Determinants of Father-Child Time Allocation
Dmitri M. Medvedovski
Bethel University
Kirk C. Allison
University of Minnesota

• This research explores associations between father-child time allocation, paternal background, and non-market & market activities.
• The more fathers positively and intentionally engage their children’s lives the healthier their socialization process will be.
• Not only ‘quality’ but time quantity is relevant for modeling and communicating values and skills to maximize a child's development and capabilites.
(Quantity is a dosed dimension of quality.)

Background
• Father-child allocation deficits contribute to negative behavioral outcomes in children, notwithstanding that many mothers do exceptional work parenting their children (Goncy and van Dulman, 2010).
• US estimates of father absence as a primary factor in
– 63% of youth suicides,
– 90% of homeless or runaway children,
– 85% of children exhibiting behavioral disorders
– 71% of national high school dropouts
(Bureau of the Census, Center for Disease Control, &
National Principals Association Report on the State of High
Schools, 2007).

Modeling Context
• Parental allocations for children can be considered an investment of human capital: monetary and temporal.
• Parents maximizing utility subject to a budget constraint must trade-off between their own consumption and investment in their children including the cost of time allocated
• Amount of investment will be positively related to the rate of return, time allocation and other factors.
When children grow up the rewards of children will depend on that investment (Goldberger, 1989).

Modeling Context
• Household production models conceive the family in part as a productive organization producing nonmarket commodities with purchased goods and the time of household members (Willis, 1987).
• Becker and Tomes hypothesis (1986):
Exogenous increases in potential benefits for children (independent of parents’ expenditures) cause parents to substitute towards their own consumption away from investment in children.

Modeling Context
• Families seen as maximizing utility (with functional arguments of quantity and quality of children along with other goods) are subject to a production function for child quality, a budget constraint and a time constraint. (Hanushek, 1992)
• Dual income arrangements require many families to make intrafamilial parental-time trade offs between work and interaction with children.
• Many studies have investigated time allocation decisions of mothers; little investigation has taken place regarding time allocation of fathers.

This research . . .
• Explores how a mother’s working hours relate to a father’s time allocation for children and measures the relationship between parents’ working hours outside of home as substitutable components to sustain family welfare
• Explores whether total family income as a child is at home impacts father-child time allocation
• Explores the relationship between wage rate, income and a father’s time allocation

This research . . .
• Investigates the impact of the father’s education on father-child time allocation
• Tests the relationship between a father’s time allocation and age of the father and of the child

Data and Methods
– Random U.S.-wide: phone, in-person, & mail survey
– New York oversampling of minority population
(book & meal post-survey incentives)
– 2000 questionnaires, 1650 returned (82.5%)
– Inclusion criteria was children at home:
=> 1135 of 1650 (69% of completed)
– Education level was somewhat higher than population mean; 43.4% reported own father absent

Sample Characteristics of the Respondents
(1,135 fathers meeting criteria of 1,651 completed questionnaires)
Characteristic N Mean SD Median Range
Age 1135 37.81
Annual Family Income 1095 $61,258
Income Increase as Father Ages 1095 $1,005
Father’s Weekly Interaction Hours 1135
7.56
Weekly Work Hours, Father 1129 46.85
Weekly Work Hours, Mother
Years Married (Current Spouse)
1113 14.60
1099 12.55
7.03
37.00
$53,575 $50,000
7.81
9.89
16.95
6.91
5
45
7
11
20 to 77
$0 to
$800,000
0.25 to 75
0 to 90
0 to 90
0 to 42

Education
Category
High School Degree
Post High School Degree (e.g. Assoc., Trade)
College Degree (includes graduate degrees)
Marital status Married / Single
Father absence Death
Divorce or Separation
Abandonment
Work
Children
Other
One child
Two children
Three children
Four children
Five or more children
Child w/ father One child
Two children
Three children
Four children
Five or more children
Paternal siblings Only child
One sibling
Two siblings
Three siblings
Four siblings
Five or more siblings
%
16.65
13.92
68.46
92.42
/
4.58
39.65
22.56
7.05
1.85
4.67
21.67
27.31
21.59
10.57
14.18
7.11
11.79
2.24
70.93
7.93
18.77
40.09
27.22
9.60
4.32
28.90

OLS Regression Models
• Model 1
Father/Child time allocation model
• Model 2
Maternal working hours outside home (check for a substitution or complement effect with paternal working hours)
• Model 3
Sociodemographic characteristics and working hours of mother & father relative to total family income
( each run on full data and by income strata:
<40K, 40+-80K, 80+-200K, 200+-800K )

OLS Regression Models
Y
1t
= father-child time allocation
Y
2t
= father’s work hours
Y
3t
= mother’s work hours
Z
1t
= family income
Z
2t
= college education
Z
3t
= high school education
Z
4t
= age of father
Z
5t
= number of father’s siblings
X
1t
= number of children in family
X
2t
= one child living at home
X
3t
= two children living at home
X
4t
= three or more children living at home

OLS Regression Models

Note:
†p

.10, *p

.05, **p

.01, and ***p

.001
(with the raw beta preceding the standardized beta)

