Distributional aspects of the quality change bias in the CPI: Evidence from Spain by Javier Ruiz-Castillo Eduardo Ley Mario Izquierdo

DOCUMENTO DE TRABAJO 2000-08

February, 2000

* Universidad Carlos III de Madrid.

** International Monetary Fund.

*** FEDEA.

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Distributional Aspects of the Quality Change Bias in the CPI: Evidence from Spain

Javier Ruiz-Castillo Dept. de Economía, Universidad Carlos III de Madrid, Spain

Eduardo Ley International Monetary Fund, Washington DC, U.S.A.

Mario Izquierdo

Fundación de Estudios de Economía Aplicada, Madrid, Spain

Version: February 28, 2000

Abstract. In this paper we address the issue of the distributional consequences of the quality change bias (QCB) in the CPI. In particular, we assess the conjecture raised by some critics of the Boskin commission report that new products and goods affected by quality effects are disproportionately consumed by the rich. Our analysis begins with the observation that the CPI is a weighted mean of household-specific statistical price indexes, with weights proportional to household total expenditures. Then, we suggest a simple but powerful procedure to evaluate the distributional consequences of eliminating the QCB by examining its impact on two scalars: (1) the CPI plutocratic bias, and (2) the change in money inequality after compensating every household for her individual inflation rate. The empirical analysis combines the detailed information pertaining the size of the QCB for the U.S. with household-specific price indexes for Spain in 1973–74, 1980–81, and 1990–91. The results show that, as conjectured, the quality bias especially affects the richer households.

Keywords. Plutocratic bias, money inequality, price index

JEL Classification System. C43, D31, D63

Address. Javier Ruiz-Castillo, Departamento de Economía, Universidad Carlos III, c/ Madrid 126, 28903-Getafe, Madrid. Phone: +34-91-624 9588. Email: jrc@eco.uc3m.es

1. Introduction

In many sectors engaged in the production of household durables, new models are often released with a host of quality improvements accompanied by a price increase (e.g., automobiles). Other sectors are characterized by a steady quality improvement linked to an increase in product durability or product safety which increase consumer welfare without raising prices (e.g., many consumer electronic products and household appliances have experienced a reduction in the incidence of repairs and in electricity consumption). On other occasions, the increase in consumer welfare is due to an increase in product variety (as in the growing availability of fresh fruits and vegetables or in advanced varieties of running shoes or iron-free synthetic fabrics). Finally, new products satisfy either existing needs at a reduced price (e.g., pharmaceutical generics) or in a more efficient way (e.g., compact discs), or they satisfy needs never met before (e.g., cellphones, or interactive videogames).

All these examples of “quality change” in a broad sense, pose phenomenal problems to agencies responsible for elaborating the CPI (Consumer Price Index) in every country. In the U.S., these issues have occupied a great deal of attention in the review of the literature carried out by the Boskin et al. (1996) Senate commission. Because the quality change bias (QCB for short) differs in magnitude, direction and timing across product categories, the Boskin commission emphasizes that the only way to narrow down the range of uncertainty of the overall magnitude of QCB is to examine the available evidence, category by category. As a result of such an examination in a 27-dimensional commodity space, the Boskin commission claims that the CPI in the U.S. overstates the true inflation by 0.61 per cent per year due to a failure on the part of the BLS (Bureau of Labor Statistics) to take fully into account the quality changes experienced in many sectors of the economy and to consider in a timely fashion the value of newly available

This paper is part of a research project partially financed by "la Caixa".

As the BLS experts admit, “This is the first systematic analysis, category by category, of quality bias in the CPI, and it is a noteworthy accomplishment” (Moulton and Moses, 1997).

goods to consumers.

In this paper we address the issue of the distributional consequences of the QCB in the CPI. In particular, we assess the conjecture raised by some critics of the Boskin commission's report that new products and goods influenced by quality effects are disproportionately consumed by the rich —see, e.g., Deaton (1998), and Madrick (1997). Our analysis begins with the fact that the CPI is a weighted mean of household-specific statistical price indexes, with weights proportional to household expenditures. From this starting point, we suggest a simple but powerful procedure for evaluating the distributional consequences of eliminating the QCB by examining this policy's impact on two scalars: (1) the CPI plutocratic bias —defined below—, and (2) the change in money inequality.

In order to do that, we need a set of household-specific CPIs. Unfortunately, such information for the U.S. economy is not readily available. For the Spanish case it is possible to construct Laspeyres price indexes for all households interviewed in the three latest Encuestas de Presupuestos Familiares (EPF), gathered in 1990-91, 1980-81 and 1973-74. These are the household budget surveys used by the Instituto Nacional de Estadística (INE) to estimate the aggregate weights of the official Spanish CPI. But in Spain we lack the monographic studies which allowed the Boskin commission to estimate the importance of the QCB in the U.S. Therefore, what we shall do in this paper is to assume that the structure of the QCB provided by the Boskin commission—appropriately modified after a careful reading of the arguments advanced by its critics in the BLS, and further adjusted to the peculiarities of the Spanish economy—can be reasonably applied to Spain.

