BLS WORKING PAPERS

U.S. DEPARTMENT OF LABOR

Bureau of Labor Statistics

 

OFFICE OF PRICES AND LIVING

CONDITIONS

The Influence of Demographics and Household Specific Price Indices on Consumption

Based Inequality and Welfare: A Comparison of Spain and the United States

Thesia I. Garner, U.S. Bureau of Labor Statistics

Javier Ruiz-Castillo, Universidad Carlos III de Madrid

Mercedes Sastre, Universidad Complutense de Madrid

Working Paper 357

May 2002

 

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, Universidad Carlos III de Madrid, or the Universidad Complutense de

Madrid.
The Influence of Demographics and Household Specific Price Indices on

Consumption Based Inequality and Welfare:

A Comparison of Spain and the United States

By

Thesia I. Garner1, Javier Ruiz-Castillo2, and Mercedes Sastre3

February 2002

1

Garner’s title and address: Senior Research Economist, Division of Price and Index Number Research, U.S.

Department of Labor, Bureau of Labor Statistics, Postal Square Building, Room 3105, 2 Mass. Ave., N. E.,

Washington, D. C. 20212; telephone: (202) 691-6576 ; fax: (202) 691-6583; email: Garner_T@BLS.GOV 2

Ruiz-Castillo’s title and address: Professor or Economics, Departamento de Economía, Universidad Carlos III,

28903-Getafe, Spain; telephone: [+34+91] 624 9588; fax: [+34+91] 624 9329; email: jrc@eco.uc3m.es 3

Sastre’s title and address: Lecturer, Departamento de Economía Aplicada VI, Universidad Complutense de Madrid,

Campus de Somosaguas, 28223 Madrid, Spain; email: msastre@ccee.ucm.es

Earlier versions of this paper were presented at the Southern Economics Association Annual Conference (Atlanta,

Georgia, November 1997) and at the Session on International Comparisons of Income and Wealth Statistics during

the 51st Session of the International Statistical Institute (Istanbul, Turkey, August 1997). Parts of this paper are

based on Sastre’s dissertation at the Universidad Complutense de Madrid (October 1999). The authors would like to

thank John P. Formby, Jorge Salazar-Carrillo, Michael Wolfson, and other participants at these meetings for their

comments and suggestions. A tremendous thanks is extended to Rob Cage of the BLS who assisted in the production

of the indexes for the U.S. portion of this study. We also thank three anonymous referees for their comments and

suggestions.

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.

The U.S. part of this project was in part supported by the ASA/NSF/BLS Research Fellow Program in which Javier

Ruiz-Castillo participated as an ASA/NSF/BLS Research Fellow at BLS in 1996. The U.S. data set was designed

and created by Javier Ruiz-Castillo, Thesia I. Garner, and Rob Cage of the BLS.
1

ABSTRACT

Previous research suggests that income inequality is lower in Spain than in the U.S. This

paper studies whether this ranking remains the same when household consumption expenditures

are used as a proxy for household welfare. Both inequality and social welfare, as components of

economic well-being, are examined. Total household expenditures from each country’s 1990-91

consumer expenditure survey are used as the basis for the analysis. For tractability, equivalence

scales depend only on the number of people in the household and not any other demographic

characteristic. Household specific price indices are used to express the 1990-91 expenditure

distributions at winter of 1981 and winter of 1991 prices. Decomposable measurement

instruments are used both for the inequality and social welfare analyses. Bootstrap methods are

used to produce confidence intervals for all estimates.

When consumption expenditures are substituted for income as the measure of economic

well-being, the ranking of Spain and the U.S. varies as both household size and the equivalence

scale adjustment change. When focusing on household size alone, inequality and welfare

comparisons are drastically different for smaller and larger households. The income inequality

ranking can only be maintained for expenditure distributions when economies of scale are

assumed to be small or non-existent. However, welfare is always higher in the U.S. than in

Spain. It is concluded that household demographic characteristics, as well as equivalence scale

adjustments, can be very important in international comparisons. With regard to householdspecific relative price effects, inflation during the 1980s in both countries has been essentially

neutral from a distributional point of view, so that all results are robust to the choice of time

period.
2

KEY WORDS: Theil Inequality; Social Welfare; Demographic Factors; Household

Expenditures; Household Specific Price Indexes
3

I. INTRODUCTION

Recent international comparisons of economic well-being that focus on individuals and

households have two characteristics. First, perhaps because of the availability of data, household1

income most often has been used as the proxy for household economic well-being. Second, most

studies have concentrated on income inequality comparisons.2 An important finding from these

international studies is that, in the late 1980s and early 1990s, the United States (U.S.) had the

least equal distribution of household income among all industrialized countries (Gottschalk and

Smeeding 1997, 2000; Atkinson et al. 1995).

Slesnick (1991, 1993), however, has pointed out that ideally we should characterize

economic well-being in terms of commodity consumption. Without entering into the discussion

of income versus consumption as proxies of economic well-being, it is fair to say that both

deserve investigation. The important fact in this respect is that, for the U.S., the consequences of

using consumption-based measures have been dramatic. First, the level and trend of Slesnick’s

(1991) series of aggregate total expenditures from 1949 to 1989 differ substantially from those of

before tax income. Second, the substitution of total expenditures for income usually results in

lower estimated poverty rates (Garner et al. 1996, Slesnick 1993). And third, the distribution of

household expenditures is substantially more equal than the distribution of income in the U.S.

(Johnson and Shipp 1997).3

 As far as recent trends for the U.S., while it is true that inequality

 

1

 The term household can be read also as ‘family’ or ‘consumer unit’ for the purposes of this research; although

conceptually they can be different.

2

 Welfare comparisons are rare even at the country level. For some exceptions, see Jenkins (1991) for the United

Kingdom, Bishop and Smith (1991) for the U.S., and Ruiz-Castillo (1998) for Spain. For international comparisons

of welfare, see Tsakloglou (1992) and Ruiz-Huerta et al. (1999). 3

 This result is not unique to the U.S. Studies using data from expenditure surveys find income inequality to be

greater than consumption-based inequality in other developed countries such as Canada (Pendakur 1998) and
4

increased during the 1980s, no matter how it was measured, the increase in consumption-based

inequality was smaller than the increase in income inequality however (Cutler and Katz 1992;

Johnson and Shipp 1997).

In order to examine whether results of consumption-based studies of household economic

well-being provide the same ranking of countries as those based on income, international

comparisons are needed. Such studies are not easy because of the preponderance of country

studies that use household income as the key variable representing household welfare, as

previously mentioned. In addition, it is difficult to make comparisons when definitions and

methodologies differ across country data sources. Unlike for income,4

 there is no data source for

which consumption expenditure data have been make comparable across countries, thus

exacerbating the challenge of conducting such comparisons. However, when micro household

expenditure data are available to researchers, such comparisons are possible. Such is the case

here.

In this paper Spain and the U.S. are compared in inequality and social welfare terms using

current household consumption expenditures as the measure of economic well-being. Household

expenditure survey data from each country are used. The Spanish data are from the Encuesta de

Presupuestos Familiares (EPF) and conducted by the Instituto Nacional de Estadística (INE).

Data for the U.S. are from the Consumer Expenditure Survey (CE), a Bureau of Labor Statistics

(BLS) product. Data from 1990-91 are used for both countries. More recent data are available

for the U.S.; however, 1990-91 represents the latest data available for Spain. Although the

survey methodologies differ in some respects, expenditures are defined as comparably as

 

Australia (Barret et al. 2000), and also in developing countries such as Bangladesh (Wodon 1999) and Taiwan

(Deaton and Paxon 1994).
5

possible and the same research methodology is used to conduct the comparison. A focus of the

study is the role of demographics and household specific price indexes for the measurement of

economic well-being. Their influence on the economic well-being rankings of the two countries

is examined. This study adds to the basic literature emerging on consumption based measures of

inequality and social welfare, and introduces the role of relative price changes in international

comparisons of distributional analysis.

The results of this study suggest that differences in demographic factors can be very

important in international comparisons. For Spain and the U.S., consumption-based inequality

and social welfare are dramatically different for smaller and larger households. Differences in

economic well-being in Spain and the U.S. also depend strongly on the assumptions made about

economies of scale in consumption within households. The main findings of the study are as

follows: (i) as economies of scale diminish, overall inequality in the U.S. is smaller, about the

same or larger than in Spain, although differences are only statistically significant when

economies of scale are small or non-existent; (ii) welfare is always significantly greater in the

U.S., but the gap between the two countries grows continuously from 12 to 40 percent as

economies of scale are assumed to be smaller; and (iii) inflation during the 1980s in both

countries has been essentially neutral from a distributional point of view, so that all results are

robust to the choice of time period.

The remainder of this paper is organized into four sections and an Appendix. Section II

includes background information, and Section III presents a description of the methods and data.

Section IV includes the empirical results and Section V concludes. The Appendix is devoted to a

brief discussion of the data for comparative purposes.

 4

 The Luxembourg Income Study (LIS) includes data sets for which income has been made as comparable as
6

II. BACKGROUND

Spain and the U.S. are rather different with respect to their economies, economic systems,

and demographic compositions. Such differences are expected to contribute to differences in the

economic well-being of the countries’ populations and thus to their well-being rankings.

