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The Plutocratic Gap in the CPI: Evidence from Spain

Robert Flood
Published Date:
April 2003
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The review of the literature carried out by a U.S. Seriate Commission headed by Michael Boston (Boston and others, 1996) identified several problems regarding the U.S. consumer price index (CPI) elaborated by the U.S. Bureau of Labor Statistics (BLS). The Boskin Commission focused on five sources of bias in the CPI and estimated that, on average, during the last few decades, the U.S. CPI has been overstating the inflation rate by LI percentage points a year.1 Despite the importance of the Boskin Commission report,2 some critics—for example, Pollak (1998), Deaton (1998), and Madrick (1997a and b)—point out some neglected topics and, in particular, the scant attention paid to distributional issues.

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 that is viewed in Pollak (1998) as encompassing three issues: “How many cost-of-living indices?”: “Beer or champagne?”; and “What type of group indices?” The first issue refers to whether we should have different indices for different groups: rich and poor, elderly and non-elderly, urban and rural, and so on. 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 (Pollak, 1980). Given the commodity space and a household budget survey representative of the reference population, we could use each household’s budget shares as the fixed weights for the construction of household-specific price indices. It has been known since Prais (1958) that the official CPI is the weighted average of such individual price indices with weights proportional to each household’s total expenditures. Because richer households have greater weights than poor ones, Prais called the CPI a plutoerarie price index. Is there a better alternative to this particular construction?3

In this paper, we suggest that the so-called democratic index, in which all households receive the same weight, is an approach worth pursuing. Thus, we define the plutocratic gap as the difference between inflation measured according to the current official CPI and according to a democratic index. One reason to pursue such an approach 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 the former case, we would say that prices have behaved in an anti-rich manner, and in the latter case, in an anti-poor manner. In the former (latter) ease, we should expect mean inflation weighted by total household expenditures to be greater (smaller) than simple average inflation. Thus, the plutocratic gap would be positive or negative according to whether prices have behaved in an anti-rich or an anti-poor manner, respectively (Fry and Pashardes, 1986).

While the importance of the plutocratic gap depends crucially on its magnitude, it must be emphasized that the lack of access to lower-level price data will likely result in an underestimation of the real gap.4 Our best estimate of the plutocratic gap in Spain during the 1990s is 0.055 percentage points a year.5 Averaging magnitudes of different signs also underestimates the real importance of this gap, however. The gap in specific years oscillates from a maximum of 0.150 percentage points to a minimum of –0.080 percentage points. The mean absolute gap is much larger, 0.090 percentage points. The gap depends negatively on the magnitude of the inflation in that subperiod. Finally, on the basis of total expenditures elasticities, a 53-dimensionaI commodity space can be conveniently reduced to two dimensions, consisting of a luxury index and a necessity index. The price behavior of these two types of good provides a convincing explanation of the oscillations observed in the plutocratic gap.

The rest of the article is organized as follows. Section I presents the empirical results on the plutocratic gap in Spain during the 1990s. Section II is devoted to examining the robustness of those results with respect to the time period and the use of weighted group indices with weights proportional to household size, Section III summarizes and discusses the political implications of our results in an indexed economy. Appendix I describes the construction of the modified Laspeyres index, and Appendix II, the data sources.

I. The Plutocratic Gap

In order to estimate the plutocratic gap (defined below), we need to construct a series of household-specific Laspeyres price indices. For that purpose, we use the following two pieces of publicly available information for Spain: the 1990–91 household-budget survey used to estimate the weights of the official CPI and a set of price sub indices at a certain level ol” spatial and commodity disaggregation. Using this information, for each household h interviewed in a quarter τ during the 1990–91 period (τ = spring, summer, and autumn of 1990, and winter of 1991), we construct a series of modified Laspeyres statistical price indices,

based on period 0 (winter of 1991), which takes as a reference the commodity vector qτh actually acquired during the interview quarter τ. (Appendix I describes the notation and the construction of the aggregate CPI. Appendix II describes the data sources and discusses issues regarding the definition of household expenditures.)

The period winter 1991-January 1998 will be divided in the seven suhperiods shown in Table 1. For each household h, we define the inflation (or deflation) caused by the evolution of prices in a given subperiod by

Table 1.The Plutocratic Gap During the 1990s(percentage points per year)
tSubperiodsPlutocraticDemocraticPlutocratic Gap
21992 to January 19935.3945.2440.150
3January 1993 to January 19945.2715.1650.105
4January 1994 to January 19954.6214.701–0.080
5January 1995 lo January 19964.0794.130–0.050
6January i 996 to January 19973.1803.0900.090
7January 1997 to January 19982.4942.3690.125
Winter 1991 to January 19984.6324.5770.055
January 1993 to January 1998, average absolute gap0.090
Source: Author’s calculations.

Winter 1991 is the average of Janu ary. February, and March of 1991.

Source: Author’s calculations.

