A comparison of family policy designs of Australia and Norway using microsimulation models

Abstract

Many of the Australian family support schemes are income-tested transfers, targeted towards the lower end of the income distribution, whereas the Norwegian approach is to provide subsidized non-parental care services and universal family payments. We contrast these two types of policies and discuss policy changes within these policy types by presenting results from simulations, using microsimulation models developed for Australia and Norway. Labor supply effects and distributional effects are discussed for the hypothetical policy changes of replacing the means-tested family payments of Australia by the Norwegian universal child benefit schedule and vice versa, and of reducing the childcare fees in both countries. The analysis highlights that the case for policy changes is restricted by the economic environment and the role of family policy in the two countries. Whereas there is considerable potential for increased labor supply of Australian mothers, it may have detrimental distributional effects and is likely to be costly. In Norway, mothers already have high labor supply and any adverse distributional effects of further labor supply incentives occur in an economy with low initial income dispersion. However, expenditure on family support is already high and the question is whether this should be further extended.

Appendices

Appendix 1

1.1 The Norwegian behavioral simulation model

The behavioral microsimulation model assumes that Norwegian families make choices among finite sets of job and care alternatives B and S, for which utility is defined as:

$$ U(C_{kr} ,H_{k} ,Q_{r} ,k,r) = \nu (C_{kr} ,H_{k} ,Q_{r} ) + \varepsilon^{*} (C_{kr} ,H_{k} ,Q_{r} ,k,r)\quad k \in B,\;r \in S, $$

(3)

where C _kr is consumption/disposable income corresponding to job k and childcare arrangement r, H _k is annual hours of work in job k for the mother, Q _r is the quality of care alternative r, and ε ^*(C _kr , H _k , k, r) is a stochastic error term, which is allowed to vary both across combinations of care and job alternatives and across individuals, for instance accounting for unobserved care quality characteristics. The error terms are assumed to be both independent of observed characteristics and of each other, and distributed according to the extreme value distribution.²⁸ ν(..) is the deterministic component of the utility function while ε^*(..) is the random component. The family’s budget constraint is determined as described in Eq. (1) in Sect. 4.1.

The sets of job and care alternatives, B and S, are represented by a common choice set D = D(H, w, M), which denotes the number of alternatives that the families face for working hours and hours of care H. That is, a fixed link between hours of work and hours of care is assumed, except for home-working mothers who may use non-parental care alternatives, although at this stage this is suppressed in the notation. It can be useful to think of the alternatives within D as packages: for working hours/hours of care H, families observe a number of job opportunities for the mother with wage rate w and other job attributes, and a number of care alternatives with fees M and care attributes, such as quality of care characteristics. Neglecting differences in wages and care prices across different choices for notational simplicity, it follows from the standard discrete choice model for utility maximizing behavior that the probability of choosing a job within D can be written as:

$$ \varphi_{H} = {\frac{{{ \exp }\left( {v(H,w,M)\theta_{H} } \right)}}{{\sum\nolimits_{x} {{ \exp }\left( {v(x,w,M)\theta_{x} } \right)} }}}, $$

(4)

where $\theta_{H}$ represents the number of combinations within D and v(H, w, M) represents the utility of choosing a care/work combination with hours H.

Equation (4) shows that the choice model is analogous to a multinomial logit model, where the representative utility terms are weighted with the number of opportunities ($\theta_{H}$) at that utility, see also Dagsvik and Strøm (2006). However, as these opportunity densities are not observed, the empirical strategy implies estimating parameters reflecting differences in the number of opportunities across different choices along with parameters of the utility function.

In Kornstad and Thoresen (2007) the choice setting is further simplified by addressing choices between three types of care and five categories of working hours/hours of care. Let m symbolize the three modes of care: care at centers (m = 1); care by other paid providers (m = 2); and own/parental care (m = 3). Jobs are divided into groups according to working hours. The model distinguishes non-participation (j = 1); three levels of part-time work, corresponding to 1–16 h per week (j = 2), 17–24 h per week (j = 3) and 25–32 h per week (j = 4); and full-time work at over 32 h per week (j = 5). Then P _hjm defines the probability that household h chooses a job with hours of work in group j and a childcare arrangement in mode m:

$$ P_{hjm} = {\frac{{{ \exp }\left( {\nu \left( {\tilde{C}_{hjm} ,\tilde{H}_{j} ,X_{h} } \right) + { \log }\left( {{{n_{jm} } \mathord{\left/ {\vphantom {{n_{jm} } n}} \right. \kern-\nulldelimiterspace} n}} \right)} \right)}}{{{ \exp }\left( {\nu \left( {\tilde{C}_{h13} ,\tilde{H}_{1} ,X_{h} } \right) + { \log }n_{13} } \right) + \sum\nolimits_{i = 1}^{5} {\sum\nolimits_{{l \in \Upomega_{h} }} {{ \exp }\left( {\nu \left( {\tilde{C}_{hil} ,\tilde{H}_{i} ,X_{h} } \right) + { \log }n_{il} } \right)} } }}}, $$

(5)

where jm = 13 represents the home care (no market work) alternative, and

$$ \Upomega_{h} = \left\{ {\begin{array}{*{20}c} { ( 1 )\quad } \hfill & {{\text{if}}\,{\text{household}}\,h\,{\text{is}}\,{\text{constrained}}\,{\text{in}}\,{\text{the}}\,{\text{market}}\,{\text{for}}\,{\text{care}}\,{\text{at}}\,{\text{centers}}} \hfill \\ { ( 1 , 2 )\quad } \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right. . $$

(6)

$\tilde{H}_{j}$ is the median working time in hours of work group j, $\tilde{C}_{jm}$ is consumption corresponding to working time $\tilde{H}_{j}$ and X _h is a taste-modifying variable. The key notion of (latent) differences in choice sets is captured by $\Upomega_{h}$, stating some households have more limited choices, as center-based care is not available to them, and by the choice opportunities n _jm , which indicate that the number of opportunities in each care and work category may vary compared to the baseline (n). An unobserved individual effect (random effect) is introduced in the representation of wages.

