intra-household resource allocation, consumer preferences and commodity tax reforms: australian...

2003 INTRA-HOUSEHOLD RESOURCE ALLOCATION 425

425

© 2003. The Economic Society of Australia. ISSN 0013–0249

THE ECONOMIC RECORD, VOL. 79, NO. 247, DECEMBER, 2003, 425–433

Intra-Household Resource Allocation, ConsumerPreferences and Commodity Tax Reforms:

Australian Evidence*

PAUL BLACKLOW and RANJAN RAYSchool of Economics, University of Tasmania, Hobart, Tasmania, Australia

Empirical analysis of household expenditure behaviour has tradi-tionally ignored the issue of resource allocation between householdmembers, assuming that they have identical or unitary preferences.This paper relaxes that assumption, develops a household sharing ruleand proposes intra-household demand systems that are able to identifydifferences in the preferences of members from conventional data. Theresulting price and expenditure elasticities are used to demonstratethat collective demand models suggest different directions for commod-ity tax reforms to those implied by the traditional unitary model.

and the ‘sharing rule’ approach, based on a Paretoefficient sharing rule between household members.4

Crucial to the non-unitary models is the relative‘power’ of individual members in the household.5

Notwithstanding significant methodological advances,empirical evidence on non-unitary or collective choicemodels in the consumer demand literature is virtu-ally nonexistent. There are two principal reasons:(a) absence of the required disaggregated informa-tion on the earnings and expenditure of the house-hold members, and (b) lack of an intra-householddemand system that is explicitly based on a resourceallocation mechanism and takes account of thevarying preferences inside the household. As Basu(2001) has recently pointed out, a distinctive, perhapslimiting, characteristic of the literature on non-unitary models is that the welfare weights assignedto the household members are fixed and exogenousto household decisions.

I IntroductionEmpirical analysis of household expenditure has

traditionally been based on the unitary model thatassumes the household members share identicalpreferences. The assumption of common preferenceordering among family members can be traced toSamuelson (1956) and Becker (1981). The assump-tion of common preferences, also underlines muchof the literature on optimal commodity taxes andtax reforms via its linkage with utility theory andmaximisation of household welfare.1 The unitarymodel has been increasingly challenged in recentyears through attempts at incorporating the divergentand conflicting preferences of different family mem-bers. Examples include the cooperative bargainingmodels,2 the non-cooperative bargaining models,3

* The research for this paper was supported by anAustralian Research Council (Large) grant to the secondauthor. A set of helpful remarks on an earlier version fromProfessor Harry Bloch and from two anonymous refereesis gratefully acknowledged. The disclaimer applies.

Correspondence: Paul Blacklow, School of Economics,University of Tasmania, GPO Box 252-85 Hobart, Tasmania7001, Australia. Email: [email protected]

1 See, for example, Atkinson and Stiglitz (1980), Ray(1999).

2 Examples include Manser and Brown (1980), McElroyand Horney (1981), Moehling (1995).

3 Examples include Kanbur and Haddad (1994), Lundbergand Pollak (1994).

4 Examples include Chiappori (1988), Browning andChiappori (1998).

5 See Pollak (1994).

426 ECONOMIC RECORD DECEMBER

The principal motivation of this study is to fillthese gaps in the empirical demand literature. Thepaper proposes a welfare maximisation-based house-hold resource-sharing rule, which is used to derivecollective household demand models. The resource-sharing rule, which is endogenously derived andestimated on budget data, is shown to play a usefulrole in identifying the separate preference parameterestimates of the individuals inside the household.The paper proposes alternative methodologies forderiving intra-household demand models that incor-porate the preferences of the individual householdmembers, based on the household-sharing rule intro-duced here. The alternative intra-household demandmodels are estimated and the expenditure and priceelasticities compared not only with one another butalso with those of the standard demand system basedon the unitary model.