Winter 1991 is the average of Janu ary. February, and March of 1991.

The distribution of individual inflation rates in each subperiod is denoted by πt=(πtI,,πtH). For the entire period, Π = (ΠI,…,ΠH) we have where ΠH=(lTh1) and T refers to the last period available; January 1998.

The aggregate inflation for the population as a whole according to the plutocratic scheme is

where Ψth=φhlt1h/(Σhφhlt1h). For the democratic scheme,

where ξth=lt1h/(Σhlt1h) Note Ψth is proportional to φhξth. For the overall period from 0 to T, since loh=1, the weights simplify to φh and (1\H). Consequently, we have

The plutocratic gap in the measurement of inflation in subperiod < will be defined by Gt = PLUTt-DEMt and for the overall period by G = PLUT-DEM.6 Notice that, as pointed out earlier, if price changes in subperiod t (or for the entire period) are relatively more detrimental to the rich—that is, if πth(orΠh) are greater for rich households than for poor households—then we expect the plutocratic mean of individual inflations to be greater than the democratic mean. In other words, Gt or G will be positive or negative, according to whether the price change in the corresponding time interval is, respectively, anti-rich or anti-poor.

If we denote by Eit = (p,it/pio) the mixedary price indices (defined in Appendix I) and let xh represent household h’s totai expenditures, so that x¯ denotes average household total expenditures, then ζ=Var(xh)/x¯ is a measure of the inequality of household total expenditures. Further define βi=Cov(xh,wih)/Var(xh) where wih denotes household h’s budget share for good i. Ley (2002) shows that the plutocratic gap may be written as

Note that βi, is a rescaled covariance and therefore may be interpreted as a regression coefficient of the budget shares, wih on total expenditures, xh. The plutocratic gap is thus determined by the dispersion of total household expenditures, measured by ζ, and the sample covariance between (βi, and Eit. The sign of the plutocratic gap is determined by the covariance term. A positive covariance term means that the luxury goods relatively more favored by richer households experience higher than average inflation and, as a consequence, necessities experience lower than average inflation. Similarly, a negative covariance implies that necessities experience higher than average inflation while luxury goods experience lower than average inflation.

It should be emphasized that the size of the gap is an empirical matter and may vary substantially at different places at different times. In particular, findings for one country may have few implications for other countries with larger income inequality, more consumption heterogeneity, and different price dynamics (equation (1)),

The Main Findings

The first two columns of Table 1 show the plutocratic and the democratic means of both Π and πt, while the third column shows the mean difference. (All figures are expressed in percentage points per year.) Notice that the aggregate inflation rate keeps decreasing over time, from a high of 6.9 percent during the first subpe-riod to a low of 2.4 percent during 1997.

Three main findings are as follows. First, for the period as a whole, the estimated plutocratic gap, G, is positive and equal to 0.055 percentage points a year.7 However, positive and negative gaps offset each other when averaged over the whole period. The mean absolute gap is much larger. 0.090. These figures could be compared with the overall upward bias for the Spanish economy, which—following ihc Boskin Commission procedures—we have estimated at 0.61 percentage points a year (Ruiz-Castillo, Ley. and Izquierdo, 1999).

Second, price behavior is not uniform over the entire period: Gt is negative during 1994 and 1995, indicating that during these two years prices caused relatively more damage to poorer households than to richer ones.

Third, at monthly frequencies, the gap is negatively, albeit weakly, associated with the level of inflation. A regression of the monthly gap on monthly (plutocratic) inflation results in a significant negative coefficient, –0.11, and an R¯2 of 32 percent (Table 2).8 The higher the inflation, the lower the estimated gap, suggesting that at higher inflation rates prices would tend to move more closely together.

Table 2.The Plutocratic Gap Versus inflation(dependent variable: monthly plutocratic gap Gt, in percentage points)
Sample (Adjusted)
Lag-12 autoregrcss term0.3530.470
Ljung-Box Q (12)3.6314.6413.19
Ljung-Box Q (24)10.930.7827.45
Number of observations6012862
Source: Authors’ calculations.Note: The r-ralios arc in parentheses.
Source: Authors’ calculations.Note: The r-ralios arc in parentheses.

In the next subsection, we will show that the gap decreases as the inflation of necessities increases. In addition, at monthly frequencies, inflation of necessities is very volatile and drives most of the movements in general inflation. Consequently. the regression of the gap on inflation produces this negative relationship.

