Journal of Economic and Social Measurement 23 (1997) 149-162
IOS Press
149
IMeasurement of the value of homemaker's time:
an empirical test of the alternative methods of the
opportunity cost approach
Deanna L. Sharpe
Department of Family and Consumer Economics, University of Missouri, Columbia, MO 65211, USA
Tel.: +1 573 882 9652; Fax: +1 573 884 8389; Email: cfedis@mizzoul.missouri.edu
Mohamed Abdel-Ghany*
Department of Consumer Sciences, Box 870158, The University of Alabama, Tuscaloosa,
AL 35487-0158, USA
Tel.: +1 205 348 7954; Fax: +1 205 348 3789; Email: mabdei-g@ches.ua.edu
Household production is typically measured by estimating the time that the homemaker spends in the
various household activities. The focus in this paper was on valuating the household production time
of Canadian full-time homemakers. Four variants of the opportunity cost approach, namely, imputed
wage, potential wage, Heckman's two-stage reservation wage, and Kidd's reservation wage were used
to estimate and compare homemaker's time. The results indicate that the four different variants yielded
different estimates of the value of household production time. One of the main conclusions is that
Heckman's two-stage reservation wage approach, albeit having the advantage of correcting selection
bias, it produced a wide range for the estimated reservation wage, which led us to doubt its reliability
as 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's
time were introduced in the 1930s with work by Kyrk [19] and Reid [34] and
in the 1960s with work by Mincer [23] and Becker [2]. Heckman's significant
contributions in the 1970s [15,16] have led to numerous research articles. In the
1980s and 1990s a number of theoretical papers have criticized the restrictive
assumptions of the Heckman's model and found that the results arising from its
application yield a wide range of the estimated reservation wage [11,17,20,28,29].
It is important to have accurate measures of household production. Underestimation of the gross national product results when the value of household production is
excluded. The magnitude of underestimation depends on the relative shares of market and household production in the economy. Comparisons of the gross national
'Corresponding author.
0747-9662/97/$8.00 © 1997 - IOS Press. All rights reserved
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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 household
production are unreliable. The value of household production and the importance
of its inclusion as a component of the gross national product has been recognized
by researchers since the early twenties [24].
Accurate use of income distribution as a measure of economic well-being necessitates the adjustment of household income to reflect the value of household
production [26,33,37]. Failure to tax the imputed value of household production
leads to discriminatory treatment of households with the same market income but
with different household production levels [22,27]. Valuing homemaker's time is
required for the assessment of damages in divorce, wrongful injury, and death
litigation.
Three general methods for valuing household production have been used by researchers over the years. One such method is value-added. This method involves
measuring household outputs in physical units and evaluating them at market prices,
then subtracting the cost of purchased inputs, resulting in the value-added by households [3,9,35]. To determine a wage rate for the homemaker, the value-added for
the different commodities produced during a specific period of time is divided by
the number of hours spent in production.
The second method of valuing household production time is replacement cost
which measures the value of household production time in terms of what it would
cost 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 a
housekeeper who provides the same package of household tasks is used to calculate
the value of time spent by the homemaker in producing household production. The
second variant is the specific services replacement cost method. It is determined
by using the equivalent market wage rate of a specialist for each task times the
number of hours spent by the homemaker performing the task [10,14,33].
The third method of valuing household production time is the opportunity cost
approach. According to this method, the value of household production time is
calculated by multiplying the total housework time by a single wage rate which
reflects the next best alternative as determined by the homemaker productivity
related 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 is
to estimate the value of homemaker's time in Canadian households using variant
methods of the opportunity cost approach and to evaluate the relative limitations
and 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 of
one'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 in
the market is estimated by multiplying the number of hours spent in household
production by the market wage rate (net of taxes). However, for individuals who
are not employed in the market, assigning a wage to reflect the value of their
household production time is problematic. Four methods of solving this problem
have been proposed.
Some researchers [7,8] have estimated the wage rate over the employed individuals in the sample and imputed the wage rate for those who are not employed in
the market according to their personal characteristics. The imputed wage is then
multiplied by the number of hours spent in household production to give a lowerbound estimate of the value of household production time. However, this method
of imputing wage to those who do not work in the market leads to a censoring
bias in the wage estimate due to the use of the endogenous criterion of labor force
participation 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 correct
for the effects of non-random sampling and the estimation of potential wages and
reservation wages. The potential wage is the wage an individual could earn in the
market given that individual's human capital endowment. The reservation wage,
on the other hand, is the minimum wage that would entice an individual to join
the labor force [18].
