The Influence of Demographics and Household Specific Price Indices

on

Expenditure Based Inequality and Welfare:

A Comparison of Spain and the United States

BY

Thesia I. Garner1, Javier Ruiz-Castillo2, and Mercedes Sastre Garcia3

Prepared for the Southern Economics Association Annual Conference

Atlanta, Georgia 21-23 November 1997

Discussant: John P. Formby, University of Alabama

1Garner's address: Division of Price and Index Number Research, U.S. Bureau of Labor Statistics, Postal Square 

Building, Room 3105, 2 Mass. Ave., N. E., Washington, D. C. 20212; telephone: (202)606-6579 extension 596; fax: 

(202)606-6583; email: Garner_T@BLS.GOV

2Ruiz-Castillo's address: Departamento de Economic, Universidad Carlos III, 28903-Getafe, Spain; telephone: 

[+34+1] 624 9588; fax: [+34+1] 624 9329; email: jrc@eco.uc3m.es 

3

Sastre Garcia's address: Departamento de Economic Aplicada VI, Universidad Complutense de Madrid, Campus de 

Somosaguas, 28223 Madrid, Spain; email: ecap6z2@emducms1.sis.ucm.es

For their comments, the authors would like to thank Jorge Salazar-Carillo, Michael Wolfson, and other participants in 

the Session on International Comparisons of Income and Wealth Statistics during the 51st Session of the International 

Statistical Institute (August 1997). A tremendous thanks is extended to Rob Cage of the BLS who produced the 

indexes for the U.S. and the primary data set used for the analysis. All views expressed in this paper are those of the 

authors and do not reflect the views or policies of the Bureau of Labor Statistics (BLS) or other BLS staff members, 

the Universidad Carlos III, or the Universidad Complutense de Madrid. The responsibility for errors remains with the 

authors.
ABSTRACT

The purpose of this research is to examine the role of household size and household 

specific price indices on inequality and welfare measurement in Spain and the U.S. Total 

household expenditures from each countries' 1990-91 consumer expenditure surveys are 

used for the analysis. Decomposable measurement instruments are used both for the 

inequality and social welfare analyses. Thus we can isolate the impact of household size 

on inequality, separating this affect from the distributional impact due to between group 

differences in inequality. For different time periods, we examine the impact of changes in 

relative prices on both inequality and welfare. To test the sensitivity of our overall results, 

different household size scale factors are applied to total expenditures to produce adjusted 

expenditures. The household specific price indices are used to express the 199091 

expenditure distributions at winter of 1981 and winter of 1991 prices. Diary data are 

employed to allocate Diary specific commodities to Interview households in the U.S. 

case. Our results show that wide differences in demographic factors can be very important 

in international comparisons. Inequality and welfare comparisons are drastically different 

for smaller and larger households. Given this diversity, decomposable measurement 

instruments help to explain how results at the household size level get translated at the 

population level. In terms of the influence of relative prices on inequality, for both 

countries, we find that from the point of view of winter 1981; the amount of expenditures 

that we would need to give to richer households to compensate them for inflation, over 

the 1981 to 1991 period, would be greater than the amount that we would need to give to 

poorer households for them to remain at the same level of welfare. However, because the 

distributional impact of relative prices is of a comparable order of magnitude, our 

inequality comparisons are rather robust to the choice of the reference price vector.

KEYWORDS: Theil Inequality; Welfare; Household Expenditures; Household 

Specific Price Indexes
1. INTRODUCTION

In this paper we compare levels of living in Spain and the United States (U.S.) 

using current household consumption expenditures as our level of living measure. As in 

most welfare analysis, we assume that social or aggregate welfare can be expressed in 

terms of two statistics of the expenditure distribution: the mean and an index of relative 

inequality.

Like intertemporal comparisons of income inequality and welfare in a single 

country, international comparisons of expenditures require the solution to the following 

four classical problems: (a) how to make comparable two heterogeneous populations 

consisting of households with different needs; (b) which measurement instruments to 

use among the admissible inequality measures; (c) which measurement instruments to 

use among the admissible welfare measures, and (d) how to make comparable the 

money distributions in both countries.

To solve the difficulties arising from the demographic heterogeneity in 

international comparisons, researchers usually compare the distributions of equivalent 

expenditures (or equivalent income) using some common equivalence scale.1 However, 

as Coulter et al. (1992a) conclude in their review of the literature, there is no single 

'correct' equivalence scale for adjusting incomes. Thus, a range of scale relativities is 

both justifiable and inevitable. In this paper, to make the analysis tractable we assume 

that equivalence scales depend only on the number of persons in the household. 

