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    • Abstract: Occasional Paper No. 64National Center for the Study of Privatization in EducationTeachers College, Columbia UniversityHome Schooling:School Choice and Women’s Time UseDecember 2002Eric IsenbergWashington University

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Occasional Paper No. 64
National Center for the Study of Privatization in Education
Teachers College, Columbia University
Home Schooling:
School Choice and Women’s Time Use
December 2002
Eric Isenberg
Washington University
Campus Box 1208, One Brookings Drive
St. Louis, MO 63130
[email protected]
Home schooling has grown rapidly and now comprises over two percent of
school children. I model home schooling choice using household-level data from the
1996 and 1999 National Household Education Survey and, in a separate model,
district-level data from Wisconsin. For families living in metropolitan statistical areas
(MSAs), the likelihood of home schooling for high-income parents increases as
academic school quality decreases; for low-income parents, as the percentage of
school funds spent at the local level decreases. Outside MSAs, home schooling is
popular among evangelical Protestants, although through peer effects or political
influence the elasticity of home schooling demand with respect to the local percentage
of evangelical Protestants decreases globally. Household characteristics are also
important. The likelihood of home schooling increases when a mother’s time budget
is expanded by extra members of the household. The presence of a husband
contributes strongly to the likelihood of home schooling outside MSAs, but inside
MSAs married couples exiting the public school system have a greater tendency to
substitute to private schools. Despite paying a higher implicit tuition, highly educated
women are more likely to home school younger children. Their children tend to return
to school in later grades.
The Occasional Paper Series produced by the National Center for
the Study of Privatization in Education promotes dialogue about
the many facets of privatization in education. The subject matter
of the papers is diverse, including research reviews and original
research on vouchers, charter schools, home schooling, and
educational management organizations. The papers are grounded
in a range of disciplinary and methodological approaches. The
views presented in this paper are those of the authors and do not
necessarily represent the official views of the NCSPE.
If you are interested in submitting a paper, please contact:
National Center for the Study of Privatization in Education
Box 181, Teachers College,
525 W. 120th Street,
New York NY 10027-6696
www.ncspe.org
email: [email protected]
1
1. Introduction
Since the mid-1980s, the number of home schooled children has increased
steadily and rapidly but research on home schooling has remained scarce. In Florida
and Wisconsin, states with time series data on home schooling, the rate of increase
has been remarkable. The net number of home schooled children grew at an average
annual rate of 12% in Wisconsin and 15% in Florida from 1990-91 to 2000-01
(Figures 1.1 and 1.2). By a conservative estimate, 2.1% of school children, or
1,040,000 children, were home schooled nationally during the 2001-02 school year,
1.8 times the number in charter schools.1 Though charter schools have attracted more
media attention and public policy debate, home schooling is the means by which far
more children are educated. In addition, understanding home schooling bridges a gap
in our understanding of women’s time use and the investment of parental time to
children’s education. As will be shown, approximately 1 in 43 mothers are home
teachers. If the average time investment in home teaching is 30 hours/week and the
average time investment of non-home teaching mothers in their school children is 5
hours/week, then home schooling accounts for fully one eighth of the total amount of
mother’s time investment in their school children, a substantial investment about
which we know little. Due to the momentum and size of home schooling, it is
incumbent upon economists and policy makers to better understand who chooses to
home school, especially as states experiment with market-based school reforms.
1
The number of children in charter schools in 2000-01 is 580,000, according to the Center for
Education Reform (www.edreform.com/press/2002/ncsd0102.htm accessed 10/01/02). This figure
includes some home schoolers. The two states with the largest number of charter schools, Arizona and
California, vaulted to the top of the list by allowing home schoolers to convert their home schools to
charter schools and collect public funds to maintain them (Finn, Vanourek, and Manno 2000).
Because most states do not keep records of homes schooling, a precise estimate of the number of
home schooled children is difficult. The National Center for Education Statistics uses the 1999
National Household Education Survey to calculate a point estimate of 1.7% of students in spring 1999
(Bielick, Chandler, and Broughman 2001). This estimate is too low, however. NCES bases their
estimate on data from a secondary interview that focused on one or two children per household, rather
than on all children in a household. In other words, NHES is not making use of data in a context in
which the number of observations is low. By using all the data, I estimate that 1.96% of children are
home schooled, rather than 1.7%. Multiplying by a conservative estimated annual rate of increase of
3% gives an estimate of 2.1% home schooled out of the total population of children.
