Where Did All Money Go

8/10/2019 Where Did All Money Go

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109Journal of Marketing Vol. 72 (November 2008), 109131

2008, American Marketing AssociationISSN: 0022-2429 (print), 1547-7185 (electronic)

Rex Y. Du & Wagner A. Kamakura

Where Did All That Money Go?Understanding How Consumers

Allocate Their Consumption BudgetAll types of consumer expenditures ultimately vie for the same pool of limited resourcesthe consumersdiscretionary income. Consequently, consumers spending in a particular industry can be better understood inrelation to their expenditures in others. Although marketers may believe that they are operating in distinct andunrelated industries, it is important to understand how consumers, with a given budget, make trade-offs betweenmeeting different consumption needs. For example, how much would escalating gas prices affect consumerspending on food and apparel? Which industries would gain most in terms of extra consumer spending as a resultof a tax rebate? Answers to these questions are also important from a public policy standpoint because theyprovide insights into how consumer welfare would be affected as consumers reallocate their consumption budgetin response to environmental changes. This study proposes a structural demand model to approximate thehousehold budget allocation decision, in which consumers are assumed to allocate a given budget across a fullspectrum of consumption categories to maximize an underlying utility function. The authors illustrate the modelusing Consumer Expenditure Survey data from the United States, covering 31 consumption categories over 22

years. The calibrated model makes it possible to draw direct inferences about the trade-offs individual householdsmake when they face budget constraints and how their relative preferences for different consumption categoriesvary across life stages and income levels. The study also demonstrates how the proposed model can be used inpolicy simulations to quantify the potential impacts on consumption patterns due to shifts in prices or discretionaryincome.

Keywords : consumer expenditures, demand system, consumption, household budget allocation

Rex Y. Du is Assistant Professor of Marketing, Terry College of Business,University of Georgia (e-mail: [email protected]). Wagner A. Kamakurais Ford Motor Co. Professor of Global Marketing, Fuqua School of Busi-ness, Duke University (e-mail: [email protected]).

The majority of models of consumer demand in themarketing literature focus on within-category pur-chase decisionsfor example, incidence, brandchoice, and quantity within a single product category (e.g.,

Chiang 1991; Chintagunta 1993; Gupta 1988). Morerecently, several models have been developed to analyzechoice behavior across multiple categories using shoppingbasket data (Seetharaman et al. 2005). For example, Man-chanda, Ansari, and Gupta (1999), Russell and Petersen(2000), and Chib, Seetharaman, and Strijnev (2002) exam-ine multicategory purchase incidence decisions. Russell andKamakura (1997), Ainslie and Rossi (1998), Iyengar,Ansari, and Gupta (2003), and Singh, Hansen, and Gupta(2005) investigate multicategory brand choice decisions.Song and Chintagunta (2006) model multicategory inci-dence and brand choice decisions jointly, and Song andChintagunta (2007) allow for incidence, brand choice, and

quantity decisions across multiple categories.In contrast to research that focuses on multicategorychoice behavior, in which the budget for a particular shop-ping trip is allocated across a few selected product cate-

gories, few empirical studies in the marketing literaturehave focused on modeling how consumers allocate theirlimited discretionary income to meet different consumptionneeds, in which trade-offs must be made across a wide range

of expenditure categories (e.g., food, apparel, recreation,transportation, medical and personal care). The empiricalstudies that examine consumer expenditures either aredescriptive in nature (e.g., Ferber 1956; Ostheimer 1958),focusing on a particular demographic group (e.g., elderly[Goldstein 1968], working wives [Bellante and Foster1984]) or a particular consumption category (e.g., food[Rogers and Green 1978], energy [Fritzsche 1981], services[Soberon-Ferrer and Dardis 1991]), or use univariate mod-els that ignore the interdependencies across consumptioncategories (e.g., Du and Kamakura 2006; Rubin, Riney, andMolina 1990; Wagner and Hanna 1983; Wilkes 1995).

Empirical studies on consumption have been far more

common in economics than in marketing. In economics, themain issue has been the intertemporal trade-offs consumersmake when choosing between current and future consump-tion (e.g., Deaton 1992; Gourinchas and Parker 2002); here,all the consumption expenditures are typically lumped intoone aggregate account, and the real focus is on the accumu-lation of assets/debts. In the instances when economistsconsider the allocation of current consumption budget intodifferent products and services, the focus has been either ona small number of broad commodity groups, such as food,clothing, and housing (e.g., Deaton and Muellbauer 1980;


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Where Did All That Money Go? / 111

of categories. The pattern of zero consumptions varies fromhousehold to household and contains important informationabout individual preferences, making it crucial to modelthem explicitly. Unfortunately, such a requirement rules outany demand systems in which all categories are assumed tobe consumed by all households, an assumption we demon-strate subsequently to be vastly violated in householdexpenditure data. In other words, heavily censored expendi-ture data render many popular demand systems, such as theAIDS, Rotterdam, or translog, inapplicable because they areall derived from first-order conditions of constrained utilitymaximization problems, assuming the existence of interiorsolutions for all goods. As a result, they would predict posi-tive expenditures in all categories for all households, whichwould be biased and inconsistent with the actual data. Incontrast, we accommodate the binding nonnegative con-straints observed in household budget allocations byproposing a budget allocation model in which both thewhether-to-spend and the how-much-to-spend deci-sions result from a common utility maximization problem,allowing for inferences about a unified preference structurefrom both zero and nonzero observations. An importantadvantage of using a common utility function for both inci-

dence and quantity decisions is parsimony, which is desir-able given the high dimensionality of the demand system.The third challenge is that of unobservable heterogene-

ity. Consumer expenditure data consistently depict largevariations in the pattern of budget allocation across house-holds. Manifested in these patterns are the different con-sumption priorities of different households. Capturing theseindividual differences is important for models of budgetallocation because doing so can provide valuable insightsinto how consumers would respond differently to changesin external (e.g., price shocks, tax rebates) and internal(e.g., life stage changes) conditions. To account for hetero-geneity in preferences, existing studies of household budget

allocation have relied solely on demographic variables,such as age, income, ethnicity, and family composition.However, as the choice modeling literature has shown,demographics can often explain only a small portion of heterogeneity in consumer preferences. In the context of budget allocation, unobservable heterogeneity may berevealed through the interdependencies of consumptionacross categories. This is not a trivial task given the twochallenges (i.e., high dimensionality and binding nonnega-tive constraints) we discussed previously. Conversely, as weshow in our empirical application, accounting for unobserv-able heterogeneity is beneficial in that it leads to a moreflexible demand system at the aggregate level.

In summary, we believe that it is important for mar-keters to be able to infer the underlying cross-categorytrade-offs households make in allocating their consumptionbudget, so that we can then predict how these allocationswill change in response to shifts in prices or discretionaryincome and how differences in preferences across house-holds lead to different consumption patterns. To understandhow households allocate their consumption budget across afull spectrum of expenditure categories, we use a budgetallocation model built on an approach first proposed byWales and Woodland (1983) and then extended by Kao,

Lee, and Pitt (2001) (hereinafter, the KLP model), assumingthat households allocate their consumption budget to maxi-mize a utility function that is linear in the logarithms of quantity consumed less a constant for each category (this isalso referred to as the StoneGeary utility). This budgetallocation model tackles the aforementioned three chal-lenges, leading to a demand system that (1) is feasible for alarge number of consumption categories (which is not thecase with the KLP model), (2) allows for corner solutionsobserved in censored expenditure data, and (3) results in aglobally flexible aggregate demand system for each con-sumption category by obtaining household-level estimatesof the direct utility function. Next, we briefly review theLES model and describe our more flexible extension to theKLP model. Then, we apply our proposed factor-analyticrandom coefficients budget allocation model to the Con-sumer Expenditure Survey (CEX) data from the UnitedStates, covering 31 consumption categories over a period of 22 years. We conclude with a discussion and directions forfurther research.