An Economic Interpretation

Which goods are primarily consumed by the richer households? Ley (2002) shows that we can relate the parameter βi, in the expression of the plutocratic gap (equation (1)) to a measure of the elasticity of the demand for good i to total expenditures, ηi

where w¯i, is the average expenditure share for good i, the weights are given by θh=(xhx¯)2/(Σh(xhx¯)2,andηih is the ratio of the percent deviation of household h’s consumption of good i with respect to its mean, divided by the percent deviation of total household expenditures with respect to its mean:

Thus, for each household h,ηih be interpreted as good f’s total-expenditure elasticity. Moreover, for each good i, the overall-demand elasticity with respect to total household expenditures can be estimated by ηi=1+(x¯/w¯i)βi Whenever βi > 0, it follows that ηηi > 1. If ηi = 1, then the plutocratic and democratic shares for good i are identical and the price behavior of this good cannot contribute to the plutocratic gap,

Although the Spanish statistical agency, the Instituto Nacional de Estadistica, collects prices for 471 goods, we have access to price data only at higher aggregation levels. For instance, we can access national price data for only 110 aggregate goods, regional price data for 57 aggregate goods, or provincial price data for only 33 aggregate goods. Our calculations are based on 53 goods (21 food commodities at a regional level and 32 nonfood commodities at the provincial level). The box-plots in Figure 1 show the narrowing of the distribution of the ηi toward 1 as a result of aggregation (110 goods, 53 goods, and 19 goods). As noted before, if ηi is genuinely unity for a good at the lowest level of aggregation, it means that this particular good does not contribute to the plutocratic gap. However, when ηi artificially approaches unity owing to aggregation, then there is no chance for the researcher to recover it, regardless of the underlying contribution to the plutocratic gap of the goods included in this aggregate commodity. This lack of lower-level price data is a serious shortcoming for researching the topics in this paper. Consequently, the actual plutocratic gap could easily be substantially larger than our estimates.

Figure 1.Boxpiots of Expenditure Elasticities at Different Levels of Aggregation

Source: Authors’ calculations.

The initial 53 goods are classified into four groups of goods according to their total expenditure elasticity. Group I (necessities) includes 20 goods with an elasticity considerably smaller than 1 (ηi < 0.9); Group III (other) includes 5 goods with an elasticity relatively close to 1 (0.9 < ηi, < 1.1); and Group IV (luxuries) includes 20 goods that have an elasticity significantly greater than 1 (ηi, > 1.1). Group II is housing (ηi = 0.9), which requires special treatment, since it accounts for 20 percent of total household expenditures and expenditures on goods in Group I move in opposite directions.9

The price indices of the goods in each group are then aggregated into four indices: necessities, housing, other, and luxuries. In Table 3. for presentation purposes, the 53 goods are aggregated into 19 goods consistent with this classification. Table 3 shows the budget shares for the quintiles of the distribution of total expenditures.

Table 3.Budget Shares in the Distribution of Total Household Expenditures and Total Elasticities for 19 Aggregate Goods
Budget Shares (in percent)
QlQ2Q3Q4Q5AlElasticitv ηiIn flation1πηi
1Food and non-alcoholic beverages233.2827.7424.0820.3114.5919.950.652.43
2Utilities and house maintenance7.656.105.144.343.234.360.642.41
3Telephone and communications epenses1.761.531.351.170.981.190.76448
4Therapeutic aides0.310.,64
5Other food and alcoholic beverages35.235.405.254.873 984.620.873.45
Group I: Necessities(1+…+5)48.2341.0636.0730.9522.9930.360.682.67
6Group II: Housing (6)26,7022.4520.1818.2919.8220.200.905.84
7Tobacco1.451.741.771.741.301 540.9211.31
8Durables1. 900.970.931.20
9Other in Group III2.993.313.443.433.113.250.993.40
Group HI: (7+8+9)5.486.
10Transportation services0.860.911.
11Medical services and health insurance1.161.311.361.571.771.571,205.25
12Personal care goods and services1.451.902.142.392.522.301.214.05
13Clothing4.646.197 368.158.577.791.232.76
14Furniture, furnishings, and household items1.171.622.032.262.692.281.343.67
15Leisure, education, and culture2.404.115.426.477.586.301.443.83
16Restaurant, hotel, and tourist services4.677.278.9110.4311.519.991.334.97
17Domestic service0.370.370.290.471.280.781.986.03
19Financial services0.
Group IV: Luxuries (10+…+19)19.5930.3837.4644.6051.8743.681.374.33
Total household expenditure100 00100.00100.00100.00100.00100.001.004.21
Source: Authors’ calculations.

Average inflation rate 1992:02–1998:01, percent per year.

Excludes beef, prepared seafood, and "other food products."

Includes beef, prepared seafood, and "other food products."

Source: Authors’ calculations.

Average inflation rate 1992:02–1998:01, percent per year.

Excludes beef, prepared seafood, and "other food products."

Includes beef, prepared seafood, and "other food products."

Intuitively, we understand how the evolution of prices affects richer households compared with poorer ones depends upon whether luxury goods (43.86 percent of total expenditures) or necessities (30.36 percent of total expenditures) experience the greatest relative increase. For the entire period studied, the average inflation experienced by luxury goods is 4.33 percent a year while that of necessities is only 2.59 percent a year. Housing experiences considerably greater inflation of 5.86 percent a year.

