Household Labour Supply, Childcare Costs and Tax Credits

Transcription

1 Household Labour Supply, Childcare Costs and Tax Credits Richard Blundell Alan Duncan Julian MacCrae Costas Meghir This version: January 2000 Abstract The UK Government is planning to replace Family Credit, the existing system of in-work support for families with children, by a new tax credit, the Working Families Tax Credit (WFTC) to be paid directly through the income tax system. This tax credit includes a generous childcare tax credit component, making childcare more affordable to working households on low incomes. In this paper we model the impact of the WFTC on work incentives and on use of childcare services. Household labour supply is modelled as a discrete choice among a finite set of hours alternatives. Our estimation strategy control explicitly for fixed and child-related costs, and allows for random preference heterogeneity, state-specific errors in perception, and local variations in the provision and cost of childcare services. In simulation we find small positive behavioural responses in aggregate to the introduction of the new tax credit Paper prepared for the workshop, The Economics of Childcare, November 15th-16th 1999, held at IZA, Bonn, Germany. Acknowledgements: We are grateful to Tom Crossley, Andrew Dilnot, Jayne Taylor, and seminar participants at ANU, Cordoba, Essex, Manchester, Melbourne and Santiago for useful comments and suggestions. The financial support of the ESRC Centre for the Micro-Economic Analysis of Fiscal Policy at IFS is gratefully acknowledged. The usual disclaimer applies. Contact: Alan Duncan, School of Economics, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom. Tel: +44 (0) alan.duncan@nottingham.ac.uk. URL: University College London and Institute for Fiscal Studies University of Nottingham and Institute for Fiscal Studies Institute for Fiscal Studies University College London and Institute for Fiscal Studies 1

2 1 Introduction and Background From April 2000 the UK will introduce a new Working Families Tax Credit (WFTC) as a replacement for Family Credit (FC), the UK s main in-work benefit. The structure of the WFTC reform is modelled closely on the existing FC system, with the exception that the WFTC is to be packaged as a refundable tax credit, rather than as a welfare benefit. The WFTC is intended to improve work incentives for families by making work pay. This is to be achieved by boosting the in-work incomes available to families with children in low wage jobs. Most of the extra resources are delivered by reducing the benefit reduction rate of the WFTC to 55%, down from the 70% taper found in FC. Additionally, the WFTC contains generous provision for the subsidy of childcare costs. The aim of this paper is to consider the effects on the labour market of the Working Families Tax Credit reform. In particular, we aim to study the impact of WFTC on hours of work and participation. Since this is a policy reform that is to be implemented in the future, an ex-ante evaluation is all that is available. Consequently, our analysis will rely on a structural simulation model of the type used in the work by Hoynes (1996) and?. However, as we document below, this is not the first in-work benefit reform in the UK and past reforms to the system will be used to assess the reliability of the model specification. Such ex-post evaluations are close in spirit to the difference-in-differences or natural experiment evaluation of reforms (see Eissa and Liebman (1996), for example). The difference-in-difference parameter will also have an interpretation within a structural model, although it is unlikely to relate directly to any specific preference parameter. One (eventual) aim of this paper is to use the history of the FC reforms in the UK to build a bridge between these evaluation methods and more structural approaches that are necessary for any ex-ante policy reform evaulation of the kind described here. There are effectively two target groups for the WFTC reform: single parents and married couples with children. Nearly 50% of currently working single parents are in receipt of some FC. For married couples with children this proportion is smaller, at around 16%. However, the latter group is more than two and half times the size of the former. The behaviour of both of these groups, and their economic circumstances, are sufficiently different to warrant a separate analysis. Consequently, we provide results for each group separately. A reasonable evaluation of such a reform requires three compenents: Firstly, a sample with a sufficiently large number from each of these two target groups. For this we use the UK Family Resources Survey (FRS) which covers almost 50,000 2

3 individuals per year. Secondly, sufficient detailed information on each household so as to reliably construct their net incomes under the FC and WFTC systems. For this we have implemented the Institute for Fiscal Studies tax and benefit simulation model, TAXBEN, on the FRS data. Finally, we need a behavioural model that can reasonably predict changes in labour supply resulting from the reforms to the welfare system. In this respect we have built an econometric model of work behaviour for lone parents and for couples with children that is implemented on the FRS data. This model is evaluated against the previous reforms to FC that have occured since its intorduction in These three requirements and the way they are developed to address the impact of WFTC are discussed in more detail below. However, it is worth pointing out two other key features of our simulations. Firstly, we construct the full budget constraint facing each individual in a family. This accounts for different levels of tax allowances and marginal tax rates as well as the detailed interactions of the benefit and WFTC systems. Secondly, we account for childcare costs and availability. This posed a particularly difficult challenge. Our approach is to assume that the reforms do not change the structure of the childcare market. The proportions choosing types and levels of childcare post-reform are determined by the pre-reform distribution of childcare. Consequently, we do not allow the childcare market to adapt to the introduction of WFTC. However, we do allow childcare usage to vary with hours worked and with the demographic composition of the household. We nevertheless recognise that the move to WFTC may impact on the childcare market in a manner which could have implications for the costs of the new program. The plan of the paper is as follows. We initially discuss the background and detail of the proposed Working Families Tax Credit, comparing the structure of WFTC with FC and the US EITC system. We go on in Section 3 to discuss the general structure of joint models of childcare demand and labour supply, with particular emphasis on the issue of identification in such models. In Section 4 we describe the basic structural discrete choice model, and how that model may be extended to control for childcare in estimation. Section 5 describes the empirical labour supply estimates, and Section 6 offers a prediction of the behavioural response to the WFTC. In Section 7 we offer some concluding remarks. 3