2
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 20 20
84- 85- 86- 87- 88- 89- 90- 91- 92- 93- 94- 95- 96- 97- 98- 99- 00- 01-
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02
Figure 1.1: Percent School children Home Schooled in Wisconsin, Grades 1-12,
1984-95 to 2001-02
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01
Figure 1.2: Number of Families & Students (ages 5-18) Home Schooled Registered
with Florida Superintendents, 1989-90 to 2000-01
In spite of its growth, little is known about which families home school or
about the effects of state education policies and household characteristics on home
schooling. Sociologists have offered case studies of home schooling families, and a
few sociologists (e.g. Bauman 2001) and economists (Houston and Toma 2001,
Belfield 2002) have used data to address this question. Descriptive statistics and
descriptive regressions have characterized the probability that a child is home
3
schooled, but no one has previously considered home schooling at the household level
nor modeled the effect of school quality and state policy on home schooling. I do so
with household-level data from the 1996 and 1999 National Household Education
Survey (NHES) and district-level data from Wisconsin.
I outline an explicit household-level utility maximization model for home
schooling. By so doing, I focus the analysis on benefits and costs. Parents considering
the benefits of home schooling weigh the use of a child’s time in school to time spent
learning at home. To understand how public and private school characteristics affect
the likelihood of home schooling, it is possible to extend the burgeoning literature in
public economics on the choice of private schooling (Hamilton and Macauley 1991,
Lankford and Wyckoff 1992, Couch, Shughart, and Williams 1993, Lankford, Lee,
and Wyckoff 1995, Downes and Greenstein 1996, Downes and Schoeman 1998).
Equally important to the trade-offs facing home schooling are those affecting home
teaching: the decision by a parent—almost always the mother—to allocate time to
home schooling and/or among labor market work, household work, and pure leisure.
This research extends the literature on the labor supply of women, particularly
research on women with preschool children (Leibowitz 1974, Leibowitz, Klerman,
and Waite 1992, Leibowitz and Klerman 1995, Hoynes 1996, summary by Blundell
and MaCurdy 1999).
Several hypotheses purport to explain home schooling, beginning with a
“grand null hypothesis” that no patterns will emerge because each case of home
schooling is driven by idiosyncratic factors of parental preferences and unobserved
child characteristics. On the other hand, assuming that causal effects can be found,
three sets of school hypotheses and three sets of household hypotheses plausibly
explain home schooling. First, home schooling may substitute for poor public school
quality, whether this is academic school quality or negative peer effects from other
children. Second, a narrow set of choices of local public and/or private schools may
compel some parents to home school (cf. Caroline Hoxby 2000, who claims that more
public school choice discourages private schooling). Third, there are political
economy explanations. Home schooling may arise if it is difficult to influence public
school policy, either because districts are too large to accommodate the views of a
dissenting minority, because there are not enough members of the minority group to
have political power in a school district, or because schools are funded and policy
decisions made at the state rather than local level. District consolidation (Kenny and
Schmidt 1994) and redistribution of school finance from the local to the state level are
long-term trends consistent with the long-term growth in home schooling.
Of course, the decision whether to home school depends not only on some
source of dissatisfaction with conventional public and private alternatives but also on
household constraints and the educational impact that a mother has on her children.
There are two types of explanations. First, following results from the labor supply
literature, one expects that income effects on the time or money budget would
increase the likelihood of home schooling, just as they increase the probability of a
mother staying home with preschool children. The presence of older children, a
husband, and other adults predicts an increase in the likelihood of home schooling by
expanding the time budget. Similarly, women with more non-labor income, for
instance government transfers or husband’s earned income, may be more likely to
home school as income increases initially. The effect of income on home schooling
may bend backward, however, due to the market alternative of “purchasing” higher
school quality through Tiebout sorting or paying private school tuition at higher
incomes. Second, through substitution effects, the mother’s education may affect the
4
likelihood that she is a home teacher, but in this case a priori reasoning produces
ambiguous results (Leibowitz 1974). More highly educated mothers incur greater
opportunity costs, but these may be counterbalanced by a greater educational impact
on her children (Datcher-Loury 1988). Which of these two substitution effects
dominates can only be determined empirically.