The inflation rates for luxury goods (Group IV) and necessities (Group I) are the main variables responsible for the positive sign of the plutocratic gap. Table 4 shows the results of regressing the monthly plutocratic gap Gt on the corresponding monthly inflation rates of the three price subindices for Groups I, II, and IV.10 The coefficients have the expected signs and the results show that the inflation rates of the luxury goods and necessities explain most of the behavior of the plutocratic gap. Consequently, for the purpose of explaining the plutocratic gap during the period studied (1992:01–1998:01), the commodity space of 53 goods could be conveniently reduced to two aggregate goods that explain 92 percent of its variance. While the housing (Group II) coefficient is statistically significant, it con-tributes only 2 percentage points of the 94 percentage points of the explained variance when it is included in the regression (Table 4, column 2).

Table 4.Regression of Plutocratic Gap on Inflation Rates of Aggregate Subindexes(dependent variable: monthly plutocratic gap Gt in percentage points)
Inflation rat
Group I: Necessitie–0.07–0.07
Group II: Housin–0.02
Group IV: Luxurie0.080.09
Lag-12 autoregressive ter0.470.45
Ljung-Box Q(12)13.015.4
Ljung-Box Q(24)17.724.7
Number of observation66
Source: Authors’ calculations.Notes: Adjusted samples for 1993:02–1998:01. The r-ratios are in parentheses.
Source: Authors’ calculations.Notes: Adjusted samples for 1993:02–1998:01. The r-ratios are in parentheses.

II. Robustness

The Time Period

In this section, we study the robustness of our results on the G trend in two different directions. First, we consider the period covered by the two previous Spanish CPI systems, which were used from August 1985 to December 1992 (base year = 1983) and from January 1977 to July 1985 (base year = 1976). (See the subsection on the “Data for 1970s and 1980s” in Appendix II for details.) The main findings are the following.

  • From winter 1981 to winter 1991, we estimate that G = 0.091 percentage points a year, a positive gap larger than what we saw for the 1990s. During some sub-periods. the gap is negative; and it oscillates from a maximum of 0.380 percentage points to a minimum, in absolute value, of 0.025 percentage points.

  • From 1973–74 to winter 1981, the plutocratic gap is always positive and reaches very high annual maxima from 1976 to 1979. becoming equal to 0.833 percentage points in 1979. For the period as a whole, G= 0.264 percentage points a year, a gap whose size is equal to the sum of the classical substitution bias and the outlet bias according to the Boskin Commission.

  • Spanish inflation during the second pan of the 1970s and during the 1980s iscon-siderably greater than during ihe 1990s. (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 it is 8.5 percent.) As before, however, there is a negative relationship between the size of the aggregate inflation in a given subperiod and the plutocratic gap (Table 2).

Finally, to appreciate the variability of the plutocratic gap during the entire period considered in this study, Figure 2 shows the evolution of the annual Gt t = January 1977,…, January 1998, as well as of the annual inflation rate for the same period.

Figure 2.Spain: Interannual Plutocratic Gap and Inflation, 1977–98

Source: Authors’ calculations.

The Aggregation Scheme

Second, it is interesting to experiment with other aggregation schemes to map a distribution of household-specific inflations to an aggregate index. We therefore examine 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 (Nicholson, 1975).11

Table 5 presents mean total household expenditures at winter 1991 prices by household size in the 1990–91 household survey, as well as the mean annual inflation from the winter of 1991 to January of 1998 for that same partition. As in the majority of other countries, there is 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. Households with two, four, or more members have a mean annual inflation below that of the population as a whole, however, which works in the opposite direction. The net result is that the new gap—defined as the difference between the plutocratic and the household-size weighted mean—is equal to 0.088 percentage points a year. Since this Figure is greater than the previous estimate of 0.055 percentage points a year for the plutocratic gap, it follows that, during this period, the second factor has had a greater impact than the first.

Table 5.Average Household Expenditures at Winter 1991 Prices and Average Annua inflation in the Partition, by Household Size
Household Size (number of persons)Frequency Distribution (percent)Average Expenditures (pesetas)Average Annual Inflation (percent)1
7 or more3.313,629,6024.619
A ll100.002,563.5024.632
Source: Authors’ calculations.

Winter 1991-January 1998.

Source: Authors’ calculations.

Winter 1991-January 1998.