Three steps are involved in using the Heckman two-stage correction procedure
to estimate the potential wage. First, probit analysis is used over the entire sample 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 inverse Mills ratio. Second, lambda is used as an additional regressor in a wage
equation which is estimated using ordinary least squares over the sample of labor
force participants. Third, parameters from the wage equation are used to estimate
the potential wage rate for individuals with specific personal and labor market
characteristics.
Kinsey [18] notes that the derived potential wage could he higher or lower
than the actual wage for labor force participants. However, it must be lower than
the reservation wage for those who are not in the labor force. According to this
model, a person participates in the labor force only if market wages exceed his
or her reservation wage. The potential wage has been used to value household
production time [22,32].
The third method, the reservation wage, can also be estimated using the Heckman
two-stage model. Three steps are involved. First, self selection bias is corrected
by using probit analysis to estimate an equation that determines the probability
of labor force participation. The parameters of this equation are used to derive
lambda (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 determining
market productivity; \nW* = log of reservation wage; Z = vector of characteristics determining household productivity; H = hours of market work; and e\
and e2 = error terms to capture unmeasurable or unobservable idiosyncratic taste
elements.
An underlying assumption of the model is that in equilibrium W* = W for employed individuals, whereas W* > W for those individuals who are not employed
in the market. Therefore, the reservation wage for a nonemployed individual is
not required to equal the wage the individual could have earned in the labor market. Rather, it signifies the wage required by the individual to make her/him
indifferent between the last hour of household production and an hour of market
work [37].
This model also assumes that the market wage does not vary with the number of hours supplied in the market. However, the reservation wage is assumed
to vary with the number of hours worked, implying that the marginal productivity of time in the household varies with the amount of time spent in household
production whereas the marginal productivity in the market is invariant to hours
worked [37].
Since the reservation wage is unobservable, its estimation can only be derived
by 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 given
that 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, respectively [17].
The restrictive nature of the assumed bivariate normality of the error terms has
been 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 the
Heckman's model are very sensitive due to departures from normality.
Kidd [17] suggested replacing Heckman's two-step procedure by a one-step
ordinary least squares regression which includes the number of dependent children
as an alternative proxy variable to Heckman's lambda. The number of dependent
children 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 it
serves 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 was
employed in the marketplace, and 705 households in which the wife was a full-time
homemaker. Table 1 shows the means and percentages of the variables used in the
analyses.
Table 1
Descriptive statistics of the sample
Variable
Wife's age
Number of children under 16
Husband's yearly income
Employed (n = 801)
mean
38.42
0.81
79,502
Non-employed (n = 705)
mean
52.44
0.68
35,586
Percentage
Region of residence
Atlantic
Quebec
Ontario
Manitoba and Saskatchewan
Alberta
British Columbia
Wife's education
Less than 9 years of elementary education
Some or completed secondary education
Some post-secondary education
Post-secondary certificate or diploma
University degree
Country of birth (Canadian bom)
17.4
23.8
22.8
14.5
12.7
8.7
3.7
44.1
8.5
28.7
15.0
80.8
•
.
16.7
21.8
19.9
19.9
10.2
11.5
19.1
49.9
7.1
17.6
6.2
76.5
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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 the
offered market weekly wage. The average offered wage per week for Canadian
wives who were employed in the market was $520.60. This wage is considered to
reflect the estimated wage per week for household production time for those who
were employed in the market.
An ordinary least squares regression equation that regressed wife's age, education, occupation, region of residence, and whether the wife is Canadian born on
offered wage for all wives who were in the labor force was run. The regression coefficients from the regression equation were then used to impute the hourly wage
of wives who were full-time homemakers. Table 2 shows the wage regression
for wives in the labor force. According to this imputation, the estimated weekly
wage 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 the
sample.
