Child Care Choices in Spain

Abstract

In this paper we examined the determinants of child care choices among families with young children in Spain, by means of a conceptual framework that encompassed need, costs, and availability. Based on data from the Spanish Time Use Survey and Household Budget Survey, our study indicated that, regardless of model specification, the age of the child, the mother’s labor force decisions, and the prices of child care services available were the most important factors that mothers considered when they chose a type of child care. Day care center services substituted for babysitters when the price of babysitters rose; and relative and parent care substituted for day care centers when these services became more expensive. We found no different sensitivity to price changes for working and non-working mothers. From a public policy perspective, child care price subsidies were found to have much stronger effects on child care decisions than child allowances or public provision of school slots.

Appendices

Appendix 1: Statistical Matching

In this section we explain how the statistical matching was performed. Matching involves pairing units, from different datasets, that are similar in terms of their observable characteristics. In this case, the recipient dataset was the Spanish Time Use—TU Survey (INE 2002/2003) and the donor dataset was the Spanish Household Budget—HB Survey (INE 2005), both representative of the Spanish population. These two sets of information share important observable characteristics.

As Dehejia and Wahba (2002) stated, with a small number of characteristics (for example, two binary variables), matching is straightforward (one would group units in four cells). However, when there are many variables, as in the present situation, we need to define a function which measures the similarity between the individuals of the two samples and solves the dimensionality problem. As emphasized by Del Boca et al. (2005), propensity score-matching methods (Rosenbaum and Rubin 1983) provide specific criteria to assign to each individual of the recipient data set a similar individual from the donor dataset. Each pair of individuals created according to this procedure will give origin to an integrated record, with the relevant information from both surveys.

For the present study, two statistical matching processes were performed, one for day care center users and one for babysitter users. We selected households with children under four using each particular type of care. For the babysitter option, 162 were selected from the Time-Use Survey and 224 from the Household Budget Survey. For the day care center option, 521 observations were selected from the Time-Use Survey, and 402 from the Household Budget Survey. As a baseline analysis, we compared the averages for the variables the two surveys had in common. Table 8 presents weighted tabulations on the most relevant variables for both care types in both surveys.

Table 8 Comparison of recipient and donor datasets (Weighted tabulations)

Apparently both surveys were very similar for day care center users. For the babysitting option, within the Household Budget Survey, some regions, like Andalusia or Valencia, were over-represented, as were also very small municipalities. On the other hand, single-parent families were under-represented. Nonetheless, most of the differences between the two surveys were not significant.

Next we needed to match observations from the two surveys for both child care types. As first suggested by Rosenbaum and Rubin (1983), we used the conditional probability of belonging to one of the samples (the so-called propensity score) to reduce the dimensionality of the matching problem previously discussed. This propensity score was computed as p(X _i ) = Pr(i ∈ T.U.|X _i  = x) (Del Boca et al. 2005). Therefore, rather than match on the regressors, matching was performed on p(X _i ).

In order to compute the propensity score, we ran a logit regression of the binary indicator taking value 1 for observations in the Time-Use sample (and 0 for the Household Budget sample) over the set of common household characteristics. We followed the algorithm proposed by Becker and Ichino (2002), which tests if the propensity score satisfies the balancing property (see Cameron and Trivedi 2005). We ended up with five blocks both when assigning babysitting expenditures and day care center expenditures; in each of them the score was balanced across the treated units and controls.⁹

As Del Boca et al. (2005) indicate, since the propensity score is a continuous variable, exact matches will rarely be achieved and a certain distance between individuals belonging to the two samples has to be allowed. Thus, we chose to use kernel-based matching (Heckman et al. 1998), where we associated a kernel-weighted average of the outcome of all donor-dataset units to the unit i of the recipient dataset:

$$ \hat{y}_{i} = {\frac{{\sum\limits_{j \in H.B.} {K(p_{i} - p_{j} )y_{j} } }}{{\sum\limits_{j \in H.B.} {K(p_{i} - p_{j} )} }}} $$

(5)

where $K\left( u \right) \propto \exp ( - u^{2} /2)$ is Gaussian, p _i and p _j are the propensity scores of units $i \in T.U.$, and $j \in H.B.$, and y _j stands for the outcome of individual $j \in H.B.$ As can be seen, the weight given to donor unit j is in proportion to the closeness between i and j.

After the statistical matching was performed, each individual from the Time-Use Survey using babysitting services (day care center services) was imputed the babysitting (day care) expenditures of a similar individual from the Household Budget Survey.

Finally, we proceeded with an internal evaluation of the statistical matching. We compared the average values of the imputed variable after the matching and the corresponding average in the donor set, that is, the H.B. sample. For the babysitting option, expenditures differed by 14.1% (slightly larger for the fused sample). For the day care option, on the other hand, the difference was 1.7% and not significant at conventional levels of testing.

Appendix 2: Correcting for Selectivity in the Price Equations

Let the price equation for each paid mode j be specified as:

$$ \ln P_{j} = \alpha^{\prime}_{pj} x_{pj} + n_{j} \quad j = 2\left( {\text{babysitter}} \right),\;3\left( {\text{day care center}} \right) $$

(6)

where x _pj represents a vector of observed determinants and n _j represents unobserved variation. Since we observe prices only if the care option is used, we must account for selection bias in the estimation of Eq. 6. Following Powell (2002) we implemented Lee’s (1983) selectivity bias correction method for multinomial choices.¹⁰

In the first stage, a reduced form multinomial logit model was estimated from $\tilde{V}_{n} = \tilde{x}_{{}}^{\prime } \tilde{b}_{n} + e_{n}.$ With these estimates $\hat{\tilde{b}}$ in hand, we calculated the selectivity correction factors $\lambda_{j}$ as:

$$ \lambda_{j} = - \sigma_{j} \rho_{j} {\frac{{\phi \left( {J_{j} (\tilde{x}^{\prime}\hat{\tilde{b}})} \right)}}{{\Upphi \left( {J_{j} (\tilde{x}^{\prime}\hat{\tilde{b}})} \right)}}}\quad j = 2,3 $$

(7)

where $\sigma_{j}$ is the standard deviation of n _j, $\rho_{j}$ is the correlation coefficient between n _j and e, the J function is the inverse of the standard normal cumulative density function, and the functions $\phi \left( \cdot \right)$ and $\Upphi \left( \cdot \right)$ are the density function and the cumulative function, respectively, of the standard normal.

In the second stage, these expressions $\lambda_{j}$ were appended to the corresponding Eq. 6 which could now be estimated by (weighted) ordinary least squares. Table 9 presents the results.

Table 9 Child care logarithm of price regressions (Weighted OLS)