The paper then demonstrates the policy use of theintra-household demand models proposed here, byusing the demand estimates in tax reform analysis.One of the chief policy applications of empiricaldemand analysis in recent years has been in usingthe price and expenditure elasticities to calculate thedirection of welfare improving marginal commoditytax reforms.6 The results of these studies, which areall based on the unitary model, generally suggestthat the direction of marginal commodity tax reformsare insensitive to changes in demand specification.The present study compares the direction of mar-ginal commodity tax reforms between the unitaryand intra-household demand models, and alsobetween the alternative variants of the latter. Animportant finding of this study is that the picture ofrobustness of marginal tax reforms to demand speci-fication in the unitary model does not extend to thenon-unitary case. The directions of commodity taxreforms are sensitive to whether the unitary or thecollective demand model is used to calculate therequired price elasticities.

The plan of this paper is as follows. The theoreticalframework is presented and the estimating equationsare derived in Section II. In Section II, Part (i)presents the resource-sharing rule inside the house-hold, Part (ii) derives the alternative intra-householddemand models that are based on the resource-sharing rule, and Part (iii) presents the marginalsocial cost expressions that provide the basis for thetax reform calculations. The data are briefly describedin Section III. The results are presented and analysed

in Section IV. The paper ends on the concludingnote of Section V.

II Theoretical FrameworkThe household is assumed to be involved in a

two-step welfare maximisation exercise in order toarrive at the intra-household demand model. Theassumption of weak separability between goods andleisure is required for this two-step exercise. In stepone, the household decides on the intra-householdresource-sharing rule by maximising its welfarefunction defined over the earnings of the individualmembers. In step two, the household, using theresource-sharing rule thus derived, decides on thevarious quantities by maximising preferences sub-ject to the individual budget constraints implied bythe resource-sharing rule. The distinction betweenthe intra-household demand equation and the tradi-tional unitary model stems from the fact that theformer recognises the individual preferences and theresource-sharing rule, the latter does not. This paperintroduces two variants of intra-household demandmodel which differ in the manner the individualpreferences are taken into account on the way toobtaining aggregate household demand that can beestimated on conventional expenditure informationon the aggregate household.

To keep this exercise manageable, we consideronly households that consist of a man and a woman,both of whom are working, with no children orelderly dependents. In Part (i), we introduce anextension of the resource-sharing rule, originallyproposed in Koolwal and Ray (2001), and inPart (ii), we derive the alternative forms of the intra-household demand model.

(i) Resource Allocation Inside the HouseholdFollowing the ‘collective approach’ outlined in

Koolwal and Ray (2001), the household welfare orutility function is given by:

U = θ(z)u1(q) + (1 − θ(z))u2(q), (1)

where u1, u2 denote, respectively, the individualutilities of the woman and the man specified as afunction of goods and leisure, q. The additivityassumption in (1) implies that the marginal rateof substitution between the utilities of the womanand of the man that keeps aggregate householdutility, U, unchanged is independent of the individualutility levels u1 and u2. The balance of power in thehousehold (θ) is dependent of the vector of earnings(z1, z2). As θ increases, the ‘power’ of the womanincreases. The ‘collective approach’ either considersθ to be fixed or specifies the earnings variables to

6 See, for example, Ahmad and Stern (1984), Decosterand Schokkaert (1990), Madden (1996), Ray (1997, 1999).


be exogenous to the analysis, so that θ is alsoexogenously given. The unitary model imposes therestriction of common preferences on (1), i.e. u1(q)= u2(q) = 8(q).

To simplify the problem, let us assume that leisurechoice is separable from the choice of goods andspecify the individual utilities u1( ) and u2( ) to befunctions of leisure only. Thus, the problem facing thehousehold is to maximise its utility of leisure subjectto achieving a certain level of expenditure, x. Specify-ing the individual utilities, u1(l1, l2) and u2(l1, l2), asfunctions of the leisure hours of the woman and ofthe man, l1 and l2, respectively, allows the individualsto care for their spouses’ leisure, besides their own.

