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Abstract

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

We estimate parametric and semi-parametric binary choice models of benefit take-up by British pensioners and use a revealed preference argument to infer the cash-equivalent value of disutility arising from stigma or complexity of the claims process. These implicit costs turn out to be relatively small, averaging about £3–4 per week across Income Support recipients. Using the Foster–Greer–Thorbecke measure of poverty among pensioners, we find that allowing for implicit claim costs incurred by benefit recipients raises the measured degree of poverty by not more than 13%. Copyright © 2007 John Wiley & Sons, Ltd.


1. INTRODUCTION

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

Welfare programme participation (or, in UK parlance, the take-up of means-tested benefits) has been the subject of much applied research. Studies by Moffitt (1983), Blundell et al. (1988), Duclos (1995), Bollinger and David (1997) and Keane and Moffitt (1998) are examples of the development of this literature. Means-testing is an obvious way of focusing welfare spending on those most in need, while controlling the burden on public finances. The drawback of means-testing is that people who are entitled to receive welfare benefit may not come forward to claim it. There is evidence that this is an important feature of many welfare programmes in practice (see Kim and Mergoupis, 1997, on AFDC and Food Stamps in the USA, and DWP, 2001, on a range of programmes in the UK). Possible reasons include the social stigma that may be associated with welfare receipt and the effort or unpleasantness entailed in the claim process (Moffitt, 1983). Other components of claim costs may include the costs of information gathering and processing and the implicit risk premium associated with the unpredictability of the claim outcome (Halpern and Hausman, 1986). Economic models of take-up are often criticised by non-economists as assuming implausible degrees of rationality and knowledge. This ignores the fact that it may be efficient to remain in ignorance of the details of welfare programmes if the costs of discovering and understanding their rules are very large and the potential benefits are moderate. It is hard to believe that, if welfare payments were raised to arbitrarily large amounts, a large number of the uninformed would not take some action to become better informed.

There are few specific estimates of the magnitude of claim costs and findings have been reported in various forms. For example, Duclos (1995) reports expected Supplementary Benefit claim costs of around £3–4 per week for single pensioners and figures as high as £30 per week for some other groups. Moffitt (1983) quotes an elasticity of AFDC participation with respect to entitlement of roughly 0.6, while Blundell et al.1988 report that a 50% increase in Housing Benefit entitlement for the average pensioner household generates a 7 percentage point increase in take-up (an elasticity of roughly 0.2). There is no simple principle established in the literature for translating results on the participation–entitlement elasticity into the implied level of underlying claim costs. One of our aims is to develop and implement a way of doing this. If the process of welfare participation gives rise to some form of disutility, then it is possible to construct an equivalent weekly cash amount which should be deducted from observed net income of benefit claimants to give a true income–metric welfare measure. However, in making this income adjustment, we allow for self-selection into participation, implying that claimants tend to be those experiencing lower than average levels of stigma and other claim costs and non-claimants tend to be those with high levels of claim cost. We have found no published empirical work taking account of this self-selection in calculating individual-specific estimates of claim costs incurred by claimants, despite the fact that take-up models are models of self-selection. A further innovation of the paper is to assess the potential impact of implicit claim costs on the measurement of poverty.

Our application is to British pensioners at least 5 years beyond the official retirement age. Apart from the inherent interest in older pensioners as a relatively low-income group, it has the advantage that labour supply is virtually zero, so that labour market complications can be avoided. British pensioners rely heavily on means-tested income from the state, despite the fact that the state pension itself is not means-tested and private pension coverage is high by international standards. In 2002/3, 32% of pensioners received means-tested state benefit (DWP, 2004b). The scope of means-tested pensioner benefits was extended from October 2003 with the introduction of a new means-tested benefit, Pension Credit, to which almost 50% of pensioners are believed to be entitled. Despite the high coverage of means-tested pensioner benefits, they are thought to suffer from a significant degree of non take-up. This is particularly so for Income Support,1 which provides general income maintenance. Official estimates are that in 2001/2 about 33% of pensioners who appeared to be entitled to IS did not receive it (DWP, 2004a).

