EUROPEAN

ELSEVIER European Economic Review 41 (1997) 619-626

Behavioural tax microsimulation with finite hours choices

Alan Duncan aYb, Melvyn Weeks ’ a University of York, Heslington, York YOl SDD, UK

b Institute for Fiscal Studies, 7 Ridgmount Street, London, WClE 7AE, UK ’ Department of Applied Economics, Sidgwick Avenue, Cambridge CB3 9DE, UK

Abstract

It is often argued that institutional factors constrain the labour supply choices open to the individual. In this paper we present an alternative to the standard neoclassical model of labour supply under the presumption that the number of hours choices are discrete and finite. We explore alternative specifications of discrete models of labour supply which are appropriate for the microsimulation of the behavioural impact of tax policy reform. Policy simulations are carried out for a basic income reform. 0 1997 Elsevier Science B.V.

.ZEL classification: C15; C35; D12; H31; J22

Keywords: Tax microsimulation; Labour supply; Simulation-based estimators

1. Introduction

Microsimulation studies of the impact of tax and benefit reform have become increasingly common in the literature. With the advent of detailed tax microsimu-

lation programs based on large and representative samples of micro data, it has been possible to examine both the distributional consequences of a reform, and the likely net cost of the reform on the Government’s finances. It is rare, however, for such tax microsimulation models to be behavioural, and to admit the possibility that a given reform to either the tax or benefit system might alter labour market behaviour. There are some reforms for which such a restriction is clearly not appropriate. Many reforms to the tax and benefit system are designed specifically

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620 A. Duncan, M. Weeks/ European Economic Review 41 (1997) 619-626

to affect work incentives. Indeed, the use of in-work benefits as an incentive to

enter the labour market has attracted considerable policy attention in the United Kingdom. As many as three structural reforms to Family Credit (the UK system of

in-work benefit) have been introduced since 1988, all of which have as their specific motivation the desire to make part-time work relatively more attractive to low-earning or non-working individuals. ’

Perhaps for this reason, there has been a resurgence in microsimulation studies

which include a behavioural labour supply component. The behavioural models

which underpin such studies derive from the standard neoclassical approach in which hours of work are presumed to be continuous. However, empirical evidence suggests that even this assumption may not be sustainable.

In this paper we examine broad patterns of labour supply behaviour among married women in the UK, paying particular attention to the presence of institu-

tional constraints on hours which stop individuals working at the level they might choose to if unconstrained. We compare a range of discrete choice specifications of labour supply behaviour, with particular focus on probit and logit based multinomial models. We consider how such models might be adapted for use in behavioural tax microsimulation. Finally, we simulate the likely behavioural impact of a hypothetical basic income reform to the UK tax and benefit system of

the form discussed in Callan and Sutherland (1996).

2. Labour supply as a problem of discrete choice

The premise behind the neoclassical model of labour supply is that the decision variable, hours of work, is continuous and unconstrained. However, in a number of recent studies (Van Soest (19951, Bingley and Walker (1995) among others) analysts have begun to examine policy issues using labour supply models based on a more realistic discretised budget set. The reasons are threefold:

First, a model which allows for a continuous substitution of hours for leisure is not realistic in the presence of institutional constraints which restrict the number of

available wage/hours contracts. Empirical evidence suggests that, for many socio-demographic groups, labour force participation is restricted to a choice between part-time work at around 20 hours per week and full-time contracts of 38 to 40 hours per week. It therefore seems more appropriate to view observed labour supply as the outcome of a discrete choice which allows for substitution across discrete regimes, but not within.

Second, discrete choice models of labour supply require knowledge of the budget constraint at a finite range of hours points rather than over the continuum of hours. As a result the treatment of taxes becomes simpler.

’ See Duncan and Giles (1996) for a discussion of the evolution of Family Credit (FC) in the UK.

