I. INTRODUCTION

In all countries, the official consumer price index (CPI), which is meant to be representative for a certain reference population, is a fixed-weight price index. At least since Konüs (1924), economists have known that a fixed-weight CPI suffers from a “substitution bias” relative to a true cost-of-living index which, instead of maintaining constant the budget shares of the households represented in the index, maintains constant their living standards or welfare levels. But according to the review of the literature carried out by a United States Senate Commission headed by Michael Boskin (Boskin and others, 1996), this is not all that is wrong with the United States CPI elaborated by the Bureau of Labor Statistics (BLS).

The Boskin Commission focused on five sources of bias in the CPI, all of which are presumed to contribute to an overstatement of the true inflation in the cost of living in the United States. The Boskin Commission estimated that, on average, during the last few decades the United States CPI has been overstating inflation by 1.1 percent per year. This bias might seem small. However, when compounded over time, the implications for (i) the public deficit created through an indexed budget; (ii) the wage bargaining process and the determination of the nominal interest rates in the private sector; and (iii) the measurement of the economic performance in real terms, are dramatic.¹ The report has become very influential.² This does not mean, of course, that it has escaped criticism. Some critics question the Commission’s analysis of each and every one of the five sources of bias (Moulton and others, 1998). Others point out toward neglected issues and, in particular, the scant attention paid to distributional issues, to which we now turn our attention—see, e.g., Pollak (1998), Deaton (1998), and Madrick (1997).

In the CPI context, the issues raised by the heterogeneity of the population are usually identified by asking “Whose cost-of-living index?” a question which is seen to contain three issues in Pollak (1998). “How many cost-of-living indexes?” “Beer or champagne?” and “What type of group indexes?” The first issue refers to whether we should have different indcxes for different groups—rich and poor, elderly and nonelderly, urban and rural, etc. The second issue refers to the selection of the appropriate set of items, qualities and outlets that are to be reflected in the index.

The third issue, which is the topic of this paper, originates with the nature of the CPI as a group index. Given the commodity space and a household budget survey representative of the reference population, we can use each household’s budget shares as the fixed weights for the construction of household-specific price indexes. Since Prais (1958), we know that the CPI is the weighted average of such individual price indexes with weights proportional to each household’s total expenditures. Because richer households weigh more than poor ones, Prais baptized the CPI as a plutocratic price index. The question is whether we can think of a better alternative to this particular construction.³

In this paper, we argue that the so-called democratic index, in which all households receive the same weight, is an option worth pursuing. Thus, we define the plutocratic bias as the difference between the inflation measured according to the current official CPI and a democratic index. One reason in favor of such a concept is that it is always interesting to know who suffers the greatest inflation: those households with the largest total expenditures, or those at the bottom of the distribution, in which case we would say that prices have behaved in an anti-rich or an anti-poor manner, respectively. In the first (second) case we should expect that the mean inflation weighted by the total household expenditures would be greater (smaller) than the simple mean. Thus, the plutocratic bias would be positive or negative according to whether prices have behaved in an anti-rich or in an anti-poor manner, respectively—this idea can be traced back to Fry and Pashardes (1985).

Nevertheless, the importance of this concept depends crucially on its empirical magnitude. Our main result is that the plutocratic bias in Spain during the 1990s is equal to 0.055 percent per year—or about one-third of the classical substitution bias estimated by the Boskin Commission for the United States. Nonetheless, averaging magnitudes of different signs underestimates the real importance of this bias. The bias in specific years oscillates from a maximum of 0.150 to a minimum of –0.080 percent per year. The mean absolute bias is much larger, 0.090. Interestingly, neither the sign nor the magnitude of the bias in a given subperiod depends on the magnitude of the inflation in that subperiod. Using the total expenditures elasticities estimated in an Engel curve system, we find that a 16-dimensional commodity space can be conveniently reduced to three dimensions, consisting of a luxury good and two necessities. The price behavior of these three goods provides a convincing explanation of the oscillations experimented by the plutocratic bias.

The paper studies the robustness of these results in two dimensions. First, we estimate the plutocratic bias for the 1980s and the second part of the 1970s in Spain. We find that, on average, the bias is small in the first period and large in the second: 0.091 and 0.264 percent per year, respectively. Second, we ask what would have been the bias in the measurement of inflation if instead of using the plutocratic CPI we were to use a group index equal to the weighted mean of the household-specific indexes with weights proportional to the household size. We find that such a bias for the 1990s, the 1980s and the second part of the 1970s would be equal to 0.088, 0.064, and 0.254 percent per year, respectively.

