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    Durables and Wives' Employment Yet AgainAuthor(s): W. Keith BryantSource: The Journal of Consumer Research, Vol. 15, No. 1 (Jun., 1988), pp. 37-47Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/2489170Accessed: 27/07/2010 00:30

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    urables a n d W iv e s mployment e t A g a i n

    W. KEITH BRYANT*

    The literature examining the relationship between consumer durables expendituresand wives' employment is analyzed. Several deficiencies in the literature are cor-rected in a revised model that is estimated with data from the 1977-1978 Surveyof Consumer Expenditures. This article concludes that durables expenditures andwives' employment time are complements.

    number of papers (four of which have appearedr in JCR), have investigated the relationships be-tween several components of consumption and sav-ing and wives' employment. Although the literaturehas focused upon an important set of relationshipsand has expanded our knowledge of consumer behav-

    ior, it contains conceptual and statistical problems.The purposes of this article are (1) to propose solu-tions to the conceptual and statistical problems foundin the literature, (2) to apply these solutions to an ex-ample analysis of the relationship between aggregatedurables expenditures and wives' employment, and(3) to shed further empirical light on the relationship.Data from the University of Michigan Survey Re-search Center's 1977-1978 Survey of ConsumerCredit are used.

    LITERATURETwo general hypotheses underlie the work on the

    relationship between durables expenditures andwives' employment. According to the earliest hypoth-esis, most married women's employment responds toand tends to offset transitory movements in othercomponents of family income (Agarwala and Drink-water 1972; Mincer 1962). If a high proportion ofwives' earnings is transitory, it is therefore saved inaccordance with the permanent income hypothesis.Consequently, durables expenditures from wives'earnings are higher than those expenditures fromother income components, because durables expen-ditures are a form of saving.

    The other more recent arguments are based on the

    economics of household production (Becker 1965).Galbraith (1973) hypothesized that durables andwives' home time are complements in household ac-tivities and, consequently, durables expenditures willdecrease as wives' employment rises. That is, durablegoods (e.g., home appliances) and family labor (pre-

    sumably wives') are used together in household activ-ities (i.e., household work and leisure), implying thatif the family's demand for wives' time spent on house-hold activities declines (and wives' devote more timeto paid employment), then so does the family's de-mand for durable goods. Strober and Weinberg's(1977, 1980) research concludes that durables andwives' time are substitutes in household activities,and, therefore, durables expenditures rise with wives'employment. The hypothesis here is that services ofdurable goods replaces labor in the household. Thus,as the demand for wives' home time declines, the fam-ily's demand for durable goods rises. Bellante andFoster (1984) argue that wives' employment and thefamily's consumption of services are substitutes.The hypothesis based on transitory income mayhave had more cogency when the labor force partici-pation rate of married women was low and they wereconsidered secondary workers (Mincer 1962).However, as married women have become in recentyears a large and permanent part of the labor force,the hypotheses based on the economics of householdproduction (Becker 1965) are more relevant. Theselatter hypotheses are examined in this article.

    Most empirical studies of the economics of house-hold production reveal no relationship between ag-gregate durables expenditures and wives' employ-ment and typically no relationship when particulardurable items are analyzed.' Bellante and Foster(1984) have had somewhat more success in findingpositive relationships between expenditures on ser-vices and wives' employment. The empirical litera-

    * W. Keith Bryant is Professor of Consumer Economics at theDepartment of Consumer Economics and Housing, Cornell Uni-versity, Ithaca, NY 14853-4401. This study was financed in partby a contract with the Economic Development Division, U.S.D.A.Thanks are due to R. Weagley or research assistance and to ShelleyWhite-Means, Robin Douthitt, Jan Pappalardo, Peter Zorn, and ananonymous reviewer or comments on earlier drafts hat materiallyimproved his article. ' See Agarwala and Drinkwater 1972), Strober (1977), Strober

    and Weinberg 1977, 1980) and Weinberg and Winer (1983).

    37? JOURNAL OF CONSUMER RESEARCH * Vol. 15 0 June 1988

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    38 THE JOURNAL OF CONSUMER RESEARCH

    ture shows that either the hypothesized relationshipsare very weak or absent or that the methods used inthe studies are flawed, which is discussed next in thecontext of durables.

    PROBLEMS

    Three major problems in testing the hypotheses ofthe economics of household production are in the lit-erature. First, although the theory relates to durablesservices, available data and, consequently, the empir-ical work relate to durables expenditures and pur-chases. Second, a rigorous test of the hypotheses re-quires that the expenditure function be appropriatelyestimated and that several exogenous variables beheld constant. Most studies have not used appropri-ate estimation techniques and have left theoreticallyrelevant variables out of the analysis. Third, the the-ory posits a causal relationship between durables ex-penditures or purchases and the price of wives' timerather than a relationship between durables expendi-tures and wives' employment. Although informationabout the relationship between durables expendituresand the price of wives' time is contained in the rela-tionship between durables expenditures and wives'employment (the relationship the literature has ex-amined), the information is obscure and statisticallybiased unless certain transformations are made andprocedures followed. After examining the basic the-ory underlying the hypothese's, each of these prob-lems are discussed and solutions to them are offered.