We estimate that the QCB in Spain during the 1990s, the 1980s and the 1970s is equal to 0.41, 0.39, and 0.35 per cent per year, respectively. As far as the distributional aspects are concerned, our results confirm that the QCB predominantly affects the individuals at the upper end of the household total expenditures distribution. Since total expenditures in real terms have been increasing from 1973-74 to 1990-91, this explains why, as we approach the present, the QCB grows in importance.

Some critics point out that there are fundamental difficulties in disentangling quality change from preferences' change (Deaton, 1998). On the other hand, BLS experts defend their numerous and occasionally sophisticated procedures to measure price changes net of quality variation, and seriously contest many of the commission's detailed claims —see Moulton and Moses (1997), and the references quoted there.

The rest of the paper consists of three Sections and a data Appendix. In Section 2 we present a comparison of the QCB in the Spanish and the U.S. economies. Section 3 is devoted to the empirical results on the consequences of eliminating the QCB in the Spanish economy in the period from 1973-74 to 1998, while Section 4 concludes.

2. The Quality-Change Bias

A statistical price index compares a vector of current prices with a given vector of base prices by means of the ratio of the cost of acquiring a reference quantity vector at current and base prices. In particular, a CPI for a given population is a group index which takes as reference the vector of mean quantities actually purchased by the households of the population in question.

Let there be a population of H households consuming I goods, and denote by the quantity of good i purchased by household h during period . Let be the vector where is the mean quantity of good i purchased by the H consumers in period . Given the vector of base prices , the CPI for any vector of prices is defined by:

\[C P I _ {t} \equiv \ell (\mathbf {p} _ {t}, \mathbf {p} _ {0}; \bar {\mathbf {q}} _ {\tau}) = \frac {\mathbf {p} _ {t} \cdot \bar {\mathbf {q}} _ {\tau}}{\mathbf {p} _ {0} \cdot \bar {\mathbf {q}} _ {\tau}}.\tag{1}\]

The CPI can be written also as the weighted mean of goods price ratios :

\[C P I _ {t} = \sum_ {i} W _ {i} \frac {p _ {i t}}{p _ {i 0}},\]

where

Let us assume that quality change has not been completely eliminated from the price ratios , and let be the best estimate of the QCB in the measurement of inflation of good i expressed in per cent per year. Then the QCB for the economy as a whole is defined by

\[Q C B = \sum_ {i} W _ {i} b _ {i}.\]

Because consumer behavior is typically investigated in a period prior to the base period 0, the reference quantity vector and the base price vector do not belong to the same period. Consequently, the group index defined in equation (1) is said to be a modified Laspeyres price index (Moulton, 1996).

2.1. The Structure of the QCB

As indicated in the Introduction, the Boskin commission distinguishes between 27 categories. Column 1 of Table 1 presents the weights of these categories in the U.S. CPI in December 1995, while column 2 lists the commission estimates of the QCB in each case, that is, the vector .⁴

What is the importance of these phenomena in a country like Spain? We simply don't know. On one hand, the INE does not provide information on the procedures they follow to detect quality change, the frequency with which their specialists make quality adjustments, or the empirical consequences of such practices. On the other hand, there are no monographic studies available to document the relevance of the QCB in specific sectors. Thus, we will assume that the structure of the QCB provided by the Boskin commission, conveniently modified to take into account some of the BLS criticisms, is also valid for the Spanish economy.

Moulton and Moses (1997) contains detailed and convincing criticisms of the Boskin commission estimates. In particular, they point out that in 9 categories (1, 2, 3, 8, 10, 14, 20, 25, and 27), in the absence of evidence, the commission is forced to fall back simply on their best judgement. This group accounts for 0.11 percentage points of the total QCB. As shown in column 3 of Table 1, taking into account Moulton and Moses' arguments, we have decided to reduce the QCB of motor fuel (category 20) to 0.15, and those of the remaining categories in this group by one-half.

It could be argued that the dynamic nature of the U.S. economy is characterized by more quality changes and the appearance of new products than what we should expect in the Spanish economy. But at the same time, the Spanish INE is much less active than the BLS in eliminating quality change from price variation. The assumption that we can import the evidence on the QCB from the U.S. and use it in the Spanish economy can only be accepted as a first approximation, which should be subject to closer scrutiny by further research into specific sectors. The advantage of this procedure is twofold: (i) we can study how our estimates of the QCB in Spain are affected by changes over time in the aggregate weights, and (ii) we can assess whether the QCB is more pronounced for the rich or the poor Spanish households in different moments in time.

