New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model

Kalb, Guyonne; Scutella, Rosanna Working Paper New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model New Zealand Treasury Working Paper, No. 03/23 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Kalb, Guyonne; Scutella, Rosanna (2003) : New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model, New Zealand Treasury Working Paper, No. 03/23, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205528 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model Guyonne Kalb and Rosanna Scutella N EW Z EALAND T REASURY W ORKING P APER 03/23 S EPTEMBER 2003 Treasury:558110v1 NZ TREASURY WORKING PAPER 03/23 New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model MONTH / YEAR September 2003 AUTHORS Guyonne Kalb Melbourne Institute of Applied Economic and Social Research The University of Melbourne Victoria 3010 Australia Email Telephone Fax [email protected] (03) 8344 7025 (03) 8344 5630 Rosanna Scutella Melbourne Institute of Applied Economic and Social Research The University of Melbourne Victoria 3010 Australia Email Telephone Fax [email protected] (03) 8344 8175 (03) 8344 5630 ACKNOWLEDGEMENTS This research was commissioned by New Zealand Treasury. Access to the data used in this study was provided by Statistics New Zealand, under conditions designed to give effect to the confidentiality provisions of the Statistics Act 1975. We should like to thank John Creedy for his helpful comments, Melissa McKenzie for providing unemployment data and Ivan Tuckwell for calculating net incomes at different discrete labour supply points for all households in the Household Expenditure Survey. The views expressed in this paper are those of the authors and do not represent the views of the Treasury or Statistics New Zealand. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz DISCLAIMER The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL i Abstract This paper presents results for four separately estimated sets of discrete choice labour supply models using the Household Economic Surveys from 1991/92 up to 2000/01. The New Zealand working-age population is divided into sole parents, single men, single women, and couples. The labour supply models use imputed wages for the non-workers. Some of the preference parameters for work and income are made dependent on personal and household characteristics to allow for heterogeneity in preferences among households. In addition, allowance is made for unobserved heterogeneity in preferences. The estimated parameters for the different groups are used to calculate confidence intervals for expected labour supply and the probability of working at the different discrete hours points. The effect of particular characteristics on labour supply is illustrated by computing marginal effects across the samples. The wage elasticities fall within the range of values found in other studies. Expected labour supply, predicted by using the estimated models, results in values close to the observed averages and confidence intervals around the expected values are reasonably narrow in most groups. The results are as anticipated and similar to results in other countries, with preferences for work being higher for people with higher education, who are in their thirties. Furthermore, for women the presence of young children decreases the preference for work. In addition to these variables, which are usually included in labour supply models, the “eligibility for New Zealand Superannuation” indicator and a “living with parents” indicator are included. For all groups, the delayed eligibility for the state provided superannuation scheme is found to increase labour supply. The indicator for living with one’s parents is found to increase labour supply for sole parents (indicating that living with one’s parents may be a childcare strategy), although the effect was not significant. JEL CLASSIFICATION C25 J22 KEYWORDS New Zealand labour supply; discrete choice labour supply model; simulated maximum likelihood; simulated confidence intervals WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 1 Table of Contents Abstract ...............................................................................................................................i Table of Contents ..............................................................................................................1 List of Tables......................................................................................................................1 List of Figures....................................................................................................................1 1 Introduction ..............................................................................................................2 2 The Economic Model ...............................................................................................3 2.1 Utility Maximisation .........................................................................................................3 2.2 Unobserved Wages ........................................................................................................5 3 The Data ....................................................................................................................6 3.1 Selection Criteria ............................................................................................................6 3.2 Distribution of hours worked ...........................................................................................7 3.3 Variables used in the Analyses ......................................................................................8 4 Econometric Specification of a Labour Supply Model .......................................11 4.1 Allowing for Nonlinear and Non-convex Budget Sets...................................................11 4.2 Specification of Utility Functions...................................................................................14 4.3 Expected Labour Supply...............................................................................................15 5 Results ....................................................................................................................16 5.1 Discussion of the Estimated parameters......................................................................16 5.2 Marginal effects.............................................................................................................24 5.3 Goodness of Fit.............................................................................................................25 6 Conclusion..............................................................................................................28 References .......................................................................................................................30 Appendix ..........................................................................................................................34 List of Tables Table 1 – Summary Statistics for the combined Household Economic Survey from 1991/92 to 2000/01 .................................................................................................................................9 Table 2 – Estimated Parameters of the Utility Function for Couples a..............................................17 Table 3 – Estimated Parameters of the Utility Function for One-Adult Households.........................20 Table 4 – Expected Labour Supply and Non-participationa..............................................................24 Table 5 – Actual and Expected Labour Supply for men (proportion in each category) ....................26 Table 6 –Actual and expected labour supply for women (proportion in each category)...................26 Table 7 – Actual and expected labour supply for sole parents (proportion in each category)..........27 Table A.1 – Minimum wage rates between 1991 and 2001..............................................................34 Table A.2 – Models for couples with alternative fixed cost of working..............................................35 Table A.3 – Models for singles and sole parents with alternative fixed cost of working...................37 List of Figures Figure 1 – Labour supply of men ........................................................................................................7 Figure 2 – Labour supply of women and sole parents........................................................................8 WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 2 New Zealand Labour Supply from 1991-2001: An Analysis Based on a Discrete Choice Structural Utility Model 1 Introduction This paper describes in detail the estimation of preference functions for hours of work and income for four subgroups of the New Zealand population, from which