Modeling Consumption Budget

AllocationOur main purpose in this study is to develop a reasonableas-if model that approximates how individual householdsallocate their consumption budget across a comprehensiveset of expenditure categories. Because each household con-sumes only a subset of all consumption categories, ourobserved expenditure data are censored. Thus, we need ademand system that can accommodate many consumptioncategories and allow for corner solutions. As we mentionedpreviously, these requirements rule out the most populardemand systems, such as the AIDS, Rotterdam, andtranslog models, all of which (1) quickly become impracti-cal for more than a couple dozen consumption categories

and (2) require nonzero consumption in all categories. Forthese reasons, we extend the KLP budget allocation modelto consider simultaneously whether-to-spend and how-much-to-spend decisions. Our model is distinguished fromthe KLP model in two important aspects. First, the KLPmodel is feasible only when the focus is on a small numberof consumption categories, accounting for only part of thehousehold budget (e.g., seven types of food items). How-ever, for a comprehensive analysis of household budgetallocation, the high-dimensionality challenge is inevitable.Rather than limiting the analysis to a high level of aggrega-tion or lumping a large number of distinct expenditure itemsinto an other category, our proposed approach affords theflexibility to cover the full spectrum of household consump-tion budget allocation at a low level of aggregation. Second,to account for a large number of consumption categorieswhile allowing for individual differences in category prefer-ences and a rich pattern of correlation in these preferencesacross categories, we extend the KLP model by imposing aflexible factor structure to the covariance matrix of the sto-chastic taste parameters that govern individual householdsconsumption priorities.

We assume that household h maximizes a continuouslydifferentiable, quasi-concave direct utility function G(x h)


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112 / Journal of Marketing, November 2008

over a set of J nonnegative quantities x h = (x1h, x2h, , x Jh),subject to a budget constraint p xh mh, where p = (p 1, p2,, pJ) > 0, p i is the price of good i, and m h is household hstotal consumption budget/discretionary income. Followingthe work of Wales and Woodland (1983) and Kao, Lee, andPitt (2001), we use the StoneGeary utility function, whichhas the following form:

where ih > 0, (x ih i) > 0, and J is the number of all avail-able consumption categories. The h subscript in ih impliesthat the utility function is household specific. The KuhnTucker conditions for the households optimization problemare as follows: G(xh)/ xih pi 0 for x ih = 0, and G(xh)/ xih pi = 0 for x ih > 0, such that p xh mh 0 , where denotes the Lagrange multiplier or marginal utility perdollar.

The budget allocation problem we described impliesthat the household incrementally allocates its discretionaryincome to the consumption category that produces the high-est marginal utility per dollar,

given the current consumption levels x h, until the budget isreached, . The solution of this optimizationproblem leads to the following expenditure system, which islinear in discretionary income and prices (thus the labelLES in the literature):

where and J* is the set of consumedgoods (i.e., with positive expenditures).

Note that the demand system given by Equation 2 isdefined only for a particular consumption regime J*. If thepattern of nonzero expenditures changes, both the interceptsand the slopes of the demand system will also change. Inother words, the model implies that there is an optimal con-sumption regime for each household at each combination of budget and prices, and only within a particular consumptionregime are category expenditures linear functions of budgetand prices; across consumption regimes, the demand sys-tem is piecewise linear. In addition, rather than imposingarbitrary censoring mechanisms, such as the Tobit regres-sion model (Amemiya 1974), the approach based on theKuhnTucker condition allows for zero consumption as acorner solution to a constrained utility maximization prob-lem. It also ensures that predicted expenditures will alwaysbe nonnegative and sum to the budget.

Unlike existing budget allocation analyses, which eitherignore heterogeneity or allow for heterogeneity onlythrough demographics, we take advantage of the multivari-ate nature of the estimation problem (i.e., 31 points of expenditure data per household) and obtain household-specific estimates of the preference parameters ( ih), which

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means that the slope parameters ( *ih) of the demand systemwill be unique to each household as well. 1 Because eachindividual household has a unique consumption regime(and, therefore, a different regime switching point) and adifferent set of demand function parameters, the impliedaggregate demand can be highly nonlinear, overcoming acommon criticism of the inflexibility of the original LESmodel.

Given the model we described, the researchers problemis to infer consumers utility function parameters (i.e., ihand i) given the observed budget allocations and prices.The KLP model deals with variation in preferences acrosshouseholds by treating ih as stochastic; that is, ih =exp( i + ih), where h ~ N(0, ). Kao, Lee, and Pitt (2001)demonstrate that estimation through maximum likelihood isfeasible only for simple problems with few consumptioncategories because it requires the evaluation of a multivari-ate normal cumulative density function. To circumvent thisserious limitation, Kao, Lee, and Pitt propose to estimatetheir model with simulated maximum likelihood.

Although the KLP approach simplifies estimation con-siderably, the model formulation still limits the number of consumption categories that can be handled (e.g., only

seven categories are considered). Specifically, the KLPmodel requires [(J 1) J]/2 parameters for the covariancematrix . An analysis of the CEX data with 31 consumptioncategories would require the estimation of (30 31)/2 =465 covariance terms. In addition, the stochastic formula-tion of ih in the KLP model does not allow for household-level estimates of the taste parameter, which can beachieved through our formulation. This distinguishing char-acteristic of our model is particularly important because theability to estimate the household-specific taste parameterih enables us to perform more realistic policy simulationsthat account for individual differences in consumption pri-orities and for a rich pattern of correlation in preferences

across categories.To account for unobserved heterogeneity in the tasteparameter ( ih) for each category i and still have a model of feasible size, we propose a factor-analytic extension of theKLP random coefficients model by extracting the principalcomponents of the covariance matrix of the stochasticterms:

(3) ih = exp( i + iZh + ih),and

(4) i = min(x i) exp(i), to ensure that x ih i > 0 for h,where


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e i = the geometric mean of the taste parameter ih forcategory i across the sample,

Zh = a p-dimensional vector of i.i.d. standard normalfactor scores for household h,

i = a p-dimensional vector of factor loadings for cate-gory i, and

ih = a random disturbance normally distributed withmean zero and standard deviation i.

Although i and i provide insights into the averagepreference for category i, the product of the factor loadings(i) and factor scores (Z h) will show how much higher orlower the (log) taste of household h is relative to the aver-age. Moreover, the factor loadings = {i} capture theessential information about how (log) tastes covary acrosscategories and households because the covariance matrixfor their distribution can be directly obtained as . Thus,if two categories i and j have high loadings ( ) of the samesign on the same dimensions of the latent factors (Z),households assigning a high (low) utility to one categorywill also assign a high (low) utility to the other. In otherwords, the results from our factor-analytic model can pro-vide valuable insights into how interrelated the consump-

tion categories are across consumers.In summary, a key benefit of our proposed factor-analytic random coefficients LES model (compared withthe KLP model) is that it enables estimation of the directutility function for each household in more realistic applica-tions with a large number of consumption categories (highdimensionality), many of which may not be consumed byall households (censored data). Moreover, our proposedfactor-analytic extension to the KLP model allows not onlyfor unobserved heterogeneity in the households taste ( ih)for each consumption category but also for a rich pattern of correlation in these tastes across categories. Details aboutthe estimation of our model with simulated maximum like-lihood appear in the Appendix.

