a comparison of income and expenditure inequality estimates: the australian evidence, 1975–76 to...

The Australian Economic Review, vol. 33, no. 4, pp. 317–29

The University of Melbourne, Melbourne Institute of Applied Economic and Social Research 2000Published by Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and

350 Main Street, Malden, MA 02148, USA

Abstract

Using Australian unit record data this papercompares income and expenditure inequalitiesover the period 1975–76 to 1993–94. The studyfinds inconsistencies between the two inequal-ity movements over much of this period. Wealso observe differences in the nature of in-come and consumption disparities. Both ap-proaches show that the ‘within group’inequality dominates the ‘between group’ com-ponent when the population is divided intohousehold types. The inequality estimates aresensitive to the equivalence scale used as thehousehold size deflator but not to the cost ofliving index used as the price deflator.

1. Introduction

This paper compares inequality estimates usingAustralian unit record data on income and ex-penditure. McGregor and Borooah (1992),Kakwani (1993), Slesnick (1994) and Johnsonand Shipp (1999), amongst others, argue thatconsumption expenditure is a more appropriateindicator of well being. We widen the analysisin Australia to include expenditure. Blundelland Preston (1998) point out that expenditure isless subject than income to short-term fluctua-tions since households can smooth consump-tion by adjusting savings.

Following the pioneering work of Kolm(1969) and Atkinson (1970), the measurementof inequality has been based on explicit socialwelfare functions. These are defined on the dis-tribution of income rather than the distributionof individual utility or welfare. Muellbauer(1974, p. 498) has shown that measures of so-cial welfare based on income coincide withthose based on individual welfare if and only ifpreferences are homothetic for all consumingunits—see, also, Roberts (1980). The restric-tions on consumer preferences, implied by theMuellbauer and Roberts analyses, are strongand unrealistic, giving us an additional reasonto distinguish between income and expenditureinequality.

The Australian literature on inequality hasmostly been based on income rather than con-sumption expenditure. Most Australian studieshave found that income inequality in Australiarose through the mid 1970s to the early1990s—see, for example, Meagher and Dixon

A Comparison of Income and Expenditure Inequality Estimates: The Australian Evidence, 1975–76 to 1993–94

Paul Blacklow and Ranjan Ray*School of EconomicsUniversity of Tasmania

* We are grateful to two anonymous referees for helpful re-marks on earlier versions. The usual disclaimer applies.The research for this paper was partly supported by an Aus-tralian Research Council (Large) Grant.

318 The Australian Economic Review December 2000

The University of Melbourne, Melbourne Institute of Applied Economic and Social Research

(1986), Saunders (1993), Borland and Wilkins(1996), and Harding (1997). The timing and se-verity of the inequality increases differedslightly according to the data, unit of analysisand the equivalence scale. Relatively little at-tention has been paid to consumption inequal-ity in Australia, except for the recent work byBarrett, Crossley and Worswick (2000).

This paper seeks to provide Australian evi-dence on the following questions. Over the pe-riod 1975–76 to 1993–94, how similar orotherwise have been the movements in incomeand consumption expenditure inequality? In at-tempting to answer this question, we extend theexercise of Barrett, Crossley and Worswick(2000) to include multiple family householdsconsisting of unrelated young adults and oth-ers. Also, we include expenditure on durablesin our analysis.

Over this period, what is the impact ofchanging equivalence scale specifications oninequality magnitudes and on their movementsover time? As the Australian evidence of Lan-caster and Ray (1998) confirms, there is a widearray of equivalence scales to choose from.This makes the issue of sensitivity of inequalitycalculations to the equivalence scale used onewith policy significance.

Is the picture on income versus expenditureinequality movements robust to the price defla-tor used in the inequality calculations? Thispaper provides Australian evidence on the sen-sitivity of inequality magnitudes and theirmovements to the use of fixed weight price in-dices, such as the consumer price index (CPI),or the true cost of living index (TCLI) thattakes account of substitution between itemsdue to relative price changes.

The rest of this paper is organised as follows.Section 2 introduces the theoretical frame-work. The data are described in Section 3. Theresults are presented and analysed in Section 4.We end on the concluding note of Section 5.