Spain has a smaller economy and has only recently moved to a more market oriented

system. In contrast, the U.S. has quite a large economy and has been rather open and marketoriented for most of its history. Since the mid-1970’s, Spain has been experiencing a strong

process of economic modernization and liberalization, including full membership into the

European Union (EU) in 1986 and becoming one of the founding states of the European

Monetary Union in 1999. This process has resulted in a much more dynamic, open and marketoriented economy than it was before the Union. For example, the share of the agricultural sector

declined from 38.7 percent of Gross Domestic Product (GDP) in the 1960s to 8.3 percent in

1997. In contrast, the services sector share surged from 31.0 percent to almost 61.7 percent of

GDP during the same period. Likewise, the degree of openness, measured by the share of exports

plus imports in GDP, increased from 8.4 percent in the 1960s to about 29.5 percent in 2000.

Overall, from 1986 to 1996 Spanish GDP per capita rose from 48.7 percent to 54.2 percent of

U.S. GDP per capita. (for a detailed description of the development of the Spanish economy over

the last four decades, see Martín 1999, and Myro 2001).

Since the mid-1970s Spain has been taking important steps toward a fully-fledged

comprehensive social safety net, in the European style, while that of the U.S. is much more

limited (see U.S. Dept. of Health and Human Services 1998). Thus, public sector expenditures,

as a percent of the GDP, rose from 14.8 in 1960 to 40.7 percent in 2000 for Spain. In contrast,

 

possible across countries. See the LIS web site for more information at: www.lisproject.org. 
7

the percentage for the U.S. only increased from 27.0 to 31.7 per cent during the same time

period.

Tax structures in the two countries are also rather different and this can contribute, not

surprisingly, to differences in economic well-being in the two countries. A modern income tax

system was not operative in Spain until 1978; however, since then the minimum and the

maximum tax rates in the graduated personal income tax system, as well as the number of tax

brackets, have been larger in Spain than in the U.S. (see Gago 2000). Both countries have excise

taxes but EU membership lead to the introduction in 1986 of a multi-stage value added national

tax in Spain, in contrast to the primarily single stage sales tax system in the U.S. with taxes

collected at the state and local levels.

The demographic structures of the two countries are also quite different. This is not

surprising since Spanish households are characterized by a higher average household size, and a

higher frequency of multigenerational households as more young adults live with their parents

and more dependent elderly live with their children. Single-person and single parent households

are also less prevalent in Spain than in the U.S.

Reflecting both the economic and demographic characteristics of Spain and the U.S.;

inequality and welfare differ in the two countries. In particular, from 1973-74 to 1990-91,

household expenditure and income inequality fell in Spain (Del Río and Ruiz-Castillo 2001a,

2001b; Ruiz-Castillo 1995). In contrast, during the 1980s in the U.S. household expenditure and

income inequality increased (for example, see Johnson and Shipp 1997).5

 

5

 For the U.S., while it is true that inequality increased during the 1980s, no matter how it was measured, the increase

in consumption-based inequality was smaller than the increase in income inequality (Cutler and Katz 1991, and

Johnson and Shipp 1997). For Spain, the decrease in income inequality during the 1980s was greater than the

decrease in expenditure inequality (Alvarez Aledo et al. 1996).
8

When comparing inequality based on income versus expenditures, Sastre (1999) found

that for Spain income is more equal than expenditures.6

 The opposite result has been reported by

Johnson and Shipp (1997) for the U.S. as noted earlier. The finding for Spain is counter to

general economic intuition about the prevalence of transitory components in current income.

However, the shorter time reference period for expenditures in the EPF relative to the reference

period for income could also contribute to this result. This point is discussed in the Data section.

With regard to the ranking of the countries, Gottschalk and Smeeding (1997) found that Spain

had less income inequality than the U.S. during the earlier 1990s. Whether the ranking of the two

countries remains the same when expenditure inequalities are compared is a question addressed

in this research.

III. METHODS and DATA

Rigorous international comparisons require high standards of comparability in the

definition of a household welfare measure. This paper constitutes an attempt to meet those

standards, starting from the best available household budget information in the two countries: the

EPF in Spain, and the CE in the U.S., and following through with the same methodology. In this

section methodological challenges faced by researchers conducting international comparisons of

economic well-being are highlighted, followed by a detailed description of the specific methods

and data used for this study.

 

6

 This is also the case in the Czech and Slovak Republics, where income and expenditures data are from household

budget surveys. According to Garner (1998), this result might be explained by fundamental differences in economic

systems and economic behavior in these two countries in the midst of a deep economic and political transition. These

reasons cannot explain the situation, however, in countries such as Portugal, Spain nor the United Kingdom where,

according to the results obtained using micro-data on household budgets, (the Survey of Family Budgets in Portugal,

the EPF for the Spanish case, and the FES -Family Expenditure Survey- in the U.K.) income inequality is also lower

than expenditures inequality (see Goodman and Webb 1995, Deaton and Paxson 1994, and Gouveia and Tavares
9

A. Issues of International Comparisons

Like intertemporal comparisons of income inequality and welfare in a single country,

international comparisons of expenditures require the solution to the following five classical

problems: (a) how to make comparable the money distributions in both countries; (b) how to

make comparable two heterogeneous populations consisting of households with different needs;

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

measurement instruments to use among the admissible welfare measures, and (e) how to

determine whether the estimated differences are statistically significant.

In addition, a primary concern for such comparisons is time period. Suppose that both

country expenditure distributions are expressed at constant prices at the same moment in time.

Expenditure inequality comparisons would reflect not only differences in the quantities of goods

and services consumed but also differences in the price structures prevailing in each country.

Ideally, in order to express the quantity vectors bought in both countries at common prices it

would be desirable to have a spatial price index relating, say, prices in the U.S. to prices in Spain.

Such a price index is not available. As an alternative, in this paper household specific price

indices are used in order to express each country’s quantity vector at prices of two different

moments in time. If, for instance, richer households have a greater rate of inflation than poorer

households do in the U.S., while the opposite pattern is experienced in Spain, the expenditure

inequality and welfare comparisons will certainly be influenced by the choice of time period.

Thus, there are reasons to study how robust expenditures inequality and welfare comparisons are

to the choice of the time period used to express the expenditure distributions at constant prices.

This aspect of international comparisons has non been dealt with in the literature before.

 

1995). This casts some doubts about previous comparisons between CPS income data for the U.S. and EPF or FES
10

In this paper, the 1990-91 household expenditure distribution in each country is expressed

at constant prices of the following two periods: January, February and March of 1991 and 1981,

or the winter of 1991 and 1981. The fact that expenditure distributions are expressed in their own

currencies does not affect inequality comparisons using relative inequality indexes, However, for

welfare comparisons, the Spanish distributions are expressed in U.S. dollars using purchasing

power parities (PPPs).

To solve the difficulties arising from the demographic heterogeneity in international

comparisons, researchers usually start by partitioning the household population into equivalent

subgroups from the point of view of needs. These subgroups form what will be referred to as the

basic partition. Then a single set of equivalence scales is usually used in order to make

interpersonal welfare comparisons among the partition subgroups. In this paper, the quest for

robustness begins by investigating whether, say, inequality in Spain, for example, is

unambiguously smaller for all subgroups of the basic partition than it is for the U.S. In addition,

independent of the answer to this question, statements for the population as a whole are usually

desirable. For this purpose, different equivalence scales are used to pool the expenditures of

households belonging to the basic partition subgroups into a unique distribution of household

equivalent expenditure. Then it is investigated whether the results at the population level are

robust to the choice of equivalence scales.

To make the analysis tractable it is assumed that equivalence scales depend only on the

number of people in the household.7

 Following Buhmann et al. (1988) and Coulter et al. (1992a,

1992b), a parametric model of equivalence scales, which allows for different views about the

 

income data for Spain, Portugal or the United Kingdom, respectively.
11

importance of economies of scale in consumption within the household, are used.8 To clarify the

passage from the partition by household size to the population level, it is illuminating to work

with additively decomposable measurement instruments. In this way, expenditure inequality

differences between the U.S. and Spain can be accounted for in terms of two factors: a) the

difference in within-group inequality (due to differences in subgroup inequality values and

subgroup population shares); and b) the difference in between-group inequality (due to relative

differences in subgroup means). In addition, following a suggestion in Coulter et al. (1992a) and

developed in Del Río and Ruiz-Castillo (2001a), a method is used to ensure that only the second

of the above factors depends on the equivalence parameter. Thus, differences in within-group

inequality across countries are independent of how large economies of scale are assumed to be.