A. Duncan, M. Weeks/ European Economic Review 41 (1997) 619-626 621

Third, the imposition of statistical coherency conditions ’ on discrete choice models of labour supply are less likely to constrain the underlying economic model, due simply to the fact that individuals optimise to a range of hours rather than to an exact hours level. The requirements of statistical coherency in the context of discrete choice models of labour supply demand that the overall probabilities (of working to a range of hours) are non-negative. As such, there is less likelihood that the estimated parameters of the discrete choice model will be forced into constrained regions of the sample space.

3. A multinomial model of labour force status

We choose to follow Duncan and Giles (1996) in examining the discrete labour market behaviour of married women in the UK. Our choice of a discrete model of labour supply stems from the presumption that women select themselves into three regimes: labour market non-participation, part-time employment of between 0 and 30 hours per week, and full-time employment in excess of 30 hours. To date, discrete choice studies of this form have chosen a logit specification for reasons of ease of estimation. In our study we take advantage of recent developments simulation-based estimation techniques to compare such models with a number alternative specifications, focussing in particular on the stochastic component choice. 3

3.1. Model specification

In our model specification we consider the utilities yj* to be enjoyed in each J labour market states. The utility for state j may be written

y; =(Yj+xjp+e,‘u+Ej, j=l,..., J, (

in of of

of

‘1

where xj represents a (K X 1) vector of state-specific attributes of choice, u represents a (TX 1) vector of state-inuariant attributes of choice, and ej is a disturbance term. The coefficients (yi, p and ej are, respectively, (1 X l), (K X 1) and (TX 1) vectors of unknown parameters. For our labour supply model, xj comprises total income (net of all taxes and including any state benefits) specific to each of the J labour market states. The vector v includes socio-demographic characteristics (age, education, numbers and ages of children, marital status) and wage rates (which we assume to remain constant across labour market state).

By assuming the parameter p in Eq. (1) to be invariant with respect to labour

2 See Gourieroux et al. (1981). 3 See Weeks (1996a).

622 A. Duncan, M. Weeks/European Economic Ret&w 41 (1997) 619-626

force state, we effectively impose an assumption of constant marginal utility of

income. This we term a constant-attribute variant of the model. While this assumption is common in the literature, the empirical justification is unclear. We also estimate a variable-attribute variant of the model in which the parameter p is

allowed to vary across states.

Collecting utilities across the J states, we may write Eq. (1) compactly for each individual i = 1 ,...,Ninoursampleas

yi* =cu+xip+Buj+ei, i=l,..., N, (2)

where the distribution of the (J X 1) vector of disturbances l i is known up to a set of unknown variance and covariance parameters. In relating the vector of unob-

served utilities y * to a set of observed outcomes y, we assume that the ith individual maximises utility by choosing outcome j according to the rule

y,; =argmax(yi;), k= l,..., J. (3)

3.2. Stochastic specification

A distinguishing characteristic of our study lies in the nature of the distribu- tional assumptions we make for the stochastic components of Eq. (2). Turning first to the additive random component of choice, we consider a variety of specifica- tions. The first mirrors the typical specification of error structures in studies of this kind, and assumes that E is distributed as Type 1 extreme value, to give the standard Multinomial Logit (MNL) model of discrete choice. The second assumes

that the components of E are normally and independently distributed, giving the Independent Multinomial Probit (IMNP) model. Finally, we assume u is dis- tributed as a multivariate normal with an arbitrary covariance structure, leading to the Multinomial Probit model (MNP).

Taking the MNL as the reference model, we adopt a non-nested testing framework to compare alternative specifications for the distribution of E, extend-

ing recent work by Pesaran and Pesaran (1993) and Weeks (1996b) by applying a variant of Cox’s non-nested test to compare two competing discrete choice models. When the reference model is IMNP, classical tests are sufficient to test for more general and flexible error structures. 4

We also allow for the existence of random taste variation in the choice model, to acknowledge the fact that individuals who face the same set of alternative specific attributes may exhibit variation in behaviour. We can isolate these two stochastic components by decomposing Eq. (2) into

yi” =a+xi( p+&*) + 8vi+ui, i= I,..., N, (4)

4 A more detailed discussion of the stochastic components of choice and the appropriate testing

strategy can be found in Duncan and Weeks (1997).

