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A discrete choice model for labor supply and childcare

Abstract

A discrete choice model for labor supply and childcare for mothers of preschoolers is presented. The mothers are assumed to make choices from a finite set of job possibilities and from a finite set of childcare options. Options in the markets for childcare are characterized by opening hours, fees and quality attributes. Similarly, jobs are characterized by a fixed wage rate, working hours and a number of variables related to job satisfaction. In the estimation of the model, we take into account that the number of options available might vary across work/care combinations and that some mothers are rationed in the market for care at day care centers. The model is employed to simulate the female labor supply effects of the Norwegian home care allowance reform.

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Fig. 1
Fig. 2

Notes

  1. 1.

    These figures apply to children 1–5 years old. Thanks to generous maternity leave provisions, very few children attend day care centers in their first year. Children start school in their sixth year.

  2. 2.

    The term “home care allowance” is in accordance with the terminology used in Ilmakunnas (1997). However, the transfer might rather be characterized as an “out-of-childcare center allowance”. Note also that Schøne (2004) names the transfer as the “cash-for-care subsidy”. The figure in the text applies to 1998, while the (maximum) benefit for 2004 is NOK43,884 ($6,300).

  3. 3.

    There are, however, signs of convergence between the sexes in Norway regarding childcare and market work, which could mean that male income should also be treated as endogenous in future model proposals.

  4. 4.

    There are differences across regions with respect to price levels at childcare centers and to what extent rebates are given for care of the second and third child of the family. The figure refers to the fee of first child. Note also that expenses are deductible in the ordinary income tax base, which means that the government covers 28% of costs, up to a threshold. Users of center-based care and users of care by childminders that report their income to the tax authorities are eligible for this deduction.

  5. 5.

    This is an a priori assumption about grandparents.

  6. 6.

    It is fair to say that the reform gave rise to a fierce exchange of views on the direction of the modern welfare state.

  7. 7.

    There have been some minor adjustments in the transfer system since it was introduced. The system for 2000 is presented here, which cost about NOK2.8 billion in total expenditure.

  8. 8.

    At least, equal support was the initial intention. State budgets in recent years show that this is not strictly the case, as subsidies to centers are separated from the home care allowance rate system.

  9. 9.

    As a consequence, we only include families with a full-time working male in the estimations. Unemployment rates are in general low in Norway, and most fathers of preschoolers are full-time employed. Families that manage to combine two careers with parental care are observed in the data. However, it is difficult to find a good representation of the costs involved in such arrangements.

  10. 10.

    Note that two full-time working parents might not employ non-parental care because of shift-work arrangements. However, according to the data, this is not common.

  11. 11.

    The participation elasticity estimates in a non-rationing situation are 0.29 (wage), −0.05 (non-labor income), −0.11 (childcare costs).

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Acknowledgements

We are in particular grateful to John K. Dagsvik and three anonymous referees for helpful suggestions. Valuable comments from seminar participants at the 57th Congress of the International Institute of Public Finance, Linz (Austria), August 2001, and the 13th Annual Conference of the European Association of Labor Economists, Jyväskylä (Finland), September 2001, are acknowledged. We have benefited from research assistance by Bård Lian. Financial support has been received from the Norwegian Research Council.

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Correspondence to Tom Kornstad.

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Appendices

Appendix 1

Table 6 Second-stage estimation results for wage regression model, Heckman's selection model. Log wage as the dependent variable

Appendix 2

Specification of the likelihood function

The likelihood function used in the estimation of the model is given by

$$\begin{array}{*{20}c} {{\log L = {\sum\limits_{h = 1}^N {\left( {{\sum\limits_{m \in \Omega _{h} } {{\sum\limits_{j = 1}^5 {y_{{hjm}} } }} }\log {\sum\limits_{t = 1}^{30} {\frac{{e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{j} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{hjmt}} ,X_{h} } \right)} + d_{{jm}} Z_{{jm}} }} }}{{e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{1} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{h13t}} ,X_{h} } \right)} + d_{{13}} Z_{{13}} }} + {\sum\limits_{l \in \Omega _{h} } {{\sum\limits_{i = 1,2, \ldots ,5} {e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{i} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{hilt}} ,X_{h} } \right)} + d_{{il}} Z_{{il}} }} } }} }}}} }} \right.} }}} \\ {{\left. { + y_{{h13}} \log {\sum\limits_{t = 1}^{30} {\frac{{e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{1} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{h13t}} ,X_{h} } \right)} + d_{{13}} Z_{{13}} }} }}{{e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{1} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{h13t}} ,X_{h} } \right)} + d_{{13}} Z_{{13}} }} + {\sum\limits_{l \in \Omega _{h} } {{\sum\limits_{i = 1,2, \ldots ,5} {e^{{v{\left( { \ifmmode\expandafter\tilde\else\expandafter\~\fi{H}_{i} , \ifmmode\expandafter\tilde\else\expandafter\~\fi{C}_{{hilt}} ,X_{h} } \right)} + d_{{il}} Z_{{il}} }} } }} }}}} }} \right)}} \\ \end{array} $$
(A2.1)

where d jm denotes parameters, subscript h denotes female h and subscript t refers to the drawing of the error term in the wage rate equation. The dummy variable y hjm is defined as

$$ y_{{hjm}} = \left\{ {\begin{array}{*{20}l} {1 \hfill} & {{{\text{if}}\;{\text{female}}\;h'{\text{s}}\;{\text{labor}}\;{\text{supply}}\;{\text{is}}\;{\text{in}}\;{\text{group}}\;j\;{\text{and}}\;{\text{her}}\;{\text{choice}}\;{\text{of}}\;{\text{childcare}}\;{\text{is}}\;{\text{in}}\;{\text{mode}}\;m} \hfill} \\ {0 \hfill} & {{{\text{otherwise}}.} \hfill} \\ \end{array} } \right. $$
(A2.2)

The dummy variables Z jm are introduced to adjust the probabilities for variations in number of opportunities across states. We assume that there might be more jobs and childcare possibilities within the groups long part-time work/childcare center (Z 41), full-time work/childcare center (Z 51) and not working/parental care (Z 13). The dummy variables are therefore activated only for j∈{4, 5} and m=1, and for j=1 and m=3. They are specified as

$$ Z_{{jm}} = \left\{ {\begin{array}{*{20}l} {1 \hfill} & {{{\text{if}}\;{\text{labor}}\;{\text{supply}}\;{\text{is}}\;{\text{in}}\;{\text{group}}\;j\;{\text{and}}\;{\text{choice}}\;{\text{of}}\;{\text{childcare}}\;{\text{is}}\;{\text{in}}\;{\text{mode}}\;m} \hfill} \\ {0 \hfill} & {{{\text{otherwise}}.} \hfill} \\ \end{array} } \right. $$
(A2.3)

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Kornstad, T., Thoresen, T.O. A discrete choice model for labor supply and childcare. J Popul Econ 20, 781–803 (2007). https://doi.org/10.1007/s00148-005-0025-z

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Keywords

  • Female labor supply
  • Childcare
  • Discrete choice
  • Rationing

JEL Classification

  • J13
  • J22
  • C25