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Appendix B: The Multivariate Models
In this Appendix, we provide additional detail on the multivariate models. In the sections that follow, we describe the causal structure of the models, discuss issues of estimation, and present the full logistic models cited in Chapter Five along with some alternative versions.
Causal Structure of the Models
Our analysis of child care modal choice is conditional on families’ previous choice to use non-parental care. In reality, these decisions (and others) may be made jointly and simultaneously. For example, a family may see its options as (a) the mother working while the child’s grandmother cares for the child or (b) the mother staying home with the child. In this case the mother’s decision to work is interlocked with her child care arrangement. Given the structure of this study, however—that our analysis sample comprises families using non-parental care while the mother works—we must make the simplifying assumption that the decision to use non-parental care is causally prior to the choice of mode.
Two other issues of endogeneity, or direction of causality, also need to be addressed. Ideally we would like to explain families’ child care modal choices in terms of predetermined characteristics such as demographics, household composition, and preferences and attitudes. (The notion that household composition is predetermined, while not invariably valid, does not seem to be seriously troubling. It is, of course, conceivable that a relative would move in for the express purpose of providing child care.) Our data on parental preferences comes from the following items:
Why did you choose (ARRANGEMENT) instead of another kind of arrangement for (CHILD)? What was the most important reason? (RECORD VERBATIM) What other things were important for you?
Our information may therefore be limited to the positive features of the modes actually chosen. For example, a parent might prefer to use a family member, but none is available, so the child is cared for by an unrelated adult in a family child care home. In choosing that provider, the preference for a family member is not expressed. Another limitation of these items is that they are asked after the fact. Families may adjust their views of what is important based on what they experience.
In mild defense of these items, it may be said that the second part of the question (“What other things were important for you?”) is sufficiently ambiguous that it could elicit responses that were not descriptive of the current provider. Furthermore, we have grouped survey responses into sufficiently broad categories that any of the five modes could in principle provide almost every feature. For example, the category “commonalities with provider” includes such responses as:
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has same values
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like a family member/close relative
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relationship to parents
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same language/ethnicity
This constellation of features would be most salient for care by a relative. Nonetheless, a Hispanic family might choose a center because it has Spanish-speaking staff.
In any event, we feel that these items, though imperfect, are potentially too interesting to ignore. We have therefore conducted all analyses both including and excluding them.
The final issue of endogeneity has to do with the complex relationship between child care arrangements and subsidies. Consider the following scenarios:
(1) Receipt of subsidy determines mode of care
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A family would like its child to have the educational advantages of center care, and applies for a subsidy so that it can afford this mode of care. If the family receives the subsidy, the child enrolls in the center. If not, the child is cared for by his grandmother. In this case receipt of subsidy determines mode.
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A family using relative care applies for and receives a subsidy. When the child turns 2 they enroll the child in a center. If they had not been subsidized they would not have made the switch. In this case, even though the subsidy award did not affect the initial mode of care, its continued receipt determined the subsequent mode.
(2) Mode of care determines receipt of subsidy
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A family applies for and is accepted by a center. The director remarks that they may be eligible for a subsidy, which they then apply for and obtain. Had they used relative care, they would not have learned about the subsidy. In this case, mode of care determines receipt of subsidy.
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A family that uses family child care for its preschooler applies for and receives a subsidy. When the child enters school, the family switches to relative care, and declines to reapply for a subsidy. In this case, change of mode affected continued receipt.
(3) Mode of care and subsidy are determined jointly
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A family on TANF is given a child care subsidy and encouraged by a caseworker to use center care. In this case as well, receipt of subsidy and child care arrangements are jointly determined.
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Some states have contracts with child care centers. A family may only be able to get the subsidy on condition of being at one of those particular centers—another instance of joint determination.40
(4) Mode of care and receipt of subsidy are unrelated
- A family is using family child care, and it hears about subsidies through friends. The two facts are causally unrelated.