2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

The state pays three main types of benefits to British pensioners: the flat-rate basic state pension, an earnings-related state pension and means-tested benefits. There are also disability-related benefits, which are not means-tested. Most pensioners are entitled to the basic state pension earned through paying social security contributions during their working lives, but not all qualify for the full rate of pension. Entitlements to the state earnings-related pension scheme (SERPS) depend on contributions and past earnings; it is possible to opt out of SERPS and contribute to a private pension instead. Recent figures show that the average total state pension payment (basic pension, SERPS and other minor components) was marginally above the full basic state pension (DWP, 2004c) but below the means-tested benefit level.

During our sample period, there were three main means-tested benefits for pensioners: Income Support (IS), providing general income maintenance; Housing Benefit (HB), giving help with rent; and Council Tax Benefit (CTB), which reduces recipients' liability for local housing-related tax. The rules for calculation of entitlement to HB and CTB mean that pensioners entitled to IS will also be entitled to maximum HB if they pay rent, and CTB if they are liable for Council Tax. People not entitled to IS may be entitled to lower amounts of HB and CTB. Entitlement to each of the three benefits can be calculated independently. In this paper our concern is with IS. There are good reasons to focus specifically on IS. Its rules are independent of receipt of HB and CTB, so there is no bias introduced by analysing IS participation separately from HB and CTB. Moreover, HB has a very high participation rate (over 90%) and CTB entitlements are generally very small, so the decision to claim IS is the critical participation decision.

Pensioner units—single pensioners or couples—are our unit of analysis. In our sample period, entitlement to IS is zero if financial holdings exceed an upper threshold (£8000, increased in 2001/2 to £12,000). Otherwise it is the difference between a guaranteed minimum (depending on age, disability and whether single or living with a partner) and assessable income (depending on the pensioner unit's income and capital). Assessable income does not include HB and CTB receipts, so entitlements to the three means-tested benefits are independent. For pensioners, the relevant disability-related addition to the guaranteed minimum is the Severe Disability Premium (SDP). Eligibility for the SDP is determined partly by receipt of Attendance Allowance (AA) or the care component of Disability Living Allowance (DLA), which are mutually exclusive, non-means-tested disability-related benefits. Sources of income therefore affect both assessable income and guaranteed amounts. Like HB and CTB, AA and DLA are excluded from assessable income. Actual income from capital is also excluded. Instead a notional income from capital between a lower threshold (£3000, increased in 2001/2 to £6000) and the upper threshold is assumed at the rate of £1 a week for each £250 or part of £250 of capital between the two limits. In addition to the change in capital limits, there was a substantial real-terms increase in the level of the income guarantee; these changes provide an important source of identifying variation. The main benefit rates prevailing over the sample period are set out in the appendix of Hernandez et al. (2006).

To receive IS, pensioners must submit a claim to the benefits agency. For most of the period, this entailed completing and returning a complex form to their local social security office. Details of all sources of income, savings and relevant personal characteristics have to be provided. Attached to the IS form are supplementary forms covering HB and CTB. Consequently, applications for IS are almost always accompanied by applications for CTB and (for renters) HB, and IS is almost never received in isolation.2 If found to be entitled to IS, payment is often made with the state pension so the pensioner does not need to attend a social security office every week. Reassessments are made annually and, between assessments, changes in circumstances should be reported immediately so that payment can be adjusted.