Biases are often estimated in different periods, all of which end in 1996. We have always taken the latest estimate, except for housing appliances. In this case, the 1994–1996 estimate is 5.6 per cent per year; but we have chosen a 3.6 estimate corresponding to the 1973–1990 period, more in keeping with the Spanish experience for the 1973–1990 period.

Moulton and Moses (1997) state that without the BLS procedures to correct for the QCB, inflation in the U.S. would have risen by an extra 1.7 per cent in the course of a single year.

Table 1. The Quality Change Bias in the U.S., and the U.S. vs. Spanish Aggregate Weight Structure in Percentage Terms

2.2. The QCB in the U.S. and the Spanish Economies

In order to compare the structure of the QCB in the U.S. and the Spanish economies, it is advisable to reduce the dimensionality of the commodity space. In column 1 of Table 2 we present the contribution of each of 7 large expenditures groups to the overall QCB in the U.S. Column 2 provides the same information for the U.S., but for the corrected QCB structure which we apply in Spain —see column 3 in Table 1. Columns 3 to 5 provide the contribution of the 7 groups to the overall QCB in Spain in 1990–91, 1980–81, and 1973–74, respectively.

Table 2. The Quality Change Bias in the U.S. and Spain

The total QCB in the U.S. economy is estimated in 0.58 per cent per year. Apparently, the QCB figure of 0.61 used by the commission —and shown in column 1 at the bottom of Table 2— is the result of taking the weight of household appliances equal to 2.13 per cent according to data on annual nominal personal consumption expenditures, rather than the low weight of 0.806 which is included in Table 1 —see note a in Table 2 in Boskin et al. (1996). We see that if we accept for the U.S. the corrections suggested by our reading of Moulton and Moses (1997), then the QCB is reduced to 0.55 per cent per year. In comparison, the estimated QCB in Spain is equal to 0.41, 0.39, and 0.35 per cent per year in the three years considered.

Let us now comment on the differences between the QCB in the U.S. (corrected case) and in 1990–91 Spain. Because the QCB for all expenditures categories has been taken to be the same in the two countries, the differences between columns 2 and 3 in Table 2 are exclusively due to the differences in aggregate weights. The contribution to the overall QCB by expenditure groups I, II and VII is larger in Spain. The total difference amounts to 0.10 percentage points per year. Given the much smaller role of the public health system in the U.S., relative to a country like Spain where most of the health expenditures correspond to the public sector, there is a very large difference in the weights of the two countries in group V —see the details according to individual categories in columns 1 and 4 of Table 1. As a matter of fact, the contribution of group V to the QCB is larger in the U.S. by 0.14 percentage points per year. This, together with the 0.10 percentage points attributable to the remaining groups III, IV, and VI, explains the difference between the U.S. QCB and the Spanish one.

Assuming the uncorrected Boskin commission QCB structure in column 2 of Table 1, the bias in the Spanish case would be raised to 0.48, 0.47, and 0.44 per cent per year in 1990–91, 1980–81, and 1973–74, respectively, in comparison with 0.61 per cent per year in the U.S.

The relative importance of “apparel” and “other goods and services” (groups II and VII) and, above all, of “housing” (group III), is monotonically decreasing in Spain as we delve further into the past. Except for food, beverages and tobacco (group I), which consists mainly of necessities and whose weight declines as household total expenditures increases over time in real terms, the remaining groups IV, V, and VI have weights which remain essentially constant over time. The end result is that the QCB declines as we move from 1990–91 to 1973–74.

3. Distributional Aspects of Eliminating the QCB in the Spanish Economy

In order to evaluate the distributional aspects of eliminating the QCB from the measurement of inflation, we suggest measuring its impact on the CPI plutocratic bias, and on the change of money inequality after compensating every household for her individual inflation rate.

3.1. Effects on the Plutocratic Bias

Let be the quantity vector acquired by household in period , and let . We will define a household-specific CPI by:

\[c p i _ {t} ^ {h} \equiv \ell (\mathbf {p} _ {t}, \mathbf {p} _ {0}; \mathbf {q} _ {\tau} ^ {h}) = \frac {\mathbf {p} _ {t} \cdot \mathbf {q} _ {\tau} ^ {h}}{\mathbf {p} _ {0} \cdot \mathbf {q} _ {\tau} ^ {h}} = \sum_ {i} w _ {i} ^ {h} \frac {p _ {i t}}{p _ {i 0}}.\tag{2}\]

Let , it follows that

\[C P I _ {t} = \sum_ {h} \phi^ {h} c p i _ {t} ^ {h}.\tag{3}\]

Equation (3) indicates that the CPI is the weighted average of the household-specific CPIs with weights proportional to household total expenditures. Because the rich households weigh more than the poor households, the CPI has been called a plutocratic price index (Prais, 1958). Similarly, let us define the household-specific quality change bias by . Then we have that , that is to say, the quality bias for the economy as a whole is the plutocratic weighted average of the household-specific quality biases.