    Theory

    The economic theory pervading the literature pos-its that the household finds satisfaction by using pur-chased one-use goods and services (e.g., food andmovie tickets), the services of durable goods (e.g., fur-niture, stoves, and VCRs), and the wives' services(e.g., time and skills) in household activities (Becker1965). See the Figure. The household's use of dura-bles services s limited by the stock of durables t ownsand its purchases of durables during the period. Itspurchases of one-use goods and services and of dura-ble stocks are limited by its income. And, its use ofwives' time is limited by the hours in a year. Theseconstraints are interdependent. The family's incomeand wives' time are interrelated, because wives maydevote some part of their year to paid employmentand augment family income. The family's stock ofdurables and its income are interrelated, because itcan spend some of its income on durables and aug-ment the stock. Subject to these limitations, however,the family chooses the quantities of one-use goodsand services, durables services, and wives' time to be

    FIGURE

    WIFE'S TIME AND DURABLES DEMAND

    Availablewife's hours

    T

    Hours n Hours npaid household work

    employment and leisureqe ql

    Family 'ncome Past durableAm stock

    One-use Presentgoods and durableservices stock

    St

    Durableservices

    qd

    Family atisfaction

    spent in household activities (or alternatively, in paidemployment) so as to maximize satisfaction.2

    A set of three annual demand functions representsthe choices made by the family: (1) one-use goods andservices, (2) durables services, and (3) wives' time inhousehold activities or paid employment, since one isthe complement of the other.3 The demand functionsare functions of prices, income, and preference andhome productivity shifters, i.e.,

    qit= h1(pdt, ot, Pet, Yt, Zit) (i = d, e, o) (1)where qit = quantity demanded (supplied) of good i in

    2 Married women's choices of the hours they work in paid em-ployment per year are well established Killingsworth 1983).

    3 If q1represents he hours of the wife's home time demanded,then qe is the wife's hours in paid employment where qe = T- qland T = total time available.

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    DURABLES AND WIVES' EMPLOYMENT 39

    year t by the family (i = d for durables, o for one-usegoods and services, and e for wife's employmenthours); pi = price of good i; Y = family income notearned by the wife;4 and Zi = vector of preference andhome productivity shifters of the family's demand for

    good i.The interest here is with the demand for durablesservices, and the other two demand equations arenecessary only because they affect our ability to esti-mate the demand for durables services. The hypothe-ses about the relationship between durables andwives' time (i.e., those made by Galbraith 1973 andStrober atid Weinberg 1977, 1980) relate to the sign ofthe effect OfPeand qd, holding satisfaction constant-positive (negative) if durables and wives' time aresubstitutes (complements).5 With the underlying eco-nomic framework established, the problems of testingit can be discussed.

    Durables Services Versus Durables StocksAlthough the empirical work has dealt with dura-

    bles purchases, the preceding theory explains the de-mand for durables services, which rarely, if ever, areobservable. Furthermore, as indicated by the Figure,past stocks of durables play an important role in de-mand (Chow 1960). Therefore, linkage between paststocks of durables and current purchases and betweenthe unobservable services and the observable stock ofdurables or annual purchases becomes important forempirical work.

    The fact that the net annual change in durablestocks, mt, must equal the sum of new and replace-ment demand provides the linkage between paststocks and purchases (see the Figure); .e.,

    Mt = (St - St-1) + aSt-, (2)

    where a = the depreciation rate, 0 < a < 1; (St - St-,)represents new demand; and aSt-1 is depreciationand, thence, replacement demand. Rearranged, mtbecomes the difference between the stock in t and thedepreciated out stock in t - 1; i.e.,

    Mt = St - (I - ae)St-1. (2a)

    The almost universally used method of linking du-rables services with stocks is to assume that durablesservices are proportional to the stock; i.e., qd = ISt,where r = the factor of proportion. If so, the demand

    for the services, hd(.) from Equation 1, divided by rcan replace St in Equation 2; i.e.,

    Mt = (l/r)hd(Pdt,Pot,Pet, Yt, Zdt) -(1 a)St-1. (3)Thus, the demand for durables purchases is a func-tion of prices, income, preference and home produc-tivity shifters, and last period's stock.

    Recall, mt, is the net annual change in the durablestock and is expressed in quantity terms. MultiplyingEquation 3 through by the price of durables, pm notto be confused with Pd, which is the user cost of dura-bles), expresses Equation 3 in more easily observeddollar terms:

    Emt = Pm( /T)rhd(Pdt, Pot, Pet, Yt, Zdt)

    - (1 - a)Est,1 (4)where Est-, = PmSt,1. Stating Equation 4 more gener-ally with the subscript t on all but Emt and Est,1 sup-

    pressed for convenience and adding a random distur-bance term, Umt,Equation 4 becomes

    E*mt = Em(pd, Po,Pe, Y, Zd, Est-1) + Umt. (5)

    The literature has attempted to shed light on E*mt,the theoretical and unobserved function. E*mt is un-observed because it is the annual net change in dura-ble stocks, i.e., last period's stock minus depreciation,sales, and trade-ins plus new purchases. If deprecia-tion plus sales and trade-ins exceed current expendi-tures, then E*mt will be negative. Otherwise, t will bezero or a positive number. Of course, the literaturehas been able to measure only new purchases in theform of expenditures that form a part, but only a part,of E*mt.Equation 5 contains the linkages between stocksand durables services and between observed expendi-tures and demanded durables services. Appropriateempirical estimation of Equation 5 will yield infor-mation about the underlying theoretical relationship.