3. THE 1997–2002 FAMILY RESOURCES SURVEY

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

The Family Resources Survey (FRS) is a continuous cross-sectional survey of British households carried out on behalf of the DWP during April 1997 to March 2002. In principle, the FRS gives all information necessary to assess each FRS pensioner unit's entitlement to IS and establish whether they are receiving IS. We have applied the following process of error detection and correction before using the data (and before making the sample deletions listed below). We first reversed data edits and imputations made by the DWP, affecting benefit receipts, private pension income and capital holdings, because we detected some inconsistencies in edits to benefit data and because some imputation procedures (such as substitution of sample means for missing values) are inappropriate for our purposes. The next stage involved detecting inconsistencies in benefit data and reconciling them where possible. Errors in recorded receipts of social security benefits are generally easier to identify than errors in other sources of income or in capital because specified benefit rates and eligibility rules allow consistency checks to be made. Missing benefit receipts were imputed where a correct value could be identified unambiguously. For example, some pensioners in the FRS are able to give a breakdown of their state pension payments which helps disentangle different benefits received as one combined payment. In other cases it is clear that a payment of IS is included in their reported pension and there is double counting if a separate amount of IS is also recorded. Where it was impossible to correct an inconsistency or impute a missing value reliably, the value was left missing. This was true for all missing values for private pension and capital holdings where there is no reliable basis for imputation. Full details of the data cleaning process are given in Hancock and Barker, 2005.

Two different versions of the dataset are used, differing in the entitlement measure used. Sample 1 uses simulated entitlement for all households and makes no use of recorded benefit amounts, beyond the receipt/non-receipt distinction; for entitled households, sample 2 substitutes recorded benefit where available, for simulated entitlement, provided it does not exceed the guaranteed minimum for the benefit unit and provided the respondent consulted some form of IS documentation when answering the survey question.3 We focus on older pensioners, defined as single people at least 5 years over state retirement age (60 for women and 65 for men) or couples where both partners are at least 5 years above retirement age. There are several reasons for this: they are a group with a high poverty rate; they have very little labour market involvement to complicate the welfare participation issue; and having been retired for a relatively long time, their adjustment to post-retirement circumstances is likely to be complete.4 This contrasts with the dynamic modelling issues faced by Anderson and Meyer, 1997. There is currently no UK longitudinal survey adequate for the purposes of simulating means-tested welfare entitlements. This means that we have no history of the evolution of individual welfare entitlements over time, and this precludes any convincing attempt to model the dynamics of participation behaviour.

The subsamples used for our analysis contain 4003 (sample 1) or 4129 (sample 2) cases after deleting those which: were not entitled (16,251); contained multiple benefit units (3708); were still repaying a mortgage (230); received allowances from an absent spouse (2); had employment or self-employment income (36); did not respond to survey questions on a core variable such as recorded IS receipt, pension or non-assessable income (2503 and 2215); or which gave rise to other miscellaneous data-quality concerns (40 and 202). These deletions are less serious than they might appear. Most are simple exclusions of pensioners known to be non-entitled, for whom participation is not an issue. Multi-unit households are excluded because of the difficulty of simulating their entitlement. We exclude the few entitled earners, mortgagors and beneficiaries from absent spouses, for whom take-up is complicated by labour supply and problems in calculating mortgage interest and assessable income, respectively. The most serious of the deletions is likely to be loss through item non-response, which we assume ignorable. Given the careful data cleaning and sample selection, we believe that the potentially serious problem of measurement error has been avoided as far as possible in the analysis samples. All data on benefits and income are adjusted to 2002 prices using the Consumer Price Index.

Table I shows estimated IS take-up rates, which are similar for the two samples. There is some variation by category of pensioner, but the typical rate of non-participation is just over one third. Although not directly comparable, these are close to the official estimate of 33% reported by DWP for 2001/2. Single females have higher take-up rates than single males and couples. Take-up rates are also higher in both samples for pensioners in the younger age groups and for those who left full-time education by the age of 14. Take-up varies considerably with housing tenure, renters having much higher rates than home owners. Respondents in the 2001/2 survey who became entitled for the first time after the reforms have very low take-up rates in both samples. This is partly due to their typically small levels of entitlement, but may also involve some lag in adjustment to the new benefit rules. We pursue this further in the applied work reported below.