The household’s welfare maximisation problem cantherefore, be written as:

max,w.r.t l l1 2{ }

θ(z)u1(l1, l2) + (1 − θ(z))u2(l1, l2) (2)

subject to

w1(T − l1) + w2(T − l2) + y ≥ x, (3)

where z denotes the vector of earnings, w1 and w2

are the market wage of women and men, respect-ively (considered exogenous in this analysis), T istotal time available, x is aggregate household expendi-ture and y is unearned income. If we recognise leisurehours as simply the total time available less labourhours (h1, h2), then household’s welfare maximisationis equivalent to minimising the function:

θ(z)u1(h1, h2) + (1 − θ(z))u2(h1, h2) (4)

subject to the constraint,

w1h1 + w2h2 + y ≥ x. (4a)

Note that the utilities are decreasing in labour hours.We choose a simple functional form for the female

power variable:

θφ

( , )

z zz

z z1 21

1 2

=+

(5)

where zi = wihi is labour earnings (i = 1, 2). φallows the female’s ‘power’ to exceed her share ofearnings if φ < 1, and to fall short of it if φ > 1. Atest of φ = 1 constitutes a test of Basu’s (2001)assumption that the female’s share of adults earningsis a correct measure of her bargaining power.

Let us choose the following functional forms foru1, u2:

u1(h1, h2) = h1−ρ11h2

−ρ12 (6a)

u2(h1, h2) = h1−ρ21h2

−ρ22 (6b)

ρ11 > 0, ρ12 > 0, ρ21 > 0, ρ22 > 0

Note that while ρ11 and ρ22 denote the individuals’disutility from their own work hours, ρ12 and ρ21

denote the disutility from their spouse’s work hours.For simplicity of estimation, we assume symmetricdisutility, i.e. ρ12 = ρ21. After routine manipulation,the welfare maximisation exercise yields the follow-ing earnings share equations for female and male,respectively.

sw h

Z

u u h u u

u u11 1 11 1 12 2 1 1 2 1

11 12 1 12 22 2

1

1

( ) ( )

( ) ( )( )≡ =

+ − + −+ + − +

θρ θ ρ θθ ρ ρ θ ρ ρ

(7a)

sw h

Z22 2 ≡

=− + + −

+ + − + ( ) ( )

( ) ( )( ),

1

122 2 12 1 2 2 2 1

11 12 1 12 22 2

θ ρ θρ θθ ρ ρ θ ρ ρ

u u h u u

u u(7b)

where Z = w1h1 + w2h2 is total household earnings,u1 and u2 are the individual utilities defined earlier

and θ ∂θ∂

θ ∂θ∂1

12

2

0 0 , = > = <h h

denote the respons-

iveness of the female’s bargaining power to femaleand male labour hours, respectively. In conven-tional treatments of the collective model, θ1 = θ2 = 0.Assuming that the unearned income variable, y, isinvariant to labour hours (h1, h2), it drops out inthe constrained minimisation of (4), subject to (4a).Consequently, y does not appear in the earnings shareequations (7a) and (7b).

(ii) The Intra-Household Demand ModelsThe two intra-household demand models that

are introduced here will be referred to as IHI (intra-household model with individual optimisation) andIHJ (intra-household model with joint optimisation).While the former is based on the individual maxim-ising her/his own preferences, the latter is based onthe household members jointly maximising theirpreferences, as a θ-weighted sum of their individualpreferences. Both these models assume ‘Price Inde-pendent Generalised Logarithmic’ (PIGLOG) pre-ferences for the individuals inside the householdbut allow the preference parameters to vary betweenthe individuals. In more detail, the alternative modelsare as follows:

Intra-Household Demand Model with IndividualOptimisation (IHI)

Individual i’s preferences are given by:

vx a

bi

i i

i

log log ( )

( )=

− pp

(8)

i = 1, 2


where xi = θ ix is the resource available to i based onthe resource allocation rule, outlined above, θ i is thewelfare weight of i, p is the vector of prices, and xis the total expenditure resources available to thehousehold. This leads to individuals i’s demand equa-tion for item j.

w ab

b

x

aji

ji j

i i

i ( )

( )