To sort out these paths of causation, it is helpful to distinguish between preferred and actual mode of care, and also between application and receipt of subsidy. We may say that:
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Family demographics and parental attitudes towards child care determine preferred mode of care.
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Subsidy receipt or nonreceipt may combine with preferred mode of care to determine actual mode of care. Alternatively, preferences may be so firm that subsidy receipt has practically no effect on the decision; it is simply treated as “found money”.
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Demographics and preferred mode of care determine subsidy application. (For example, if the preferred mode is “relative care” and the value of the subsidy is low, as well as the price of such care, it may be considered not worth the trouble to apply for a subsidy.)
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Actual mode of care may also influence subsidy application (as in the case where a licensed provider encourages a family to apply, or an unlicensed provider refuses to accept subsidy payments).
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In some situations, actual mode of care may further determine subsidy receipt. Whether an eligible applicant is approved should, in principle, be unaffected by the chosen arrangement, as long as it is legal. But agencies may make it difficult for applicants to obtain subsidies if they are using in-home care, because of concerns about fair labor law practices and other issues. In order to protect children in otherwise unregulated family child care and relative care, the agency may impose different requirements on these caregivers that may create additional barriers. They may also make different, and more cumbersome, arrangements for reimbursing caregivers.
- Finally, actual mode of care may also determine current subsidy receipt because a family that has applied and receive a subsidy may decline to reapply if it switches to a less expensive mode.
The multivariate models attempt to sort out these alternative paths of causation.
Issues of Estimation
Because child care modal choice is multidimensional, an ordered framework is helpful. That is, rather than consider how each characteristic affects the relative probability of a family choosing each of five modes, we may consider a series of binary choices. This simplification greatly eases interpretation of the results.
The most natural way to formulate modal choice appears to be as follows. First, does the family use relative care? This decision is likely to be influenced by such considerations as ethnicity, the presence of adult relatives in the household or living nearby, and the regularity of the mother’s work schedule. We do not attempt to model the distinction between relative care in the child’s home and the relative’s home. The chosen locale for relative care is somewhat arbitrary and variable, and not strongly related to family characteristics.
For families that do not use relative care, we then ask whether they fall in the relatively small group using in-home care provided by an unrelated adult. This highly flexible choice is likely to be influenced by ethnicity, the presence of an unrelated adult in the household, and the regularity and hours of the mother’s work schedule.
Finally, for families that use neither relative care nor in-home care by an unrelated adult, we examine the choice between non-relative family child care and center care. Again, this distinction is liable to depend on ethnicity and the regularity and hours of the mother’s work schedule.
In addition to the types of factors just mentioned, other family characteristics (education, income, age of child) are certainly expected play a role, as well as the questionable measures of parents’ child care values—and possibly receipt of subsidy. Differences are also seen among regions of the country. For example, regulations are less restrictive in the South, making it easier for center care to enter the market in response to demand.
The models of subsidy application and current subsidy receipt are restricted to families that are apparently eligible for subsidies, given their states’ eligibility criteria and their income as reported on the survey. (This constraint only eliminates about 200 observations.) We considered estimating separate models of subsidy receipt for recent TANF recipients and other families, because of the special priority given to the former group. Ultimately, however, we decided to keep the two groups together, but to allow TANF receipt to interact with mode of care. As shown in Chapter Five, while recent TANF receipt is a very powerful predictor of subsidy application and receipt, TANF recipients are by no means certain to receive a subsidy.
An important distinction between the modal choice and subsidy models is that modal choice pertains to a specific child—the focus child—while subsidy application and receipt pertain to the entire family.
Information on child care arrangements is only available for the focus child.41 We therefore explain subsidy application and current receipt in terms of the parental considerations and mode of care used for one particular child, which may not be the entire picture. For example, we would not know if a younger sibling is in center care given that the focus child is cared for by a relative after school. We have included additional family descriptors in the subsidy models, in particular the age of the youngest child. This latter variable will presumably explain subsidy status better than the age of the focus child.