the expected hours of labour supply can be derived. The groups are the following: couples with and without children, single men, single women, and sole parents. Each of these groups is relatively homogenous and we specify one separate utility function for each group. The four groups together add up to a sample representing the New Zealand working-age population. No individual structural labour supply models have been estimated for New Zealand. Chiao and Walker (1992) estimated a discrete choice model using four earnings levels instead of a choice model based on different levels of labour supply and Maloney (2000) estimated a reduced form labour supply and participation equation based on average labour supply and participation of groups of individuals with similar characteristics. The lack of information on earnings in the data he used complicated his analysis. The model in this paper allows for the presence of fixed costs associated with working and for observed and unobserved heterogeneity in preferences for labour supply and income. A similar specification has been estimated for Australia (Kalb, 2002) allowing a comparison with the results from New Zealand. In addition, the estimation of similarly specified models for different groups allows us to compare the effect of characteristics on labour supply across the different demographic groups. The emphasis of the basic framework is on the separation of income into different categories and on a correct representation of net income at all levels of gross income, taking taxes and benefit withdrawal rates into account. This results in a highly nonlinear and non-convex budget set which differs for each individual. Estimation of a continuous labour supply model for two persons, using this budget constraint, is complicated and computationally intensive, which is one of the reasons to discretise labour supply for all groups.1 This simplification with regard to hours of work allows us to take the full details of the benefit and tax system into account. Following Van Soest (1995), we use a multinomial logit specification in the discrete choice model, which allows us to choose a relatively large number of labour supply points for both adults in the household. The models estimated in this paper can be used to simulate the behavioural effects of policy changes, as long as these policy changes are of a financial nature, affecting net 1 There has also been some evidence that a discrete presentation can be a more accurate representation of actual labour supply compared to a continuous specification (Van Soest, Woittiez and Kapteyn, 1990; Tummers and Woittiez, 1991). Often only a limited number of discrete hours points are available to people looking for employment. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 3 household income levels, such as for example, a change in the withdrawal rate of a benefit payment, a change in the level of payment or a change in eligibility rules. For a policy simulation, the model is usually calibrated to make sure that the prediction in the starting situation is equal to the observed situation. Section 2 briefly discusses the economic model. Section 3 describes the data. Section 4 contains the econometric details. The results from the models for the different groups are discussed in Section 5. First the estimated parameters are discussed and then predicted labour supply using the estimated parameters is presented. Finally, in Section 6 some conclusions are presented. 2 The Economic Model 2.1 Utility Maximisation In the model chosen in this paper, the household is assumed to be the decision-making unit on labour supply and consumption. Thus, we use a household utility function or a unitary utility function, which does not explicitly take into account individual consumption or utility, but assumes there is one common utility function for the whole household. Although alternative models are available, which incorporate perhaps more realistic assumptions on utility maximization in the household or allow for home production to enter the model independently, these models would introduce additional complications2. To estimate a model where all household members have their own utility functions, information is needed on the private consumption of individuals or on the amount of income allocated to them. No data set combines all necessary information on consumption or home production, income sources, and labour supply. Therefore strong assumptions are often needed on how income is shared to allow estimation of collective utility models or on the value and amount of home produced goods to estimate models that explicitly allow for home production, rather than implicitly as in the unitary utility models. To deal with these additional complications other parts of the model need to be simplified and as a result retaining the complexity of the tax and transfer system would be very difficult. The literature that studies the effect of policy changes in taxation or social security systems mostly favours the neoclassical approach for its suitability to incorporate detailed budget constraints. Given the aim of incorporating the details of the tax and transfer system in the labour supply model, this literature is followed. By setting up the model in the familiar neoclassical way, starting from utility maximization under a budget constraint, a logical and consistent framework can be built to analyse labour supply (see for example Deaton and Muellbauer, 1980; or Killingsworth, 1983). For example, take a two-adult household (with or without dependent children), where the adults choose their labour supply to optimise the households utility. Their utility depends on household consumption (which is assumed to be equal to net household income x3), on the amount of leisure time of adult 1, and the amount of leisure time of adult 2. 2 See for example, Bourguignon and Chiappori (1994), Browning et al. (1994), and Apps and Rees (1996, 1997, 2000). 3 There is no provision in the model for intertemporal transfers of money. However, the payout of dividends on investments and the payout of interest on savings in the current period are included in the “other income” variable. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 4 In this paper, the term ‘leisure’ is used to indicate both pure leisure time and home production time. The combination of leisure and income that delivers the highest utility to the household is regarded as the optimal choice. The choice of labour supply is simultaneously determined for both adult members of the household. Depending on the utility function chosen, this approach allows for direct interdependencies between the two adults’ labour supply or one adult’s labour supply and household income. This utility is maximized conditional on the restricted total amount of time available to each adult and the restricted amount of total household income. It is expected that utility increases with an increase in leisure and income. Usually more income means less leisure time for one of the adults, except when more income is obtained through social security benefits4. In short, maximizing a household’s utility involves balancing the amount of leisure and income. With regard to the assumption of free choice underlying this economic model; it is often not known whether the observed labour supply is the optimal labour supply or, alternatively, whether people are restricted in their labour supply choice by demand side factors5. It would be interesting to analyse desired hours of work rather than actual hours of work or to allow for the restrictions in actual hours caused by the demand for labour (see for example Euwals and Van Soest (1999) or Euwals (2001)). However, the information necessary to do this is not available in the data. A simple utility maximizing model would look as follows: max U(x,l1,l2) (1) subject to: T= l1 + h1= l2 + h2 =+++ 12 1 2 (,)()()(()) x gh h ny ny nBc where: U( ) is the utility function of a two-adult household, l1 and l2 indicate the aggregate of leisure time and home production time per week of the husband and wife (married or de facto) respectively, x indicates net income per week, T is the total available time for each person in the household, h1 and h2 are the hours of work of husband and wife, g(h1,h2) is the net income of husband and wife at the different hours of work h1 and h2 taking into account taxation and withdrawal of benefits, y1 and y2 are the non-labour incomes of husband and wife, c is household composition, 4 In the current specification of the model it is assumed that everyone who is eligible for benefits takes them up. 5 See for example, Laisney et al. (1992), Bingley and Walker (1997) or Duncan, Giles and MacCrae (1999). WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 5 B(c) is the amount of benefit households are eligible for, given their