    Estimation Techniques and VariablesMuch of the literature has used inappropriate ech-

    niques to estimate durables expenditures functions.It has also omitted variables that theoretically shouldhave been included and has included some thatshould have been omitted. In order to discuss these

    points, the general form of the expenditures functionas estimated in the literature should be stated. It is:

    E'mt =f(Zd, Am, q') + Vmt (6)

    where E'mt = observed expenditures on durables inyear t; q' = actual hours of wife's work in paid em-ployment in year t; Am = total family income includ-ing wife's earnings (i.e., Am= Y+ Peqe); Zd is the vec-tor of preference and productivity shifters; and vmt sthe random error term. A comparison of Equation 5

    I Wife's earnings are not included in income since qe is endoge-nous.

    5 The effect of pe on qd, holding satisfaction constant, is called thecompensated cross-price effect of Pe on qd. It is denoted as

    JqdIbPe1u=cn nd is linked to the cross-price effect (which does nothold utility constant), &qd/lSPe, by the Slutsky equation, bqd/6Pe1u=cn= 'qd/lPe - qe(&qdlb Y), where &qdlb Y s the effect of income on thedemand for durable services. See Henderson and Quandt (1971, p.29).

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    40 THE JOURNAL OF CONSUMER RESEARCH

    and Equation 6 reveals some of the problems with theliterature.

    Although E*m, (annual net change in durablestocks demanded) can be positive, zero, or negative,E'm, (actual current durables expenditures) can be

    positive or zero. In other words, E'm, is an index ofE*mt that is truncated at zero. Fitting Equation 6 viaOLS produces biased estimates of Equation 5. Esti-mating Equation 6 via tobit provides consistent esti-mates as long as the sample is large (Kinsey 1981).Only Weinberg and Winer (1983) used tobit. The restof the literature contains truncation biases.

    Although the theory posits effects of prices (Pd, Pm,po. and Pe) on durables purchases, the empirical liter-ature has ignored these variables at the risk of biasedresults. With respect to Pm,Pd, and po, the risk is quitesmall since, in the cross-section samples used, theseprices are constant or are held constant with regional,rural/urban, and racial dummy variables. The risk ofbiased results increases with respect to the price ofwife's time, Pe, which varies widely in a cross-section.The price of wife's time, however, is determined byher age and education as well as the family's demo-graphic characteristics and income excluding herearnings (Zick and Bryant 1983). The inclusion ofsuch variables in a cross-section expenditure equa-tion will normally take care of the cross-section varia-tion in Pe

    Contrary to the theory (i.e., Equation 5), last peri-od's stock of durables, Es,-,, also has been excludedas an independent variable n the literature Equation6). This, too, creates statistical bias, possibly causingproblems in the interpretation of the coefficient on qein such equations. However, Appendix II shows thatthis bias should not affect the sign of the coefficienton qe.

    In an attempt to determine whether wives' house-hold work time and durables are substitutes or com-plements, the literature has analyzed the relationshipbetween durables expenditures and actual wife's em-ployment, q'e (see Equation 6). Putting aside the in-terpretation of the coefficient on qe until the next sec-tion, the use of actual wife's paid hours, q', as a re-gressand yields a statistically biased estimate of theeffect of wife's employment on durables expendi-tures, because along with durables expenditures andexpenditures on one-use goods and services the actualwife's employment hours are endogenous to the sys-tem (see the Figure). Consequently, qe is correlatedwith the random disturbance term, VM, in suchequations (Johnston 1972), and produces statisticallybiased estimates of the coefficients in Equation 6.

    One reason for this correlation arises out of thefamily's decision process, which is subject to incomelimitations. As a result of family decision-making be-ing subject to budget and time limitations, plannedand actual total expenditures must equal planned and

    actual total family income, respectively. Planned to-tal expenditures refer to durables expenditures, Pmm,plus expenditures on one-use goods and services,p,q,. Planned total family income refers to Peqe + Y-Am. Thus,

    PMM + poqo = Peqe + Y-Am (7)

    Denoting actual magnitudes with a prime (i.e., m',q', q'), the difference between planned and actualmagnitudes is random error, ui (i = m, o, e). Thus,

    Pmm' = Pmm + PmUm,

    poq0 = poqo + po uo, and

    Peqe=Peqe+PeUe. (8)Since total actual expenditures also must equal totalactual income,

    pmm'+poqo=Peqe+ Y. (9)Substituting Equation 8 with Equation 9 yields

    pmm +poqo = Peqe + Y (PmUm + PoUoU PeUe).

    (10)

    Since actual total expenditures must equal total fam-ily income, the expression in parentheses must, there-fore, equal zero. Thus,

    PmUm+ Po Uo= PeUe; (11)that is, the sum of the random errors on the two ex-penditure functions must equal the random error at-tached to wife's paid employment hours times herwage rate. In Equation 6, the regression of durablesexpenditures, E'm on qe and other variables, pmum= Pe Ue-Po Uo= Vm.Therefore, vm and qe n Equation6 include Ueand are correlated, causing simultaneousequations bias in the estimates (Pollak and Wales1969; Summers 1959).

