the role of economic and demographic factors in explaining time-use of single and married mothers

The Role of Economic and Demographic Factors in Explaining Time-Use of Single and Married Mothers

Robin A. Douthitt University of Wisconsin

Cathleen D. Zick University of Utah

Jane McCullough Utah State University

ABSTRACT: The number of households headed by single mothers has been increasing in recent years. Yet, little is known about how this growing segment of the population differs, if at all, from married mothers in their time allocation patterns. In the study reported here, a system of time allocation equations based on household production theory is estimated for both married and single mothers. The results indicate that married and single mothers make different decisions about how to allocate their time to household production, child care, leisure, and paid work. Specifically, single and married mothers responded differently to a change in their shadow wage rates, unearned income, paid child care, and the ages of the children in each of the estimated equations.

KEY WORDS: Family Time Use, Mother's Time Allocation, Single Parent

Introduction

The ranks of single-parent households have been growing in recent years. In 1960, roughly 4% of all households were headed by a single

A portion of this project was funded by the Wisconsin Agricultural Experiment Sta- tion. W. Keith Bryant, Jutta M/Joesch, Robert N. Mayer, Ken R: Smith and two anon- ymous reviewers provided helpful insights at several stages of this research. Sarah Stiefvater and Susan Bruns provided valuable research assistance on this project. All remaining errors are the responsibility of the authors.

Direct all correspondence to Robin Douthitt, Family Resources and Consumer Sci- ence, 1300 Linden Drive, University Of Wisconsin, Madison, WI 53706. The authors are Associate Professors at the University of Wisconsin, University of Utah, and Utah State University, respectively.

Lifestyles: Family and Economic Issues, Vol. 11(1), Spring 1990 © 1990 Human Sciences Press 2 3

24 Lifestyles: Family and Economic Issues

parent. By 1986, approximately 23% of American families with children under the age of 18 were headed by single parents (U.S. Depart- ment of Commerce, 1988). Contributing to this trend has been an increase since the mid-sixties in both the incidence of divorces I and births outside of marriage. 2 Although much has been written about the problems and coping strategies of single parents, few studies actu- ally have documented the influence of marital status on parents' time-use patterns.

Many authors have documented the fact that most marriages are characterized by a division of labor. Becker (1981) went so far as to argue that individuals in fact married to enjoy the gains from trade arising from specialization. Whatever the reason, this view held that couples divided home and market work responsibilities between themselves and shared the fruits of their labors. Thus, upon dissolution of a marital or common law relationship, custodial parents often faced having to meet their children's demands with half or fewer of the resources they had while married.

Increased labor force participation has been a common strategy employed by the single parent to meet the economic demands of the children (e.g., Eblen, 1981). However, a single parent's increased market work may have proven to be a two-edged sword when substitutes had to be found for child care and other home responsibilities they previ- ously performed themselves. Brandwein, Brown, and Fox (1974) noted that such reduced household labor contributions, in turn con- tributed to a decline in the single-parent family's standard of living.

Glasser and Navarre (1965) were some of the earliest authors to document the consequence of marital breakdown on the task structure faced by one-parent families. Buehler and Hogan (1980) identified the need for single parents to implement new management tech- niques such as role adjustment and routine adaptation based on their different, that is reduced, resource base. Smith (1980) and Bould (1977) documented the effects that lost economic and emotional support have had on instilling a feeling of powerlessness among single parents. Other authors (Hungerford & Paolucci, 1977; Schorr & Moen, 1979) have identified areas of public policy that have needed developing to ease the restructuring task of single parents. However, surprisingly little has been written about the influence of household organization on the time allocation decisions of single parents.

The organization of this paper is as follows. First, the existing literature will be reviewed to ascertain both what is known and what remains to be learned from time-use data about single parents' time allocation decisions. Next, a theoretically plausible model of single

Robin A. Douthitt, Cathleen D. Zick, and Jane McCnllough 25

and married mothers' time use is specified and tested using four different data sets. The focus of this work is to assess the role economic and sociodemographic factors play in determining single mothers' and married mothers' time-use. Finally, the implications of the findings are discussed in the context of household production theory.

S i n g l e - P a r e n t T i m e - U s e L i t e r a t u r e

The literature on single parents can be divided along gender lines. Ironically, although single men who have had sole custody of their children have been in the minority, 3 a disproportionate share of the literature has focused on them. Single-parent task restructuring has been the primary area where researchers have devoted attention to single fathers. In particular, researchers have analyzed single fathers' adjustments to assuming primary responsibilities for home production (Defrain & Eirick, 1981; Gasser & Taylor: 1976; Grief, 1985; Katz, 1979; Mendes, 1976; Orthner, Brown, & Ferguson, 1976). In contrast, studies of women who were single parents have generally focused on their economic status (e.g., Duncan & Hoffman, 1985; Ep- stein, 1979; Johnson, 1980; Lino, 1989; McEaddy, 1976; Vickery, 1978).

Very little single-parent time-use research has been conducted to date and virtually all of it has focused on single mothers. The major studies have included work by Lyerly (1969), Rowland, Nickols and Dodder (1986), Sanik and Mauldin (1986), 4 and Dismukes and Abdel- Ghany (1988). All four studies analyzed time-use data that were collected using time diaries.

In 1967-68, time-use data for 56 single-parent families living in Onondaga County, New York, were collected. Lyerly analyzed these data in her 1969 comparative study of single- versus two-parent households' time-use. She restricted her study to only those families with either pre-school or elementary school age children. She controlled not only for the ages of the children but also for the numbers of children present in the household. Single- and two-parent households were grouped into family composition cells, and the Wilcoxon matched pairs signed-rank test was used to test most of Lyerly's hypotheses.

Major findings from the Lyerly study included the fact that single mothers (a) spent more time in paid work, (b) spent less time in home work, and (c) were more likely to have placed their children in the care of non-family members for 9 or more hours per day than mothers in two-adult families. After controlling for labor force status, 5 differences remained. Single mothers who spent more than 6 hours per day


in non-household work (a) spent less time in home production, (b) spent less time in personal care activities, and (c) had more help with housework from other family members than their female counterparts in two-parent families.