4.2. Potential wage approach
The first step in the estimation of potential wage was to use probit analysis
to estimate the probability of the wife's labor force participation over the whole
sample. The dependent variable in the probit equation was the labor force participation criterion which assumed a value of one if the wife's hours of market work
exceeded zero, zero otherwise. The independent variables that were regressed on
the criterion included wife's age, education, number of children under the age of
sixteen, husband's income, value of dwelling, region of residence, and whether the
wife is Canadian born. Table 3 presents the probit estimates of the parameters of
the labor force participation index.
As seen in Table 3, the wife's age and education had a positive and significant
effect on the wife's probability of being employed in the market. However, the
number of children under the age of sixteen and husband's income had a negative
effect 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 equation was estimated using the ordinary least squares regression over the employed
sample. Coefficients of the regression were then used to estimate the potential
wage rate for full-time homemakers.
The results of the ordinary least squares estimation appear in Table 4. As indicated in the table, the coefficient of the probit A was significantly different from
D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
155
Table 2
Wage regression for Canadian wives in the labor force
Independent
variables
Constant
Regression coefficient
(Standard error)
5.729***
(0.247)
Age
0.021
(0.012)
Age^
-0.0002
(0.0001)
Region of residence"
Atlantic
-0.094*
(0.039)
Manitoba and
Saskatchewan
-0.220**
(0.071)
Alberta
-0.208***
(0.057)
British Columbia
Some post-secondary
education
Post-secondary
certificate or diploma
Canadian born*^
Occupation''
Managerial and
administrative
Professional and
-0.251**
(0.083)
Quebec
Education''
Less than 9 years of
elementary education
Independent
variables
University degree
category
category
category
category
0.037
(0.041)
0.200***
(0.041)
0.266***
technical
(0.052)
Teaching
0.148*
(0.071)
Sales
-0.082
(0.062)
Service
-0.321***
(0.053)
-0.090
(0.057)
Fanning, fishing,
forestry, and logging
operations
-0.135
(0.273)
-0.111
(0.087)
Mining, processing
and machinery
-0.179
(0.151)
-0.100
(0.063)
Product fabricating.
assembling and repair
-0.210*
(0.089)
Construction
-0.289
(0.268)
0.117**
(0.041)
Adjusted R}
"Omitted
''Omitted
"^Omitted
''Omitted
Regression coefficient
(Standard error)
0.296***
(0.057)
is "Ontario".
is "some or completed secondary education".
is "non-Canadian bom".
is "clerical".
0.26***
*p < 0.05
**p<0.01
***p < 0.001
zero, indicating tbat there were differences in unobservable factors between fulltime homemakers and wives who were employed in the market. The estimated
potential 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 previous
studies that contipared the imputed and potential wage models [8]. This potential
wage is considered a lower-bound estimate of home production time for full-time
homemakers.
156
D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
Table 3
Parameter estimates for the probability of labor force participation by Canadian wives
Independent variables
Constant
Age
Probit coefficient (Standard error)
-2.613***
(0.537)
0.222***
(0.026)
Age2
-0.003***
(0.0003)
Husband's yearly income
-0.0O9E-O3***
(0.002E-03)
0.008E-04
(0.004E-04)
-0.394***
(0.042)
Value of dwelling
Number of children under 16
Region of residence"
Atlantic
-0.204
(0.200)
Quebec
-0.042
(0.096)
Manitoba and Saskatchewan
-0.210
(0.165)
0.001
Alberta
(0.145)
British Columbia
Education''
Post-secondary certificate or diploma
University degree
Canadian bom'^
"Omitted category is "Ontario".
''Omitted category is "some or completed secondary education".
'^Omitted category is "non-Canadian bom".
-0.239
(0.135)
0.334***
(0.098)
0.705***
(0.139)
0.106
(0.094)
-Log-likelihood 555.35*
***p < 0.001
4.3. Heckman's two-stage reservation wage model
Whereas the potential wage indicates the lower-bound estimate of the home
production time by a full-time homemaker, the reservation wage reflects the wage
required by the individual to make her/him indifferent between the last hour of
household production and an hour of market work. The empirical results of the
wage equation, hours of work equation and the calculated reservation wage are
presented in Table 5.