II. INDIVIDUAL AND GROUP INDEXES

III. THE PLUTOCRATIC BIAS

In order to estimate the plutocratic bias defined below, we need to construct a series of household-specific Laspeyres price indexes. For that purpose, we use the following two pieces of publicly available information in Spain: the 1990–91 household-budget survey (EPF) used to estimate the weights of the official CPI, and a set of price subindexes at a certain level of spatial and commodity disaggregation. Using this information, for each household h interviewed in a quarter τ during the 1990–91 period (τ = Spring, Summer, Autumn of 1990, and Winter of 1991), we construct a series of modified Laspeyres SPIs, $\ell ({\mathbf{p}}_t,{\mathbf{p}}_0;{\mathbf{q}}_{\tau }^h)$ based on period 0 = Winter of 1991, which takes as a reference the commodity vector ${\mathbf{q}}_{\tau }^h$ actually acquired during the interview quarter τ. (See Appendix I for a description of these data sources and some issues regarding the definition of household expenditures.)

A. A Definition of the Plutocratic Bias

We will divide the period Winter 1991–January 1998 in the seven subperiods shown on Table 1 below. For each h we define the inflation (or deflation) caused by the evolution of prices in a given subperiod by:

Table 1.

The Plutocratic Bias During the 1990s

(In percent per year)

Source: Authors’ calculations.

Table 1.

The Plutocratic Bias During the 1990s

(In percent per year)

		Inflation
t	Subperiods	Plutocratic	Democratic	Plutocratic bias
1	Winter 91 to 1992	6.989	6.911	0.078
2	1992 to Jan 1993	5.394	5.244	0.150
3	Jan 93 to Jan 94	5.271	5.165	0.105
4	Jan 94 to Jan 95	4.621	4.701	-0.080
5	Jan 95 to Jan 96	4.079	4.130	-0.050
6	Jan 96 to Jan 97	3.180	3.090	0.090
7	Jan 97 to Jan 98	2.494	2.369	0.125
	Winter 91 to Jan 98	4.632	4.577	0.055
	Jan 93 to Jan 98, average absolute bias			0.090

Source: Authors’ calculations.

View Table

Table 1.

The Plutocratic Bias During the 1990s

(In percent per year)

		Inflation
t	Subperiods	Plutocratic	Democratic	Plutocratic bias
1	Winter 91 to 1992	6.989	6.911	0.078
2	1992 to Jan 1993	5.394	5.244	0.150
3	Jan 93 to Jan 94	5.271	5.165	0.105
4	Jan 94 to Jan 95	4.621	4.701	-0.080
5	Jan 95 to Jan 96	4.079	4.130	-0.050
6	Jan 96 to Jan 97	3.180	3.090	0.090
7	Jan 97 to Jan 98	2.494	2.369	0.125
	Winter 91 to Jan 98	4.632	4.577	0.055
	Jan 93 to Jan 98, average absolute bias			0.090

Source: Authors’ calculations.

${\pi }_t^h=\frac{{\ell }_t^h-{\ell }_{t-1}^h}{{\ell }_{t-1}^h}.$

The distribution of individual inflations in each subperiod is denoted by ${\pi }_t=({\pi }_t^1,\dots ,{\pi }_t^H)$ For the entire period, we have II = (IT¹,…,II^H), where ${\prod }^h=({\ell }_T^h-1)$ and T = Jan 98. The aggregate inflation for the population as a whole according to the plutocratic scheme is

${\text{PLUT}}_t=\frac{{\displaystyle {\sum }_h{\phi }^h({\ell }_t^h-{\ell }_{t-1}^h)}}{{\displaystyle {\sum }_h{\phi }^h{\ell }_{t-1}^h}}=\frac{{\displaystyle {\sum }_h{\phi }^h({\ell }_{t-1}^h)({\ell }_t^h-{\ell }_{t-1}^h)/{\ell }_{t-1}^h}}{{\displaystyle {\sum }_h{\phi }^h{\ell }_{t-1}^h}}={\displaystyle \sum _h{\psi }_t^h{\pi }_t^h,}$

where ${\psi }_t^h={\phi }^h{\ell }_{t-1}^h/{\displaystyle {\sum }_h{\phi }^h{\ell }_{t-1}^h}$ For the democratic scheme,