As in most welfare analyses (for instance, see Slesnick 1998 and Shorrocks 1983), social

or aggregate welfare is expressed in terms of two statistics of the income (or expenditure)

distribution: the mean and an index of relative inequality. Consequently, it is natural to work

with social evaluation functions that permit the explanation of welfare differences in terms of

differences in the mean and differences in relative inequality. In addition, for reasons explained

later in this section, we are interested in social evaluation functions that penalize the inequality

between the subgroups of the basic partition. As in the inequality case, additively decomposable

social evaluation functions with those two features have been found useful in intertemporal

welfare comparisons within a single country (see Ruiz-Castillo 1998). In this paper, these

methods are shown to be equally useful in international comparisons. This is important in a

 7

 Atkinson and Bourguignon (1987) suggest an alternative approach for ranking income distributions that allows for

differences regarding the treatment of different types of families. This approach (sequential stochastic dominance)

uses methods that do not require cardinal specifications of equivalence scales.
12

situation characterized by considerable welfare and demographic inter-country differences

between the subgroups in the partition by household size.

Bootstrap methods are used throughout to obtain confidence intervals for all estimates as

in Mills and Zandvakili (1997).9

 Finally, following Cowell et al. (1999), systematic trimming at

both ends of the household expenditure distributions is used to check the robustness of the

inequality results.

B. Methods

1. Interpersonal Comparisons of Welfare

Assume there is a population of h = 1,..., H households whose levels of living can be

adequately represented by a one-dimensional variable that will be called expenditure10, xh.

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

above, the partition by household size is taken to be what is called the basic partition.

Households of the same size are assumed to have the same needs and, therefore, their

expenditures are directly comparable. Larger households have greater needs, but also greater

opportunities to achieve economies of scale in consumption. Assume that there is m = 1,..., M

household sizes. Welfare comparisons across households of different size are made according to

the following model of equivalence scales first used by Buhmann et al. (1988) and Coulter et al.

(1992a, 1992b). For each household h of size m adjusted expenditure is defined by

z

h(Θ ) = xh/mΘ , Θ ∈ [0,1]. (1)

 8

 For the use of this model in international comparisons, see Atkinson et al. (1995). For other recent papers that

stress the issue of the sensitivity of international poverty comparisons to the choice of equivalence scales, see

Burkhauser et al. (1996), De Vos and Zaidi (1997), and Duclos and Mercader-Prats (1999). 9

 The dominance approach (as presented by Shorrocks 1983) could have been used to for the inequality and welfare

comparisons, along with the statistical inference procedures developed by Bishop et al. (1989, 1994). 10 The methods described in this section are applicable to any one-dimensional variable representing a household’s

level or standard of living. Given the actual data used in this paper, that variable has been called “expenditure”.
13

Taking a single adult as the reference type, the expression mΘ can be interpreted as the number

of equivalent adults in a household of size m. Thus, the greater is the equivalence elasticity Θ ,

the smaller are the economies of scale in consumption or, in other words, the larger is the number

of equivalent adults. In particular, when Θ = 0 economies of scale are assumed to be infinite and

adjusted consumption coincides with unadjusted household expenditures, while if Θ = 1 there

are no economies of scale and adjusted expenditures become per capita household expenditures.

Let xm and z

m(Θ ) be, respectively, the vector of original and adjusted expenditures for

households of size m. Notice that, if I (.) is any index of relative inequality, then for each

household size, m

I(z

m(Θ )) = I(xm/(mΘ ) = I(xm). (2)

Thus, within each subgroup with the same needs, households of size m, this model implies that

the inequality of adjusted expenditure is equal to the inequality of original expenditure,

independently of individual preferences and prices.

This is possibly the simplest and most convenient of all interesting equivalence scale

models11. Household size is undeniably a crucial characteristic underlying all models; the scheme

adopted is widely used, and it allows for a wide range of assumptions about the importance of

economies of scale. Moreover, this model combines very well with the decomposition procedure

introduced in the next subsection in which the effects of changing the value of Θ are

conveniently isolated in a single term.

In welfare economics, the focus is on individual economic well-being and welfare, rather

than that on that of households. Thus, following standard practice for overall inequality and

 

11 For two parameters empirical models that take into account household composition, see Cutler and Katz (1991)

and Jenkins and Cowell (1994). For a critical survey of econometric and other methods, see Coulter et al. (1992a).
14

welfare measurement, household adjusted expenditure is weighted by the number of people in

the household. Or in other words, each person is assigned the adjusted expenditure of the

household to which he or she belongs.

2. Inequality Measurement

An inequality index is said to be decomposable by population subgroups if the

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

valid for any arbitrary population partition. 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 population subgroups.

(See, for example, Shorrocks 1980, 1984). The family can be described by means of the

following convenient cardinalization:

I

c(z(Θ )) = (1/H) (l/(c2- c)) ∑h {(zh(Θ )/ μ (z

h(Θ ))c - 1} c ≠ 0 ,1 (3)

where μ (.) is the mean of the distribution. The parameter c summarizes the sensitivity of Ic , the

inequality index, in different parts of the expenditure distribution: the more positive (negative) c

is, the more sensitive Ic is to differences at the top (bottom) of the distribution (Cowell and Kuga

1981). When c = 0, 1 the following results:

I

0(z(Θ )) = (1/H) ∑h ln{ μ (z

h(Θ )/zh(Θ )}. (4)

 I1(z(Θ ))=(1/H) ∑h {(z

h(Θ )/ μ (zh(Θ )}ln{zh(Θ )/ μ (zh(Θ )}. (5)

I0 is the mean logarithmic deviation, while I1 is the original Theil index. Coulter et al. (1992a,

1992b) have shown how the inequality estimates provided by the GE family vary systematically

with the parameter Θ which captures the generosity of the scale. They illustrate their analysis
15

with U.K. data12. However, incomplete or incorrect information about the equivalence scale

chosen can arise. For example, household size may not adequately account for differences in the

needs of household members. Given this, the GE family is quite useful, in its decomposable

form, for isolating the impact or “contamination” on the inequality orderings that can arise when

this situation exists. Some robust conclusions, independent of the equivalence scale, can be

obtained by applying the decomposable formulation. To see this, consider the formula for the GE

index when written in decomposable form for the partition by household size:

 Ic(z(Θ )) = ∑m (vm(Θ ))c (pm)

1 - c Ic(zm(Θ )) + Ic( μ1(Θ ),..., μM(Θ )). (6)

where vm(Θ ) is the share of total adjusted expenditure held by households of size m for each

scale factor adjustment, Θ ; pm is group m's population share, and Ic( μ1(Θ ),..., μM(Θ )) is the

between-group inequality calculated as if each household of a given size m received that group's

mean adjusted expenditure μm(Θ ). Recall that, for each household size m, Ic(z

m(Θ )) = Ic(xm).

When c = 0 the expression vm(Θ )

c (pm)1 - c reduces to group m’s population share pm, so that

using the “wrong” equivalence scale impacts or contaminates only the between group

component. Denoting the uncontaminated and the contaminated terms by U and C(Θ ),

respectively, we have:

I0(z(Θ )) = U + C(Θ ), (7)

where 

U = ∑m pm I0(xm) (8)

is the weighted average of the inequality within each household size with weights equal to

population shares, and

 

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

(1995) for the period 1973-74 to 1980-81. For Spain and the U.S. during the period 1980-81 to 1990-91, see Section
16

C(Θ ) = I0( μ1(Θ ),..., μM(Θ )) (9)

is the between-group inequality that depends on Θ, the scale adjustment factor. The between

group inequality component is referred to as “contaminated” since this part of the inequality

decomposition will change with different values of the scale adjustment factor. Regardless of the

scale adjustment factor applied, the within group inequality component of the decomposition will

not be affected, thus the term “uncontaminated” is used.

3. Welfare Measurement

A social evaluation function (SEF for short) is a real valued function S defined in the

space RH of adjusted expenditures, with the interpretation that for each expenditure distribution

x = (x1,...,xH), S(x) provides the "social" or, simply, the aggregate welfare from a normative

point of view. Consider SEFs which satisfy the requirements discovered by Dutta and Esteban

(1992) for expressing welfare as a function of the mean and an index of relative inequality, I(.).

In addition, assume a multiplicative trade off between the mean and inequality, that is:

S(x) = μ (x)(1 - I(x)). (10)

But which SEFs within these classes should be used in applied work? The following

property leads to an appropriate selection. Suppose that there are two islands where expenditures

are 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 (or

expenditure) inequality theory we search for additively separable measures capable of expressing

this intuition. In this context, for any partition it is interesting to express the population’s social

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

 

4 of this paper.
17

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

subgroups. In this case, the SEF is said to be additively decomposable.

Consider SEFs that 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. Herrero and Villar (1989) show that

the only SEF among them with the property of additive decomposability with demographic

weights, is the following:

 W(x) = μ (x)(1 - I1(x)) = ∑m pm W(xm) - μ (x) I1( μ1,..., μM), (11)

where I1 is the original Theil index. These authors also show that W(x) = Σi αi

 xi, where αi

 = [1

– ln(xi/μx)]/N, so that individuals whose expenditures equal the population mean receive a

weight equal to 1/N, and individuals with expenditures above or below the mean receive weights

increasingly smaller or greater, respectively, than 1/N. 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.13 Taking into account the

definition of adjusted expenditures, we have:

W(z(Θ )) = A(Θ ) - B(Θ ) (12)

where:

A(Θ ) = ∑m pm [W(xm)/mΘ ], (13)

and

B(Θ ) = μ (z(Θ ))I1( μ1(Θ ),..., μM(Θ )),∈ Θ [0,1]. (14)

Equation (13) is the within-group welfare, while equation (14) is the penalty associated to

between-group inequality in the partition by household size.