In Ruiz-Castillo et al. (1999b) we define the plutocratic bias (PB for short) as the bias in the measurement of inflation we commit when we use the current plutocratic CPI rather than a (democratic) group price index in which all households have the same weight. When prices behave in an anti-rich (anti-poor) way, that is to say, when the price of luxuries increases relatively more (less) than the price of necessities, we expect the plutocratic weighted mean of household-specific price indexes to be greater than the simple mean. Thus, the PB would be positive or negative according to whether prices behave in an anti-rich or anti-poor manner, respectively.

The individual price index after the correction for the QCB is simply . Analogously, . Thus, whether new products and goods affected by quality effects are disproportionately consumed by the rich households can be ascertained by whether or not the PB declines after the elimination of the QCB.

As indicated in equation (2), to construct household-specific price indexes we need two pieces of information: (i) the relative prices , which official statistical agencies regularly publish at certain levels of commodity (and spacial) disaggregation; and (ii) a vector of budget shares for each household at the same level of commodity disaggregation as the price information described in point (i) above.

In order to construct those indexes in the U.S., we must confront the difficulty that the statistical instrument to investigate household consumption expenditures —namely, the Consumer Expenditure Survey— has two components and a complex time structure: the first component is a Diary or record-keeping survey which is designed to be completed by participating consumer units for two consecutive one-week periods, while the second component is an Interview survey in which the expenditures of consumer units are to be obtained in five interviews conducted once every three months. (Data from the first interview is only used to ‘bound’ expenditures for subsequent interviews.) The interview sample, which is different from the diary sample, is selected on a rotating panel basis, targeted at 5,000 consumer units each quarter. Thus, about twenty percent of the sample is interviewed for the first time each quarter while twenty percent is interviewed for the last time. Survey participants record dollar amounts for goods and services purchased during the week of data collection for the Diary, and report these amounts to an interviewer for the previous three months from the date of the interview for the Interview. Therefore, one must somehow integrate the information coming from the Diary and the Interview components, and decide whether or not to treat as an independent observation each quarterly data of the four periods available from the same interview households as an independent observation. In Cage et al. (1997), an effort was launched to solve these problems and deal with other idiosyncratic features of the Consumer Expenditure Survey. Unfortunately, the results from this research are not yet definitive nor available for this occasion. This is why we have turned our attention to a country where this crucial piece of information is readily available.

As we have already indicated, in Spain there is a set of household-specific price indexes for all consumers interviewed in the 1990–91, 1980–81, and 1973–74 EPFs. This allows us to estimate the PB during the periods Winter 1991–January 1998, Winter 1981–Winter 1991, and 1973/74–Winter 1981. The results, reported in Ruiz-Castillo et al. (1999b), are that the PB in these three periods was equal to 0.055, 0.091, and 0.265 per cent per year, respectively. This means that in all three periods prices have behaved—with different intensities—in an anti-rich way, i.e., that the inflation experienced by the rich households has been relatively greater than the one experienced by the poor households. As we see in Table 3, when we compute the PB in the three periods in terms of the indexes in which we have eliminated the QCB, we find that it is equal to 0.035, 0.073 and 0.249 per cent per year, respectively. This means that 36.4, 19.8 and 6.0 per cent of the PB can be attributed to the QCB.

Table 3. The Plutocratic Bias in Spain: Before and After the Correction for the Quality-Change Bias

(The plutocratic bias is expressed in percentage points per year.)

Thus, in the three cases the conjecture that this phenomenon is more prevalent among the rich households appears to be supported by the facts. Furthermore, the fact that the importance of the decline in the PB as a result of the elimination of the QCB is less the further we go into the past, is consistent with the fact that household total expenditures in real terms decline as well when we move in that direction.

3.2. The Effect on the Change in Income Inequality

Suppose that we want to compare the household income or expenditures distributions in two different time periods, and , where are the household h's total expenditures in period t and is not necessarily equal to H. Let and be the price vectors in the two situations. For each h, we can express the household's total expenditures in situation 1 at prices , , by multiplying her original money income in period 1, , by a statistical price index of the modified Laspeyres type:

\[x _ {1, 2} ^ {h} = x _ {1} ^ {h} \ell (\mathbf {p} _ {2}, \mathbf {p} _ {1}; \mathbf {q} _ {1} ^ {h}) = \mathbf {p} _ {1} \cdot \mathbf {q} _ {1} ^ {h} \frac {\mathbf {p} _ {2} \cdot \mathbf {q} _ {1} ^ {h}}{\mathbf {p} _ {1} \cdot \mathbf {q} _ {1} ^ {h}} = \mathbf {p} _ {2} \cdot \mathbf {q} _ {1} ^ {h}.\]