2. Theoretical Framework

2.1 Inequality Measures

Inequality measures estimate the level of in-equality of the population units by measuring

the dispersion of a variable associated withwelfare. In this study real per adult equivalentdisposable income, , and real per adult equiv-alent expenditure, , are used as alternativemeasures of the welfare variable,

w

.A widely used measure of the dispersion in

welfare is the Gini coefficient,

G

. Consider apopulation of

H

households with welfare

w

h

enjoyed by household

h

, and let denote meanwelfare. Then:

(1)

where

w

1

>

w

2

> … >

w

H

. The Gini coefficientis not readily decomposable. If the inequalitymeasures are scale invariant (that is homoge-nous of degree zero in income or expenditure)and replication invariant (that is remain un-changed when the population and distributionare replicated), then Shorrocks (1984) showsthat the only admissible indices are the ‘Gener-alised Entropy’ (GE) family of indices. Theseare given by:

c

≠

0, 1 (2)

(3)

(4)

The parameter

c

reflects different percep-tions of inequality; as

c

decreases the GE indexbecomes more sensitive to transfers lowerdown the distribution. The GE class of inequal-ity measures includes the mean logarithmic de-viation (

I

0

), the Theil Index (

I

1

), and half thesquare of the coefficient of variation (

I

2

).

I

0

,

I

1

and

I

2

are particularly sensitive to changes inthe bottom, middle and top, respectively, of thewelfare distribution. In the calculations re-ported below, we divided the population into

k

subgroups of households and exploited theproperty that all members of the GE family areadditively decomposable by population sub-groups as follows:

yx

w

G1

2H2w-------------- wi w j–

j∑

i∑=

Ic1H---- 1

c c 1–( )-------------------

wh

w------

c

1–h∑=

I01H---- w

wh------

logh∑=

I11H----

wh

w------

wh

w------

logh∑=

Blacklow and Ray: Comparison of Income and Expenditure Inequality Estimates 319


I

c

=

I

w

+

I

B

(5)

where

I

w

=

Σ

k

( / )

c

I

k

refers to the inequal-ity arising within subgroups; is the popula-tion share of the subgroup of type

k

;

w

k

is thesubgroup mean of the welfare variable,

w

; isthe corresponding mean for the entire popula-tion; and

I

k

is the value of the inequality indexfor subgroup

k

. In addition to the GE inequalityindices,

I

0

,

I

1

and

I

2

, we also used the Gini in-dex. In contrast to

I

0

and

I

2

, the Gini coefficientis insensitive to changes in the tails of the wel-fare distribution.

2.2 Consumer Preferences and Equivalence Scale Specification

The inequality calculations require the use ofequivalence scales as deflators of income orexpenditure to correct for differences in house-hold size or composition. In addition to the tra-ditional scales, we also employ utility theoryconsistent equivalence scales. These ‘pricescaled’ equivalence scales are obtained by ap-plying the price scaling (PS) demographictechnique, proposed in Ray (1983), to the rank3 ‘Generalised Almost Ideal’ (GAI) demandmodel (see Banks, Blundell and Lewbel 1997;Lancaster and Ray 1998). This demand systemcollapses to the restrictive rank 2 form of the‘Almost Ideal’ (AI) demand model as a specialcase. In the empirical applications reported be-low, we refer to the equivalence scales corre-sponding to the GAI and AI demand models asPS-GAI and PS-AI respectively (for more de-tails see Blacklow and Ray 1998).

We choose the following functional form forthe equivalence scale,

EP

, namely:

(6)

where

n

a

,

n

1

,

n

2

,

n

3

denote, respectively, thenumber of adults, children under 5 years old,dependants aged between 5 and 14 years old,and dependants aged between 15 and 25 yearsold, living in the household. While the

δ

’s rep-resent their corresponding resource cost as aproportion of an adult, (1 –

θ

) reflects the econ-omies of scale in household size (see Buhmannet al. 1988; Lancaster, Ray and Valenzuela

1999b).

EP

is the number of ‘adult equivalent’persons in the household in the base year whenprices are normalised at unity. The alternativescales are as follows:

(i) Demand System Based Scales (PS-GAI, PS-AI)

The equivalence scale parameters (

δ

i

,

θ

) are es-timated along with the demand parametersfrom the PS-GAI and PS-AI demographic de-mand systems—see Blacklow and Ray (1998,Appendix) for details. The PS-AI scales thatare used assumed an absence of economies ofhousehold size; that is

θ

= 1.

(ii) Engel

EP

is set at the value at which two householdswith the same per adult equivalent expenditure,

, have an identical budget share of food—seeBinh and Whiteford (1990) and Lancaster andRay (1998) for more details and Australian es-timates of Engel scales.

(iii) OECD

A standard equivalence scale used in OECDstudies is to assign a value of one for the firstadult in the household with every extra adult inthe household worth 0.7, and every child worth0.5 of a single adult household.

(iv) Per Capita

δ

1

=

δ

2

=

δ

3

=

θ

= 1; that is,

EP

equals the un-weighted number of household members.

