Number 9: Means-tested benefits, incentives and earnings distributions




Author:  John Creedy and Rosanna Scutella

This report was published by the former Department of Families, Community Services (FaCS).

Executive Summary

This paper  considers the question of whether, in the absence of data on hours worked by individuals, it is possible to identify  labour  supply incentive effects  of a tax and transfer  system using  information on only the distribution of earnings. An indirect approach is explored in which the major characteristics of the earnings distributions arising  from a simple  labour supply model  are examined. These characteristics include the existence of modes  and antimodes caused by kinks where effective marginal tax rates increase and non-convexities in budget  constraints arising  from means  testing. Actual earnings distributions, concentrating on unemployment benefit  recipients, are then examined. It is suggested that the use of such an approach must be severely limited, in view  of the fact that there  is no one-to-one correspondence between the form of the earnings distribution and the parameters of a tax and transfer  system.

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1  Introduction

This paper  considers the question of whether it is possible, using  information about only the distribution of earnings, to identify  some of the labour  supply incentive effects  of a tax and transfer  system. The mere  identification of high marginal tax rates caused by means  testing, and the existence of high replacement rates, are not sufficient to demonstrate the importance or magnitude of effects  on labour  supply. Ideally, it would  be required to have sufficient information, for individuals in a large  sample, about their  precise budget  constraint (which in turn requires knowledge of wage  rates), along  with  the actual  number  of hours worked, so that a fully specified labour  supply model  could  be estimated.

In the absence of such information, it is often suggested that indirect information can be obtained simply  by observing the distribution of earnings. In particular,‘spikes’ in the distribution are thought to arise from thresholds at which the effective marginal tax rate increases substantially. While  this argument appears at first sight to be reasonable, the complexity of the aggregation process resulting in the earnings distribution, particularly allowing for the population heterogeneity involved, suggests that it is far from obvious  that labour  supply features are clearly reflected in earnings distributions.

This paper  explores the use of such an indirect approach. First, the major characteristics  of the earnings distributions arising  from a model  in which individuals select  hours of work  in order  to maximise utility, expressed in terms  of leisure and net income, are examined. The approach concentrates entirely on the supply side of the labour  market. The earnings distribution characteristics include the existence of modes  and antimodes caused by kinks and non-convexities in budget  constraints arising  from means  testing. Empirical  earnings distributions are then compared with  the types  of distribution that can be generated by labour  supply models.

Section  2 begins  by examining the possible form of the distribution of earnings of benefit claimants in simplified tax and transfer  systems. The shape  of the distribution depends on the labour  supply function  of individuals and on the nature  and degree of population heterogeneity. Section  3 reports  a simulation analysis of the overall  distribution of benefit  recipients and non- recipients. It is shown  that important characteristics of labour  supply behaviour in the face of a tax and transfer  system  may be concealed when  examining data for broad population groups. This presents a limitation to the potential value  of the indirect approach considered here.

Observed  income distributions are examined in section 4. First, data from the Income Distribution Surveys  for 1995  and 1996  are presented. These data contain  comprehensive information about each  income distribution. Second, a special Department of Family and Community Services (FaCS) longitudinal sample  of approximately 1 per cent  of Centrelink/Department of Social Security1clients is used. This data set is drawn  from fortnightly extracts of all records over the period  June 1995  to June 1999. The survey  includes those  in receipt of payment for the preceding fortnightly period, along  with  those  who  were otherwise eligible but received no payment, perhaps because of their  earnings.2 It does not contain information about hours of work  or the wage  rate during  the benefit  period; only earnings over each  fortnightly period  are available. Furthermore, no details  of earnings or hours worked are known for periods between benefit  claims.3Emphasis is given  to those  receiving unemployment benefits, the largest  component of which concerns the Newstart Allowance, generally about 17 per cent  of total benefit  payments.4  Conclusions are in section 5.

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2  Labour supply and earnings

This section considers models  of labour  supply behaviour within a framework in which individuals maximise utility  (specified in terms  of net consumption and leisure) subject to a nonlinear budget  constraint. The aim is to investigate the possible implications for the distribution of earnings, including the aggregate distribution and that of the restricted group  of individuals who  claim  a means-tested benefit. The simplifying assumption is made  that all income is obtained from employment. Furthermore, the model  assumes  that individuals are able to choose  their  hours of work  continuously. In practice available hours of work  may be more limited. The model  necessarily concentrates on the supply side of the market. Hence, it cannot be expected that such a model  would  provide  a sufficient explanation for the large  number  of individuals who  do not work, and who  are treated as ‘voluntary non-participants’ in the labour supply models. The model  is also static. However, additional complications are likely  to introduce more ‘noise’ into the relationship between the tax system  and the observed earnings distribution, and therefore reinforce the major conclusion of this paper.

2.1   A means-tested benefit

Suppose  that a specified level  of benefit  is obtained if the individual does not work  (and therefore has zero income). The benefit  is withdrawn at a relatively high ‘taper  rate’, s, if the individual works. Thus, if the individual’s wage  rate is w and the hours of work  are h, gross earnings are y = wh and the transfer  payment received is s(a – y). Eventually, at the earnings threshold, a, the benefit  falls to zero. Beyond  this level, the individual pays income tax of t(y – a) on earnings. The marginal tax rate, t, is below the taper  rate, s, applied to the benefit.