 

13 If we take the index Ic in equation (3) with c = 2 and define the SEF S2(x) = μ(x) (1 – I2(x)), then the weights in

the within-group term in equation (11) are the subgroups’ income shares, a less desirable choice from a normative

point of view. For all the remaining values of c, the weights in that expression do not even add up to one.
18

As an alternative to this approach, Atkinson and Bourguinon (1987) take as given a

social ranking of all subgroups from the point of view of increasing needs; for instance: singles,

couples, lone parents with a child, couples with a child, and other household types. Instead of

using equivalence scales to make welfare comparisons across these demographic types, these

authors develop dominance criteria to establish whether one distribution is socially preferred to

another one. However, this procedure depends on the assumption of a utilitarian SEF of the form

W(x) = Σi

 xi, Unfortunately, this SEF is not additively separable in the sense defined above, and

does not penalize the inequality between subgroups.

C. Data

As noted earlier, this paper uses data from national government consumer expenditure

surveys. The Spanish data are from the EPF conducted by the INE, and the U.S. data are from

the CE Interview (augmented with data from the Diary) from the BLS. The latest available EPF

data, conducted from April 1990 to March 1991, determines the 1990-91 comparison period

although more recent data are available for the U.S. (Further information concerning the data can

be found in the Appendix including the definition of expenditures.) For both expenditure

surveys, data are collected from consumer or economic units (referred to in this paper as a

household, as noted earlier) defined as a collection of people sharing some expenditures and

possibly living quarters.14 Comparability issues are of four types, referring to the population

covered, the nature of the survey and its effect on the way annual expenditures are estimated in

each country, the sample size, and the definition of household current total expenditures as a

measure of household economic well-being.

 

14 See BLS (1993) and INE (1992) for the definitions of a consumer unit in the U.S. and a household in Spain. See

also the Appendix.
19

The U.S. population is defined as the total civilian non-institutional population and a

portion of the institutional population living in 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. For the U.S. CE,

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. The Spanish

population refers exclusively to the civilian non-institutional population living in residential

housing. However, the Spanish EPF records the transfers made to household members who are

dependent on household resources but who live elsewhere at the time of the interview, including

those living in institutional or collective housing (e.g., university residences, student apartments,

hotels, hospitals, and elderly residences). The U.S. CE survey only includes the expenditures for

individuals who reside in this consumer unit. Transfers to others outside the unit, including to

college students living away from home, are considered gifts. Expenditures for gifts of goods and

services are considered to be among the consumption expenditures of the consumer unit for the

purposes of this unit in the CE.

More serious are the differences about the way expenditures on any good are annualized.

As indicated, the EPF is a household budget survey in which interviews are spread out uniformly

over a period of 52 weeks from April 1990 to March 1991. All household members, 14 years of

age or older, are supposed to record, in a Diary, all expenditures taking place during a sample

week. Naturally, many goods and services with frequency of purchase beyond a week escape

from this Diary. Thus, an in-depth interview is conducted in each household to register past

expenditures made within reasonable reference periods, determined by experts, prior to the

sample week. These reference periods cover expenditures made during the past one, two, three or
20

twelve months. From that information, the INE estimates annual household total expenditures. In

this paper, annual expenditures on food and drinks take into account the available information on

bulk purchases according to the procedure developed in Peña and Ruiz-Castillo (1998). Annual

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

reference 1990-91 period. Notice, however, that the estimates of annual household total

expenditures obtained from a sample spread out over 52 weeks during a year will be subject to

seasonality bias

The U.S. CE has two components, a Diary or record-keeping survey and an Interview.

The Diary captures all expenditures made during two consecutive weeks, and the Interview

captures all expenditures made during the previous three months prior to the beginning of the

month of the interview. Five consecutive personal interviews are conducted once every three

months. Data from the first interview are used to ‘bound’ expenditures for subsequent interviews

and are not used in estimation. For official publication purposes, the BLS assumes that the

quarters of expenditures are independent and annualize the quarterly data essentially by

multiplying each quarter of data by four. There is no accounting for the panel aspects of the

survey in official estimates. For this study the correlation of expenditures across quarters is

considered however.

This paper limits itself to CE Interview survey consumer units only, since they provide

the maximum of data over the longest period of time, relative to the Diary sample. However, data

from both the Diary and Interview are used to define annual total expenditures following a

method developed by Rob Cage at the BLS (for more details, see the Appendix and Cage et al.

2002). The advantage of this procedure is twofold. In surveys where each household is

interviewed only once per year, reference periods must cover a full year prior to the date of the
21

interview. In surveys where each household is interviewed once per quarter during four

consecutive quarters, like the CE, reference periods must cover only the three months prior to the

date of the interview. Consequently, the infrequency of purchase problem is much less damaging

in the CE than in surveys like the EPF. When the panel aspects of the CE are exploited,

seasonality bias is reduced.

The Interview sample is selected on a rotating panel basis. For the 1990-91 period, the

sample was 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. The continuous and rotating nature of the CE Interview in the U.S. case posed 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. For this study,

quarterly expenditure reports were not assumed to be independent (as in official CE publications,

see BLS 1993), but each household was required to have reported expenditures for two, three, or

four quarters during the time period 1990-1991. By way of example, consider a household having

reported expenditures only from Spring 1990 to Autumn 1990. How can its expenditures for

Winter 1991 be estimated? As explained in Cage et al. (2002), current expenditures from Winter

1990 in a 207-dimensional commodity space can be expressed at 1991 prices. Annual

expenditures are the sum of commodity quantities bought from Spring to Autumn of 1990 at

current prices, plus the quantities bought in Winter 1990 at Winter of 1991 prices. In this way,

the seasonal nature of consumption patterns is preserved as best as possible.

To obtain annual expenditures for the U.S. we could have restricted our attention to

households with four quarters of complete data. However, that would have been unnecessarily

restrictive. Including some households who do not have a year’s worth of data results in a larger
22

sample size. If households had been selected with interviews occurring over the exact time

period as in the Spanish case (Spring 1990 to Winter 1991) and the sample had been restricted to

those with four complete interviews only, there would only be 1,367 observations in the U.S.

sample. In contrast, the final U.S. sample is composed of 6,284 households, representing

118,481,815 households and 307,204,548 people in the sample population over 1990-91. The

1990-91 EPF consists of 21,155 sample households for a population of 11,298,509 households

and 38,494,006 people living in residential housing over all of Spain, including the African cities

of Ceuta and Melilla, during the interview period.

In brief, the CE does a better job than the EPF as far as frequency of purchase and

seasonality problems are concerned. Thus, it may be conjectured that, for any definition of

household annual total expenditures and abstracting from large differences in sample size,

expenditures inequality in Spain would tend to suffer from an upward bias relative to

expenditures inequality in the U.S. However, no conjectures can be made on these grounds about

the possible relative bias of mean household expenditures estimates in both countries.

As far as the measurement of economic well-being is concerned, consumption

expenditures are used as a proxy for consumption. The starting point is the set of expenditures

used by the statistical agencies for the production of their official Consumer Price Indexes

(CPIs). These are then adjusted in order to reflect more accurately household current

consumption (see the Appendix for a detailed description and a discussion of possible bias).

Consider the construction of statistical price indexes of the Laspeyres type for a set of

households interviewed in a survey like the CE in the U.S. or the EPF in Spain. For this purpose,

two pieces of information are needed: price changes Rit for a set of goods indexed by i = 1,..., n,

published by the BLS in the U.S. and the INE in Spain; and a set of vectors of household budget
23

shares, w

h

 = (wh

1,..., w

h

n), h = 1,..., H. An individual consumer price index (cpih

) for household

h is then defined by

cpih

t = Σi w

h Rit

15. (15)

(For descriptions of the production of these indexes for the U.S. and Spain, see Cage et al. 2002

and Ruiz-Castillo et al. 1999, respectively).

Assume for simplicity that the period in which households are interviewed coincides with

the base year of the official CPI system. Then, to convert any household magnitude in nominal

terms at base year prices, for instance, household expenditures x

h

, into period t prices, all that is

needed is to apply the following formula: x

h

 cpih

t = x

h

t. In this paper, the 1990-91 household

expenditures distributions for the U.S. and Spain are expressed at constant prices using

household specific price indexes for two periods in each country: the winter of 1991 and the

winter of 1981. In this way, the distributional role of price changes during the 1980s in both

countries can be analyzed. These results are presented in Section IV.D.

In order to standardize the comparisons of expenditures and welfare in the two countries,

purchasing power parities (PPPs) for private consumption expenditures are used. These are

defined as “the number of currency units required to buy goods equivalent to what can be bought

with one unit of the currency of the base country; or with one unit of the common currency of a

group of countries” (United Nations 1992).16 PPPs based on the Elteto-Koves-Szulc (EKS)

 

15 As pointed out by Prais (1958), the official Consumer Price Index (CPI) of the Laspeyres type for a population of

H households, published regularly by statistical offices in most countries of the world, is a weighted average of

household specific statistical price indexes of the same type with weights proportional to household total

expenditures. That is: CPIt = Σh αh

 cpih, where αh = xh/Σh x

h

, and x

h is household’s h total expenditures. 16 PPPs have an 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.
24

method of aggregation are used (OECD 1993). Although the EKS indexes are not additive, the

OECD notes that the EKS can be used to compare levels.17 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. Therefore, 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;

OECD 1993).