Following Buhmann et al. (1988) and Coulter et al. (1992a, 1992b), to pool all 

households into a unique distribution within each country we use a parametric model of 

equivalence scales which allows for different views about the importance of economies 

of scale in consumption within the household. 2

1

See Phipps and Garner (1994) and Burkhauser et al. (1996). 

2

For the use in this model in international comparisons, see also Atkinson et al. (1995).

2
In the equivalence scales model, expenditures for households of the same size 

are directly comparable. Thus, we believe it is important to start our analysis from 

inequality (or welfare) comparisons separately for each of subgroups in the partition by 

household size. Then, in order to go from the household size to the population level, we 

find illuminating to work with additively decomposable measurement instruments. For 

every population partition, decomposable measures of (relative) inequality allow us to 

express overall inequality in a cross-section as the sum of two terms: a weighted sum of 

within-group inequalities, plus a between-group inequality component calculated as if 

each person within a given group received the group's mean income.

Using decomposable measures, in this paper we explain the overall inequality 

differences between the U.S. and Spain in terms of three factors: i) the difference in 

within-group inequality (due to differences in subgroup inequality values), ii) the 

difference in between-group inequality (due to the relative differences in subgroup 

means), and iii) the demographic change across partition subgroups (due to differences 

in subgroup population shares). In addition, following a suggestion in Coulter et al 

(1992a) and developed in Del Rio and Ruiz-Castillo (1997b), we use a method to free 

the decomposition analysis from the possible ‘contamination’ that will arise if we use an 

inappropriate equivalence scale.

As far as the measurement of welfare is concerned, we are interested in social 

evaluation functions (SEF for short) which permit the explanation of welfare 

differences in terms of differences in the mean and differences in relative inequality. As 

in the inequality case, additively decomposable SEFs have been found useful in 

intertemporal welfare comparisons within a single country.3In this paper we show that 

these methods are equally useful in international comparisons. This is important in a 

context in which we find considerable welfare and demographic inter-country 

differences between the subgroups in the partition by household size.

3See Ruiz-Castillo (1998).

3
We address each of these issues using data from household budget surveys. The 

Spanish data are from the Encuesta de Presupuestos Familiares (EPF) conducted by the 

Instituto Nacional de Estadistica (INE), and the U.S. data are from the Consumer 

Expenditure Survey (CEX) from the Bureau of Labor Statistics (BLS). We compare 

annual consumer unit (referred to here as household) expenditures, which were 

collected by the agencies from April 1990 through March 1991 for Spain and from 

January 1990 through December 1991 for the U.S. We refer to this time period as 

1990-91. We express both distributions at constant prices for two periods in each 

country: the winter of 1991 and the winter of 1981. Since we use household specific 

price indices, we are able to take into account the distributional role of changes in price 

relatives during the 1980's in both countries. Finally, we express the Spanish 

distributions in U.S dollars using EKS Purchasing Power Parities (Godbout 1997; 

OCED 1993).

The comparison between Spain and the U.S. is an interesting one. First, Spain has 

been experiencing a complex process of economic modernization and liberalization since 

the mid-1970's, including full membership into the European Union in January 1986, 

resulting in a more open and market oriented economy. In contrast, the U.S.- has a much 

larger economic system which is rather open and market oriented. Second, during this 

period Spain has been taking important steps toward a fairly comprehensive social safety 

net, in the European style, while that of the U.S. is rather limited. Third, tax structures 

are rather different too. Although a modern income tax system did not start in Spain until 

1978, it is more progressive today than is the U.S. tax system. On the other hand, the EU 

membership lead to the introduction in 1986 of a value added tax in Spain, in contrast to 

the indirect tax system in the U.S. Fourth, recent trends in inequality and welfare are 

quite different. In particular, from 1973-74 to 1990-91, expenditure inequality has fallen 

in Spain (Del Rio and Ruiz-Castillo 1997a, 1997b; Ruiz-Castillo 1995b), but has 

increased during the 1980's in the U.S. (for example, see Johnson and Shipp 1997). And
fifth, the demographic structure of the two countries is very different, with 

larger consuming units in Spain on average than in the U.S.

The remainder of this paper is organized into four sections. Section two presents 

the methods and Section three, a description of the data. Section four includes our results 

and Section five summaries and concludes.