For any , let be any convenient inequality index satisfying continuity, S-concavity, scale independence and replication population invariance. The change in money income inequality, , is seen to be the sum of two terms:

\[\Delta M = \mathcal {I} (\mathbf {x} _ {2}) - \mathcal {I} (\mathbf {x} _ {1}) = [ \mathcal {I} (\mathbf {x} _ {2}) - \mathcal {I} (\mathbf {x} _ {1, 2}) ] + [ \mathcal {I} (\mathbf {x} _ {1, 2}) - \mathcal {I} (\mathbf {x} _ {1}) ] = \Delta R + \Delta P,\]

where is the change in real income inequality and captures the distributional impact of price changes on inequality measurement according to the first-period households' preferences. From a social point of view, we are primarily interested in the sign of . However, in the absence of household-specific household price indexes —which is the dominant situation in the empirical literature—we can only measure . Therefore, it is important to know the relationship between and when the change from to is not neutral, that is, when is different from 0.

p1

We could have expressed the distribution in situation 2 at prices by using an appropriate Paasche type price index. In this case, would have measured the distributional impact of price changes according to the second-period households' preferences.

The compensating variation introduced by Hicks (1940), , is the amount of money that household h must receive in order to compensate her from the price change from to , i.e.,

\[C V ^ {h} = x _ {1, 2} ^ {h} - x _ {1} ^ {h} = \left(\ell (\mathbf {p} _ {2}, \mathbf {p} _ {1}; \mathbf {q} _ {1} ^ {h}) - 1\right) x _ {1} ^ {h} = \pi^ {h} x _ {1} ^ {h},\tag{4}\]

where . In this context the plutocratic bias is defined as , where . Intuitively, when , for example, household inflation tends to be greater for the rich than for the poor households. Taking equation (4) into account, in this case we expect the compensating variation to be greater also for the rich than for the poor households. Given that , where , as long as we have that or, in other terms, . Taking equation (4) into account, we can expect that as . This means that when , for instance, so that the price change from to is anti-rich, then the term is positive and we expect . In this case, (i) if the normatively significant term is positive, so that there has been an increase in real income inequality, then the change in money income inequality would overstate the socially relevant magnitude. (ii) Conversely, if , then would understate the reduction in real income inequality.

We have seen in subsection 2.1 that the question of whether new products and goods affected by quality effects are disproportionately consumed by the rich households can be ascertained by whether or not the PB declines after the elimination of the QCB. If this is the case, then the term should be lower in absolute value after the elimination of the QCB. Therefore, depending upon whether is positive (or negative), the change in money income inequality would provide a better (or worse) approximation to the change in real income inequality .

The idea that price movements should be included in intertemporal income inequality comparisons was originally suggested by Iyengar and Battacharya (1965). Subsequently, in a social welfare context Muellbauer (1974) showed that under general assumptions on individual preferences real income inequality comparisons are not price independent.

, i.e.

CV. A

Notice that the converse need not be the case. It might be that because the vector CV is very unequal and there are a lot of reorderings between and CV. A reordering between and CV means that, for a pair of households h and , but . Therefore, , i.e., inflation would be greater for the rich than for the poor household and the weighted mean of could be smaller than the simple mean. Thus, in spite of we can have PB < 0.

Let us identify situations 1 and 2 with the Winter of 1991 and January of 1998, respectively. Since, as we have seen, per cent per year during this period, we expect the term in equation (4) to be positive. This is also the case when we consider the periods Winter 1981-Winter 1991, and 1973-Winter 1981. To verify whether the term is positive in the three periods, we must select an inequality index of adjusted household expenditures. It is well known that the Generalized Entropy family of inequality indices is the only measures of relative inequality that satisfies the usual normative properties required from any inequality index and, in addition, is decomposable by population subgroup (Shorrocks, 1984). The family can be described by means of the following convenient cardinalization:

\[\begin{array}{r l} & {\mathcal {I} _ {c} (\mathbf {y} (\theta)) = \frac {1}{c (c - 1) H} \sum_ {h} \left\{\left(\frac {y ^ {h} (\theta)}{\mu (\mathbf {y} (\theta))}\right) ^ {c} - 1 \right\}, \quad c \in (0, 1)} \\ & {\mathcal {I} _ {0} (\mathbf {y} (\theta)) = - \frac {1}{H} \sum_ {h} \ln \left(\frac {y ^ {h} (\theta)}{\mu (\mathbf {y} (\theta))}\right);} \\ & {\mathcal {I} _ {1} (\mathbf {y} (\theta)) = \frac {1}{H} \sum_ {h} \frac {y ^ {h} (\theta)}{\mu (\mathbf {y} (\theta))} \ln \left(\frac {y ^ {h} (\theta)}{\mu (\mathbf {y} (\theta))}\right),} \end{array}\tag{5}\]

where is the distribution of adjusted household total expenditures with , and stands for the mean of the distribution of . The greater the equivalence elasticity , the smaller the scale economies in consumption or, in other words, the larger the number of equivalent adults. The parameter c summarizes the sensitivity of in different parts of the household total expenditures distribution: the more positive (negative) c is, the more sensitive is to differences at the top (bottom) of the distribution (Cowell and Kuga, 1981). is the original Theil index, while is the mean logarithmic deviation.