4 2 The New Working Families Tax Credit The fact that the UK Government has chosen to replace Family Credit seems initially surprising, since among means-tested benefits Family Credit is perhaps the most efficient at delivering well-targetted support. 1 So why alter a system which appears to be working well? There are three major problems perceived in the UK tax and benefit systemthat have motivated the proposed move from Family Credit to a tax credit system of in-work support: 1.Tax credits are associated with reduced stigmatisation of in-work state support. Those advocating the use of the tax system claim that giving benefits as part of an income tax refund would reduce the stigma associated with welfare receipt for those in work. If true, a reduction in stigma could encourage those people to enter employment who are presently discouraged because in work they still feel dependent on Government largesse. 2.Payment of benefit could be automatic. If employers administered an in-work tax credit, as in the UK income tax system, the Government could guarantee those who needed help would get it immediately and assistance would no longer depend on individuals having to make a claim for Family Credit. 3.Shifting in work support to the tax system could have presentational benefits. If there is public disquiet over the level of welfare spending, elements of state support disguised as a tax refund might be accepted more readily. In particular, increasing the generosity of the support could then be presented as a tax cut rather than an increase in Government spending. It is often cited that this has proved remarkably important in the US debate, even though the majority of EITC expenditure counts as public spending rather than tax foregone in the US and indeed in all countries public accounts. For these reasons, the UK government announced in the March 1998 budget that Family Credit was to be replaced by a new income tax credit to be known as the Working Families Tax Credit (WFTC). The WFTC 2 can be summarised as a more generousversionoffcwithanalteredmethodofpayment. Theimpactofthe structural change, as opposed to the increase in generosity, hinges on whether the re-branding of FC as a tax credit will have any impact on behaviour. 1 The fact that the structure of Family Credit has been altered to increase generosity three times in recent history is testimony to this contention. 2 full details of which can be found in HM Treasury (1998) 4

5 2.1 The Structure of FC and WFTC Family Credit is designed to provide support for low wage families with children who are working. Once someone in a family with children works more than 16 hours a week, they become eligible for FC. Each family is potentially eligible to a maximum amount, depending on the number of children in the household and a small addition if they work full time. Currently, the maximum level of FC comprises a weekly adult credit of and child credits starting at per child for children under 11. This maximum amount is payable if the family s net income (after income tax and National Insurance Contributions) is lower than a threshold ( per week in ). Net income in excess of this threshold reduces entitlement to FC from the maximum by 70p for every 1 of excess income. Family Credit is payable on a six monthly flat rate regardless of changes in the claimants circumstances in order to minimise administrative and compliance costs and to hide the effects of the high withdrawal rate over the period of the fixedpayment. TakeupofFCafter its introduction in 1988 was initially low but has increased. The present estimated take-up rates are 69% of recipients and 82% of potential expenditure. The WFTC will be substantially more generous than FC. By the end of the century, the government expects to be spending 5bn per year on the WFTC, which is 1.5bn more than was expected under FC. The WFTC will increase the generosity of in-work support relative to the FC system in three ways 1.an increase in the credit for children under 11 from to per child 2.an increase in the threshold from 79 to 90 per week 3.a reduction in the taper from 70% to 55% 4.a childcare tax credit of up to 105 per week for those who pay for some form of formal childcare. A stylised comparison of the structure of WFTC with FC is shown in Figures 1 and 2. Those currently receiving the maximum payment see a small increase in the level of their payment if they have children under 11. Those with net incomes between 79 and 90 move from being on the taper to receiving maximum support. The others on the taper see the taper rate fall from 70% to 55%. The largest cash gains go to those people who are currently just at the end of the taper. The increased generosity of in work support also creates new entitlement to in work support. We also include in 1 the structure of the US Earned Income Tax Credit (EITC) system, in which payments to families under the American earned income tax credit 5

6 Figure 1: Alternative Structures of In-Work Support Family Credit/WFTC Hours of work WFTC with childcare WFTC Family Credit are related to the number of children and the annual level of earned income of the family. For a family with two or more children, the credit is phased in at a rate of 40c per $ over the first $8890 ( 5,454) of earnings reaching a maximum payment of $3556 ( 2,182). The credit remains level at this rate until earned income rises to $11,610 ( 7,123). From this point onward the EITC is reduced at a rate just over 21c per $ until the family is no longer eligible. Whilst families earning less than this amount, $28,495 ( 17,481) will still pay income tax throughout the year, they receive a EITC as a tax refund at year end. This comparison is instructive in a number of ways. First, note how much more generous is the WFTC relative to FC. The combination of a larger credit (particularly for those taking advantage of the childcare credit), a higher applicable amount and a lower withdrawal rate suggests that a significant number of households who were not eligible for FC will be entitled to receive WFTC. This is likely to have two major effects - the direct redistribution through transfer payments and an alteration in labour supply incentives. Previous research has shown that in most cases the distributional effect of a reform is by far the most important. 3 For workless families, the WFTC will unambiguously increase the financial returns to working. It lowers some of the highest marginal tax rates, but only to levels just below 70%. Others will become entitled to the WFTC and will therefore see their marginal tax rates increase substantially. Notice also the difference between WFTC and EITC. The US credit 3 see Duncan and Giles (1996). 6

