IMeasurement of the value of homemaker's time: an ... · second variant is the specific services...

Journal of Economic and Social Measurement 23 (1997) 149-162 149IOS Press

IMeasurement of the value of homemaker's time:an empirical test of the alternative methods of theopportunity cost approach

Deanna L. SharpeDepartment of Family and Consumer Economics, University of Missouri, Columbia, MO 65211, USATel.: +1 573 882 9652; Fax: +1 573 884 8389; Email: [email protected]

Mohamed Abdel-Ghany*Department of Consumer Sciences, Box 870158, The University of Alabama, Tuscaloosa,AL 35487-0158, USATel.: +1 205 348 7954; Fax: +1 205 348 3789; Email: [email protected]

Household production is typically measured by estimating the time that the homemaker spends in thevarious household activities. The focus in this paper was on valuating the household production timeof Canadian full-time homemakers. Four variants of the opportunity cost approach, namely, imputedwage, potential wage, Heckman's two-stage reservation wage, and Kidd's reservation wage were usedto estimate and compare homemaker's time. The results indicate that the four different variants yieldeddifferent estimates of the value of household production time. One of the main conclusions is thatHeckman's two-stage reservation wage approach, albeit having the advantage of correcting selectionbias, it produced a wide range for the estimated reservation wage, which led us to doubt its reliabilityas a practical measure of the value of household production time.

Keywords; Household production time, opportunity cost approach, reservation wage

1. Introduction

Major conceptual frameworks pertaining to measuring the value of homemaker'stime were introduced in the 1930s with work by Kyrk [19] and Reid [34] andin the 1960s with work by Mincer [23] and Becker [2]. Heckman's significantcontributions in the 1970s [15,16] have led to numerous research articles. In the1980s and 1990s a number of theoretical papers have criticized the restrictiveassumptions of the Heckman's model and found that the results arising from itsapplication yield a wide range of the estimated reservation wage [11,17,20,28,29].

It is important to have accurate measures of household production. Underestima-tion of the gross national product results when the value of household production isexcluded. The magnitude of underestimation depends on the relative shares of mar-ket and household production in the economy. Comparisons of the gross national

'Corresponding author.

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150 D.L Sharpe and M. Abdel-Ghany / Measurement of ihe value of homemaker's time

product between different countries that do not include the value of householdproduction are unreliable. The value of household production and the importanceof its inclusion as a component of the gross national product has been recognizedby researchers since the early twenties [24].

Accurate use of income distribution as a measure of economic well-being ne-cessitates the adjustment of household income to reflect the value of householdproduction [26,33,37]. Failure to tax the imputed value of household productionleads to discriminatory treatment of households with the same market income butwith different household production levels [22,27]. Valuing homemaker's time isrequired for the assessment of damages in divorce, wrongful injury, and deathlitigation.

Three general methods for valuing household production have been used by re-searchers over the years. One such method is value-added. This method involvesmeasuring household outputs in physical units and evaluating them at market prices,then subtracting the cost of purchased inputs, resulting in the value-added by house-holds [3,9,35]. To determine a wage rate for the homemaker, the value-added forthe different commodities produced during a specific period of time is divided bythe number of hours spent in production.

The second method of valuing household production time is replacement costwhich measures the value of household production time in terms of what it wouldcost to replace it in the market. There are two main variants of replacement cost.The first is the equivalent homemaker method [5] in which the wage rate of ahousekeeper who provides the same package of household tasks is used to calculatethe value of time spent by the homemaker in producing household production. Thesecond variant is the specific services replacement cost method. It is determinedby using the equivalent market wage rate of a specialist for each task times thenumber of hours spent by the homemaker performing the task [10,14,33].

The third method of valuing household production time is the opportunity costapproach. According to this method, the value of household production time iscalculated by multiplying the total housework time by a single wage rate whichreflects the next best alternative as determined by the homemaker productivityrelated characteristics.