A. Duncan, M. Weeks/European Economic Reuiew 41 (1997) 619-626 623

where ui = ei - xi pi*. If pi* is fixed across i then individuals are characterised as having identical tastes with regard to the observed state-specific attributes of choice. Placing a distribution on pi* leads to a model which allows for random unobserved taste variation.

3.3. Identification of parameters

The key issue in parameter identification for models of discrete choice is the appropriate normalisation to use. The necessity to normalise stems from the fact that we learn about the underlying utilities of choice alternatives only through observing discrete choices, which are themselves functions of d@erences in utilities. The identification condition for a discrete model specified in terms of differences is that, for a J-dimensional choice problem, only J - 1 mean equation parameters are formally identified for each regressor.

Similar restrictions are required for any covariance parameters included in the model specification, as would be the case, for example, with the MNP model with full covariance structure. As in the case of mean equation parameters, the explanation stems from the fact that the original J-dimensional MNP may be expressed in terms a (J - ll-dimensional problem based upon utility differences. Subsequently we see that in the differenced model there exist J(J - 1)/2 free covariance parameters. 5

Hence, in the trinomial model of labour force status there are two free parameters. In our study we allow one free parameter which represents the contemporaneous correlation of omitted attributes and individual characteristics for the part-time and full-time states.

4. An application

We choose for our empirical application the labour supply behaviour of a sample of married women drawn from the 1993 Family Expenditure Survey @ES), a data source which contains information on the labour supply, consump- tion decisions and socio-demographic make-up of around 8600 households. For this study we select a sample of 1971 women with employed partners.

To generate state-specific net incomes as conditioning variables for the struc- tural discrete choice mode, we simulate tax liabilities, benefit receipts and total net incomes at 0, 20 and 40 hours for each member of the sample using the tax

5 In fact, there are only J( J - 1)/2 - 1 free parameters. We need to further restrict by 1 the number

of free parameters in order to adjust for a scale effect which, if uncorrected, would leave a situation

where a proportionate change in all mean equation parameters and covariance terms would alter the

estimated probabilities of the multinomial model. Weeks (1996a) provides a full discussion of these

issues.

624 A. Duncan, M. Weeks/European Economic Reuiew 41 (1997) 619-626

microsimulation model EBOR-TAX. For those in the FES whose wages are not observed, we base our calculations on a predicted wage. 6

4.1. Estimation results

Our discussion of the theoretical discrete choice model of labour supply suggests a wide range of model specifications. We consider combinations which take account of random taste variation feeding through the income parameter (termed the heterogeneous preference variant), which vary the income parameter across labour market state (the uariabZe attribute variant), and which admit the possibility of an arbitrary covariance structure to the normally distributed additive disturbance term (giving a full multinomial probit specification).

A full discussion of the results of these variants (10 in all) is beyond the scope of this paper. 7

However, our main finding is that the full MNF’ with heterogeneous prefer- ences, contemporaneous correlation and variable attributes is most acceptable to the data we use. Our conclusion is arrived at from pairwise statistical comparisons using either Cox’s non-nested or classical nested tests.

The empirical results from the most preferred MNP specification are broadly in line with earlier work, and indicate a strong positive wage effect for each in-work labour market state (relative to not working). Controlling for wage rates, we also estimate that increases in net income available in each labour market state have significant positive effects on predicted state probabilities. However, the assump- tion of constant marginal utility of income across labour market state was conclusively rejected (p = 0.000).

4.2. Microsimulation results

In demonstrating the relevance of our estimated model for behavioural tax microsimulation, we simulate a hypothetical reform to the UK tax and benefit system which replaces all in-work and social assistance benefits with a basic income guarantee (set at the level of social assistance for a single person with additions for children). Tax allowances and social insurance contributions are abolished, and the graduated income tax rate structure is replaced by a single flat rate. The approximate revenue-neutral rate in the absence of any behavioural response is calculated at 40.7%, similar to Callan and Sutherland (1996).