7 Figure 2: Example budget constraint: one-parent household Family disposable income ( p.w.) Hours of work WFTC Family Credit extends over a much broader hours range down to the point of nonparticipation, but is less generous at the maximum level. To reproduce the EITC structure at maximum generosity levels close to WFTC would be prohibitively expensive. 3 Childcare and Labour Supply: some theoretical issues 3.1 Identification Although the literature on childcare demand and labour supply is wide, the number and strength of assumptions underpinning many empirical models are not always clear. In fact, many assumptions which are typically made for empirical feasibility or through limited data availability actually serve as identifying assumptions in the estimated model. We lay out in this section a theoretical framework with which to analyse issues of identification in the modelling of childcare and labour supply. The particular specification we use involves a slight modification of standard theoretical models presented in the literature. 7

8 3.2 A theoretical framework Let us start with a typical set of preferences U defined over consumption c and full leisure l 4 1, but augmented to include a measure Q of child quality among the arguments. This is a familiar starting point in much of the existing literature, as evidenced for example in work by Ribar (1991), Connolly (1991), Hotz and Kilburn (1991) and Blau and Robins (1988). Let these preferences be written as U = U(c, l 1,Q), (1) with Uc 0 > 0, Ul 0 1 > 0 and UQ 0 > 0. The child quality index Q may be interpreted as some production function for child quality, with inputs of maternal childcare l, formal (external) childcare H, and the quality q of the formal care used. Consider the following general form for child quality; Q = F (l,h,q), (2) with F 0 l > 0, F 0 H > 0 and F 0 q > Let us now suppose that expenditure e on formal childcare may be given by e = phq, (3) where p represents the price per unit of childcare of standard quality (that is, formal care with quality q =1). Turn now to the constraints on the use of time. We consider first the mother, for whom the full time endowment T is shared between employment h and non-work time according to T = h + l +(l 1 l ). (T1) So, the mother s time away from work (that is, l 1 ) is shared between maternal childcare (l ) and non-childcare (l 1 l ) time. We require l 1 l 0 (or alternatively H h), with equality when the mother devotes the entirity of her non-work time to maternal care. This alternatively requires that A second time constraint centres on the formal care requirement for the child. Specifically, we require that H = h +(l 1 l ). (T2) 4 by which we mean all time spent by the mother away from employment. 5 Note however that this does not imply an unambiguous sign for Q/ H. Given some relationship l = g(h) between maternal and formal care, with g 0 < 0, this full derivative becomes Q/ H = FH 0 + g0.fl

9 That is, the amount of care required for the child is the sum of the mother s time at work and any non-work time not spent in childcare. A third time constraint requires that the child is always in someone s care, such that T = H + l. That is to say, the sum of formal and maternal care exhausts the child s time endowment. However, this constraint is naturally implied by a combination of (T1) and (T2). Turning to the budget constraint facing the mother, we have that takes the following general form; wh + τ + v = c + qhp (BC) where τ = T (h, w, v) represents tax payments minus benefit receipts, assumed to depend on the hours of work, gross wages w and unearned income v. The price of consumption is normalised to unity The optimisation problem The optimisation problem facing the mother involves the maximisation of preferences (8) subject to a number of constraints. Noting that U = U[c, l 1,F(l,H,q)] = U[c, l 1,F(h + l 1 H, H, q)] from (T2) = u (c, T h, H, q) from (T1) (4) the full optimisation problem may be written max {c,h,h,q} u (c, T h, H, q) subjectto(bc)andh h (5) This program may be solved with reference to the following Lagrangian: L = u (c, T h, H, q)+λ.(wh + τ + v c qhp)+µ 1.(H h) (6) for which the general First-Order conditions are u λ c = 0; λ 0 (FOC1) u h + λw µ 1 = 0 (FOC2) u H λqp + µ 1 0; µ 1.[H h] =0; µ 1 0 (FOC3) u λph q = 0 (FOC4) 6 This notation remains consistent for a two-person household under the assumption that the male partner is a non-carer whose labour supply is taken as exogenous (in which case his earned income forms part of v). 9

10 together with (BC). One can consider solutions to this optimisation program under two regimes, the first of which restricts the second constraint in (4) to hold with equality. That is to say, the level of childcare required by the mother in a household is just sufficient to cover her time in employment Regime 1. Equality constrained optimisation Under this scenario, H = h (or l 1 = l ) which implies µ 1 > 0. The First Order conditions for this case become u λ c = 0; λ 0 (C1) u h + λw µ 1 = 0; (C2) u H λqp + µ 1 0; (C3) u λph q = 0, (C4) together with (BC). Combining (C2) and (C3) and substituting out for λ using (C1) gives a revised set of conditions µ u H u (pq w). u h c = 0; (C1 0 ) u q ph. u c = 0. (C2 0 ) So, the two conditions C1 0 to C2 0 imply three endogenous variables (q,h and c) with two exogenous instruments (p and w). The system is therefore identifiable in principle on the basis of data alone, without any further restrictions required on the form of preferences over consumption, leisure and child quality. The condition (C1 0 ) is of particular interest here, in that it clarifies just what is being identified in models of labour supply which do not control for childcare costs (and indeed benefits) in estimation. What (C1 0 ) demonstrates is that the marginal (dis)utility of hours may not be separated from the marginal utility of formal childcare in equilibrium without further restrictions on the form of preferences. When standard labour supply models are estimated with no controls for childcare costs, what is in fact identified is not the pure marginal disutility of hours; rather, it is this marginal disutility compensated by the marginal utility of childcare. Hence, even with monotonicity of preferences, the difference u u H h may be non-monotonic, leading to a bliss-point in the marginal preferences for (childcare conditioned hours of work. 10