${\text{DEM}}_t=\frac{{\displaystyle {\sum }_h{\ell }_t^h-{\ell }_{t-1}^h}}{{\displaystyle {\sum }_h{\ell }_{t-1}^h}}={\displaystyle \sum _h{\xi }_t^h{\pi }_t^h,}$

where ${\xi }_t^h={\ell }_{t-1}^h/{\displaystyle {\sum }_h{\phi }^h{\ell }_{t-1}^h}$—note that ${\psi }_t^h$ is proportional to ${\phi }^h{\xi }_t^h$ Since ${\ell }_0^h=1$, for the overall period from 0 to T the weights simplify to φ^h and $\frac{1}{H}$ and we have $\text{PLUT}={\displaystyle {\sum }_h{\phi }^h({\ell }_T^h-1)}$, and $\text{DEM}=\frac{1}{H}{\displaystyle {\sum }_h({\ell }_{t-1}^h-1)}$ We define the plutocratic bias in the measurement of inflation in subperiod t by B_t = PLUT_t –DEM_t, and for the overall period by B = PLUT — DEM.⁷ Notice that, as pointed out in the Introduction, if price changes in subperiod t (or for the entire period) are relatively more detrimental to the rich, i.e., if ${\pi }_t^h$(or II^h) are greater for the rich than for the poor households, then we expect the plutocratic mean of individual inflations in the plutocratic case to be greater than the democratic mean. That is, B_t or B are positive (negative) according to whether the price change in the corresponding time interval is anti-rich (anti-poor).

C. An Economic Interpretation

Which goods are primarily consumed by the poor or the rich households? To answer this question, we must begin by recognizing the fact that, in a heterogeneous world, total expenditures of households with different characteristics are not directly comparable. Following Buhmann and others (1988) and Coulter and others (1992a, 1992b), we adopt an equivalence scale model in which scale economies in consumption depend only on household size, s^h, and adjusted total household expenditures are defined by

$\begin{array}{ccc}{y}^h=\frac{x^h}{{(s^h)}^{\theta }},\theta \in [0,1].& & (3)\end{array}$

When θ = 0, adjusted household expenditures coincide with unadjusted household expenditures, while if θ = 1, it becomes per capita household expenditures. Taking a single adult as the reference type, the expression s^θ can be interpreted as the number of equivalent adults in a household of size s. Thus, the greater the equivalence elasticity θ, the smaller the scale economies in consumption or, in other words, the larger the number of equivalent adults.

In Table 2, we present the budget shares for the quintiles of the distribution of adjusted total expenditures for an intermediate value of $\theta =\frac{1}{2}$ The commodity space consists of 16 goods, classified in three groups according to whether their total expenditures elasticity is greater than 1 (luxuries), considerably less than 1 (necessities I, dominated by Food expenditures), or slightly less than 1 (necessities II, dominated by Housing expenditures). The total expenditure elasticities are estimated at the mean of the variables in the following system of Engel-curve regressions:

$w_i^h={\alpha }_i+{\beta }_i{ln}(y^h)+{\gamma }_i{z}^h+{\epsilon }_i^h,i=1,\dots ,16,$

Table 2.

Budget Shares in the Distribution of Adjusted Household Expenditures (θ = 0.5), and Total Expenditure Elasticities for 16 Goods

Source: Author’ calculations.

^1/Except “Other Food Products” (beef, processed fish, fruit preserves and other unclassified foods).

^2/“Non-alcoholic Drinks” and “Other Food Products.”

Table 2.

Budget Shares in the Distribution of Adjusted Household Expenditures (θ = 0.5), and Total Expenditure Elasticities for 16 Goods