A behavioural simulation of the impact of this reform is generated by adjusting the incomes for each individual in our sample to take account of the new basic

6 Full wage equation estimates available from the authors on request.

’ The interested reader is referred to Duncan and Weeks (1997).

A. Duncan, M. Weeks/ European Economic Review 4X(1997) 619-626 625

Table 1

Simulated transitions in labour market state a

Pre-reform status

Post-reform status

Non-work Part-time Full-time Total

Non-work 149 1 0 150

Part-time 17 719 35 771

Full-time 9 29 561 599

Total 175 749 596 1520

a Simulations based on full variable attribute multinomial probit model with heterogeneous preferences

and contemporaneous correlation.

income structure. Adjustments are again calculated using a detailed tax-benefit model. By feeding these post-reform simulated incomes back into the estimated model of labour force status, we compare predicted probabilities for each state under the basic income system with the original predictions from the estimated model. By assigning each individual to their most probable state, we are able to build the matrix of simulated transitions described in Table 1.

It is immediately clear that the incentive effects of the basic income reform are mixed. The majority of simulated transitions are negative, and mainly relate to households not currently on benefits for whom the basic income represents an absolute state-invariant increase in net income. The predicted negative response is therefore a pure income effect. However, we also predict significant increases in labour supply. These responses belong typically to lower-earning households for whom part-time work becomes relatively less attractive as in-work benefits are abolished and replaced by the basic income. Whilst some such individuals choose to reduce their labour supply (17 in our sample), more (35 from Table 1) seek to compensate for the loss in income by moving to full-time employment.

5. Conclusions

We have demonstrated that in the estimation of discrete choice models of labour force state the stochastic component has important ramifications in terms of model adequacy. In a series of nested and non-nested tests, i.i.d. logit and probit models were rejected in favour of more general multinomial probit variants. We highlight the usefulness of our approach by simulating behavior& responses to a hypothetical basic income reform.

In future work we intend to develop discrete choice models of labour supply which extend to more than three labour force states, to improve the accuracy of simulating behavioural responses and costing policy reforms.

626 A. Duncan, M. Weeks/European Economic Review 41(1997) 619-626

Acknowledgements

The authors would like to thank Hashem Pesaran, Holly Sutherland and Chris Giles for helpful comments. Anonymised Family Expenditure Survey data were supplied by the Central Statistical Office, which bears no responsibility for their subsequent interpretation. The FES is Crown Copyright 1995.

References

Bingley, P. and I. Walker, 199.5, Labour supply, unemployment and participation in in-work transfer

programmes, Working paper W95/16 (Institute for Fiscal Studies, London).

Callan, T. and H. Sutherland, 1996, The impact of comparable policies in Europe: A microsimulation

approach, European Economic Review (this issue).

Duncan, A. and C. Giles, 1996, Labour supply incentives and recent Family Credit reforms, Economic

Journal 106, 142-155.

Duncan, A. and M. Weeks, 1997, Testing models of labour supply with finite hours choices,

Discussion paper 97/9 (University of York, York).

Gourieroux, C., J.-J. Laffont and A. Montfort, 1981, Coherency conditions in simultaneous linear

equation models with endogenous switching, Econometrica 48, 675-695.

Pesaran, M. and B. Pesaran, 1993, A simulation approach to the problem of computing Cox’s statistic

for testing non-nested models, Journal of Econometrics 57, 377-392.

Van Soest, A., 1995, Structural models of family labour supply, Journal of Human Resources 30,

63-83.

Weeks, M., 1996a, The multinomial probit model revisited: A discussion of parameter estimability,

identification and specification testing, Journal of Economic Surveys (forthcoming).

Weeks, M., 1996b, Testing binomial and multinomial choice models using Cox’s non-nested test,

American Statistical Association (papers and proceedings), 1995.