Household population weights are used throughout. When means and distributions by

household sizes are shown, each household weight is multiplied by the number of people in each

unit in order to obtain a person-population weight for each household member. For the U.S., the

average household weight for the number of quarters that the household is in the sample is used;

for the household size variable, the average size is also assumed.

IV. RESULTS

A. Household Size and Mean Household Expenditures

In this section some fundamental demographic and economic features in both countries are

examined. Table 1 shows the population distributions by household size.18 One- and two-person

households are much more prevalent in the U.S. than in Spain (around 57 percent versus 32

percent of all households, respectively) while the opposite is true for larger households.19 The

 

17 An alternative is to use the Geary-Khamis (GK) index. 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).

18 Due to the small size of the remaining groups, only households with one to seven members that represent about 99

per cent of all households and 97 per cent of all persons in the population are included. We use these households to

examine in detail differences between Spain and the U.S. However, when we produce inequality and welfare results,

we use data from the entire weighted samples (where each household size is represented as a separate group and all

households are accounted for).

19 Duclos and Mercader-Prats (1999) find also similar differences between Spain and the U.K. in 1980-81: there are

about four times as many one-adult households in the U.K. as there are in Spain, while there are many more
25

age distribution of these two types of households differs considerably between both countries,

with Spanish singles and couples older and with a lower purchasing power than their U.S.

counterparts (results not shown).20

Table 1 around here

Some of these differences are attributable to population definitions since, as was said

before, students living in college residences are counted as separate units in the CE, even if they

are economically dependent on their parents. In contrast, such students are counted as members

of their parent households in the EPF. Yet, students living in college residences represent only

1.4 percent of all households in the U.S. sample population for 1990-91 and 7.4 percent of all

households whose heads are less than 31 years of age (results not shown).

Table 2 shows mean household expenditures by household size, the only demographic

characteristic considered in this study, as well as for the population as a whole for different

equivalent scales denoted by adjustment factor, Θ 21. Using person-weighting, U.S. households

have higher mean expenditures than same sized households do in Spain. The differences are

statistically significant (at the 0.05 level) in all cases, except for households with six members,

and are especially important for smaller households. Adjusting expenditures by an equivalence

scale also result in higher values for the U.S.: adjusted expenditures are greater in the U.S.

relative to those in Spain for all values of Θ.

 

households with three and more adults in Spain. This, together with the fact that the presence of children in Spain is

much greater than in the U.K., turns out to be a crucial factor in the poverty comparison between these two countries. 20 Singles aged 65 or older represent 64 per cent of the Spanish single population versus 34 percent in the U.S. On

the other hand, around a quarter of the single population are under age 31 in the U.S. versus 5.5 percent of Spanish

singles.

21 All comparisons in this paper for the population as a whole are made for common values of the parameter Θ .

Given the fact that the age composition of various household size groups differs considerably between both countries

this assumption can be justifiably questioned. For the impact on poverty measurement from applying different

definitions of equivalent income in each country, see Duclos and Mercader-Prats (1999).
26

Table 2 around here

In brief, the differences in household size are sufficiently large to indicate important

differences in living arrangements and to explain some of the divergences in the levels of living

of different size households between both countries. This is an important fact in inequality and

welfare comparisons, as will be seen below.

B. Relative Inequality

Generalized Entropy indices for households of size one to seven, based on 1990-91

expenditures in Winter 1991 prices, are presented in Table 3. For both the U.S. and Spain,

inequality is greater for the indices more sensitive to differences at the top and the bottom of the

distribution (I2 and I-1, respectively), which means that in both countries inequality in the tails of

the distributions is larger than in the middle part. In spite of the fact that (except for households

of size three and four) differences between estimated inequality indices are of a considerable

magnitude (between 20 and 30 per cent), only in smaller households (singles and two people)

expenditures are significantly less unequally distributed in the U.S. than in Spain. The relatively

smaller number of observations in the U.S. sample for larger households mostly contribute to this

effect (see the first two columns in Table 1).

Table 3 around here

The use of decomposable inequality measures facilitates the understanding of the results

for the population as a whole. Table 4 provides the results on the decomposition for the basic

partition using the mean logarithmic deviation, or the index I0. As was seen in equation (7), this

index can be decomposed as the sum of two terms: (i) the within-group (or uncontaminated)

term, i.e., the weighted average of the inequality within each household size, with weights equal
27

to population shares; and (ii) the between-group inequality (or contaminated) term which

depends on the equivalence scale considered. Denote by ∆ I

0(Θ ), the difference in inequality

between Spain (country 1) and the U.S. (country 2), according to the mean logarithmic deviation

index, I0,, i.e., ∆ I(Θ ) = I0(z2(Θ )) - I0(z1(Θ )). This magnitude can be expressed as

∆ I(Θ ) = ∆ U + ∆ C(Θ ), (16)

where: ∆ U = U2 - U1 (17)

∆ C(Θ ) = I0( μ 2

1 (Θ ),..., μ 2M(Θ )) - I0( μ 11(Θ ),..., μ 1M(Θ )). (18)

Equation (17) is the difference in within-group expenditure inequality. This term is independent

of Θ , the scale adjustment factor, which only affects equation (18), namely, the difference in

contaminated expenditure inequality in the partition by household size. The lower panel of Table

4 presents the results of the above decomposition.

Table 4 around here

The difference in within-group expenditure is determined by the differences between

countries in the expenditure inequality in the partition by household size. As was seen in the

lower panel of Table 3, expenditure inequality is smaller in the U.S. for small households

comprising one person or two people, statistically equal in both countries for three- and fourperson households, and larger (although not statistically) in the U.S. for greater household sizes.

As it can be seen in columns three and six of Table 4, when such differences are weighted by

population shares, within-group expenditure inequality is larger in the U.S., but this difference is

not statistically significant22.

 

22 It would be possible to introduce a further decomposition of the differences in within-group inequality, that could

be expressed as the sum of two terms: a weighted sum of differences in inequality within each subgroup, and an

additional term capturing the impact on within-group inequality of demographic differences across countries.

However, this further decomposition is not worthy since the differences in within-group inequality are not
28

In both countries, the importance of between-group inequality as an explanatory factor of

overall inequality follows a non-linear pattern with Θ, the scale adjustment factor. As can be seen

in Table 4, when no allowance is made for household size and economies of scale are assumed to

be infinite, i.e., Θ = 0, between-group inequality accounts for a sizable percentage of overall

inequality, 13 to 18 per cent. As the adjustment factor Θ increases, reflecting the decreasing

importance of economies of scale in consumption, re-orderings take place: larger households,

who have larger unadjusted expenditures, tend to occupy lower positions as household size

increases its role in the definition of adjusted expenditures. The opposite is the case for smaller

households, whose adjusted expenditures depend relatively less on household size. As a

consequence of this complex process in which the identity of households at the top and the

bottom of the distribution is changing dramatically, the ratio “between-group inequality/overall

inequality” rapidly declines and increases again as the scale factor Θ approaches one and

adjusted total expenditures become per capita total expenditures.

However, there are differences across countries that explain the differences in the

between-group term which represents the difference in the contaminated part, ∆ C(Θ ), shown in

column 3 in the bottom panel of Table 4. Although mean expenditures are essentially an

increasing function of household size in both countries (see Table 2), smaller households in the

U.S. are found to be younger, more affluent (as represented by their expenditures), and more

prevalent than in Spain. As a consequence, on average the range of variation between mean

household expenditure by household size is smaller in the U.S. than in Spain. Thus, for low

values of the scale adjustment factor Θ , between-group inequality is lower in the U.S. than in

 

statistically significant. Moreover, given the large demographic differences between the two countries already

examined, the explanation of the differences in within-group inequality in terms of the above components would be

dominated by the demographic component.
29

Spain. On the other hand, for larger households the relationship between mean expenditures and

household size is smoother in Spain (as a matter of fact, mean expenditure for six-person

households in the U.S. is lower than for five-person households). It is also observed that the

difference in favor of the U.S. tends to decline as household size increases (for six-person

households, those differences are not statistically significant). As the scale factor grows toward

one, these differences manifest themselves in a different U pattern for the ratio “between-group

inequality/overall inequality” (see the upper panel in Table 4). The re-orderings among

households of different sizes which take place as the scale factor increases are more dramatic in

the U.S, where between-group inequality reaches a minimum before and increases afterwards

more rapidly than in Spain. Consequently, for larger values of the scale adjustment factor

Θ between-group inequality is larger in the U.S.

Since the difference in contaminated inequality tends to dominate the difference in

uncontaminated inequality, the results on overall inequality depend on the assumptions

concerning economies of scale. Thus, when economies of scale are assumed to be large (for

values of Θ below 0.5), expenditures are marginally more unequally distributed among Spanish

households than in the U.S., although the difference is not statistically significant. On the

contrary, when economies of scale are assumed to be low (for values of Θ above 0.5), overall

expenditure inequality is significantly greater in the U.S.