This system  gives rise to the piecewise linear  budget  constraint shown  as ABC in Figure 1(a), in which net income is measured on the vertical axis and hours of leisure are measured on the horizontal axis. The price  index  is normalised to unity, and savings  are ignored in this static framework, so that net income measures real consumption.5 Despite  the simplicity of this constraint, it provides a good approximation to the overall  shape  produced by many means- tested  systems  found in practice, including that in Australia, which contain  many (often overlapping) benefits and means  tests.

The slope  of the section BC is equal  to the net wage, w(1 – s). The slope  of the section AB is w(1 – t), so that as s > t, BC is flatter  than AB and the budget  set is non-convex. The point C is associated with  a benefit  equal  to sa. The point B corresponds to the hours of work  for which earnings are such that the individual neither receives a benefit  nor pays any income tax.

Consider  the individual’s labour  supply function  showing the variation in the number  of hours worked as the wage  rate increases.6The optimal  position is given  by the highest indifference curve  that can be reached subject to the budget  constraint. There are several  possibilities. First, for a low value  of the wage  rate, w, combined with  a high taper  rate, s, there  could  be a corner solution  at C where the individual does not work, and receives the maximum value  of the transfer  payment; this is shown  in Figure 1(a). Given a specific form for the individual’s utility function, it would  be possible to determine the threshold value  of the wage  rate, wL, such that lower values  would  place  the individual at this corner. This threshold would  obviously be higher, the higher  is the taper  rate applied to the benefit. As the wage  rate rises above wL, the section BC (which becomes steeper) may provide  a tangency solution  where the individual works  and continues to receive some benefit  income, as shown  in Figure 1(b).

Consider  how  hours worked and earnings are expected to vary as the wage  rate continues to increase beyond  wL. Figure 1(c)  shows  a situation in which, at the wage  rate, say wS, the individual is indifferent between working and paying tax, at point D, and working and receiving partial  benefits, at E. Where  this type  of double  tangency arises, the individual would  not work over the range  of hours between D and E; there  is a discontinuity in the individual’s labour supply function  relating hours worked to the wage  rate. The rate wSis a ‘switching’ wage, since the individual would  make a discrete jump or switch from one section of the budget  constraint to another.

An alternative labour  supply response is shown  in Figure 1(d), where an indifference curve  is tangential to section AB, at D, and simultaneously touches the point C. In this case, the individual would  never  be observed both working and receiving benefits. The person  would either  be at point C or at some point beyond  D on the section of the budget  constraint where income tax is paid and no benefit  is received. Again, there  is a ‘switching’ wage  rate at which a discrete jump in labour  supply takes  place. In both cases, the earnings level  jumps  across  the income threshold, a.

Figure 1: A means-tested benefit

Figure 1: A means-tested benefit


2.2   The earnings distribution

In this type  of system, all individuals would  face common  values  of the three  tax parameters, t and s, and the income threshold, a, above which income tax is paid.7 However, in any population, there  is a distribution of wage  rates and, in addition, there  are differences between individuals in their  preferences. The question arises  of how  a joint distribution of wages and preferences would  be expected to generate distributions of earnings and hours worked.

Suppose  that the preferences of individuals can be distinguished by a single  parameter, a. For any individual, the number  of hours worked, h, can be expressed as a function  of w and a, that is, by h(w,α). The associated earnings are therefore given  by y = wh(w,α).Suppose  furthermore that there  is a joint distribution of w and a, expressed in general as f(w,α). The form of the distribution of earnings, f(y), is therefore given  by the expression:

f (y) = ∫{∫ wh (w,α) f (w|α) dw } f (α) dα                                                                     (1)

where f(w|α) and f(α) respectively denote  the conditional distribution of w, given  α and the marginal distribution of α. Integration is over the relevant ranges. However, it has already been seen  that the function  h(w,α) has discontinuities, where the relevant wage  thresholds (such  as wLand wS) are themselves functions of preferences (and the tax parameters). For this reason, the expression in (1) is unlikely to be tractable, even  for very simple  tax systems. The present subsection therefore discusses the form of the distribution in general terms, while simulation results  are reported in the next  section.

Some individuals would  be observed at a point such as C on the respective budget  constraint, depending on their  wage  rates. However, the threshold value, wL, varies  among  individuals depending on both the wage  rate and preferences (in particular the relative strength of the taste for leisure). Of those  who  have labour  supply functions associated with  Figures  1(b)  and 1(c), a proportion (depending on their  wage  rates)  are among  the ‘working poor’ (earning and receiving partial  benefits), while others  pay income tax only. With some heterogeneity in preferences, there  is likely  to be an antimode in the distribution of earnings, at the earnings threshold, a, instead  of a complete gap. A complete gap would  only arise if all individuals were to have the same preferences, but face different  wage  rates.

A lower mode would  be expected among  benefit  claimants, but the position of the mode depends on the precise joint distribution and in some cases  it could  be at zero earnings. This is unlikely and is certainly not a necessary implication. In practice, demand-side considerations are likely  to produce a mode at zero.

Of those  who  have labour  supply functions associated with  Figure 1(d), there  would never  be any ‘working poor’. All claimants would  have zero incomes and receive the full benefit. The situation shown  in Figure 1(d)  is more likely, the higher  is the level  of the taper  rate at which benefits are withdrawn. The range  of wage  rates over which earnings are positive nevertheless varies, depending on the precise distribution of preferences. Among such a group, the distribution of earnings would  be expected to be bimodal, with  the lower mode at zero. The extent of the antimode again  is likely  to depend on the precise form of the joint distribution of wage  rates and preferences, though  its location is, as before, affected  by the income threshold, a.