Model F1 Father-Child Time Allocation (Income Bands)
Father’s Age
Mothers Working Hours
Children < 12 vs. 18+
-0.132** -.111
0.117*** .202
3.820** .169
Income Efficiency = $/(M+F hrs) 1.224*** .154
Income < 40K Base
Income 40K-<80K -1.584** -.079
Income 80K-<200K
Income 200K-800K
-2.497** -.087
-7.633**, -.093
Note progressive neg. relationship of income and father’s time with children; but positive for income efficiency

Model F2 Father-Child Time Allocation (Total Income)
Father’s Age
Mothers Working Hours
Children < 12 vs. 18+
-0.136** -.115
0.116*** .200
3.892** .169
Father College vs. High School -1.263* .-060
Household Inc. Efficiency ($/hrs) 1.195*** .150
Total Income (continuous) -0.017 † -.088
Note Father’s College Degree emerges as strong negative predictor vs. High School while income remains negative

Model F3 Father-Child Time Allocation (<$40K)
Father’s Age NS
Mothers Working Hours
Total Number of Children
0.132***
-0.970†
.194
-.101
Children < 12 vs. 18+
Number of Father’s Siblings
Father College vs. High School
5.833* .215
0.433* .094
NS
Household Inc. Efficiency ($/hrs) NS
Total Income (continuous in band) NS
Note: Children < 12 strengthens with total number negatively associated, and father’s siblings positive
(socialization or inclusive network?)

Model F4 Father-Child Time Allocation ($40-<$80K)
Father’s Age
Mothers Working Hours
Total Number of Children
-.126* .110
0.120*** .227
NS
Children < 12 vs. 18+
Number of Father’s Siblings
Father College vs. High School
2.837* .161
NS
NS
Household Inc. Efficiency ($/hrs) NS
Total Income (continuous in band) -0.017 † -.088
Note: Children < 12 & mothers working hours continue consistent positive relationship, but total income in band a negative relationship. (Father’s age reemerges neg.)

Model F5 Father-Child Time Allocation ($80K-<$200)
Father’s Age -.272* .213
Mothers Working Hours
1 Child at Home
0.088*
4.511*
.166
.228
2 Children at Home
3 Children at Home
Total Number of Children
-3.672*
-3.609*
2.155*
Children < 12 vs. 18+ NS
Total Income (continuous in band) NS
-.202
-.193
.277
Note: Income, age and children’s age rise together: here children < 12 are now nonsignificant. 1 child home is strongly + but 2 or 3 negative. Yet total # of children is positive: emptying nest compensation?

Model F6 Father-Child Time Allocation ($200K-<$800K)
Father’s Age NS
Mothers Working Hours
1 Child at Home
0.489*
NS
.861
2 Children at Home
3 Children at Home
Total Number of Children
16.925*
NS
NS
Children < 12 vs. 18+ NS
Total Income (continuous in band) NS
.607
Note: Mothers outside work contiues to be positively associated. 2 children now extraordinarily positive
(caution: few data points in this range).

Negatively Associated
• Father’s age
• Income (banded)
• Total income
• Higher education
• # of Children (<40K)
Positively Associated
• Mother’s mkt work hrs
• Fam. Income efficiency
• Children
• 1 Child at home
• # of Children (200-800K)
• # of Father’s siblings

Model M1 Mothers Outside Work Hrs (Income Bands)
Fathers Working Hours / Week
1 Child at home
Total # of Children
Children < 12 vs. 18+
Father College Degree
Income < 40K
Income 40K-<80K
Income 80K-<200K
-0.283*** -.161
-3.891** -.103
-1.758*** -.115
5.156**
-2.981*
Base
6.727***
9.174***
-.130
-.081
.194
.185
Income 200K-800K 44.068*** .306
House Inc. Efficiency = $/(M+F Hrs) -6.446*** -.464
Note signs reverse of Father-Child model:
1 Child home, Children < 12, Income Efficiency (now -);
Income (now +)

Model M2 Mothers Outside Work Hrs (Total Income)
Fathers Working Hours / Week
1 Child at home
Total # of Children
-0.436*** -.928
-3.530** -.094
-1.682*** -.110
Children < 12 vs. 18+ 5.211** -.131
Father College Degree -3.462*** -.095
Father’s Father absent (death, aband) 3.139* .050
House Inc. Efficiency
Total Family Income
-12.888*** -.928
0.266*** .804
Note: With continuous income variable neg. coefficient on household efficiency doubles (M/F wage gradient).
Father’s father absence as strong predictor.

