Taxes and Labour Supply

Transcription

1 Taxes and Labour Supply Lecture notes Dan Anderberg RoyalHollowayUniversityofLondon January 2007

2 1 Introduction Labour supply is an important factor of production The most important source of income. Taxes are levied directly on income from labour supply. Means-tested welfare benefits are add to the effective marginal tax.

3 Many important dimensions: effort to exert on the job, when to leave education and join the labour force, and when to retire. We will nevertheless focus here primarily on the hours of work decision. Outline: Consider a number of extensions to the simple static labour supply model. Provide examples of real life budget sets using existing UK taxtransfer policy.

4 How to empirically model/estimate labour supply. Look in detail at one type of policy in particular, so-called in-work benefits(eitcintheusandworkingtaxcreditintheuk). Summing up some of the main insights from the literature regarding key labour supply elasticities.

5 2 Generalizing the Basic Labour Supply Model The fact that economists put a lot of faith in the basic labour supply model is also witnessed in the fact that it is used to not only for generating testable predictions, but also directly as a model that can be estimated. However, needs to be extended for empirical purposes.

6 2.1 The Participation Decision Observe a number of individuals who work zero hours. In the basic static an individual will be supply zero hours when the wage that she can obtain is less than her reservation wage, w r,defined as her marginal rate of substitution at zero hours, see Fig 1. FIG 1 However, very few individuals work very few hours.

7 The basic static model may not give a sufficiently rich description of the participation decision: the data suggests that individual s make more discrete adjustments to their labour supplies. If we maintain the assumptions that individuals have continuous preferences, that they can freely choose between hours in a continous way, then non-marginal responses to marginal wage changes can only occur if the budget set is non-convex. Means-tested transfers combined with a progressive income tax system tend to generate marginal tax rates that are U-shaped functions on income (Fig 2).

8 FIG 2 A second possibility is that there are costs associated with participating (L >0) in the labour market (commuting costs, childcare costs etc.) A participation cost creates a non-convexity in the individual s budgetconstraint(seebelow). Also raises interesting questions on how labour supply is affected by taxation.

9 A Simple Model of Labour Supply with Participation Costs Simplest extension to the basic labour supply model. Assume for simplicity that the individual s preferences are quasi-linear, u (c, L) =c φ (L), where φ ( ) is continous, strictly increasing, strictly convex, φ (0) = 0 and I =0. Tax-transfer system T (z) that taxes income z = wl. The only addition is a participation cost δ 0: this modifies the individual s budget constraint to c = wl T (wl) δ 1(L>0)

10 For simplicity we assume that the tax system is progressive (the marginal tax rate is increasing). Characterizing the Individual s Labour Supply Think of the solution to the individual s decision problem in two steps. Step 1: The maximum utility from participation First, solve the problem given participation max {wl T (wl) δ φ (L)} L [0,L max ]

11 First order condition (assuming a strictly interior solution) is necessary and sufficient, w ³ 1 T 0 (wl) = φ 0 (L) Thus the choice of hours is a function of the net-of-tax wage, L = φ 0 1 (ω ) with ω = w ³ 1 T 0 (wl ) The maximum utility associated with participation can then be written where c wl T (wl ). u (T ( ), δ) =c φ (L ) δ Step 2. Comparing with the utility from non-participation.

12 Consider now the utility from non-participation: at non-participation L =0andc 0 T (0) and hence her utility will be u 0 (T (0)) = c 0 = T (0) The individual will participate if and only if u (T ( ), δ) u 0 (T (0)) or equivalently, δ δ c φ (L ) c 0 = wl T (wl ) φ (L )+T (0) Characterize the individual s choice of labour supply as follows: L = ( 0 if u 0 (T (0)) >u (T ( ), δ) L (ω ) if u 0 (T (0)) u (T ( ), δ)

13 The Participation Rate and Average Hours Consider then a group of individuals who are identical in every respect except in terms of the participation cost. Let δ 0 be distributed according to some CDF P (δ) (with associated PDF p (δ)). The participation rate is then P (δ ). Figure 3 illustrates the critical participation cost δ as the one that makes the individual indifferent between participating and not participating.

14 Quasi-linearity implies that all participating individuals work the same number of hours L (ω ). FIG 3 Compute the average hours worked in this group of individuals. E [L ]= Z δ 0 L (ω ) p (δ) dδ = L (ω ) P (δ ) which is simply the product of the optimal hours L (ω ) times the participation rate. Consider how the participation rate and average hours of work are affected by the tax system; let α be some parameter of the tax system, T = T (z; α).