Table I. Percentage take-up rates by demographic groups (1997/8–2001/2 FRS estimation sample)
 Take-up rate (SE)
Sample 1Sample 2
Sample size40034129
Full sample63.1364.25
(0.76)(0.75)
Single male56.2457.14
(2.08)(2.05)
Single female66.8367.95
(0.86)(0.84)
Couple47.6048.72
(2.33)(2.31)
Head under 7077.7077.86
(2.02)(2.00)
Head 70–7964.0065.11
(1.14)(1.11)
Head 80–8959.6360.86
(1.22)(1.19)
Head 90 +52.5556.13
(3.57)(3.41)
Education < 1466.1467.01
(3.44)(3.38)
Education equal to 1464.3165.52
(0.89)(0.87)
Education > 1458.6959.54
(1.64)(1.62)
Not registered disabled62.2963.06
(0.83)(0.82)
Registered disabled67.8270.48
(1.89)(1.77)
Owner occupier46.8148.30
(1.47)(1.46)
Renter70.2771.18
(0.87)(0.85)
Newly entitled 01/0238.1938.53
(2.44)(2.59)
Not newly entitled 01/0265.8866.66
(0.79)(0.77)

In Figure 1 we plot the proportion of IS non-claimants who are entitled to an amount of IS in excess of a proportion p of their pre-IS income. Although many non-participants are entitled to small benefits, over half of non-claimants could increase their income by at least 10% and over 25% could increase their income by at least 20% if they were to take-up their entitlements. Thus non-participation in the IS programme has important consequences for a large minority of potential recipients.

thumbnail image

Figure 1. Distribution of IS non-claimants by size of unclaimed benefit as a proportion of original income

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4. THE COMPENSATING VARIATION APPROACH

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

Our analysis is based on the idea that individuals will claim the benefit to which they are entitled when they see it as being in their best interests, after allowing for all costs associated with benefit claim and receipt. These claim costs can be financial (such as the cost of travel to the social security office), tangible but non-financial (for example, the time or physical difficulty involved), social (for example, social stigma) or psychological (such as feelings of inadequacy or shame induced by dependency). Lack of information can also be viewed as a claim cost equivalent, in a specific sense outlined below, to the cost of ignorance. The notion of claim costs is broad enough to encompass a wide range of factors. Someone who suffers difficulty with the process of claiming benefit because of physical or mental impairment is seen as suffering from high claim costs. Those with access to external assistance from family, neighbours or other carers will find it easier to make a claim than similar people with no such support. Thus claim costs depend on personal characteristics and circumstances, as well as the design of application procedures. It is therefore important to allow for wide variations in claim costs across benefit units.

4.1. The Basic Take-up Model

Consider first the simplest case of static choice under certainty. Let the long-term welfare of the benefit unit be represented by a utility function U0(Y;X, V), where Y is net income in the absence of means-tested benefit, X is a vector of observable characteristics and V represents unobservable characteristics which vary randomly across benefit units. When means-tested benefits are claimed, there is a possible shift in welfare represented by a transformed utility function U1(Y + B;X, V), where B is the additional benefit income. The shift from U0 to U1 is induced by some form of claim costs. Under the assumption of strict rationality, the condition for take-up to occur is

  • equation image(1)

Since utility is monotonic and continuous in income, this can be rewritten as

  • equation image(2)

where the function equation image (.; X, V) is U1 inverted with respect to its first argument. Note that if the functions U0 and U1 are identical, equation image is equal to 0 and benefit is claimed whenever the entitlement is strictly positive. When equation image is positive, it is the compensating variation: the cash equivalent of any barriers acting as a disincentive to take-up.

4.2. The Model as Reduced Form

It is important to realise that the model outlined above is applicable as a reduced form in a much wider range of cases. In practice, take-up behaviour may involve non-stationarity, uncertainty and perceptions that change over time in response to new information. There is no possibility of a convincing structural model for the UK, since there are no longitudinal datasets which are adequate for benefit simulation and no direct observation of information and perceptions. Our approach sees the binary choice model as a reduced form construct, permitting the derivation of a compensating variation. We first establish that expressing claim costs as an equivalent annual amount does not entail an assumption that they are actually incurred in that form. Suppose there is an up-front ‘hassle’, C0, involved in the initial claim, followed by a lower annual renewal hassle, C1. This stream of costs can be expressed as an equivalent annual amount, just as a capital sum can be annuitised. When receiving benefit, lifetime discounted utility is equation image, where we have assumed static circumstances and a known lifetime T. Call this function U1(Y + B, X, V). Then condition (2) applies. The only difference between this case and conventional annuitisation is the lack of a secondary market, implying that the annuitisation process involves the subjective discount factor, ρ, rather than a market rate.