In brief, I find support for the school quality hypothesis for both academic
quality and peer effects. Similarly, two versions of the political economy explanation
hold: as states finance education more at the state level, home schooling increases.
Also, when there are many evangelical Protestants in a rural school district, the
overall level of home schooling declines, possibly due to political influence in public
schools. I reject the school choice hypothesis among families living within
metropolitan areas and within non-metropolitan areas, but find evidence that a lack of
private schools in non-metropolitan areas is partly responsible for the higher
likelihood of home schooling in those areas. Among the household hypotheses,
increases in the time budget increase the likelihood of home schooling; increases in
the money budget appear to have a backward-bending effect, as wealthier families
substitute away from home schooling to private schooling. Generally, more educated
mothers are more likely to home school younger children. Older children tend to
return to school, where they can take advantage of specialized teachers. The strength
of these factors varies markedly between subgroups of families. For instance, urban
families base the decision to home school on different criteria than rural families;
similarly high-income families differ from low-income families.
2. Home Schooling Background
2.1. History and Qualitative Evidence
“Home schooling” was the dominant means of education before the common
school movement of the nineteenth century, but modern home schoolers have little
connection with their nineteenth century predecessors. After the public school system
became entrenched in the late nineteenth century, home schooling became a little used
alternative. By the mid-twentieth century, it was limited to families living in remote
areas of Alaska, a few religious groups (Mormons, Seventh-Day Adventists, and
Amish), and itinerant families, such as military and missionary families, in which
mothers taught children while their fathers shuttled from place to place (Lines 1991).
Beginning in the 1970s, the modern home schooling movement had a dual impetus,
one group “fervently religious and . . . the rest might best be characterized as the
philosophical heirs of Jean-Jacques Rousseau” (Guterson 1992). Jane Van Galen, a
sociologist, distinguishes between these groups (1991), writing that the essential
motive for “fervently religious” fundamentalist Protestants (frequently Baptists or
Pentecostals) is their belief that local public and even private schools teach a
curriculum objectionable to their religion.2 For others, home schooling is a way to
provide a superior education. Sociologist Mitchell Stevens similarly contrasts
religious and secular groups, based on field work (2001). Among popular home
schooling magazines, newsletters, web sites, and support groups, the split between
2
The Home School Legal Defense Association (HSLDA) is a powerful national lobbying and legal
assistance organization representing the interests of religious home schoolers. It was founded by former
Moral Majority leader Michael Farris and has ties to national Republican Party politics. A catalog of
complaints about public schools, such as sex education and the teaching of evolution, are posted on the
HSLDA web site (www.hslda.org).
5
two culturally distinct groups is evident. The work of Van Galen, Stevens, and others
is largely descriptive, but is useful in that it indicates the potential importance of
unobserved heterogeneity in home schooling. The practical consequence is the
necessity of examining not only complete data sets, but also subsets separated by
exogenous characteristics.3
During the 1980s, secular and religious home schoolers worked as allies to
establish legal rights to home schooling within state educational laws. Either by
favorable state judicial decisions or statutes, home schooling rights became
established in every state, but each state regulates home schooling differently
(Richardson and Zirkel 1991). In general, states impose minimal regulation on home
schoolers, allowing them broad authority to define their approach and curriculum. At
the same time, state laws restrict the data that can be collected on home schoolers. By
the early 1990s, home schooling rights were well-established, the number of home
schooled children continued to grow, and the alliance between secular and religious
home schoolers began to fracture (Stevens 2001).
Several home school leaders claim that many parents began to home school
across the country in the aftermath the massacre at Columbine High School in 1999
(e.g. Krumbine 2001; cf. Hetzel 1997, who suggests a link between school violence
and home schooling). The extent of the impact of perceived school violence on home
schooling is unknown. Others have suggested that parents home school because
children have been expelled from school (M. Hancock 2002), have special education
needs (Carothers 2001), have exceptional talent in one area (e.g. music), or have
recently moved. The 1996 and 1999 NHES include survey data on why parents have
chosen to home school. There are a wide range of stated reasons. The motives of
home schoolers taken together have probably become increasingly varied over time,
and are to some extent overlapping (Nemer 2002).