Following Buhmann et al. (1988) and Coulter et al. (1992a, 1992b), we adopt an equivalence scale model in which scale economies in consumption depend only on household size, . When , adjusted expenditures coincide with unadjusted household expenditures, while if , it becomes per capita household expenditures. Taking a single adult as the reference type, the expression can be interpreted as the number of equivalent adults in a household of size s.

In Table 4 we present the estimates for —expressed in percentage terms of — for different parameter values of . These estimates have been estimated using 1,000 Bootstrap samples. In each Bootstrap sample we draw 21,155 households using stratified resampling according to the 260 strata in the original survey. For each pair, we obtain a Bootstrap distribution of 1,000 inequality measures.

Table 4. Changes in Inequality Before and After the Correction by the Quality Change Bias

In the first place, we observe that, as expected, is positive for all values of c and in the three panels of Table 4. However, in line with the size of the plutocratic bias in the three periods (0.055, 0.091, and 0.265 per cent per year, respectively), the distributional impact of the change in relative prices is between 2–4 per cent, 4–9 per cent, and 6–14 per cent in 1991–1998, 1981–1991, and 1973–1981, respectively.

See Hall (1992) for a description of Bootstrap methods and Mills and Zandvakili (1997) for an application to income inequality measurement.

In the second place, the correction of the QCB gives rise to a statistically significant decrease in such a distributional effect. For c = 0 and , for instance, this decrease amounts to a 24, 12 and 5 per cent reduction of the term in each of the three periods.

4. Conclusions

As the Boskin commission points out, in an economy as dynamic as the U.S., new products are introduced all the time and existing ones improved constantly, while others exit the market. The relative prices of different goods and services change frequently, in response to the changes in income and technological factors affecting costs and quality. In this context, it is not surprising that measurement issues relating to quality change and the introduction of new products have attracted a lot of attention among the CPI experts.

The Boskin commission concluded that in the U.S., in around 1995, there was an upward QCB in the measurement of inflation of about 0.61 per cent per year. But what are the distributional aspects of this bias? What do we know about the possibility that the QCB has different impacts across different demographic groups?

The members of the Boskin commission have few doubts. Gordon and Griliches (1997) conclude that their main point as far as the QCB is concerned is that “current procedures miss a significant fraction of the contribution of new and improved goods and services to the advance of the average standard of living”. Reference to the average standard of living is in keeping with their general lack of concern with the distributive aspects of inflation. But Boskin et al. (1998) are very explicit on the issue at hand: “While we are certainly concerned about the economic well-being of our least well-off citizens, it is important to understand how dramatically improved the standard of living of even the poorest in the population has been. It is simply incorrect to argue that quality improvements and new products accrue only to the rich, rather than broadly through the population.” However, other experts think differently. Deaton (1998), for instance, states that “the bias in the CPI from ignoring quality effects is surely related to income, in spite of the denials by Boskin and his coauthors in this issue. The welfare benefits of exogenous increases in quality are in proportion to the quantity of the goods consumed, so that the benefits of quality upgrading and of new goods will only be distributionally neutral if the affected goods are neither luxuries nor necessities ... When new goods are consumed disproportionately by the rich, whose price indexes are weighted in the CPI according to their incomes, the quality-corrected plutocratic index can provide a very poor measure of prices for the average consumer."

To really find out about the distributional aspects of the QCB, we should possibly start by descending to the price collection stage in the construction of the CPI. At this level we might investigate whose consumer behavior is captured by the set of items, qualities and outlets actually covered by the index. Naturally, this is a task that could be carried out only by the statistical agencies responsible for the CPI construction. But even under the assumption that all individuals in a given geographical area buy all goods and services at the same prices, in this paper we have argued that we can evaluate some of the distributional aspects of the QCB by taking into account household differences in consumption patterns.

In the U.S. household-specific price indexes are not readily available. In Spain we have constructed such indexes for different moments in time, but we have no information on the size of the QCB for different goods. Therefore, what we have done in this paper is to combine the detailed information on the size of the QCB for the U.S. economy with the household-specific price indexes for the Spanish economy. If many of the goods affected by the QCB are luxuries, we expect that the more affluent the society is, the greater the overall QCB should be. This is indeed what we find. The U.S. economy in 1995 is more affluent that the Spanish economy in 1990-91. In turn, real incomes in Spain are greater in 1990-91 than in 1980-81 and in 1973-74. Correspondingly, the overall QCB which we estimate in this paper is equal to 0.55 per cent per year in the U.S. in 1995, and 0.41, 0.39 and 0.35 per cent per year in Spain in 1990-91, 1980-81 and 1973-74, respectively.