11 3.3.2 Regime 2. Inequality constrained optimisation Under this scenario, H > h (or l 1 >l ) which implies µ 1 =0. The First Order conditions for this case become u λ c = 0; λ 0 (I1) u + λw h = 0; (I2) u λqp H = 0; (I3) u λph = 0, (I4) q along with (BC). The combination of (I2) and (I3) still give u u H h λ(pq w) = 0. However, the full set of conditions conditions (I1) to (I4) imply four endogenous variables (q, H, h and c) with the same two exogenous instruments (p and w). The system is therefore not identified without further restrictions on preferences, unless some information from Regime 1 can be brought to bear. One can see, for example, that we may combine (I2) and (I3) to give u h Á u H = w. Under an additional assumption of separability of q in (4), this leads to a relationship between q, H and h of the general pq form f(h) =g(h, q)+ε. (7) The imposition of a relationship of the form (7) would serve to identify the general economic model which underpins the optimisation program (4). We return to the issue of factoring controls for childcare expenditures into a fully structural model of labour market participation and hours following some discussion of a structural specification of labour supply appropriate to the simulation of actual or hypothetical childcare policy reforms. 4 A Discrete Choice Modelling Framework The traditional approach to the modelling of labour supply maintains that the decision variable, hours of work, is continuous and unconstrained. Utility is assumed to derive from net household income Y (shared between current and future consumption) and the leisure L = {L 1,L 2 } enjoyed by each individual in a two-person household. 7. Let these preferences be represented by U = U(Y,L 1,L 2 ; X), (8) 7 The simplifications necessary to model the labour supply behaviour of single person households are obvious, and covered in Duncan and Giles (1998). 11

12 where X represents characteristics for the household and each individual therein. Behavioural decisions are constrained to lie within a budget set defined in terms of the set of gross wage rates W = {W 1,W 2 } for each individual, total household income V from assets and other unearned sources, and the tax system. Let H k = T L k, k =1, 2 forsometimeendowmentt. Then the household budget set takes the following general form; Y = W 1 H 1 + W 2 H 2 + V T (H, W,V; X) FC 1 (Z 1 ) FC 2 (Z 2 ), (9) where T (H, W, V; X) represents tax payments minus benefit receipts, assumed to depend on the hours and wages of each household member, unearned income and household characteristics, and FC k (Z k ) represents the fixedcostofemploymentfor the kth individual with characteristics Z k. One may assume that households choose a point on the edge of their budget set, which ignores the potential to save for future consumption. Alternatively, one may replace income by current consumption expenditure (if data are available) to make the model consistent with a life-cycle behavioural pattern; see Blundell and Walker (1986). In the standard continuous model households are assumed to maximise (8) subject to (9) over a continuum of hours. That is, desired hours Hk for each household member stem from the solution to the following problem; max U (Y,T H 1,T H 2 ) s.t. Y {H 1,H 2 } 2X 2X W k H k +V T (H, W,V; X) FC k (Z k ). k=1 (10) The maximisation problem is not straightforward, however, because of the fundamentally non-linear character of the tax function T (.). What tends instead to happen insteadisthat(10)issolvedforaconstant marginal tax rate to recover parametric forms for the Marshallian labour supply functions for each household member. 8 The complexities of the tax schedule are then dealt with in estimation (see, for example, Hausman and Ruud (1984); Hausman (1985); Blundell, Duncan, and Meghir (1998)). However, in a number of recent studies analysts have begun to examine policy issues using labour supply models which are characterized by a more realistic discretized budget set. 9 There are a number of reasons for this. Firstly, analysts increasingly question whether a model which allows continuous substitution of hours 8 Note that this derivation ignores any element of jointness in the household labour supply decision. 9 See, for example, Bingley and Walker (1997); Duncan and Giles (1996); Duncan and Weeks (1997); Keane (1995);?; Van Van Soest (1995). 12 k=1

13 for leisure constitutes a realistic representation of the supply choices open to the individual. For many socio-demographic groups labour market participation takes the form of fixed wage-hours contracts, with individuals choosing from among a discrete set of hours combinations (most often at part-time levels of around 20 hours, and at full- time levels of between 38 and 40 hours per week). Secondly, there are statistical and practical reasons to favour a discrete approach to the modelling of labour supply in preference to more classical continuous models. These largely stem from the difficulties associated with the treatment of non-linear budget constraints in continuous estimation (see Gourieroux, Laffont, and Montfort (1980), and Blundell, Duncan, and Meghir (1992)). The strategy adopted in the discrete approach is to replace the entire household budget set with a finite number of points thereon, and optimise only over those discrete points. The procedure supposes that hours choices can be approximated by the discretized hours level H k(.) {H 1,H 2,..,H P } for individual k accordingtothe grouping rule H k(.) = H 1 if H k H B 1 = H 2 if H B 1 <H k H B 2... = H P 1 if HP B 2 <H k HP B 1 = H P if H k >HP B 1, giving P alternative values for H k(.). 10 Household net incomes may then be calculated for the set of discrete hours combinations H (.) ={H 1(.),H 2(.) }as Y [H (.) ]=Y [H 1(.),H 2(.) ]= 2X W k H k(.) +V T (H (.), W,V; X) for H 1(.),H 2(.) {H 1,H 2,.., H P } k=1 The household is assumed to maximise the following; max U Y [H 1(.),H 2(.) ],T H 1(.),T H 2(.) for H1(.),H 2(.) {H 1,H 2,..,H P } H 1(.),H 2(.) {H 1,H 2,..,H P } (11) This approach removes from the optimisation problem many of the complexities of a nonlinear tax schedule, but at the cost of introducing rounding errors in the hours 10 For example, a five-state labour supply regime for each household member might be described bythechoiceseth k(.) = {0, 10, 20, 30, 40} for k =1,.., K where H1 B =5,H2 B =15, H3 B =25, and H4 B =35. 13