Individual home schooling families are not isolated cells. Home schooling
support groups have proliferated. In such states as Florida, California, and Maryland,
state law authorizes “umbrella schools” that collect tuition from home schooling
families in exchange for record-keeping services, access to textbook discounts, and/or
book and video libraries (S. Hancock 2002). In Florida, home schoolers have
organized themselves into a statewide organization with an elected chairperson and
twelve elected regional officers. Anecdotal evidence indicates a shift from an
antagonistic to a cooperative relationship between home schoolers and some public
and private schools. Some home schooled students enroll in courses or extracurricular
activities at school. In the 1999 NHES, 19% of home schooling respondents indicated
that they home schooled part-time and sent their children to school part-time.
Although there is little data on how the burden of home teaching is distributed among
mothers, fathers, older children, other relatives, and tutors, the existing evidence
singles out the mother as the dominant home teacher. My interviews with home
schooling leaders (Dickinson 2001, Krumbine 2001, Daniels 2002, M. Hancock 2002,
S. Hancock 2002), a regional survey (Bliss 1989), qualitative evidence (Stevens
2001), survey data on work hours, and anecdotal evidence confirm this.
In sum, the qualitative evidence shows that unobserved parental preferences are likely
to be important determinants of home schooling, and that consequently we should
examine subsets of the data. Given the high opportunity costs of home schooling,
home schoolers will have strong preferences for school quality, but some home
3
Compare economist Martin Carnoy, commenting on school choice in developing countries: “Powerful
locational and cultural variables may be more influential than either school or income variables in
determining school attendance and sele ction choices” (1995).
6
schoolers emphasize an academic component of school quality—the effect of a school
on their child’s literacy and numeracy—and others emphasize a curricular component,
for example whether evolution is taught. There may also be a role for unobserved
child characteristics, but these will not necessarily undermine econometric testing.
Cross-state variation in regulation ought to be examined. Finally, a reasonable
simplifying assumption is that mothers are the actual or potential home teachers of
their children.
2.2 Descriptive Statistics
Because relatively little is known about which families home school, I present
an overview of the household data before proceeding to form and test hypotheses. An
initial look at sample means and cross-tabulations of key variables uncovers notable
patterns.
For instance, it is not true that if parents home school one child in a household,
they will necessarily home school the rest, nor is this true of private schooling. See
Tables 2.1a-b and 2.2. Simply summing the data from the 1996 and 1999 NHES
shows that in home schooling households with more than one schoolchild, at least one
other child was sent to a school in 220 of 398 cases (55%). For households with three
or more children, the distribution of children home schooled or private schooled is
bimodal, with peaks at one child and all children. In addition, taking advantage of a
set of questions on home schooling history in the 1996 NHES, we see that much home
schooling lasts less than four years (Figure 2.1a-f). Psychologist Walter Schumm
(1994), in a small-scale study of home schooling in western Kansas, recognized that
families mix home schooling with conventional schooling. Other than his study, these
data are the first to describe within-household home schooling patterns and the
duration of home schooling.
Table 2.3 shows sample data on women’s labor force participation from
NHES 1996 and 1999. Home teaching mothers are much more likely not to work at
all than non-home schooling mothers: 46% of home teaching mothers do not work in
the 1996 data compared to 20% of non-home schooling mothers, and figures are
comparable for 1996. It is notable, however, that a majority of home teaching mothers
work at least one month a year, and about a third work 10-12 months a year. On
average, home teaching mothers who also work do so for fewer hours per week than
non-home teachers. Home schooling households are only slightly more likely than
average to be headed by two parents: 18% (1996) or 19% (1999) of home schooling
households in the sample are headed by a single mother compared to 23% (1996) or
26% (1999) of non-home schooling households. This does not include cohabitating
couples. There are two other notable facts about home schooling households (not
shown in Table 2.3). First, home schooling does not seem to affect father’s labor force
participation, either in the decision to work or in the number of hours. Second, almost
all home schooled children are the own children of the mother, i.e. the birth, adopted,
step, or foster children, but almost never a niece, nephew, or nonrelative.