II. METHODS

A. Interpersonal Comparisons of Welfare

Assume we have a population of h = 1,...,H households whose living standards 

can be adequately represented by a one-dimensional variable we call income, xh. 

Households can differ in income and/or a vector of household characteristics. As 

indicated in the Introduction, we assume that equivalence scales depend only on the 

number of persons in the household. Households of the same size are assumed to have 

the same needs and, therefore, their incomes are directly comparable. Larger households 

have greater needs, but also greater opportunities to achieve economies of scale in 

consumption. Assume that there are m = 1,...,M household sizes. Following Buhmann et 

al. (1988) and Coulter et al. (1992a, 1992b), for each household h of size m we define 

adjusted income by
Thus, within each subgroup with the same needs, we assume that the inequality of adjusted 

income is equal to the inequality of original income, independently of individual income 

and prices.

In welfare economics, we are mostly interested in personal economic 

well-being and welfare, rather than that of the household. Thus, following standard 

practice for overall inequality and welfare measurement, household adjusted income is 

weighted by the number of persons in the household. Or in other words, each person is 

assigned the adjusted income of the household to which he or she belongs. In the next 

section, notice that for the decomposition by household size partition, we obtain the 

same results if we use adjusted or unadjusted household income and weight by persons 

or households. So we use unadjusted incomes and household weighting. 4

Inequality Measurement

1. Decomposition of Overall Inequality for the Partition by Household Size

We say that an inequality index is decomposable by population subgroup, if the 

decomposition procedure of overall inequality into a within-group and a between-group term 

is valid for any arbitrary population partition. It is well known that the Generalized Entropy 

(GE) family of inequality indices are the only measures of relative inequality that satisfy the 

usual normative properties required from any inequality index and, in addition, are 

decomposable by

4

If the partition is by any other characteristic than household size, adjusted incomes and person weighting would 

need to be used.

6
population subgroup. (See, for example, Shorrocks (1984)). The family can be described 

by means of the following convenient cardinalization:

Coulter et al. (1992a, 1992b) have shown how the inequality estimates provided 

by the GE family vary systematically with the parameter O which captures the generosity 

of the scale. They illustrate their analysis with UK data. 5 However, using the GE family 

in its decomposable form restricts the ‘contamination’ of the inequality orderings that 

will arise if there is incomplete or incorrect information about the equivalence scales. To 

see this, consider the formula for the GE index when written in decomposable form for 

the partition by household size:

5 This has been confirmed in other countries. For Portugal, see Rodrigues (1993). For Spain, see Ruiz-Castillo 

(1995b) for the period 1973-74 to 1980-81. For Spain and the U.S. during the period 1980-81 to 1990-91, see 

Section four of this paper.

Equation (11) is the difference in uncontaminated inequality, which is seen to be the 

sum of two terms: equation (12), which is the weighted sum of inequality differences 

within each household size, and equation (13) which captures the impact on the 

uncontaminated inequality of demographic differences across the partition by household 

size. Both are independent of  , which only affects equation (14), namely, the 

difference in between-group inequality in the partition by household size.

Of course, demographic shares for country 2, rather than for country 1, and 

the inequality for country I can be used in the above decomposition. In this case, we 

have:

C. Welfare Measurement

1. Admissible Social Evaluation Functions

9
But which SEFs within these classes should we use in applied work? The following 

property leads us to an appropriate selection.

Suppose that we have two islands where income is equally distributed but whose 

means are different. If they now form a single entity, there will be no within-island 

inequality but there would be inequality between them. In income inequality theory we 

search for additively separable measures capable of expressing this intuition. In our 

context, for any partition we are interested in expressing social welfare for the 

population as the sum of two terms: a weighted average of welfare within the subgroups, 

with weights equal to demographic shares, minus a term which penalizes the inequality 

between subgroups. In this case, we say that the SEF is additively decomposable.

Consider SEFs which can be expressed as the product of the mean and a term 

equal to one minus a member of the GE family of inequality measures. Ruiz-Castillo 

(1995a) shows that the only SEF among them with the property of additive 

decomposability with demographic weights, is the following:
where I1 is the original Theil index. Thus, social welfare is seen to be a weighted average

of the welfare within each subgroup with weights equal to demographic shares, minus the 

between-group inequality weighted by the population mean. Taking into account our 

definitions of adjusted income, we have:

Equation (18) is the within-group welfare, while equation (19) is the penalty associated 

to between-group inequality in the partition by household size. Between group inequality 

is the inequality that arises if we give each household the mean of the household size. As 

for the inequality decomposition by household size, we only consider households of size 

1-7 persons since we needed to simplify our analysis. 