household composition c, n( ) is the amount of income after the deduction of taxes. The first two restrictions are time restrictions for the two adults. The third restriction, the budget constraint, denotes the level of available income in the household. If the first two restrictions are substituted in the third equation, the budget constraint may be written: +−−= + + + 12 1 2 (, )(,)()()(()) x gT hT h gTT ny ny nBc (2) For households with only one adult, the model can be simplified by leaving out everything relating to the second adult: max U(x,l1) (3) subject to: T= l1 + h1 =++ 11 () () (()) x gh ny nBc Or combining the two restrictions: +−= + + 11 ()()()(()) x gT h gT ny nBc (4) 2.2 Unobserved Wages Like other researchers in this area, we have to deal with unobserved market wages for people who are not working. In this paper, we use the popular approach of estimating the wage equation separately and using estimated wages as if they represented the true values of the unobserved wages6. To correct for a possible selection bias as a result of only observing wage rates for those gainfully employed the Heckman correction term for participation is included in the wage equation (Heckman, 1979). Estimating wages and labour supply simultaneously is computationally more demanding and it is not attempted very often7. Separate wage equations have been estimated for the five demographic groups. The specification of the wage equation is discussed in a separate paper (Kalb and Scutella, 2003). For each non-participant we impute an expected value for the wage rate in the labour supply model. Some observed values for wage income seem unrealistically small when compared to the corresponding hours worked. In the estimation of the labour equation in this paper, the observed wage level for all persons earning less than half the minimum wage or more than $100 per hour have been replaced by the predicted value8 as such low and high values seem likely to be due to measurement error9. Over the years the minimum wage levels varied. See Table A.1 in the appendix for the relevant minimum wage levels. 6 Van Soest (1995) uses this approach and points out that most of the papers in a special issue on Taxation and Labor Supply in Industrial Countries of the Journal of Human Resources (Moffitt, 1990) follow this approach as well. An alternative approach is to use imputed values for all individuals in the sample. 7 Exceptions are for example Fraker and Moffitt (1988), Gerfin (1993) and Murray (1996). 8 17 sole parents, 51 single men, 27 single women, 71 married men and 132 married women fall into this group. 9 None of the imputed wage rates fall into this category of wages that seem too low or too high. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 12 Restricting the number of possible working hours to a limited set of discrete values, as is done by other authors (for example Van Soest, 1995; Duncan, Giles and MacCrae, 1999; Keane and Moffitt, 1998) facing the same problem, appears an attractive solution.16 For this limited set of hours, one can calculate the level of utility that each possible combination of hours would generate, according to the specified utility function. An additional (computational) advantage of the discrete approach is that quasi-concavity does not have to be imposed before using maximum likelihood methods to estimate the model, as is necessary in the case of continuous labour supply for some utility functions (see Van Soest, Kapteyn and Kooreman, 1993), but can be checked after estimation. Instead of being defined on a continuous set of working hours [0,T], in the discrete choice case the budget constraint is defined on a discrete set of points }h ,...,h ,h {0, = h }h ,...,h ,h {0, = h 2k222121m12111 B A ∈∈ and on the interval [0,T]. 0, h11, h12, and etcetera represent the discrete values that labour supply can take. Using these sets, net income x(h1,h2) is calculated for all (m+1)×(k+1) combinations of h1 and h2 (where m+1 is the number of discrete points for h1 and k+1 is the number of discrete points for h2). The static microsimulation model at New Zealand Treasury, TaxMod, can be used to calculate net income at all chosen discrete labour supply points in the different survey years. It is assumed in these calculations that all benefits, for which the household is eligible, are taken up. By increasing the number of different hours in the choice set, the quality of the representation improves. However, the computational load also increases, so a compromise between quality and computational feasibility is necessary. Furthermore, some of the theoretically possible hours ranges may not be observed in the data such as low part-time hours for men, which may mean fewer discrete points are necessary in that range. Net income x is dependent on labour supply and wage rates of both adults, on non-labour income, on household composition and on eligibility for benefits. Net income for the records originating from the earlier data sets are inflated up to the 2001 level by multiplying the amount by the relevant CPI. In this way, net incomes in the different years are comparable. Wage rates, non-labour income and household composition are considered to be exogenous in this model. The model becomes: max U(x,l1,l2) (5) subject to: += += ∈× 11 22 12 (, ) lhT lhT where h h AB τ = + +++ + ++ − +++ +++ 11 22 1 2 11 22 1 2 11 221211 2212 (, ) ( ( , ), ) xwhwh y y Bcwhwh y y Bcwh wh y y wh wh y y (6) w1 and w2 are the gross wage rates of husband and wife respectively, B A and are the sets of discrete points from which values can be chosen for h1 and h2, 16 A more extensive introduction of the estimation and specification of discrete labour supply models can be found in Creedy and Kalb (2003). WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 13 B(.) is the amount of benefit, for which the household is eligible, given household composition c and income, τ (.) is the tax function that indicates the amount of tax to be paid. Adding an error term to the utility function allows for optimization errors made by the household, preventing contributions to the likelihood in any data point from becoming zero. A likelihood function can be formed using the above utility function. Based on the assumption of utility maximization for each household the following can be stated. The contribution of each household to the likelihood function is the probability that its observed hours result in an optimal utility for the household of interest when compared with all other possible choices for hours. This probability looks as follows: Pr {U[x((h1, h2)r), (h1, h2)r, εr] ≥ U[x((h1, h2)s), (h1, h2)s, εs] for all s} (7) where: r stands for the combination h1 and h2 that is preferred, s stands for all (k+1)×(m+1) possible combinations that can be made, given the discrete choice sets for hours worked, ε r and ε s represent error terms. Choosing an Extreme Value specification for the error term in (7) results in a multinomial logit model (see Maddala, 1983). If we can calculate utility levels for each of the possible combinations of leisure and income, and the error terms are specified, then for each possible combination we can calculate the probability of that combination being preferred according to the estimated model: =∑'' '' , exp( ) exp( ) ij ij ij ij U PU (8) Taking the logarithm of this probability, the log likelihood contribution for couples looks as follows:  ==−   ∑ '' '' , log log( ) log exp( ) ij ij ij ij LPU U (9) where: i indicates the husband’s labour supply; j indicates the wife’s labour supply; i’, j’ are the preferred (observed) states of labour supply (combination r in equation 7); Uij is the level of utility derived from the state where the husband has labour supply i and the wife has labour supply j. Expression (8) denotes the probability that the utility in the observed combination of hours is higher than the utility in any other situation. The log likelihood function for all households in the sample is formed by summing all individual contributions. The aim is to WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 14 choose parameter values for the utility function that maximize the log likelihood function in the observed data points. For single adult households equation (8) simplifies to:  ==−   ∑ '' log log( ) log exp( ) ii i i LPU U (10) 4.2 Specification of Utility Functions The form of the utility function used here is a quadratic specification (following Keane and Moffitt, 1998). This specification is simple but flexible in that it allows for the leisure of each person and income (or consumption) to be substitutes or complements. This means the model can represent complex interactions. Furthermore, the quadratic utility function can be expressed as a function of labour supply rather than leisure without the need to choose a value for total endowment of time (T). T is