Rowland (1983) and Rowland, Nickols, and Dodder (1986) in their comparative studies of single and two-parent two-child families' time use, analyzed data on 29 single mothers and 30 two-parent households, collected in 1981 in Tulsa, Oklahoma. All 59 households had two children present and the youngest child was between the ages of 7 and 11. Pearson correlation coefficients were used to test for significant relationships among categories of ~ime-use. Analysis of variance was used to test differences in means among different types of parental groups.

Consistent with the Lyerly study, Rowland, Nickols, and Dodder (1986) found that single female heads allocated about twice as much time to employment, half as much time to household work, and about two-thirds as much time to leisure activities as compared to mothers in two-parent families. Consistent with the resource management theories of Buehler and Hogan (1980), they concluded that employment of single mothers required a broad range of task adjustments. However, after holding constant employment status, their examina- tion of home work by activity revealed no significant differences between the two groups in time spent in family care where family care was defined to include both physical and nonphysical care of family members.

Sanik and Mauldin (1986), in their study of single- and two-parent families' time-use, used data from a 1977-78 study of 81 single parents with two children conducted in the Sacramento, California, area. Using one-day recall data, they compared 58 of the single-parent households' time-use with that of 144 two-parent households. Unlike either the Lyerly study or the Rowland study, no restrictions were placed on the age of the youngest child used in the final samples. Analysis of covariance was used to examine whether significant differences between employed and unemployed single-parent versus married mothers' time-use emerged among six different time-use categories. Because their sample included only those families with two children, family size was held constant. A difference between this study and previous ones was that they also controlled for the effects of family income and age of the younger child.

Like Rowland et al., Sanik and Mauldin found that after controlling for employment status, single parents did not spend any less

Robin A. Douthitt, Cathleen D. Zick, and Jane McCullough 27

time with their children than their married counterparts. And as found in previous studies, single mothers were more likely than married mothers to have worked in the paid labor force, and, if employed, they spent less time in personal care and recreation activities.

Dismukes and Abdel-Ghany (1988) also used the 1977-78 Califor- nia time-use data to examine factors influencing household work in single-parent and two-parent families. Pair-wise t-tests of homer makers' time spent in various types of household work revealed only one significant difference between single parents and married parents, that difference being in the category of housecleaning time. Dis- mukes and Abdel-Ghany estimated multiple regression equations for each category of household work separately for the single-parent and two-parent households. The independent variables in the equations included education, age, employment status, and sex of the homer maker, age of the younger child, housing status, and household income. Although no direct tests of coefficient differences were made, the authors did conclude that homemakers from both single-parent and two-parent households allocated their time in a similar fashion. The conclusions of the Dismukes and Abdel-Ghany paper thus differed from the previous three studies.

While these benchmark studies have provided the first insights into the time allocation patterns of single and married mothers~ all four must be viewed as initial, exploratory research for several reasons. First, any discussion of a theoretical framework used to guide the empirical testing of hypothesized relationships was absent from the papers. Indeed, the articles contained little or no discussion of the underlying decision-making process that led to the parental time allocation patterns that were observed. These empirical formulations implied that mothers first made decisions about market work and then decided how much time to allocate to various activities in the home. This conditional orientation may not have reflected reality. On any given day, a parent may have taken actions that altered his/her market work time (e.g., a parent may have left work early to care for a sick child). A more general model would have explicitly allowed for the possibility that mothers made simultaneous decisions regarding the allocation of their time to market work, child care, housework, and leisure activities.

Second, in all three papers the empirical relationships were tested using small, non-random samples of two-parent and single-parent households. These sample characteristics limited the external val- idity of the results. Additional sample restrictions imposed by some of

28 Lifestyles: Family and Economic I s s u e s

the authors further increased the likelihood that their study findings were not generalizable to any larger population. For instance, in Rowland, Nickols, and Dodder's paper, all time diary information was restricted to weekday records during April and May of 1981. This meant the authors' findings only described differences between married and single mothers' time allocation patterns on weekdays when all of their children age five and older would have been in school. Similarly, Sanik and Mauldin purposefully excluded all employed mothers who did not work outside of the home for more than four hours on the day the recall time diary information was collected. Their study findings thus described the differences between nonemployed mothers' time allocation using data collected across all seven days of the week, and employed mothers' time allocation using data gathered only on the days they worked outside of the home. Hence, Sanik and Mauldin's findings may not have been generally representative of employed parents' time-use because they excluded all observations where the employed parents supplied recall diary information for one of their days off work.

Finally, none of the four studies adequately controlled for other socioeconomic and demographic characteristics of single-parent and two-parent households that might have been responsible for any of the observed differences in the time mothers devoted to various activ- ities2 The authors concluded that any observed differences in time allocation were due to household structure. However, it is quite possible that omitted socioeconomic and/or demographic characteristics that varied by household structure may have been responsible for some or all of the differences in mothers' time allocation that were observed.

In sum, while these four studies provided some information about the differences between married mothers' and single mothers' time- use, they stopped short of testing theory-based hypotheses. Further- more, the time-use picture they provided may not have been generalizable. At best, these pieces presented preliminary empirical work from which hypotheses could be generated. However, the authors did not generally engage in any such inductive exercises.

The work presented in this paper extends past research efforts by (a) using an explicit model of time-use to generate behavioral hypotheses, (b) testing these hypotheses with several data sets (including a nationally representative data set), and (c) using the empirical findings to generate hypotheses about the role marital status plays in mothers' time allocation decisions.


T h e T h e o r e t i c a l F r a m e w o r k

The theoretical framework guiding the analysis was drawn from Becker's (1965) "new home economics." The primary assumption underlying this theory was that individuals (or households) maximize their satisfaction by al- locating financial and time resources subject to existing resource constraints. In this particular application, mothers received satisfaction from four elements, market goods (X), leisure time (L), child services (Zc), and all other home-produced services (Zh). Mathematically:

(1) U = u(X, L, Z¢, Zh).