Advantages and disadvantages of these methods are discussed in Chadeau [4],Ferber and Birnbaum [7], Goldschmid-CIermont [12], Hawrylyshyn [14], Kinsey[18], Murphy [25,26] and Zick and Bryant [36,37]. The objective of this study isto estimate the value of homemaker's time in Canadian households using variantmethods of the opportunity cost approach and to evaluate the relative limitationsand merits of these various methods.

2. Methodological variants of the opportunity cost approach

The basic premise of the opportunity coat approach is that the alternative use ofone's time is worth the value at the margin. This premise implies that the value of

D.L. Sharpe and M. Abdel-Ghany / Measuretnent of the value (if homemcticer's time 151

household production time is at least the market value of the next best alternative,as determined by the homemaker's productivity-related characteristics.

The opportunity cost of household production time for individuals who work inthe market is estimated by multiplying the number of hours spent in householdproduction by the market wage rate (net of taxes). However, for individuals whoare not employed in the market, assigning a wage to reflect the value of theirhousehold production time is problematic. Four methods of solving this problemhave been proposed.

Some researchers [7,8] have estimated the wage rate over the employed individ-uals in the sample and imputed the wage rate for those who are not employed inthe market according to their personal characteristics. The imputed wage is thenmultiplied by the number of hours spent in household production to give a lower-bound estimate of the value of household production time. However, this methodof imputing wage to those who do not work in the market leads to a censoringbias in the wage estimate due to the use of the endogenous criterion of labor forceparticipation as the basis for selecting the sample [8,13,15,16,22,37].

Seminal work by Heckman [15,16] led to development of models that correctfor the effects of non-random sampling and the estimation of potential wages andreservation wages. The potential wage is the wage an individual could earn in themarket given that individual's human capital endowment. The reservation wage,on the other hand, is the minimum wage that would entice an individual to jointhe labor force [18].

Three steps are involved in using the Heckman two-stage correction procedureto estimate the potential wage. First, probit analysis is used over the entire sam-ple to determine the probability that an individual participates in the labor force.The parameters of the probit model are then used to derive lambda (A), the in-verse Mills ratio. Second, lambda is used as an additional regressor in a wageequation which is estimated using ordinary least squares over the sample of laborforce participants. Third, parameters from the wage equation are used to estimatethe potential wage rate for individuals with specific personal and labor marketcharacteristics.

Kinsey [18] notes that the derived potential wage could he higher or lowerthan the actual wage for labor force participants. However, it must be lower thanthe reservation wage for those who are not in the labor force. According to thismodel, a person participates in the labor force only if market wages exceed hisor her reservation wage. The potential wage has been used to value householdproduction time [22,32].

The third method, the reservation wage, can also be estimated using the Heckmantwo-stage model. Three steps are involved. First, self selection bias is correctedby using probit analysis to estimate an equation that determines the probabilityof labor force participation. The parameters of this equation are used to derivelambda (A).

152 D.L Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time

Second, a two equation system is used to estimate the reservation wage:

\nW = Xa-\-ei, (1)

\nW* = Z/3 + H6 + e2, (2)

where In VF = log of market wage; X = vector of characteristics determiningmarket productivity; \nW* = log of reservation wage; Z = vector of charac-teristics determining household productivity; H = hours of market work; and e\and e2 = error terms to capture unmeasurable or unobservable idiosyncratic tasteelements.

An underlying assumption of the model is that in equilibrium W* = W for em-ployed individuals, whereas W* > W for those individuals who are not employedin the market. Therefore, the reservation wage for a nonemployed individual isnot required to equal the wage the individual could have earned in the labor mar-ket. Rather, it signifies the wage required by the individual to make her/himindifferent between the last hour of household production and an hour of marketwork [37].

This model also assumes that the market wage does not vary with the num-ber of hours supplied in the market. However, the reservation wage is assumedto vary with the number of hours worked, implying that the marginal productiv-ity of time in the household varies with the amount of time spent in householdproduction whereas the marginal productivity in the market is invariant to hoursworked [37].