There are therefore two possibilities for the form of the overall  distribution of earnings. First, it could  be bimodal, particularly if there  is a relatively small proportion of people for whom Figure 1(d)  is relevant, with  a lower mode at positive earnings. For a considerable degree of population heterogeneity, it would  be possible for the overall  distribution of earnings to look as if it were unimodal, especially if a histogram is produced using  quite  large  class widths. The second  alternative is that the overall  distribution of earnings is trimodal. The lowest mode would  be at zero, while the second  mode would  refer to the working poor, and the upper  mode would  apply  to workers paying income tax. Again, the distance between the modes  depends crucially on the degree of population heterogeneity.

Under this type  of nonlinear tax and transfer  system, the income distribution among  claimants only could  therefore have two modes, with  a large  number  of individuals bunched at zero income and a second  mode for the working poor. Alternatively, the distribution may have one mode, with  no mode at zero earnings.

A policy change, such as a reduction in the taper  rate, could  introduce a substantial change in the form of the earnings distribution, perhaps eliminating the lowest mode in a trimodal case. In the case of a bimodal  distribution, it is quite  possible for such a policy change to lead to a partial  filling of the density mass between the two modes. These aspects are investigated further in section 3.

2.3   A cost of claiming benefits

The nonlinear budget  constraint examined in the previous subsection needs  to be modified  if claiming benefits imposes a non-recoverable cost on claimants. The effect of this is to shift section BC of the budget  constraint in Figure 1 downwards by the amount  of the cost. The resulting budget  constraint is shown  as ABCD in Figure 2(a), where the section BC corresponds in this case to the situation in which the individual neither earns  enough to pay income tax, nor finds it worthwhile to claim  the means-tested benefit; hence the slope  of the segment BC is the gross wage  rate, w. The amount  of benefit  that would  be received is less than the cost of claiming.8

Consider  the labour  supply function. For low wage  rates (or high taper  rates)  the highest indifference curve  produces a corner  solution  at point D in Figure 2(a). As the wage  rate increases, several  possibilities arise. The individual may be induced to work  and simultaneously claim  benefits, but for further  increases in w there  may be a discrete jump to a point along  the range  BC, caused by the situation, also shown  in Figure 2(a), where an indifference curve  is tangential to points  on sections BC and CD. Further  increases in the wage  rate would push the individual to the corner. The individual would  remain  at the corner, B, over a range  of further wage  increases, until the wage  becomes sufficiently high to move the individual to a point on the segment AB, where income tax is paid.

Alternatively, an increase in the wage  rate from a low level  may lead to a discrete jump from the corner  at D to the corner  at B; this corresponds to the situation in Figure 2(b). A further possibility is that the individual could  jump to a tangency position along  BC, as shown  in Figure 2(c). Both of these  alternatives are situations in which the individual would  never simultaneously work  and claim  benefits. In Figure 2(c), it is possible, but not worthwhile, to claim  the means-tested benefit  because the entitlement is less than the cost of claiming.

Yet another  possibility is shown  in Figure 2(d). As the wage  rate increases, the individual jumps from a tangency along  CD to the corner  at B where earnings are equal  to the income threshold, a. There are no relevant wage  rates for which such an individual would  not claim benefits, if entitled to them.

The shape  of the distribution of earnings within a heterogeneous population, where individuals face different  wage  rates and have different  preferences, can take several  forms, depending on the precise form of the joint distribution as well  as the tax parameters. From the earlier argument, there  is likely  to be an antimode caused by the range  BCD, though  there  may be a mode at the corner, D, as well  as a mode corresponding to earnings of benefit  claimants along the range  CD. There is likely  (but not certain) to be another  mode corresponding to the kink, B, since  each  individual remains at this type  of corner  for a range  of wage  rates. In addition, it is possible to have another  mode corresponding to tangency solutions along  the range  AB.

It is therefore possible to have a distribution with  four modes, though  only the mode corresponding to the income threshold, a, can be directly linked  to a parameter of the tax and transfer  system. Although  the number  of hours worked, h, associated with  the point, B, differs among  individuals, this point involves  the same value  of gross earnings for each  person.

The existence of a cost of claiming benefits may be an important factor in the labour  supply and benefit  take-up behaviour of a significant number  of individuals. Depending on the degree of wage  and preference heterogeneity, this may be associated with  an earnings distribution that is hard to distinguish from a distribution associated with  the first system considered above, of Figure 1, where there  is always a complete take-up of benefits.

Figure 2: Take-up and the means-tested benefit

Figure 2: Take-up and the means-tested benefit

2.4   Further complication

In practice, there  may be a ‘free’ area whereby earnings do not give rise to a reduction in benefits. This creates a further  kink in budget  constraints and, from the point of view  of the earnings distribution, the potential for another  mode. In cases  where there  is a threshold at which a benefit  taper  is introduced, or where it involves  an increase in the taper  rate, there  is a discrete increase in the effective marginal tax rate facing  individuals. The budget  constraint has a kink or corner  where it becomes flatter  as the threshold is crossed.