    Another reason for the correlation of qe and vm nEquation 6 is heterogeneous preferences (Rosen-zweig and Wolpin 1980). Because the householdmakes decisions about the magnitudes of both dura-bles expenditures and wife's employment hours, eachis affected by unobserved variables not included inthe systematic portion of Equation 6. For instance,the spouse's health affects the current demand for du-rables as well as current employment of the wife. Ahost of other unobserved variables affects both. Theseleft-out variables common to E'm and qeare capturedin vm and are present implicitly in qe through theircorrelations with it. Consequently, qe and vmare cor-related and the parameters of Equation 6 contain sta-tistical bias. This same correlation between qe and vmalso contaminates total family income, Am. Since to-tal family income includes wife's earnings, Peqe, thenAm and vmare correlated.

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    DURABLES AND WIVES' EMPLOYMENT 41

    Unless the correlation between vm and qe s purged,the statistical bias introduced throws into doubt theevidence on the major hypothesis investigated by theliterature: whether durables and wives' time are com-plements or substitutes. The Empirical Analysis sec-tion provides a procedure for purging q'eof Ue, andthence of vm.

    The Theoretical Relationship BetweenEm, and qe

    In the literature, the effect of q'eon E', in regres-sions like Equation 6 has implied that durables andwives' home time are either complements or substi-tutes. This is clearly inappropriate since the hypothe-sis is about the effect Of Pe on E*m in an equation likeEquation 5. Unless a theoretical link between theeffects of qe on E'm and of Pe on E*m can be estab-lished, the empirical literature cannot be used to de-

    termine whether durables and wives' home time arecomplements or substitutes.Equation 6 has the form of a conditional expendi-

    ture function. The relationship between uncondi-tional and conditional expenditure functions pro-vides the needed theoretical link between the effectsof q'e n E'm nd Of Pe on E*m (Pollak 1969). A condi-tional expenditure function is the expenditure on agood, i, when the quantity consumed of some othergood, j, has been fixed and the consumer is unableto choose it. When the wife's..employment ime (and,therefore, home time) is fixed, the conditional dura-bles expenditures function has the following argu-ments:

    Em e =Em e(pd, pO, qe, Am, Zd, St-l) (12)where Em e(.) denotes the demanded durables ex-penditures conditional on wife's employment; qe= the fixed annual hours the wife is employed, and Am= Y + Peqe = total family income.

    The idea behind the inclusion of qe in the condi-tional durables expenditures function is that the fixedlevel of consumption of the wife's home time (q1= T- qe, where T = total time available) affects the con-sumer's preferences for all other goods including du-rables. Therefore, the wife's fixed hours of paid em-ployment becomes an exogenous variable affectingdurables expenditures. Am is family income not

    earned by thewife

    plusher

    earnings, i.e.,total

    family6income.

    In the unconditional case, when the wife's employ-ment time is not fixed and she can choose her ownhours of paid work, the durables expenditures func-tion is Equation 5. The relationship between Equa-tion 12 and Equation 5, therefore, provides the neces-sary link between the effect of q, on Em. e and theeffect of Pe on Em. If the consumption of the fixedgood, qe, is fixed at the level the family would havechosen had it been able to choose, then the uncondi-tional durables expenditures function, Em(.), mustequal the conditional demand, Em. e(.); i.e.,

    Em . e(pd, po, qe, Am, Zd, Est-,)

    Em(pd, Po, Pe, Y, Zd, Est-,) (13)

    where qe is the hours of paid wife's employment thefamily would have chosen if it had had the choice.

    The relationship between the effect of qe on Em. e(i.e., what the literature has studied) and the effect ofPe on Em (i.e., the effect that indicates whether dura-bles and wives' home time are complements or substi-tutes) can be derived from Equation 13 (see AppendixI):

    bEm *el/qe Q6Em/Pe1u=,cn)/(6qe/3Pe)

    - Pe(QEm * el/Am ) (14)

    where bEm *e/lqe is the effect of qe on durables expen-ditures from the conditional durables expendituresfunction (i.e., the left-hand side of Equation 13);6Em/6Pe1u=cn s the effect of wife's wage rate on dura-bles expenditures, holding utility constant, and is de-rived from the unconditional durables expendituresfunction (i.e., the right-hand side of Equation 13 orEquation 5); 3qel/Pe effect of wife's wage rate onwife's hours employed, not holding utility constant,and is derived from the wife's labor supply function,qe = he(.) (see Equation 1); and, bEm * /bAm s the in-come effect on durables expenditures in the condi-tional durables expenditures equation (i.e., left-handside of Equation 13).

    The effect of wife's employment time, qe, on dura-bles expenditures, Em * , as shown by Equation 14 isclearly more complicated than what has been recog-nized in the literature. It includes the effect OfPe ondurables expenditures, holding utility constant,bEm/pel u=cnwhich determines whether durables andwives' time are substitutes or complements. It also in-cludes the effect OfPe on wife's employment time andthe effect of total family income, Am, on durables ex-penditures and its sign will depend on the signs of allthree terms.

    6Em/6pe1u=cnwill be positive (negative) as durablesand wives' household time are substitutes (comple-ments). Much empirical evidence confirms that iqe/bPe s positive, i.e., that married women increase theannual hours they are employed in the face of an in-

    6 When her employment time is not fixed and is a matter or fam-ily choice, her earnings are implicitly a matter of choice as well,being chosen simultaneously with durable expenditures. Conse-quently, her earnings are not exogenous and not included in theincome variable. When her employment time is fixed as in Equa-tion 12, however, her earnings are also and should be included inthe income variable. n this formulation, pe has no effect other thanthrough Amand, therefore, s dropped as a separate exogenous vari-able.