Implications of the BudgetAllocation Model

A common criticism of the StoneGeary utility functionassumed in Equation 1 is that it does not allow for potentialcomplementarity between categories. Although thisassumption could be limiting when studying consumptionat a more micro level (e.g., pasta and pasta sauce should becomplementary because the utility derived from consumingthem together is greater than the sum of utilities derivedfrom consuming them separately), the additive separableutility assumed by the StoneGeary function is not asrestrictive in a broader analysis of how consumers allocatetheir discretionary income, because at that point, all con-sumption categories are ultimately substitutes as they com-pete for the same budget.

Furthermore, as Gentzkow (2007, pp. 71415) dis-cusses, separating complementarity between consumptioncategories from correlation of consumer preferences acrosscategories would require additional variables that discrimi-nate among consumption categories and/or longitudinaldata for each household. Unfortunately, because consumer

expenditure surveys (e.g., the CEX) are usually done on anannual basis, so that the analyst has only one observation onhow the household allocated its consumption budget acrossvarious expenditure categories, it is not possible to discerntrue complementarity between categories from correlationin consumer preferences across categories. Finally, giventhe high dimensionality involved in modeling householdsbudget allocations across a comprehensive list of expendi-ture categories, it is empirically intractable to considerpotential interaction effects among all the categories (e.g.,[30 31]/2 = 465 additional parameters would be needed toallow for all the potential interaction effects in the utilityfunction in our analysis). In summary, for both theoreticaland practical purposes, in a household budget allocationanalysis such as ours, a main-effect-only utility function,such as the StoneGeary utility, should be viewed as a rea-sonable as-if model, which precludes complementaritybetween consumption categories.

By accounting for unobservable heterogeneity in prefer-ences across households, our factor-analytic random coeffi-cients LES model produces a globally flexible demand sys-tem when aggregated cross-sectionally. At the individuallevel, the additive separable StoneGeary utility function

implies that consumption of one category does not interactwith consumption of another category. This means thatpreferences for different consumption categories are locallyindependent (i.e., within a particular household, consump-tion of one category does not affect the marginal utility of consuming another category). However, in our proposedmodel, preferences for different consumption categories donot need to be independent across households, because thefactor structure embedded in ih allows tastes to be globallycorrelated, making it possible, for example, that consumerswho have a high (relative to other households) preferencefor tobacco products also have a high preference for alcoholconsumption.

The own- and cross-price elasticities implied in ourmodel for consumption categories i and j are defined at thehousehold level, respectively, as follows:

where

Note that these elasticities depend on the households factorscores (Z h) and the factor loadings for the particular cate-gories involved ( i).

Note also that the elasticities are defined at the house-hold level. Given that the taste parameters ih are correlatedacross consumption categories and households (accordingto the pattern reflected in the latent factors), our model

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model parameters ( i), and then we averaged these expectedshares within each income decile. We report the actual andmodel-implied cross-sectional Engel curves for some of theproduct categories in Figure 4, which shows that the curvesimplied by our proposed model conform well to theirobserved counterparts. Most important, Figure 4 shows thatour factor-analytic random coefficients formulation canaccommodate monotonically increasing shares (as incomedecreases) for essential categories (e.g., electricity, tele-phone, food at home) and decreasing shares (as incomedecreases) for nonessential categories (e.g., food outside thehome, recreation, education, lodging away from home).Moreover, the model is flexible enough to capture certain

inflections in the Engel curve, as is evident for the food-at-home category (from concave to convex as incomedecreases). It also captures nonmonotonic shapes, such asan inverted U shape for motor fuel and a U shape for publictransportation, reflecting that at the lowest income deciles,more private transportation is substituted with publictransportation.

The Principal Components of Consumption

From Equations 1 and 3, we can write the log-marginal util-ity given x ih as i + iZh + ih ln(x ih i). Accordingly, i ln(i) represents the average initial (when the quantityconsumed is still zero) log-marginal utility for consumption


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FIGURE 2Percentage of Households Reporting Expenditures in Each Consumption Category

category i. The factor scores (Z h) for a household, weightedby the factor loadings ( i) for a consumption category, showwhether the households log-marginal utility is higher orlower than average for that category at a given consumptionlevel. Therefore, consumption categories that have largeloadings of the same sign for the same factor have posi-tively correlated log-marginal utilities across households.For example, because jewelry and watches as well as educa-tion have large loadings of the same sign for Factor 1,households with a higher-than-average score on this factorwill have higher-than-average log-marginal utilities for bothconsumption categories. By the same token, through thesign and magnitude of these loadings, it is possible to iden-tify sets of consumption categories that tend to have higher

(or lower) marginal utilities for the same households. Foreasier interpretation, Table 2 shows in bold the largest load-ings (in absolute value) for each consumption category.From these loadings, households with a higher-than-average score on Factor 1 would be expected to have higherlog-marginal utilities for categories, such as jewelry andwatches, education, alcohol, and recreation, suggesting thatthis factor is associated with nonessential consumption.Factor 2 is associated with smoking and drinking and couldbe labeled a sin factor. Factor 3 is associated with largefamily-oriented consumption needs, such as insurance,household operations, electricity, and utilities. Factor 4 isassociated with health care. Factor 5 has the highest load-ings for public transportation (which includes trains and


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FIGURE 3Share of Nonzero Expenditures Allocated to Each Consumption Category

taxis), airfare, and lodging away from home and thereforecould be labeled a travel factor. Finally, Factor 6 has rela-tively weaker loadings than the other factors, but it hashigher loadings for categories related to the operation of motor vehicles.

Most important, these factors account for both hetero-geneity in the log-marginal utilities across households andthe correlation among these log-marginal utilities acrossconsumption categories. We further investigated how con-sumption preferences differ across households by perform-ing an analysis of variance (ANOVA) on the factor scoresusing three variables that describe the households: (1) lifestage, as we defined it previously; (2) income quintile, rela-tive to other households reporting expenditures in the same

year; and (3) year of data collection, which is classified intofive categories (early or late 1980s, early or late 1990s, andearly 2000s). This ANOVA, which we performed across all66,683 households for Factor 1 (nonessential consumption),showed that only the life stage income quintiles and lifestages year interactions (along with the main effects) werestatistically significant at the .01 level. Therefore, we reportaverages only for these two interactions in Figure 5, PanelA. Moreover, to simplify the exposition, we focus only onthe six life stages with the largest number of households,which account for more than 70% of our sample. Figure 5,Panel A, shows that average log-marginal utilities fornonessential consumption have increased over time and,as expected, are higher for the high-income quintiles. How-


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N o

1 1 . 2

S 2

D i v o r c e

d /

s i n g

l e

2 7 4

1

W o r

k i n g

N . A .

N o n e

N o

T h r e e o r

t w o

Y e s

Y e s

Y e s

8 . 8

S 3

D i v o r c e

d /

w i d o w e d

4 4 6

2

W o r

k i n g

N . A .

O n e

/ t w o

Y e s

T w o o r

t h r e e

N o

N o

Y e s

7 . 0

S 5

W i d o w e d

6 6 8

4

R e t

i r e d / h o m e

N . A .

N o n e

N o

O n e

N o

N o

N o

8 . 6

S 4

D i v o r c e

d /

s i n g

l e

4 9 7

1

W o r

k i n g

/ r e t i r e d

N . A .