Each of these  corners is associated with  a certain amount  of stability, in the sense  that earnings are unchanged over a range  of wage  rates.9 The existence of such a range  of wage  rates (though the precise values  may differ among  individuals) means  that there  may be a mode in the earnings distribution at each  corner. Here the modes  are clearly associated with  tax and transfer policy variables. Their relative importance again  depends on the extent of population heterogeneity, along  with  the size of the change in the marginal tax rate involved. However, it is not certain to produce a mode at the kink.

Another situation, in which a mode at zero earnings is likely  to exist, could  arise from the existence of fixed  costs of employment. These may include costs of travel  to work, clothing, and child  care  costs. They are likely  to differ among  individuals. Fixed costs of working imply  that non-wage income drops sharply as the number  of hours worked becomes positive. In terms  of the constraint of the previous subsection, it is possible for an indifference curve  to touch  the tip of the spike  at zero hours and be tangential to the constraint along  the range  BC.

A group  of individuals with  heterogeneous preferences would  produce an earnings distribution of benefit  claimants having  an antimode corresponding to hours of work  to the right of the tangency solution, with  a mode at zero hours. In the case where there  is also a ‘free area’, which may be expected to give rise to a mode where a taper  begins  to operate, the existence of fixed costs of employment could  eliminate such a mode. The resulting earnings distribution would
be hard to distinguish from some of those  arising  in the simpler case discussed at the start of this section.

An important implication of the above discussion is that there  is no clear ‘one-to-one’ relationship between possible earnings distributions and the tax and transfer  system. The transformation from various  forms of labour  supply function  to the earnings distribution involves the joint distribution of wage  rates and preferences in the population. Population heterogeneity could  almost entirely mask crucial features of incentive effects  and labour  supply functions, or lead to quite  different  tax models  giving  rise to similar  distributions. Some forms of mode that may be expected are associated with  discrete increases in marginal tax rates at specified income thresholds, though  they  may not always appear, depending on the nature of the relevant wage  and preference distributions.

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3  A simulation analysis

3.1   Simulated distributions

Explicit  solutions of the expression for the earnings distribution in () cannot  be obtained. However, the distributional properties discussed in the previous section can usefully be investigated further  using  a simulation approach. Suppose  that all individuals have a Cobb- Douglas utility  function, U = cαl1-α, where c and l are consumption (net  income) and the proportion of time spent  in leisure. The Cobb-Douglas is convenient as it requires only one parameter. Population heterogeneity can therefore be modelled by specifying a joint distribution for the wage  rate, w, and the preference parameter, α. The following examples assume  that they are jointly  lognormally distributed. It is therefore possible to select  a large  number  of individuals at random  from the specified distribution and then to examine the labour  supply behaviour of each  individual under  alternative tax structures.10

Consider  the basic  tax and transfer  scheme of Figure 1, in which there  is a single  means-tested benefit  with  a taper  of s for those  with  earnings below a threshold, a, and a single  marginal income tax rate of t applied to earnings above a. The government cannot  set these  three parameters independently because a degree of freedom  is lost as a result  of the government’s own  budget  constraint. For given  values  of t and s, the value  of the tax threshold, a, required for revenue neutrality, can be calculated using  an iterative search  procedure. This ensures that each individual selects the value  of l (and therefore labour  supply) by maximising U subject to the nonlinear budget  constraint, and maximisation by each  individual is consistent with  the government raising  sufficient revenue from income tax in order  to finance non-transfer expenditure as well  as the cost of the means-tested transfer  payment.

Simulated distributions were based  on 3 000 individuals and were obtained for alternative values of s, t, the non-transfer  revenue per capita, R, and the variance of logarithms, V(α), of the preference coefficient, α. Examples  are shown  in Figure 3. In all cases  a negative correlation between (the  logarithms of) wages and preferences of –0.75  was assumed. This implies that the high-wage individuals have, on average, a stronger preference for consumption (net  income) compared with  leisure. The arithmetic mean  of α was set equal  to 0.75, and the variance of logarithms of the wage  rate was 0.5. The absolute value  of the mean  of logarithms of w is unimportant, since  thresholds can be expressed in terms  of ratios of the median  wage  rate.11

Figure 3(a)  shows  the bimodal  earnings distribution for s = 0.5 and t = 0.2, and with  a determined endogenously (using  the iterative process mentioned above)  in order  to finance the ‘pure  transfer’ system. There is no mode at zero earnings, and the preference heterogeneity leaves  a relatively small gap between the two modes  (one  that would  virtually disappear if a larger  class width  were chosen for the histogram). The need  to raise non-transfer  revenue (of 11 per cent  of the median  wage  per person12) means  that, with  the same tax rates, the revenue- neutral value  of the threshold, a, must be lower. This in turn reduces the size of the transfer payment available; for those  not working it is equal  to as. The effect of this change is shown  in Figure 3(b), where the lower mode is substantially reduced, and only a small change in the class width  chosen for the histogram would  conceal its existence. This example is more realistic than the pure  transfer  system. Despite  the crucial role of endogenous labour  supply choices in a utility-maximising framework, in which individuals can select  the preferred number  of hours of work, the resulting earnings distribution reveals  little  about the complex range  of incentive effects  of the taper  rate.