( )log

( ),= +

p

p

p p(9)

where aij(p), bi

j(p) are the derivatives of log ai(p),bi(p), respectively, with respect to the log of priceof j. Assuming the ‘Almost Ideal Demand System’(AIDS) functional forms for ai(p) and bi(p), the indi-vidual’s budget-share for item j is given by:

w px

aji

ji

jki

kk j

ii

i log log

( )= + +

∑α γ β

p(10)

i = 1, 2j = 1, . . . , n

where

log a pi iji

j

n

j jki

kj

( ) log p = + +=∑ ∑∑α α γ0

1

12 log pj log pk

and b pik

k

ki

( ) .p = ∏β β0

Since the individual budget-shares, w ij, are not

observed on conventional survey data, only the aggre-gate budget-shares, we aggregate the individuals’budget-shares wi

j into household level budget-shares,wj, as follows:

wj = θw 1j + (1 − θ)w2

j (11)

where w1j, w2

j are given by (10) above. To keepthe analysis simple and the estimation manageable,we have assumed that the weight parameter θ is com-modity invariant, i.e. θj = θ for all j. In the empiricalapplication, we assume that the γ jks are invariant be-tween individuals, i.e. γ i

jk = γ jk. The IHI budget-shareequations are given by:

w pjh h j h j jkk

n

k ( ) log = + − +=∑θ α θ α γ1 2

1

1

+ + − log( ) ( ) log( )θ β θ βh j h h j h1 1 2 21L L (12)

j = 1, . . . , nwhere the subscript h denotes household, and L i

h

denotes the price deflated real expenditure of indi-vidual i in household h, i.e.

log( ) log

( )Lh

i hi

hi

x

a=

θp

(13)

i = 1, . . . , 2If individual preferences are identical, i.e. α1

j = α2j,

β1j = β2

j, then the intra-household AIDS (IHI), givenby (12), specialises to the unitary AIDS model, with

the resource-sharing variable, θh, having an impacton the budget-share only through the intercept term.

The estimation of (12) follows the two-stepdecision-making outlined earlier. In step one, weestimate φ, ρ11, ρ12, ρ22, from (7a) on earnings data.Since s1 + s2 = 1 (7b) is not independent of (7a). Con-sequently, the sharing rule parameters are estimatedby single equation estimation of (7a) using non-linear least squares. In step two, the estimated φ isused to generate the θh variable via (5). These (θh)are then used to identify and estimate the individualspecific parameters, (α i

j, β ij), besides the common

preference parameters, γ jk, in the second step estima-tion of (12) using full information maximimumliklihood estimation (FIML). One limitation of thistwo-step estimation procedure is that the θhs, havingbeen generated in the first step, will become randomregressors with measurement errors leading to poss-ible inconsistency in the demand estimates.

Intra-household Demand Model with JointOptimisation (IHJ)

The household utility function, V, is defined as aθ-weighted function of the individual utilities, vi:

V = θv1 + (1 − θ)v2 (14)

where vi is defined in (8). Hence,

Vx a

b

log( ) log ( )

( )=

−

θ θ 1

1

pp

+ −− −

( )

log(( ) ) log ( )

( ),1

1 2

2θ θ x a

b

pp

(15)

where, as before, θ is the female power variable.Assuming, as before, AIDS functional forms for ai(p)and bi(p), we obtain, after routine manipulation, thecost or expenditure function, x, of the household. Inlogarithmic form, it is given by:

log x = B0 − B1 + β0B2V, (16)

where:

Bb b0 2 1

1

1

( ) ( ) ( )=

+ −θ θp p

θ θ˜ ( ) ( ) ˜ ( )a b a b1 2 2 11p p+ −[ ] (17a)

Bb b1 2 1

1

1

( ) ( ) ( )=

+ −θ θp p

( log ) ( ) ( )log( ) ( )θ θ θ θb b2 11 1p p+ − −{ }[ ] (17b)

Bb b

b b2

1 2

2 11

( ) ( )

( ) ( ) ( )=

+ −p p

p pθ θ(17c)

and ã i = log ai(p). (17d)


On application of Shephard’s Lemma to (16), weobtain the IHJ budget-share equations as follows:

w B BB

Bx B Bj log ,= − + − +[ ]′ ′

′0 1

2

20 1 (18)

where

BB

pB

B

pB

B

pi i i

′ ′ ′0 1 2 log

, log

, log

= = =∂

∂∂

∂∂

∂0 1 2

Note that, as with IHI (12), if individual’s prefer-ences are identical, then IHJ (8) specialises to theconventional unitary AIDS model.