N o n e

N o

O n e

N o

N o

N o

2 . 1

C 7

C o u p l e

6 3 7

7

R e t

i r e d

H o m e / r e

t i r e d

O n e

/ n o n e

N o

T h r e e o r

t w o

N o

N o

N o

1 . 0

N o t e s : N . A . =

n o t a p p

l i c a b

l e .

T A B L E 1

S u m m a r y

D e s c r

i p t i o n o

f L i f e

S t a g e s


12/24


T A B L E 2

P a r a m e t e r

E s t

i m a t e s

f o r

t h e

S i x - F a c

t o r M o

d e l

F a c

t o r

L o a d

i n g s

H i t R a t

i o

( % )

C o n s u m p

t i o n

C a t e g o r y

/ P r i c e

I n d e x

G a m m a

S i g m a

B e t a

F a c

t o r

1 F a c

t o r

2 F a c

t o r

3 F a c

t o r

4 F a c

t o r

5 F a c t o r

6

R 2 ( % )

F o o d a t

h o m e

. 0 0 0

. 0 0 0

. 7 0 1

. 0 0

. 0 0

. 0 0

. 0 0

. 0 0

. 0 0

9 0

1 0 0

F o o d a w a y

f r o m

h o m e

1 . 2

5 2

. 5 0 1

. 2 1 2

. 5 1

. 1 2

. 2 4

. 0 6

. 2 1

. 1 0

1 8

9 5

T o b a c c o a n

d s m o k

i n g p r o d u c t s

2 . 1

9 3

. 8 8 6

. 2 2 9

. 1 0

. 4 0

. 1 0

. 0 5

. 0 7

. 0 3

8

6 3

A l c o h o l

i c b e v e r a g e s a t

h o m e

3 . 0

5 9

. 6 6 4

. 1 1 8

. 3 2

. 6 0

. 0 9

. 0 6

. 2 1

. 0 2

4 0

7 9

A l c o h o l

i c b e v e r a g e s a w a y

f r o m

h o m e

4 . 0

0 7

. 7 9 6

. 0 3 5

. 7 6

. 8 0

. 1 2

. 0 6

. 4 8

. 0 3

4 2

8 2

A p p a r e l

1 . 4

0 2

. 4 8 7

. 1 9 0

. 5 5

. 0 1

. 0 9

. 0 4

. 0 9

. 0 2

2 9

9 7

A p p a r e l s e r v

i c e s o t

h e r

t h a n

l a u n

d r y a n

d d r y c l e a n i n g

3 . 9

0 5

1 . 0 4 7

. 0 2 7

. 5 2

. 1 2

. 0 6

. 0 4

. 3 4

. 0 6

1 1

7 4

J e w e l r y a n

d w a t c h e s

4 . 4

9 3

1 . 2 6 7

. 0 3 2

. 9 7

. 0 5

. 1 0

. 1 0

. 1 4

. 0 5

9

6 5

P e r s o n a

l c a r e s e r v

i c e s

2 . 6

6 7

. 6 0 4

. 0 6 3

. 2 7

. 0 1

. 2 3

. 1 1

. 1 6

. 0 2

6

9 1

M i s c e

l l a n e o u s p e r s o n a l s e r v

i c e s

3 . 2

3 4

1 . 1 8 4

. 0 2 6

. 5 5

. 1 0

. 2 9

. 2 2

. 1 0

. 1 8

0

7 8

L i f e i n s u r a n c e a

1 . 9

8 2

. 7 4 0

. 3 1 0

. 2 4

. 0 0

. 3 2

. 1 4

. 0 2

. 0 1

4

6 5

P r e s c r i p

t i o n

d r u g s

3 . 5

5 8

1 . 0 9 8

. 0 2 0

. 0 4

. 1 1

. 4 1

. 8 3

. 0 4

. 0 1

3 5

7 7

N o n p r e s c r

i p t i o n

d r u g s a n

d m e d

i c a l s u p p

l i e s

3 . 6

0 3

. 9 0 5

. 0 9 1

. 2 4

. 0 1

. 2 8

. 3 7

. 1 3

. 0 6

1

6 3

P r o

f e s s

i o n a

l m e d

i c a l c a r e s e r v

i c e s

2 . 4

2 9

. 8 9 0

. 0 6 7

. 3 3

. 0 3

. 2 3

. 5 2

. 0 6

. 0 4

1 6

8 3

H o s p i

t a l a n d r e

l a t e d s e r v

i c e s

5 . 2

8 7

1 . 8 6 3

. 0 6 4

. 1 5

. 0 5

. 1 4

. 8 0

. 1 3

. 0 2

6

6 9

H e a

l t h i n s u r a n c e

1 . 4

8 6

. 7 3 8

. 2 7 1

. 1 2

. 0 3

. 4 2

. 4 0

. 1 6

. 0 8

3 3

7 5

M o t o r v e

h i c l e m a i n t e n a n c e a n d r e p a

i r

1 . 8

4 7

. 7 0 5

. 1 3 0

. 5 2

. 0 9

. 2 9

. 1 1

. 0 2

. 3 3

1 9

9 1

M o t o r

f u e l

1 . 1

2 8

. 4 0 3

. 4 1 3

. 2 8

. 1 0

. 2 5

. 0 0

. 0 8

. 2 0

3 5

9 4

M o t o r v e

h i c l e

i n s u r a n c e

1 . 4

1 0

. 4 9 6

. 2 5 0

. 2 1

. 0 8

. 3 3

. 1 1

. 0 1

. 2 4

1 8

8 5

P u b

l i c t r a n s p o r t a t

i o n

4 . 7

5 6

1 . 4 5 2

. 0 3 5

. 3 3

. 0 2

. 1 0

. 0 2

1 . 1 4

. 1 4

3 1

6 9

A i r l i n e

f a r e

2 . 4

6 3

. 7 1 1

. 3 2 9

. 4 4

. 0 9

. 2 3

. 1 0

. 7 2

. 1 8

3 9

8 5

R e c r e a t

i o n

. 9 5 0

. 5 0 3

. 2 0 3

. 5 4

. 0 8

. 1 8

. 1 1

. 1 7

. 0 9

1 9

9 8

E d u c a

t i o n

3 . 8

0 2

1 . 7 1 2

. 0 1 4

1 . 1 8

. 1 6

. 0 5

. 1 2

. 2 2

. 2 9

5

6 9

C h a r i t y a

2 . 7

4 1

1 . 2 6 8

. 1 1 1

. 4 9

. 2 7

. 4 8

. 3 7

. 2 6

. 0 4

1 4

6 6

T e l e p h o n e s e r v

i c e s

1 . 7

6 9

. 5 0 1

. 0 7 4

. 1 4

. 0 5

. 2 5

. 0 4

. 0 8

. 1 0

1 9

9 9

L o d g i n g a w a y

f r o m

h o m e

2 . 6

9 9

. 6 7 4

. 1 4 5

. 6 1

. 0 7

. 2 7

. 1 3

. 4 6

. 2 2

3 0

7 8

H o u s e

h o l d f u r n

i s h i n g s a n

d o p e r a

t i o n s

2 . 0

9 9

. 9 3 0

. 1 0 6

. 6 8

. 0 1

. 1 8

. 1 7

. 0 4

. 0 4

1 1

8 7

H o u s e

h o l d o p e r a t

i o n s

2 . 1

6 1

. 7 7 0

. 1 5 5

. 3 2

. 0 0

. 4 2

. 2 7

. 1 3

. 0 7

1 2

8 3

E l e c t r i c

i t y

1 . 3

6 6

. 4 2 1

. 2 4 3

. 0 5

. 0 4

. 3 0

. 0 6

. 0 5

. 0 4

3 5

9 6

W a t e r a n

d s e w e r a n

d t r a s h c o l

l e c t

i o n s e r v

i c e s

2 . 1

3 1

. 4 7 3

. 1 7 7

. 0 5

. 0 3

. 3 8

. 1 3

. 0 3

. 0 3

1 3

7 9

G a s , h

e a t i n g o i

l , a n

d c o a l

1 . 8

3 0

. 6 6 7

. 3 1 3

. 0 4

. 0 8

. 3 0

. 0 8

. 0 2

. 0 4

6

7 6

a G e n e r a l p r

i c e

i n d e x w a s u s e d

f o r

t h e s e

t w o c o n s u m p t

i o n c a

t e g o r i e s .