Figure 3(c)  shows  the effect of increasing both the taper  rate (to s = 0.7)  and the tax rate (to t = 0.3), for a pure  transfer  system. The higher  level  of the transfer  available (financed by the higher  tax rate, combined with  the fact that the maximum benefit  is as) discourages participation in employment and creates a third mode at zero earnings. Again, the introduction of additional revenue per person  (in this case about 18 per cent  of the median  wage  rate13) changes the earnings distribution considerably, as shown  in Figure 3(d). This difference is brought about by the need  to raise the additional revenue, and therefore a reduction in the tax threshold and the size of transfers, rather  than any changes in the taper  and tax rates. As before, Figure 3(d)  largely conceals the complexity of the labour  supply functions of different individuals.

The assumptions underlying Figure 3(e)  are similar  to those  of Figure 3(a), except that the income tax rate is higher, at t = 0.3. This allows  a higher  tax threshold, a, to be financed, thereby shifting  much  more of the distribution to the range  where individuals simultaneously work  and receive reduced means-tested transfer  payments. Finally, Figure 3(f) shows  how  the distribution in Figure 3(e)  is affected  by a reduction in the degree of preference heterogeneity; there  is a complete gap in the distribution between the two modes.

Figure 3: Simulated earnings distributions

Figure 3: Simulated earnings distributions

3.2   Some general properties

These histograms suggest the following results  which reinforce the general arguments made above. A trimodal earnings distribution is likely  to be produced by the following characteristics: a relatively high dispersion in the value  of a (associated with  high values  of the variance of logarithms); a high value  of the taper  rate, s; and a relatively large  difference between the income tax rate, t, and the taper  rate, s.

In cases  where three  modes  exist, an increase in the revenue needed for non-transfer  purposes reduces the value  of the income threshold, a, that can be financed with  any given  tax rate. This in turn reduces the number  of modes  to two, so that there  is no longer  a mode at zero earnings. Furthermore the lower mode, applying to those  who  are described as ‘working poor’, is substantially reduced.

Where  two modes  exist, a large  degree of preference heterogeneity produces a relatively small gap between the modes. Indeed, small increases in the class widths used to generate the earnings distribution histograms are capable of producing distributions that look like conventional unimodal positively skewed earnings distributions. Hence, such histograms may conceal the distributional implications of the incentive effects  of the tax and transfer  system.

This suggests that it would  be unwise to be optimistic about the possibility of observing clear effects  on incentives of nonlinear tax structures simply  by examining earnings distributions, especially where broad population groups  are considered.

There are further  simplifying assumptions made  by the static  labour  supply model  considered here. Some individuals may work  a number  of hours that are not optimal, at the relevant wage rate, from the point of view  of a single  period. From a longer-term point of view  it may be worthwhile being  in the labour  market  in that particular job, which may offer future  prospects, including on-the-job training, experience, contacts (social  and professional) and other  in-work benefits. Furthermore, some individuals may in practice be constrained, in the sense  that there may not be the opportunity to select  the optimal  number  of hours; the model  is entirely a supply-side analysis.

The simulations discussed above imply  strongly negatively-skewed and bimodal  distributions of hours worked, with  a large  dispersion. The exception is associated with  Figure 3(c), where there is a lower mode at zero hours. Furthermore, only broad demographic groups  can be identified in observed earnings distributions. In addition, the model  assumes  that all income is derived from earnings from employment, whereas in practice income is obtained from other sources, and there  are various  allowances in the income tax system, introducing further heterogeneity by making  the threshold, a, individual-specific. All these  factors  introduce a further substantial amount  of ‘noise’ into the observed distributions, in addition  to the type  of preference heterogeneity discussed earlier.

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4  Empirical distributions

4.1   Income distribution survey data

The simulated distributions may be compared with  those  obtained using  the main source of Australian  income distribution data, the Income  Distribution Survey  (IDS). In view  of the fact that means  tests are based  on income from all sources, rather  than simply  earnings from employment, distributions of income from all sources (excluding transfer  payments and partner’s income, where relevant) are shown  in Figure 4, for several  demographic groups. These histograms exclude those  with  zero incomes, although there  is a large  mode at zero which is mainly  associated with  demand-side factors. The diagrams are based  on pooled  data from the 1995  and 1996  surveys, in order  to increase the sample  size. The very low incomes in each  of the cases  of Figures  4(c)  to 4(f) relate  to small amounts  of interest income.

These distributions reveal  that, within each  demographic group, there  is much  heterogeneity; the distributions are far from smooth. The levels  of means-tested benefits, in relation to tax rates, are influenced by the need  to raise substantial non-transfer  revenue, so that the simulated distributions of the form of Figures  3(b)  and 3(d)  are most relevant here. Except  for the figure for lone parents, which reflects a considerable degree of variability, the figures  show  that the distributions conform  approximately to the bimodal  form expected from a means-tested system.14 Nevertheless, they  conceal a large  amount  of detail  concerning the complex nature  of the incentive effects  generated by the tax and transfer  system.

It was mentioned above that individuals may be to some extent constrained in the extent to which hours of work  can be varied. Examination  of the associated distributions of hours worked (not shown  here)  revealed that, while the distributions were generally of the negatively skewed form expected, and covered the entire  range  of hours, they  typically had more peaked modes  (especially for males), less density in the lower hours and, not surprisingly, much  more variability than the corresponding types  of hours distribution generated in the simulations.