14 levels used for estimation. The degree of aggregation may therefore have a potentially detrimental effect on the authenticity of the parameters estimated under a discrete regime, and ought at the very least to be subjected to sensitivity analysis. 4.1 a structural discrete model of labour supply and childcare choice To operationise the discrete model of household labour supply, we choose to model household preferences as a unitary quadratic direct utility function of household net income and individual labour supply (or equivalently, leisure time). Our estimation strategy allows both for random preference heterogeneity and state-specific errors in perception. Let U H(.) = U(Y H(.),T H 1(.),T H 2(.) ; X), for H k(.) {H 1,H 2,..,H P },k =1,.., K, (12) where the unified preference function now depends both on the (discrete) hours set H (.) ={H 1(.),H 2(.) } and household net income Y H(.) = Y [H 1(.),H 2(.) ].Comparedwith other discrete approaches, this method is parsimonious in its parameterisation and preserves the same preference structure over the whole range of hours. Random disturbances are added to utilities in each joint labour market state {H 1(.),H 2(.) } {H 1,H 2,.., H P } to give random utilities UH(.) = U(Y H(.),T H 1(.),T H 2(.) ; X)+ε H(.), (13) where each ε H(.) is assumed to be independently distributed as a Type I Extreme Value. The probability of choosing the labour market state for which H 1(.) = H j and H 2(.) = H k is therefore Pr[H 1(.) = H j,h 2(.) = H k )] = = Pr[U {H j,h k } >U {H p 1,H p 2} for all p 1 6= j, p 2 6= k, {p 1,p 2 } {1,.., P exp[u(y {H j,h k },T H j,t H k ; X)] P P p 1 =1 P P p 2 =1 exp[u(y {H p 1,H p 2 },T H p 1,T H p 2; X)]. (1 For our empirical analysis we choose the quadratic direct utility function favoured by?, where U(Y,H 1,H 2 φ) = α YY.Y 2 + α H1 H 1.H1 2 + α H2 H 2.H2 2 + α YH1.Y H 1 + α YH2.Y H 2 + α H1 H 2.H 1 H 2 +β Y.Y + β H1.H 1 + β H2.H 2 (15) for parameters φ =(α YY, α H1 H 1, α H2 H 2, α YH1, α YH2, α H1 H 2, β Y, β H1, β H2 )=(α, β). This function is tractible, yet permits a wide range of possible behavioural responses See Stern (1986) for an excellent discussion of the properties of this and other functions. 14

15 Observed heterogeneity is introduced linearly through parameters β =(β Y, β H1, β H2 ) 0.Specifically, β Y = β y0 + β 0 yx (16) β H1 = β 1 h0 + β 10 h X (17) β H2 = β 2 h0 + β 20 h X (18) The characteristics we include in the empirical estimates include dummies for the age of the youngest child, age, age squared and the age at which the woman left school. For the basic structural model, the likelihood contribution corresponding to (15) for parameters φ =(α, β) is `(φ X) = = PX j=1 k=1 PX j=1 k=1 PX d jk ln Pr[H 1(.) = H j,h 2(.) = H k ] PX d jk U(Y {H j,h k },T H j,t H k X, φ) (19) P P p 1 =1 P P p 2 =1 U(Y {H p 1,H p 2 },T H p 1,T H p 2 X, φ)] (20) where d jk = 1 H 1(.) = H j,h 2(.) = H k. 4.2 random preference heterogeneity To incorporate random preference heterogeneity we choose to randomise the linear utility parameters β =(β Y, β H1, β H2 ) 0 in (15), giving β Y = β Y + v Y (21) β H 1 = β H1 + v H1 (22) β H 2 = β H2 + v H2 (23) where v =(v Y,v H1,v H2 ) 0 are assumed jointly normal with covariance Σ v. Estimation typically requires simulation methods, either using a simple method of Simulated Maximum Likelihood or the more complex Method of Simulated Moments. Both are coveredindetailin?, although they do note that the simpler method is not unbiased for a finite number of parameter draws. For models which factor random preference heterogeneity into estimation, the simulated likelihood is conditioned on n m draws from the assumed distribution of 15