Since the reservation wage is unobservable, its estimation can only be derivedby equating Eqs (1) and (2) and estimating a labor supply function:

H=l{Xa-Zf3 + ei-e2). (3)0

After estimating Eqs (1) and (3), the reservation wage may he retrieved giventhat at least one variable in the X vector is not included in the Z vector (see [36]for detailed derivation of the reservation wage).

Several researchers have used this model to estimate the reservation wage [6,8,21,30,31,36,37]. Note, the model also assumes that the error terms in the criterion(probit) equation and the market wage equation are jointly normally distributed,with both means equal to zero and with a variance-covariance matrix equal to

where e and ei are the error terms in the probit and market wage equation, respec-tively [17].

The restrictive nature of the assumed bivariate normality of the error terms hasbeen criticized by some researchers [20,28,29]. Duncan [6], Ferber and Green [8],

D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time 153

and Goldberger [11, p. 79] found that the results arising from application of theHeckman's model are very sensitive due to departures from normality.

Kidd [17] suggested replacing Heckman's two-step procedure by a one-stepordinary least squares regression which includes the number of dependent childrenas an alternative proxy variable to Heckman's lambda. The number of dependentchildren was chosen as valid proxy for lambda because it satisfies two conditions:(1) it is highly correlated with the probability of women labor force participation,and (2) it has no a priori rationale for its inclusion in the wage equation, so that itserves to capture the essence of the omitted variable problem.

3. Data and characteristics of the sample

Data for this study are from the 1990 Canadian Survey of Family Expenditures.The sample used in this study consisted of 801 households in which the wife wasemployed in the marketplace, and 705 households in which the wife was a full-timehomemaker. Table 1 shows the means and percentages of the variables used in theanalyses.

Table 1Descriptive statistics of the sample

Variable

Wife's ageNumber of children under 16Husband's yearly income

Region of residence

AtlanticQuebecOntarioManitoba and Saskatchewan

AlbertaBritish Columbia

Wife's educationLess than 9 years of elementary educationSome or completed secondary educationSome post-secondary educationPost-secondary certificate or diplomaUniversity degree

Country of birth (Canadian bom)

Employed (n =mean

38.42

0.8179,502

17.4

23.822.814.512.78.7

3.744.1

8.528.715.0

80.8

801) Non-employed (n = 705)mean

52.44

0.6835,586

Percentage

16.7• 21.8

19.919.9

. 10.211.5

19.149.9

7.117.66.2

76.5

154 D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time

4. Results and discussion

4.1. Imputed wage approach

Since the survey did not include direct information about the hourly wage rates,total earnings were divided by the number of weeks of market work to derive theoffered market weekly wage. The average offered wage per week for Canadianwives who were employed in the market was $520.60. This wage is considered toreflect the estimated wage per week for household production time for those whowere employed in the market.

An ordinary least squares regression equation that regressed wife's age, educa-tion, occupation, region of residence, and whether the wife is Canadian born onoffered wage for all wives who were in the labor force was run. The regression co-efficients from the regression equation were then used to impute the hourly wageof wives who were full-time homemakers. Table 2 shows the wage regressionfor wives in the labor force. According to this imputation, the estimated weeklywage for a full-time homemaker was $470.17. As has been discussed earlier,this method of imputation leads to biased estimates due to selection bias of thesample.

4.2. Potential wage approach

The first step in the estimation of potential wage was to use probit analysisto estimate the probability of the wife's labor force participation over the wholesample. The dependent variable in the probit equation was the labor force partici-pation criterion which assumed a value of one if the wife's hours of market workexceeded zero, zero otherwise. The independent variables that were regressed onthe criterion included wife's age, education, number of children under the age ofsixteen, husband's income, value of dwelling, region of residence, and whether thewife is Canadian born. Table 3 presents the probit estimates of the parameters ofthe labor force participation index.