2. Decomposition of Overall Welfare Change
Equation (21) is the difference in the A () terms, which is seen to be the sum of two terms: 

equation (22), which is the weighted sum of welfare differences within each household size, and 

equation (23) which captures the impact of demographic differences across the partition by 

household size. Both terms depend on  , but in a way that allows us to establish a clear link 

between the household size and the population level. Finally, equation (24) captures the 

difference in the penalty attributed to between-group inequality in the partition by household 

size.

Of course, demographic shares for country 2, rather than for country 1, and 

welfare for country 2 can be used in the above decomposition. In this case, we have:

D. Accounting for Differences in Prices

Differences in prices over time affect the differences in mean expenditures of the 

countries as well as differences in inequality and overall welfare. In this section, we present an 

approach to identify the impact of price change on overall inequality between country l and 

country 2. A similar analysis can be done for welfare.
Suppose that the rate of inflation during this period has been greater for the rich than for 

the poor, in which case we say that the change in relative prices from t' to t has been pro-poor. 

Then the Paasche indices to express money magnitudes in period t at period t' prices are greater 

for the rich than for the poor. The income necessary to acquire the period t bundle of goods at t' 

prices is reduced for everyone, but is reduced by more for the rich. Therefore, inequality at t' 

prices is smaller than inequality at t prices, that is
III. DATA

For our analysis, we use data from household budget surveys. The Spanish data 

are from the Encuesta de Presupuestos Familiares (EPF) conducted by the Instituto 

Nacional de Estadistica (INE), and the U.S. data are from the Consumer Expenditure 

Survey (CEX) Interview (augmented with data from the Diary) from the Bureau of Labor 

Statistics (BLS). For both budget surveys, data are collected from consumer or economic 

units. In general a consumer unit (referred to in this paper as a household) is a collection 

of people who share a budget and some living quarters. The U.S. population is defined as 

the total civilian noninstitutional population and a portion of the institutional population 

living in the following group quarters: boarding houses, housing facilities for students 

and workers, staff units in hospitals, and homes for the aged, infirmed or needy, 

permanent living quarters in hotels and motels, and mobile home parks. The Spanish 

population is defined similarly with the additional requirement that persons living in 

institutional or collective housing must be economically independent from other 

household units. For the U. S. CEX, students living in college residences are considered 

separate consumer units even if they are economically dependent upon the financial 

support of their parents or others.

We use consumption expenditures as our measure of income. We start with the 

expenditure bundle used by the statistical agencies for the production of their official 

Consumer Price Indexes (CPIs) to define expenditures. To this base expenditure bundle

14

the winter of 1981. Since we use household specific price indices, we are able to take 

into account the distributional role of changes in price relatives during the 1980's in 

both countries.

For comparing expenditures and welfare in the two countries, we use purchasing 

power parities (PPPs) for private consumption expenditures. These are rates of currency 

conversion that equalize the purchasing power of the two countries. This means that a 

given sum of money, when converted into different currencies at the PPP rates, will buy 

the same basket of goods and services. PPPs have the advantage over exchange rates in 

that they reflect only differences in the volume of goods and services purchased; in 

contrast, exchange rates reflect both differences in the volumes purchased in each 

country and also differences in price levels. PPPs based on the Elteto-Koves-Szulc (EKS) 

method of aggregation are used (DECD 1993). Although the EKS indexes are not 

additive, the DECD notes that the EKS can be used to compare levels? The EKS indexes 

are used since we are interested in comparing levels of expenditures and welfare. For 

1991, the PPP conversion factor is 108.9 so that Spanish expenditures in pesetas are 

divided by 108.9 to obtain Spanish expenditures in U.S. dollars. For 1981, the PPP 

conversion factor is 74.74 (Godbout 1997; DECD 1993).