16 the random preference components. Assuming that disturbances v are distributed multivariate normally around zero mean with variance Σ v, and that the mth draw from that distribution yields realisations v m =(vy m,vh m 1,vH m 2 ) 0, define the mth set φ m of preference parameters as φ m =(α, β + v m ) 0 =(α, β m ) 0. For n m draws, the Simulated log likelihood for (15) given random preferences is written as `(φ, Σ v X, n m ) = = n m X PX m=1 j=1 k=1 n m X PX m=1 j=1 k=1 X n m PX d jk ln Pr[H 1(.) = H j,h 2(.) = H k X, φ m ] PX d jk U(Y {H j,h k },T H j,t H k X, φ m ) m=1 P P p 1 =1 P P p 2 =1 U(Y {H p 1,H p 2 },T H p 1,T H p 2 X, φ(24) m )] The estimation of covariance parameters in iterative models of this form can be difficult, since for each iteration conditions are required on the relative values of variance and covariance terms in Σ v. Rather than impose conditions directly, we choose to parameterise the Cholesky of Σ v rather than Σ v itself. 4.3 modelling participation The participation decision is probably the hardest aspect of labour supply decision to get right. Yet the work incentive impact at the point of participation is often the most important consideration when assessing the incentive and welfare impact of tax or benefit reformproposals. 12 Most empirical evidence suggests that the participation elasticity is strong relative to conditional hours elasticities, suggesting a low reservation wage for many groups. There are other reasons for observing individuals out of the labour market (including involuntary unemployment, and potential participants discouraged from seeking work by fixedorsearchcostsofemployment)whichaffect the likelihood that a potential worker will get a job, and which ideally ought to be accommodated in model estimation. Blundell, Ham, and Meghir (1987) discuss a likelihood-based approach which exploits sample information to differentiate those who are unemployed but seeking work and those who are self-reported non-participants, and Cogan (1981) describes a method to control directly for fixed costs in estimation. We also see the implementation of selection-type models to separate the participation decision from the choice of hours conditional on participation, thereby breaking the reservation wage condition. This is consistent with fixed costs, but reduced form to the extent 12 See Heckman (1993). 16

17 that the empirical model of participation typically doesn t explicitly depend on the detail of the tax and benefit system. In consequence, such models make at best an uneasy transition into microsimulation, where tax and benefit changes ought explicitly to affect participation decisions. In fact, most microsimulation studies of the impact of tax reform on labour supply deal with participation simply by assuming that reservation wages exceed the market wage on offer. There is, however, ample empirical evidence that this corner solution characterisation of nonparticipation is statistically unsustainable (see Mroz (1987)). Our source of microdata allows us to separate various types of individuals not in paid employment. Some report that they are looking for work, some report that they want to work but aren t looking (including those who cite the need to care for children as a reason for not looking), and some report that they don t want to work. We take advantage of this information to differentiate individuals. Specifically, if we attribute to those who want to work but don t look for work an unobserved (shadow) fixed cost, parameterise it in terms of observable characteristics and a random element, and identify the expected level of fixed costs through systematic differences in those observed characteristics thought to influence fixed costs, then we have the basis of an empirical model which is consistent in estimation, yet structural enough to provide a valid framework for microsimulation. What we have in mind is a discrete version of Cogan (1981). This gives us the potential to condition labour market decisions (participation and hours) on simulated (shadow) fixed costs, taking account of unobserved variability. By breaking the reservation wage condition most commonly applied to as an explanation of nonparticipation in microsimulation studies, we enjoy an abiliy to separate out discouraged workers from labour market nonparticipants and unemployed seekers. That said, we do not attempt to separate non-employed males into discouraged workers, unemployed seekers or labour market non-participants. The main reason for this simplification is that, from casual observation, male labour market decisions are restricted to a choice between non-participation and full-time work at between 37 and 40 hours per week. Given this lack of variability in hours of work among working males, it is extremely difficult statistically to identify separate fixed costs and involuntary unemployment terms from the taste parameters that would define male non-participants. Instead we pool all non-working males into one group and estimate their labour market choice as a simple binary decision. 17

18 4.3.1 controlling for the involuntarily unemployed Our approach to modelling the involuntarily unemployed among the women in our sample follows Blundell, Ham, and Meghir (1987) by specifying an employment equation of the form I = Z.δ + v I, (25) where δ represents a parameter vector, Z denotes a series of characteristics thought to influence the probability of getting a job, and where v I is assumed independent standard normal. The probability of getting a job is therefore Pr(I > 0 Z) = Φ(Z.δ). We use regional dummies (Metropolitan area, Greater London and North) to identify the model, together with years of formal education (squared and in levels) and age. Introducing the involuntarity unemployed into estimation requires a modification to the likelihood. Let d e represent an indicator variable for which d e =1if a labour market participant finds a job, 0 otherwise. Conditioning on the labour market status H 1(.) of the male partner, the probabilities of observing a non-participant (NP), an unemployed seeker (US) and a working woman are, respectively, Pr[H 1(.),NP X, Z, φ] = U (Y {H1(.),0},T H 1(.),T X, φ) > Pr, max [U(Y {H1(.),H 2(.) },T H 1(.),T H 2(.) X, φ)] H 2 (.)>0 Pr[H 1(.),US X, Z, φ] = U (Y {H1(.),0},T H 1(.),T X, φ) < [1 Φ(Z.δ)]. Pr max {H 1(.),H 2(.) },T H 1(.),T H 2(.) X, φ)] H 2 (.)>0 Pr[H 1(.),H 2(.) = U (Y H j {H1(.),H X, Z, φ] =Φ(Z.δ). Pr },T H 1(.),T H j X, φ) < max {H H 2 (.)6=H j 1(.),H 2(.) },T H 1(.),T H 2(.) X factoring fixed costs into estimation In continuous studies, fixed costs of work are typically accommodated by modelling the participation and hours decisions separately using the selection-type models of Heckman (1979) (see Blundell, Duncan, and Meghir (1998) inter alia). Specifically, by including in the model of participation instruments which are thought to be correlated with fixed costs, one may control for the effects of fixed costs in estimation. However, as Blundell (1992) notes, this method is less appropriate when the model is to be extended to simulate the impact of tax or benefit reform on participation. Firstly, the statistical model of participation is typically unaffected by changes in tax parameters. And secondly, fixed costs of work are generally neither measured nor explicitly predicted. Hence, one cannot factor such costs into a comparison of utility 18