15 What we are interested in knowing is what aspects of the tax system affect the participation rate. P (δ ( ) = p (δ ) δ T (wl ) α α = p ) T (0) (δ ) α α whereweusedthefirst order condition for L. Thus the tax system impacts on the participation rate in two ways. An increase in the tax pressure on individuals with positive earnings tends to decrease the participation rate. An increase in the transfer to non-working individuals tends to decrease the participation rate.

16 Contraststhestandardmodelwhereonlythenet-of-taxwagerateat L = 0, and hence T 0 (0), matters. The impact on average hours E [L ] can be written as E [L ( ] = L (ω ) p (δ T (wl ) ) T (0) ) P (δ ) L (ω ) α α α ω w T 0 (wl α Hence the tax sysem has two effects: An impact via the participation rate (as above) An impact on the hours worked by those who supply positive hours (as in the standard model).

17 2.2 Dynamics It is reasonable to expect that individuals plan their labour supply over longer time horizons (deciding on when to leave education and enter the labour force, when to have children, how to combine childcare with work, when to retire). Do these type of dynamic considerations invalidate the predictions of the basic labour supply model? Does taking a dynamic perspective change the model s interpretation? Answers are generally no and yes.

18 A Multi-Period Model of Labour Supply The individual lives for T periods, t =1,...T. Preferences for consumption and leisure in a given period depends on her characteristics, e.g. number and ages of children, which we can denote x t. Preferences over the entire path of consumption and labour supply, {c t,l t } T t=1. Assume that preferences are additively separable over time, U = TX t=1 β t u (c t,l t ; x t ) (1)

19 where β (0, 1) is her discount factor. Assume that she can save in an asset that earns a return r t and ignore taxes and transfers and uncertainty. Thus her lifetime budget constraint can be written in present value form as TX t=1 {R t (w t L t c t )} + R 1 A 1 =0 (2) where R t = Q t τ=1 (1 + r τ ) 1 and where A 1 is the value of her initial assets.

20 Write the problem in a recursive form. In period t conditional on assets A t, the individuals solves υ t (A t )= max ct,l t,a t+1 u (c t,l t ; x t )+βυ t+1 (A t+1 ) A s.t. t+1 (1+r t+1 ) = A (3) t + w t L t c t where υ t (A T ) is the value function the indirect utility from period t onwards with assets A t. The first order conditions for this problem can be written as u c (c t,l t ; x t ) λ t = 0 (4) u L (c t,l t ; x t )+w t λ t = 0 (5) βυ 0 t+1 (A λ t t+1) (1 + r t+1 ) = 0 (6) where the multiplier λ t measures the marginal value of wealth in period t.

21 The first two first order conditions imply that the standard marginal rate of substitution should equal the wage rate result holds u L (c t,l t ; x t ) u c (c t,l t ; x t ) = w t (7) Solve the first two first order conditions for c t and L t conditional on λ t ; hence we obtain c t (w t, x t ; λ t ) and L t (w t, x t ; λ t ) (8) Knownasthe Frischdemandfunctions. The idea is that the marginal utility of wealth, λ t, captures all information from other periods that is needed to solve the current-period maximization problem: within any period, the individual acts as if she solves a standard static labour supply problem.

22 It remains to consider the marginal value of wealth; can be thought of as an individual fixed effect. To see this, note that υ 0 t (A t)=λ t ; hence from the last first order condition, λ t+1 = λ t β (1 + r t+1 ) (9) This implies the following path for the log-multipliers ln λ t+1 =lnλ t + κ t (10) where κ t = ln [β (1 + r t+1 )]. Note in particular that κ t is not individual-specific. Hence by repeated substitution ln λ t = t 1 X τ=1 κ τ +lnλ 1 (11)

23 Consider e.g. the case where the Frisch labour supply function is log linear (and add an error term) ln L t = α ln w t + ζ ln λ t + ρx t + e t (12) Suppose that κ t is constant across individuals and across time; then where b = ζκ. ln L t = α ln w t + bt + ζ ln λ 1 + ρx t + e t (13) Taking first differences in this equation eliminates the individual fixedeffect ln L t = α ln w t + b + ρ x t + e t (14)

24 With panel datat this equation can be estimated to obtain estimates of the wage elasticity α. α in this case is the elasticity of L t to the current wage, holding the marginal utility of wealth constant. Interpreted as labour supply reponses to variation in wages along the individual s lifetime wage profile. Thus α in this case is naturally interpreted as an intertemporal elasticity of substitution. If we wish to consider the impact of (permanent) wage differences across individuals we must recognize that such differences will lead to differences in λ t. We then have to model the individual s wage profiles and to model the individual fixed-effect ln λ 1 as a function of the wage profile and initial assets and demographics characteristics.