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

III. Concluding Remarks

In Spain, more than twenty-four thousand price movements are aggregated into a single Index.12 What are the distributional implications of such an aggregation scheme? We propose examining two mixeds. First, whether price behavior in a given period hurts rich or poor households relatively more can be expressed in terms of a single scalar: the plutocratic gap. The plutocratic gap is the difference between inflation measured using the official CP1 and inflation measured using an alternative group index in which all households are weighted equally. Second, we are able to reduce the size of the price space to only two dimensions: a luxury good and a necessity with considerably different total expenditure elasticities. Price behavior at this level provides an intelligible explanation of the sign and magnitude of the plutocratic gap. accounting for 92 percent of its variance.13

In most countries, income taxes, public pensions, other public transfers, and minimum wages are revised in terms of a plutocratic CPI. Why should a dollar logic rather than a household or personal logic be followed in this matter’?14 The answer may lie in the widespread belief that the CPI represents an “average consumer.” The consumer whose expenditure pattern is represented by the CPI, however, turns out to be less than fully representative. For the United Kingdom, Muellbauer (1976) found this “average consumer”—whose budget shares correspond to the official CPI—in the seventy-first percentile in the household expenditure distribution. For the United States in 1990, Deaton (1998) estimates that this consumer occupies the seventy-fifth percentile; for Spain during the 1990s, we find the CPI-represented consumer in the sixty-ftrst percentile of the mean-adjusted household expenditure distribution.

Indexing by the current CPI has the following perverse effects that have not been sufficiently emphasized before. When prices behave in an anti-poor way—that is, when the plutocratic gap is negative—then spending on public programs, which primarily benefit the poor, is revised below what it would have been if a democratic group index had been used. (The reverse is true when prices behave in an anti-rich way.) Similarly, if the plutocratic gap is negative, then direct tax revenues would be larger than they would have been if a democratic group index had been used.

From this point of view, the current plutocratic formula can be conceptually criticized. Admittedly, this matter would be more important, the greater the size of the plutocratic gap (and, perhaps, depending on the sign of the gap). For Spain, we have shown that this gap (i) has had a positive sign over an extended period, (ii) presents a rather unstable pattern over the short run, and (iii) has been large during certain periods. There is relatively little information on this issue for other countries,15 particularly in developing countries where changes in the relative prices of a few staples may cause havoc in the standard of living of the majority of the population. It may be advisable for their governments to estimate the plutocratic gap on a regular basis.

Statistical agencies could compute and make available, at least annually, sets of household-specific price indices. Given the set of (official) individual price indices, anyone could study the differential inflation suffered by various subgroups of the population—something that needs to be considered before attempting to formulate a political solution to the issue of “How many cost of living indices?” Similarly, anyone would be in a position to estimate the difference in the measurement of inflation created by the use of the current plutocratic CPI, as opposed to other, politically interesting alternative group price indices. Note that reporting household-specific price indices goes beyond the simple reweighting of the CPI with group-specific weights as practiced by some statistical offices. since price information from the relevant geographical area for each household should be used—there is empirical evidence that geography is an important determinant of price variation.16 Moreover, anybody could evaluate the distributional consequences of the methodological decisions of statistical offices. Take, for example, the Boskin Commission’s analysis of the quality issue and the introduction of new products—surely the most debated and criticized part of their report. Various social critics—Madrick (1997a and b) and Deaton (1998), for instance—conjecture that new goods and goods affected by quality effects are disproportionately consumed by the rich. The impact of quality correction on household inflation could be investigated if household price indices were available from the statistical office.17

Finally, Muellbauer (1976) indicates that he 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 that drive government policies affecting relative prices and attempting to shift them in particular directions. Within this context, a set of publicly available household-specific price indices would allow both the government and others to evaluate, both ex ante and ex post, the distributional consequences of different policies.


I. The Modified Laspeyres Price Index

First, a word on notation. Subscripts will be used for goods, i= 1,…, N, and time, t= 1….. T, while superscripts will be used for households, h = 1,…, H. Boldface symbols denote vectors. Price vectors, Pt = (p1t,…, pNt) will be row vectors while quantity vectors, qth=(q1th,,qNth), will always be column vectors; and “.” will be used to denote the inner product: pt.qsh=Σi=1Npitqish. Household h’s budget shares will be denoted by wih and its total household expenditures by xh. Finally, uppercase symbols will be used for aggregation over households—for example. x=Σhxh—while a bar over a symbol will denote an average quantity—for example, x¯=X/H.

To understand the relation between a CPI and an aggregate Laspeyres statistical price index (SPI), we have to start by recognizing that statistical agencies partition the country’s physical space into a set of J geographical areas, which we index by j = 1,,.., J. For every item i in every area j, during each period f (typically a month), statistical agencies collect price quotes for a number of previously determined item specifications in a certain predetermined sample of outlets. (This is where Pollak places the “beer or champagne” issue.) These price quotes are aggregated in mixedary price indices Eijt. (This is where the Boskin Commission places the “lower substitution level” problem. Neither this problem nor the “beer or champagne” issue should concern us in this study.)