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    42 THE JOURNAL OF CONSUMER RESEARCH

    crease in their wage rates (Killingsworth 1983). And,the fact that durables are normal goods means thatPe3bEme/bAm s positive. This analysis leads to threealternative nterpretations of Equation 14, dependingupon which one of the following conditions is met

    empirically.Cl: If bEm. e/lqe> 0, then durables and wives'

    time are substitutes as per Strober and Wein-berg(1977, 1980).

    C2a: If 3Em. el3qe < 0 and

    C2b: bEm *e/lqe + Pe(bEm *ePbAm < 0, then du-rables and wives' home time are comple-ments as per Galbraith (1973).

    C3a: If bEm *e/lqe < 0 and

    C3b: bEm. e/lqe + Pe(3Em el6A,) > 0 then du-rables and wives' home time could be sub-stitutes or complements.

    The empirical literature on the subject has used thesign of the coefficient on the wife's employment in du-rables expenditures or purchase equations to judgewhich of the substitutes and complements hypothesesis correct. Actually, the analyst also must determinewhether Condition 2b or Condition 3b holds empiri-cally. Condition 3 reveals that interpretation of thedata still is ambiguous when;.both Condition 3a andCondition 3b hold.

    EMPIRICAL ANALYSISIn this section, we conduct an example cross-sec-

    tion analysis of aggregate durables expenditures andapply solutions to the problems discussed. After thedata are discussed, an instrumental variable approachis described that purges wife's employment, qe, of itscorrelation with vm. We then discuss the results of es-timating the durables expenditures function.

    DataThe data come from the 1977-1978 Survey of Con-

    sumer Credit in which the same sample families wereinterviewed in 1977 and 1978. Information on dura-bles expenditures was collected for 1976 and 1977,and data on wives' employment were collected for1977.7A sample of married-with-spouse-present am-ilies was selected in which no secondary family units

    were present and the husband was employed (he wasneither a student nor retired).8

    In 53 percent of the 1,208 families sampled in 1977,the wife was employed some time during the year.The average expenditure of the families who made

    durables purchases (3.7 percent) in 1977 was $934,and the average expenditure for sample families mak-ing purchases (10.9 percent) in 1976 was $920. Aver-age total family income for 1977 sample families was$16,311.

    PURGING q' OF ueIn estimating Equation 6, the conditional durables

    expenditures function, recall that actual wife's em-ployment, qe, is correlated with vmbecause both con-tain Ue. The correlation causes the estimated coeffi-cients to be statistically biased. This section describesan instrumental variable for qe hat is purged of thecorrelation.

    Purging qe of Ue involves estimating by a two-stepprocess the wife's labor supply function, qe= he( ) (seeEquation 1), for each sample wife. The first step is tocalculate an adjustment for any sample selection biasinvolved in using data on employed wives to estimatethe labor supply function for all wives, employed ornot. The second step is to estimate qefor each wife inthe sample using the adjustment for sample selectionbias (see Heckman 1979).

    Data on whether the wife worked and usual weeklyhours worked were available for 1977. Wife's employ-ment time, qe, was defined as usual weekly hoursworked multiplied by 50 weeks. The following proce-dure was employed to purge qeof its correlation withUeand hence vm. A probit equation was estimated us-ing the total sample (1,208 sample points) and havingas its dependent variable a dummy variable taking onthe value of one, if the wife was employed during1977, or zero, if not. From this probit equation a vari-able that was equal to z(X)/(l - Z(X)) and calledlambda was calculated for each sample point.9Lambda is the adjustment for sample selection bias.Utilizing the part of the sample with employed wives(640 sample points), an annual hours of work equa-tion was estimated via OLS with lambda included asone of the explanatory variables.

    The independent variables in both equations were

    7 Durables are defined in the survey to include all home appli-ances, furniture and home electronic equipment, musical instru-ments, lawn, garden and workbench equipment and tools, recre-ation and sports equipment, and so on. Cars, real property, andmobile homes are excluded.

    8 A reviewer suggests hat response bias may result from the in-creased time pressures hat accumulate when two spouses are em-ployed, and therefore ewer wo-career amilies will have respondedto the questionnaire. Perhaps his is true. However, the procedureused to purge e of ue, devised originally o adjust or sample selec-tion bias, also adjusts or this sort of response bias.

    9 z(X) is the value of the unit normal density function estimatedfrom the probit function, and Z(X) is the value of the unit normaldistribution function also estimated from the probit function(Heckman 1979).