As seen in Table 3, the wife's age and education had a positive and significanteffect on the wife's probability of being employed in the market. However, thenumber of children under the age of sixteen and husband's income had a negativeeffect on wife's labor force participation.

The parameters of the probit estimation were used to calculate lambda (A) which,in turn, was used to adjust for censoring bias in the wage equation. The wage equa-tion was estimated using the ordinary least squares regression over the employedsample. Coefficients of the regression were then used to estimate the potentialwage rate for full-time homemakers.

The results of the ordinary least squares estimation appear in Table 4. As indi-cated in the table, the coefficient of the probit A was significantly different from


Table 2Wage regression for Canadian wives in the labor force

IndependentvariablesConstant

Age

Age^

Region of residence"Atlantic

Quebec

Manitoba andSaskatchewan

Alberta

British Columbia

Education''Less than 9 years ofelementary education

Some post-secondaryeducation

Post-secondarycertificate or diploma

Regression coefficient(Standard error)

5.729***(0.247)

0.021(0.012)

-0.0002(0.0001)

-0.251**(0.083)

-0.094*(0.039)

-0.220**(0.071)

-0.208***(0.057)

-0.090(0.057)

-0.111(0.087)

-0.100(0.063)

0.117**(0.041)

Independentvariables

University degree

Canadian born*̂

Occupation''Managerial andadministrative

Professional andtechnical

Teaching

Sales

Service

Fanning, fishing,forestry, and loggingoperations

Mining, processingand machinery

Product fabricating.assembling and repair

Construction

Adjusted R}

Regression coefficient(Standard error)

0.296***(0.057)

0.037(0.041)

0.200***(0.041)

0.266***(0.052)

0.148*(0.071)

-0.082(0.062)

-0.321***(0.053)

-0.135(0.273)

-0.179(0.151)

-0.210*(0.089)

-0.289(0.268)

0.26***

"Omitted category is "Ontario".''Omitted category is "some or completed secondary education"."̂ Omitted category is "non-Canadian bom".''Omitted category is "clerical".

*p < 0.05**p<0.01

***p < 0.001

zero, indicating tbat there were differences in unobservable factors between full-time homemakers and wives who were employed in the market. The estimatedpotential weekly wage for household production by full-time homemakers was$325.54.

Note, the potential wage for a full-time homemaker is less than the imputed wage(unadjusted potential wage) estimated previously. The results agree with previousstudies that contipared the imputed and potential wage models [8]. This potentialwage is considered a lower-bound estimate of home production time for full-timehomemakers.


Table 3Parameter estimates for the probability of labor force participation by Canadian wives

Independent variables Probit coefficient (Standard error)

Constant

Age

Age2

Husband's yearly income

Value of dwelling

Number of children under 16


Quebec

Manitoba and Saskatchewan

Alberta

British Columbia

Education''

Post-secondary certificate or diploma

University degree

Canadian bom'̂

-2.613***(0.537)0.222***

(0.026)

-0 .003***(0.0003)

-0.0O9E-O3***(0.002E-03)0.008E-04

(0.004E-04)-0.394***(0.042)

-0.204(0.200)

-0.042(0.096)

-0.210

(0.165)

0.001

(0.145)

-0.239(0.135)

0.334***(0.098)

0.705***(0.139)

0.106(0.094)

-Log-likelihood 555.35****p < 0.001

"Omitted category is "Ontario".''Omitted category is "some or completed secondary education".'̂ Omitted category is "non-Canadian bom".

4.3. Heckman's two-stage reservation wage model

Whereas the potential wage indicates the lower-bound estimate of the homeproduction time by a full-time homemaker, the reservation wage reflects the wagerequired by the individual to make her/him indifferent between the last hour ofhousehold production and an hour of market work. The empirical results of thewage equation, hours of work equation and the calculated reservation wage arepresented in Table 5.