4.2   Unemployment benefit claimants

This subsection examines the earnings distributions of unemployment benefit  recipients using the FaCS data described in the introduction. Newstart Allowance is the main unemployment benefit  in Australia, and for the period  between September 1996  and July 1998  was the only unemployment benefit  for those  aged  between 18 to 21 years. Since  July 1998  unemployed persons under  the age of 21 were no longer  eligible for Newstart Allowance but could  claim the Youth Allowance (which also replaced Youth Training  Allowance, Sickness Allowance for those  aged  under  21 years  and AUSTUDY for students up to 25 years  old).15

Individuals can receive Newstart Allowance and undertake suitable paid work  or engage in an activity that improves their  prospects of finding  suitable paid work. An income test is applied, the main characteristics of which are that (before  the cut-out point is reached) there  are two taper  rates. Fortnightly earnings between $60 and $140  dollars  per fortnight reduce thefortnightly allowance by 50 cents  in the dollar. For earnings above $140  per fortnight, the allowance is reduced by 70 cents  in the dollar. For further  details, see the appendix to this paper.

Figure 4: Non-benefit weekly income ($): IDS data

Figure 4: Non-benefit weekly income ($): IDS data

The budget  constraint facing  each  individual depends on the precise wage  rate and a range  of demographic characteristics. These constraints are typically extremely complicated, having many kinks and, in some cases, discontinuities. Many important labour  supply effects  are unlikely to be evident from overall  earnings distributions. Nevertheless, it is worthwhile investigating the earnings distributions of unemployment benefit  recipients to see if any of the characteristics discussed earlier are revealed. In particular, the question arises  of whether modes appear at the $60 and $140  thresholds.

The FaCS data contain  information only about DSS/Centrelink clients during  the benefit  period. Hence the distributions provide  limited  information about the overall  earnings distribution. This may be considered to be made  up of a mixture of two separate distributions of beneficiaries and other  workers. It is likely  that there  is a substantial overlap in the relevant ranges  of the components that form this ‘mixture distribution’. Hence it is not possible to evaluate the extent and nature  of the expected antimode produced by the typical non-convexity of budget  sets.16

Histograms  of fortnightly earnings for single  males  in a range  of age groups, using  all observations over the period  June 1995  to June 1999, are shown  in Figure 5. As mentioned above, these  histograms omit frequencies for zero earnings, as a substantial mode otherwise appears that would  reduce the detail  shown  in the remainder of the distribution. Hence in what follows  it should  be remembered that there  is another  dominant mode at zero earnings. This (unshown) mode is consistent with  the existence of a non-participation corner  solution  in labour supply behaviour. However, it is most unlikely that it can be explained entirely by supply-side considerations.

These figures  show  a lower mode in what  could  be a trimodal overall  earnings distribution. The distribution for single  males  aged  55 and over shows  some evidence of modes  associated with the $60 and $140  thresholds in the Newstart Allowance income test, though  these  are not pronounced. Similar modes  are not revealed for other  age groups, though  the mode in each  case appears within the range  where the 50 per cent  taper  rate, rather  than the 70 per cent  rate, applies. The absence of a mode at these  thresholds is nevertheless consistent with  the existence of a significant role in labour  supply determination. As stressed earlier, the earnings distribution depends on the precise form of the wage  rate distribution and the nature  and heterogeneity  of preferences of the sample  groups  (as shown  by the above simulations). The lack of prominence of the thresholds may also partially result  from the operation of an Earnings Credit, which effectively provided a certain amount  of income averaging in calculating benefit  entitlement; this is discussed in the following subsection.17

Histograms  for single  females  in a number  of age groups  over the same period  are shown  in Figure 6. Again, at this level  of aggregation, no modes  are revealed at the threshold income levels, though  the mode does lie within the 50 per cent  taper  range. These distributions, as for the males, reveal  considerable variation in fortnightly earnings.

Figure 5: Earned fortnightly income for unemployment benefit recipients (single males)

Figure 5: Earned fortnightly income for unemployment benefit recipients (single males)

Figure 6: Earned fortnightly income for recipients of unemployment benefit (single females)

Figure 6: Earned fortnightly income for recipients of unemployment benefit (single females)

Some selected examples for married/partnered individuals, with  further  disaggregations according to the number  of dependent children, are shown  in Figure 7. Like the previous examples, the figures  for males  reveal  considerable variation in earnings with, in most cases, a mode covering (in addition  to the zero mode not shown) the range  of earnings where the 50 per cent  taper  applies. In some cases  where there  are more children, a further  mode appears in the higher  earnings range. There are also examples where the $60 threshold is associated with a relatively stronger mode. The histograms for women reveal  more variability, though  in most cases  the dominant mode (other  than at zero)  is within the 50 per cent  taper  range.

A feature  of the Newstart Allowance for part of the period  was the Earnings Credit.18 This credit, introduced in 1994, was accruable up to a maximum amount  of $500  dollars. It could  be used to offset income if the recipient’s income was below the income test cut-out for that fortnight. The credit  was accrued at a rate equal  to the ‘free area’ of a particular allowance or pension. Hence it provided a type  of income averaging provision. However, the condition regarding the cut-out level  means  that recipients could  only use the credit  if they  would  have been  entitled to some level  of payment in that fortnight without the use of the credit. However, it means  that the threshold income levels  were effectively to some extent ‘variable’, depending on the degree of variability in fortnightly earnings. The existence of the credit  may perhaps be thought partially to explain why, in the majority of demographic groups  identified, there  were no modes  at the $60 and $140  earnings levels.