N o t e s : L a r g e r

l o a d

i n g s a r e m a r k e d

i n b o l d f o r e a s i e r

i n t e r p r e

t a t i o n o f

t h e

f a c t o r s .


13/24


FIGURE 4Actual and Estimated Engel Curves for Some of

the Consumption Categories

Notes: Engel curves implied by the proposed model are repre-sented by solid lines; Engel curves based on observed dataare represented by dots.

ever, these patterns of change are distinct for each life stage.As would be expected, the nonessential factor scores arehigher in the richest quintiles. They also tend to be lower inthe later life stages (S5) than in the earlier stages (Co/So,C1, and S1). To our surprise, these scores declined at differ-ent rates for different life stages in the 22 years covered byour data, suggesting that the marginal utility for nonessen-tial consumption (compared with food at home) decreasedover time.

Similar results for the health-related Factor 4 (see Fig-ure 5, Panel B) suggest that average log-marginal utilitiesfor the older life stages (C6 and S5) do not vary substan-tially with income, but they increase with income for theyounger life stages (C1 and S1). Figure 5, Panel B, alsoshows a trend upward in the average log-marginal utilitiesfor health care.

Consumption Priorities, Household Life Stage,and Income In addition to investigating each factor separately, we cancapture the variation of preferences for a particular con-sumption category across households by the preferenceshares,

which represent the expected expenditure shares for house-hold h when there is no budget constraint. We report theaverage estimated preference shares in Table 3. For clarity,we report these averages only for the six most populated lifestages and for the richest/poorest income quintiles. Theseresults show that though there are substantial differences inpreferences between the two extreme income quintiles, thedifferences across the six main life stages are relatively

minor, particularly for the richest quintile. In general, thepoorest 20% of our sample have higher preference sharesthan the richest 20% for food at home; tobacco and smok-ing products; health insurance; telephone services; electric-ity; water and sewer and trash collection services; and gas,heating oil, and coal, suggesting that these are the moreessential consumption categories. For categories such asmotor fuel, being considered essential depends on the lifestage; the poorest 20% have higher preference shares thanthe richest 20% among some life stages (Co/So, C1, S1, andC6) but lower shares in other stages (S2 and S5), againdemonstrating the importance of accounting for unobservedheterogeneity in tastes in modeling consumption budgetallocation.

Policy Simulations A major advantage of demand systems, such as the one wepropose here, is that they are consistent with budget-constrained utility-maximizing behavior, leading to pre-dicted expenditures that are always logically consistent (i.e.,nonnegative and sum up to the budget). Such a multicate-gory structural approach makes our proposed budget alloca-tion model valuable in anticipating consumers reactions toenvironmental shocks, such as price hikes or shifts in dis-

ih

j

J

Ze

e

e

e

ih

jh

i i h i

= =

=

+ +

112

2

j j j h jZ

j

J + +=

, 1

21

2


14/24


15/24


T A B L E 3

A v e r a g e

E s t

i m a t e d

P r e

f e r e n c e

S h a r e s

f o r

M a j o r

L i f e

S t a g e s a n

d R

i c h e s

t / P o o r e s t

I n c o m e

Q u

i n t i l e s

S e l e c

t e d L i f e

S t a g e

C o

/ S o

C 1

S 1

C 6

S 2

S 5

R i c h e s

t P o o r e s t

R i c h e s t

P o o r e s t

R i c h e s

t

P o o r e s t

R i c h e s

t P o o r e s t

R i c h e s

t P o o r e s t

R i c h e s

t P o o r e s t

C o n s u m p

t i o n

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u i n t i l e

Q u

i n t i l e

Q u

i n t i l e

C a t e g o r i e s

( % )

( % )

( % )

( % )

( % )

( % )

( % )

( % )

( % )

( % )

( % )

( % )