Missing data were not a huge problem, although there was some tendency for respondents to drop out before the end of the survey (affecting primarily the income questions and whether relatives lived nearby). We took the following empirical approach.
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For variables which were missing in only a handful of cases (e.g. fewer than 5), we imputed the modal value. For example, those few families that did not report mother’s education were assigned to the “high school graduate” category.
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Because we already had a “miscellaneous” category for ethnicity—comprising non-Hispanic families that were reportedly American Indian/Alaska native, Asian, Native Hawaiian or other Pacific Islander, or “other”, as well as non-Hispanic families that reported multiple ethnicities such as both “black” and “white”—we assigned the dozen or so cases with no reported ethnicity to this catchall group.
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For variables that were missing in substantial numbers of cases (a few hundred), we zeroed out the missings and included “missing data” indicators. Thus, “income as percent of poverty” was supplemented with a “missing income” indicator.
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For variables that were ever used as dependent variables (mode of care, application for and receipt of subsidy), missings were left missing, and the affected observations were dropped from the relevant analyses.
The models presented here include all theoretically relevant variables, regardless of statistical significance. Although we may ultimately want to delete some variables for parsimony, we feel that their inclusion for now does no practical harm. Furthermore, in many cases (such as the effect of household income), the absence of statistical significance represents important information—“the dog that didn’t bark in the night”.
Multiple versions of each model are presented side by side, to show the effects of including variables which—depending on the direction of causation—may or may not belong in the model. For the models of modal choice, these variables are the indicator of subsidy receipt and the parental consideration indicators. For the models of subsidy receipt and application, these variables are the indicators of chosen mode of care.
Software is available (STATA 7) for estimating the three dichotomous mode of care models simultaneously. For this draft we have presented the more transparent binary logistic models only.
Results: Logistic Coefficients and Marginal Impacts
The estimated logistic models are presented in Exhibits B.1-B.5 below. Calculation of percentage point impacts in nonlinear models like these is somewhat arbitrary, because impacts vary across the sample. The marginal impact estimates shown in Chapter Five were derived by calculating the change in likelihood associated with a one unit change in each variable for a representative family. This family was chosen to have the following characteristics, corresponding in general to the regression “reference categories”:
- ethnicity: white
- mother’s education: high school graduate
- nativity: United States
- age of focus child: preschool
- number of children: one
- household composition: no spouse or partner present, no other related adults, no other unrelated adults
- no relatives living nearby
- working regular hours
- income: 100% FPL
- not recent TANF recipient
- region: Northeast
- no subsidy
- mode of care: non-relative family child care
Choice of a particular set of values for family characteristics has the advantage of making the percentage point impacts comparable across the models but the disadvantage of underestimating the impacts relative the their value at the sample mean. The significance levels shown in the exhibits in Chapter Five appertain to the logistic coefficients themselves. A variable could have significant effect in the model, but not for a family with particular characteristics, if that family was far from the sample mean.