A mother's ability to maximize her level of satisfaction was limited by home production capabilities, income, and time constraints. The production constraints were specified to be:

(2) Zc = zc(Tc;Gc) (3) Zh = Zh(Th;Gh)

where. Tc - time spent by the mother in child care activities, Gc = exogenous household characteristics that affect the mother's abil-

ity to produce child services, such as the number of children in the home and age of the youngest child,

Th - time spent by the mother in housework activities other than child care, and

Gh -- exogenous household characteristics that affect the mother's ability to produce household services, such as the mother's age and marital status.

Similarly, the income constraint was specified as:

(4) p X = w H + V

where, P X W

H V

= the price of market goods, = market goods, = the woman's market wage rate, = hours of market work by the woman, and = the market earnings of the husband (if present) plus any nonwage

income received by the household.

Finally, the mother's time constraint was written as:

(5) T = L + H + T c + T h

where, T = total time available to the mother, and all other variables remain

defined as above.


By substituting equations (2) and (3) into equation (1), and combining equations (4) and (5) it was determined that mothers maximized a utility function:

(6) U = u(X, L, Zc(T¢;G¢), Zh(Th;Gh))

subject to a full income constraint:

(7) wT + V = pX + wL + wTc + wTh.

Thus, the specific problem faced by the mother was to choose market goods, leisure time, child care time, and home production time so that her satisfaction was maximized subject to the full income constraint and exogenously determined levels of Gc and Gh.

To expedite estimation of the model, two simplifying assumptions were made. First, it was assumed that prices for market purchased goods and services were constant, thus permitting an estimate for a t ime allocation system of equations. To ensure that this system of equations satisfied the classical assumption of adding-up, the time budget constraint had to be satisfied. One way of ensuring this property was by estimating a logistic (non-linear ~ form of time allocation budget shares. As suggested by Phlips (1974) and applied by Tyrrell and Mount (1982), it was possible to approximate such a model with linear regression by normalizing the dependent variable time shares with the omitted time share and logging the result. In this application, the property of adding up was ensured by taking each of the mother's time allocation shares and dividing it by the proportion of the day she spent in paid work."

Second, it was assumed that each time allocation decision was influenced by a similar set of economic and family composition variables. Thus, although the normalization procedure introduced cross-equation correlation, because all of the regressors in the model were the same. the system could be estimated with ordinary least squares and would be computationally identical to the jointly estimated generalized least squares model (Kmenta, 1986).

Thus, the final form of the estimating equations was:

k (8) ln(Si/SH) = Bo + ~ BjXj + ( e l - el)

j = l

where, Si = proportion of total time spent in activity i (i = Th, Tc, L), SH = proportion of total t ime spent in market work, and Xj = all the independent variables, including the value of time, non-

wage income, and the household characteristics that affect the mother's production of household and child services.

The framework outlined above could be used to test the role household structure played in influencing mothers' time use by examining household structure effects while controlling for other socioeconomic and demographic characteristics of the family. In this context, particular attention was given


to the role that economic factors, such as the value of time, unearned income~ and day care usage, played in determining mothers' time use. Careful consid- eration was also given to demographic effects. Specifically, by capturing the influence of numbers of children on time allocation decisions, this model allowed for demographic effects that three of the four existing single-parent time-use studies could not have assessed because their data consisted solely of two-child families. 8

The time-use share normalization implied that the Bj coefficients were in- terpreted as the difference between an independent variable's effect on the i th time-use share (Si) and the share of time allocated to paid work (SH) (Tyrrell & Mount, 1982). As such, predictions about the signs of the economic variables in the model, that is, the value of time and unearned income, could not be made a priori. In the case of the mother's value of time, it could be predicted that as her value of time rose, her share of time spent in both household work and market work declined, ceteris paribus. However, no prediction about the relative magnitudes of these changes could be made and thus, no prediction about the sign of the value of time coefficient could be made (because a negative relationship minus a negative relationship may be either positive or negative)?

Similarly, an increase in unearned income was hypothesized to have an indeterminate effect on the share of time spent in household production and child care relative to paid work. An increase in unearned income should have decreased the share of time mothers allocated to household production and child care. At the same time, an increase m unearned income would decrease the share of time mothers spent in paid work, ceteris paribus. Thus, the over- all sign prediction for the unearned income coefficient was also indeterminate. However, it was expected that an increasing share of mother's time would be allocated to leisure (if leisure was a normal good) in response to an increase in unearned income. Thus the predicted sign on that variable in the leisure equation was positive.

While some a priori predictions about the economic variables could not be confidently made, predictions about the influence of some of the demographic variables were relatively straightforward. In particular, it was hypothesized that as the ages of the children increased, the relative shares of time spent in both home work and child care by the mother would decrease, that is. a negative household production effect minus a positive paid work effect.

D a t a U s e d in A n a l y s i s

Three data sets were used in the analysis. They included the 1979 Califor- nia family time-use data, the 1979 and 1985 interview waves from the Panel Study of Income Dynamics, and 1987-88 Utah Time-Use Study. TM

The California data set used in this analysis was funded as part of the 1977-78 NE-113 project, an 11 state cooperative enterprise. The joint objec- tives of the project were to collect time-use data for urban and rural two- parent two-child families. In addition to collecting data for two-parent families, researchers in California also surveyed single-parent, two-child families.


The California data contained complete records for 210 two-parent, two-child households and 81 single-parent, two-child households. A convenience sam- pling technique was used to identify the single-parent sample. Thus, it was necessary to weight the data in order to ensure that inferences drawn from this analysis were applicable to the population of single-parent families living in the state of California. 11

In the California study, homemakers were asked to record each members ' time-use in 10 minute increments for two 24-hour periods. On one day (the recall day) homemakers were asked in an interview to recall their family's previous day's activities. For a second day (the record day) they were asked to complete time diaries prospectively. Thus, there were two observations for each mother's time-use in the California data. TM

The second data set used here was the Panel Study of Income Dynamics (PSID), conducted by the Institute for Survey Research (ISR) at the Univer- sity of Michigan. The PSID, a longitudinal panel study, was begun in 1968 when a national sample of over 5,000 U.S. households were surveyed regarding their socioeconomic status and their demographic composition. The origi- nal 5,000 respondents and their families have been re-interviewed annually up to the present. Weights were applied to these data in order to make the data representative of all U.S. households. Although the collection of time- use data was not the primary focus of the PSID, in each year male respondents in the married-couple households were asked about the amount of housework done by themselves and other family members in an average week. Responses to this recall question were used in the present analysis.

