paid by survey households for the goods and services they 

purchase. It is possible that poorer households are restricted in their choice of outlets and, thus, 

prices they pay for goods, but there is no definitive empirical information on this. (2) The 

treatment of quality change in durable goods can affect the choice of index type. This is 

especially true for those goods for which the purchase decision may be discrete (not “how much”, 

but “do I buy one or not”), (Erickson (1998)). (3) The level of detail at which commodities and 

services are defined for the CPI also does not allow a fine discrimination of which specific items 

within a goods category are being purchased by individual survey households. Expenditure shares 
 16

can be derived for steak, but not the grade or the cut (filet mignon or top sirloin). In a very 

complex economy such a level of detail would be extremely difficult to capture for price index 

computation. Yet, it may be at this level of detail that differences in expenditure patterns, and 

thus the experience of inflation, may differ across household groups. (4) The assumption of a 

fixed weight index, or the choice of which index formula to employ to best describe a 

household’s behavior to minimize the impact of price increases, can affect the comparison. The 

expenditure shares observed in a given sample of households in a given survey period might well 

be different from those of households in another period, under different relative prices and other 

economic conditions. 

 

 
 17

References 

Diewert, W.E. (1983) “The Theory of the Cost-of-Living Index and the Measurement of 

Welfare Change,” in W.E. Diewert and C. Montmarquette (eds.) Price Level Measurement, 

Statistics Canada, pp. 163-233. 

Erickson, T. (1998) “The Ambiguous Effect of New and Improved Goods on the Cost-ofLiving” , forthcoming Economics Letters.

Hagemann, R.P. (1982) “The Variability of Inflation Rates across Household Types,” 

Journal of Money, Credit, and Banking, vol. 14, pp. 494-510. 

Kokoski, M. F. (1987) “Consumer Price Indices by Demographic Group,” BLS Working 

Paper No. 167, April. 

Michael, R. T. (1979) “Variation Across Households in the Rate of Inflation,” Journal of 

Money, Credit, and Banking, vol. 11, pp. 32-46. 

Pollak, R. (1981) “The Social Cost-of-Living Index”, Journal of Public Economics, vol. 

26, pp. 126-134.