2.3 Price Indices

Nominal variables need to be divided by a priceindex for comparisons under different pricelevels. The CPI series, constructed by the Aus-tralian Bureau of Statistics (ABS), is a weightedaverage of prices, where the weights are the av-erage budget shares of working households.The CPI, in using fixed weights, does notexplicitly consider the substitution effects ofprice changes. This is allowed in the TCLI. Inthe calculations reported below, the PS-GAI

pk wk wpk

w

EP na δ1n1 δ2n2 δ3n3+ + +( )θ=

xh



Table 1 Alternative Equivalence Scales

PS-GAIPS-AIno ES Engel OECD Per capita

Equivalence scale parametersa, b

δ1 0.0877 0.0339 0.1277 0.5000 1.0000(.0189) (.0176) (.0222)

δ2 0.4760 0.4140 0.5403 0.5000 1.0000(.0162) (.0158) (.0218)

δ3 0.8415 0.8195 0.8674 0.5000 1.0000(.0374) (.0390) (.0503)

θ 0.5868 1.0000 0.9872 na 1.0000(.0229) (.0136)

Household type na n1 n2 n3

1 0 0 0 1.00 1.00 1.00 1.00 1.00

1 1 0 0 1.05 1.03 1.13 1.50 2.00

1 0 1 0 1.26 1.41 1.53 1.50 2.00

1 0 0 1 1.43 1.82 1.85 1.50 2.00

1 1 1 1 1.67 2.27 2.51 2.50 4.00

2 0 0 0 1.50 2.00 1.98 1.70 2.00

2 1 0 0 1.54 2.03 2.11 2.20 3.00

2 0 1 0 1.70 2.41 2.51 2.20 3.00

2 0 0 1 1.85 2.82 2.83 2.20 3.00

2 1 1 1 2.05 3.27 3.48 3.20 5.00

2 2 0 0 1.58 2.07 2.23 2.70 4.00

2 0 2 0 1.89 2.83 3.04 2.70 4.00

2 1 2 1 2.22 3.68 4.00 3.70 6.00

3 0 0 0 1.91 3.00 2.96 2.40 3.00

4 0 0 0 2.26 4.00 3.93 3.10 4.00

5 0 0 0 2.57 5.00 4.90 3.80 5.00

6 0 0 0 2.86 6.00 5.86 4.50 6.00

7 0 0 0 3.13 7.00 6.83 5.20 7.00

8 0 0 0 3.39 8.00 7.79 5.90 8.00

9 0 0 0 3.63 9.00 8.75 6.60 9.00

Notes: (a) The equivalence scale is given by EP = (na + δ1n1 + δ2n2 + δ3n3)θ where na = number of adults; n1 = number of

children aged 0–4 years; n2 = number of children aged 5–14 years; and n3 = number of dependants aged 15–25 years.(b) Figures in brackets denote standard errors.

demographically modified utility function wasused for deriving the TCLI expression (formore details see Blacklow and Ray 1998).

3. Data

All estimation and analysis are based on apooled cross-section of the unit record filesfrom the Household Expenditure Surveys(HES) conducted by the ABS for the years1975–76, 1984, 1988–89 and 1993–94. The

household is chosen as the unit of analysis,using the HES household weights. Certain ad-justments had to be made to the data sets tomake them comparable (see Appendix 1).However, no observations were removed fromthe full sample of 25 649 households. Theprices used are based on the ABS (2000) Con-sumer Price Index quarterly series (see Appen-dix 2).

Table 1 compares the different equivalencescales and associated parameters, implied for



the various household types by the five alterna-tive scale specifications discussed above. Thereis little difference between the PS-GAI and PS-AI scales for smaller households; the latter ex-ceed the former as household size increases.The Engel scales generally exceed the utility-based scales since the former ignore substitu-tion between food and non-food items inducedby household composition changes. The OECDscales, in several cases, are out of step with theothers. The per capita scale tends to overesti-mate the costs of children by assuming that theyhave the same resource needs as an adult.

4. Results

4.1 Movements of Aggregate Inequality

Table 2 reports the aggregate income and con-sumption expenditure inequalities, using thePS-GAI equivalence scales and the TCLI tocorrect for household composition changes andprice movements. The table also reports, re-spectively, the disposable income and expendi-ture per equivalent adult (in December 1997dollars) for each of the subperiods.

The inequality measures show that over thesample period as a whole (that is 1975–76 to1993–94), while income inequality increased,expenditure inequality fell. All Ic measures ofincome inequality recorded a rise during themid 1980s, and most recorded rises between1988–89 and 1993–94, while the Gini coeffi-cient recorded significant rises in income

inequality throughout the sample period. Ex-penditure inequality fell significantly in thelate 1970s and experienced further small fallsin the 1980s and 1990s. In other words, the pic-ture on inequality movement over this period issensitive to the choice of income or expendi-ture as the welfare variable. However, the pic-ture on movements in inequality is robust bothbetween the Gini and the GE Ic measures.