Conceptually, we can view an mixedary price index as the relative price of item i in area j in period t with respect to the base period 0—that is,

Household budget surveys provide information, however, not on individual prices and quantities, which are often hard to define, but on individual expenditures in each good, xh;

total household expenditures, xτh=Σhxh;
and budget shares, wh=xh/xτh.
For each areaj, we observe the aggregate expenditures on each good, Xijτ=Σhxh
and aggregate budget shares, Wijτ=Xijτ/Xτ
, where Xτ=Σhxτh
is the aggregate total expenditure for the entire population. Under the assumption that all households living in the same area face the same prices, we can view observable household expenditures nn item j by a household h living in areaj and that is interviewed in period τ as the product of (generally unobserved) prices pijτ and (unobserved) quantities qh
—that is, xh=pijτqh
Denote the vector of aggregate quantities actually purchased during the survey period τ by Qτ = (Q…..Q) where Q = ΣjQijτ and Qijτ=Σhqh.
Then we have

If we define the plutocratic weights φth=xτh/Xτ, then

If we have information on what we call the adjustment factors for each i, Aijτ = (pijτ/pij0), then we can define the mixedary price index based in period τ as

For each household h living in areay, the Laspeyres SPI that takes as a reference the quantity vector qτh,, is defined as

where pji = (pijt,…..pNjt).

At the aggregate level, let pt = (p1t,…pNt), where p,it = Σj(Qijτ/Q)pijτ. Then the aggregate Laspeyres SPI that takes as a reference the vector Q is given by

For each good i in an area j, let Wij = pijoQijτ/(po · Qτ). The CPI based on period 0 is an aggregate SPI defined by

which is what the Bureau of Labor Statistics calls a modified Laspeyres aggregate price index (Moulton. 1996), with base year 0 and reference consumption patterns surveyed τ.

Finally, for each household h in an area j, we now redefine the plutocratic weights as ϕh=(pj0·qτh)/(p0·Qτ) and the budget shares as ωih=(pij0qh). Then, as before, aggregate expenditure shares can be expressed as a plutocratic-weighted mean of individual expenditure shares:


II. The Data

Data for 1990s

The EPF (Encuesta dc Presupuestos Familiares) collected by the Spanish statistical agency, INE (Instituto Nacional de Estadfstica), from April 1990 to March 1991 is a household budget survey of 21,155 household sample points representing a population of approximately 11 million households and 38 million persons occupying residential housing in all of Spain, including the North African cities of Ceuta and Melilla.

The INE collects mixedary price indices (denoted by Eijt, in Appendix I) for a commodity basket consisting of 471 items in each of the country’s 52 provinces under the present CPI system, based in 3992. For confidentiality reasons, the INE does not publish this information at the maximum disaggregation level. Instead, it publishes on a monthly basis price subindices for January 1993 to January 1998 for a commodity breakdown of 110 subclases, 57 rúbricas, 33 subgrupos, and 8 grupos at the national level; the rúbricas, subgrupos, and grupos at the 18 Autonomous Community level;18 and the subgrupos and grupos at the 52-province level.

For any commodity breakdown, it is possible to reconstruct the official CPI series using an appropriately defined aggregate-bud get-shares vector. Similarly, defining a budget-shares vector for every household in the 1990–91 sample, we can obtain a series of household-specific CPIs for any commodity breakdown. In principle, the only difference between alternative specifications of the commodity space is that the dispersion of the set of individual CPIs should be greater, the greater the disaggregation level of the price information used in their construction. Unfortunately, in spite of the fact that we used the same informational basis as the INE—namely, the 1990–91 EPF—we found several small discrepancies between our estimates of the aggregate-budget-shares vectors and those published by the INE—for the details, see Ruiz-Castillo, Ley, and Izquierdo (1999). Thus, the CPI series that we can reconstruct vary slightly, depending on the different commodity breakdowns characterizing the price information we use. Ruiz-Castillo, Ley, and Izquierdo (1999) find that the specification consisting of the 21 food rúbricas at the Autonomous Community level and the 32 nonfood subgrupos at the provincial level outperforms the rest of the alternatives according to various statistical and economic criteria.

It should be emphasized that our series of household-specific price indices defined over this 53-commodity space differs from the series underlying the official CPI in two ways. First, there are several practices incorporated in the official definition of total household expenditures for which we believe there are superior alternatives. We specifically refer to (i) the definition of housing expenditures for households occupying nonrental housing; (ii) the inclusion of imputations for home production, wages in kind, and subsidized meals; and (iii) the estimation of annual food and drink expenditures using all the available information on bulk purchases in the 1990–91 EPF. The joint impact of these modifications is important: because of them, the official CPI understates true Spanish inflation from 1992 to January of 1998 by 0.241 percentage points a year.

Second, it should be noted that die Spanish CPI is not the modified Laspeyres price index that takes as a reference the mean quantity vector actually acquired by the EPF households when they were interviewed in the 1990–91 survey period. The reason is that the INE does not use the adjustment factors Aijτ defined in Appendix I (Ruiz-Castillo, Ley, and Izquierdo, 2002b). Fortunately, Lorenzo (1998) provides such factors for the 110 subclases at the national level. Using this information, for each household h interviewed in a quarter τ during the 1990–91 period (τ = spring, summer, and aurumn of 1990, and winter of 1991), we construct a series of modified Laspeyres SPIs, l(pt,p0;qτh) based on period 0 = winter of 1991, that take as a reference the commodity vector qτh actually acquired during the interview quarter τ. If we normalize this series at prices of period 0 = 1992, we can obtain the conceptually correct CPI for household h—that is, cpi(pt,p0;qτh)=l(pt,pτ;qτh)/l(pt,pτ;qτh)=(pt·qτh)/(p0·qτh)..