Model M3 Mothers Outside Work Hrs (<$40K)
Fathers Working Hours / Week
1 Child at home
Total # of Children
Children < 12 vs. 18+
# Father’s Siblings
Father College Degree
House Inc. Efficiency
Total Family Income
-0.404*** -.226
NS
-1.625*** -.114
8.750** -.220
0.552* .081
NS
-22.101*** -.517
0.474*** .225
Note: Lowest income strata ~ Father’s Sibling # now significant, Father College NS, Children<12 (+) and
Income Efficiency (-) stronger

Model M4 Mothers Outside Work Hrs ($40K-<$80K)
Fathers Working Hours / Week
2 Children at home
Total # of Children
Children < 12 vs. 18+
Children 12-18
# Father’s Siblings
Father’s College Degree
House Inc. Efficiency
Total Family Income
-1.04*** -.476
-1.285 † -.036
NS
NS
2.146 †
NS
.042
-1.962* -.051
-54.78*** -1.039
0.983*** .618
Note: Father’s College again significant with higher income strata (-); Income Efficiency higher (-)

Model M5 Mothers Outside Work Hrs ($80K-<$200)
Fathers Working Hours / Week -0.669*** -.405
Total # of Children NS
Children < 12 vs. 18+
Children 12-18 NS
Father’s Father absent (death, aband) 5.721*
Father’s College Degree
NS
-8.088**
.098
-.167
House Inc. Efficiency
Total Family Income
-14.71*** -.957
0.234*** .441
Note: Father’s College highest magnitude in this strata; also strong coefficient on absence of Father’s Father with income efficiency continuing to show strong wage gradient.

Model M6 Mothers Outside Work Hrs ($200K-<$800K)
No Significant Coefficients
(sparse data in this strata)

Negatively Associated
• Father’s working hours
• Father’s college degree
• Children < 12 (full,<40K)
• # Children (full, <40K)
• 1 Child at home (full)
• Income Efficiency
Positively Associated
• Income strata (progr.)
• Total family income
• Father’s father absent due to death, abandonment or other

Model for Total Family Income
•
Includes Father’s Age
•
Includes both Father & Mother’s Working Hours
•
Indicators for Children at home (1,2,3) and <12, 12-18
•
Total # of Children
• # Father’s Siblings
•
Indicators for post-High School and College vs. HS
• Indicators for absence of Father’s father

Model I1 – Total Family Income (All Data)
Father’s Age
Fathers Working Hours
Mothers Working Hours
# Father’s Siblings
Children < 12
Children 12-18
Father’s College Degree
0.630**
NS
NS
.107
-1.183 † -.050
15.560* .131
19.905** .129
15.664*** .142
Note: Small children, esp. teens, drive income seeking,
+college degree effect & secular trend ~ age. Father’s siblings (-) previously ~ + child & maternal work time

Model I2 – Total Family Income (<40K)
Father’s Age
# Father’s Siblings
1 Child at home
NS
NS
-1.737 † .104
2 Children at home 2.818** .179
Father Post High School (Associates) 2.008*
Father College 3.623***
.099
.231
Fathers father absent (death, aband.) -4.607
.161
Note: Father post-HS education (associates/trade) &
College + effect, but strong negative intergenerational absent father effect (death, abandonment) in strata. Signs flip between 1 & 2 children.

Model I3 – Total Family Income ($40K-<$80K)
Father’s Age
Fathers Working Hours
Mothers Working Hours
0.183* .138
0.098 †
.075
0.089** .141
1 Child at home
2 Children at home
NS
NS
Father Post High School (Associates) NS
Father College 3.175*
Fathers father absent (death, aband.) NS
.131
Note: Age, working hours (both) and higher education

Model I4 – Total Family Income ($80K-<$200K)
Father’s Age
Fathers Working Hours
Mothers Working Hours
NS
NS
-0.260* -.138
Total # of Children
Children < 12
Children 12-18
5.846** .211
19.890 † .297
16.579 † .210
Fathers father absent (death, aband.) NS
Note: Negative coefficient on mothers’ outside work hours on income implies net negative substitution effect on fathers’. Large positive coefficients on # and presence of children across ages in this college-conscious strata

Model I5 – Total Family Income ($200-$800)
Intercept NS
Fathers Working Hours -8.794 † -1.208
Fathers Father absent (Death, aband) -491.322 † -1.295
Note: Sparse data and weak significance (negative coefficient on father’s working hours: indicative of nonwage income?). Absent father datum at low end of
(upper) income band.

Total Family Income Tendencies Summary
•
Negatively Associated
• # of Fathers Siblings
(Full)
1 Child at Home (<40K)
• Father’s Father absent by death, abandonment
(<40K, 200K-800K)
Ambiguous
• Mother Work Hrs
(40K-<80K +, 80K-<200K -)
• Father Work Hrs
(40K-<80K +, 200K-800K -)
Positively Associated
• Fathers Age
(Full, 40K-<80K)
• 2 Children at Home (<40K)
• Children < 12,12-18, total
(Full, 80K-200K)
• Fathers Post-HS Ed (<40K)
• Fathers College
(Full, <40K, 40K-<80K)

• Our results suggests that quantity of a father’s interactive time allocation for his children correlates with market activities, income utility, and working hours with a ‘paradoxical’ effect associated with paternal education and an incomplete substitution effect with a working spouse.
• An economic approach to father-child time allocation is a useful tool for analyzing father-child relationships and can provide a basis for developing both an analysis of the research and recommendations to enhance positive family relationships.