7
Figure 2.1a-f: Distribution of Years Home Schooled by Grade Equivalent
and Current Home School Status (1996 NHES)
(Ntotal = 501; Unweighted)
Elementary School Students
Elementary School Students
Currently Home Schooled Formerly Home Schooled
40 60
50
30
40
20 30
Frequency
20
Frequency
10
10
0 0
1 2 3 4 5 1 2 3 4
Years Home Schooled Years Home Schooled
2.1a N = 84 2.1b N = 72
Middle School Students
Middle School Students
Currently Home Schooled Formerly Home Schooled
30 60
50
20 40
30
10 20
Frequency
Frequency
10
0 0
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6
Years Home Schooled
Years Home Schooled
2.1c N = 84 2.1d N = 96
High School Students
High School Students Formerly Home Schooled
Currently Home Schooled
30 70
60
50
20
40
30
10
Frequency
Frequency
20
10
0 0
1 2 3 4 5 6 7 10 11 12 13 1 2 3 4 5 6
Years Home Schooled Years Home Schooled
2.1d N = 76 2.1f N = 89
Table 2.4 summarizes a weighted average of some key child characteristics
using all of the children enumerated in the NHES 1996 Household Data. It shows that
on average children are more likely to be home schooled when they are a) in
elementary school (ages 5-9, corresponding to grades K-4) or high school (ages 14-
17, corresponding to grades 9-12); b) white, and c) non-Hispanic. The evidence on
age must be interpreted cautiously, however, because the number of high school
dropouts does not appear in the denominator.
Considering the survey questions on public school participation from the 1999
NHES, the within-household statistics of Table 2.1, the duration statistics in Figure
2.1a-f, and the labor force participation results of Table 2.3, it is clear that in general
8
home schooling families are not withdrawn from society. They may participate in the
public or private school system by sharing educational responsibilities with a school,
by sending other children to school while home schooling one child, or by sending
children to school in a later grade. Mothers may work in the labor market part-time or
part-year and home teach as well.
3. Home Schooling as School Choice and Women’s Time
Use
3.1. Literature Review
Before the NHES data became available, non-economists pursued research on
home schooling choice by collecting their own data (Thompson 1994, Ray 1997,
Hetzel 1997). Due to small sample sizes and selection issues in the data-gathering
process, it has been difficult to establish causal effects. Both sociologists (e.g.,
Bauman 2001) and an economist (Belfield 2002) have modeled home schooling
choice based on the 1996 or 1999 NHES. The results are intended as descriptive
regressions, and are useful on that basis, similar to the descriptive statistics of Tables
2.3 and 2.4. A general problem with previous literature using NHES surveys,
however, has been that they have focused on NHES data collected on a focal child in
a secondary interview that took place after a screener interview identified the home
schooling status of all children in the family. See Appendix Two for details. Parent
and family characteristics are less accurate when statistics describe a focal child,
because if a sibling of a non-home schooled child is home schooled, those families
will be improperly classified as non-home schooling. This sampling scheme also
overrepresents families who home school all their children.
Another approach has been to use district-level state data, similar to the
approach taken in Section 5 on Wisconsin. As described in Section 5 and shown in
Appendix One, aggregate data do not allow for the identification of household effects.
An economics dissertation (Houston 1999) and subsequent working paper (Houston
and Toma 2001) model home schooling choice for Kentucky and a group of ten
states, using aggregate data for school years 1991-92 to 1995-96. Houston and Toma
find that greater heterogeneity of income within a school district is associated with an
increase in home schooling relative to public schooling. They interpret the result to
mean that a greater heterogeneity of tastes leads to greater difficulty for the public
schools to satisfy all families.
Apart from these few papers on home schooling itself, there has been
provocative work in economics on the joint production of children’s human capital by
parents and schools. Carnoy (1995) applies Hirschman’s (1970) analysis of “exit” and
“voice” to a model of joint production. Beginning with a backward bending labor
supply curve, Carnoy proposes that parents who earn wages in an intermediate range
will be the most constrained for time and therefore least able to spend time investing
in their children’s education. He further suggests that, controlling for wages, couples
and better educated parents will have greater ability to effect child quality through
time investments. Overall, Carnoy concludes that better educated and higher income
parents will have more ability to exercise both exit (investing in child quality by
purchasing more school quality) and voice (investing in child quality through direct
time investments). Note that with these definitions of exit and voice, home schooling
is not an exit strategy but a voice strategy, although one pursued by direct time
9
investments in children, rather than by political involvement in the local public
school.