Finally, the model was estimated with data from the 1987-88 Utah Time- Use Study. These data included time diary information on 214 two-parent, two-child households and 101 single-parent, two-child households in the Salt Lake City, Cedar City, and St. George areas. The time diary instrument was based largely on the NE-113 instrument and, like the California study, both 24-hour record and recall information was collected. Similarly, all seasons of the year and all days of the week were represented in this data set. The mother in each household was asked to record in a time diary how each family member over the age of six had spent her/his time over two 24-hour periods. In addition, each woman was also asked to answer a series of questions designed to gather information about household equipmenL socioeconomic status, and family management strategies.

Although neither the California nor Utah samples were randomly selected, the former had been widely used in past single-parent time-use research, while the latter provided the most recent estimates of single mothers' and married mothers' time-use. The two waves chosen from the PSID, 1979 and 1985, helped assess the representativeness of the other two data sets. Thus, each data set had some appeal. Data from all three of these studies were used to test the time-use model.

Caution had to be exercised when comparing the PSID estimates to those obtained using the California and Utah data. In the case of the PSID, the dependent variable was the answer to a survey question that asked about the amount of time the mother spent doing housework in an average week, including "time spent cooking, cleaning, and doing other work around the house" (Survey Research Center, 1985, p. 265). In contrast, the housework


dependent variable in the California and Utah data was constructed from diary reports of the time the mother spent in eight different categories of household work during a 24-hour period. As a result, some people would have argued that the PSID variable captured long-run behavior while the Califor- nia and Utah variables reflected short-run behavior.

Alternatively, it could have been argued that while the data collection methodologies differed, the California and Utah data also approximated long- run behavior, because the time diary information was collected over all 7 days of the week and all 4 seasons of the year. In this context, these data represented typical time allocation patterns over the course of a year. The model presented and tested in the study reported here was a long-run model, and it was therefore assumed that the PSID, California, and Utah data all approximated long-run behavior. I f the estimated coefficients for the Califor- nia and Utah samples differed markedly from those of the PSID, it would indicate that perhaps this assumption was an appropriate one.

Households were included in the analysis if (a) the household was headed by a couple or a single mother with no other adults present and (b) children less than 18 years old were present in the home. Homemakers that reported being either permanently disabled, retired, or a student were eliminated from the samples. Record and recall days were pooled for each of the California and Utah samples. To control for repeated measure and day of week sequenc- ing effects, two dummy variables were constructed for the Utah and Califor- nia data sets to indicate whether the measure was taken on (a) a record day and (b) a weekend. These two dummies were included in the estimating models.

E m p i r i c a l A n a l y s i s

Consistent with the theoretical model, the dependent variables included the mother's t ime spent in Household Production, Child Care, and Leisure activities divided by the time a mother spent in paid work. Household Pro- duction time included mother's time spent doing cooking, cleaning, laundry, etc. Child Care included mother's time spent in the physical and non-physical care of family members. Leisure activities was a residual category defined by subtracting the previous two time uses and paid work from total t ime available. Because the PSID contained no information on parental child care, that t ime was implicitly included in the leisure activities category and no child care equation was estimated for those data sets.

In addition to the reservation (or shadow) wage and unearned income4 independent variables in the analysis included exogenous household characteristics assumed to influence the woman's time allocation (i.e., the components of Gc and Gh). These consisted of variables indicating whether the household reported using paid day care services, mother's age, ages of both the youngest and the oldest children, and number of children. Number of children varied only in the PSID data, and therefore this variable was excluded from the equations estimated with the California and Utah data. Variable definitions


and descriptive statistics for all of the variables are reported in Tables 1 and 2.

The measurement of the shadow (or reservation) wage variable in this study was complicated and merits a brief discussion before turning to the systems' estimates. According to the new home economics theory, individuals were hypothesized to make time allocation decisions based in part on the value or opportunity cost of their time. For employed women, their market wage was an observable measure of their value of time. However, many women in these samples were not employed, thus necessitating the use of a valuation method other than the market wage rate. Although there were a number of home work pricing strategies that could have been used in this circumstance, Heckman's (1979) reservation wage procedure was chosen.

The Heckman estimation technique was based on the assumption that individuals allocated their t ime to market and nonmarket activities so that their values of t ime in both arenas were equated at the margin. For women who worked outside of the home, their reservation wage was presumed to be equal to their marginal utility of nonmarket time which in turn was equivalent to their market wage. For women who were full-time homemakers, their reservation wage was equal to their marginal utility of nonmarket time which was greater than the wage they could have earned in the labor market (Zick & Bryant, 1983). Thus, constructed shadow wages were the preferred measure of the value of t ime in this study because they captured the marginal utility of nonmarket time in an equivalent fashion for both groups of women. 18

To test for structural differences in single versus married mother's time allocation behavior, a dummy variable, set equal to one if the woman was a single parent, was interacted with all of the independent variables (i.e., the full model) and those results were compared to equations estimated without these marital status interaction terms (i.e., the restricted model). Tests of the full versus restricted models indicated that, with the exception of California, single mothers in all samples made time allocation decisions in system- atically different ways from their married counterparts. I4 Because it appeared that married and single mothers behaved in significantly different ways, the study reported here focused on the full, interactive equations. These equations are presented in Tables 3, 4, and 5. The interaction variables are de- noted by ',X" prefixes attached to their respective variable names in each of these tables. 15