The decomposition of the original Theil inequality index, I1, follows the same pattern as

that of the mean logarithmic deviation I0 (results not shown but available from the authors). On

one hand, differences in within-group inequality are not statistically significant. On the other

hand, for low values of Θ between-group inequality is lower in the U.S. while the opposite

happens for higher values of Θ . In any case, overall differences are not statistically significant
30

except when Θ = 1, in which case per capita expenditures inequality in the U.S. is larger than in

Spain.

Inequality comparisons are very vulnerable to what happens at both ends of the

distributions, where data imperfections might be particularly serious. Following Cowell et al.

(1999), the robustness of the above results is analyzed by trimming each country’s distribution.

In order to do so, one percent and then five percent of the observations from each tail of the

distribution were removed in both one-tailed and two-tailed exercises. However, the results

obtained (which are available upon request), are essentially the same and increase only slightly

the possibility of re-ranking the distributions between the two countries.

The conclusion is that expenditure inequality comparisons in the basic partition crucially

depend on household size. Expenditures are most unequally distributed in both countries for oneperson households. On average, inequality decreases by household size for Spain. For the U.S.

the results are more mixed but generally inequality is higher for larger households. As a

consequence, expenditure inequality for the population as a whole is very similar for both

countries. Only when economies of scale are small or non-existent do expenditures in the U.S.

appear to be significantly more unequally distributed than in Spain.23

C. Welfare

Table 5 contains estimations of social welfare for households with one to seven

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

 

23 In general, comparisons for the remaining members of the GE family of inequality indexes are not any more

conclusive than these results. Only when Θ = 0.7 and 1.0 and the index is I-1 -is an unambiguous ranking produced,

indicating that expenditure inequality is significantly greater in the U.S. than in Spain (see Table 1 in the Appendix).
31

expenditure inequality. For this analysis, the GE inequality index I1 is used24 (see Section III.

B.3 for a justification).

Table 5 around here

According to equation (11), for each household size we have

W(xm) = μ (xm)F(xm) (19)

where F(xm) = 1 - I1(xm). Table 2 showed that, except for six-person households, mean household

expenditures are greater in the U.S. than in Spain. The difference is considerably larger for

smaller households. On the other hand, for one- and two-person households, expenditures are

more equally distributed in the U.S. than in Spain, while the differences in expenditure inequality

for the rest of household sizes are not statistically significant (see Table 3). Consequently, the

inequality adjustment, F(xm), in equation (19) will tend to increase welfare differences for small

households. As shown in Table 5, the social welfare of singles and two-person households in the

U.S. is almost 75 per cent greater than that of their Spanish counterparts, and around 30 percent

and 16 percent greater for three- and four-person households. For larger households, differences

in welfare between both countries are not statistically significant.

How does this pattern manifest itself for the population as a whole? Recall that, according

to the SEF selected in Section III, social welfare is a weighted average of within-group welfare,

minus a penalty imposed on between-group expenditure inequality:

W(z(Θ)) = A(Θ) - B(Θ) (20)

where:

A(Θ ) = ∑m pm [W(xm)/mΘ ], (21)

 

24 Results for other SEFs are shown in the Appendix (Table 1).
32

and

B(Θ ) = μ (z(Θ ))I1( μ1(Θ ),..., μM(Θ )),∈ Θ [0,1]. (22)

As the scale adjustment factor Θ increases, the role of household size in the denominator

of equation (21) increases also, causing within-group welfare to decline. Naturally, this effect is

more pronounced for larger households. Consequently, as Table 6 shows, the decrease in the

within-group term is larger in Spain than in the U.S.

Table 6 around here

On the other hand, between-group expenditure inequality according to I1 is greater in

Spain than in the U.S. for Θ, the scale adjustment factor, equal to 0.0 and 0.3, and the opposite is

the case for larger values of Θ. Thus, the penalty imposed on social welfare through this term is

correspondingly larger (smaller) for Spain when the scale factor is low (high). This effect works

in the opposite direction to the previous one (the variation in within-group welfare with the

adjustment factor Θ) but it is of a much lower order of magnitude. Therefore, the conclusion is

that although social welfare in the U.S. is significantly greater than in Spain, the difference grows

continuously from 12 to 40 percent as the scale factor increases and economies of scale

diminish.25,26

D. Accounting for Differences in Prices

As pointed out before, when expenditure distributions are expressed at constant prices,

expenditure inequality and welfare comparisons reflect both differences in the quantities of

goods and services purchased, and also differences in the price structures prevailing in each

 

25 This is also the case for SEFs that correct mean expenditures by between-group inequality using members of the

GE family different from I1. Results are available upon request.
33

country. Lacking a spatial price index to compare prices across countries, this section examines

the robustness of the results to the choice of the time period for reference prices. If the

distributional impact of price changes between periods t and t’ in country 1 is very different from

the one in country 2, then expenditure inequality and welfare comparisons at prices of period t

will typically differ from comparisons at prices of period t’.

Let ∆ I

t

(Θ ) denote the difference in expenditure inequality between two countries 1 and

2 at prices of period t, i.e.,

 ∆ It

(Θ ) = I0(z2t(Θ )) - I0(z1t(Θ )). (23)

Similarly, at prices of period t’ < t we have

 ∆ It’(Θ ) = I0(z2t’(Θ )) - I0(z1t’(Θ )). (24)

For each country i = 1, 2, let ∆ Pi(Θ ) denote the distributive effect of price changes from period

t’ to period t, that is,

 ∆ Pi

(Θ ) = I0(zit(Θ )) - I0(zit’(Θ )). (25)

Suppose, for instance, that the rate of inflation in country i during this period has been greater for

the rich than for the poor, in which case the change in prices from t’ to t is said to be anti-rich.

This means that the Paasche indices required to deflate money magnitudes in period t to express

them at period t’ prices are greater for the rich than for the poor. Thus, the expenditure necessary

to acquire the period t bundle of goods at t’ prices is reduced for everyone, but is reduced by

more for the rich. Hence, inequality at t’ prices is smaller than inequality at t prices, that is to

say, ∆ Pi

(Θ ) = I0(zit(Θ )) - I0(zit’(Θ )) > 0.

It is easy to see that

 26 See the Appendix for differences in the definition of total expenditures that could affect the welfare results.
34

 ∆ I

t

(Θ ) = ∆ P2(Θ ) - ∆ P1(Θ ) + ∆ I

t’(Θ ). (26)

That is:

 I0(z2t(Θ )) - I0(z1t(Θ )) = (I0(z2t(Θ )) - I0(z2t’(Θ ))) - ((I0(z1t(Θ )) - I0(z1t’(Θ )))

+ (I0(z2t’(Θ )) - I0(z1t’(Θ ))). (27)

Therefore, the difference in expenditure inequality between country 1 and country 2 is the

same at prices of both periods, i.e., ∆ It

(Θ ) = ∆ It’(Θ ), if and only if the distributive effect of

price change s from period t’ to period t is the same for both countries: ∆ P2(Θ ) = ∆ P1(Θ ).

In our case, we take t = winter 1991 and t’ = winter 1981. The estimates of ∆ P2(Θ ),

∆ P1(Θ ), ∆ It(Θ ), and ∆ It’ (Θ ) for the population as a whole according to the index I0 are

presented in Table 7 (results by household size are available upon request). The positive sign of

∆P2(Θ ) and ∆ P1(Θ ) reveals that changes in prices from the winter of 1981 to the winter of

1991 are anti-rich in both countries, meaning that the rich faced higher inflation over the time

period. However, neither of the two terms is significant for any value of the adjustment factor,

which indicates that inflation during this period in both countries has been essentially neutral

from a distributional point of view. Therefore, it can be concluded that the results on expenditure

inequality and welfare comparisons between the two countries are robust to the choice of the

reference time period. In particular, for expenditure inequality comparisons at winter of 1981 and

winter of 1991 prices, respectively (see columns three and four in Table 7), the conclusion is that

expenditure inequality in the U.S. and Spain are indistinguishable when economies of scale are

assumed to be large (low values of Θ), while U.S. expenditure inequality is significantly greater

when economies of scale are assumed to be small or non-existent (high values of Θ).
35

Table 7 around here

V. SUMMARY AND CONCLUSIONS

This paper has highlighted the role of demographics and the choice of the reference time

period on expenditure inequality and welfare comparisons for Spain and the U.S. In order to

assess the statistical significance of all results, bootstrap estimates of the sampling variance of all

magnitudes have been computed throughout.

Using a model in which equivalence scales are assumed to depend only on household size

and a parameter reflecting different views about the importance of economies of scale, the results

show that differences in demographic factors can be very important in international comparisons.

Inequality and welfare comparisons of similarly defined 1990-91 expenditure distributions for

both countries are drastically different for smaller and larger households. In particular, smaller

households in the U.S. are more prevalent, younger, more affluent (based on expenditures) and

exhibit less inequality than their Spanish counterparts; while larger households are relatively less

prevalent, not as affluent and have greater inequality. Given this diversity, decomposable

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

the population level.