	Quintiles
GOODS	Ql	Q2	Q3	Q4	Q5	All	Elasticities
1. Personal Transportation	5.00	7.65	9.51	11.51	14.87	11.54	1.655
2. Clothing	4.98	6.24	7.52	8.36	8.58	7.79	1.593
3. Furniture	0.55	0.85	1.05	1.30	1.64	1.28	1.734
4. Domestic Services	0.14	0.19	0.25	0.57	1.46	0.78	2.242
5. Leisure, Education, Cultural	3.27	4.74	5.80	6.68	7.34	6.30	1.189
6. Other Personal Services	7.88	10.55	11.94	13.43	14.71	12.92	1.340
7. Other Household Goods	1.65	1.86	1.94	1.94	2.09	1.97	1.239
8. Medicine	2.07	2.37	2.65	2.65	2.76	2.62	1.253
LUXURY GOODS (1 + … + 8)	25.54	34.45	40.66	46.44	53.45	45.20	1.451
9. Food 1/	33.75	27.41	23.37	19.39	13.23	19.69	0.566
10. Housing Utilities	4.63	3.61	3.11	2.61	2.04	2.74	0.482
NECESSITIES I (9 + 10)	38.38	31.02	26.48	22.0	15.27	22.43	0.555
11. Alcoholic Drinks and Tobacco	3.16	3.02	2.82	2.57	1.97	2.48	0.847
12. Remainder of Group I 2/	4.48	4.53	4.58	4.14	3.25	3.94	0.811
13. Shoes	1.79	2.03	1.98	1.95	1.61	1.82	1.097
14. Housing	21.72	20.31	19.24	18.81	21.16	20.20	0.874
15. Other Transport and Comm.	2.46	2.40	2.37	2.44	2.15	2.31	0.775
16. Household Maintenance	2.46	2.24	1.88	1.64	1.14	1.62	0.795
NECESSITIES II (11 + … + 16)	36.07	34.53	32.87	31.55	31.28	32.37	0.866

Source: Author’ calculations.

^1/Except “Other Food Products” (beef, processed fish, fruit preserves and other unclassified foods).

^2/“Non-alcoholic Drinks” and “Other Food Products.”

View Table

Table 2.

Budget Shares in the Distribution of Adjusted Household Expenditures (θ = 0.5), and Total Expenditure Elasticities for 16 Goods

	Quintiles
GOODS	Ql	Q2	Q3	Q4	Q5	All	Elasticities
1. Personal Transportation	5.00	7.65	9.51	11.51	14.87	11.54	1.655
2. Clothing	4.98	6.24	7.52	8.36	8.58	7.79	1.593
3. Furniture	0.55	0.85	1.05	1.30	1.64	1.28	1.734
4. Domestic Services	0.14	0.19	0.25	0.57	1.46	0.78	2.242
5. Leisure, Education, Cultural	3.27	4.74	5.80	6.68	7.34	6.30	1.189
6. Other Personal Services	7.88	10.55	11.94	13.43	14.71	12.92	1.340
7. Other Household Goods	1.65	1.86	1.94	1.94	2.09	1.97	1.239
8. Medicine	2.07	2.37	2.65	2.65	2.76	2.62	1.253
LUXURY GOODS (1 + … + 8)	25.54	34.45	40.66	46.44	53.45	45.20	1.451
9. Food 1/	33.75	27.41	23.37	19.39	13.23	19.69	0.566
10. Housing Utilities	4.63	3.61	3.11	2.61	2.04	2.74	0.482
NECESSITIES I (9 + 10)	38.38	31.02	26.48	22.0	15.27	22.43	0.555
11. Alcoholic Drinks and Tobacco	3.16	3.02	2.82	2.57	1.97	2.48	0.847
12. Remainder of Group I 2/	4.48	4.53	4.58	4.14	3.25	3.94	0.811
13. Shoes	1.79	2.03	1.98	1.95	1.61	1.82	1.097
14. Housing	21.72	20.31	19.24	18.81	21.16	20.20	0.874
15. Other Transport and Comm.	2.46	2.40	2.37	2.44	2.15	2.31	0.775
16. Household Maintenance	2.46	2.24	1.88	1.64	1.14	1.62	0.795
NECESSITIES II (11 + … + 16)	36.07	34.53	32.87	31.55	31.28	32.37	0.866

Source: Author’ calculations.

^1/Except “Other Food Products” (beef, processed fish, fruit preserves and other unclassified foods).

^2/“Non-alcoholic Drinks” and “Other Food Products.”

where: ${\epsilon }_t^h$ is an error term; $y^h=x^h/\sqrt{s^h}$ is total household expenditures adjusted for household size with parameter $\theta =\frac{1}{2}$ and z^his a vector of household characteristics including (i) demographic variables (household size and composition, the household head’s age and age squared); (ii) socioeconomic variables (number of income earners, educational level and socioeconomic category of the household head, educational level and labor status of the spouse, number of dwellings and characteristics of the residential unit); as well as (iii) seasonal and geographic variables (municipality size and Autonomous Community of residence). In Figure 1 we display the joint distribution of the individual budget shares for these three goods and the logarithm of the adjusted total household expenditures,⁹ the last panel shows the estimated Engel curves (trimming the 1 percent tails off the support of the adjusted household expenditures).