7An alternative is to use the Geary-Khamis (GK) index which is additive. This index is most appropriate to use when 

comparing structures and applying subindexes such that the sum of the adjusted subcomponent expenditures, for 

example, will equal total PPP adjusted expenditures. Since we are using the overall index and not subcomponent 

indexes to make our PPP adjustments for total expenditures, it is acceptable to use the EKS indexes. Dukhanov (1997) 

has noted that substantial differences result however when the two different indexes are used in adjusting 

subcomponents and then adding up to produce overall national account incomes, for example. However, for our study, 

we do not expect major differences, given that the GK PPP index for 1981 is 73.3 (versus 74.74) and the index for 

1991 is and 106.8 (versus 108.9).

16
For all analyses, consumer unit population weights are used. For the U.S., the 

average consumer unit weight for the number of quarters that the consumer unit is in 

the sample is used; for the household size variable, the average size is also assumed. 

A. Spanish Data

The Spanish EPF is a household budget survey in which interviews are spread 

out uniformly over a period of 52 weeks. All household members, 14 years of age or 

older, are supposed to record all expenditures taking place during a sample week. Then 

indepth interviews are conducted to register past expenditures over reference periods 

beyond a week and up to a year. From that information the INE estimates annual 

household total expenditures. Annual expenditures on food and drinks in Spain take into 

account the available information on bulk purchases according to the procedure 

developed in Pena and Ruiz-Castillo (1995). For our study, annual household total 

expenditures, based on this set of different reporting periods, are assigned the reference 

1990-91 period according to the quarter in which the interview took place.

Data from the two most recent EPFs, collected from April 1980 to March 1981 

and from April 1990 to March 1991, are used for our analysis (for details on the 1980-81 

and 1990-91 surveys, respectively, see INE (1983) and INE (1992)). In the 1990-91 

period, approximately 23,000 households were included in the sample. These households 

represent 11,298,509 households in the population and 38,494,006 persons. 

B. U.S. Data

The U.S. CEX has two components: a Diary or recordkeeping survey completed 

by participating consumer units for two consecutive one-week periods, and an Interview 

survey in which the expenditures of consumer units are obtained in five interviews

17
conducted every three months. Survey participants record dollar amounts for goods and 

services purchased during the week of data collection for the Diary and during the 

previous three months (from the date of the interview) for the Interview. The 

expenditure amounts (full purchase price regardless of financing with the exception of 

vehicles and housing) include all sales and excise taxes for all items purchased by the 

consumer unit for itself or for others. Excluded from both surveys are all 

business-related expenditures and expenditures for which the consumer unit is 

reimbursed.

The Interview sample is selected on a rotating panel basis, targeted at 5,000 

consumer units each quarter. About twenty percent of the sample are interviewed for 

the first time each quarter while twenty percent are interviewed for the last time. 

Consumer units are interviewed up to five times, at three-month intervals. Data from 

the first interview are used to `bound' expenditures for subsequent interviews and are 

not used in estimation.

Since we are interested in total expenditures, we use data from both the Diary 

and Interview following a method developed by Rob Cage at the BLS (Cage et al. 1997. 

The BLS (1995) estimates that about 80 to 95 percent of all expenditures are accounted 

for in the Interview. Not accounted for in the Interview are roughly 40 specific goods 

and services, e.g., soaps, laundry and cleaning products, tolls, over-the counter drugs, pet 

food, and personal care products. We use data from the Diary to impute additional 

expenditures for these omitted items to the Interview households. This was 

accomplished by calculating the expenditure for the Diary-unique item, as a percent of 

total food expense, and taking the product of this factor and the total food expense 

reported in the Interview. The budget shares for these items were produced by 

index-area and consumer

18
unit size in the Diary sample. These shares were then mapped to the CEX Interview 

sample by index area and consumer unit size, and used to impute expenditures for 

these additional items in the Interview.

The continuous and rotating nature of the CEX Interview in the U.S. case poses 

special problems for the determination of the 1990-91 household expenditures 

distribution at current prices, that is, the equivalent of the expenditure distribution in the 

Spanish case. We limit ourselves to the Interview survey consumer units only, since 

these consumer units provide the maximum of data over the longest period of time, 

relative to the Diary sample. For our analysis we do not assume that the quarterly 

expenditure reports are independent (as in official CEX publications, see BLS 1995), but 

require each consumer unit to have reported expenditures for two, three, or four quarters 

during the time period of our study. We refer to our sample as horizontal. Restricting 

ourselves to households with four quarters of complete data would have been 

unnecessarily restrictive, while including some incomplete households allows us to 

increase the sample size. If we selected our households with interviews occurring over 

the exact time period as in the Spanish case (Summer 1990 to Spring 1991), there would 

only be 1,367 consumer units in the U.S. sample. In contrast, our horizontal sample is 

composed of 6,284 consumer units, representing 118,481,815 consumer units in the 

population and 307,204,548 persons. The U. S. data were collected from January 1990 to 

December 1991. Data from the reported quarters, during this time period, are used to 

produce annualized expenditures for each consumer unit. The consumer unit 

characteristics of household size8 and age of head are based on the average of the

______________________________

8 Rounded values of average household size were used for our analysis.
quarterly values for the values reported. The population weights used for our analysis 

are also the result of averaging the quarterly weights over the number of quarters for 

which the consumer unit participates in the survey.