Results

The p r i m a r y focus of the empi r i ca l work was to ident i fy the economic and d e m o g r a p h i c factors t h a t se rved to a l t e r the t ime-use pa t - t e rn s of mothers . G iven the differences be tween the PSID a n d the o the r d a t a sets, th i s m e a n t t h a t the model specif icat ion m u s t h a v e va r i ed across t he s am p l e s so t h a t in each ins tance it ref lec ted the bes t opera t iona l i za t ion of the theore t i ca l ly posi ted re la t ionships . B e c a u s e of the specif icat ion differences, no fo rma l t e s t i ng of the e s t i m a t e s ' ro-


T A B L E 1

V a r i a b l e D e f m i f i o n s

Variable name Variable definition

LNY WSTAR DAYCARE

MAGE AOYC A00C NUMKID

NUMAD WEEKEND

RECALL HPSHARE

CCSHARE

LSHARE

Log of unearned income Log of the mother's reservaton wage rate Dummy variable -- i if paid day care; 0 =

otherwise Age of mother in years Age of youngest child in years Age of oldest child in years Number of children present in household less than

18 years old Number of adults in household Dummy variable = 1 if weekend day; 0 =

otherwise Dummy variable = 1 if recall day; 0 = otherwise Relative share of time mothers spent in home

production (compared to paid work~ Relative share of time mothers spent in child care

[compared to paid work) Relative share of time mothers spent in leisure

(compared to paid work)

bustness across the data sets could b e conducted. At best, only descriptive comparisons could be made. Several consistent findings did appear across the estimates obtained using the four data sets.

Household Production

There were four consistent findings across the Household Produc- tion equations that merit discussion. The first finding was that an increase in unearned income led to a decline in the share of time married mothers spent in Household Production vis4t-vis paid work. However, the est imates indicated less support for this relationship among the single mothers2 ~ If Leisure was a normal good, then for married mothers, an increase in unearned income led them to reduce their share of time spent in both household work and paid work, but the reduction in household work was greater. That is, a larger nega-

" ~ # ~ # o #

LeD

< ~ ~

o ~ ~


TABLE 3

H o u s e h o l d P r o d u c t i o n Share Equat ions Ful ly Interacted wi th Single P a r e n t D u m m y Variable

(Standard Errors in Parentheses )

Variable UTAH PSID'85 PSID'79 CALIF

C o n s t a n t 30 .298 - 39 .279* 54,720** - 44 .657 (29.459) (18.480) (19.050) (36.990)

L N Y 1.549 - 2 .539** - 1 .567"* - 3 .416"* (1.196) ( .450) ( .588) (1.310)

W S T A R - 5.479** - 5 .216"* - 3 .428 12 ,957"* (.673) (1.427) (2 .032) (2.780)

D A Y C A R E - 5.994** - - - 16 .029"* - 3 . 1 4 2 ' (1.557) ( .733) (1.610)

M A G E .172 .255** .211"* - .078 (.107) (.054) ( .052) ( .134)

A O Y C - . 6 8 5 * - . 3 5 8 * * - 1 .163"* .064 (.280) ( .127) (.124) ( .335)

A O O C .227 - .386** .039 .395 (.252) ( .127) ( .130) ( .326)

N U M K I D - - 2 .578** ,935* - - (.473) ( .419)

W E E K E N D 2.153 - - - - 1.153 (1.309) (1.530)

R E C A L L 1.558 - - - - .951 (1.166) (1.320)

N U M A D - 12.504 40.985** - 8 .025 28 .094 (17.968) (10.02) (10.57) (21.34)

X L N Y - 2 .779 .997 - 2 .436* 3 .719"* (1.967) ( .841) (1.014) (1.354)

X W S T A R 2.554 8.605** 1.878 - 2 .016 (1.327) (3.072) (3.169) (5.817)

X D A Y C A R E 4.246 - - 12.55"* .672 (2.654) (2.16) (3.557)

X M A G E .051 - .083 - .297* - .025 (.231) ( .117) (.136) (.299)

X A O Y C .541 .434 1 .162"* - .146 (.583) ( .330) ( .423) (.697)

X A O O C - .260 .241 - .027 - .306 (.530) ( .345) ( .431) (.779)

Robin A. Douthltt, Cathleen D. Zick, and Jane McCullough 39

T A B L E 3 (Continued)

Variable UTAH PSID'85 PSID'79 CALIF

X N U M K I D - - - 2.384 - 1.526 - - ( t .426) (1.598)

XENI) 10.065"* - - - - - .848 (2.488) (3.128)

X REC ALL 2~032 - - - - - 1.152 (2.086) (2.557)

~2 .224 .133 .312 .096 F a 2.552** 18.529"* 14.718"* 1.418

*p < .05; **p < .Ol. aTest of the full versus restricted models.

t i r e re la t ionsh ip minus a smal le r nega t ive re la t ionship led to a ne t re la t ionsh ip t h a t was negat ive .

Second, the coefficient on paid Day Care a lways had a nega t ive sign and th is s ignif icant re la t ionsh ip exis ted for bo th the m ar r i ed and single mothe r s wi th the except ion of the 1979 PSID est imates . 17 The a priori predic ted sign on paid Child Care was ambiguous. The use of

T A B L E 4

C h i l d C a r e S h a r e E q u a t i o n s F u l l y I n t e r a c t e d w i t h S i n g l e P a r e n t D u m m y V a r i a b l e s ( S t a n d a r d E r r o r in P a r e n t h e s e s )

Variable UTAH CALIF

Cons tan t 13.485 27.740 (13.981) (14.730)

LNY .880 .7O6 (.568) (.522)

WSTAR - 2.335** 2.732** (.320) (1.107)

DAYCARE - 4.497** - 1.997"* (.739) (.641)

MAGE .027 .079 (.051) (.053)

40 Lifestyles: Fami ly and Economic Issues

TABLE 4 (Continued)

Variable UTAH CALIF

AOYC - .387** - .190 (.133) (.134)

AOOC - .359** - .494** (.120) (,130)

W E E K E N D .338 - :376 (.621) (.609)

R E C A L L .294 - .308 (.553) (.526)

N U M A D - 3.677 - 16.927 (8.527) (8.497)