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    DURABLES AND WIVES' EMPLOYMENT 43

    TABLE I

    ESTIMATE OF PROBIT EQUATION OF PROBABILITY OF WIFEBEING EMPLOYED AND OLS ESTIMATE OF

    ANNUAL HOURS WORKED BY WIFE

    Ordinary eastIndependent variable Probit equation squares

    Intercept -.4731 -1507.9948Age -.1486-01 58.1101Age squared .6961-05 -1.2441Education .1001a 110.9461Agea education .2649-03 1.6026Family size -.1 140c -244.5530bAge of youngest child .2363-01 48.2487cAge of oldest child .1291-02 -13.25001, if own home .7258-02 103.6828a1, if white .3834-01 -330.0071 b1, if black .2575 163.48401, if North Central -.6435-01 -9.72611, if South -.3489-01 71.70201, if West -.1609 -374.9191 b

    1, if city .1582 a 238.04271, if rural .1566 127.1348Husband's income -.9942-05c -.02011 bLambda 2458.5372aX2 134.4c -Adjusted R2 .1 Oc

    ap < 0.10.b

    cp < 0.01.NOTE:OLS estimate adjusted or sample selection bias.

    identical with the exception of lambda, which was in-cluded in the hours of work equation and estimatedon the basis of the probit results. The remaining inde-pendent variables were: wife's age in years; wife's agesquared; wife's education in years of school com-pleted; wife's age interacted with wife's education;family size; age of youngest child in the family; age ofoldest child in the family; house tenure dummy, tak-ing on the value of one if the home was owned; previ-ous marital status dummy, taking on the value of oneif the head of the household had been previously mar-ried; race dummies, measuring whites and blacks ver-sus others; region dummies, measuring the NorthCentral, South, and West versus the Northeast region;residential location, measuring city and rural resi-dence versus suburban residence; and husband's in-come measured as total family income minus wife'searned income. The age and education variables areincluded for their own sakes and as proxies for thewage rate, a variable unavailable in the data set.

    Table 1 shows the results of these two equations.Husband's ncome, family size, education of the wife,and city residence have effects significantly differentfrom zero in the probit equation, but husband's in-come, family size, age of youngest child, home owner-ship, white race, location in the West, and lambdawere significant in the employment hours equation.

    That lambda was significant indicates sample selec-tion bias was present and lambda is successfully ad-justing for it. These results are reasonable and consis-tent with other labor supply studies (Killingsworth1983).

    The results of the OLS equation were then used toestimate the hours of work supplied, qe, by each wifein the sample; qe, then, is the instrumental variableused as an explanatory variable in place of q'e in theconditional durables expenditures function, Equa-tion 6. As constructed, qe is a consistent estimate ofthe hours of employment for each wife in the sample,employed or not. What is crucial in the present con-text, however, is that qe is purged of its correlationwith vm.

    DURABLES EXPENDITURESFUNCTION

    The analysis used expenditures on durables by sam-ple families in 1976 and 1977 as the dependent vari-ables. Estimated hours of market work per year sup-plied by the wife, qe, was the explanatory variable onwhich this study focused. Family size and the wife'sage controlled for size and stage in the life cycle. Non-real estate net wealth (financial assets plus the valueof the family's car stock minus nonreal estate debts)and family income less wife's earnings in 1977 repre-sented the family's resources.'0 Wife's earnings weresubtracted from family income to remove the wagerate effect implicit in the income effect if wife's earn-ings were included. The family's housing tenure (adummy equal to one, if the residence was owned) wasincluded, based on the hypothesis that durables pur-chases and owned housing stock are related (ownedhousing representing a component of family wealth).Region (dummy variables for North Central, West,and South versus the Northeast), race (whites andblacks versus others), and residential location(dummy variables for rural and city residence versussuburban residence) were included not only as prefer-ence shifters, but also as control for price differencesacross the sample. The problems of leaving prices outof the equation were thus minimized. Although lastperiod's durable stock, Se,-, was left out because itwas not available, Appendix II shows that its omis-sion would not affect the sign of the coefficient on qe.

    Two durables expenditures functions for 1976 and

    '? The data contained information on the makes and ages of upto three cars per family. Blue book values were assigned given themake and age of each car.

    Total family income rather than total family income minuswife's earnings was used in all previous articles on this subject.Since total family income includes wife's earnings, Peqe = Pe,e+ PeUe (see Equation 8), total family income is also correlated withvm. Using total family income minus wife's earnings removes thiscorrelation and prevents statistical bias.

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    44 THE JOURNAL OF CONSUMER RESEARCH

    TABLE 2

    1976 AND 1977 TOBIT ESTIMATES OF DURABLESEXPENDITURES FUNCTION

    Normalized tobit

    coefficientsVariable 1976a 1977a

    Constant -153.39 -2892.57f1 if own home 417.35 84.041 if rural -526.98 1830.25'1 if city 325.48 1664.25f1 if white -606.89e -350.121 if North.'Central 833.25e 798.83d1 if South 723.25e 688.101 if West 342.20 -379.23Wife's age -65.14f -52.04fFamily size -30.73 -78.64Family ncome less wife's earningsb 4.03 15.19Expected wife's hours workedc -292.43' -264.1 9dNet wealthb -11.75e _7.39

    Standard error 2116.29 2155.51a Likelihood ratio test for equation significant at 0.01.b In thousands of dollars.c In thousands of hours.dp< .10.ep < 0.05.fp < 0.01

    1977 were estimated via multivariate tobit to avoidany truncation biases. These equations yielded esti-mates of bEm * l5qe and bErn e/bAm, the coefficientscrucial to the hypotheses. The 1977 estimates ofwife's employment hours were used in 1976 and 1977

    equations because only the 1977 hours were avail-able. This tactic may have further purged qe of Vm,since 1977 estimated wife's employment hours can beviewed as an instrumental variable for 1976 wife'semployment hours, resulting n somewhat better esti-mates for 1976 than for 1977.