Data for 1970s and 1980s

The EPFs that serve to estimate the official weights were conducted from April 1980 to March 1981 and from July 1973 to June 1974. These are household budget surveys strictly comparable to the 1990–91 EPF, containing 23,972 and 24,151 household sample units, respectively, that approximately represent a population of 9–10 million households and 34–37 million persons in 1980–81 and 1973–74, respectively. In this case, we do not depart from the official definition of household total expenditures, but, as before, we must take into account the fact that the Spanish CPI is not a modified Laspcyres price index.

We construct two series of appropriate household-specific price indices with the information provided by (i) the 1980–81 and 1973–74 EPFs; (ii) the official monthly price information for 106 and 88 subclases at the national level using the 1983 and 1976 bases, respectively; and (iii) a series of adjustment factors for 52 goods that constitute the minimum common denominator between the 58 official rúbricas and the 60 goods provided by Catasus and others (1986) for the first period and for the 5 goods at the national level provided by Garcia Espafia and Serrano (1980) for the second period.

Further details can be found in Ruiz-Castillo and others (1999) and Ruiz-Castillo, Ley, and Izquierdo (1999). All the datasets used in this paper, including the series of modified Laspeyres price indices, are available at

In statistical matter throughout this issue,

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a dash (—) indicates that the figure is zero or less than half the final digit shown, or that the item does not exist;

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a comma (,) separates thousands and millions;

“billion” means a thousand million; and “trillion” means a thousand billion;

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components of tables may not add to totals shown because of rounding.

The term “country,” as used in this publication, may not refer to a territorial entity that is a state as understood by international law and practice; the term may also cover some territorial entities that are not states but for which statistical data are maintained and provided internationally on a separate and independent basis.

Design: Luisa Menjivar-Macdonald and Sanaa Elaroussi


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Mario Izquierdo is an Economist in die Research Department of the Banco de Espaiia, Eduardo Ley is a Senior Economist in the Asian Division of the IMF Institute. Javier Rui it-Castillo is Professor of Economies at the Universidad Carlos 111 de Madrid. The authors have benetited greatly from the comments of an anonymous referee. They have also received valuable comments from Liam Ebrill, Diego Moreno. Marshall Reinsdorf, and participants in seminars at the Fundacion de Estudios dc Economfa Aplicada, the Banco de Espaiia, the Institute de Estudios Fiscales. the Universidad Carlos Hide Madrid, the Universidad Complutense, Ihe Inter-American Development Bank, the World Bank, the IMF Institute, the XVII] Latin American Econometric Society Meetings (July 26–28. 2001, Buenos Aires), and the Nalional Bureau of Economic Research workshop on Output and Price Measurement (July 30–31, 2001. Boslon).

This bias might seem small. When compounded overtime, however, the implications for (i) the public deficit created through an indexed budget, (ii) the wage-bargaining process and the determination of the nominal interest rales in the private sector, and (iii) the measuremenl of the economic performance in real terms are little short of catastrophic.

As Diewert (1998, page 56) puts it, “with a total budget of $25,000, Boskin. Dulbcrger. Griliches. Gordon and Jorgensun have probably written the most important measurement paper of the century in lenns of its impact: Every statistical agency in the world is reevaluating its price measurement techniques as a direel result of [heir reporl and Ihe widespread publicity it has received.”

As pointed out by Pollak (1998), the first two matters are given a cursory treatment in footnote 2 and on page 71 of Boskin and others (1996). The Boskin Commission never addresses the third problem directly, although Pollak selects some passages ofits report that appear to reflect an implicit judgment thai ihe CPI oughi to be a plutocratic price index.

Staiistical agencies could compute house ho Id-specific price indices using prices taken a! the maximum level of geographical dis aggregation. In this ease, analysis would be able to obtain the belter estimates of the plutocratic gap. Nonetheless, given the data-col lection practices currently in place in most countries, first-level indices can only be constructed on a plutocratic basis, so there is a portion of the real plutocratic gap that can nol be recovered. See Chapter 8, “Whose Index? Aggregating Across Households.” in Schultzc and Mackie (2002) for a review of the praclical diffieullies involved in the construction of a democratic index in the United Stales.

This amounts to about one third of the classical substitution bias estimated for the United Slates by the Boskin Commission.

Note thai the inflation rale does not display temporal separability—that is. the inflation for a given period does not equal the sum of inflations for a partition of that period. If the inflation rale were defined instead as the log-price change, then temporal separability would hold bul group separability would be lost.