This is what Pollak (1998) calls the “beer or champagne (or the choice between the domestic or imported beer)” question.

Next we ask, what would be the consequences of eliminating the QCB? In the first place, if the consumption of new and quality improved products is more prevalent among the rich households, then we expect that this policy would tend to decrease by a larger amount the inflation rate measured according to the plutocratically weighted official CPI, than the inflation rate measured according to a democratic group index in which each individual price index receives the same weight. Consequently, we expect that what we call the plutocratic bias (PB) —which has been positive in Spain since 1973 to 1998— decreases after the elimination of the QCB. This is indeed what we find. Furthermore, the greater the overall QCB, the greater the reduction in the PB.

In the second place, if the evolution of prices is anti-rich in the sense that richer households tend to be negatively affected by inflation to a greater extent than poorer ones, then we expect that the inequality of the income distribution, after all households are differentially compensated for inflation according to household-specific price indexes, should be greater than the inequality of the original income distribution. As we have seen, this is the case for Spain from 1973 to 1998, with different intensities depending on the subperiod considered. In these circumstances, if the QCB is larger for richer than for poorer households, the elimination of the QCB would tend to reduce the change in income inequality before and after the compensation for inflation. This is what we find in Spain for every subperiod, and for a wide range of parameter values reflecting different degrees of aversion to inequality and different degrees of economies of scale in consumption within the household.

What can we extrapolate to the U.S. economy from these findings? In Garner et al. (1999) there is some evidence indicating that the U.S. prices during the 1980s have behaved in a slight, not statistically significant, anti-rich manner. Taking into account that the overall QCB in the U.S. is larger than in Spain, if there was a slightly positive PB during the 1980s in the U.S., then after the elimination of the QCB it is highly likely that we would find a negative PB, indicating that the QCB-corrected prices had actually behaved in an anti-poor manner. Clearly, this issue calls for further research.

Specifically, the result is that, under different assumptions about the importance of economies of scale within the household, the inequality of the household total expenditures distribution in the Winter of 1991, measured by the general entropy index with parameter c = 0, is smaller than the inequality of this distribution at the prices of the Winter of 1981.

We want to stress that, once we have household-specific price indexes in a given country, a host of applications are possible. To begin with, we can study the relationship between the individual inflation rates and other demographic, geographic and socioeconomic household characteristics different from household income or total expenditures. A multivariate analysis of this sort, before and after the elimination of the QCB, would complete the analysis of the distributional consequences of this policy carried out in this paper —for examples of this approach, see Hagemann (1982), Michael (1979), and Ruiz-Castillo et al. (2000). Furthermore, as pointed out in Ruiz-Castillo et al. (1999b), one could evaluate the first-round distributional consequences of (i) other methodological decisions related to the construction of the CPI, and (ii) any government policy measure affecting relative prices in particular directions, including policy measures aimed at fighting inflation by reducing the prices of commodities characterized by large aggregate weights in the CPI.

5. Appendix: The Spanish Aggregate Weights

In Spain, the last three CPI systems are based on 1992, 1983 and 1976. The household budget surveys which have served to estimate the corresponding weights are the EPFs, gathered by the INE from April 1990 to March 1991, April 1980 to March 1981, and July 1973 to June 1974, respectively. We refer to them as the 1990–91, 1980–81 and 1973–74 EPF, respectively. These EPFs are large comparable samples consisting of 21,155, 23,972 and 24,151 household sample points, respectively. They represent a population of, approximately, 11, 10 or 9 million households and 38, 37 or 34 million persons in 1990–91, 1980–81 and 1973–74, respectively, occupying residential housing in all of Spain, except for the 1973-74 EPF which excludes the North African cities of Ceuta and Melilla. People living in collective housing, such as residences for the aged, hospitals, prisons, hotels, and the like, are excluded from the EPFs. The three surveys share the same sample stratification design, and the same methodology for investigating household expenditures —for further details, see INE (1992), INE (1983), and INE (1975).

Consider the 1990–91 EPF by way of example. In Ruiz-Castillo et al. (1999a) we construct a series of household-specific indexes of the Laspeyres type for the period starting in each of the four quarters of the 1990-91 annual period and ending in January 1998. It should be emphasized that this series of individual indexes differs from the one underlying the official Spanish CPI in two ways. In the first place, our definition of total household expenditures is different from the one used by the INE. In the second place, the Spanish CPI is not a proper Laspeyres price index which takes as reference the quantities actually acquired by households at the time they were interviewed in a EPF. At any rate, if we define the plutocratic weights in terms of households total expenditures at current prices, due to inflation during the 1990–91 period, households interviewed in a later quarter would tend to have a greater weight in the CPI weights for the population as a whole. To correct this problem, we express all magnitudes at prices of Winter of 1991. Our estimates of the 1990–91 aggregate weights in the Boskin commission 27-dimensional commodity space are listed in column 4 of Table 1.