X L N Y - 1.304 - .492 (.934) (.539)

X W S T A R 1.192 - 2.531 (.630) (2.316)

X D A Y C A R E 3.631"* - .194 (1.260) (1.416)

X M A G E .036 - . 1 8 2 (.110) (.119)

XAOYC .344 - .049 (.276) (.278)

XAOOC .083 .168 (.251) (,310)

X E N D 3.450** - .524 (1.181) (1.246)

X R E C A L L - .019 1.329 (.990) (1.018)

~2 .336 .270 F ~ 2.672** .779

*p < .05; **p < .01. aTest of the full versus restricted models.

pa id child care should effect ively h a v e lowered the mo the r ' s m a r k e t wage and thus the re should h a v e been a nega t i ve r e l a t ionsh ip be- t w e e n pa id child care and t h e sha re of t i m e m o t h e r s spent in pa id work. The cons i s ten t ly nega t i ve coefficient i m p l i e d t h a t use of pa id


TABLE 5

Leisure Share Equat ions Ful ly Interacted With Single Parent D u m m y Variable (Standard Errors i ~ Parentheses)

Variables UTAH PSID'85 PSID'79 CALIF

C o n s t a n t 248 .592** - 4 0 . 6 4 2 237.073** - I 2 8 , 2 2 0 (70.560) (59.760) (53.100) (87.440)

L N Y 4.311 - 7 .583** - 2 .607 - .872 (2.864) (1.455) 1.638 (3.097)

W S T A R - 1 4 . 2 7 6 " * - 1 3 . 2 6 6 " * .708 40 .027** (1.613) (4.616) (5.664) (6.572)

D A Y C A R E - 18 .372"* - - - 50.689** - 5 .703 (3.729) (2,042) (3,805)

M A G E .441 .867** .353** - .568 (.257) ( .173) ( .144) ( .317)

A O Y C - 1 .911"* - 1 .462"* - 3 .236** .899 (.671) ( .409) .346 (.793)

A O O C - .253 - .918" .113 .598 (.604) ( .410) ( ,361) ( .770)

N U M K I D - - 4 .812"* - .911 - - 1 .528 (1.167)

W E E K E N D 12.898"* - - - - 5 .524 (3.135) (3.617)

R E C A L L 1.120 - - - - 6 .809** (2,792) (3.121)

N U M A D - 114 .333"* 85.474** - 76.445** 36 .444 (43.035) (32.410) (29.470) (50.440)

X L N Y - 14 .087"* - 5 .255* - 8 .098** 2 .643 (4.712) (2.719) (2.826) (3.201)

X W S T A R - 1 . 1 4 1 37.763** - 3 .499 1.344 (3.179) (9.934) (8.833) (13.750)

X D A Y C A R E 13 .084"* - - 26.969** 2 .789 (6.358) (6.008) (8.409)

X M A G E .376 - . 6 5 5 - 1 .015"* .954 ( .554) ( .377) ( .389) (.796)

X A O Y C 3.224* 2.965** 2.655* - 1.081 (1.395) (1.068) (1.189) (1.647)

X A O O C - 1 .519 .318 .442 - 1 .704 (1.269) (1.116) (1.202) (1.842)


T A B L E 5 (Continued)

Variables UTAH PSID'85 PSID'79 CALIF

XNUMKID - - - .967 - 7.840 - - (4.612) (4.455)

XEND 24.281"* - - - - 13.377 (5.959) (7.394)

XRECALL - .723 - - - - - 1.868 (4.995) (6'044)

~2 .348 .114 .322 .160 F a 3.802** 19.161"* 10.622"* 1.180

*p < .05; **p < .01. "Test of the full versus restricted models.

child care led mothers to spend less time in complementary household work activities. Furthermore, the magnitude of this negative relationship between paid child care and share of time spent in household work was greater than the relationship between paid child care and share of time spent by the mother in market work. That is, a larger negative effect minus a smaller negative effect would lead to the negative coefficient that was estimated.

Third, as the age of the younger child increased, married mothers reduced the share of t ime they spent in household work relative to the share of time they spent in market work. This relationship was confirmed in three of the four data sets (the exception being Califor- nia) and it conformed with the hypothesis that was made. However, the relationship appeared to be more ambiguous for the single-parent households, with the significant negative effect holding in only two of the single-mother samples (Utah and PSID 1985).

Finally, the estimated coefficients associated with the value of time were significant in three of the four samples (the exception being PSID 1979), but the direction of the relationship varied for married and single mothers and it varied across samples. TM (Recall that no prediction was possible about the direction of the relationship between the mother's relative share of household work and her value of tim&) The consistent significance of the shadow wage in these equations was evidence of its theoretical importance and the inconsistency in its


sign was supportive of the ambiguous relationship between the shadow wage and time allocation.

Child Care

The Child Care equations were estimated only for the Utah and California samples because no data on time spent in child care were collected in the PSID interviews. As such, there was less confidence about identifying "consistent" findings for these equations. Three results in the Child Care share equations were noteworthy. First, if the household purchased child care, this decreased the relative share of time spent in Child Care for both single and married mothers, although the size of the decline was smaller for single mothers. This implied that paid child care decreased the proportion of time spent by the mother in Child Care more than it decreased the proportion of time she spent in paid work; that is, the negative child care effect was larger than the negative paid work effect.

Second, as the age of the older child increased, the relative share of time spent in Child Care by both single and married mothers declined, ceteris paribus. This relationship supported the idea that as children grew older, mothers may have been substituting the oldest child's time for the mother's time in Child Care, and/or mothers increased the share of time they spent in market work.

Finally, the shadow wage of both single and married mothers was significantly related to the relative share of time they spent in Child Care, but the signs on these coefficients were opposite in the two samples. For both single and married Utah mothers, an increase in the shadow wage was associated with a relative decline in the share of time spent in Child Care. In the California sample, the relationship was reversed.