F o o d a t

h o m e

1 3 . 4

1 9 . 5

1 4 . 7

2 2 . 0

1 1 . 7

2 0 . 4

1 4 . 1

2 0 . 0

1 5 . 9

2 5 . 0

1 2 . 5

1 9 . 5

F o o d a w a y

f r o m

h o m e

6 . 4

5 . 3

6 . 6

5 . 7

6 . 2

5 . 2

5 . 9

4 . 2

6 . 5

5 . 7

5 . 3

4 . 0

T o b a c c o a n

d s m o k


2 . 3

3 . 8

2 . 3

4 . 0

2 . 3

4 . 2

2 . 3

3 . 6

2 . 7

4 . 4

2 . 2

3 . 4

A l c o h o l


h o m e

1 . 2

1 . 2

1 . 0

1 . 2

1 . 4

1 . 3

1 . 0

. 9

1 . 2

1 . 1

1 . 1

. 8

A l c o h o l


f r o m

h o m e

. 8

. 6

. 6

. 5

1 . 2

. 6

. 6

. 3

. 8

. 4

. 7

. 3

A p p a r e l

5 . 7

4 . 4

5 . 7

4 . 5

5 . 8

4 . 3

5 . 4

3 . 5

5 . 6

4 . 4

5 . 0

3 . 5


i c e s o t

h e r

t h a n

l a u n

d r y a n


. 8

. 6

. 7

. 6

. 9

. 6

. 7

. 4

. 7

. 6

. 7

. 5

J e w e l r y a n

d w a t c h e s

. 8

. 4

. 7

. 4

. 9

. 4

. 7

. 3

. 7

. 3

. 7

. 3

P e r s o n a

l c a r e s e r v

i c e s

1 . 4

1 . 4

1 . 4

1 . 3

1 . 4

1 . 4

1 . 4

1 . 4

1 . 4

1 . 4

1 . 4

1 . 4

M i s c e


i c e s

1 . 7

1 . 2

1 . 6

1 . 2

1 . 8

1 . 2

1 . 6

1 . 1

1 . 5

1 . 0

1 . 7

1 . 1

L i f e i n s u r a n c e

2 . 9

3 . 0

3 . 0

2 . 9

2 . 7

2 . 9

3 . 0

3 . 2

2 . 8

2 . 9

3 . 1

3 . 3

P r e s c r i p

t i o n

d r u g s

. 8

1 . 0

. 8

. 8

. 6

. 9

1 . 1

1 . 8

. 7

. 7

1 . 3

1 . 9

N o n p r e s c r

i p t i o n

d r u g s a n

d

m e d

i c a l s u p p

l i e s

. 7

. 7

. 7

. 6

. 6

. 6

. 7

. 8

. 6

. 6

. 8

. 8

P r o

f e s s

i o n a

l m e d

i c a l c a r e

s e r v

i c e s

2 . 3

2 . 1

2 . 3

1 . 9

2 . 1

1 . 9

2 . 6

2 . 5

2 . 2

1 . 6

2 . 7

2 . 5

H o s p i

t a l a n d r e

l a t e d s e r v

i c e s

. 5

. 5

. 5

. 5

. 4

. 4

. 6

. 8

. 4

. 4

. 6

. 7

H e a


3 . 9

5 . 6

4 . 0

4 . 8

3 . 5

5 . 6

4 . 9

8 . 4

4 . 0

4 . 9

5 . 5

8 . 8

M o t o r v e

h i c l e m a i n t e n a n c e a n d

r e p a

i r

4 . 2

3 . 3

4 . 0

3 . 2

4 . 3

3 . 1

3 . 7

2 . 8

3 . 9

2 . 6

3 . 8

2 . 6

M o t o r

f u e l

5 . 8

6 . 2

5 . 8

6 . 4

5 . 5

6 . 1

5 . 4

5 . 6

5 . 9

5 . 8

5 . 4

5 . 3

M o t o r v e

h i c l e

i n s u r a n c e

4 . 4

4 . 8

4 . 4

4 . 7

4 . 2

4 . 7

4 . 3

4 . 9

4 . 4

4 . 2

4 . 4

4 . 7

P u b


i o n

. 7

. 6

. 6

. 5

1 . 0

. 7

. 8

. 4

. 7

. 8

. 7

. 6

A i r l i n e

f a r e

2 . 6

1 . 8

2 . 3

1 . 6

3 . 3

2 . 0

2 . 6

1 . 6

2 . 4

1 . 7

2 . 8

1 . 9

R e c r e a t

i o n

9 . 3

6 . 9

8 . 9

6 . 6

1 0 . 0

6 . 8

8 . 7

5 . 7

8 . 7

6 . 2

8 . 7

5 . 8

E d u c a

t i o n

3 . 9

1 . 7

3 . 6

1 . 5

4 . 4

1 . 4

3 . 3

1 . 0

3 . 4

1 . 2

3 . 1

. 8

C h a r i t y

3 . 1

2 . 2

3 . 0

1 . 9

3 . 1

2 . 0

3 . 4

2 . 5

2 . 6

1 . 7

3 . 8

2 . 9


i c e s

2 . 9

3 . 4

3 . 0

3 . 4

2 . 8

3 . 4

2 . 9

3 . 5

3 . 0

3 . 5

2 . 9

3 . 5


f r o m

h o m e

2 . 1

1 . 3

1 . 9

1 . 2

2 . 5

1 . 3

2 . 0

1 . 1

1 . 8

1 . 1

2 . 1

1 . 2

H o u s e

h o l d f u r n

i s h i n g s a n

d

o p e r a t

i o n s

4 . 4

2 . 9

4 . 3

2 . 8

4 . 6

2 . 7

4 . 2

2 . 4

4 . 0

2 . 5

4 . 2

2 . 4

H o u s e

h o l d o p e r a t

i o n s

2 . 7

2 . 5

2 . 7

2 . 2

2 . 7

2 . 4

3 . 0

2 . 8

2 . 5

2 . 1

3 . 3

3 . 0

E l e c t r i c

i t y

3 . 9

5 . 1

4 . 1

5 . 2

3 . 5

5 . 1

4 . 1

5 . 7

4 . 1

5 . 3

4 . 2

5 . 7

W a t e r a n

d s e w e r a n

d t r a s h

c o l l e c t

i o n s e r v

i c e s

1 . 9

2 . 4

1 . 9

2 . 3

1 . 7

2 . 4

2 . 0

2 . 8

1 . 9

2 . 3

2 . 2

2 . 9

G a s , h

e a t i n g o i

l , a n

d c o a l

2 . 8

3 . 7

2 . 9

3 . 6

2 . 6

3 . 8

3 . 0

4 . 1

2 . 9

3 . 8

3 . 1

4 . 2


16/24


ance and funding or rebates for child care, to certain seg-ments of the population.

The third simulation is an attempt to quantify consumerwelfare losses due to the dramatic increases in prices forprescription drugs in the past 22 years, which grew by262% from 1982 to 2003 (an annual rate of 6.3%), com-pared with an inflation rate of 91% (or 3.1% per year) dur-ing the same period. Here, we consider a hypothetical sce-nario in which the costs of prescription drugs followed thegeneral inflation rate observed in the past 22 years. In thiscounterfactual simulation, we consider the income effectsof the dramatic price increases, attempting to estimate howhouseholds shifted their discretionary income away fromother consumption categories to pay for the increasing costsof prescription drugs. In this scenario, we consider allhouseholds that spent discretionary income on prescriptiondrugs in the past 22 years and compare their actual expendi-tures with those predicted by our budget allocation model,assuming that the extra discretionary income resulting fromthe lower prescription drug prices would be allocated to theother categories according to the estimated utilities for eachhousehold and consumption category. This comparisonshows how these households reduced their expenditures in

all the other categories to compensate for the dramaticincreases in prescription drug prices in the past 22 years,thus providing some insights into welfare losses potentiallycaused by these price increases.

For each household in our sample, we simulate theirbudget reallocation decisions by solving the constrainedutility maximization problem, using the estimated parame-ters ( and i for household h and category i) andobserved versus simulated prices (p i versus p i + pi) andbudget (m h versus m h + mh). The solution can be derivedthrough a five-step procedure, which we detail in theAppendix.

Policy Simulation 1: reactions to shifts in energy costs .Table 4 reports the simulated effects of a dramatic increasein oil prices, showing the percentage changes in quantityconsumed in response to a 50% increase in prices for motorfuel and gas, heating oil, and coal. As would be expected,the price increases affect the poorest quintile more dramati-cally than the richest quintile. The difference between thetwo income quintiles is the largest in the demand for motorfuel among households in the S5 stage, in which the poorest(richest) quintile reduces the quantity consumed by 43%(20%). In other words, the demand among the pooresthouseholds in the S5 stage is elastic, whereas those in therichest quintile have an inelastic demand. Table 4 alsoshows how households in different life stages would adjust

their expenditures in other categories to compensate for theshift of discretionary income toward motor and home fuels.As would be expected, the more essential categories, suchas food at home, telephone services, electricity, and waterand sewer and trash collection, are the least affected, alongwith addictions, such as tobacco and alcoholic beveragesat home. The consumption categories most affected are theless essential ones, such as education (which includes booksand other educational expenses), miscellaneous personalservices, and charity. The category showing substantial

ih

3Our analysis of preferences (Table 3) across life stages andincome quintiles showed that preferences vary with income (cross-sectionally). In this policy simulation, we assumed that a relativelysmall increment of $500 in discretionary income would not causesubstantial shifts in preferences.

differences in response across life stages is jewelry andwatches, for which the highest percentage drop in demandoccurs in the richest quintile of S5 (31%), compared with adrop of only 3%13% in the lowest quintiles, probablybecause they already spend the least in this category. A sur-prising and worrisome effect is the substantial drop in pre-scription drugs and other health care expenses, particularlyamong the older (C6 and S5) and poorer households.