25 The main insights from the attempt to put the basic model into a dynamic framework are thus that 1. Estimation of a seemingly static labour supply model can be consistent with a fully dynamic individual choice framework, 2. The interpretation of the model and its parameters generally depend on what variables are included as control variables.

26 2.3 Other Extensions Social Welfare Stigma The take-up rate for nearly all benefits is well below 100 percent. Why? It may be the case that receipt of welfare benefits is negatively perceived and, in particular, social stigma is likely to reduce the individual s well-being (Moffitt, 1983) Family Labour Supply NEXT TIME!!!!

27 3 UK Budget Sets Will show some typical UK budget constraints and how they are composed of earnings, taxes and transfers. Consider the case of a single parent. A lone parent, depending on her hours choice, in principle eligible for all major benefits means-tested benefits targeted at available to individuals with good working health. Income Support (IS), Working Tax Credit, Housing Benefit (HB), and Council Tax Benefit (CTB). Consider the 1999 reform which relaunched the earlier version of the working tax credit system, called Family Credit, as Working Families Tax Credit.

28 A Stylized Case Consider a lone parent (aged 36) with one child (aged 7) observed in the year When she works she earns an hourly wage of $4. She has no savings; her gross rent is $50/week and her council tax liability is $10/week. She also pays $25/week in child care cost. Figure 4 illustrates her budget constraint as a function of the number of hours that she works per week and it shows how that budget is made up of earnings, taxes and transfers. FIG 4 (budget 100.jpg)

29 The most striking features of the budget constraint are The flat region caused by the 100 percent benefit reduction rate in the IS system, The jump at 16 hours caused by the tax credits, and The fact that some of the means-tested benefits, notably HB and CTC, can be kept in part even at relatively large number of hours of work.

30 The Effective Marginal Tax Rate Consider what this means in terms of the effictivemarginaltaxrate. This is the formal marginal tax rate plus the sum of the relevant benefit reduction rates. FIG 5 (margtax 100.jpg)

31 AHigherWage How much does a higher wage expand the individual s budget constraint? In figure 6 the hourly wage rate has been increased to $10/hour. FIG 6 (HigherWage.jpg)

32 The 1999 WFTC Reform One of the main policy reforms to encourage labour supply by single parents adopted by the labour government was to increase the generosity of the tax credits given to the working poor. Figure 7 shows the budget constraint for the same individual at the beginning of FIG 7 (budget 99.jpg) Indeed, the most noticable difference between 1999 and 2000 is the increase in the tax credits.

33 4 Estimating Labour Supply 4.1 The Structural Approach versus the Natural Experiments Approach The Natural Experiments Approach Recent years: a number of studies using various versions treatment evaluation methods, most often versions of the difference-in-differences approach.

34 The Structural Approach A structural model starts from an assumed form of the utility function or labour supply function and then uses the data to try to uncover the parameters of that function. Assumptions are made regarding the way in which stochastic terms are introduced into the model. E.g. randomness in observed choices may reflect measurement errors, preference heterogeneity, or optimization errors.

35 Pros and Cons The natural experiments approach avoids having to explicitly parameterize either the complex nonlinear budget constraint faced by the individual or his utility function. The main conceptual drawback is that it is hard to generalize to consider the potential impact of policy changes other than those considered in the specific analysis. The practical challenge for the difference-in-differences approach is to find a suitable control group.

36 The structural approach provides global information which can be used to simulate the effect of any reform on labour supply. This is the biggest advantage of this approach. Structural methods have been criticized on various grounds. Assumes that the individual has a perfect knowledge of the parameters of all the tax and transfer programs; also, the functional form used to represent preferences often lacks flexibility etc.

37 4.2 A Prototypical Structural Model Outline a simple structural labour supply model for single individuals. Allows observed heterogeneity to affect the individual s preferences and a fixed cost of labour force participation. Start by specifying a deterministic part of the individual s utility function. A flexible and convenient choice is the assumption of quadratic utility, u (c, h) =β 1 c + β 2 h + α 11 c 2 + α 22 h 2 + α 12 ch (15) where c is consumption and h is hours of work.