In absolute terms, increasing the parameter cin the GE inequality measure, Ic, increases theexpenditure inequality estimates. However,this is not the case for income inequality. Forexample, in 1993–94 the income inequality es-timate falls sharply from the mean logarithmicdeviation (I0) to the Theil Index (I1), but thenrises again in the case of half the square of thecoefficient of variation index (I2) to almost theI0 level. In contrast to income, the expenditureinequality estimates in 1993–94 are remark-ably similar between the I0 and I1 measures.This suggests that over our sample period notonly the trend but also the nature of inequalityhas been sharply different between disposableincome and aggregate expenditure. Keeping inmind the fact that I0 is more sensitive to in-equality in the left-hand tail of the distributionand I2 to the right-hand tail, Table 2 suggeststhat for much of this period, and especially inthe late 1980s and early 1990s, the income dis-parities among the poor and among the upperclasses dominated that among the middleincome groups. In contrast to income, theexpenditure estimates I0, I1 and I2 show that

Table 2 Aggregate Income and Expenditure Inequalitya, b

Income inequality Expenditure inequality1975–76 1984 1988–89 1993–94 1975–76 1984 1988–89 1993–94

µ c 480.76 456.86 423.57 414.84 437.83 449.17 419.18 420.31

I0 0.1508 0.1591 0.1775 0.2013 0.1799 0.1588 0.1581 0.1504

(.0083) (.0096) (.0081) (.0087) (.0082) (.0086) (.0067) (.0060)

I1 0.1299 0.1352 0.1573 0.1608 0.1812 0.1548 0.1532 0.1491(.0094) (.0093) (.0128) (.0098) (.0157) (.0131) (.0096) (.0092)

I2 0.1412 0.1401 0.2018 0.1862 0.2389 0.1825 0.1766 0.1764(.0129) (.0106) (.0247) (.0152) (.0284) (.0194) (.0126) (.0125)

Gini 0.2782 0.2892 0.2984 0.3070 0.3191 0.3043 0.3034 0.2976(.0034) (.0036) (.0028) (.0025) (.0031) (.0034) (.0027) (.0025)

Notes: (a) The PS-GAI equivalence scale was used as the household size deflator, and the TCLI as the price deflator.(b) Figures in brackets denote standard errors.(c) µ denotes mean disposable income and expenditure (in December 1997 dollars) per equivalent adult.



consumption disparities within the lower andmiddle expenditure groups are similar butlower than that within the upper classes.

The non-robustness of the picture on in-equality in Table 2 is further reflected in themovement over time in the scale-adjusted peradult equivalent means of disposable incomeand aggregate expenditure. While the formerfell, the latter rose over our sample period,1975–76 to 1993–94. Consequently, there wasnet dissaving at the end of our sample period. Itis worth noting, however, that the contrarymovements in the two per adult equivalent fig-ures are only in the first subperiod (1975–76 to1984)—they have practically moved in thesame direction in the second half of our sampleperiod.

A comparison of the income and expenditureIc-based inequality estimates shows that whileat the beginning of our sample period (1975–76) the expenditure inequality estimates ex-ceed the corresponding income inequality fig-ures, the reverse was the case at the end (1993–94). Let us focus on I0, which is particularlysensitive to the bottom tail of the distribution.In 1975–76, expenditures were much more un-equal than income (0.1799 for the former in-equality, 0.1508 for the latter). There was asharp rank reversal in the end (0.1504 for theformer, 0.2013 for the latter). This suggests

that over the two earlier subperiods with con-trary movements in the two inequalities, duringan increase in income disparities the ultra poorwere able to smooth the income fluctuations byeither using savings or borrowing, as suggestedby Blundell and Preston (1998). It is worth not-ing that over 1988–89 to 1993–94, a large partof which was characterised by severe reces-sion, our sample figures suggest that Australiawent into negative savings because of, apartfrom other reasons, excessive borrowings bythe less well off to smooth out their incomefluctuations.

4.2 Inequality Estimates by Household Composition

The above discussion raises the followingquestion. Is the picture on aggregate inequalitypresented above robust between the varioushousehold types, distinguished by their sizeand composition?

Table 3 presents the disaggregated picture byreporting the income and expenditure inequal-ity estimates for six household types, whileTable 4 shows the population proportions ofthe household types over the sample period.