(iii) Marginal Tax ReformsIf λ j ( j = 1, . . . , n) denotes the marginal social cost

of raising an extra unit of revenue by taxing the jthcommodity, then

λ∂ ∂∂ ∂j

j

j

W p

R p

/

/,= − (19)

where W is social welfare defined over the house-hold utilities, pj is the tax inclusive consumer priceof j, and R is the aggregate revenue that is to beraised. Equation (19) assumes that taxes (tj) are passedon fully to the consumer. Using Roy’s identity, λ j

can be expressed as follows.7

λω

j

h jhh

j k k kjk

n

x

X X e

,=+

∑

∑=

K1

(20)

j = 1, . . . , nwhere xjh is money expenditure on item j by house-

hold h, X xj jhh

= ∑ is aggregate money expenditures

on item j, Kk

k

k

t

p = is the tax rate on k, ωh is the

social marginal utility of income to household h, andekj is the aggregate uncompensated price elasticity ofk w.r.t. j.

If λj ≠ λk, then social welfare can be increasedby reducing taxes on commodities with high λj andraising taxes on others. In other words, a welfareimproving tax reform rule is: if λj > O (mean λ),then tax on j (tj) should be reduced, and if λj < O,then, tj should be increased. The scope for welfareimproving commodity tax changes exists until theλjs are all equal, which characterises the state wherecommodity taxes are optimal. Hence, a ranking ofthe λjs in increasing order of magnitude provides thedirection of marginal tax reforms, with items withlower ranked λj being candidates for tax increases,

and those with higher ranked λj candidates for taxdecreases. It is clear from (20) that λjs depend on,among others, the uncompensated price elasticities(ekj), which are calculated from the demand systemparameter estimates. This establishes the potentialsensitivity of tax reform direction to the demand sys-tem used to calculate the price elasticities, an issuethat we examine empirically in this study.

Following Ahmad and Stern (1984), nearly all themarginal tax reform studies use the isoelastic socialwelfare function to calculate the welfare weights,ωh. We continue this practice in this study. Normal-ising ω1 = 1 for the poorest household, this leads to

ωε

hh

x

x ,=

1 (21)

where ε ≥ 0 denotes inequality aversion, and xh isthe aggregate expenditure of household h.8 Note thatsince we are considering only two-adult householdsconsisting of a working woman and a working man,there is no need to correct for household size andcomposition using equivalence scales.

III DataThe demand estimation is based on pooled ex-

penditure data for 19 716 adult couples (both spousesworking), with no dependents, from the 1975–76,1984, 1988–89, 1993–94 and 1998–99 HouseholdExpenditure Surveys (HES) published by the Austra-lian Bureau of Statistics (ABS). The prices for thebroad commodities are derived from the capital citybased CPI series. The demand estimation, usingFIML, is based on observations that are weighted bythe household’s survey weights.

The resource-sharing parameter, φ, is estimated,along with the labour hours disutility parameters (ρ11,ρ12, ρ22), from the application of non-linear leastsquares to (7a) on the 1998–99 HES. The earningsand hours information are taken directly from theperson records in the 1998–99 HES. As with thedemand estimation, the resource-share equation isestimated with data on adult-couple households withboth spouses working and with no dependents.

The tax reform calculations are performed on thedata in the 1998–99 HES on two-adult householdswith no children or dependents.9 The actual tax rates

7 See Ahmad and Stern (1984).

8 However, a referee criticises this social welfare functionby arguing that ‘not only is it undemocratic, but this SWFalso violates Harberger’s third basic postulate of appliedwelfare economics that a dollar is a dollar’.

9 Note that the tax rules implied by the empirical resultspresented later should be considered to be illustrative ratherthan taken seriously for policy purposes.