not important in this specification, as it is a constant, which can be incorporated in the parameters to be estimated. The above advantages make the quadratic utility function a good choice, even though this utility function is not automatically quasi-concave. However, the latter is not a problem in a discrete labour supply model, because two simple conditions, outlined in Van Soest (1995), can be used to establish whether U is quasi-concave at any data point. In the discrete approach taken here, these two conditions can be tested at all data points after estimation of the parameters. In a model with continuous hours of labour supply, these conditions have to be imposed a priori to guarantee coherency, as has been mentioned earlier. Many earlier models had the problem of overpredicting part-time hours and underpredicting non-participation. An intuitively appealing approach is to include a fixed cost of working parameter in the income variable x to indicate the cost of working versus non-participation (Callan and Van Soest, 1996). As a result of the inclusion in x, this cost of working parameter is measured in dollars per week. The utility derived from leisure and income can be written as: ()()() 211222121211 2 222 2 111 2 2122112121 hhh)x(h)x( hhxhh)x()h,h,xU( xx xxx α+γ−γ−α+γ−γ−α +α+α+γ−γ−α+β+β+γ−γ−β= (11) where α.., β., and ϕ are preference parameters that have to be estimated; and 21 and γ γ are the fixed cost of working parameters to be estimated for husband and wife, they are zero when the relevant person is not working. This quadratic utility function has a simple form and heterogeneity of preferences is easy to include. To account for differences in preferences between households, the parameters β, α, and γ can be made dependent on household and individual characteristics. In the first instance, it is assumed that only 1 β , 2 β , x β , γ1 and γ2 depend on personal and household characteristics (described in Section 3.2). Simple linear specifications are chosen to include the observed heterogeneity in 1 β , 2 β , x β , γ1 and γ2. As an alternative to the individual characteristics in the fixed-cost-of-working parameters, we also estimated separate cost parameters for the different labour supply levels. This is equivalent to making the parameter dependent on the number of hours of work. Instead of specifying a single parameter for all hours of work, separate parameters are introduced for WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 15 categories of hours. Here parameters are specified for 1 to 10 hours of work, 11 to 20 hours of work, 21 to 30 hours and over 30 hours of work. In addition to allowing for the fixed cost of working, this specification also allows for different costs associated with different hours levels, such as for example the cost of part-time work which may be high if few jobs in this category are available, because a larger search effort is then required. Adding unobserved heterogeneity to the linear equations in personal characteristics for the preference and fixed-cost-of-working parameters, in the form of a normally distributed error term with zero mean and unknown variance, is quite simple, although exact maximisation would involve a likelihood function with multiple integrals. However, Van Soest (1995) outlines an easier method, replacing the expectation of the log likelihood by a simulated mean and optimising an approximate likelihood function instead of the exact likelihood function. It is straightforward to obtain a simulated mean by: drawing error terms from the distribution based on the current parameter estimates for the covariance matrix for each observation in the sample; calculating the log likelihood function based on these draws; and averaging the log likelihood function over a certain number of draws. Van Soest found that 10 draws seemed sufficient, so the estimation of unobserved heterogeneity in this paper is carried out with the same number of draws. 4.3 Expected Labour Supply Once the model has been estimated, the results can be used to calculate the expected labour supply from the probabilistic outcomes for people with certain known characteristics and under known social security and taxation rules. To obtain the expected labour supply of the husband, we first calculate the utility U(x(h1,h2), h1, h2) for each possible combination of labour supply for both adults in the household. This is achieved by substituting the estimated parameter values into equation (10) along with the net income for the relevant combination. Once the utility values are known, a simple logit transformation provides the probability of each possible combination occurring according to the estimated model: ()()() ()()() ∑ = 21 2121 2121 21 h,h allover h,h,h,hxUexp h,h,h,hxUexp )h,h(p (12) These probabilities can be used to calculate the expected value of preferred labour supply for the husband by simply aggregating the probabilities over all possible values of h2 for each value of h1. In this manner, the marginal probability of h1 is obtained, which can be used to calculate the expected value of h1 in the usual way. The formula for this procedure looks as follows: ∑∑                 = 12 1211 hh h)h,h(p)h(E (13) The expected value for the wife’s labour supply can be obtained in a similar way. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 16 5 Results Parameters of the preference functions are estimated using imputed wage values for nonworkers as described in Section 2.2. The next subsection presents the results of the labour supply models for both couples and single adult units. In the second subsection, the estimated results are used to predict labour supply probabilities so that predicted and actual results can be compared. 5.1 Discussion of the Estimated Parameters To show how the results of a model as discussed in section 4 are interpreted, we first discuss the parameters of two-adult income units. Table 2 gives the parameter estimates of the quadratic specification of the utility function for a model with six discrete labour supply points for men and eleven points for women. The location of the points is defined in a footnote to the table. The linear terms The effects of different characteristics on the preference for leisure of both adults in the household are the first results to be discussed. We only discuss those parameters that are significant at the 5-percent level. To begin with the parameterised preference for work for the male adult, a significant positive effect17 is found for the linear term of age. This means that older men have a higher preference for work and thus a lower preference for leisure. However, on the other hand the quadratic term for age seems to have a significant negative effect on the preference for work, which combined with the linear effect of age means that the preference for work increases for men up to around 36 years of age after which it decreases with age. Thus young men and older men have a lower preference for labour supply. A positive effect is further observed for households where the man has a higher level of education. The partner’s education tends to increase male labour supply as well, with the exception of partners with a postgraduate degree, the presence of which decreases the preference for work. There also seems to be an increase in the preference for work over time even after controlling for unemployment levels. It may be partly due to the change in the age of eligibility for the New Zealand Superannuation. This effect may not have been completely captured by the approximating variable constructed by us. None of the variables related to the number and age of dependent children in the household influence the preference for work. The current unemployment rate amongst men has a negative effect on the preference for work. This is probably mostly due to involuntary unemployment but it could also be partly due to a discouraged worker effect, as may for example be reflected in early retirement decisions. Being older than 60 years of age has a negative effect in addition to the negative age squared term. More interestingly however, those who are eligible for the New Zealand Superannuation clearly have a lower preference for work than others even after controlling for being over 60.18 The policy change has had a substantial effect. There 17 This indicates a higher preference for work and thus a smaller taste for leisure. 18 This parameter is a mixture of the effect of superannuation income and a change in preferences directly caused by the eligibility for New Zealand Superannuation. The HES data does not provide enough detail on age to determine eligibility for all individuals with certainty in TaxMod. As a result, net income cannot be determined with certainty at all discrete labour supply points and thus the effect of eligibility per se and the effect through changed net incomes cannot be separated completely. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 17 even seems to be some effect from the partner’s eligibility as well, which is however only significant at the 10-percent level. Table 2 – Estimated Parameters of the Utility Function for Couples a Estimated coefficient z-valueb Quadratic terms income× 100,000 -0.0177 -4.13 Labour supply husband × 100 -0.4990 -17.06 Labour supply wife × 100 -0.1339 -16.48 Crossproduct Inc. & lab. Sup. Husband × 10,000 -0.3826 -12.59 Inc. & lab. Sup. Wife × 10,000 -0.1930 -9.76 labour supply Husband & wife × 100 -0.0728 -11.52 Linear terms Income × 100 constant 0.5215 20.13 Number of children -0.0030 -1.20 Labour supply husband constant 0.2945 12.23 Youngest child <1 yr old 0.0039 1.31 Youngest child 1-3 yrs old 0.0036 1.49 Youngest child 4-5 yrs old 0.0005 0.16 Youngest child 6-9 yrs old 0.0033 1.23 Number of children -0.0012 -1.09 Age/10 0.0487 8.94 Age squared/100 -0.0067 -9.79 Vocational education 0.0165 9.87 Certificate 0.0125 5.93 Bursary/scholarship 0.0135 4.96 Postgraduate degree/other 0.0127 2.41 Bachelor degree 0.0180 5.96 Postgraduate 0.0213 4.50 Vocational education (partner) 0.0020 1.07 Certificate (partner) 0.0076 4.31 Bursary/scholarship (partner) 0.0108 4.40 Postgraduate degree/other (partner) 0.0020 0.39 Bachelor degree (partner) 0.0017 0.52 Postgraduate (partner) -0.0146 -2.68 Time trend 0.0009 2.12 Quarterly male unemployment rate -0.0016 -2.89 Aged 60 or over -0.0078 -2.01 Eligible for New Zealand Superannuation -0.0236 -5.13 Partner is eligible for New Zealand Superannuation -0.0096 -1.79 Labour supply wife constant 0.0465 3.33 Youngest child <1 yr old -0.0637 -11.62 Youngest child 1-3 yrs old -0.0672 -18.67 Youngest child 4-5 yrs old -0.0584 -12.90 Youngest child 6-9 yrs old -0.0383 -11.56 Number of children -0.0058 -6.54 Age/10 0.0385 7.07 Age squared/100 -0.0064 -9.22 Vocational education 0.0201 10.17 Certificate 0.0133 7.12 WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 18 Table 2 – Continued a Estimated coefficient z-valueb Bursary/scholarship 0.0164 7.22 Postgraduate degree/other 0.0277 5.72 Bachelor degree 0.0298 9.69 Postgraduate 0.0410 7.81 Vocational education (partner) -0.0081 -4.58 Certificate (partner) -0.0039 -1.77 Bursary/scholarship (partner) -0.0042 -1.58 Postgraduate degree/other (partner) -0.0123 -2.42 Bachelor degree (partner) -0.0189 -7.07 Postgraduate (partner) -0.0226 -5.76 Time trend 0.0006 1.41 Quarterly female unemployment rate -0.0009 -1.20 Aged 60 or over -0.0034 -0.54 Eligible for New Zealand Superannuation -0.0268 -2.58 Partner is eligible for New Zealand Superannuation -0.0017 -0.45 Fixed cost husband/100 18.7221 14.50 Fixed cost wife/100 Constant 8.0863 18.81 Youngest child <1 yr old 1.3763 3.20 Youngest child 1-3 yrs old -0.7997 -2.97 Youngest child 4-5 yrs old -1.7622 -4.92 Youngest child 6-9 yrs old -1.8085 -6.02 Live in Wellington/Auckland 0.0962 0.78 Unobserved heterogeneity Variance in income parameter 0.0000 0.33 Variance in husband’s labour supply 0.0000 0.00 Variance in wife’s labour supply 0.0000 0.00 Variance in wife’s fixed cost 0.0030 0.46 Log likelihood -30565 a Six discrete points of labour supply are distinguished for each man: 0 hours for nonparticipants and people working less than 2.5 hours, 10 hours for people working from 2.5 to 15 hours, 20 hours for people working from 15 to 25 hours, 30 hours for people working from 25 to 35 hours, 40 hours for people working from 35 to 45 hours, and 50 hours for people working more than 45 hours. Eleven discrete points of labour supply are distinguished for each woman: 0 hours for non-participants and people working less than 2.5 hours, 5 hours for people working from 2.5 to 7.5 hours, 10 hours for people working from 7.5 to 12.5 hours, 15 hours for people working from 12.5 to 17.5 hours, 20 hours for people working from 17.5 to 22.5 hours, 25 hours for people working from 22.5 to 27.5 hours, 30 hours for people working from 27.5 to 32.5 hours, 35 hours for people working from 32.5 to 37.5 hours, 40 hours for people working from 37.5 to 42.5 hours, 45 hours for people working from 42.5 to 47.5 hours, and 50 hours for people working more than 47.5 hours. b The z-value indicates the level of significance of the estimated coefficients. A value of 1.96 or more means that the parameter is significantly different from zero at the 5% level at least. The higher the z-value the more precise the estimated coefficient. According to expectation, the preference for work of the female adult seems to be lower than that of her male partner, at least as far as this is reflected in the size of the constant term of β2. A significant positive effect is observed for women with higher education levels. The effect of education seems more important for women than for men. This could be caused by the fact that almost all men are working or looking for work, whereas women’s labour supply is more variable. Additionally, if the partner’s education level is higher, then a woman’s preference for work is reduced to some extent. However, the effects are smaller than those resulting from her own education. From the linear and quadratic age parameters it can be derived that the maximum preference for work is around 30 years of age. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 19 All variables relating to children have a significant negative effect on a married woman’s preference for work. The effect for children between six and nine years old is much smaller than for younger children. As expected, and as is seen in many other studies (Australian examples are Eyland, Mason and Lapsley, 1982; Ross, 1986; Murray, 1996; and Kalb, 2002), having a pre-school child under four years of age has a large negative effect on the female preference for work. Children of primary school age affect the mother’s preference for work to a smaller extent. Finally, women with more children have a lower preference for work. Similar to the effect for men, the eligibility for the New Zealand Superannuation clearly affects women’s preferences for work as well. The partner’s eligibility seems irrelevant for women. To keep the model manageable the preference for income only depends on the number of children, which was significant for Australian data (Kalb, 2002). Similar to the Australian case a lower preference for income is estimated with an increase in household size, but the effect is not significant.19 The results for single men, single women and sole parents are presented in Table 3 and are discussed more briefly. Comparing the effects found for couples with those for singles and sole parents, similar variables are found to be important. High education levels increase the preference for work for all groups. The effect on the preference for income is less clear; higher education levels increase the preference for some whilst decreasing it for others. The effect of age on the preference for work for single men is similar to that for married men. The preference is at a maximum around 35 years of age. Furthermore, single women’s maximum preference for work occurs around 29 years of age, which is close to the age at which this occurs for married women. For sole parents, neither age nor age squared are significant. Similar effects are found for Australia (Kalb, 2002). Comparing the effect of children for sole parents and married women it is obvious that the age of the youngest child is important for both groups. However, for sole parents the effect decreases much less than for married mothers when the youngest child’s age increases, with the exception of moving from having a newborn child to having a 1 to 3 year old child (the effect of having a newborn child is not significant however). On the other hand, their preference for income is also at its highest when they have children in this age group, but this effect is insignificant as well. The time trend is nearly significant for sole parents, indicating an increase in the preference for work over time, similar to the effect for married men and women. The unemployment rate is nearly significant for single men. Eligibility for the New Zealand Superannuation is significant for all groups and it reduces the preference for work, as it did for married men and women. The models for one-adult households include an additional variable, which indicates whether the individual lives with one or both parents. Surprisingly, the effect is only significant for single men and the sign is opposite to expectations. The preference for income is higher when a single man lives with his parents. Perhaps this picks up a motivational effect where individuals who have a high preference for income, are more likely to be frugal and save for future events, which can be achieved by living at home with their parents and thus saving on living expenses. The effect for single women is positive 19 This negative effect is likely to be a spurious relationship reflecting the often-observed correlation between low income and the number of children, which may be driven by similar household and personal characteristics. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 20 as well but insignificant. Although insignificant, the coefficient in the preference for work parameter has the expected sign for sole parents, indicating a larger preference for work when living with one’s parents, possibly because of the potential childcare that can be provided by the parents. Table 3 – Estimated Parameters of the Utility Function for One-Adult Households Single men Single women Sole parents Estimated coefficient z-valueb Estimated coefficient z-valueb Estimated coefficient z-valueb Quadratic terms Income × 100,000 -0.1747 -2.98 -0.4846 -5.33 -0.0448 -0.94 Labour supply × 100 -0.2998 -8.46 -0.2600 -10.37 -0.0222 -0.96 Cross product Inc. & lab. sup. × 10,000 -1.4016 -9.11 -1.5650 -7.47 -0.1917 -1.07 Linear terms Income × 100 constant 1.0377 5.30 2.0119 7.75 0.6118 2.55 Youngest child <1 yr 1.1686 1.24 Youngest child 1-3 yrs old 0.0384 0.55 Youngest child 4-5 yrs old 0.0624 0.98 Youngest child 6-9 yrs old -0.0069 -0.20 Number of children 0.0161 1.48 Age/10 0.1990 2.17 0.0032 0.03 -0.1205 -1.83 Age squared/100 -0.0171 -1.35 0.0016 0.10 0.0152 1.78 Vocational education -0.1123 -2.39 -0.0462 -0.69 -0.0549 -1.86 Certificate -0.0899 -2.16 -0.0242 -0.36 -0.0483 -1.77 Bursary/scholarship -0.1833 -4.08 -0.1340 -1.94 -0.0142 -0.54 Postgraduate degree/other -0.2291 -2.80 0.1177 0.96 -0.0239 -0.44 Bachelor degree -0.0851 -1.36 0.2237 2.30 0.0555 1.07 Postgraduate 0.0787 0.80 0.4139 2.66 0.0186 0.32 Live with parents 0.0636 3.08 0.0491 0.84 female -0.2281 -2.37 Labour supply constant 0.1685 6.03 0.0947 4.21 0.0288 0.48 Youngest child <1 yr -0.0608 -1.37 Youngest child 1-3 yrs old -0.0301 -3.18 Youngest child 4-5 yrs old -0.0381 -4.05 Youngest child 6-9 yrs old -0.0319 -4.89 Number of children 0.0003 0.10 Age/10 0.0295 3.34 0.0308 4.72 0.0079 0.32 Age squared/100 -0.0041 -3.48 -0.0051 -5.86 -0.0013 -0.41 Vocational education 0.0140 3.44 0.0250 7.50 0.0230 3.70 Certificate 0.0113 2.90 0.0195 6.46 0.0044 0.64 Bursary/scholarship 0.0008 0.20 0.0262 7.87 0.0294 3.45 Postgraduate degree/other 0.0000 0.00 0.0249 4.18 0.0334 2.11 Bachelor degree 0.0056 1.06 0.0280 6.40 0.0595 5.68 Postgraduate 0.0102 1.23 0.0303 3.06 0.0457 2.92 female -0.0603 -4.83 Time trend -0.0001 -0.14 -0.0003 -0.44 0.0017 1.73 Unemployment rate -0.0013 -1.79 -0.0012 -1.04 0.0004 0.24 Aged over 60 -0.0154 -1.75 -0.0212 -2.32 -0.0254 -0.37 Eligible for NZ superannuation -0.0374 -2.61 -0.0309 -2.63 -0.1793 -1.97 Live with parents 0.0090 1.33 Fixed costs/100 Constant 5.9696 11.18 2.7718 12.96 12.6306 2.20 Live in capital city -0.0182 -0.22 0.1618 3.08 -0.1990 -0.48 Youngest child <1 yr -10.5666 -1.87 Youngest child 1-3 yrs old 0.4599 0.18 Youngest child 4-5 yrs old -2.3726 -1.02 Youngest child 6-9 yrs old -0.7688 -0.45 Female 1.4647 1.25 WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 21 Table 3 – Continued Single men Single women Sole parents Estimated coefficient z-valueb Estimated coefficient z-valueb Estimated coefficient z-valueb Unobserved heterogeneity Variance income 0.0000 0.14 0.0003 0.43 0.0000 0.18 Variance labour supply 0.0000 0.23 0.0000 0.58 0.0000 0.26 Variance fixed cost 0.0017 0.29 0.0016 0.66 0.0033 0.46 Covariance inc. & labour supply 0.0000 0.27 0.0000 -0.34 0.0000 -0.44 Covariance inc. & fixed cost -0.0002 -0.15 -0.0006 -0.46 0.0000 -0.20 Covariance lab.sup. & fixed cost 0.0000 -0.25 0.0000 0.56 0.0000 0.32 Log likelihood -7660 -7280 -2796 a Eleven discrete points of labour supply are distinguished for each person: 0 hours for nonparticipants and people working less than 2.5 hours, 5 hours for people working from 2.5 to 7.5 hours, 10 hours for people working from 7.5 to 12.5 hours, 15 hours for people working from 12.5 to 17.5 hours, 20 hours for people working from 17.5 to 22.5 hours, 25 hours for people working from 22.5 to 27.5 hours, 30 hours for people working from 27.5 to 32.5 hours, 35 hours for people working from 32.5 to 37.5 hours, 40 hours for people working from 37.5 to 42.5 hours, 45 hours for people working from 42.5 to 47.5 hours, and 50 hours for people working more than 47.5 hours. b The z-value indicates the level of significance of the estimated coefficients. A value of 1.96 or more means that the parameter is significantly different from zero at the 5% level at least. The higher the z-value the more precise the estimated coefficient. c For sole parents people with a degree are categorized in a group with those having a diploma, because of the limited number of observations on sole parents with a higher level of education. Finally, the model for sole parents contains one additional explanatory variable, gender, because this group consists of both men and women. The coefficient shows that sole mothers have a lower preference for work and income than sole fathers. Overall, the characteristics included in the labour supply model had the expected effects on the preferences for labour supply. That is, the preference for employment goes up with age at first and declines again after an age of about 30 (for women) and 35 (for men) is reached. Well-educated individuals have higher labour supply preferences. Children decrease female preferences for labour supply, in particular when it concerns preschool children. The effect on male preferences is not significant, similar to what is found in other studies (Section 3 briefly discusses the results from other research). The increase in the age of eligibility for the New Zealand Superannuation is found to affect all groups significantly by increasing the relevant individuals’ preferences for labour supply. Quadratic and crossproduct terms Taking the first derivative with respect to labour supply of men, the following expression for the marginal utility of labour supply for men is obtained: β αα α γγ ∂ ==+ + + −− ∂ 11111122112 1 2() x U Uhhx h Similar expressions can be formulated for labour supply of women and for net income. From this formula and the results in Table 2, we conclude that couples seem to see each other’s labour supply as substitutes. If one of the two persons works more, the marginal utility of work of the other person decreases (since α12=-0.0730). This is contradictory to other studies where it is found that if one in a couple had more leisure time then the other’s marginal utility for leisure time increased (Kalb, 1999, 2000). The parameter was also positive for the data used here before the inclusion of the fixed costs of working parameter. The fixed cost of working parameter is discussed in the next subsection. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 28 Comparing the labour supply in the three age groups for the different demographic groups, it is clear that labour supply is highest in the age category of 31 to 50 years for single and married men. Labour supply is only slightly lower for the youngest age group, but individuals over 50 years seem to reduce their labour supply considerably. Not unexpectedly, married women and sole parents behave differently. Married women have a similar level of labour supply when they are younger than 30 and when they are between 31 and 50 years of age. There is also much less decrease in the labour supply of sole parents and married women going from the middle to the older aged group. An altogether different pattern is observed for sole parents, who have the lowest labour supply when they are under 30 and the highest when they are between 31 and 50 years of age, which only reduces slightly for those over 50. This is most likely linked to the age of their children. The expected effects of certain policy changes could be calculated by computing the expected hours in each of the categories, accounting for the changed tax and benefit rules in the computer programs, and comparing these results to the expected hours using the current tax and benefit rules. Calibration is often used to fix the results in the base case to the observed discretised values, so that the simulation starts from these values. Examples of policy simulations using similar models to the ones described in this paper can be found in Creedy, Kalb and Kew (2003) or Kalb, Kew and Scutella (2003). 