| Model (1) | Model (2) | Model (3) | ||
|---|---|---|---|---|
| Ethnicity (reference category: White) | Black | 0.11 | 0.21 * | 0.23 * |
| Hispanic | 0.23 * | 0.27 * | 0.28 * | |
| Other | 0.18 | 0.39 ** | 0.49 *** | |
| Mother’s education (reference category: high school graduate) | Not a high school graduate | 0.10 | 0.05 | -0.01 |
| Some college | -0.23 ** | -0.21 ** | -0.11 | |
| Mother’s country of birth (reference category: United States) | Other | -0.25 * | -0.33 ** | -0.54 *** |
| Age of focus child (reference category: preschooler) | Infant | 0.54 *** | 0.59 *** | 0.25 |
| Toddler | 0.28 * | 0.30 ** | 0.12 | |
| School-aged | 0.72 *** | 0.61 *** | 0.41 *** | |
| Number of children in household | 0.01 | 0.06 | 0.02 | |
| Mother's spouse/partner in household | 0.16 | 0.00 | 0.05 | |
| Other adult relatives in household | Child's grandparent(s), greatgrandparent(s) | 0.99 *** | 1.01 *** | 0.91 *** |
| Child's aunt(s), uncle(s) | 0.31 * | 0.22 | 0.45 ** | |
| Other relatives | 0.17 | 0.15 | 0.19 | |
| Unrelated adults in household | -0.58 *** | -0.66 *** | -0.73 *** | |
| Relatives living nearby | 0.79 *** | 0.80 *** | 0.79 *** | |
| Mother’s work schedule (reference category: regular hours) | Irregular hours | 0.41 *** | 0.35 *** | 0.35 *** |
| In school or training | 0.61 *** | 0.51 *** | 0.40 *** | |
| Household income as a percent of FPL | -0.05 | -0.08 | -0.09 | |
| Recent TANF receipt | -0.03 | 0.27 * | 0.35 ** | |
| Currently receive child care subsidy | -1.33 *** | -1.10 *** | ||
| Parents’ considerations in choosing child care | Cost | 0.59 *** | ||
| Convenience | -0.41 *** | |||
| Safety | 0.06 | |||
| Provider warmth | -0.42 *** | |||
| Child's cognitive development | -1.47 *** | |||
| Commonalities with provider | 1.44 *** | |||
| Region (reference category: Northeast) | South | -0.18 | -0.17 | -0.15 |
| Midwest | -0.13 | -0.05 | -0.08 | |
| West | 0.15 | 0.16 | 0.09 | |
| Constant | -1.49 *** | -1.26 *** | -1.18 *** | |
| Sample Size | 2337 | 2325 | 2325 | |
| Pseudo R-squared | 0.08 | 0.11 | 0.24 | |
| *** = p<.001, ** = p<.01, * = p<.05 |
| Model (1) | Model (2) | Model (3) | ||
|---|---|---|---|---|
| Ethnicity (reference category: White) | Black | -0.41 | -0.34 | -0.35 |
| Hispanic | -0.42 | -0.39 | -0.42 | |
| Other | -0.42 | -0.26 | -0.23 | |
| Mother’s education (reference category: high school graduate) | Not a high school graduate | 0.42 * | 0.39 | 0.37 |
| Some college | -0.30 | -0.27 | -0.27 | |
| Mother’s country of birth (reference category: United States) | Other | 0.35 | 0.32 | 0.26 |
| Age of focus child (reference category: preschooler) | Infant | 1.55 *** | 1.67 *** | 1.44 *** |
| Toddler | 0.66 * | 0.77 ** | 0.66 * | |
| School-aged | 1.39 *** | 1.44 *** | 1.33 *** | |
| Number of children in household | 0.22 *** | 0.24 *** | 0.21 ** | |
| Mother's spouse/partner in household | 0.04 | -0.03 | 0.01 | |
| Unrelated adults in household | 0.55 * | 0.52 * | 0.41 | |
| Mother’s work schedule (reference category: regular hours) | Irregular hours | 0.83 *** | 0.84 *** | 0.88 *** |
| In school or training | 0.92 *** | 0.91 *** | 0.82 *** | |
| Household income as a percent of FPL | 0.15 | 0.14 | 0.13 | |
| Recent TANF receipt | -0.18 | -0.02 | 0.07 | |