10 See Blacklow and Ray (2002).

Table 1Non-Linear Estimates of Earnings Share Equation

Parameters (7a, 7b)

Parameter Estimate (standard error)

φ0 0.832 (0.0058)ρ11 0.013 (0.0002)ρ12 3.957 (0.0176)ρ22 4.326 (0.0114)

Table 2Preference Heterogeneity Between Women and Men

Difference in Estimated difference (standard error)preferenceparameters IHI IHJ

α11 − α2

1 −0.010 (0.017) −0.106 (0.154)α1

2 − α22 −0.075* (0.030) 0.215 (0.238)

α13 − α2

3 −0.012* (0.004) 0.188 (0.134)α1

4 − α24 0.064* (0.015) −1.512* (0.315)

α15 − α2

5 0.003 (0.031) −1.544* (0.353)α1

6 − α26 0.002 (0.011) 0.973* (0.138)

α17 − α2

7 0.097* (0.021) 1.485* (0.340)α1

8 − α28 −0.116* (0.013) −2.167* (0.297)

α19 − α2

9 0.047* (0.016) 2.255* (0.285)β1

1 − β21 −0.002 (0.003) −0.0025 (0.002)

β12 − β2

2 0.011* (0.005) −0.0014* (0.0007)β1

3 − β23 0.001 (0.0007) −0.0004 (0.0004)

β14 − β2

4 −0.008* (0.002) 0.0064* (0.001)β1

5 − β25 0.0003 (0.005) 0.0115* (0.003)

β16 − β2

6 −0.0009 (0.002) 0.0014* (0.0003)β1

7 − β27 −0.013* (0.003) −0.0036* (0.001)

β18 − β2

8 0.018* (0.002) −0.003* (0.0006)β1

9 − β29 −0.006* (0.003) −0.008* (0.002)

* Statistically significant at 5 per cent.Note: The items are: Food & Non-Alcoholic Beverages; Housing(rent, mortgage interest, equipment and services); Fuel, Electri-city and Gas; Clothing and Footwear; Transport & Equipment;Health and Personal Care; Alcohol & Tobacco; Entertainment;Miscellaneous.

(Kk) that are required to calculate the marginalsocial cost, λj (see (20)) are the post-GST effectivetax rates in Australia in 2000–01 calculated and usedin our study on optimal commodity taxes.10

The demand estimation and the tax reform analysisare carried out on the following nine good disag-gregation of consumer expenditure: food and non-alcoholic beverages; housing (rent, mortgage interest,equipment and services); fuel, electricity and gas;clothing and footwear; transport and communications;medical and personal care; alcohol and tobacco; enter-tainment; and miscellaneous (including education andcredit card interest payments as the main items).

IV ResultsTable 1 presents the results of estimating the

resource-share equation (7a). The parameter estimates,which are all well determined, suggest that the femalecares more for the leisure of her partner (W12 = 3.96)than for her own (W11 = 0.013). Moreover, the male’sdisutility from work (W22 = 4.33) exceeds that of thefemale (W11 = 0.013) by a long margin. The par-ameter of crucial importance for the rest of this studyis the resource-sharing parameter, φ. The φ estimateof 0.831, which is similar to the φ estimate of 0.889for Nepal reported in Koolwal and Ray (2001),suggests that the woman’s share of wage earningsin the household is an understatement of her truebargaining power. Note from Table 1 that φ = 1 iseasily rejected by the data.

Table 2 contains evidence on the preferenceheterogeneity between women and men that formsthe basis of the intra-household demand models thatare proposed and estimated here. For reasons of spaceand clarity of presentation, we do not report theparameter estimates themselves but these are avail-able on request. Table 2 reports, for the two intra-household demand models, the difference (along withits standard error) in the estimates of αi, βi betweenthe spouses, i.e. M1

i − M2i, N1

i − N2i (i = 1, . . . , 9). Note

that M1i = M22

i and N1i = N2

i for the unitary AIDS, andthat the γijs are identical across individuals in all themodels. Table 2 provides considerable evidence ofpreference heterogeneity between the spouses, sinceseveral of the differences between the parameterestimates are statistically significant. However, theintra-household demand systems don’t agree beyondthat. The magnitude of the difference and, some-times, even the sign vary sharply between the twointra-household demand models. One of their rarepoints of agreement is that the food parameterestimates (α1, β1) are invariant between the spousessince the difference is statistically insignificant inall four cases. The overall message is that, while theassumption of identical preferences underlying theunitary demand model is decisively rejected bythe data, the nature and magnitude of preferenceheterogeneity is sensitive to the manner in whichthe individual preferences are aggregated into thehousehold demand model.