The picture, presented earlier, of income in-equality increasing and expenditure inequalitydecreasing over the sample period as a whole,

Table 3 Income and Expenditure Inequalitya (I0) for Different Household Typesb

Income inequality Expenditure inequalityHousehold type 1975–76 1984 1988–89 1993–94 1975–76 1984 1988–89 1993–94

1 adult (aged 25–64 years)with no children

0.196 0.207 0.252 0.344 0.279 0.171 0.196 0.180(.033) (.034) (.031) (.035) (.034) (.027) (.021) (.018)

1 adult (aged 25–64 years)with 1 or more children

0.134 0.076 0.081 0.109 0.147 0.149 0.120 0.108(.044) (.026) (.023) (.025) (.042) (.037) (.027) (.020)

2 adults (aged 25–64 years)with no children

0.129 0.158 0.174 0.193 0.160 0.139 0.132 0.132(.019) (.024) (.020) (.019) (.017) (.018) (.014) (.012)

2 adults (aged 25–64 years)with 1 or more children

0.103 0.116 0.144 0.139 0.115 0.093 0.114 0.100(.012) (.015) (.013) (.013) (.010) (.011) (.010) (.009)

Pensioners (aged 65 years and above) with no dependants

0.155 0.107 0.146 0.117 0.229 0.200 0.163 0.147(.024) (.020) (.018) (.018) (.027) (.025) (.018) (.015)

Other households 0.120 0.123 0.113 0.152 0.141 0.135 0.119 0.130(.015) (.018) (.013) (.017) (.016) (.018) (.013) (.013)

Aggregate 0.151 0.159 0.177 0.201 0.180 0.159 0.158 0.150(.008) (.010) (.008) (.009) (.008) (.009) (.007) (.006)

Note: (a) The PS-GAI equivalence scale was used as the household size deflator, and the TCLI as the price deflator.(b) Figures in brackets denote standard errors.



seems to hold for most household types. Thesignificant exception is old age pensioners forwhom income inequality fell sharply in the firsthalf of our sample period, and then increasedonly marginally in the second half.

The contrary movements of income and ex-penditure inequalities are particularly strikingfor households with one adult and no children.In the mid 1970s, such households faced muchhigher expenditure inequality than income in-equality. However, by the mid 1990s the situa-tion had reversed itself sharply, thus suggestingthat the propensity to smooth consumption, inthe face of exogenous income shocks by draw-ing on savings or borrowing, is at its highest forsingle adults with no dependent children. Thetables also show that single parent families ex-perienced lower income and expenditure in-equalities than single adult households with nodependent children. It is worth noting fromTable 3 that single parent households and oldage pensioners are the only household typesthat witnessed a decline in income inequalityover the sample period, 1975–76 to 1993–94.

We exploit the additive decomposabilityproperty of the Ic inequality measure to presentthe breakdown of total inequality into ‘withingroup’ and ‘between group’ inequalities,where the six demographically varying house-hold types of the previous discussion constitutethe various groups. Table 5 presents the de-composition, using I0, of income and expendi-ture inequality respectively. It is clear that, forboth types, the within group inequality domi-nates the between group component. More-over, most of the movements in aggregateinequality over our sample period have resultedfrom changes in the within group component.In comparison, the between group inequalityhas not changed much, especially over the pe-riod 1984 to 1993–94.

4.3 Sensitivity of Inequality Estimates to the Equivalence Scale and the Price Deflator

Table 6 presents the aggregate income and ex-penditure inequality estimates, under the fivealternative equivalence scales discussed earlier

Table 4 Population Proportions of Household Types

Household type 1975–76 1984 1988–89 1993–94

1 adult (aged 25–64 years) with no children 0.084 0.111 0.126 0.130

1 adult (aged 25–64 years) with 1 or more children 0.031 0.044 0.046 0.057

2 adults (aged 25–64 years) with no children 0.190 0.197 0.197 0.222

2 adults (aged 25–64 years) with 1 or more children 0.363 0.313 0.294 0.252

Pensioners (aged 65 years and above) with no dependants 0.115 0.137 0.136 0.153

Other households 0.217 0.197 0.201 0.186

Table 5 Income and Expenditure Inequalitya (I0) Decomposition by Household Types

1975–76 1984 1988–89 1993–94

Income inequality

Within group 0.1265 0.1328 0.1545 0.1750

Between group 0.0243 0.0263 0.0230 0.0263

Total 0.1508 0.1591 0.1775 0.2013

Expenditure inequality

Within group 0.1572 0.1360 0.1358 0.1305

Between group 0.0227 0.0228 0.0223 0.0198

Total 0.1799 0.1588 0.1581 0.1504

Note: (a) The PS-GAI equivalence scale was used as the household size deflator, and the TCLI as the price deflator.



(see Table 1). Once again the trends in inequal-ity movements are robust to the treatment ofhousehold size and composition. However, theinequality magnitudes are sensitive to thehousehold size deflator. The ‘per capita’ fig-ures overstate inequality in relation to the oth-ers that incorporate adult/child relativities.This is consistent with the cross-country evi-dence presented in Lancaster, Ray and Valen-

zuela (1999a). In contrast, the inequalityestimates are fairly robust to the rank of the de-mand system, namely between the quadraticand AI demand models.