Individual Budget Shares and Adjusted Household Expenditures

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Individual Budget Shares and Adjusted Household Expenditures

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Individual Budget Shares and Adjusted Household Expenditures

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Intuitively, the evolution of prices would tend to damage to a relatively greater extent the richer households over the poorer ones depending on whether the luxury good or the necessities experience the greatest relative increase. For the entire period, the inflation experienced by the luxury good and the two necessities are 31.59, 21.08, and 38.46 index points, respectively. In Figure 2 we represent the evolution of the inter-annual inflation of the three goods in relation to the general inflation as well as the inter-annual B_t, t = January 1992,…,January 1998.

Inflation Rates of Different Goods: January 1992–January 1998

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Inflation Rates of Different Goods: January 1992–January 1998

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Inflation Rates of Different Goods: January 1992–January 1998

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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In spite of the fact that the second necessity shows the stronger price growth, the behavior of the luxury good and the first necessity is the main explanatory force behind the positive sign of the plutocratic bias. To test this, we run a regression of the inter-annual (January-to-January) plutocratic bias B_t, from t = January 1992,…, January 1998, on the corresponding monthly inter-annual price subindexes for the three goods and a constant. The results, with robust t-ratios in parentheses (generalized least-squares and Cochrane-Orcutt regressions yield identical results), are the following:

${\widehat{B}}_t=\underset{(1.80)}{0.025}+\underset{(9.95)}{0.050L_t}-\underset{(-42.14)}{0.056N{I}_t}-\underset{(-0.75)}{0.0043NI{I}_t}{R}^2=0.96$

All the coefficients have the expected sign—although the one corresponding to Necessities II (NII) is not statistically significant—and the results corroborate the explanatory power of the Luxury good (L) and Necessities I (NI).

IV. ROBUSTNESS

A. The Time Period

In this subsection, we study the robustness of our results on the B trend in two different directions. In the first place, we consider the period covered by the two previous Spanish CPI systems, which run from August 1985 to December 1992 (base year = 1983), and from January 1977 to July 1985 (base year = 1976), respectively. (See Appendix I for details.)

The main findings are the following:¹⁰ (1) From Winter 1981 to Winter 1991 we estimate that B = 0.091 percent per year, a positive bias larger than witnessed for the 1990s. During different subperiods the bias is negative, and oscillates from a maximum of 0.380 to a minimum, in absolute value, of −0.025 percentage point. (2) From 1973–74 to Winter 1981 the plutocratic bias is always positive and reaches high annual maxima from 1976 to 1979, in 1979 it equals 0.833 percentage point. For the period as a whole, B = 0.264 percent per year, a bias equal in size to the sum of the classical substitution bias and the outlet bias reported by the Boskin Commission. (3) We must point out that the Spanish inflation during the second part of the 1970s and 1980s is considerably greater than during the 1990’s: the mean annual inflation from the midpoint of 1973 and 1974 to Winter 1981 is 17.9 percent, and from Winter 1981 to Winter 1991 is 8.5 percent. However, as before, there is no relationship between the size of the aggregate inflation in a given subperiod and the sign or the magnitude of the plutocratic bias. Regressing the bias in absolute values against inflation yields a nonsignificant coefficient (0.002 with a standard error of 0.006, using generalized least squares correcting for autocorrelation).

Finally, to appreciate the variability of the plutocratic bias during the entire period considered in this paper, Figure 3 shows the evolution of the inter-annual (month-to-month) B_t, t = January 1977,…, January 1998. as well as the inter-annual inflation rate.

Plutocratic Bias and Interannual Inflation: 1976–98

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Plutocratic Bias and Interannual Inflation: 1976–98

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

Source: Author’s calculations.