Tables 3 and 4 compare the expenditure and ownprice elasticities between the unitary and the twovariants of the intra-household demand models. Theown price elasticities show a good deal of variation


Table 3Expenditure Elasticities

Item Unitary IHI IHJ

1. Food and non-alcoholic beverages 0.526 0.595 0.6032. Housing: rent, mortgage interest, equipment and services 1.059 1.051 1.0503. Fuel, electricity and gas 0.012 0.210 0.1714. Clothing and footwear 1.437 1.343 1.3355. Transport and equipment 1.298 1.265 1.2606. Health and personal care 0.772 0.796 0.8007. Alcohol and tobacco 1.294 1.237 1.2358. Entertainment 0.746 0.857 0.8689. Miscellaneous 1.409 1.331 1.271

IHI, intra-household demand model with individual optimisation; IHJ, intra-household demand model with joint optimisation

Table 4Own Price Elasticities


1. Food and non-alcoholic beverages −0.256 −0.405 −0.4892. Housing: rent, mortgage interest, equipment and services −0.905 −0.904 −0.8393. Fuel, electricity and gas 0.377 0.409 0.8264. Clothing and footwear 0.702 0.754 0.4955. Transport and equipment −1.058 −1.025 −0.7786. Health and personal care 0.174 0.143 0.1747. Alcohol and tobacco −1.151 −1.326 −1.9348. Entertainment −0.508 −0.705 −1.1539. Miscellaneous −0.840 −0.877 −1.634


between the demand models, though more for someitems, less for others. The variation generally seemsto be much less between the unitary and the IHImodels than between the intra-household demandmodels (IHI, IHJ). In contrast, the expenditure elasti-cities seem quite robust to demand specification.

Table 5 provides the λj estimates, i.e. the socialmarginal cost of raising revenue by taxing item j(see (20)) implied by the elasticities, tax rates etc.The table reports the λj estimates, correspondingto the different demand models, at three values ofinequality aversion (ε). The numbers in bracketsdenote the λj ranking when they are arranged inincreasing order. Let us recall that lower ranked itemsare candidates for tax increases, higher ranked itemsare candidates for tax reductions. The λj rankings,rather than the magnitudes, are of policy interest sincethey indicate directions of marginal tax reform. Con-sistent with our earlier observation, the λj rankingsvary a good deal more between the non-unitarymodels than between the unitary model and the

individual optimising version of the intra-householdmodel (IHI). This reflects the fact that IHI is closerin spirit to the unitary model than IHJ. The steadyincrease in the ranking of λFood in the IHJ case fromthird (ε = 0.0) to seventh (ε = 5.0), is consistent withAhmad and Stern’s (1984) observation that atlow ε-values food is a candidate for tax increase,but becomes a candidate for tax decrease at highε-values. This result is explained by the fact that atvery low values of ‘inequality aversion’, efficiencyconsiderations prevail, but at high levels of inequal-ity aversion, equity dominates so that the directionof tax reform reverses for a necessity item such asfood. Note, however, that in contrast to the IHJ case,the λFood ranking is reasonably robust to ε in case ofthe unitary and IHI models.

Table 6 provides formal evidence on the sensitivityof the directions of marginal tax reform to demandsystem by reporting the Spearman rank correlation(Js) (with standard errors and z-values for H0: rs = 1)between the λ rankings in the three demand systems.