The sources of difference are the following three. (i) While the INE sets housing expenditures for households occupying non-rental housing equal to zero, we use the imputed rental value estimated in the EPF by the occupying household. (ii) We include all imputations for home production, wages in kind and subsidized meals, which are excluded by the INE. (iii) We estimate annual food and drink expenditures using all the available information on bulk purchases in the 1990-91 EPF, while the INE uses only the information gathered during the sample week. The joint impact of these modifications on the measurement of inflation is important: according to Ruiz-Castillo et al. (1999c), the official CPI understates the true Spanish inflation from 1992 to January of 1998 by 0.241 per cent per year.

The reason is that the INE does not make any adjustment to take into account the price change between the EPF's collection period and the base year of the CPI system. This gives rise to several

Similarly, in Ruiz-Castillo et al. (1999a) we construct a series of household-specific indexes of the Laspeyres type for the period starting in each of the four quarters of the 1980-81 annual period and ending in the Winter of 1991. This series of individual indexes differs from the one underlying the official CPI only because the latter is not a proper Laspeyres price index which takes as reference the quantities actually acquired by households at the time they were interviewed in an EPF. We express the 1980–81 aggregate weights at constant prices of the Winter of 1981 (see column 5 in Table 1).

Finally, lacking information on the quarter when households were interviewed during the 1973-74 period, in this case we must work with the uncorrected aggregate weights defined at current prices of the EPF's annual collection period (see the sixth column of Table 1).

problems, including the appearance of a bias in the measurement of inflation —which we call the Laspeyres bias— defined as the difference between measuring inflation according to the official Spanish CPI and according to a Laspeyres type index. For an analysis of this question and an estimate of the Laspeyres bias during the last 12 years in Spain, see Ruiz-Castillo et al. (1999d).

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COLECCION RESUMENES

98-01: “Negociación colectiva, rentabilidad bursátil y estructura de capital en España”, Alejandro Inurrieta.

TEXTOS EXPRESS

99-02: “Economic implications of the demographic change in Spain: Call for research”, Namkee Ahn.

99-01: “Efectos macroeconómicos de la finalización de las ayudas comunitarias”, Simón Sosvilla-Rivero y José A. Herce.

DOCUMENTOS DE TRABAJO

2000-08: “Distributional aspects of the quality change bias in the CPI: Evidence from Spain”, Javier Ruiz-Castillo, Eduardo Ley y Mario Izquierdo.

2000-07: “Testing chaotic dynamics via Lyapunov exponents”, Fernando Fernández-Rodríguez, Simón Sosvilla-Rivero y Julián Andrada-Félix.

2000-06: “Convergencia: Un análisis conjunto de los sectores. Aplicación al caso de las regiones española”, Pablo Álvarez de Toledo, Jaime Rojo, Álvaro Toribio y Carlos Usabiaga.

2000-05: "The Laspeyres bias in the Spanish consumer price index". Javier Ruiz-Castillo, Eduardo Ley y Mario Izquierdo.

2000-04: “Evaluación de los efectos del Plan Prever a partir de un modelo de simulación de reemplazos del parque español de automóviles”, Omar Licandro y Antonio R. Sampayo.

2000-03: “Minimum consumption, transitional dynamics and the Kuznets curve”, María José Alvarez y Antonia Díaz.

2000-02: “Vintage human capital, demographic trends and endogenous growth”, Raouf Boucekkine, David de la Croix y Omar Licandro.

2000-01: “Vintage capital and the dynamics of the AK model”, Raouf Boucekkine, Omar Licandro, Luis A. Puch y Fernando del Río.

99-21: “Los efectos macroeconómicos de la Agenda 2000”, Simón Sosvilla-Rivero y José A. Herce. 99-20: “Unemployment duration and workers’ wage aspirations in Spain”, Namkee Ahn y J. Ignacio García-Pérez.

99-19: “El patrón inversor de los establecimientos industriales de la Comunidad de Madrid”, Ana Goicolea, Omar Licandro y Reyes Maroto.

99-18: “Crecimiento óptimo, depreciación endógena y subutilización del capital”, Omar Licandro, Luis A. Puch y J. Ramón Ruiz Tamarit.

99-17: “Panel data and tourism demand. The case of Tenerife”, F. J. Ledesma-Rodríguez, M. Navarro-Ibáñez y J. V. Pérez-Rodríguez.

99-16: “Redistribution in the Spanish pension system: An approach to its life time effects”, Joan Gil y Guillem López-Casasnovas.

99-15: “The plutocratic bias in the CPI: Evidence from Spain”, Javier Ruiz Castillo, Eduardo Ley y Mario Izquierdo.

99-14: “Local responses to a global monetary policy: The regional structure of financial systems”, Juan J. de Lucio y Mario Izquierdo.

99-13: “The importance of the embodied question revisited”, Raouf Boucekkine, Fernando del Río y Omar Licandro.