Table 7 presents evidence on the sensitivityof inequality estimates to the price deflator byreporting the calculations using the preference-based TCLI and the fixed weight CPI asprice indices. The picture of contradictory

Table 6 Aggregate Income and Aggregate Expenditure Inequality (I0) Estimates under Alternative Equivalence Scalesa, b

Income inequality Expenditure inequalityEquivalence scale 1975–76 1984 1988–89 1993–94 1975–76 1984 1988–89 1993–94

PS-GAI 0.1508 0.1591 0.1775 0.2013 0.1799 0.1588 0.1581 0.1504(.0083) (.0096) (.0081) (.0087) (.0082) (.0086) (.0067) (.0060)

PS-AI 0.1403 0.1471 0.1645 0.1914 0.1721 0.1423 0.1428 0.1428(.0079) (.0091) (.0078) (.0084) (.0077) (.0079) (.0063) (.0058)

Engel 0.1490 0.1587 0.1736 0.1962 0.1810 0.1572 0.1558 0.1479(.0081) (.0094) (.0079) (.0085) (.0078) (.0083) (.0065) (.0059)

OECD 0.1601 0.1667 0.1826 0.2052 0.1847 0.1628 0.1604 0.1539(.0084) (.0096) (.0081) (.0086) (.0080) (.0085) (.0067) (.0060)

Per capita 0.1882 0.1936 0.2069 0.2261 0.2104 0.1864 0.1830 0.1746(.0090) (.0102) (.0085) (.0089) (.0084) (.0090) (.0070) (.0064)

Note: (a) Figures in brackets denote standard errors.(b) The PS-GAI TCLI was used as the price deflator.

Table 7 Inequality Estimates under Alternative Price Deflatorsa, b

1975–76 1984 1988–89 1993–94TCLI CPI TCLI CPI TCLI CPI TCLI CPI

Income inequality

I0 0.1508 0.1453 0.1591 0.1560 0.1775 0.1792 0.2013 0.2024(.0083) (.0082) (.0096) (.0095) (.0081) (.0081) (.0087) (.0087)

I1 0.1299 0.1248 0.1352 0.1328 0.1573 0.1596 0.1608 0.1622(.0094) (.0091) (.0093) (.0092) (.0128) (.0130) (.0098) (.0099)

I2 0.1412 0.1349 0.1401 0.1377 0.2018 0.2062 0.1862 0.1886(.0129) (.0126) (.0106) (.0104) (.0247) (.0251) (.0152) (.0155)

Gini 0.2782 0.2729 0.2892 0.2867 0.2984 0.3004 0.3070 0.3081(.0034) (.0035) (.0036) (.0036) (.0028) (.0028) (.0025) (.0025)

Expenditure inequality

I0 0.1799 0.1786 0.1588 0.1786 0.1581 0.1638 0.1504 0.1528(.0082) (.0081) (.0086) (.0081) (.0067) (.0068) (.0060) (.0061)

I1 0.1812 0.1801 0.1548 0.1801 0.1532 0.1597 0.1491 0.1521(.0157) (.0151) (.0131) (.0151) (.0096) (.0102) (.0092) (.0095)

I2 0.2389 0.2344 0.1825 0.2344 0.1766 0.1874 0.1764 0.1814(.0284) (.0248) (.0194) (.0248) (.0126) (.0139) (.0125) (.0130)

Gini 0.3191 0.3186 0.3043 0.3186 0.3034 0.3089 0.2976 0.3002(.0031) (.0031) (.0034) (.0031) (.0027) (.0026) (.0025) (.0025)

Note: (a) The PS-GAI equivalence scale was used as the household size deflator.(b) Figures in brackets denote standard errors.



movements in income and expenditure in-equalities is robust to the price deflator used.However, unlike in the case of equivalencescales, the inequality magnitudes are insensi-tive to the price index used in converting thecurrent figures into constant prices.

4.4 Sensitivity of Inequality Estimates to the Unit of Analysis, to Sample Selection and to the Exclusion of Durables

Our study parallels that of Barrett, Crossleyand Worswick (2000) (BCW), referred to earl-ier. Both these studies compare income and ex-penditure inequalities in Australia over theperiod 1975–76 to 1993–94 using the House-hold Expenditure Surveys published by theABS. Notwithstanding the choice of an identi-cal time period and use of the same data set,the studies arrive at substantially different con-clusions. For example, BCW report an increasein expenditure inequality over this period,though less than that in income. In contrast, thepresent study observed reverse movements inthe two inequalities, with expenditure inequal-ity registering a small decline on most mea-sures (see Table 2). The explanation for theseinconsistent findings lies in the fact that thestudies differ principally in the following re-spects: (i) the unit of analysis used, namely theindividual in the case of BCW, and the house-hold or family in the present exercise; (ii) useof gross income in the income inequality cal-culations by BCW, unlike the use of net in-come here; (iii) the exclusion of durables fromthe expenditure inequality calculations byBCW, unlike here; (iv) BCW’s use of a re-stricted sample, namely households headed byindividuals aged 25–29 years, and omission ofthe top and bottom 3 per cent of householdsfrom their analysis; and (v) different equiva-lence scales used by BCW from those usedhere, and BCW’s use of the CPI as the pricedeflator, unlike the TCLI used in the presentstudy.