Table 5Marginal Social Cost (λj) Estimates

Demand Model†


ε = 0 ε = 2 ε = 5 ε = 0 ε = 2 ε = 5 ε = 0 ε = 2 ε = 5

Food and non-alcoholic beverages 0.126 0.057 0.018 0.116 0.043 0.011 0.114 0.003 0.0003(6) (6) (5) (5) (6) (5) (3) (5) (7)

Housing: rent, mortgage interest, 0.110 0.047 0.014 0.110 0.038 0.009 0.113 0.002 0.0002equipment & services (3) (4) (4) (4) (3) (4) (2) (2) (4)Fuel, electricity and gas 0.120 0.056 0.019 0.109 0.041 0.011 0.142 0.005 0.0005

(5) (5) (6) (3) (5) (6) (6) (7) (8)Clothing and footwear 0.390 0.159 0.044 0.335 0.111 0.023 0.294 0.005 0.0002

(9) (9) (9) (9) (9) (9) (8) (8) (3)Transport & equipment 0.096 0.040 0.011 0.098 0.033 0.007 0.096 0.002 0.0001

(2) (1) (1) (2) (2) (1) (1) (1) (1)Health and personal care 0.092 0.040 0.013 0.091 0.032 0.008 0.120 0.003 0.0003

(1) (2) (2) (1) (1) (2) (4) (3) (6)Alcohol & tobacco 0.238 0.099 0.028 0.304 0.102 0.022 0.376 0.023 0.001

(7) (7) (7) (8) (8) (8) (9) (9) (9)Entertainment 0.301 0.132 0.041 0.220 0.078 0.018 0.129 0.003 0.0003

(8) (8) (8) (7) (7) (7) (5) (4) (5)Miscellaneous 0.110 0.045 0.013 0.120 0.040 0.008 0.202 0.003 0.0002

(4) (3) (3) (6) (4) (3) (7) (6) (2)O‡ 0.147 0.063 0.019 0.149 0.051 0.011 0.289 0.005 0.0003

† Figures in brackets denote λ-rank in ascending order.‡ O is a weighted average of the λ j’s, where the weights are the quantity demand by all households of commodity j.

11 See, for example, Apps and Rees (1988), Piggott andWhalley (1996).

Note that, while at 5% significance level the hypoth-esis of rank invariance between the unitary AIDSand IHI cannot be rejected, the reverse is true for theother comparisons. In other words, the directions ofmarginal tax reforms do alter significantly betweenunitary AIDS and IHJ and between IHI and IHJ.The results confirm that the general picture of insen-sitivity of marginal tax reforms to demand system,which the literature conveys, is not true once weallow for resource-sharing between spouses andvarying preference inside the household in an intra-household demand system.

VI ConclusionsThis paper examines the implications of model-

ling intra-household behaviour and allowing prefer-ences to vary within the household for commoditytax reforms. Notwithstanding significant methodo-logical advances in modelling intra-household beha-viour via the various types of collective choicemodels, the empirical evidence remains limited.Moreover, there has been little attempt to work outthe public policy implications of departing from theconventional unitary model of household behaviour.

In the taxation literature, while there have beenattempts to examine the issue of tax unit in theincome tax context from the view point of intra-household behaviour,11 there has not been any suchattempt in the context of commodity taxes. This paperattempts to overcome these gaps in the literature byproviding Australian evidence on intra-householdpreferences and examining its implications for mar-ginal commodity tax reforms. Methodologically, thepaper proposes and uses an intra-household resource-sharing rule that helps to identify, up to a point, theintra-household preference parameters on conven-tional budget data. The empirical evidence rejectsthe assumption of identical preferences inside thehousehold underlying the unitary household model.The policy significance of this result is underlinedby the further empirical evidence, which confirmsthe sensitivity of the directions of marginal tax re-forms to departures form the unitary model frame-work used in tax reform analysis.


Table 6Spearman Rank Correlation (with z-statistics)

Between λ-rankings of Unitary, IHI, and IHJ Demand Models

ε = 0 ε = 1 ε = 2 ε = 5 ε = 25

Unitary, IHIRank Correlation (Js) 0.900 0.933 0.950 0.983 0.983z-Stat. (H0: rs = 1) −1.60 −1.07 −0.80 −0.27 −0.27

Unitary, IHJRank Correlation (Js) 0.633 0.633 0.667 0.467 0.700z-Stat. (H0: rs = 1) −5.87 −5.87 −5.33 −8.53 −4.80

IHI, IHJRank Correlation (Js) 0.717 0.800 0.783 0.533 0.750z-Stat. (H0: rs = 1) −4.53 −3.20 −3.47 −7.47 −4.00


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