| Currently receive child care subsidy | -0.58 ** | -0.37 | ||
| Parents’ considerations in choosing child care | Cost | 0.77 *** | ||
| Convenience | -0.20 | |||
| Safety | -0.01 | |||
| Provider warmth | -0.25 | |||
| Child's cognitive development | -1.39 *** | |||
| Commonalities with provider | 0.80 *** | |||
| Region (reference category: Northeast) | South | -1.09 *** | -1.09 *** | -1.11 *** |
| Midwest | -0.67 ** | -0.69 *** | -0.72 *** | |
| West | -0.83 *** | -0.84 *** | -0.93 *** | |
| Constant | -3.49 *** | -3.48 *** | -3.31 *** | |
| Sample Size | 1234 | 1226 | 1226 | |
| Pseudo R-squared | 0.10 | 0.10 | 0.17 | |
| *** = p<.001, ** = p<.01, * = p<.05 |
| Model (1) | Model (2) | Model (3) | ||
|---|---|---|---|---|
| Ethnicity (reference category: White) | Black | -0.13 | -0.05 | -0.10 |
| Hispanic | 0.24 | 0.33 | 0.37 | |
| Other | -0.39 | -0.25 | -0.18 | |
| Mother’s education (reference category: high school graduate) | Not a high school graduate | 0.23 | 0.11 | 0.00 |
| Some college | -0.21 | -0.21 | -0.31 ** | |
| Mother’s country of birth (reference category: United States) | Other | 0.93 *** | 0.84 *** | 0.74 *** |
| Age of focus child (reference category: preschooler) | Infant | 1.04 *** | 1.09 *** | 0.94 *** |
| Toddler | 0.65 *** | 0.71 *** | 0.61 *** | |
| School-aged | 0.76 *** | 0.69 *** | 0.57 *** | |
| Number of children in household | 0.06 | 0.11 | 0.09 | |
| Mother's spouse/partner in household | 0.33 ** | 0.17 | 0.12 | |
| Unrelated adults in household | -0.54 ** | -0.63 ** | -0.74 *** | |
| Mother’s work schedule (reference category: regular hours) | Irregular hours | 0.21 | 0.15 | 0.18 |
| In school or training | 0.35 | 0.31 | 0.31 | |
| Household income as a percent of FPL | -0.02 | -0.06 | -0.06 | |
| Recent TANF receipt | -0.24 | 0.07 | 0.14 | |
| Currently receive child care subsidy | -0.90 *** | -0.88 *** | ||
| Parents’ considerations in choosing child care | Cost | 0.50 *** | ||
| Convenience | 0.18 | |||
| Safety | 0.50 *** | |||
| Provider warmth | 0.51 *** | |||
| Child's cognitive development | -0.78 *** | |||
| Commonalities with provider | 0.68 *** | |||
| Region (reference category: Northeast) | South | -1.01 *** | -0.96 *** | -0.90 *** |
| Midwest | -0.15 | -0.04 | 0.02 | |
| West | -0.30 | -0.22 | -0.31 | |
| Constant | -0.68 * | -0.47 | -0.77 * | |
| Sample Size | 1090 | 1083 | 1083 | |
| Pseudo R-squared | 0.11 | 0.13 | 0.18 | |
| *** = p<.001, ** = p<.01, * = p<.05 |
| Model (1) | Model (2) | Model (3) | ||
|---|---|---|---|---|
| Ethnicity (reference category: White) | Black | 0.54 *** | 0.53 *** | 0.54 *** |
| Hispanic | -0.02 | 0.02 | 0.01 | |
| Other | 0.64 *** | 0.65 *** | 0.66 *** | |
| Mother’s education (reference category: high school graduate) | Not a high school graduate | -0.19 | -0.15 | -0.17 |
| Some college | 0.22 * | 0.15 | 0.13 | |
| Mother’s country of birth (reference category: United States) | Other | -0.77 *** | -0.77 *** | -0.76 *** |
| Age of youngest child (reference category: preschooler) | Infant | -0.53 *** | -0.38 ** | -0.36 * |
| Toddler | -0.19 | -0.10 | -0.09 | |
| School-aged | -0.52 *** | -0.36 *** | -0.34 *** | |
| Number of children in household | 0.20 *** | 0.23 *** | 0.23 *** | |