Houtenville and Conway (2001) investigate the empirical relationship between
school quality and parents’ time investment without extending their analysis to home
schooling. Nevertheless, their results are instructive. They find that, all else equal,
there is an inverse relationship between the quality of the school a child attends and
the parents’ time investment in their children’s education. This result is especially
interesting in light of Carnoy’s model, as it suggests that in practice even parents with
greater latitude for both exit and voice tend to substitute one for the other. Extending
this argument suggests that families will home school if their children would
otherwise attend schools of poor quality.
3.2. Modeling Home Schooling Choice
Families are assumed to maximize a household utility function
uik = u z , tif , f ( Qi )  . Family i in local area k receive utility from composite private

 i

l


l
good z, children’s quality Q, and mother’s pure leisure time tif . There are income,
time, and school attendance constraints, as well as a child quality production function.
Families choose a school district in which to live and a school type (public, private,
home) for each child; mothers decide how many hours to work.
Details of the model are given in Appendix One. It is sufficient here to note
three key simplifying assumptions. First, only the mother’s time use decision is
modeled. Fathers, if present, are assumed to work year-round; their choice of hours is
not affected by their wives’ labor force participation or children’s schooling (cf. Hill
1989). Empirical distributions of weekly hours worked for fathers with children in
school and with home schooled children show no significant differences. I thereby
lump non-labor income and husband’s earnings into a single composite called
“exogenous income.”
Second, a primary job ties a household to local area k, but the household is
free to choose a community within that region and therefore may sort among local
public school districts (Tiebout 1956; cf. Nechyba and Strauss 1998, Brasington 2000,
Hoxby 2000). This is a key identifying assumption. Consequently, the most local
neighborhood variables, such as demographic variables based on zip codes, are
endogenous. Local variables at the level of metropolitan statistical area and state
variables are exogenous.
Third, there is no compensating differential for home teaching: the utility
function is written as u  zi , tif , f ( Qi )  , not u  zi , tif , tif , f ( Qi )  , where tif is the time


l




l HS


HS
the mother spends home schooling her child(ren). This opens the model to Pollak and
Wachter’s general critique of household production models (1975). In producing
household “commodities” from a technology of a time input and basic market
“goods,” there is joint production of both the commodity and the value of the
experience of producing the commodity, i.e. the compensating differential. As the
theoretical model is specified, the compensating differential for home schooling is
absorbed by the error term of the econometric model. If the compensating differential
varies over mothers, there is an omitted variable problem because a mother’s attitude
to home schooling is presumably an important part of the decision. To compound the
problem, it is not known whether the attitude variable is orthogonal to other
regressors, such as mother’s education. One can construct plausible stories to explain
10
why, for instance, a mother who is a college dropout might have preferences that
would predispose her to home schooling, apart from the cost/benefit calculations that
underlie the utility maximization approach, i.e. an “attitude” factor that is correlated
with both mother’s education and the likelihood of home schooling. Empirically, by
dividing the data set, omitted variable bias will be reduced since the attitudes of
people in each subsample will be more similar to each other.
3.3 Estimation
With this household maximization model in mind, we would like to know the
conditional probability that a child is home schooled in order to test hypotheses on the
causes of home schooling. With a very large data set, it might be possible to partition
families by the number of school children, and proceed to estimate integer count
models or multivariate probit models separately for families with one child, two
children, and so on. Because families with home schooled children compose a small
fraction of a representative cross-section, this option is not available. Instead, I pool
households with different numbers of children and estimate a discrete choice model
for the probability that at least one child is home schooled, or, equivalently, the
probability that a mother is a home teacher.
The model assumes three endogenous behavioral choices—school choice,
women’s labor supply, and residential choice. A natural estimation strategy might
seem to be a system of equations or a home schooling equation with instruments for
women’s work hours and public school quality. This model is unworkable, however,
because home schooling is modeled by a discrete choice equation, and the structural
equations for the endogenous variables depend on the realized outcome of home
schooling, not on the propensity to home school. For a discussion of the technical
details of this problem, see Maddala (1983).
This leaves a reduced form discrete choice model. One might specify a nested
logit specification that models the joint outcome of women’s labor force participation
and home schooling, based on a two-stage budge


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