Leisure

Five consistent findings emerged in the Leisure share equations. First, paid child care significantly decreased the share of time mothers spent in Leisure relative to paid work, although the negative effect was larger for married women than it was for single women. This result was contrary to what would be predicted if Leisure was a normal good. If paid child care decreased the effective market wage, then there should have been a positive relationship between paid child care and share of time spent in Leisure, and a negative relationship


between paid child care and the share of time spent in market work. On balance then, the paid child care coefficient would have been un- ambiguously positive; that is, a positive relationship minus a negative relationship.

It was possible that the negative paid child care coefficients in the 1979 and 1985 PSID Leisure equations were an artifact of how the Leisure variable was constructed. (Recall, Leisure included time spent in child care in the PSID specification.) However, no such explanation could be offered for the parallel finding in the Utah sample. There were two other possible explanations for this anomalous finding: (a) mother's Leisure was not a normal good, and/or (b) paid child care was serving a proxy for the mother's labor force participation.

Second, unearned income was associated with a significant decline in the relative share of t ime single mothers spent in Leisure, but no consistently significant relationship was observed for married mothers. This negative relationship was again inconsistent with what one would predict. If single mothers' Leisure was a normal good, an increase in nonwage income should have been associated with (a) an increase in the share of t ime single mothers spent in Leisure, and (b) a decrease in the share of t ime single mothers devoted to market work. On balance then, a positive coefficient would have been predicted. The relatively consistent finding of a negative relationship suggested that perhaps single mothers' Leisure was not a normal good.

Third, as the age of the youngest child increased, married mothers decreased their relative share of time allocated to Leisure. In contrast, the age of the youngest child had no significant impact on the single mothers' relative Leisure share. 19 This finding did not necessarily in- form the relationship between mother's Leisure and age of the youngest child, but it did confirm the a priori hypothesis that the older the youngest child was, the greater the share of time married mothers allocated to paid work.

Fourth, the shadow wage significantly altered the relative share of t ime that was spent in Leisure. However, the estimates showed that the direction of the relationship varied across samples and across household types. This finding paralleled the ones observed in the other share equations.

Finally, number of adults (single versus married) was statistically significant in three of the four Leisure share equations (the exception being California), but the signs on these coefficients varied across the samples. In the Utah and 1979 PSID samples, married mothers spent a smaller share of their t ime in Leisure relative to market work corn-


pared to single mothers. In the 1985 PSID sample, married mothers spent a larger relative share of time in Leisure than did their single counterparts. The presence of another adult in the household affected a mother's relative time allocation to Leisure. However, the effect's direction could not be clearly ascertained from these equations.

D i s c u s s i o n a n d C o n c l u s i o n s

Married and single mothers appear to make different decisions about how to allocate their time to Household Production, Child Care, Lei- sure, and paid work. In this sense, the research presented here is supportive of the findings of most past studies (i.e., Lyerly, 1969; Rowland et al., 1986; Sanik & Mauldin, 1986). However, this work goes beyond past studies to test hypotheses regarding the sources of the observed differences using four different data sets. In the context of a Household Production model, it has been posited that differences in married and single mothers' time-use are a function of economic factors, including unearned income, the mother's shadow wage, fixed household production characteristics (e.g., age of the mother, number of adults), and fixed child services production characteristics (e.g., age of the youngest child, age of the oldest child, number of children, use of paid child care).

Each of the four data sets that has been used to test the model reveals considerable support for the a pr ior i hypotheses. It had been anticipated that some differences in the estimates would be observed because the PSID's data collection methodology differs substantially from the methodology used to collect the Utah and California data. The fact that estimates using both samples of the PSID generally parallel those obtained using the Utah data is somewhat of a surprise given the differences in the data collection methodologies. Indeed, the relative inconsistency of the California data, especially in the Leisure share equation, suggests that analyses done with these data should be viewed with caution.

Consistent differences between single and married mothers are often observed for at least three of the four samples in the analyses. Specifically, single and married mothers responded differently to a change in their shadow wages, unearned income, paid child care, and the ages of their children, in each of the estimated share equations? ° The differences in single mothers' and married mothers' responses appear to be somewhat systematic. In most instances, the estimates in-


dicate that single mothers are less responsive than married mothers to a change in one of the exogenous variables. For example, the impact of paid child care on married mothers' t ime allocation is consistently negative and the coefficients are quite large in all three shares equations. In contrast, while these negative effects of paid child care are still present for single mothers, the magnitudes of the associated coefficients are generally much smaller. Similar stories can be told about the relatively subdued responses of single mothers to changes in (a) their shadow wages in the Household Production equation, and (b) age of the youngest child in the Leisure equation.

Why is it that married mothers react differently than single mothers to changes in their economic and sociodemographic environment? One possible answer is that underlying the married mothers' choices regarding time allocation are the preferences of the couple. In contrast, the preferences that underlie a single mother's time allocation choices are strictly her own. If the married mother's true preferences can be assumed to be analogous to the single mother's revealed preferences, then the differences observed between single and married mothers' time allocations could reflect the impact of the husbands' preferences in the couples' uti l i ty function.

Alternatively, it is possible that the differences observed between married and single mothers is a reflection of their differing budget and time constraints. For example, a single mother who has few child care options in the early morning and/or late evening may- be less able than a married mother to adjust her time allocation pat terns in response to a change in her shadow wage. The married mother should be able to turn to her spouse for child care assistance in most instances. Thus, if her shadow wage changes, the married mother may be able to alter her time-use pat terns extensively because she faces a less binding child care time constraint.

Yet another plausible explanation for the observed differences is that married and single mothers find themselves in different employ- men~ situations. Specifically, some jobs require strict adherence to certain time schedules (e.g., jobs that require employees to punch a time clock) while others are characterized by flexibility in the sched- uling of work time. Mothers may find themselves sorted into these two different types of jobs for a couple of reasons. First, single mothers may elect to take jobs with set hours because it reduces some of the time management uncertainty they face. In contrast, married mothers may opt for jobs with flexible hours because they can rely on their spouses to cope with some of the time management problems tha t are


introduced with this type of employment. Second, employers may view single mothers to be less desirable employees than married mothers (Schwartz, 1989). If this is true, these employers may engage in sub- tle forms of discrimination by channeling single mothers into less desirable jobs that have set hours. In either case, the result could be that single mothers would be less able than their married counterparts to respond to changes in any of the exogenous variables by al- tering their t ime allocation patterns.