IV. RESULTS

Our study confirms that, in international comparisons, demographic structure and 

prices are important. In this section we examine the population distributions by 

household size, expenditures of households, inequality, and welfare. Unadjusted 

expenditures are used for the inequality analysis when we examine within group 

differences by household size. However, adjusted expenditures are used when examining 

overall inequality since between group differences are dependent on the adjustment 

factor. Since welfare for each household size depends on the scale adjustment factor, we 

present the unadjusted values by household size, but focus most of our attention on the 

results for all persons.

As shown in Table 1, we observe one and two person households in the U.S. are 

more numerous and have much greater mean expenditures than those in Spain. For three 

person households, representing about 20 percent of all persons in each country, mean 

expenditures are still substantially higher for the U.S. For four person households, 

representing about 30 percent of all persons in Spain and 24 percent in the U.S., mean 

expenditures are greater in the U.S., but not as great as for smaller household sizes. 

Except for six person households, larger households have greater mean levels of 

expenditures in the U.S.
The results in Table 2 illustrate the impact on means expenditures of using person 

versus household weighting. With person weighting, each person in a household is 

assigned the adjusted expenditure while with household weighting each household only 

is assigned a weight of 1. This means persons living in larger households will have more 

weight in the overall distribution of expenditures. When comparing the person weighted 

and household weighted expenditures, expenditures are greater in the U.S. relative to 

those in Spain for each scale adjustment factor. However, when comparing person 

weighted versus household weighted expenditures for each country, household weighted 

expenditures are less than person weighted expenditures when the scale factor 

adjustment is smaller for the U.S. (= 0.0 or 0.3). The pattern is more pronounced for 

Spain; household weighted expenditures are less for all scale adjustment factors other 

than for the per capita adjustment (  =1.0).

The Theil indexes for households of size one to seven, based on expenditures in 

winter 199-91 prices, are presented in Table 3. As noted earlier, the parameter c (here 

equal to -1, 0, 1, and 2) summaries the sensitivity of the inequality index in different parts 

of the expenditure distribution: the more positive (negative) c is, the more sensitive the 

index is to differences at the top (bottom) of the distribution. For both the U.S. and Spain, 

inequality is greater when c=-1 than when c=0, and also when c=2 versus c=1. In general, 

inequality in Spain is greatest when c=2 across household sizes. For the U.S., inequality 

is greatest when c=-1 or c=2, with greater values for c=-1 for households with three, four, 

five, or seven members. Inequality in the U.S. is less than inequality in Spain for one and 

two person households when c=-1, 0, or 1. Thus we could conclude that differences at the 

lower end of the distribution are greater for Spain than for the U.S. for

21
these households. When c=2, inequality is less in the U.S. for households with 

fewer than five persons. For these households we can surmise that the differences in 

expenditures at the top of the Spanish distribution are greater than the differences in 

expenditures at the top of the U.S. distribution.

The use of decomposable inequality measures facilitates our understanding of the 

results for the population as a whole. In particular, for the person weighted distributions 

(Table 4), within group inequality is smaller in Spain than in the U.S., while the results 

on overall inequality depend crucially on our assumptions about the importance of 

economies of scale (denoted by our scale adjustment factors). As the scale adjustment 

factor (  ) varies from 0 to 1 and economies of scale tend to diminish, overall inequality 

in the U.S. is smaller, about the same, or considerably larger than in Spain. This 

difference is due to the between group differences in inequality.