Since the income and expenditure figures inthe HES data sets used here relate to the house-hold rather than the individual, it was necessaryfor BCW to assume that ‘resources are equallyshared within the household’ (BCW 2000, p.

120). This was an assumption we were not pre-pared to make, especially given the mountingconcern in the recent literature over intra-household inequality (see, for example, Had-dad and Kanbur 1990). As BCW acknowledgein their paper, ‘an important consequence ofthis assumption is that … income inequalitywill by definition be lower than the level of in-equality found in analyses of the distribution ofindividual earnings and income’. The inequal-ity calculations, reported in the present study,make no such assumption and describe in-equality between households or families ratherthan between individuals. The present exerciseis in line with recent studies1 of the distributionof family income and expenditure in Canada,Portugal and the United States.

The above discussion raises the question ofrobustness of our principal conclusions to theuse of the individual rather than the householdas the unit of analysis. To investigate this issue,and make our estimates comparable with thoseof BCW, we recalculated the inequalities,weighting the data and using the informationon the number of individuals in each house-hold, just as BCW did, thus treating the indi-vidual as the unit of analysis. The recalculatedincome and expenditure inequality estimatesare presented in Table 8. In order to allowready comparison with the BCW estimates,these tables report, besides GE (Ic), the Giniand Atkinson (Aε) inequality estimates, the lat-ter corresponding to ‘inequality aversion’ (ε)levels of 0.5, 1.0 and 2.0.

The principal conclusion of our study—namely that while income inequality rose, ex-penditure inequality fell over our sample pe-riod—is robust to changes in the unit ofanalysis. It is significant that the GE (Ic) andAtkinson (Aε) inequality measures agree onthis result.

A comparison with Table 2 shows that theuse of the individual as the unit of analysisleads to a reduction in the inequality magni-tudes. The Atkinson inequality estimates, pre-sented in Table 8, compare well with thosepresented in BCW (see their Tables 1 and 3),especially if one remembers that any remainingdifferences are due to the truncated sampleused by BCW, and the different price and



Table 8 Aggregate Income and Expenditure Inequality (I0) with Individuals as the Unita, b, c

Income inequality Expenditure inequality1975–76 1984 1988–89 1993–94 1975–76 1984 1988–89 1993–94

µ d 493.17 469.55 436.77 426.97 453.16 465.30 434.68 432.63

I0 0.1300 0.1396 0.1525 0.1716 0.1433 0.1341 0.1343 0.1308

(.0078) (.0089) (.0074) (.0077) (.0072) (.0078) (.0062) (.0056)

I1 0.1115 0.1184 0.1371 0.1437 0.1482 0.1327 0.1322 0.1319(.0087) (.0086) (.0116) (.0095) (.0143) (.0117) (.0089) (.0089)

I2 0.1214 0.1220 0.1739 0.1686 0.1963 0.1549 0.1528 0.1580(.0120) (.0098) (.0210) (.0151) (.0266) (.0166) (.0116) (.0122)

Gini 0.2570 0.2693 0.2771 0.2888 0.2881 0.2821 0.2811 0.2788(.0037) (.0039) (.0030) (.0027) (.0033) (.0036) (.0029) (.0027)

A0.5 0.0569 0.0610 0.0673 0.0723 0.0697 0.0644 0.0643 0.0634(.0080) (.0090) (.0081) (.0075) (.0098) (.0098) (.0077) (.0072)

A1 0.1219 0.1303 0.1414 0.1577 0.1335 0.1255 0.1257 0.1226(.0078) (.0089) (.0074) (.0077) (.0072) (.0078) (.0062) (.0056)

A2 0.4355 0.4521 0.5689 0.7154 0.2554 0.2409 0.2440 0.2339(.0129) (.0145) (.0127) (.0122) (.0123) (.0128) (.0101) (.0093)

Number of observations 5 543 4 492 7 225 8 389 5 543 4 492 7 225 8 389

Number of individuals 12 791 080 14 202 810 14 986 470 17 394 260 12 791 080 14 202 810 14 986 470 17 394 260

Notes: (a) The PS-GAI equivalence scale was used as the household deflator and the TCLI as the price deflator.(b) Figures in brackets denote standard errors.(c) Household equivalent adult figures have been weighted by the number of individuals in the household (as well as surveyweights).(d) µ denotes mean disposable income and expenditure per equivalent adult.

household size deflators used in the two stud-ies.