38 Observed characteristics x. x is assumed to shift the marginal utilities through the β 1 and β 2 β 1 = xβ 1 and β 2 = xβ 2 (16) This implies that β 1 and β 2 are not parameters but rather variables in the sense that they vary in the population. A fixed cost ζ of participating in the labour market. The parameters ofthemodelarethus b =(β 1, β 2, α 11, α 22, α 12, ζ). (17)

39 Discretize the hours choices to some finite set of choices h H with e.g. H = {0, 10, 20, 30, 40}. Denote the tax-transfer system by B (z, h, x) describing the total benefit entitlement less tax liability Consider now a individual i with wage w i.eachchoiceofh j H will be associated with a particular level of disposable income c ij, c ij = w i h j + B ³ w i h j,h j, x i ζ1 ³ hj > 0 (18) Fig 8 illustrates a hypothetical example. FIG 8

40 Compute the individual s predicted utility at each possible hours choice h j H, u ij = u ³ c ij,h j (19) In order to make the model stochastic let each choice to be associated with an additional random utility component ε ij. Hence the utility to individual i from choosing h j H is U ij = u ij + ε ij (20) A popular choice is to assume that ε ij are i.i.d. extreme value distributed. Implies that Pr ³ h i = h j b =Pr ³ U ij U ik k = exp ³ u ij P (21) k exp (u ik )

41 We can now easily formulate the (log) likelihood function ln L (b) = X ln [Pr (h i b)] = X " exp (uii ) ln P i i k exp (u ik ) # (22) Maximum likelihood estimation of the model thus entails maximizing ln L (b) with respect to b.

42 An Illustration 2,512 women (without partners) obtained from the FRS Let x =(age, agelf te, kid04, kid510, kid1115) (23) 16 parameters in the model Beforeestimationthedisposableincomeforeachwomanateachhours choice is calculated using tax- and benefit rules.

43 Then ssing information on the individual s budget constraint, her actual hours choice, and her demographic characteristics, the model can then be readily estimated. The maximum likelihood estimates of the model is presented in Figure 9 FIG 9 (EstimationRes.jpg) There are significant non-linearities in the individuals utilities; decreasing marginal utility, complementarity between leisure and consumption etc.

44 The results suggest that, plausibly, the presence of children increase the marginal utility of consumption. Similarly, the presence of younger children increase the marginal disutility of labour supply (or, equivalently, increases the marginal utility of leisure) The model indicates that there is a significant participation cost.

45 Application: Microsimulation The estimated preferences are taken as primitive in the sense that they are not policy-contingent. Hence we can then predict their labour supplies under a counterfactual policy. The general idea is easily illustrated in a figure 10 FIG 10 Real world example of this approach is presented below.

46 Extensions Unobserved Heterogeneity* It is natural to suppose that individuals differ also in unobserved ways that permanently affect their preference, i.e. across possible hours choices (e.g. due to unobserved health conditions etc.) The model can be extended to allow for unobserved heterogeneity e.g. by letting marginal utilities have a individual-specific random component β 1 = xβ 1 + υ 1 and β 2 = xβ 2 + υ 2 (24)

47 The two individual fixed effects (υ 1, υ 2 ) are not observed. Estimation recovers the parameters of the distribution of e.g. (υ 1, υ 2 ) N (0, Σ).

48 Welfare Participation Costs and Benefit Takeup For many benefits the take-up rate is well below 100 percent. Above methods assume that everyones operates on the boundary of her budget constraint. Why incomplete takeup? Stigma costs and more direct participation costs. Moreover, individual participation costs may be correlated with preferences for consumption and leisure. Takeup costs/behaviour should be modelled jointly with labour supply, Keane and Moffitt (1998).

49 Extend by letting ψ m denote the utility cost associated with receiving benefit m, u (c, h) =β 1 c + β 2 h + α 11 c 2 + α 22 h 2 + α 12 ch where P m is a take-up dummy for benefit m. X m M ψ m P m (25) Also,take benefit receipt into account in the budget constraint: c = wh + X m M P m B m (wh, h, x) T (wh) Keane and Moffitt model ψ m as ψ m = xψ + υ m (26)

50 Interesting for several reasons. Provides direct estimates of the costs of participating in various benefit programmes. Useful for considering the full response to benefit reform. In principle required for consistent estimates of labour supply responses. Keane and Moffitt consider three benefit programmes: AFDC, Food Stamps, and subsidised housing in a model estimated on 968 women from the 1984 SIPP data. FIG 11 (Keane and Moffitt, Table 2)

51 4.3 An Example of Natural Experiments Approach A number of studies employdifference-in-differences to study the impact of taxes and transfers on labour supply. Many studies of tax credits (see below). Nada Eissa (1995) focuses particularly on the effect of a major US tax refrom the 1986 Tax Reform Act (TRA) on the labour supply of married women. Neat illustration of the approach.

52 Eissa s Study of the Tax Reform Act of 1986 Background: The Tax Reform Act of 1986 TRA86 was one of the most extensive tax reforms ever passed in the US. Reduced the number of tax brackets from 14 to 3 and eliminated special treatment of capital gains, deductions for contributions to Individual Retirement Accounts (IRAs) and a host of other special provisions. In the US couples (usually) file for tax jointly. Significant impact on the labour supply incentives particularly for women (who are also generally

53 perceived to be more responsive to marginal changes in labour supply incentives than men). Model assumption: secondary earner model The TRA86, by eliminating the top income tax brackets, significantly reduced the effective marginal tax rates for wife to (very) high earning husbands.