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Plutocratic Bias and Interannual Inflation: 1976–98

Citation: IMF Working Papers 2000, 167; 10.5089/9781451858174.001.A001

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B. The Aggregation Scheme

In the second place, it is interesting to experiment with other aggregation schemes to map a distribution of individual inflations to an aggregate index. Given that the discipline of welfare economics is more interested in personal rather than household welfare, it is natural to ask for the consequences of estimating the inflation for the population as a whole as the weighted mean of individual inflations with weights proportional to household size.¹¹

In Table 3 we present mean total household expenditures at Winter 1991 prices by house-hold size in the 1990–91 EPF, as well as the mean annual inflation from the Winter 1991 to January of 1998 for that same partition. As in the majority of other countries, we observe a positive association between total expenditures and household size. Therefore weighting household inflation by household size should have a similar effect, although of a lesser magnitude, than weighting directly by total household expenditures as in the plutocratic scheme. On the other hand, the fact that two, four, and more member households have a mean annual inflation below the population as a whole works in the opposite direction. The end result is that the new bias—defined as the difference between the plutocratic and the household size weighted mean—is equal to 0.088 percent per year. That this figure is greater than the previously estimated 0.055 percent per year for the plutocratic bias, indicates that during this period the second factor has had a greater impact than the first one.

Table 3.

Average Household Expenditures at Winter 1991 Prices and Average Annual Inflation in the Partition by Household Size

Source: Authors’ calculations.

Table 3.

Average Household Expenditures at Winter 1991 Prices and Average Annual Inflation in the Partition by Household Size

Household size size	Frequency Distribution (percentages)	Average Expenditures (pesetas)	Average Annual Inflation (percentages)
1 member	9.99	1.147,338	4.842
2 members	22.30	1,795,808	4.625
3 members	20.77	2,559,993	4.634
4 members	24.97	3,091,959	4.611
5 members	13.22	3,277,244	4.623
6 members	5.44	3,516,374	4.627
≥ 7 members	3.31	3,629,602	4.619
ALL	100.00	2,563,502	4.632

Source: Authors’ calculations.

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Table 3.

Average Household Expenditures at Winter 1991 Prices and Average Annual Inflation in the Partition by Household Size

Household size size	Frequency Distribution (percentages)	Average Expenditures (pesetas)	Average Annual Inflation (percentages)
1 member	9.99	1.147,338	4.842
2 members	22.30	1,795,808	4.625
3 members	20.77	2,559,993	4.634
4 members	24.97	3,091,959	4.611
5 members	13.22	3,277,244	4.623
6 members	5.44	3,516,374	4.627
≥ 7 members	3.31	3,629,602	4.619
ALL	100.00	2,563,502	4.632

Source: Authors’ calculations.

The same computations for the 1980s and 1970s lead to an estimate of 0.064 and 0.254 for the new bias versus a plutocratic bias of 0.091 and 0.264, respectively. The fact that the new bias is smaller than the plutocratic bias indicates that the positive association between total household expenditures and household size dominates the size of the new bias during these two periods.

V. IMPLICATIONS

In Spain, a commodity basket of 471 goods is priced in each of the 52 provinces in order to construct the set of elementary price indexes which form the core of the current 1992 CPI system. We have been able to work in a 53 dimensional commodity space, consisting of the 21 food rúbricas at the 18 Autonomous Community level, and the 32 non-food subgrupos at the 52 province level. For such a commodity breakdown, we construct 21,155 household-specific Laspeyres price indexes representative of a 1990–91 population of about 11 million households. Because of the fixed-weight nature of our construction, the individual inflation variation we observe during the Winter 1991-January 1998 period is the consequence of the price variation publicly disseminated by the INE in this 53 commodity space.

How can the distributional consequences of such a complex multidimensional process be grasped? In this paper we propose a procedure which combines two elements. First, whether price behavior in a given period hurts relatively more the rich or the poor households can be expressed in terms of a single scalar: the so-called plutocratic bias, incurred when inflation is measured using the current plutocratic CPI instead of using an alternative group index in which all households receive equal weight. Second, the estimation of an Engel curve system in a 16 goods commodity space, would permit reduction in the size of the price universe to only three dimensions: a luxury good and two necessities with considerably different total expenditures elasticities. Price behavior at this level provides an intelligible explanation of the sign and magnitude of the plutocratic bias.¹²