Since there is no rule provided in the literature for the selection of the identifier
to be used in the derivation of the reservation wage, with the exception that it
D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
157
Table 4
Wage regression for Canadian wives in the labor force after adjusting for censoring bias
Independent
variables
Constant
Regression coefficierit
(Standard error)
5.401***
(0.280)
Age
0.035**
(0.013)
Age^
-0.004E-01**
(0.002-01)
Region of residence"
Atlantic
Quebec
Independent
Regression coefficient
variables
Canadian bom'^
Occupation''
Managerial and
administrative
(Standard error)
0.047
(0.041)
0.203***
(0.049)
Professional and
technical
0.264***
(0.052)
-0.267***
(0.083)
Teaching
0.144*
(0.071)
-0.098**
(0.039)
Sales
-0.078
(0.062)
Manitoba and
Saskatchewan
-0.245***
(0.071)
Alberta
-0.203***
(0.056)
British Columbia
-0.100
(0.057)
Education''
Less than 9 years of
elementary education
-0.191*
(0.092)
Some post-secondary
education
0.101
(0.062)
Post-secondary certificate
or diploma
0.141***
(0.42)
University degree
0.344***
(0.060)
Service
-0.320***
(0.053)
Fanning, fishing,
forestry and logging
operations
-0.098
(0.273)
Mining, processing
and machinery
-0.167
(0.150)
Product fabricating.
assembling and repair
-0.206*
(0.089)
Construction
-0.275
(0.267)
A
"Omitted
''Omitted
'^Omitted
''Omitted
category
category
category
category
is
is
is
is
Adjusted B?
"Ontario".
"some or completed secondary education".
"non-Canadian bom".
"clerical".
0.197**
(0.079)
0.27***
*p < 0.05
**p < 0.01
***p < 0.001
should be significant, wife's age was used alternatively to derive the reservation
wage. Tbe estimated reservation wage was $2,192.29.
The restrictive nature of the assumed bivariate normality of the error terms has
been 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 arising
from application of the Heckman's model are very sensitive due to departures from
normality.
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D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
Table 5
Parameter estimates for wife's market wage, hours worked, and calculated reservation wage
Independent variables
Constant
Age
Age^
LN (wage)
(St. error)
5.401***
(0.280)
0.035**
(0.013)
-0.004E-01**
(0.002E-01)
Husband's yearly income
Value of dwelling
2.857**
(0.925)
-0.037**
(0.013)
0.005E-02
-0.006E-02
(0.004E-02)
0.732E-06
0.009E-03
(0.O05E-03)
-O.OllE-05
-4.321**
(1.423)
Number of children under 16
Region of residence"
Atlantic
Dependent variables
LN (res. wage)
Hours
(age used as identification)
(St. error)
5.508
-8.774
(17.42)
0.053
-0.267***
(0.083)
-3.881
(2.132)
-0.220
Quebec
-0.098**
(0.039)
-2.994**
(0.971)
-0.061
Manitoba and
Saskatchewan
-0.245***
(0.071)
-3.316
(1.857)
-0.204
Alberta
-0.203***
(0.056)
-0.658
(1.381)
-0.195
British Columbia
-0.100
(0.057)
-1.716
(1.614)
-0.078
Education''
Less than 9 years of
elementary education
-0.191*
(0.092)
-8.631*
(3.649)
-0.085
Some post-secondary
education
0.101
(0.062)
1.648
(1.533)
0.080
Post-secondary certificate
or diploma
0.141***
(0.042)
0.084
University degree
0.344***
(0.060)
4.617**
(1.463)
5.962**
(2.456)
Canadian bom'^
0.047
(0.041)
1.739
(1.058)
0.026
A
0.197**
(0.079)
14.552*
(6.930)
0.27***
46.5
0.39***
Average weekly hours
Adjusted R}
"Omitted category is "Ontario".
''Omitted category is "some or completed secondary education".
'^Omitted category is "non-Canadian bom".