An important conclusion of the BCW studyis that ‘consumption is much more equal thanincome’ (2000, p. 116). BCW observed this tobe the case throughout the sample period. Theinequality estimates presented in Table 8 show,however, that this is not true for the first half ofour sample period. As a consequence of risingincome inequality and falling expenditure in-equality over the sample period, consumptionbecame more equal than income only from themid 1980s until the end of the sample period(1993–94). In other words, BCW’s observationseems to be conditional on the truncated sam-ple used and omission of expenditure on dura-bles from their analysis.

5. Conclusion

Much of the inequality literature in Australia isbased on the use of income as the welfare vari-able. This paper attempts to contribute to thealmost non-existent literature on expenditure

inequality in Australia by comparing the natureand movement of the two inequalities over thesample period 1975–76 to 1993–94. The prin-cipal result of this study is that while incomeinequality has been increasing throughout oursample period, expenditure inequality fellsharply over 1975–76 to 1984, and then regis-tered smaller declines over the rest of the pe-riod. The study performed sensitivity exercisesto confirm that the picture of contrary move-ments in income and expenditure inequalitiesis robust to most household compositionchanges, to the equivalence scale used as thehousehold size deflator and to the cost of livingindex used as the price deflator. However, theinequality estimates are sensitive to the equiv-alence scale. All the measures show that ex-penditure inequality was greater than theinequality of income in 1975–76, but this situ-ation had reversed by 1993–94.

The nature of inequality has also varied be-tween income and expenditure. The incomedisparities in the tails, especially the bottomtail, dominate that among the middle income



group. In contrast, consumption disparitieswithin the lower and middle expendituregroups are similar, though appreciably lessthan that among the upper expenditure classes.The results generally seem to provide supportto the view that households tend to smooth outincome fluctuations by drawing on their sav-ings or borrowing. Consequently, our resultson the HES data suggest that the net savingsper equivalent adult dropped throughout oursample period, and became negative in theearly 1990s. Notwithstanding differences intheir nature and temporal movements, incomeand expenditure inequalities share one com-mon feature; namely that the within groupinequality dominated the between group com-ponent throughout our sample period.

First version received September 1998;final version accepted May 2000 (Eds).

Appendix 1: Problems and Adjustments Made to HES Data

The major problem of surveys of this nature isthat income and even expenditure are often un-derreported. This is a difficult problem toavoid. We assume a constant level of underre-porting by respondents over the four surveys.

While the 1988–89 and 1993–94 surveys aresimilar, the 1984 survey differed in that ittreated negative income from business or rentalproperty losses as zero and did not impute in-come tax paid. Comparison of the results of thepast three surveys with the first two in 1974–75and 1975–76 has limitations as the first twosurveys used a different approach to construct-ing the data, reporting period and HES Com-modity Code List. Ideally, we require thenegative income values for business and rentalproperty from the 1984 survey, but this is notpossible. An alternative is to change any nega-tive income for business and rental propertyfrom the 1988–89 and 1993–94 surveys to zeroand recalculate disposable income. This ap-proach was used in order to maintain continuitybetween the surveys.

The data on net direct tax from the 1984HES are reported by respondents as the taxpaid in previous years and so had to be esti-

mated based on the tax system in 1984. Thevalues imputed are, on average, slightly higherthan those reported but in line with the aggre-gate tax to income ratio of the other surveyyears.

In all the surveys, negative expenditure ispossible when refunds, trade-ins, or sales aregreater than the costs of acquisitions. Thisoften results in low or negative consumption.The absolute values of any negative valuesfound in broad expenditure categories wereadded to the household expenditure category inorder to remove the negative amount. Theamount was also added to household incomesince negative expenditure is a form of in-come.

A few households reported negative valuesof disposable income or expenditure. In orderto include these households in the analysis neg-ative values were converted to $0.10.

Appendix 2: Prices and Commodities Used

The prices used are originally from the ABSConsumer Price Index quarterly series but re-weighted to match the HES Commodity CodeList and converted to have a base period ofDecember 1997. For the 1975–76 and 1984surveys where the quarter of enumeration wasnot given, an average of the four quarterlyprices was taken to prevail over the survey pe-riod. The prices were then re-weighted by themean budget shares for each period, wherenecessary, in order to obtain prices for the ninecommodities used in the demand system(namely food, power, accommodation, cloth-ing, medical expenses, transport, alcohol andtobacco, entertainment and miscellaneous ex-penses).

Endnote

1. See Pendakur (1998), Gouveia and Tavares(1995), and Cutler and Katz (1992).

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