54 The Predicted Effect on Married Women Labour Supply Predicted effect of the TRA86? Under the assumption of the secondary earner model the labour supply of the wives can be analysed using the basic labour supply model treating the husband s income as unearned income. The lowering of the marginal tax rate should, in principle, have both an income and a substitution effect. However the TRA86 also greatly expanded the tax base. Hence Eissa (1995) argues that the reform effectively eliminated the income effect.

55 Forming a Treatment Group and a Control Group Hard to form a natural control group everyone is in principle liable to pay taxes. Eissa argues that while high earning families saw a reduction in their effective marginal tax rates families further down in the distribution saw little or no change in the marginal tax rates. FIG 12. FIG 12 Hence the treatment and the control group comes from different points along the distribution in terms of the husband s earnings (and other unearned family income).

56 Data is from the CPS and Treatment group married women at or above the 99 percentile of their CPS income distribution She considers two control groups: Women between the 75 and the 80 percentiles of the income distribution and women between the 90 and the 95. Treatment and control groups are not identical in characteristics.

57 Results Eissa verifies is that the treatment and control group(s) indeed saw different changes in their marginal tax rates: an average reduction in the marginal tax rate of 13.9 percentage points for the treatment group and smaller reductions for the control groups. Eissa proceed to consider whether these changes were accompanied by changes in relative labour supplies, both in terms of participation rates and average hours of work. The simple difference-in-difference calculations are shows in Fig (Tab 3a,b,c in Eissa)

58 FIG13(Tab3ainEissa) Participation. Estimated effects of 3.7 and 4.5 percentage points respectively. Hours of work conditional on participation. Treatment effect of between 67 and 108 hours/year. FIG14(Tab3binEissa) Unconditional annual hours (i.e. to include those women working zero hours) yields similar results

59 FIG15(Tab3cinEissa) To account for changing demographic composition and to reduce standard errors Eissa then places the difference-in-differences approach in a regression framework. Since participation is a binary outcome, she applies a Probit model: Pr (h it > 0) = Φ (α 0 + α 1 Q it + α 2 High it + α 3 Post it + α 4 High it Post it ) (27) where High it indictates whether woman i observed at time t is in the high income (treatment) group, where Post it indicates whether the observation belongs to the post-tax reform years, and where Q it contains a range of observable characteristics.

60 A test for a treatment effect of the tax reform is hence a test that α 4 > 0. To obtain estimate of treatment effect on participation Eissa calculates the predicted participation rates with and without the reform for the treatment group. Results are similar to raw difference in difference calculations. Estimates imply an elasticity of annual hours with respect to the aftertax wage that is in the range , much of which is due to the participation decision.

61 Conclusions Shows how treatment evaluation methods can be used to obtain estimates of parameters that are of key importance for policy purposes, most notably the participation- and the overall labour supply elasticities with respect to after-tax wages. Her findings suggest the participation elasticity makes up a significant part of the overall labour supply elasticity (albeit, smaller than in the influential papers by Mroz (1987) and Triest (1990), see below.).

62 5 The Rise in In-Work Benefits 5.1 Background: A UK Perspective Increase in the the number of households headed by lone parents. This trend was combined with low or declining employment rates among lone parents. A large gap between the employment rate of lone mothers and married mothersisparticulartotheuk.

63 Clear association between lone parenthood and child poverty. FIG 16 (Blundell and Hoynes, Fig 2.1) The policy dilemma is well-known: How can one support low income families without destroying work incentives? One policy perceived to circumvent this problem is to condition benefits on labour force participation, i.e. to provide benefits to individual who are in employment. Such a benefit program already existed in the UK (and in the US) since the 1970 but had been relatively small. Major reform in 1999 launched the Working Families Tax Credit (WFTC).

64 5.2 The UK Working Tax Credits We will focus primarily on the 1999 reform and hence on the system as it existed between 1999 and Basic Eligibility Criteria and Benefit Calculation Description of WFTC system Eligibility: An eligible household must have some adult working at least 16 hours a week and have at least one dependent children under 16. There is also a savings condition: eligible households cannot have capital exceeding $8,000.

65 Couples need to claim jointly but need not be married. Description of WFTC system Amounts: There is a basic credit of $59; A 30hr credit for households where some adults work at least 30hrs/week worth $11.45 A credit of $26 for each child. Supplementary childcare tax credit covering 70 of childcare costs up to a maximum level. The maximum WFTC entitlement would be the sum of the relevant above components.