19 in and out of the labour market. In consequence, many microsimulation studies report a relative inertia in the propensity to move into work in response to tax or benefit reforms which ought in principle to improve work incentives. In this study, we choose to follow Callan and Van Soest (1996) in which fixed costs are imputed directly from the structure of the economic model. We exploit observed differences in labour market status among women who are largely homogeneous in the characteristics thought to influence tastes for work. By relating those observed differences to instruments which proxy fixed costs, any systematic relationships are picked up in the parameters of a shadow fixed cost equation of the form FC = X FC.γ + v f, (26) where the unobserved fixed cost component v f is distributed normally around zero mean. In our most general specification we also allow for potential correlation between v f and the random preference parameters v Y, v H1 and v H2.Thefixedcost relationship (26) is factored into estimation in a relatively straightforward manner; since fixed costs impact only on workers, we replace utilities U (Y {H1(.),H 2(.) },T H 1(.),T H 2(.) X, φ) in the likelihood (20) by U (Y {H1(.),H 2(.) } FC,T H 1(.),T H 2(.) X, φ) for all states H j > 0. To characterise a worker in the presence of fixed costs therefore requires that max U (Y {H1(.),H H 2(.) >0 2(.) } FC,T H 1(.),T H 2(.) X) >U (Y {H1(.),0},T H 1(.),T X, φ) (27) where U0 = U (Y {H1(.),0},T H 1(.),T X, φ). This adds a fourth labour market state to the likelihood. Specifically, a discouraged worker is one who would like to work, but is not seeking employment because of fixed costs. The probability of observing a discouraged worker is Pr[H 1(.),DW X, X FC,Z,φ] =Pr max H 2(.) >0 U (Y {H1(.),H 2(.) } FC,T H 1(.),T H 2(.) X, φ) <U 0 and max H 2(.) >0 U (Y {H1(.),H 2(.) },T H 1(.),T H 2(.) X, φ) >U controlling for costs of childcare in estimation To simulate the full impact of the WFTC on work incentives among families with children requires a specific consideration of the role of childcare costs on labour market decisions. At the very least childcare costs act as an extra tax on employment, although a fuller consideration of labour supply in the presence of childcare would recognise the benefits of good quality childcare both for the child and the mother. 19

20 Figure 3: Alternative Labour Market States I * Workers Labour Market Nonparticipants 0 Discouraged Workers + + U(y) -U(y-FC) Unemployed Seekers + U(y) -U 0 13 The childcare credit component of the WFTC is a potentially generous benefit for those who purchase formal childcare. To assess the implications for work incentives of the new WFTC requires that we take account of the likely childcare costs incurred by households in different labour market states. In the absence of complete sample information in the FRS on childcare costs and utilisation, we adopt a probabilistic approach to integrate out childcare costs in estimation. We use empirical distributions of hourly costs of formal childcare together with imputed relationships between hours of work and hours of formal childcare to predict childcare costs for different demographic groups at different labour market states for specific childcare prices. By integrating the likelihood (20) over the range of childcare costs we are able to control for childcare costs in estimation. Furthermore, when introducing the WFTC in simulation, the level of the childcare credit component is assessed on the basis of the imputed distribution of childcare costs. Let the variable P c represent the hourly price of childcare, and let f Xc (p c ) represent the corresponding distribution of childcare prices for a household with characteristics X c. Furthermore, let us assume that there exists a relationship between 13 In some studies, childcare is treated as a good in its own right in order to rationalise the purchase of formal childcare by households with non-working members. 20

21 hours of work and hours of childcare per child of the form H cc = G(H 1,H 2 X c ). (28) Then, given a price P c per hour of childcare, the childcare costs for a household with characteristics X c whose members work H 1 and H 2 hours of work respectively is 14 CC(H 1,H 2 P c,x c )=P c.g(h 1,H 2 X c ). (29) Net household incomes for a household facing a price P c for childcare must therefore be adjusted. Specifically, Y (P c )=W 1 H 1 +W 2 H 2 +V T (H, W,V,CC; X) FC 1 (Z 1 ) FC 2 (Z 2 ) CC(H 1,H 2 P c,x c ). (30) Note that T (H, W,V,CC; X) may potentially adjust to take account of the level of childcare expenditure, as would be the case for example with the childcare credit component of the WFTC. We condition for childcare costs in estimation in the following way. 15 Let Pr[H 1(.) = H j,h 2(.) = H k ) P c = p c ] represent labour market state probabilities conditional on apricep c per hour for childcare, and let `(φ X, P c = p c )= PX PX d jk ln Pr[H 1(.) = H j,h 2(.) = H k P c = p c ] (31) j=1 k=1 represent the corresponding conditional likelihood. Assuming a continuous distribution f Xc (p c ) for childcare prices among households with characteristics X c,wemay integrate (31) over the range of prices to give PX PX Z `c(φ X) = d jk ln Pr[H 1(.) = H j,h 2(.) = H k P c = p c ].f Xc (p c ) p c. (32) j=1 k=1 From a computational point of view it is easier to work with a discrete distribution for childcare prices. Specifically, if F Xc [p c ]=Pr[P c = p c X c ] for P c P, where P = {p0,p 1,.., p n } represents a finite set of prices, then `c(φ X) = PX PX X d jk ln Pr[H 1(.) = H j,h 2(.) = H k P c = p c ].F Xc [p c ]. (33) j=1 k=1 P c P For our empirical work we choose to work with a six-point empirical distribution for hourly childcare prices. 14 This characterisation admits the possibility of free formal or informal care (P c =0). 15 For (relative) notational simplicity we derive the likelihood in the absence of controls for random preferences. 21