Concerning the influence of prices, our results reveal that changes in relative 

prices from the winter of 1981 to the winter of 1991 are pro-poor in both countries 

(Table 5). This means that from the point of view of winter 1981, the amount that we 

would need to give to richer households to compensate them for inflation would be 

greater than the amount that we would need to give to poorer households for them to 

remain at the same level of welfare. However, in Spain the strength of this phenomenon 

decreases with household size, while the opposite is the case in the U.S. The percentage 

difference in inequality in the U.S. 1990-91 expenditure distribution relative to the 

Spanish one is rather robust to the choice of the reference price vector. The percentage 

differences in inequality in the U.S. relative to Spain are sensitive to household size and 

to our choice of

22
the scale adjustment factor. For households of size 1 or 2 and when the scale 

adjustment factor equals 0.0 or 0.3, inequality is greater in Spain.

Recall that welfare is equal to mean expenditures corrected by a factor related to 

inequality. For the welfare analysis, we use the Theil inequality index with c=1. In Table 

6 we present overall welfare for households with one to seven members. For this table, 

unadjusted expenditures are used. The differences in welfare exhibit the same pattern as 

for the means presented in Table 2. Welfare is greater in the U.S. than in Spain for all 

households with the exception of those with six members.

Not surprisingly, results presented in Table 7 indicate greater overall welfare for 

households in the U.S. as compared to those in Spain regardless of the value of . The 

greatest percentage of this difference is due to differences in within group inequality. 

Between group inequality is greater in Spain than in the U.S. when  = 0.0 or 0.3. Thus, 

for the U.S.-Spanish case, we conclude that between group inequality is sensitive to the 

assumption about economies of scale.

The influence of changing prices on welfare can be examined using the results 

presented in Table 8. The change in welfare is a function of the ratio of the change in 

mean expenditures and the change in inequality when inequality is defined as the Theil 

index with the parameter c=1. When changes in prices are greater in the U. S. relative to 

Spain, the ratio of the differences in means will be less than one. Since inequality, as 

measured by the Theil index with c=1, is dependent upon the scale adjustment factor, 

the ratio of the differences in inequality in the U.S may be less than, equal to, or greater 

than inequality in Spain. If the index value is greater in period two than in period one, 

then prices can be considered to be pro-poor. Thus we cannot predict the whether the

23
differences in welfare are greater in the U.S. than in Spain when prices from one 

period are used versus those from another period. The ratio of the means is the impact 

of inflation on mean expenditures, the inequality indexes, and welfare.

As seem in Table 8, for all adjusted expenditures, inflation is greater over the 

1981 to 1991 period in Spain than in the U.S. The impact on welfare is slightly less. 

Inequality in 1981 and 1991 for both countries is similar. However, in contrast to the 

impact on means, the impact of inflation on inequality is marginally greater in the 

U.S. than in Spain. The result of these divergent influences of inflation are reflected 

in the ratios of welfare at the two price vectors.

The ratios of the changes in the means, indexes, and welfare from 1981 to 1991 

are presented in the last two columns of the Table 8. When the ratio is less than one, the 

impact of price change in the U.S. is less than the impact of price change in Spain. Our 

results reveal that the effect of price change in the U.S. is greater in the U.S. than for 

Spain for the means and for overall welfare. However, the influence on inequality is in 

the opposite direction.

V. SUMMARY AND CONCLUSIONS

The purpose of this research was to examine the role of demographics and 

household specific price indices on expenditure based inequality and welfare 

comparisons for Spain and the U.S. Equivalence scales were assumed to depend only on 

household size. The 1990-91 expenditure distributions in both countries were expressed 

at winter of 1991 and winter of 1981 prices. Our results show that differences in 

demographic factors can be very important in international comparisons. We find that 

inequality and welfare

24
comparisons are drastically different for smaller and larger households. Given this 

diversity, decomposable measurement instruments help to explain how results at the 

household size level get translated at the population level. In terms of the influence of 

relative prices on inequality, for both countries, prices are pro-poor. This implies that we 

would need to give more income to richer households than to poorer households to 

compensate them for inflation, over the 1981 to 1991 period. Because the distributional 

impact of relative prices is of a comparable order of magnitude, our inequality 

comparisons are robust to the choice of the reference price vector. When examining the 

impact of changes in overall welfare over time and across the two countries, we found 

less change in the U.S. in means and overall welfare, but greater changes in inequality.

In future analyses we plan examine the impact on inequality and welfare of 

demographic changes across partition subgroups (due to shifts in subgroup population 

shares over time), in addition to the impact due to differences in tastes and preferences as 

reflected in expenditures from an earlier period of time. Decompositions by other 

demographic subgroups would also be useful in helping us understand the differences 

that we obtain for Spain and the U.S.

25
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