6 Conclusion In this paper, four separate basic labour supply models for couples, single men, single women and sole parents are estimated for New Zealand. The preference parameters for labour supply and income and the parameters for fixed costs include observed heterogeneity in the form of the number and age of children in the income unit, age and education of the head and partner (if present), and the place of residence of the income unit. It was found that adding unobserved heterogeneity did not change the estimated values of the other parameters and the unobserved heterogeneity parameters were all very small and insignificant. The results are similar for all demographic groups. The basic results seem sensible (and similar to results found in other countries, such as Australia and to earlier more aggregate results for New Zealand), with the preference for labour supply highest for people who are in their thirties with a high education level, although education levels (including those of the partner) seem somewhat more important for women than for men. The preference for labour supply is lower for women with children, in particular when the children are young, whereas no effect is found for married men. Finally, the predicted distribution over the different labour supply hours using the point estimates of the parameters is similar to the actual distribution. This leads us to conclude that the four models in this paper seem a good starting point for further experimentation with alternative specifications and extensions in future research and as the basis for policy simulations. However, the model for sole parents may need to be refined further. The available data from 1991 to 2001 allowed us to include some variables in the preference parameters, which do not usually form part of labour supply models. The most interesting of these was the eligibility for New Zealand Superannuation indicator. In addition to this variable, a time trend, a dummy variable for being 60 years or older and an unemployment rate were included to take out possible other effects that might pollute the eligibility parameter. For all groups, a significant effect is found for the Superannuation indicator, even after controlling for the other possible influences. The delayed eligibility for WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 29 this state provided superannuation scheme has increased labour supply for all groups. Finally, an indicator for living with one’s parents was included to explain labour supply preferences and found to have the expected sign for sole parents (indicating that living with one’s parents may be a childcare strategy for sole parents), although the effect was not significant. The models estimated in this paper can be used to simulate the behavioural effects of policy changes, as long as these policy changes are of a financial nature, affecting net household income levels, such as for example, a change in the withdrawal rate of a benefit payment, a change in the level of payment or a change in eligibility rules. For a policy simulation, the model is usually calibrated to make sure that the prediction in the starting situation is equal to the observed situation. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 30 References Aaberge, R., U. Colombino and S. Strøm (1999). Labour supply in Italy: an empirical analysis of joint household decisions, with taxes and quantity constraints. Journal of Applied Econometrics, 14, 402-422. Apps, P.F. and R. Rees (1996). Labour supply, household production and intra-family welfare distribution. Journal of Public Economics, 60, 199-219. — (1997). Collective Labor Supply and Household Production. Journal of Political Economy, 105(1), 178-190. — (2000). Household Production, Full Consumption and the Costs of Children. Discussion Paper no. 157, Institute for the Study of Labor (IZA), Bonn. Bingley, P. and I. Walker (1997). The labour supply, unemployment and participation of lone mothers in in-work transfer programmes. Economic Journal, 107, 1375-1390. Bourguignon, F. and P.-A. Chiappori (1994). The collective approach to household behaviour. in The measurement of household welfare ed. by R. Blundell, I. Preston and I. Walker, Cambridge: Cambridge University Press. Browning, M., F. Bourguignon, P.-A. Chiappori and V. Lechene (1994). Income and outcomes: a structural model of intrahousehold allocation. Journal of Political Economy, 102(6): 1067-1096. Burtless, G. and J.A Hausman (1978). The effect of taxation on labor supply: evaluating the Gary Negative Income Tax experiment. Journal of Political Economy, 86(6), 1103-1130. Callan, T. and A. van Soest (1996). Family Labour Supply and Taxes in Ireland. Discussion paper, mimeo, Tilburg University. Chiao, Y-S. and Walker, I. (1992) Labour market behaviour of prime age individuals. In M. Prebble and P. Rebstock (eds). Incentives and Labour Supply: Modelling Taxes and Benefits, Institute of Policy Studies, Wellington. Creedy, J. and G. Kalb (2003). Discrete Hours Labour Supply Modelling: Specification, Estimation and Simulation. Melbourne Institute Working Paper Series, WP No. 16/03, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. Creedy, J., Kalb, G. and H. Kew (2003). Flattening the Effective Marginal Tax Rate Structure in Australia: Policy Simulations Using the Melbourne Institute Tax and Transfer Simulator. The Australian Economic Review, 36(2), 156-172. Deaton, A. and J. Muellbauer (1980). Economics and Consumer Behavior. New York: Cambridge University Press. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 31 Duncan, A., C. Giles and J. MacCrae (1999). Household labour supply, childcare costs and in-work benefits: modelling the impact of the working families tax credit in the UK. Paper, Institute for Fiscal Studies, London. Duncan, A. and M.N. Harris (2002). Simulating the Effect of Welfare Reforms among Sole Parents in Australia. Economic Record, 78, 249-263. Duncan, A. and J. MacCrae (1999). Household labour supply, childcare costs and in-work benefits: modelling the impact of the working families tax credit in the UK. Mimeo, Institute for Fiscal Studies, London. Euwals, R. (2001). Female labour supply, flexibility of working hours, and job mobility. The Economic Journal, 111(May), C120-C134. Euwals, R. and A. van Soest (1999). Desired and actual labour supply of unmarried men and women in the Netherlands. Labour Economics, 6, 95-118. Eyland, E.A., C.A. Mason and H.M. Lapsley (1982). Determinants of female employment. Economic Record, 58, 11-17. Fraker, T. and R. Moffitt (1988). The effect of food stamps on labor supply: a bivariate selection model. Journal of Public Economics, 35, 25-56. Gerfin, M. (1993). Simultaneous discrete choice model of labour supply and wages for married women in Switzerland. Empirical Economics, 18, 337-356. Hagstrom, P.A. (1996). The food stamp participation and labor supply of married couples; an empirical analysis of joint decisions. Journal of Human Resources, 31(2), 383403. Hausman, J.A. (1979). The econometrics of labor supply on convex budget sets. Economics Letters, 3, 171-174.  (1985). The econometrics of nonlinear budget sets. Econometrica, 53, 1255-82. Heckman, J.J. (1979). Sampled selection bias as a specification error. Econometrica, 47(1), 153-161. Hoynes, H.W. (1996). Welfare transfers in two-parent families: labor supply and welfare participation under AFDC-UP. Econometrica, 64(2), 295-332. Kalb, G. (1999). Labour Supply and Welfare Participation in Australian Two-adult Households; Comparing 1986/1987 with 1994/1995. Working Paper No. BP-34, Centre of Policy Studies, Monash University, Australia. Kalb, G. (2000). Labour Supply and Welfare Participation in Australian Two-Adult Households: Accounting for involuntary unemployment and the ‘cost’ of part-time work. Working Paper No. BP-35, Centre of Policy Studies, Monash University, Australia. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 32 Kalb, G. (2002). Estimation of Labour Supply Models for Four Separate Groups in the Australian Population. Melbourne Institute Working Paper Series, WP No. 24/02, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. Kalb, G., H. Kew and R. Scutella (2003). Effects of the Australian New Tax System on Government Expenditure With and Without Behavioural Changes. Melbourne Institute Working Paper Series, WP No. 9/03, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. Kalb, G. and R. Scutella (2003), Wage and Employment Rates in New Zealand from 1991 to 2001. New Zealand Treasury Working Paper 03/13, New Zealand Treasury, Wellington. Keane, M. and R. Moffitt (1998). A Structural Model of Multiple Welfare Program Participation and Labor Supply. International Economic Review, 39(3), 553-589. Killingsworth, M.R. (1983). Labor Supply. New York: Cambridge University Press. Laisney, F., M. Lechner, A. van Soest and G. Wagenhals (1992). A life cycle labour supply model with taxes estimated on German panel data: the case of parallel preferences. Discussion Paper no. 93-01, Zentrum für Europäische Wirtschaftsforschung GmbH, Labour Economics and Human Resources Series. Maddala, G.S. (1983). Limited Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press. Maloney, T. (2000). The impact of welfare reform on labour supply behaviour in New Zealand. Labour Economics, 7, 427-448. Moffitt, R. (1986). The econometrics of piecewise-linear budget constraints: a survey and exposition of the maximum likelihood method. Journal of Business and Economic Statistics, 4(3), 317-328.  (1990). Taxation and Labor Supply in Industrial Countries. Journal of Human Resources, 25(3), 313-558. Murray, J. (1996). Modelling the labour supply behaviour of sole parents in Australia. In M. McAleer, P.W. Miller and C. Ong, Proceedings of The Econometric Society Australasian Meeting 1996, 4: Microeconometrics. Perth: University of Western Australia, 507-546. Nolan, P. (2002). New Zealand’s Family Assistance Tax Credits: Evolution and Operation. New Zealand Treasury Working Paper 02/16, New Zealand Treasury, Wellington. Ross, R.T. (1986). Analysis of the 1980 Sydney Survey of Work Patterns of Married Women: further results. Economic Record, 62, 325-337. Tummers, M. and I. Woittiez (1991) A simultaneous wage and labour supply model with hours restriction. Journal of Human Resources, 26, 393-423. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 33 Van Soest, A. (1995). Structural models of family labor supply; a discrete choice approach. Journal of Human Resources, 30(1), 63-88. Van Soest, A., M. Das and X. Gong (2002). A structural labour supply model with flexible preferences. Journal of Econometrics, 107, 345-374. Van Soest, A., A. Kapteyn and P. Kooreman (1993). Coherency and regularity of demand systems with equality and inequality constraints. Journal of Econometrics, 57, 161188. Van Soest, A., I. Woittiez and A. Kapteyn (1990) Labor supply, income taxes, and hours restrictions in the Netherlands. The Journal of Human Resources, 25, 517-558. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 34 Appendix Table A.1 – Minimum wage rates between 1991 and 2001 Time period minimum wage in $/hour for those 20 years of age and over under 20 years of age 1991 to April 1994 6.125 n.a. April 1994 to April 1995 6.125 3.680 April 1995 to April 1996 6.250 3.750 April 1996 to April 1997 6.375 3.825 April 1997 to April 2000 7.000 4.200 April 2000 to April 2001 7.550 4.550 18 years of age and over under 18 years of age April 2001 to April 2002 7.700 5.400 WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 35 Table A.2 – Models for couples with alternative fixed cost of workinga,b Estimated coefficient z-valuec Quadratic terms income× 100,000 -0.0127 -3.70 Labour supply husband × 100 -0.1298 -22.61 Labour supply wife × 100 -0.3199 -17.80 Crossproduct Inc. & lab. Sup. Husband × 10,000 -0.2143 -10.94 Inc. & lab. Sup. Wife × 10,000 -0.2956 -14.45 labour supply Husband & wife × 100 -0.0170 -2.34 Linear terms Income × 100 constant 0.5324 28.52 Number of children -0.0161 -6.88 Labour supply husband constant -0.0319 -2.59 Youngest child <1 yr old 0.0042 1.42 Youngest child 1-3 yrs old 0.0039 1.56 Youngest child 4-5 yrs old 0.0002 0.06 Youngest child 6-9 yrs old 0.0026 0.98 Number of children 0.0006 0.86 Age/10 0.0483 9.04 Age squared/100 -0.0066 -10.13 Vocational education 0.0163 9.41 Certificate 0.0122 5.91 Bursary/scholarship 0.0129 4.38 Postgraduate degree/other 0.0124 2.45 Bachelor degree 0.0174 5.92 Postgraduate 0.0200 4.39 Vocational education (partner) 0.0018 0.88 Certificate (partner) 0.0076 4.10 Bursary/scholarship (partner) 0.0108 4.32 Postgraduate degree/other (partner) 0.0018 0.34 Bachelor degree (partner) 0.0009 0.28 Postgraduate (partner) -0.0157 -3.17 Time trend 0.0009 2.10 Unemployment rate -0.0016 -2.81 Aged 60 or over -0.0077 -2.08 Eligible for New Zealand Superannuation -0.0227 -4.97 Partner is eligible for New Zealand Superannuation -0.0104 -1.78 Labour supply wife constant 0.1723 9.17 Youngest child <1 yr old -0.0796 -25.36 Youngest child 1-3 yrs old -0.0608 -25.44 Youngest child 4-5 yrs old -0.0439 -14.33 Youngest child 6-9 yrs old -0.0247 -9.71 Number of children -0.0094 -9.64 Age/10 0.0418 7.78 Age squared/100 -0.0068 -9.91 Vocational education 0.0211 10.80 Certificate 0.0138 7.35 Bursary/scholarship 0.0171 7.03 Postgraduate degree/other 0.0289 6.03 Bachelor degree 0.0316 11.29 Postgraduate 0.0440 9.97 Vocational education (partner) -0.0073 -4.11 Certificate (partner) -0.0032 -1.47 Bursary/scholarship (partner) -0.0028 -1.04 Postgraduate degree/other (partner) -0.0112 -2.30 Bachelor degree (partner) -0.0168 -6.33 Postgraduate (partner) -0.0198 -5.39 Table A.2 – Continued a,b WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 36 Estimated coefficient z-valuec Time trend 0.0006 1.44 Unemployment rate -0.0009 -1.22 Aged 60 or over -0.0027 -0.48 Eligible for New Zealand Superannuation -0.0254 -2.72 Partner is eligible for New Zealand Superannuation -0.0034 -0.88 Fixed cost husband/100 0-10 hours 7.2060 22.01 11-20 hours 7.5002 22.43 21-30 hours 7.6978 23.47 Fixed cost wife/100 0-10 hours 9.3387 22.87 11-20 hours 11.8440 19.43 21-30 hours 13.9671 17.84 >30 hours 13.0489 15.28 Log likelihood -29542 a Six discrete points of labour supply are distinguished for each man: 0 hours for nonparticipants and people working less than 2.5 hours, 10 hours for people working from 2.5 to 15 hours, 20 hours for people working from 15 to 25 hours, 30 hours for people working from 25 to 35 hours, 40 hours for people working from 35 to 45 hours, and 50 hours for people working more than 45 hours. Eleven discrete points of labour supply are distinguished for each woman: 0 hours for non-participants and people working less than 2.5 hours, 5 hours for people working from 2.5 to 7.5 hours, 10 hours for people working from 7.5 to 12.5 hours, 15 hours for people working from 12.5 to 17.5 hours, 20 hours for people working from 17.5 to 22.5 hours, 25 hours for people working from 22.5 to 27.5 hours, 30 hours for people working from 27.5 to 32.5 hours, 35 hours for people working from 32.5 to 37.5 hours, 40 hours for people working from 37.5 to 42.5 hours, 45 hours for people working from 42.5 to 47.5 hours, and 50 hours for people working more than 47.5 hours. b This specification does not include unobserved heterogeneity terms, because no convergence took place, with the heterogeneity terms remaining at their starting values and the other parameters at the values estimated without the unobserved heterogeneity term. c The z-value indicates the level of significance of the estimated coefficients. A value of 1.96 or more means that the parameter is significantly different from zero at the 5% level at least. The higher the z-value the more precise the estimated coefficient. WP 03/23 | NZ LABOUR SUPPLY FROM 1991-2001: AN ANALYSIS BASED ON A DISCRETE CHOICE STRUCTURAL UTILITY MODEL 37 Table A.3 – Models for singles and sole parents with alternative fixed cost of working Single men Single women Sole parents Estimated coefficient z-valueb Estimated coefficient z-valueb Estimated coefficient z-valueb Quadratic terms Income × 100,000 -0.1241 -3.55 -0.2948 -4.96 -0.0505 -1.66 Labour supply × 100 -0.8778 -12.02 -0.6814 -11.81 -0.2794 -4.74 Cross product Inc. & lab. sup. × 10,000 -1.6333 -9.73 -1.8331 -8.67 -0.5342 -2.69 Linear terms Income × 100 constant 0.9509 7.42 1.5547 9.62 0.5902 2.97 Youngest child <1 yr 0.1221 1.92 Youngest child 1-3 yrs old 0.0514 1.70 Youngest child 4-5 yrs old 0.0030 0.13 Youngest child 6-9 yrs old -0.0201 -1.17 Number of children 0.0138 1.60 Age/10 0.1430 2.67 0.0568 0.76 -0.0973 -1.61 Age squared/100 -0.0118 -1.61 -0.0052 -0.54 0.0120 1.55 Vocational education -0.0469 -1.74 -0.0204 -0.49 -0.0570 -2.33 Certificate -0.0542 -2.14 -0.0324 -0.80 -0.0516 -2.33 Bursary/scholarship -0.1022 -3.83 -0.0883 -2.08 -0.0102 -0.44 Postgraduate degree/other -0.1611 -2.99 0.0758 0.90 -0.0177 -0.45 Bachelor degree -0.0423 -1.13 0.1971 3.19 0.0602 1.59 Postgraduate 0.0528 0.83 0.3318 3.31 0.0487 0.92 Live with parents 0.0352 4.38 0.0682 3.20 female -0.1629 -3.71 Labour supply constant 0.4866 9.07 0.3600 8.65 0.2089 2.83 Youngest child <1 yr -0.0117 -0.43 Youngest child 1-3 yrs old -0.0213 -1.72 Youngest child 4-5 yrs old -0.0398 -3.39 Youngest child 6-9 yrs old -0.0357 -4.18 Number of children 0.0025 0.61 Age/10 0.0487 3.44 0.0336 3.39 -0.0071 -0.22 Age squared/100 -0.0056 -2.91 -0.0053 -4.12 0.0005 0.12 Vocational education 0.0109 1.59 0.0236 4.45 0.0117 1.37 Certificate 0.0052 0.79 0.0167 3.26 -0.0068 -0.73 Bursary/scholarship -0.0100 -1.46 0.0190 3.57 0.0283 2.50 Postgraduate degree/other -0.0220 -1.61 0.0317 3.28 0.0317 1.69 Bachelor degree 0.0020 0.21 0.0453 6.06 0.0702 4.74 Postgraduate 0.0206 1.39 0.0586 4.79 0.0610 2.55 female -0.0836 -5.22 Time trend 0.0000 -0.03 -0.0001 -0.19 0.0018 1.84 Unemployment rate -0.0013 -1.78 -0.0011 -0.99 0.0003 0.21 Aged over 60 -0.0153 -1.82 -0.0204 -2.37 -0.0261 -0.46 Eligible for NZ superannuation -0.0339 -2.51 -0.0259 -2.37 -0.1545 -2.09 Live with parents 0.0085 1.28 Fixed costs/100 0-10 hours 7.5338 12.98 4.1489 12.91 13.4319 3.19 11-20 hours 11.2123 12.04 5.8588 11.78 17.7789 3.16 21-30 hours 14.1347 12.22 7.1534 11.54 21.3914 3.09 >30 hours 13.7870 11.56 6.8353 10.58 20.2658 3.00