Beyond all the measurement issues, what are the practical policy consequences of our research? The first question to consider is how to adjust income taxes and public transfers annually. At this point, we have little to add to the arguments offered by others¹³ but note that, in most countries, income taxes, public pensions, other public transfers, and minimum wages are revised in terms of a plutocratic CPI. Why should we follow a dollar rather than a household or a person in this matter? Perhaps because both people and experts believe that the CPI represents an “average consumer.” However, when in an important paper Muellbauer (1976a) asked for the consumer whose budget shares are equal to the official CPI aggregate weights, he answered that in the United Kingdom this consumer occupied the 71 percentile in the household expenditures distribution.¹⁴ At any rate, indexing by the current CPI has the following unintended effects which may not have been sufficiently emphasized before: when prices behave in a anti-poor (anti-rich) way—i.e., when the plutocratic bias is negative (positive)—then we revise public programs, which primarily benefit the poor, below (above) what would be the case with a democratic group index. Similarly, if the plutocratic bias is negative (positive), then direct tax revenues would be larger (smaller) than what would be the case under the democratic alternative.

From this perspective, the current plutocratic formula is open to some critique. Admittedly, these critiques would be more important the greater the size of the plutocratic bias (and perhaps, depending on the sign of the bias). In the Spanish case, we have shown that this bias: (i) has had a positive sign over an extended period of time; (ii) presents a rather unstable pattern over the short run; and (iii) has had a considerable magnitude during certain periods of time. There is relatively little information on this issue in other countries,¹⁵ in particular in underdeveloped countries where the relative price of a few staples may loom large in the standard of living of the majority of the population. It is likely advisable to estimate the plutocratic bias on a regular basis. For this and other purposes, we recommend that statistical agencies in charge of the CPI compute and make available, at least annually, a set of household-specific price indexes. This approach would have the following advantages:

1. The farther down one goes toward the elementary price level, the greater will be the dispersion of the distribution of household-specific price indexes. However, onewould also expect a larger number of zero expenditures in most households. Therefore, there are advantages and disadvantages in enlarging the commodity space. Given that, for confidentiality reasons, the price information at the elementary level is not publicly available, the statistical agencies are the only institutions in a position to determine the optimal disaggregation level for the construction of individual price indexes.

2. Given the set of (official) individual price indexes, anyone can study the differential inflation suffered by the subgroups of interesting population partitions, an issue to be considered prior to the political solution to the issue of “How many cost of living indexes.” Similarly, anyone would be in a position to estimate the bias in the measurement of inflation created by the use of the current plutocratic CPI, instead of other politically interesting definitions of what a group index should be.

3. Perhaps more importantly, statistical offices (and others) can evaluate the distributional consequences of their methodological decisions. Take, for example, the Boskin Commission’s analysis of the quality issue and the introduction of new products, surely the most debated and critized part of their report. Different critics— Madrick (1997) and Deaton (1998), for instance—conjecture that new goods and goods affected by quality effects are disproportionately consumed by the rich. In our own terms, this implies that the set of household-specific price indexes after the correction of this bias should exhibit a smaller plutocratic bias. Are these critics correct? In Ruiz-Castillo and others (1999d), we have put this idea to a test by combining the structure of the bias for the United States economy with the consumer behavior of Spanish households as given in the 1990–91, 1980–81 and 1973– 74 EPFs. The plutocratic bias after the correction of the quality bias in the intervals (Winter 1991, January 1998), (Winter 1981, Winter 1991), (1973–74, Winter 1981) is 0.035. 0.073, and 0.249 percent per year, respectively. Since, as we have seen, the plutocratic bias before the correction is 0.055, 0.091, and 0.264 percent per year, we can conclude that there is some evidence indicating that the point made by those critics is well taken.

4. Muellbauer (1976a) does not regard the historical bias of inflation as the most important issue. Given that keeping down inflation is such an important policy goal, it is natural that any government should be very sensitive to the effects of policy change on the official CPI. Thus, the aggregate weights are the forces which push government policy affecting relative prices into particular directions. Within this context, armed with a set of publicly available household-specific price indexes, both the government (and others) would be in a position to evaluate, both ex ante and ex post, the distributional consequences on the CPI of certain policy actions.

Finally, it could be argued that, given the public opinion’s potential sensitivity to the distributional issues embedded in the construction of a single CPI, officially publishing a set of household-specific price indexes would ultimately affect the credibility of the CPI, itself. As noted by Muellbauer (1976a): “aggregate index numbers are not neutral political indicators.” However, as shown here, anyone can come up with a reasonable version of these indexes using already publicly available information. After all. in an open society. the dissemination of relevant—albeit controversial—information should always be encouraged for the sake of transparency.