While one or more of these mechanisms may be serving to differen- t iate the time allocation behavior of married and single mothers, their relative effects cannot be evaluated in the context of this research. What this study does show is that economic conditions inter- act with mari tal status to alter mothers' choices about time allocation. Indeed, the results presented here suggest that new insights about the impact of family policies can be gained if these policies are assessed in the context of household structure. For example, increases in the availabili ty of paid child care are likely to decrease the share of time spent in Home Production, Child Care and Leisure (relative to paid work) more so for married women than for single women. Many of the proposals to increase access to paid child care rest on the argu- ment that it is the single mothers who will be helped most by these proposed policies. However, in reality, it may be the married mothers who would be the most responsive to such a change.

Similarly, one can use these findings to examine how recent federal legislation intended to increase both the level of, and collection rates for, child support will alter mothers' t ime use. The evidence from this s tudy suggests that increases in child support awards (a potential source of nonwage income for both single and re-married custodial mothers) will have mixed effects on mothers' time allocation. Both single and re-married mothers will spend relatively less time in household work if child support awards rise. However, the increase of such awards would also reduce single mothers' relative share of leisure time.

Policy changes such as the ones described above may have differing impacts on mothers depending on their mari tal status. The findings presented here suggest that proposals to increase access to child care and/or increase child support awards are likely to affect married mothers more than single mothers. If this is true, then policy analysts must be alerted to the political importance of conducting separate family policy impact assessments for married and single-paren~ households.


N o ~ s

1. The National Center for Health Statistics (1988) reported that the divorce rate rose fairly steadily through the 1960s and 1970s, peaking in 1979 and 1981. Subsequently, divorce rates stabilized and most recently declined to their lowest rate since 1975.

2. Birth rates per 1,000 unmarried women increased from 21.6 in 1960 to 32.8 in 1985 (U.S. Bureau of the Census, 1987b).

3. In 1987, about 11% of children living with only one parent were living with their father (U.S. Bureau of the Census, 1987a).

4. Although Sanik and Mauldin's title indicates that theirs is a study of single mothers, in fact about 10% of their sample included men heading single-parent households.

5. Lyerly controlled for employment status by dividing the sample respondents into two groups; those who engaged in 6 or more hours of other (non-household~ work each day and those who did not.

6. As noted earlier in the text, Sanik and Mauldin did control for household income and age of the younger child in their analysis. They elected only to control for these two variables because their preliminary work showed that the two-parent and single-parent households in their sample had statistically different mean values only on these two characteristics. No significant differences were found for mother's education, mother's age, age of the older child, gender of the children, or use of child care services by the household (Sanik & Mauldin, 1986, p. 55). Regardless of the outcomes from their bivariate tests, it was possible that these household characteristics affected time use. To allow for this possibility, a more general model of single parents and married parents would include these factors.

7. Because the log of zero is undefined, a small constant (.01) is added to each budget share before the normalization is conducted.

8. In 1980 46.5% of all single parents in the U.S. headed a household with only one child; 31.6% two children; 13.7% three children; 8.9% four or more children (U.S. Bureau of the Census, 1980).

9. It should be noted that the effect of an increase in the shadow wage would be indeterminate a priori regardless of the functional form. In an economic model, the effect of the value of time can be decomposed into a substitution effect and an income effect. In the case of household work, an increase in the shadow wage would translate into a negative substitution effect and a positive income effect, and thus on balance, no sign prediction could be made. By using Tyrrell and Mount's specification, the shadow wage predictions were further complicated because the estimated coefficient was now a relative effect.

10. The PSID, California, and Utah data sets represented three of the four major sources of information on single and married mothers' time use. The fourth is the University of Michigan's 1975-76 and 1981-82 Time Use in Economic and Social Accounts data.

11. A weight was calculated based on California single-parent households' geographic, gender, age, and income distributions as reported by the Census Bureau in 1980.


12.

13.

14.

15.

16.

17.

18. 19.

20.

A complete description of the instruments and survey method used in collecting two-parent household time-use data can be found in Family Time Use: A n Eleven-State Urban~Rural Comparison (1981). The interested reader is referred to Zick and Bryant (1983) for specifics regarding the shadow wage estimation procedure. Their specification of the reservation wage equation was replicated as closely as possible for each of the data sets used here. Due to space considerations, details of the shadow wage estimation are not reported in this article, but the estimates are available from the authors upon request. This test statistic is calculated as

where, R2t = the unadjusted R e for an equation in the full model, R2r = the unadjusted R 2 for the same equation in the restricted model, N - the sample size, T = the number of parameters in the full model, and R = the number of estimated parameters in the restricted model (Kmenta, 1986). These computed F-statistics are reported at the bottom of Tables 3-5. The results of the restricted model are not presented but are available from the authors upon request. In separate equations run only on the single-mother samples, the impact of unearned income was significantly different from zero in only the two PSID samples. The reservation wage and mother's age effects were both positive and significant in the California and 1985 PSID samples, respectively, and negative and significant in the Utah sample. While these separate regressions are not reported here in a table format, they are available from the authors upon request. The 1985 PSID interview did not include a question about paid day care arrangements that was asked of the entire sample. Thus, this variable was omitted from the household work, child care, and leisure equations that were est imated with these data. See endnote 16. While the lack of relationship between age of the youngest child and single mothers' Leisure share is not obvious from Table 5, in separate regressions run only an the single-mother households, age of youngest child was not statistically significant. These separate regressions are available from the authors upon request. I t should be noted that the weekend versus weekday dummy (WEEK- END) and the record versus recall day dummy (RECALL) were generally not significant. WEEKEND was significant for single mothers only in the system estimated with the Utah sample. RECALL was only significant once in the leisure share equation estimated with the Califor- nia data.


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the role of economic and demographic factors in explaining time-use of single and married mothers

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