| Mother's spouse/partner in household | -0.84 *** | -0.82 *** | -0.83 *** | |
| Mother works full-time | 0.14 | 0.14 | 0.13 | |
| Household income as a percent of FPL | 0.13 | 0.10 | 0.08 | |
| Recent TANF recipients using: | Relative care | 0.46 ** | 0.72 *** | 0.72 *** |
| In-home non-relative care | 0.21 | 0.69 | 0.65 | |
| Non-relative family child care | 1.85 *** | 1.81 *** | 1.84 *** | |
| Center care | 1.65 *** | 1.01 *** | 1.00 *** | |
| Mode of care (reference category: non-relative family child care) | Relative | -0.28 * | -0.20 | |
| Center | 0.65 *** | 0.66 *** | ||
| In-home non-relative | -0.52 * | -0.44 * | ||
| Parents’ considerations in choosing child care | Cost | -0.07 | ||
| Convenience | 0.29 *** | |||
| Safety | 0.04 | |||
| Provider warmth | 0.27 *** | |||
| Child's cognitive development | 0.24 * | |||
| Commonalities with provider | 0.15 | |||
| Region (reference category: Northeast) | South | 0.26 | 0.13 | 0.17 |
| Midwest | 0.67 *** | 0.62 *** | 0.62 *** | |
| West | 0.34 * | 0.28 | 0.27 | |
| Constant | -0.98 *** | -1.04 *** | -1.40 *** | |
| Sample Size | 1961 | 1951 | 1951 | |
| Pseudo R-squared | 0.13 | 0.15 | 0.15 | |
| *** = p<.001, ** = p<.01, * = p<.05 |
| Model (1) | Model (2) | Model (3) | ||
|---|---|---|---|---|
| Ethnicity (reference category: White) | Black | 0.59 *** | 0.61 *** | 0.56 *** |
| Hispanic | 0.20 | 0.30 | 0.22 | |
| Other | 0.85 *** | 0.90 *** | 0.85 *** | |
| Mother’s education (reference category: high school graduate) | Not a high school graduate | -0.19 | -0.19 | -0.23 |
| Some college | 0.28 * | 0.14 | 0.13 | |
| Mother’s country of birth (reference category: United States) | Other | -0.72 *** | -0.72 *** | -0.69 *** |
| Age of youngest child (reference category: preschooler) | Infant | -0.21 | 0.05 | 0.05 |
| Toddler | 0.25 | 0.41 ** | 0.40 ** | |
| School-aged | -0.64 *** | -0.41 ** | -0.40 ** | |
| Number of children in household | 0.23 *** | 0.27 *** | 0.29 *** | |
| Mother's spouse/partner in household | -1.05 *** | -1.01 *** | -1.04 *** | |
| Mother works full-time | 0.22 | 0.22 | 0.22 | |
| Household income as a percent of FPL | 0.05 | -0.07 | -0.06 | |
| Recent TANF recipients using: | Relative care | 0.26 | 1.02 *** | 0.93 *** |
| In-home non-relative care | 0.62 | 0.52 | 0.33 | |
| Non-relative family child care | 1.43 *** | 1.34 *** | 1.37 *** | |
| Center care | 2.18 *** | 1.27 *** | 1.28 *** | |
| Mode of care (reference category: non-relative family child care) | Relative | -0.85 *** | -0.70 *** | |
| Center | 0.88 *** | 0.84 *** | ||
| In-home non-relative | 0.00 | 0.16 | ||
| Parents’ considerations in choosing child care | Cost | -0.76 *** | ||
| Convenience | 0.42 *** | |||
| Safety | 0.09 | |||
| Provider warmth | 0.33 ** | |||
| Child's cognitive development | 0.22 | |||
| Commonalities with provider | 0.11 | |||
| Region (reference category: Northeast) | South | 0.06 | -0.14 | -0.11 |
| Midwest | 0.54 ** | 0.46 * | 0.44 * | |
| West | 0.10 | 0.04 | 0.00 | |
| Constant | -2.29 *** | -2.26 *** | -2.58 *** | |
| Sample Size | 1957 | 1947 | 1947 | |
| Pseudo R-squared | 0.16 | 0.21 | 0.23 | |
| *** = p<.001, ** = p<.01, * = p<.05 |
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