The deterministic part of preferences is represented by a “Box-Cox” type utility function:

$$ v\left( {\tilde{H}_{j} ,\tilde{C}_{hjm} } \right) \equiv \gamma_{0} {\frac{{\tilde{C}_{hjm}^{{\alpha_{1} }} - 1}}{{\alpha_{1} }}} + {\frac{{\left( {1 - {\frac{{\tilde{H}_{j} }}{T}}} \right)^{{\alpha_{2} }} - 1}}{{\alpha_{2} }}}X_{h} \beta , $$

(7)

where T = 8760 is the total number of annual hours, γ ₀ , α ₁, α ₂ and β are parameters, and X _h is the number of children below 19 years of age. The utility function is quasi-concave if α ₁ < 1 and α ₂ < 1. If α ₁ → 0 and α ₂ → 0, the utility function converges to a log-linear function.

Appendix 2

2.1 The Australian behavioral simulation model

The behavioral microsimulation model assumes that Australian families make choices among a finite set of hours worked, for which utility is defined as:

$$ U(C_{{h_{1} h_{2} }} ,h_{1} ,h_{2} ) = \nu (C_{{h_{1} h_{2} }} ,h_{1}, h_{2} ) + \varepsilon^{*} (h_{1} ,h_{2} )\quad {\text{with}}\,h_{1} \in \{ 0,h_{11} , \ldots ,h_{1n} \} ,h_{2} \in \{ 0,h_{21} , \ldots ,h_{2m} \} ,$$

(8)

where $C_{{h_{1} h_{2} }}$ is consumption/disposable income (exclusive of childcare expenditure) corresponding to the male partner working h ₁ hours and the female partner working h ₂ hours and $\varepsilon^{*} \left( {h_{1} ,h_{2} } \right)$ is a stochastic error term, which is allowed to vary both across combinations of hours of work of both partners and across individuals. The error terms are assumed to be independent of observed characteristics and of each other, and are distributed according to the extreme value distribution.²⁹ ν(..) is the deterministic component of the utility function while ε^*(..) is the random component. The family’s budget constraint is determined as described in Eq. (2) in Sect. 4.1. Childcare is only included through the budget constraint.

It follows from the standard discrete choice model for utility maximizing behavior that the probability of choosing labor supply h ₁ and h ₂ can be written as:

$$ P_{{h_{1} h_{2} }} = {\frac{{{ \exp }\left( {v(C_{{h_{1} h_{2} }} ,h_{1} ,h_{2} )} \right)}}{{\sum\nolimits_{i = 0}^{n} {\sum\nolimits_{j = 0}^{m} {{ \exp }\left( {v(C_{{h_{1i} h_{2j} }} ,h_{1i} ,h_{2j} )} \right)} } }}} .$$

(9)

The deterministic part of preferences is represented by a quadratic utility function:

$$ \begin{aligned} \nu (C_{{h_{1} h_{2} }} ,h_{1} ,h_{2} ) = & \beta_{C} (C_{{h_{1} h_{2} }} - \gamma_{1} - \gamma_{2} ) + \beta_{1} h_{1} + \beta_{2} h_{2} + \alpha_{CC} (C_{{h_{1} h_{2} }} - \gamma_{1} - \gamma_{2} )^{2} + \alpha_{11} h_{1}^{2} + \alpha_{22} h_{2}^{2} + \\ & \alpha_{C1} (C_{{h_{1} h_{2} }} - \gamma_{1} - \gamma_{2} )h_{1} + \alpha_{C2} (C_{{h_{1} h_{2} }} - \gamma_{1} - \gamma_{2} )h_{2} + \alpha_{12} h_{1} h_{2}, \\ \end{aligned}$$

(10)

where the αs and βs are preference parameters and γ₁ and γ₂ are the fixed cost of working parameters to be estimated (where the indices 1 and 2 denote the husband and wife, respectively). The fixed cost is zero when the relevant person is not working. Observed heterogeneity can be included by allowing β₁, β₂, β _C , γ₁ and γ₂ to depend on personal and household characteristics. Unobserved heterogeneity can be added to β₁, β₂, β _C , and γ₂, in the form of a normally distributed error term with zero mean and unknown variance. The model is estimated using simulated maximum likelihood. In estimation, the unobserved heterogeneity parameters were found to be insignificant and were dropped.

Probability distributions of labor supply for Australia are obtained using a user-specified number of random draws (100 in our case) rather than use Eq. 9 since this allows us to calibrate to observed hours. The deterministic component of utility, $\nu (C_{{h_{1} h_{2} }} ,h_{1} ,h_{2} )$, is obtained using the parameter estimates of the quadratic preference function. To generate the random component of utility, a draw is taken from the distribution of the error term for each hours level (an Extreme Value Type I distribution). The utility-maximizing hours level is found by adding the two components of utility for each hours level and choosing the hours with the highest utility. Draws from the error terms are taken conditionally on the observed labor supply; that is, they are taken in such a way that the optimal pre-reform labor supply is equal to the actually observed labor supply. As a result, the post-reform labor supply outcome is computed conditional on the observed pre-reform labor supply. Using the repeated draws, an empirical probability distribution for the hours of work can be constructed at the individual level and aggregated up to the population level. The probability distribution can then be used to simulate expected labor supply responses or changes in expenditure at the individual level which can then again be aggregated up to the population level.