When the 1990-91 expenditure distributions in both countries are expressed at winter of

1991 and winter of 1981 prices, inflation over the time period in both countries is essentially

neutral from a distributional point of view. Because the distributional impact of price changes is

of a comparable order of magnitude, expenditure inequality and welfare comparisons are robust

to the choice of the reference price vector. Those comparisons are also robust to the choice of
36

the inequality or social welfare index, and to potential problems associated with the data in the

tails of the expenditure distributions.

There are good reasons to identify people’s economic well-being with consumption

[expenditures] rather than income, but there are few country-wide and international studies that

take this view although the number is growing. Previous studies (Gottschalk and Smeeding

1997) show that around the year 1990, household income inequality was clearly greater in the

U.S. than in Spain. However, when expenditures are substituted for income as the measure of

economic well-being, the ranking of the two countries cannot be maintained unequivocally. The

ranking can be maintained only for the expenditure distributions when economies of scale are

assumed to be small or non-existent. Otherwise, expenditure inequality is smaller in the U.S.

although the differences are not statistically significant. On the other hand, social welfare is

significantly greater in the U.S than in Spain for all values of the equivalence scale parameter,

and the difference increases as economies of scale diminish.

If it is desirable to reduce expenditure inequality, then Spain would have to strive to

lower expenditure inequality within small households while the U.S. would have to pay special

attention to larger households. However, to be able to draw useful policy conclusions much more

work would have to be done. Decomposition analysis could be applied to learn about the main

factors, together with household size, which account for expenditure inequality differences

between the two countries. But, ultimately, policy conclusions will need to wait until the explicit

modeling of such differences has been empirically tested.
37

APPENDIX

A. The Household Definition

In the EPF, a household is defined as one person or more than one person who shares

living quarters, or part of them, and consumes food and other products financed from a common

budget. In the CE, a household (or consumer unit) comprises either: all members of a particular

household who are related by blood, marriage, adoption, or other legal arrangement; a person

living alone or sharing a household with others or living as a roomer in a private home or lodging

house or in permanent living quarters in a hotel or motel, but who is financially independent; or

two or more people living together who use their incomes to make joint expenditure decisions.

Financial independence is determined by the three major expense categories: housing, food, and

other living expenses. To be considered financially independent, a least two of the three major

expense categories have to be provided entirely, or in part, by the respondent. For further details

on the Spanish and the U.S surveys used for this study, see INE (1992) and Bureau of Labor

Statistics (1993).

B. The Merge of the Diary and the Interview in the CE

As indicated in Section III, data from both the Diary and Interview are used to define total

expenditures following a method developed by Rob Cage at the BLS (Cage et al. 2002). The

BLS (1993) estimates that about 80 to 95 percent of total household 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. Data from the Diary are used to impute additional expenditures for these

omitted items to the Interview households. This is 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 are

produced by index-area and consumer unit size in the Diary sample. These shares are then

mapped to the CE Interview sample by index area and consumer unit size, and are used to impute

expenditures for these additional items in the Interview.

Household size and age of head are based on the average of the quarterly values for the

values reported (rounded values of average household size were used for our analysis). The

population weights used are also the result of averaging the quarterly weights over the number of

quarters for which the consumer unit participates in the survey.

C. Definition of household expenditures

In this paper, household economic well-being is identified with household consumption.

It would have been desirable to include the value of all the items that households consume in this

measure, but the exercise was restricted by the available data. Given this, the focus remained on

current consumption expenditures.

The starting point is the expenditure bundle used by the statistical agencies for the

production of their official Consumer Price Indexes (CPIs). Included in the U.S. CPI bundle but

not the Spanish CPI bundle are items like funeral articles, gambling expenditures, fines, hunting,
38

fishing and other fees, rent and food in-kind from work, and expenditures for automobile

insurance. All of these are considered current consumption for our study and were added to the

Spanish bundle as well.

Expenditures for the acquisition of vehicles for private transportation, house maintenance

and repairs, and life insurance are considered to be more of a form of savings than current

consumption. Thus, they are excluded for the analysis. Expenditures for housing (rent for

renters and some type of rental equivalence for owners, as well as utilities), and health and

vehicle insurance are included. In addition, for the U.S., adjustments are made to account for the

flow of services from selected household durables (see Cage et al. 2002).

However, some differences in the Spanish and U.S. definition of household consumption

expenditures remain. For example, it is known that in both countries health care and education

are consumed by the population; however, households may or may not pay for these consumption

services and related goods, or they may pay relatively little. This is of particular importance when

making international comparisons when one country has national health insurance, for example,

and the other does not, as is the case with Spain and the U.S. To include the household’s

expenditures for the U.S., and not the comparable expenditures made by Spanish households and

the government on the part of Spanish households means that an item like health care (and its

value) in Spain will be underestimated. About 2.28 percent of total expenditures for Spain are for

out-of-pocket health expenditures. This is in contrast to the share for the U.S. that is about 7

percent. Included in the Spanish measure, however, but not the U.S. one are (i) cash

contributions to non-profit institutions and cash transfers to members of the household who are

not living at the residence27 (for example, college students), as well as (ii) the value of home

production28. As noted in the main part of the paper, cash transfers are not collected each quarter

in the CE data so they could not be included in the U.S. total. No information is collected in the

CE on home production. However, when these last two sets of expenditures are excluded, the

overall results with respect to inequality and social welfare in Spain as compared to the U.S.

change very little29.

 

27 Cash contributions to non-profit institutions and to persons not living in the household data are only collected in

the fifth quarter of the CE Interview. Our sample includes households who may not have a fifth interview; based on

this, expenditures were defined so that they would be the same across all quarters covered. Thus, these contributions

are not included in the U.S. definition of current consumption expenditures.

28 Home production includes self-consumption and self-supply. Self-consumption is defined to be goods (mainly

food) produced on one’s own farm, in one’s own factory or workshop, or by one or some member of the household.

These goods are consumed by household members or given as gifts to others not of this household during the

reference period. These goods are valued at local retain market prices.

29 When the overall inequality (I0) results were produced for each Θ with cash transfers and home production not

included, the sign of the U.S.- Spanish differences did not change. However, expenditure inequality in Spain

increased marginally with the exclusion of these expenditures. When Θ = 0.0, the overall inequality index value

was 0.171 (versus 0.166), when Θ = 0.3, the index was 0.149 (versus 0.145), when Θ = 0.5, the index was 0.143

(versus 0.139), when Θ = 0.7, the index was 0.143 (versus 0.140), and when Θ = 1.0, the index was 0.158 (versus

0.155).
39

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Population Distribution Population Distribution

of Persons of Households

Household Percent Percent

Size Spain United States Spain United States Difference Spain United States Difference

1 2,174 1,672 2.9 10.3 252.1 10.0 26.8 168.02 4,735 1,837 13.1 23.4 78.8 22.3 30.3 36.13 4,427 1,106 18.3 19.8 8.1 20.8 17.1 -17.84 5,052 968 29.3 23.7 -19.2 25.0 15.3 -38.55 2,822 428 19.4 12.7 -34.3 13.2 6.6 -50.06 1,206 162 9.6 5.4 -43.5 5.4 2.3 -57.07 471 63 4.5 2.1 -52.8 2.2 0.8 -64.1

Size 1 to 7 20,887 6,236 97.1 97.4 0.4 98.9 99.3 0.4

Total 21,155 6,284 100.0 100.0 100.0 100.0

Sample size

Table 1. Sample Size and Population Distributions by Household Size in Spain and the United States. 1990-91 Distributions
Table 2. Mean Household Expenditures in Spain and the United States for 1990-91 Distributions

of Expenditures in Winter 1991 Prices and U.S. Dollars1

Mean Household Expenditures

Household Size Spain United States Percent Difference2

1 $9,993 $15,726 *57.4

2 15,417 25,127 *63.0

3 21,702 27,970 *28.9

4 26,646 30,665 *15.1

5 28,016 31,647 *13.0

6 29,785 29,006 -2.6

7 30,056 37,383 *24.4

Adjustment

Factor

Θ Spain United States Percent Difference

0.0 $24,727 $27,643 *11.8

0.3 16,230 19,498 *20.1

0.5 12,356 15,657 *26.7

0.7 9,471 12,712 *34.2

1.0 6,445 9,504 *47.5

1

Based on EKS purchasing price parity conversion factor of 108.9 Spanish pesetas to $1 U.S. for 1991

2

Percent difference = ((U.S. - Spain) / Spain)*100

*Difference statistically significant at the 0.05 level

All Households

Mean Adjusted Household Expenditures (person weighted)
Table 3. Relative Inequality Indexes by Household Size for Spain and the United States 

Based on 1990-91 Distributions of Household Expenditures in Winter 1991 Prices

Generalized Entropy Inequality Indices (I c )

Household Size I -1 I 0 I 1 I 2

1 0.315 0.243 0.244 0.323

[0.017] [0.013] [0.018] [0.042]

2 0.207 0.177 0.181 0.230

[0.007] [0.006] [0.009] [0.023]

3 0.149 0.128 0.131 0.159

[0.007] [0.006] [0.010] [0.023]

4 0.146 0.128 0.133 0.172

[0.007] [0.007] [0.011] [0.030]