From March 1996  the Earnings Credit  could  be accrued at a lower rate, equal  to the unused portion  of the free area. Furthermore, the maximum usable  credit  in any fortnight was limited  to $100. Once the maximum credit  was used, the recipient could  not access any more credits for 12 months. The Earnings Credit  was abolished in March 1997.

For comparison purposes, the sample  was therefore divided  into two periods, before  March 1996  and after March 1997. In some cases, after the abolition of the Earnings Credit, stronger modes  appear at the one or more of the threshold levels  and often the distributions become more highly  (positively) skewed. It would  be valuable to be able to identify  a control  group with  similar  characteristics to the demographic group  potentially affected  by the policy change. However, in the present context it is not possible to identify  such control  groups. All pensioners and allowees had access to the Earnings Credit  and all were in principle affected  by its abolition in 1997. Hence, caution must be used in interpreting the earnings distribution.19

Figure 7: Earned fortnightly income for recipients of unemployment benefit

Figure 7: Earned fortnightly income for recipients of unemployment benefit

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5  Conclusions

This paper  has considered the question of whether, in the absence of data on the actual  number of hours worked of each  individual, it is possible to identify  any labour  supply incentive effects of a tax and transfer  system  using  information on only the distribution of earnings. An indirect approach was explored in which the major characteristics of the earnings distributions arising from a simple  labour  supply model  were first examined, and illustrated using  simulation methods. These characteristics include the existence of modes  and antimodes caused by kinks where effective marginal tax rates increase, and non-convexities in budget  constraints arising from means-testing. Actual earnings distributions, concentrating on unemployment benefit recipients, were then compared with  the types  of distribution that can be generated by labour supply models.

It was suggested that the use of such an approach must be severely limited, in view  of the fact that there  is no one-to-one correspondence between the form of the earnings distribution and the parameters of a tax and transfer  system. The form of the joint distribution of wage  rates and preferences plays  a substantial role in combining with  a variety  of types  of labour  supply response to generate the earnings distribution. Furthermore, in practice only broad demographic groups  can be identified, so that any sample  must contain  considerable heterogeneity.

Despite  these  limitations, the examination of a wide  range  of distributions revealed, for a number of demographic groups, some of the expected characteristics associated with  the Newstart Allowance means  test. In addition, the abolition of the Earnings Credit  (which, in view of its averaging provisions, would  have ‘blurred’ the income thresholds, depending on the degree of variability of earnings over time)  was found in some cases  to be associated with changes in earnings distributions that are consistent with  incentive effects. No such conclusions could  be reached for a large  number  of other  demographic groups  examined. Caution  is required in view  of the impossibility of identifying a control  group.

The paper  therefore has the negative conclusion that the identification of labour  supply incentive effects  of tax structures by the examination of earnings distributions is limited. In order to examine the labour  supply effects  of tax and transfer  systems, there  is no real alternative to a full-scale  econometric study. However, there  is some evidence, however indirect, that incentives matter. Of course, economists have known for a long time that, in designing tax and transfer  systems, and reforms  to them, such incentive effects  need  to be taken  seriously.

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Appendix: The Newstart Allowance

The Newstart Allowance is the main unemployment benefit  in Australia. For the period between September 1996  and June 1998, in order  to qualify  for the allowance a person  must: be aged  18 or over and under  Age Pension  age or aged  under  18 and in receipt of Job Search Allowance as at 1/1/95; be unemployed; be registered with  Centrelink; be prepared to enter into, comply with  or vary an existing activity agreement; and satisfy the activity test.20 Individuals satisfy the activity test if they  are: 1) actively seeking and willing to undertake suitable paid work; or 2) complying with  a requirement (if any)  from Centrelink to undertake suitable paid work  or engage in an activity (approved by Centrelink) that improves their prospects of finding  work  or assists  them in seeking suitable paid work. Approved  activities must help  the prospect of finding  work  or assist in seeking suitable paid work. The types  of activity that may be undertaken include: training, vocational, personal development, literacy and migrant  language courses; self-employment development and group-community cooperative enterprise development; voluntary work; vocational rehabilitation; and an activity nominated by a client  living  in a remote  area. Clients  receiving Newstart Allowance must apply  to Centrelink for approval to undertake specified activities.

Rates of payment (at March 1998) are:


  • 18–20  at home, $174.80
  • 18–20, away  from home, no children $265.50
  • 21 or over, no children, $321.50
  • 18 or over, with  children $347.80
  • 60 or over, after 9 months, $347.80


  • both over 21, or over 18 with  children (each) $290.10
  • no children, one partner over 21, $290.10
  • for partner aged  21 and over, $290.10
  • for partner aged  18–20, $265.50
  • or partner under  18, $240.00

In addition, a Pharmaceutical Allowance of $5.40  is paid (single or couple combined).

The income test relating to Newstart Allowance may be expressed as follows. Let the unemployed person’s fortnightly income be yu and the income of the spouse, where relevant, be Ys. The basic  rate, NSAB, is given  if Yu ≤$60 and ys Yc, where Yc is referred to as the ‘cut-out’ income, which also depends on demographic characteristics. The Newstart Allowance, NSA, is reduced by 50 cents  for each  dollar earned in excess of $60 per fortnight, and by a further  20 cents  for each  dollar earned in excess of $140  per fortnight. Similarly, NSA is reduced by 70 cents  for each  dollar that the spouse  of an unemployed person  earns  in excess of $497.27 per fortnight.