    RESULTSThe 1976 and 1977 tobit estimates of the expendi-

    ture equation are shown in Table 2. The normalizedtobit coefficients shown in the table are bi/s where biis the tobit coefficient on the ith variable and s is thestandard error of the equation. The tobit estimateswere obtained by means of the SAS Tobit program.

    This section focuses on the results for the estimatedwife's working hours and the income variables. Thecoefficients on the estimated wife's hours worked, qe,are negative and significantly different from zero atthe 0.10 percent level for 1977 and 0.01 for 1976. The1976 coefficient is the larger of the two. Both of theseresults are consistent with the view that qe has beenmore completely purged of its correlation with therandom disturbance term in the 1976 equation than

    in the 1977 equation. Thus, it is apparent that the to-tal effect of wives' employment on durables purchasesis negative. As the wives' involvement in employmentgrows larger, the demand for durables falls.

    The income effects are both positive and not statis-tically different rom zero. They have been kept in theequation despite their nonsignificance to provide theestimates of the income effects needed to evaluateEquation 14 and, thus, to interpret the coefficienton qe.

    What do these results tell us about whether dura-bles and wives' time are substitutes or complements?Because the hypothesis concerns the underlying de-mand structure-i.e., whether wives' time and dura-bles are substitutes or complements-we are inter-ested in the tobit coefficients themselves rather thanthe marginal effects derived from them after the fash-ion of Kinsey or MacDonald and Moffitt.12 The co-efficients displayed in Table 2 are normalized (i.e., bi/s) whereas the sign of the bi speaks to the hypotheses.Since the normalization is the same for all coeffi-cients, the normalized coefficients can be used to testthe hypotheses.

    Recall from Condition 2 and 3 in the Problems sec-tion that if the coefficient on qe s negative, Condition2b also must hold if durables and wives' home timeare complements. Because the coefficients on wife'semployment are negative, we must also obtain an es-timate of Equation 14. We possess the estimates ofbEm- e/lqe and bEm * PbAm. Dividing the sample av-erage annual wife's earnings ($4,311.92) by the esti-mated annual hours worked (1389.24 hours) gives usan estimate OfPe, wife's wage rate. This yields an aver-age hourly wife's wage rate of $2.56 per hour. Multi-plying the normalized income effect by $2.56 yieldsthe estimates of PebEm-e/lbAm f 38.9 in 1977 and10.3 in 1976. When these estimates of the last termon the right-hand side of Equation 14 are added to theestimates of the first term on the right-hand side ofEquation 14, the results are -264.19 for 1977 and-292.43 for 1976. Condition 2 is met; consequently,we can accept the Galbraith (1973) hypothesis thatwives' time and durables are complements.

    Residence location (rural versus city versus suburb)was quite important in 1977, but less so in 1976. Re-gion of residence variables are significant as a group,but the variables are not very significant ndividually.A chi-squared test of whether the region variables asa group contributed to the explanation of durables ex-penditures was significant at the 0.01 level. Wife's agehad a significant effect in each equation, but familysize was unimportant in both years.

    Nonreal estate net wealth had a negative effect inboth equations but was different from zero only in

    12 See Maddala 1983, Section 6.6).

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    DURABLES AND WIVES' EMPLOYMENT 45

    1976. One would have expected this variable to havea positive effect since it represents resources as doesincome. However, the negative coefficient may reflecta number of other influences, such as multicollinear-ity between net wealth and income. Or, since the non-

    real estate net wealth variable and durables are partof the family's asset and debt portfolio, portfolio sizeand composition effects may overshadow any incomeeffect on durables expenditures.

    CONCLUSIONSThe%purposes f this article were to identify and

    propose solutions to the problems that have beset theliterature analyzing the effects of wives' employmenton consumption patterns, to utilize the proposed so-lutions in an example analysis of durables expendi-tures, and to shed light on the issue.

    The literature has drawn erroneous conclusionsabout the relationship between expenditures or pur-chases and the value of wive's time from analyses ofthe relationship between expenditures or purchasesand wive's employment. This article developed thetheoretical linkage between the two relationships sothat such analyses could be properly interpreted. Aninstrumental variable approach was suggested bywhich statistical estimates of the relationship betweenexpenditures or purchases and wives' employmentcould be purged of statistical biases. The theoreticalrelationship and the statistical procedure are general.They can be applied in any analysis of consumptionbehavior that focuses on a cross-price effect (e.g., theeffect of the price of wives' time on durables expendi-tures), but that has no data on the price in question.In the empirical analysis, when the correlation be-tween the random disturbance term in the durablesexpenditures function and wives' employment wasremoved, the estimates of the effect of wives' employ-ment on durables expenditures were uniformly nega-tive and significantly different from zero. These nega-tive signs, in conjunction with those found for Equa-tion 14, clearly indicate that wives' time and durablesare complements rather than substitutes.

    These results contrast with the literature's results,which either show no relationship between wives' em-ployment and durables expenditures, or, in a fewcases, show that specific durables and wives' time aresubstitutes. The present results relate to total durablesexpenditures, but the results in the literature ypicallyare much more disaggregated. Nothing in this articledenies that certain types of durables may be substi-tutes for wives' time (or anyone else's, for that mat-ter). Indeed, a determination of which types are sub-stitutes and which are complements is of interest tostudents of consumption and the family. The resultsin this study, however, indicate that durables andwives' time are complements.