The price effects we report in Table 4 show negativecross-elasticities, so that increases in fuel prices producedecreases in demand for all other categories, which happensbecause income effects dominate substitution effects, asdiscussed previously. In other words, because demand formotor and home fuel is inelastic, increases in fuel pricesleave less discretionary income to be spent elsewhere, lead-ing to a decrease in expenditures in all other categories.After we partial out these income effects (Equation 8), thesubstitution effects (Equation 9) are all indeed positive,which implies that there is no complementarity betweencategories. It might be argued that price increases in motorfuel would lead consumers to reduce their car use, whichwould lead to spending less on motor vehicle maintenanceand repair and, thus, complementarity between these two

categories (though it could also be argued that the impacton motor vehicle maintenance and repair might take longerto observe). However, after we account for income effects,these two categories become substitutes because the utilityfunction is assumed to be additive separable, and account-ing for complementarity with the CEX data is infeasible(because it is not a truly longitudinal panel).

Policy Simulation 2: reaction to a tax rebate . Table 5reports the simulated effects of a hypothetical $500 taxrebate for each household, distributed by the federal gov-ernment to boost demand and thus earmarked for consump-tion. Simulations such as this could help policy makersanticipate and quantify the differential impacts of such ashift in discretionary income on different population sectorsacross different consumption categories. 3 Across the sixmain life stages, food at home receives the highest share of the extra $500 in discretionary income, more so among thepoorest quintile. In general, for essential categories, such ashealth insurance; telephone services; electricity; and gas,heating oil, and coal, there is a larger increase in spendingamong poorer households. After food retailing, recreationwould be one of the industries that would benefit the mostfrom the $500 tax rebate, particularly among the wealthierhouseholds. Similarly, we observe a larger increase inspending among richer households for other nonessentialcategories, such as airline fare, education, charity, and

household furnishings.


17/24


18/24


T A B L E 5

E x p e c

t e d A l l o c a

t i o n

o f a n

I n c r e m e n

t a l $ 5 0 0 i n t h e C o n s u m p

t i o n

B u

d g e t

S e l e c

t e d L i f e

S t a g e

C o

/ S o

C 1

S 1

C 6

S 2

S 5

R i c h e s

t P o o r e s t

R i c h e s t

P o o r e s t

R i c h e s

t

P o o r e s t

R i c h e s

t P o o r e s t

R i c h e s

t P o o r e s t

R i c h e s

t P o o r e s t

C o n s u m p

t i o n

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u

i n t i l e

Q u i n t i l e

Q u

i n t i l e

Q u

i n t i l e

C a t e g o r i e s

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

( $ )

F o o d a t

h o m e

6 7

1 0 1

7 2

1 1 6

5 6

1 1 0

6 9

1 0 2

7 9

1 3 5

5 3

1 0 3

F o o d a w a y

f r o m

h o m e

3 6

2 6

2 8

2 1

4 5

2 8

3 2

2 0

3 2

2 3

3 4

2 1

T o b a c c o a n

d s m o k


9

1 9

8

2 1

9

2 4

9

1 6

1 1

2 2

6

1 0

A l c o h o l


h o m e

6

6

5

6

7

7

6

4

6

5

5

2

A l c o h o l


f r o m

h o m e

5

3

3

2

8

4

3

1

5

2

3

1

A p p a r e l

2 9

2 2

2 9

2 6

2 9

2 1

2 7

1 6

3 1

3 0

2 2

1 8


i c e s o t

h e r

t h a n

l a u n

d r y a n


4

4

3

4

6

5

3

2

3

5

3

3

J e w e l r y a n

d w a t c h e s

5

2

4

2

5

2

4

1

4

1

4

1

P e r s o n a

l c a r e s e r v

i c e s

7

7

6

6

6

7

7

7

7

7

7

8

M i s c e


i c e s

8

1 0

7

6

1 1

5

8

7

1 2

6

1 9

5

L i f e i n s u r a n c e

1 7

1 2

1 6

1 2

1 3

1 0

1 8

1 6

1 3

1 0

1 6

1 5

P r e s c r i p

t i o n

d r u g s

3

6

3

3

2

5

6

1 4

3

3

5

1 3

N o n p r e s c r

i p t i o n

d r u g s a n

d

m e d

i c a l s u p p

l i e s

3

2

3

2

3

2

4

3

3

1

3

4

P r o

f e s s

i o n a

l m e d

i c a l c a r e

s e r v

i c e s

1 1

1 1

1 0

1 1

1 1

9

1 5

1 4

1 1

8

2 7

1 3

H o s p i

t a l a n d r e

l a t e d s e r v

i c e s

2

4

3

3

2

2

3

5

2

1

4

3

H e a


1 8

2 4

1 8

2 0

1 6

2 5

2 4

4 6

1 9

1 8

2 3

5 1

M o t o r v e

h i c l e m a i n t e n a n c e a n d

r e p a

i r

2 2

1 7

2 1

1 7

2 4

1 6

1 7

1 5

1 9

1 3

1 3

1 2

M o t o r

f u e l

2 8

3 4

2 6

3 6

2 2

3 1

2 4

2 9

3 0

2 8

2 0

2 3

M o t o r v e

h i c l e

i n s u r a n c e

2 2

2 2

2 0

2 2

2 0

2 0

1 9

2 3

2 2

1 6

2 0

1 9

P u b


i o n

4

3

2

3

5

5

4

2

4

5

2

3

A i r l i n e

f a r e

1 3

5

1 0

4

1 7

4

1 3

4

1 1

3

1 2

5

R e c r e a t

i o n

4 9

3 3

4 9

3 2

5 4

3 3

4 5

2 6

4 4

3 0

3 8

2 6

E d u c a

t i o n

1 2

1 2

2 8

9

8

1 0

9

2

1 8

9

1 5

2

C h a r i t y

1 6

9

1 4

8

1 7

8

2 4

1 3

1 2

6

3 1

1 5


i c e s

1 4

1 9

1 4

1 9

1 5

2 2

1 2

1 6

1 6

2 3

1 1

1 9


f r o m

h o m e

1 1

5

9

4

1 3

3

1 1

4

8

2

1 0

3

H o u s e

h o l d f u r n

i s h i n g s a n

d

o p e r a t

i o n s

2 4

1 4

2 4

1 6

2 2

1 2

2 3

1 3

1 8

1 2

2 0

1 2

H o u s e

h o l d o p e r a t

i o n s

1 5

1 2

2 2

1 2

1 6

1 1

1 8

1 3

1 6

1 0

2 5

1 8

E l e c t r i c

i t y

1 9

2 9

1 8

2 8

1 7

2 9

2 0

2 9

1 9

3 3

2 1

3 2

W a t e r a n

d s e w e r a n

d t r a s h

c o l l e c t

i o n s e r v

i c e s

9

1 0

1 0

1 2

9

1 0

1 0

1 4

1 0

1 1

1 0

1 5

G a s , h

e a t i n g o i

l , a n

d c o a l

1 3

1 9

1 3

1 9

1 2

2 0

1 3

2 2

1 4

2 3

1 4

2 7

T o t a l

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0

5 0 0


19/24


Policy Simulation 3: welfare losses due to spiralingcosts of prescription drugs . Table 6 reports the simulatedpercentage changes in household expenditure if the pricesof prescription drugs had increased at the same rate as theCPI. If that had been the case, consumers could havereduced their prescription drug expenditure by an averageof 37%, while maintaining the same level of treatment. Thesavings could then have been spent in other categories.Older, retired, and poor households (bottom income quin-tiles of the C6 and S5 life stages) would have benefitedmore, percentage-wise, than younger, working, and wealth-ier households. For example, the oldest and poorest house-holds could have increased their spending on additional lifeinsurance (3.5%), water and sewer and trash collection ser-vices (3.2%), motor vehicle insurance (3.1%), tobacco andsmoking products (3%), and motor fuel (2.6%).