22 5 Results 5.1 data We use the Family Resources Survey to examine the income and incentive impact of tax credits. This is an annual budget survey of individual, family and household incomes, characteristics and labour market attachment. It is a new survey in the UK and contains a much larger and more representative sample of households than the surveys, principally the family Expenditure Survey, on which the vast majority of previous work has been carried out. For this analysis, we use the and FRS datasets, together combining information on over 50,000 UK households. We select for our empirical work two samples; single parent households and married or de facto married couples. Excluding self-employed and retired households, together with students and those in HM forces, leaves samples of 1807 single parents and 4694 two-person households for use in estimation. 5.2 net incomes To generate net incomes we use the Institute for Fiscal Studies tax and benefit model TAXBEN. 16 TAXBEN is a microsimulation model of the UK tax and benefit system that calculates taxes due and benefit entitlements for the Family Resources Survey data, and calculates the financial returns for each working age individual to employment at all possible hours by calculating gross and net incomes at these levels. For workers we assume their current wage remains unchanged, and for non-workers, we estimate wages using a wage equation based on their characteristics. The use of TAXBEN combined with varying the potential hours of individuals allows us to generate highly accurate budget constraints for each individual in the survey in order to estimate the labour supply effect of the reforms to taxation. 5.3 childcare expenditures and childcare use The childcare credit component of the Working Families Tax Credit could potentially offer generous benefits for those women who purchase some form of registered formal childcare. It is therefore important both in estimation and in our simulations of the work incentive impact of the WFTC reform that we account in some way for childcare expenditures. Ideally, we would like to observe actual childcare expenditures and childcare use among the full sample of women drawn from the Family 16 See Giles and McCrae (1995). 22

23 Resources Survey. Previous work has established that up to 30% of non-working households may purchase formal childcare to some degree, which suggests that any model designed to assess work incentives in the presence of childcare ought ideally to include childcare expenditures among non-working households. However, these data are not available to us. Instead, we are forced to impute childcare expenditures because the Family Resources Survey neglects to record childcare expenditures among non-working households. Our strategy uses sample information on hourly prices of childcare (given in Table 1), and the relationship between formal hours of childcare and hours of work (Table 2). We allow for the fact that similar households may purchase different types or levels of childcare by using information on the distribution of childcare prices paid by specific demographic groups directly in our estimation procedure via a likelihood of the form (33). Table 1: Average hourly childcare costs: percentages in range lower bound upper bound no cost Married Women one child, youngest < one child, youngest two children, youngest < two children, youngest three+ children, youngest < three+ children, youngest Single Parents one child, youngest < one child, youngest two children, youngest < two children, youngest three+ children, youngest < three+ children, youngest Total Average price within range Notes: data drawn from the and Family Resources Surveys. 5.4 Model Estimates For the main series of estimates we choose a five-state labour supply regime for women and a two- state choice set for men. Specifically, for women we allow for 23

24 Table 2: Estimated hours of childcare Constant (t-value) Slope (t-value) Married Women one child, youngest < (1.569) (26.746) one child, youngest (3.026) (8.839) two children, youngest < (2.431) (20.167) two children, youngest (3.414) (10.504) three+ children, youngest < (0.061) (9.216) three+ children, youngest (3.821) (5.158) Single Parents one child, youngest < (0.605) (13.763) one child, youngest (5.234) (5.671) two children, youngest < (1.052) (9.362) two children, youngest (5.651) (3.632) three+ children, youngest < (1.720) (3.310) three+ children, youngest (1.352) (3.143) Notes: Dependent variable: average hours of childcare per child; independent variable: hours of work by mother. Data drawn from the and Family Resources Surveys. hours choices to take one value in the set H (.) = {0, 10, 20, 30, 40} using the following allocation rule: H (.) = 0 if H 5 = 10 if 5 <H 15 = 20 if 15 <H 25 = 30 if 25 <H 35 = 40 if H>35. For married or cohabiting couples, a cursory view of the data reveals that male partnersareessentiallyfacedwiththesimplechoiceofwhetherornottowork. Conditional on working, male partners tend in the main to work somewhere between 35 and 40 hours per week, with few men in part-time employment. In consequence we choose to model the household labour supply decision of a two-person household by restricting the male partner to a simple participation choice, and define participants to be those who work more than 5 hours per week. Women in couples are allocated the same five-state choice set as one-parent households. The instruments we choose to include to pick up variation in tastes for work include dummies for the age of the youngest child (0-2, 3-4 and 5-10), the age of the parent (squared also), whether or not the parent left school at 16, and the number 24