    Therefore, wives' time and the family's total dura-bles tend to be used together n home activities. Dura-bles are not substituted for the time wives spend inhousehold activities as wives become more involvedin the labor market. As wives' time becomes more

    valuable and they are drawn nto the labor force, theyspend less time in household activities, with the ex-ception of entertainment and social activities (Koore-man and Kapteyn 1987). When this happens, familiessubstitute one-use goods and purchased services suchas meals away from home and child day care for thewives' home time (Bellante and Foster 1984). Themarkets for both of these services are burgeoning.13

    APPENDIX IThis appendix derives Equation 14, the relation-

    ship between the effect of qeon durables expenditures,Em. e, in the conditional expenditure function and

    the effect OfPe on Em in the unconditional expendi-tures equation.Equation 13 says that the conditional and the un-

    conditional durables expenditures functions areequal to each other when qe is fixed at the level thehousehold would have chosen had it been able to. Tofind the effect of qe on Em. e, differentiate Equation13 with respect to Pe:

    (Emm e/1qe)(5qe/5Pe) + (5Em * /5Am )[(5Am/tPe)

    + (bAm/&qe)(qe/15PeA)] = bEm/5Pe. (15)

    Recognizing that 5Am,/Pe = qe ( Aml/tqe = Pe, bEm/lPe= Pm(5Cm/5Pe) and solving Equation 15 for bEm. el5qe

    yieldsbEm e/lqe = pm(bcm/5pe)/(5qe/5Pe)

    - qe(5Em. eP5Am)/(5qe/5pe) - Pe(bEm e/bAm), (16)

    where cm = the unconditional demand for durablesand Em *e is the demand for expenditures on durablesgiven wife's employment hours, qe, are fixed. bCm/lpeis the cross-price effect of the price of wife's timeon the unconditional demand for durables. It canbe decomposed into a cross-substitution effect,bCm/lpelu=cn where the lu=cnnotation means utilityheld constant), and an income effect, qebCm/bY, ac-cording to the Slutsky equation (Henderson and

    Quandt 1971) as follows:bCml/Pe = bCml/Pelu=cn + qebcm/lY. (17)

    The cross-substitution effect is the effect OfPe on dura-bles demand, holding satisfaction constant. The signof this cross-substitution effect indicates whether du-

    13 See Steiner (1971, p. 52) for 1969 day care figures and Coelen,Glantz, and Calore (1979. p. 74) for 1977 day care figures. SeeBunch ( 1984) for the trends n the away-from-home ood market.

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    46 THE JOURNAL OF CONSUMER RESEARCH

    rables and wife's time are substitutes or complements(Henderson and Quandt 1971).

    Substituting Equation 17 into Equation 16 yields

    bEm * e/lqe = Pm(b Cm/15Pe1 =cn /(5qe/5Pe)

    + qe[QbEm/5Y) - (bEm *e/bAm ]/(bqe/1Pe)- Pe(5Em * e/bAm). (18)

    Given that qe s fixed at its equilibrium level, bEm/l Y5bEmr PbAm,making the term in the square brack-

    ets equal zero so that Equation 14,

    bEm e/bqe (bEm/lpeI u=cn/(&qe/5Pe)

    - Pe(Em *ePbAm),

    where bEm/5pe1u=cn = Pm(Cm/15PeIu=cn), i.e., the in-come-compensated effect of the price of wife's timeon durables expenditures.

    APPENDIX IIThis appendix discusses the extent of the statistical

    bias involved in excluding from the durables expendi-tures function the stock of durables n t - 1 evaluatedat period t prices, Es,-,.

    Begin with the purchase identity, Equation 2a. As-suming durables services are proportional to the du-rables stock, we can express the demand for durablesservices as the demand for the stock. Writing the de-mand for the stock in its conditional form,

    Stf = gde (qet, Am,, ZdI) (19)

    and substituting Equation 19 into Equation 2a yieldsml = gd e(qet, Am,, Zdl) - (1 - a)St-Id. (20)

    Now, since 511d is typically unavailable in cross-section data,

    mt = g (qet, Am,, ZdI) (21)

    is usually estimated, creating left-out variable bias inthe coefficients. In particular, the expected value ofthe coefficient on qe, n such a regression will be

    E(#3*) = f3e + bset3s, (22)

    where f3e = true value of the coefficient on qe; 13e*= OLS estimate Of e; s3s true value of the coefficienton S_ id in Equation 20; and bse = the coefficient on qein a regression of S_-1don qe. Note that Os= -( 1- a).

    Although Equation 19 is the equation for the de-mand for the stock in t, the equation for the demandfor S_ Id is identical except for the time subscripts.That is, f3e is the effect of qe on the demand for thestock, regardless of the year. Consequently, the re-gression of S1_d on qelcan be regarded as a two-vari-able approximation to the multivariate relation.Thus, bse is an approximation Of 13e, .e.,

    bse f3e. (23)Given this approximation and the fact that fs = -(1- a) = a - 1, then

    E(e*)- de Oe(a O = Oe( 1I+ a - 1) (24)or

    E( e* dae (25)Since 0 < a < 1, then any conclusion as to the sign ofafe will also hold for e. That the empirical modeltreats purchases and not stocks and also excludesSt-Id iS unfortunate, but not fatal.

    [Received March 1985. Revised September 198 7.]

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