0.271
*p < 0.05
**p < 0.01
**p < 0.001
D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
159
Table 6
Wage regression for Canadian wives in the labor force incorporating "Number of children under 16"
variable
Independent
variables
Constant
Regression coefficient
(Standard error)
5.774***
(0.255)
Age
0.018
(0.013)
Age^
0.002E-01
(0.002E-01)
Region of residence"
Atlantic
Quebec
-0.251**
(0.083)
Independent
variables
Canadian bom*^
Regression coefficient
(Standard error)
0.039
(0.041)
Occupation''
Managerial and
administrative
Professional and
technical
Teaching
0.202***
(0.049)
0.266***
(0.052)
0.145*
(0.072)
-0.94*
(0.039)
Sales
-0.80
(0.062)
Manitoba and
Saskatchewan
-0.222**
(0.071)
Service
-0.321***
(0.053)
Alberta
-0.206***
(0.057)
Farming, fishing,
forestry and
logging operations
-0.124
(0.274)
British Columbia
-0.087
(0.057)
Education''
Less than 9 years of
elementary education
-0.110
(0.087)
Some post-secondary
education
0.098
(0.063)
Post-secondary certificate
or diploma
0.116**
(0.041)
University degree
0.297***
(0.057)
•'Omitted
''Omitted
'^Omitted
''Omitted
category
category
category
category
is
is
is
is
Mining, processing
and machinery
-0.178
(0.151)
Product fabricating.
assembling and repair
-0.213*
(0.089)
Construction
-0.284
(0.268)
Number of children
under 16
Adjusted PJ
"Ontario".
"some or completed secondary education".
"non-Canadian bom".
"clerical".
0.014
(0.018)
0.26***
*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 the
ordinary least squares wage equation as a proxy for A. Table 6 presents the regressioti estimates of the parameters of Kidd's model. The results indicate that the
number of children under age sixteen variable is not significant at the 0.05 level.
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D.L. Sharpe and M. Abdel-Ghany / Measurement of the value of homemaker's time
This result indicates that the variable does not capture the differences in the unobservable characteristics between the working wives and the full-time homemakers
as has been suggested by Kidd [17]. Using this method, the calculated weekly
reservation wage for a full-time homemaker amounted to $416.21.
5. Conclusions
The underlying economic principle of using the opportunity cost approach in
valuing homemaker's time is that the alternative use of a homemaker's time is worth
the value at the margin. The four different variants of the opportunity cost approach
used in this study yielded different estimates of the value of household production
time as might be expected. Is there a basis for evaluating which estimation method
is to be preferred?
The imputed wage approach has been refuted in the literature on grounds of
selection bias being embedded in selection of the sample. The potential wage
approach corrects for censoring bias and yields the lower bound estimate for the
estimated wage of household production time.
Heckman's two-stage reservation wage approach, has the advantage of correcting
selection bias and reflecting the wage the homemaker would place on her household
production time. This method has been the most used in the literature for estimating
the value of household production time. Unfortunately, this method yields a wide
range for the estimated reservation wage as indicated by the results of this and
other studies. Further, we also believe that a value placed on household production
by an individual reflects an intrinsic value rather than a value that can be used
in practical evaluation of household production. So, while the theoretical base
for the Heckman two-stage reservation wage procedure is appropriate for welfare
economic analysis, we doubt its reliability as a practical measure of the value of
household production time.
Kidd's approach is a simpler method of estimating the reservation wage than
the Heckman's approach. It also avoids the restrictive condition of the assumed
bivariate normality of the error terms in Heckman's model. However, the use of
the number of dependent children as a proxy for Heckman's lambda needs to be
validated. In this study Heckman's lambda was significantly different from zero.
Table 7
Estimated wage of household production time of Canadian
full-time homemakers using variants of the opportunity cost
approach
Model
Itnputed wage model
Potential wage model
Heckman's reservation wage model
Kidd's model
Estimate
470.17
325.54
2,192.29
416.21
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-time
homemakers and wives who were employed in the market.
In general, the opportunity cost approach has limitations. This approach is used
to estimate household production time of the homemaker rather than the value
of the household production itself. Thus, the opportunity cost reflects one's own
wage only. Household production, on the other hand, requires capital inputs and
entrepreneurship in addition to the time spent by the homemaker in producing the
commodities.
Given these limitations of the opportunity cost approach, in our judgment, the
value-added approach measuring household production would be more appropriate
for placing a monetary value on home produced commodities. With information
about the number of hours spent by the homemaker in different productive activities one can estimate the reservation wage for his/her time. A drawback of this
method, however, is that it requires collection of a massive amount of information
regarding the produced commodities as well as their correspotiding prices in the
marketplace. But, given current technological advances in data gathering and the
increased availability of information regarding prices of products collecting data of
this sort may become easier in the future. Therefore, we would strongly encourage
researchers to consider using this method in the future.
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