66 E.g. single mother with one child working 35 hours with no childcare costs the maximum WFTC would be = If household earnings exceed a certain value known as the applicable amount, $92.90 in 2001, the benefit is reduced at a rate of 55 percent. Figure 17 shows above example assuming an hourly wage of $4. FIG 17 (WFTCexample.jpg)

67 Research Questions The policy approach raises a number of interesting research questions (Blundell and Walker, 2001) Impact on behaviour: Do the tax credits promote work incentives? Dothetaxcreditsaffect the type of jobs that individuals choose? Dothetaxcreditsaffect the incentives to: Have children? Have a partner?

68 Use childcare? Do the tax credits affect the incentives to acquire human capital? Does the design of the tax credits promote benefit take-up? Impact on welfare: What are the distributional effects of tax credits? Does giving more generous benefits to parents improve the welfare of children? Finally, one may also ask whether an in-work benefit policycanbe rationalized on normative grounds:

69 Are in-work benefits part of an optimal redistributive policy?

70 5.3 The Impact of the WFTC Reform on Work Incentives Policy perceived to encourage labour force participation in several ways: The minimum work requirement of 16 hrs/week is intended to give incentives to choose part-time over inactivity. 30 hrs bonus is intended to give incentives to choose full-time work over part-time work. A low benefit withdrawal rate (relative to effectively 100 percent withdrawal rate in IS) is indented to to give incentives to choose hours of work above the minimum requirement. Childcare credits are intended reduce the effective cost of participation.

71 The 1999 Reform WFTC replaced the previously exising Family Credit from October It increased the generosity in four ways: Increasing the credit for younger children, Increasing the threshold above which the tax credit was withdrawn, Reducing the withdrawal rate from 70% to 55%, Extending childcare credit.

72 A Structural Evaluation The effects of the WFTC reform has been evaluated both using structural methods and using treatment evaluation methods. The use a structural evaluation is attractive given that other policy changes occurred at the same time. A Structural Labour Supply Model The analysis presented below is from Blundell, Duncan and Meghir (2002).

73 Structural labour supply model of the type outlined above. Separate models for single parents and couples with children Hours are discretized into five categories, h {0, 10, 20, 30, 40}. Utility is taken to be quadratic, u ij = α 11 c 2 ij + α 22h 2 j + α ijc ij h j + β i1 c ij + β i2 h j + ε ij (28) Observed and unobserved heterogeneity enter through β 1 and β 2, β i1 = x i β 1 + υ and β i2 = x i β 2 (29)

74 Disposable income for woman i choosing hours h j is c ij = w i h j + I i T ³ w i h j,h j,i i ; x i where T ( ) represents the combined system of taxes and transfers. The features that the authors add to the model include: 1. A model for fixed cost of labour force participation: the cost of participation for female i is F i = x i γ. 2. Childcare expenditures are imputed for each individual for every possible hours choice.

75 Estimated on data from the FRS (1994 and 1995) with 1807 single parents and 4694 two-person households. Themainresultsfromthestructuralestimationofthemodelforsingle parents are given in Fig 18 FIG 18 (Tab C1 in Blundell, Duncan and Meghir) The estimates for married couples are similar. Fig 19 FIG 19 (Tab C2 in Blundell, Duncan and Meghir)

76 Simulating the Effect of the 1999 WFTC Reform Contrast the predicted choices of the individuals in the sample under their pre-reform budget constraints with the corresponding predicted choices under their post-reform budget constraints. Predicted effects: For lone parents the WFTC reform should unambiguously increase the incentives to participate by working at least 16 hours/week The predictions for the labour supply by couples is more complicated. May well discourage labour supply by married women.

77 ThemainresultsfromthesimulationsarepresentedinFig20(forlone parents) and Fig 21 for married (or cohabiting) women. FIG 20 (Tab 7 in Blundell, Duncan and Meghir) FIG 21 (Tab 8 in Blundell, Duncan and Meghir) Discussion The ex ante evaluation using a structural labour supply model shows has both strengths and weaknesses. Indeed it may be the only available technique if e.g. simultaneous changes in the economy prevent the use of treatment evaluation methods. Compares well with available difference-in-difference estimates.

78 5.4 US Policy: The Earned Income Tax Credit The Earned Income Tax Credit (EITC) is the main US in-work benefit. Began in 1975: The credit began as part of a broader effort by Senator Russell Long (D-LA) to derail Congressional and Presidential interest in a negative income tax (NIT) in the late 1960s and early 1970s.... Senator Long s primary objection to the NIT was that it provided its largest benefits to those without any earnings, and hence would dull the labor market attachment of poor families. His alternative, initially called the work bonus, would phase in and so increase with earnings up to a point. (Hotz and Scholz, 2001) Has grown through a sequence of expansions in 1986, 1990 and 1993.