Conclusions and Directions forFurther Research

The main purpose of this study was to develop a feasibledemand system that would enable us to investigate budgetallocation decisions by individual households across a com-

prehensive set of consumption categories. This developmentwas motivated by the belief that marketers, research ana-lysts, and policy makers need a better understanding of howconsumers allocate their discretionary income to meet dif-ferent consumption needs, and they must be able to antici-pate how the resultant consumption patterns will change inresponse to changes in prices and budgets.

When studying consumption at this basic level, it isimportant to emulate the consumers resource allocationproblem. Our basic premise is that every household allo-cates its discretionary income among competing needs andwants so that when the consumption budget is exhausted,all expenditure categories offer the same marginal utility

per dollar. Because we attempt to develop a reasonable as-if model to approximate the households basic resource allo-cation problem, when we obtain estimates of each house-holds direct utility function, we can simulate the house-holds reaction to changes in prices or income andunderstand how these changes will affect different con-sumption categories representing different industries acrossdifferent consumer segments.

By definition, a model is a simplified representation of observed phenomena, and therefore we made some simpli-fying assumptions in developing our proposed factor-analytic random coefficients budget allocation model. Animportant assumption to make the model parsimonious andfeasible is that of a direct utility function that is additiveseparable across consumption categories. In other words,we assume that for an individual household, expenditure inone category does not increase or decrease the marginalutility derived from consuming another category. This doesnot imply that consumption is independent across cate-gories, because all categories compete for the same budget.It also does not imply that preferences are independentacross categories and households, because our factor struc-ture accounts for possible correlations of preferencesamong the categories across households. However, the addi-

tive separable utility assumption implies that the resultantdemand system will not be able to capture potential com-plementarities among consumption categories, which couldnot be discerned from correlations in preferences becauseof the one-shot nature of the CEX (Gentzkow 2007). Webelieve that this is a critical limitation only in detailedanalyses that consider a limited number of potentially com-plementary product categories, such as the type of cross-category choice modeling commonly performed for con-sumer packaged goods in the marketing literature usinglongitudinal scanner panels, but this is not as critical inexpenditure analyses performed across a comprehensive setof broad consumption categories. We leave for furtherresearch the methodological challenge of extending ourmodel beyond additive separable utilities, while addressingthe issues of high dimensionality (more than a couple dozencategories), binding nonnegative constraints (householdshave no spending in many categories), unobservable hetero-geneity (unique household preferences that cannot be cap-tured by demographics), and correlation in individualhouseholds category preferences.

Substantively, there are several directions for extendingour work. First, the proposed framework for modeling

household consumption budget allocation could be adaptedfor forecasting industry sales and assessing market poten-tial. As a model of primary demand, our structural approachhas the advantage of simultaneously considering householdspending across a full spectrum of expenditure categories.Because all types of consumer expenditures ultimately viefor the same household budget, primary demand in oneindustry can be better predicted in relation to consumerexpenditures in other industries. For example, fast-foodrestaurant chains may be able to forecast sales trends betterif they can understand how consumers spending on foodaway from home is influenced by their spending on foodat home, apparel, motor fuel, and so on. Moreover, our

approach explicitly links household discretionary income,category price indexes, and demographics (through thehousehold-specific taste parameters) to household categoryexpenditures. This enables analysts in forecasting industrysales or assessing market potential to factor in projectionsabout household income, inflation rates, and demographictrends through an integrated framework.

Second, although developed under a different context,we believe that there is a potential to adapt our consumptionbudget allocation model for shopping-basket data analysis.As such, researchers can study many more categories

jointly without needing to focus on a few categoriesselected a priori or lump a large number of distinct itemsinto an other category.

Finally, in a more realistic setting, consumers make notonly cross-category allocations but also intertemporal allo-cations (e.g., consume more today versus save more fortomorrow). In our work, we ignored the intertemporalaspect by treating the consumption budget as exogenouslydetermined. Further research could relax this assumptionand model both cross-category and intertemporal alloca-tions explicitly. However, this would require a true panelwith longitudinal information about individual householdsexpenditure patterns.


20/24


21/24


AppendixEstimating the Proposed Budget Allocation Model The problem faced by household h is to choose a consump-tion plan, x h(x1h, , x Jh 0), that maximizes the utilityfunction, , where ih > 0,(xih i) > 0, and J is the number of all available expendi-ture categories. Given the prices (p 1, , pJ) of unit con-sumption in each category, the households allocation plan

must satisfy the budget constraint,mih mh, where m ih represents household hs expenditures(in dollars) in category i. The households optimizationproblem implies the following KuhnTucker conditions:

where 0 is the Lagrange multiplier. Given our parame-terization of

ih= exp(

i+

iZ

h+

ih) in Equation 3, Equa-

tions A1 and A2 lead to, respectively,

(A3) i + iZh + ih ln(x ih i) ln(p i) ln(), for x ih = 0,and

(A4) i + iZh + ih ln(x ih i) ln(p i) = ln(), for x ih > 0,

where Z h is a p-dimensional vector of i.i.d. standard normalfactor scores for household h and ih is a random distur-bance normally distributed with mean zero and standarddeviation i. The parameters to be estimated, given theobserved consumptions x ih (=m ih /pi) and prices p i, are i, i,i [= min(x i) exp( i)], and i, which we collect in the set. Every household in our sample has positive consumptionfor the first category, food at home (i.e., x 1h > 0 for h), andfor identification purposes, we set 1, 1, and 1 to zero,which means that Equations A3 and A4 can be simplifiedas, respectively,(A5) ih (ih 1h) ( i + iZh), for x ih = 0,and

(A6) ih = (ih 1h) ( i + iZh), for x ih > 0,where ih = ln(x ih i) + ln(p i) = ln(p ixih p ii).

Let *ih(xh) ln(p ixih pii) ln(p1x1h p11) ( i +iZh). Based on Equations A5 and A6, for a given set of model parameters and factor scores Z h, the likelihood con-tribution of household h, L h(Zh), or L(|Zh, xh, p) = L( 2...lh,lh + 1...J , 2... lh, lh + 1...J , 2...lh, lh + 1...J , 1...J|Zh, X1h...Jh , p1...J), is

where x ih > 0 for i (2, , lh), x ih = 0 for i (lh + 1,, J), is the density function of ih, andf ih ( )

( ) , , , ,A L Z x p f x Z p

f

h h x h hh

ih

7 L Zh h( ) = ( ) = ( )

=

| |

ih hi

h

hihx x

f h

h

hih

* ,*

,( )

(=2

2

2

ll

l

))

( )

= + -

ih h

h

x

i

J *

,l 1

( )( )

( )A

G xx x

phih

ih

ih ii1

=

, for x = 0,ih

annd

, for x > 0ih( )( )

( )A

G xx x

phih

ih

ih ii2

= =

,,

iJ i ih iJp x= ==1 1

G x xh iJ

ih ih i( ) ln( )= = 1

is the determinant of the ( lh 1) (lh 1) Jacobian of thetransformation from x 2...lh,h to ...lh,h, which is a continuousone-to-one mapping, because p 1x1h = (m h lhi = 2pixih).

Given that ih ~ N(0, i), we can write Equation A7 asfollows:

where and are, respectively, the probability and cumu-lative density function of the standard normal distributionand

(For a detailed derivation, see Kao, Lee, and Pitt 2001, pp.

21011.)Because Z h is unobservable, the likelihood contributionof household h, L h, needs to be integrated over Z h ~ N(0,

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