5 0.142 0.122 0.122 0.141

[0.007] [0.005] [0.006] [0.008]

6 0.159 0.128 0.131 0.161

[0.015] [0.010] [0.013] [0.025]

7 0.143 0.122 0.117 0.127

[0.010] [0.008] [0.008] [0.011]

1 0.208 0.164 0.163 0.222

[0.012] [0.009] [0.016] [0.058]

2 0.156 0.136 0.140 0.175

[0.008] [0.007] [0.009] [0.019]

3 0.163 0.133 0.129 0.145

[0.011] [0.007] [0.007] [0.011]

4 0.151 0.127 0.124 0.140

[0.011] [0.008] [0.008] [0.0125]

5 0.171 0.148 0.156 0.210

[0.018] [0.017] [0.025] [0.058]

6 0.200 0.158 0.165 0.222

[0.044] [0.026] [0.032] [0.065]

7 0.192 0.162 0.160 0.184

[0.043] [0.033] [0.035] [0.050]

1 *-34.0 *-32.5 *-33.2 -31.1

2 *-24.7 *-23.1 *-22.6 -23.9

3 9.4 3.7 -1.3 -9.2

4 3.5 -0.8 -6.7 -18.4

5 20.1 21.2 27.2 48.8

6 25.9 23.7 26.3 37.9

7 34.2 32.6 36.1 44.7

Bootstrapped standard errors in brackets: 1000 replications

1

Percent difference = ((U.S. - Spain) / Spain)*100

*Difference statistically significant at the 0.05 level

Spain

United States

Percent Difference Between the United States and Spain1
Table 4. Decomposition of Relative Inequality Index I 0 for Spain and the United States

Based on 1990-91 Distributions of Adjusted Household Expenditures in Winter 1991 Prices 

(person weighted)

Adjustment

Factor

Overall Within-Group Between-Group Overall Within-Group Between-Group

0.0 0.166 0.136 0.030 0.161 0.140 0.021

[0.0032] [0.0027] [0.0014] [0.0053] [0.0042] [0.0029]

0.3 0.145 0.009 0.144 0.004

[0.0034] [0.0007] [0.0044] [0.0010]

0.5 0.139 0.003 0.146 0.006

[0.0029] [0.0004] [0.0037] [0.0013]

0.7 0.140 0.004 0.160 0.020

[0.0033] [0.0005] [0.0045] [0.0020]

1.0 0.155 0.018 0.201 0.061

[0.0030] [0.0013] [0.0050] [0.0032]

Difference in 

Difference "uncontaminated"

Adjustment in overall (within group)

Factor inequality inequality

0.0 -0.005 0.004

0.3 -0.001

0.5 ~0.008

0.7 *0.020

1.0 *0.046 1

Groups partitioned by household size with all households accounted for

Bootstrapped standard errors in brackets: 1000 replications

~Difference statistically significant when expenditure distributions trimmed to eliminate top and bottom 5 % of the weighted sample

*Difference statistically significant at 0.05 level

(between group)

Spain United States

"contaminated"

*0.016

*0.043

All Households1

inequality

*-0.009

*-0.005

*0.004

Decomposition of I 0 by Household Size 

Decomposition of Differences in Inequality according to I0: U.S. Inequality - Spain Inequality

Difference in 

Θ ∆ I ( Θ ) ∆ U ∆ C ( Θ )

Θ
Table 5. Social Welfare by Household Size in Spain and the United States Based on 1990-91

1990-91 Distributions of Unadjusted Household Expenditures in Winter 1991 Prices and U.S. Dollars1

Social Welfare Based on Social Evaluation Function W

Household Size Spain United States Percent Difference2

1 $7,553 $13,160 *74.2

[155.5] [255.5]

2 12,624 21,601 *71.1

[158.3] [291.2]

3 18,867 24,365 *29.1

[188.8] [425.5]

4 23,102 26,859 *16.3

[267.5] [490.3]

5 24,591 26,723 8.7

[302.0] [835.8]

6 25,891 24,216 -6.5

[529.9] [1295.7]

7 26,529 31,412 18.4

[681.4] [2752.9]

1

Based on EKS purchasing price parity conversion factor of 108.9 Spanish pesetas to $1 U.S. for 1991

2

Percent difference = ((U.S. - Spain) / Spain)*100

Bootstrapped standard errors in brackets: 1000 replications

*Difference statistically significant at 0.05 level
Table 6. Social Welfare in Spain and the United States Based on 1990-91 Distributions of Adjusted Household Expenditures 

in Winter 1991 Prices and U.S. Dollars1 (person weighted)Adjustment

Factor

Overall Within-Group Between-Group Overall Within-Group Between-Group Overall Within-Group Between Group

0.0 $20,749 $21,412 $663 $23,212 $23,757 $545 *11.9 11.0 -17.8

[129.7] [230.9]

0.3 13,885 14,022 137 16,679 16,762 83 *20.1 19.5 -39.6

[80.7] [133.9]

0.5 10,621 10,656 35 13,362 13,458 96 *25.8 26.3 172.7

[60.2] [122.9]

0.7 8,119 8,151 32 10,687 10,924 237 *31.6 34.0 631.2

[40.3] [107.6]

1.0 5,412 5,526 115 7,602 8,160 557 *40.5 47.7 385.4

[29.4] [77.8]

1Based on EKS purchasing price parity conversion factor of 108.9 Spanish pesetas to $1 U.S. for 19912Percent difference = ((U.S. - Spain) / Spain)*100

Bootstrapped standard errors in brackets: 1000 replications*Difference statistically significant at 0.05 level

All Households

Social Welfare Based on Social Evaluation Function 

W

United States Percent Difference2 Spain

Θ
Table 7. The Impact of Prices on Relative Inequality (I 0 ) in the United States and Spain in 1981 and 1991 Using 

1990-91 Adjusted Household Expenditures. All Households (person weighted)

Adjustment Inequality in United States Minus Inequality in Spain

Factor Spain United States In Winter 1981 Prices In Winter 1991 Prices

0.0 0.005 0.003 -0.004 -0.0050.3 0.004 0.005 -0.001 -0.0010.5 0.004 0.006 0.005 0.0080.7 0.003 0.007 *0.016 *0.0201.0 0.002 0.009 *0.041 *0.046

*Difference statistically significant at 0.05 level

Inequality Based on Winter 1991 Prices Minus 

Inequality Based on 1981 Prices

Θ ) (Θ ∆ 1 P ) (Θ ∆ 2 P ) (’ Θ ∆ t I ) (Θ ∆ t I
Adjustment

Factor

I-1 I1 I2 I-1 I0 I2 I-1 I0 I2

0.0 0.218 0.161 0.193 0.202 0.160 0.199 ~-7.6 -0.4 2.8

[0.004] [0.005] [0.012] [0.006] [0.008] [0.017]

0.3 0.178 0.144 0.176 0.175 0.145 0.177 -1.8 0.1 0.6

[0.004] [0.005] [0.014] [0.006] [0.006] [0.012]

0.5 0.166 0.140 0.173 0.177 0.147 0.180 ~7.1 4.3 4.1

[0.003] [0.004] [0.012] [0.006] [0.005] [0.009]

0.7 0.164 0.143 0.178 0.196 0.159 0.198 *19.7 11.5 11.2

[0.004] [0.005] [0.014] [0.007] [0.006] [0.015]

1.0 0.182 0.160 0.208 0.258 0.200 0.260 *42.1 *24.8 ~24.9

[0.004] [0.004] [0.012] [0.009] [0.006] [0.0199]

0.0 $19,336 $20,622 $19,948 $22,073 $23,191 $22,153.5 *14.2 *12.5 *11.1

[123.9] [125.7] [250.1] [244.7] [202.0] [390.4]

0.3 13,342 13,876 13,381 16,092 16,684 16,055 *20.6 *20.2 *20.0

[91.1] [67.2] [165.8] [173.4] [151.7] [234.6]

0.5 10,310 10,639 10,223 12,878 13,363 12,844 *24.9 *25.6 *25.6

[71.4] [61.3] [133.2] [148.6] [123.3] [192.5]

0.7 7,918 8,149 7,783 10,215 10,682 10,193 *29.0 *31.1 *31.0

[56.9] [46.1] [80.9] [133.3] [108.6] [155.8]

1.0 5,275 5,449 5,105 7,052 7,594 7,036 *33.7 *39.4 *37.8

[41.7] [27.5] [70.6] [120.7] [91.6] [185.3]

1Based on EKS purchasing price parity conversion factor of 108.9 Spanish pesetas to $1 U.S. for 1991

Bootstrapped standard errors in brackets: 1000 replicationsPercent difference = ((U.S. - Spain) / Spain)*100*Difference statistically significant at the o.o5 level~Difference statistically significant when expenditure distributions trimmed to eliminate top and bottom 5 % of the weighted sample

Percent Difference

Appendix Table. Relative Inequality and Overall Welfare for Spain and the United States Based 

on 1990-91 Distributions of Adjusted Household Expenditures in Winter 1991 Prices 

and U.S. Dollars (person weighted)

United States Spain

Relative Inequality

Overall Welfare

Θ