Since there is no rule provided in the literature for the selection of the identifierto be used in the derivation of the reservation wage, with the exception that it


Table 4Wage regression for Canadian wives in the labor force after adjusting for censoring bias

Independent

variablesConstant

Age

Age^


Quebec


Alberta

British Columbia



Post-secondary certificateor diploma

University degree

Regression coefficierit(Standard error)

5.401***(0.280)

0.035**(0.013)

-0.004E-01**(0.002-01)

-0.267***(0.083)

-0.098**(0.039)

-0.245***(0.071)

-0.203***(0.056)

-0.100(0.057)

-0.191*(0.092)

0.101(0.062)

0.141***(0.42)

0.344***(0.060)

Independent Regression coefficientvariables

Canadian bom'̂



Teaching

Sales

Service

Fanning, fishing,forestry and loggingoperations



Construction

A

Adjusted B?

(Standard error)

0.047(0.041)

0.203***(0.049)

0.264***(0.052)

0.144*(0.071)

-0.078(0.062)

-0.320***(0.053)

-0.098(0.273)

-0.167(0.150)

-0.206*(0.089)

-0.275(0.267)

0.197**(0.079)0.27***

"Omitted category is "Ontario".''Omitted category is "some or completed secondary education".'̂ Omitted category is "non-Canadian bom".''Omitted category is "clerical".

*p < 0.05**p < 0.01

***p < 0.001

should be significant, wife's age was used alternatively to derive the reservationwage. Tbe estimated reservation wage was $2,192.29.

The restrictive nature of the assumed bivariate normality of the error terms hasbeen criticized by some researchers [20,28,29]. Abdel-Ghany et al. [1], Duncan[6], Ferber and Green [8], and Goldberger [11, p. 79] found tbat the results arisingfrom application of the Heckman's model are very sensitive due to departures fromnormality.


Table 5Parameter estimates for wife's market wage, hours worked, and calculated reservation wage

Independent variables

Constant

Age

Age^

Husband's yearly income

Value of dwelling

Number of children under 16


Quebec


Alberta

British Columbia




University degree

Canadian bom'̂

A

Average weekly hoursAdjusted R}

LN (wage)(St. error)

5.401***(0.280)

0.035**(0.013)

-0.004E-01**(0.002E-01)

-0.267***(0.083)

-0.098**(0.039)

-0.245***(0.071)

-0.203***(0.056)

-0.100(0.057)

-0.191*(0.092)

0.101(0.062)

0.141***(0.042)

0.344***(0.060)

0.047(0.041)

0.197**(0.079)

0.27***

Dependent variables

Hours(St. error)-8.774(17.42)

2.857**(0.925)

-0.037**(0.013)

-0.006E-02(0.004E-02)

0.009E-03(0.O05E-03)

-4.321**(1.423)

-3.881(2.132)

-2.994**(0.971)

-3.316(1.857)

-0.658(1.381)

-1.716(1.614)

-8.631*(3.649)

1.648(1.533)

4.617**(1.463)

5.962**(2.456)

1.739(1.058)

14.552*(6.930)

46.50.39***

LN (res. wage)(age used as identification)

5.508

0.005E-02

0.732E-06

-O.OllE-05

0.053

-0.220

-0.061

-0.204

-0.195

-0.078

-0.085

0.080

0.084

0.271

0.026

"Omitted category is "Ontario".''Omitted category is "some or completed secondary'̂ Omitted category is "non-Canadian bom".

education".*p < 0.05

**p < 0.01**p < 0.001


Table 6Wage regression for Canadian wives in the labor force incorporating "Number of children under 16"variable

Independent Regression coefficientvariablesConstant

Age

Age^


Quebec


Alberta

British Columbia




University degree

(Standard error)5.774***

(0.255)

0.018(0.013)

0.002E-01(0.002E-01)

-0.251**(0.083)

-0.94*(0.039)

-0.222**(0.071)

-0.206***(0.057)

-0.087

-0.110(0.087)

0.098(0.063)

0.116**(0.041)

0.297***(0.057)

Independent Regression coefficientvariables

Canadian bom*̂



Teaching

Sales

Service

Farming, fishing,forestry andlogging operations



Construction

Number of childrenunder 16Adjusted PJ

(Standard error)

0.039(0.041)

0.202***(0.049)

0.266***(0.052)

0.145*(0.072)

-0.80(0.062)

-0.321***(0.053)

-0.124(0.274)

(0.057)

-0.178(0.151)

-0.213*(0.089)

-0.284(0.268)

0.014(0.018)0.26***

•'Omitted category is "Ontario".''Omitted category is "some or completed secondary education".'̂ Omitted category is "non-Canadian bom".''Omitted category is "clerical".