79 The EITC share many similarities with the UK tax credits: It is available to families with at least one child and where there is some working adult. Benefit entitlement depends on number and ages of children. The benefit is means-tested against family income and is phased out above a certain threshold level. However, there are also some key differences between the programs: In the EITC there is no minimum hours requirement. Instead, there is a phase in region.. There is (since 1994) a small benefit available also to childless households.

80 The EITC Benefit Formula The EITC is an annual credit which is a fraction of annual income up to a maximum level. Above an earnings threshold the benefit is phased out. The EITC benefit parameters for the year 2000 are reproduced in Table 1. Figure 21 illustrates how the benefit entitlement depends on earnings and the number of children using the parameters in Table 1. FIG 21 (EITCExample.jpg)

81 Children Phase-in Rate Max Benefit Earn. Threshold Phase-out Rate % $353 $5, % 1 34% $2,353 $12, % 2+ 40% $3,888 $12, % Expansions of the EITC Table 1: Parameters of the EITC (year 2000) The 1986 Expansion Real value of benefit eroded between the mid 1970s and the mid 1980s. In connection with the TRA86 the real value of the credit was increased and indexing for inflation was established.

82 The 1990 Expansion A second expansion came in 1990 (phased in over three years) as part of the political bargaining over policies to budget deficit reduction packages. The credit was also made larger for taxpayers with two or more children. The 1993 Expansion Clinton expansion: the EITC was again increased, and sharply increased for families with two or more children. (Hotz and Scholz, 2001). E.g. increase in the subsidy rate from 19.5 percent to 40 percent for tax payers with two or more children; increased the maximum credit and the phaseout rate.

83 Theoretical Effect of EITC on Work Incentives Single Parents Figure 22 shows how shows how the introduction of the EITC shifts the budget set of an (otherwise untaxed) individual. FIG 22 (EITCExample2.jpg) The EITC has an unambiguous positive impact on labour force participation. The theoretical impact on worked hours (conditional on participation) is more complex and ambiguous.

84 Married Couples For married couples the effect is also ambiguous, particularly for the secondary earners who might even see their participation incentives being reduced (e.g. when the primary earner s income places the family on the phase-out region.)

85 5.5 Evaluating the Impact of the EITC on Labour Supply Difference-in-Difference Methods The most common approach for estimating the impact of the EITC; we will give a fairly detailed description of one study: Eissa and Liebman (1996) Quasi-Structural Methods A couple of studies combine ideas from structural labour supply model with explicit identification strategies based on variation in policy across time/space. We will highlight Meyer and Rosenbaum (2001).

86 The Difference-in-Difference Approach in Action Eissa and Liebman (1996) study the TRA86 which included a significant expansion of the EITC. Since the EITC was available (at the time) only to families with children, the expansion of the credit would have affected an easily identifiable group single women with children but not another group single women without children. The focus of the paper is on single women with children. It is a large group

87 The impact of the policy on this group in particular is key to the success of the policy in tackling povery; Standard labour supply model offers straightforward predictions Natural control group can be formed single women without children. However, as noted above, the TRA86 also contained features other than the expansion of the EITC.

88 Choice of Treatment and Control Groups The choice of treatment and control groups is directly based on the eligibility criteria of the EITC policy. In order to focus the analysis on low-income families, EL consider a narrower definition of treatment and control groups by restricting their attention is some estimates to women with low education. Data used comes from the CPS and EL use as Pre-reform period the years and as Post-reform period the years The sample includes unmarried females (widowed, divorced, and never married) who are between 16 and 44 years old.

89 The treatment and control groups are not identical in terms of demographic characteristics. Figure 23 FIG 23 (EL Tab 1) This raises standard concerns associated with the use of the differencein-difference estimator.

90 Empirical Results: Participation The basic difference-in-difference calculations are reproduced in Figure 24 (Table 2 in EL) FIG 24 (EL Tab 2) Leading case where the treatment and control groups contain all women with and without children respectively. The observed growth in participation for single mothers is ³ y T A yb T = = (30)

91 while the corresponding observed growth in participation for single women without children is ³ y T A yb T = = 0 (31) Hence the difference-in-difference estimate is ³ y T A yb T ³ y T A yb T =0.024 (32) i.e. a 2.4 percentage point increase. Several points are worth noting: In Panel B, EL use as one potential control group high educated women with children. The idea behind this is that most women with more than high school education are unlikely to be affected by the EITC.