This is approximately one-third of the substitution bias estimated by the Boskin Commission for the U.S. economy, which is 0.1 5 percentage points a year.

Founeen percentage points of the explained variance are due to the seasonal autoregressive term—thai is. the R¯2 drops to 18 percent when the lag-12 autoregressive term is dropped.

As pointed out in Appendix II, die official CPI system based in 1992 includes only rental housing, resulting in a Lolal housing share of only 7.17 percent of total expenditures. In Lhis paper, by contrasl, Ihe housing share also includes the rental equivalent or owner-occupied housing and the rest of nonrental housing, using available rent data from the rental housing sector to approximate rents for owner-occupied housing. See Ruiz-Castillo, Ley, and Izquierdo (1999) for a justification of this procedure.

The constanl term, as well as the index for Group 111. are not statistically significant. Inspection of the correlogram indicates existence of aulocorrelation of order 12. After the inclusion of the lag-12 autoregressive term, there is no evidence of further serial correlation. The estimation is carried out using nonlinear least squares.

Alternatively, one could define an aggregate priec index that gives greater weight to poorer households. Given the results of this study, the corresponding gap in the measurement of inflation should he greater than the plutocratic gap. See Ley (2002) for several other possible aggregation schemes.

A commodity basket of 471 goods is priced in each of the 52 provinces in order to construct the set of 24,492 mixedary price indices that form the core of the current 1992 CPI system. A few goods are priced at the national level, however, slightly reducing this number.

As we show in Ruiz-Castillo, Ley, and Izquierdo (2002a), the gap between the change in money income inequality and the socially relevant change in real income inequality is given by a term thai captures the distributional role of price changes. The sign of this term is largely determined by the sign of the plutocratic gap. In consonance with the results of the present study, using the mean logarithmic deviation and a value of 0.5 for the parameter that reflects the economies of scale within the household, in Ruiz-Castillo, Ley, and Izquierdo (2002a) we find that this term is positive. Thus, we conclude that the decreases in real household expenditure inequality in Spain during the second part of the 1970s and the 1980s and 1990s have, respectively, been 9.07, 4.82, and 2.97 percent larger than the decrease in nominal household expenditure inequality owing to the distributive role of price changes during these periods.

For a discussion of this issue, sec Triplet! (198?). Fry and Pashardcs (1986), Griliches (1995), and Pollak (1998): and, in connection to the poverty line, sec National Research Council (1995).

For the United Kingdom. Carruthers, Sell wood, and Ward (1980) indicate dial from January 1975 to January 1979 the democratic index has increased by around 0.1 percentage points a year faster than the official CPI. Fry and Pashardcs (1986) also find that from 1974 to 1982 the plutocratic gap was negative. For 1975–76, Deaionand Muellbauer (1980) report lhat the inflation rale for the poor was around two percentage points higher lhan for the rich. Crawfoixl (1996) jlnds, however, that between 1979 and I he end of 1992. inflation for richer households was 0,16 percentage points higher than the average for all households. Newberry (1995) finds that the distributional effects were negligible and not significantly different from zero in Hungary and the United Kingdom during the 1980s. For the United States, Kokoski (2000) finds lhat from 1972 to 1980 the democratic and the plutocratic Laspeyres indices are rather close in value for most demographic groups, but, in general, the former exceeds the latter by I to 3 index points. Slesnick (1991) finds that cost of living indices are surprisingly insensitive to the choice of the form of the index. Garner, Ruiz-Castillo, and Sastre (1999) find evidence that the plutocratic gap during the 1980s indicates that prices behaved in a slightly anti-rich way. See Ley (2002) for a summary of studies.

Cechetti, Mark, and Sonora (2000) study the dynamics of price indices for major U.S. cities using panel econometric methods and find that relative price levels in different cities revert to the mean at an exceptionally slow rate. The surprisingly slow rate of convergence can he explained by a combination of the presence of transportation costs, differential speeds of adjustment to small and large shocks, and the inclusion ot’nontraded goods prices in the overall price index. Alberola and Marques (1999) present similar evidence for Spain.

In our context, this implies that the set of household-specific price indices after the correction of this bias should exhibit a smaller plutocratic gap. Are these critics correct’? In Ruiz-Castillo, Ley, and Izquierdo (2002a), we have tested this idea by combining the siructure of the bias for the U.S. economy with the consumer behavior of Spanish households as revealed in the 1990–91, 19X0–81, and 1973–74 household surveys. The plutocratic gaps after the correction of the quality bias in the intervals (winter 1991 to January 1998, winter 1981 to winter 1991, and 1973–74 to winter 1981) are 0.035, 0.073, and 0.249 percentage points a year, respectively. Since, as we have seen, the plutocratic gaps before the correction are 0.055. 0.091, and 0.264 percentage points a year, respectively, we can conclude that there is some evidence indicating that the point made by those social critics is well taken.

The 52 Spanish provinces are grouped in 18 Autonomous Communities.

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