*p < 0.05**p <O.OI

***p < 0.001

4.4. Kidd's reservation wage approach

In tbis study, the number of children under age sixteen was iticluded in theordinary least squares wage equation as a proxy for A. Table 6 presents the re-gressioti estimates of the parameters of Kidd's model. The results indicate that thenumber of children under age sixteen variable is not significant at the 0.05 level.


This result indicates that the variable does not capture the differences in the unob-servable characteristics between the working wives and the full-time homemakersas has been suggested by Kidd [17]. Using this method, the calculated weeklyreservation wage for a full-time homemaker amounted to $416.21.

5. Conclusions

The underlying economic principle of using the opportunity cost approach invaluing homemaker's time is that the alternative use of a homemaker's time is worththe value at the margin. The four different variants of the opportunity cost approachused in this study yielded different estimates of the value of household productiontime as might be expected. Is there a basis for evaluating which estimation methodis to be preferred?

The imputed wage approach has been refuted in the literature on grounds ofselection bias being embedded in selection of the sample. The potential wageapproach corrects for censoring bias and yields the lower bound estimate for theestimated wage of household production time.

Heckman's two-stage reservation wage approach, has the advantage of correctingselection bias and reflecting the wage the homemaker would place on her householdproduction time. This method has been the most used in the literature for estimatingthe value of household production time. Unfortunately, this method yields a widerange for the estimated reservation wage as indicated by the results of this andother studies. Further, we also believe that a value placed on household productionby an individual reflects an intrinsic value rather than a value that can be usedin practical evaluation of household production. So, while the theoretical basefor the Heckman two-stage reservation wage procedure is appropriate for welfareeconomic analysis, we doubt its reliability as a practical measure of the value ofhousehold production time.

Kidd's approach is a simpler method of estimating the reservation wage thanthe Heckman's approach. It also avoids the restrictive condition of the assumedbivariate normality of the error terms in Heckman's model. However, the use ofthe number of dependent children as a proxy for Heckman's lambda needs to bevalidated. In this study Heckman's lambda was significantly different from zero.

Table 7Estimated wage of household production time of Canadianfull-time homemakers using variants of the opportunity costapproach

ModelItnputed wage modelPotential wage modelHeckman's reservation wage modelKidd's model

Estimate

470.17325.54

2,192.29416.21

D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homettiaker's time 161

but the number of dependent children variable was not statistically significant,indicating that there were no differences in unobservable factors between full-timehomemakers and wives who were employed in the market.

In general, the opportunity cost approach has limitations. This approach is usedto estimate household production time of the homemaker rather than the valueof the household production itself. Thus, the opportunity cost reflects one's ownwage only. Household production, on the other hand, requires capital inputs andentrepreneurship in addition to the time spent by the homemaker in producing thecommodities.

Given these limitations of the opportunity cost approach, in our judgment, thevalue-added approach measuring household production would be more appropriatefor placing a monetary value on home produced commodities. With informationabout the number of hours spent by the homemaker in different productive activ-ities one can estimate the reservation wage for his/her time. A drawback of thismethod, however, is that it requires collection of a massive amount of informationregarding the produced commodities as well as their correspotiding prices in themarketplace. But, given current technological advances in data gathering and theincreased availability of information regarding prices of products collecting data ofthis sort may become easier in the future. Therefore, we would strongly encourageresearchers to consider using this method in the future.

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