92 The small participation growth for the control groups suggests small macro-economic shocks; this increases the confidence in the results. The results can be criticized on the grounds that the labour supply for the control group is already very high Since the treatment- and the control groups were not identical and, moreover, the data used is of the repeated cross-sectional type it is important to control for demographic characteristics when Thecomposition of the control- or the treatment group changes over time and Thedemographic characteristics are correlated with the outcome variable.

93 In order to account for this, EL apply a basic regression of the form Pr (h it > 0) = Φ (α + βz it + γ 0 SM it + γ 1 Post86 it + γ 2 (SM it Post86 it )) (33) Since the outcome variable is binary, Eissa and Liebman estimate equation (33) as a probit model. Find a slightly lower estimate of the impact of the EITC expansion on the participation rate of single mothers, percentage points. Potential alternative explanations: Differential long-run trends in labour force participation between single mother and single women without children.

94 Empirical Results: Hours Applies some methodology; estimate (33) using as outcome variable y it hours worked (now estimated as linear regression model using OLS). Look separately at hours conditional on working and unconditional hours. Results reproduced in Figure 25. FIG 25 (EL Tab 5) Quite a lot larger effect when the participation margin is included. (37 hrs. v 25 hrs).

95 Summary of Main Findings The TRA86/EITC expansion incresed the labour force participation rate by lone mother by about 2.5 percentage points. The reform on the other hand seems to have had very little impact on the annual hours worked for those already participating. Hence the main labour supply response seems to have been on the participation margin.

96 Other Difference-in-Difference Based Studies Eissa and Hoynes (1998) consider the impact of the EITC expansions on the labour supply of married couples with children: find negligable effect for married men but reduced the likelihood of labor market participation for married women by around 1.2 percentage points (or 2percent). Hence they conclude that the EITC effectively subsidizes married mothers to stay at home.

97 Potential Problems with the Diff-in-Diff Approach Changes in policies other than the EITC or other environmental factors are coincident with the EITC expansions. Consider e.g. the changes to the AFDC that occurred in many states under waivers prior to the 1996 welfare reform. Since AFDC was primarily avaiable to single mothers with children, it is plausible that these reform had differential impact on the labour supplies of single mothers and single (childless) women. With data from repeated cross-sections, DiD is sensitive to changes in the composition of the treatment and control groups over time.

98 The participation rate of single women has increased over time; hence analysis of e.g. hours of work may be problematic.

99 A Quasi-Structural Approach Structural model are often criticized for identification not being clear. However there is nothing that precludes structural models from being based on identification strategies similar to those used when applying treatment evaluation methods! The approach taken in the quasi-structural approach is to build simple models with a structural interpretation that are identified using variation in tax-transfer policy across time/space. Meyer and Rosenbaum (2001) develop a model of labour force participation

100 Utility enjoyed by an individual is a function c, h, andprogramparticipation p, and her characteristics x, plus a random component U = u (c h,h,p,x)+ε h Think about the woman as choosing between non-participation h = 0 and participation h = 1. Due to the random utility component the probability of participation can be written as Pr (h =1)=Pr(u (c 1, 1,p,x) u (c 0, 0,p,x) > ε) (34) where ε = ε 0 ε 1.

101 Variation in taxes and transfers across time and space induce variation in c 1 and c 0 for women with the same characteristics and the same wages. Meyer and Rosenbaum specify c 0 and c 1 as functions of the EITC, federal and state tax rules and the characteristics of other welfare programs facing women at different times and in different states, utilizing an exhaustive set of data on the tax structure and welfare programs. Linearizing the indirect utility function (and assuming normality of ε) the model is a Probit model. Moreover, by including detailed controls for family structure, identification comes from changes over time or differences across states in how different families are treated under the tax-transfer system.

102 Having estimated the model Meyer and Rosenbaum can then use micro-simulation techniques to explore the implied impact of separate policy reforms. They conclude that that EITC changes account for 63 percent of the increase in the employment rate of single mothers from 1984 to 1996 and 37 percent of the increase from 1992 to 1996 (similar to EL)

103 6 Labour Supply Elasticities Indeed, much of the work on estimating labour supply models focus on uncovering key labour supply elasticities. Recent work has however emphasized that it is important to distinguish between labour supply reponses on the intensive versus the extensive margin. A key finding in the empirical literature is that labor supply elasticities are low at the intensive margin (Heckman, 1993). Indeed, it used be thought that women s labour supplies were more responsive to wage changes. However, the current wisdom is that this

104 is due primarily to response on the participation margin: once labor supply is estimated conditional on labor force participation, it turns out that the female hours-of-work elasticity is close to that of males.