The Newstart Allowance can be calculated by: NSA = max [0,NSA1]

NSA1= NSAB– max[0,0.5(Yu– 60)]

– max[0,0.2(Yu– 140)]

– max[0,0.7(YsYc)]

The Newstart Allowance is taxable.

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  1. The Department of Family and Community Services was created in 1998  out of elements of four different  agencies, one of which was the Department of Social Security.
  2. It also includes those  not in receipt of a payment but who  are partners of recipients, along with  those  in receipt of a payment not classed as an income security payment, but who  are partners of customers receiving an income security payment.
  3. Furthermore, there  is insufficient information about individuals’ characteristics to be able to assign  wage  rates to individuals, using, for example, estimated wage  equations based  on other data (such  as the Income  Distribution Survey).
  4. This is the largest  proportion after the Age Pension, which makes  up about 36 per cent  of claims.
  5. The two-rate  model  was first examined in detail  by Lambert (1985) using  Cobb-Douglas preferences. For the extension to the CES case, see Creedy  (1994, 1996).
  6. The nature  of the budget  constraint means  that simple  continuous functions, such as those examined in Stern (1986) in which hours worked are expressed in terms  of the net wage, are inappropriate. On the econometrics on piecewise-linear budget  constraints, see Moffitt (1986).
  7. The government could  not set these  three  policy instruments independently, as a degree of freedom  is lost by the need  to satisfy a government budget  constraint. In some cases  the threshold, a, may depend on individuals’ characteristics.
  8. This situation is examined in detail  in Creedy  (1999).
  9. However, labour  supply falls, since  the labour  supply function, over the range  of wage  rates for which the kink is relevant, is a rectangular hyperbola in view  of the fact that wh = y is constant.
  10. For further  discussion of the simulation procedure in the context of a joint distribution of w and α, see Creedy  (1996).
  11. In the simulations, it was arbitrarily set at 4. This may be kept  in mind when  considering the values  of revenue per capita, in the two cases  that are not of ‘pure  transfer’ systems, and the earnings levels  shown  in the figures.
  12. It was set at 6, so that with  a mean  of log w of 4, the revenue requirement is 6/exp 4 = 0.11.  
  13. It was set at 10 units in the simulations.
  14. As expected, the lower mode is in most cases  reduced somewhat if only earnings are considered.
  15. 18–20  year  olds who  were in receipt of Newstart Allowance at 17 June 1997  and still on payment on 1 July 1998, remain  on Newstart Allowance.
  16. For a treatment of bimodal  distributions using  mixture distributions, see Bakker and Creedy (1999).
  17. A further  complication arises  from the existence of a partner income test; see the appendix.
  18. For further  discussion of the Earnings Credit, concentrating on the possible impact  of its removal  on the number  of earners, see FaCS (1999). This argues, using  time series information, that the reduction in the number  of earners was related to the abolition of the Earnings Credit. However, no ‘control group’ was used.
  19. The identification of a control  group  is problematic in other  contexts. For example, during the relevant period, in 1997, there  was a 25 per cent  reduction in the maximum rate of Rent Assistance for sharers. This may be thought to encourage higher  labour  supply. However, sharers  (single non-home  owners in rental  accommodation who  are sharing) cannot  be precisely identified in the data. One approach may be to take those  single individuals aged  less than 30 who  are renters. Those in the same age group  who  are non- renters might  be a control  group, but an analysis using  this classification proved  to be inconclusive. Average  earnings of the ‘treatment’ group  actually fell by about 15 per cent, compared with  about 6 per cent  for the control  group, while the median  increased for the former group  and was constant for the latter  group.
  20. From July 1998  18 to 24 year  old Newstart and Youth Allowance customers, in receipt of payments for six months, are required to undertake one or a combination of a range  of approved activities (part  time work, part time study, voluntary work  and Work for the Dole) in return  for income support. This is in addition  to job search  activity.

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Bakker, A. & Creedy, J. 1999,‘Macroeconomic variables and income inequality in New Zealand: an exploration using  conditional mixture distributions’, New Zealand Economic Papers, 33, no. 2, pp. 59–79.

Creedy, J. 1994,‘Taxes and transfers  with  endogenous earnings: some basic  analytics’, Bulletin of Economic Research, 46, pp. 97–130.

Creedy, J. 1996, Fiscal Policy and Social Welfare: An Analysis of Alternative Tax and Transfer Systems, Edward Elgar, Cheltenham.

Creedy, J. 1999,‘Take-up of means-tested benefits with  labour  supply responses’, University of Melbourne Department of Economics  Research Paper, no. 695.

Department of Family and Community Services (FaCS), Labour Market Analysis Section, Labour Market Branch 1999,‘The impact  on unemployment allowances of abolishing the Earnings Credit  Scheme’.

Lambert, P. J. 1985,‘Endogenising the income distribution: the redistributive effects, and the Laffer effects, of a progressive tax-benefit structure’, European Journal of Political Economy, 1, pp. 3–20.

Moffitt, R. 1986,‘The econometrics of piecewise-linear budget  constraints’, Journal of Business and Economic Statistics, no. 4, pp. 317–28.

Stern, N. 1986,‘On the specification of labour  supply functions’, in Unemployment, Search and Labour Supply (ed. by R. Blundell  and I. Walker), pp. 143–89, Cambridge University Press, Cambridge.

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