A second example demonstrates the use of the model as an approximation in a case with uncertainty, where information is acquired sequentially, with updating of perceptions. Suppose the pensioner initially has perceptions of entitlement represented by a prior distribution equation image, where equation image is perceived entitlement and B is actual entitlement. The individual's post-retirement circumstances persist for a sequence of periods 1…t, during which a stochastic flow of new information I1It is received. With Bayesian updating, perceptions at t are represented by a posterior distribution equation image, where l(.) is the likelihood reflecting the information acquired and the individual's understanding of the relationship between that information and true entitlement. The dependence of the likelihood on B, X reflects between-individual variations, including differences in access to information. After t periods, the expected utility of claiming is equation image, where Et is the expectation with respect to the distribution ft(.). Thus, at time t, take-up will be observed if B is positive and equation image. The left-hand side of this inequality has the general form Ū1(Y, B, X, V, I1It). Under the reasonable assumption that increasing true entitlement shifts the posterior distribution equation image rightwards, Ū1 will be increasing in B and the analogue of the take-up condition (2) is equation image. In this expression, V, I1It are unobservable stochastic terms. Since different individuals will have different-length sequences of information, elapsed time (represented mainly by age) will appear in the mean of equation image conditional on Y, X, even if preferences do not evolve with age. In this case, the compensating variation will reflect the cost of risk and imperfect information in addition to stigma and hassle costs.

4.3. The Econometric Specification

Empirically, the best fit has been obtained by working with the logarithm of benefit entitlement (see also Blundell et al., 1988). We thus approximate the log of the right-hand side of (2) directly by a linear stochastic function + V, where Z is a vector of variables constructed from (Y, X), rather than using explicit specifications for U0 and U1. The stochastic term V now represents the effect of a combination of unobservable preference parameters and information available to the individual but unobserved by the analyst. The take-up condition is5

  • equation image(3)

The conditional take-up probability is then

  • equation image(4)

where σ2 = var(V) and F(.) is the distribution function of the random variable V/σ. The probability (4) is a standard binary response model of discrete choice, using lnB and Z as explanatory variables. Note that B is directly observable, from application of the IS rules to the data. There are no parameters requiring estimation in the function B(Y, X). In the model (4), the coefficients of lnB and Z are 1/σ and − α/σ respectively, so that α can be estimated as minus their ratio. Given α, a conditional distribution of claim costs C = exp( + V) can be constructed for each individual benefit recipient, given a specific form for the function F.

Participation models raise endogeneity issues. We are modelling participation conditional on entitlement and original income, which might be endogenous in the sense that people who know themselves to suffer particularly from stigma (implying negative V) will take steps to accumulate relatively high pension entitlements and other assets, which, in turn, raise post-retirement income and reduce IS entitlement (implying low B). This positive correlation between V and B might be thought to generate an upward bias in the coefficient (1/σ). However, the problem is not this simple. Under endogeneity, income Y is negatively correlated with V; it is also negatively correlated with B. Under these circumstances, the biases in the coefficients of lnB and Y cannot be signed a priori since each has two components of opposite sign. Moreover, the potential biases are moderated by the fact that the model is fitted only to those with strictly positive entitlement. Anyone whose fear of stigma is sufficiently large to increase their pension income or assets above the critical level will not be included in the estimation sample and will make a smaller bias contribution than would be the case under exogenous sample selection. A further consideration is that the important decisions governing pension income and asset accumulation were typically made many years earlier than the IS participation decision and often involved little real choice—the basic state pension scheme was all that was available to most of this cohort of poorer pensions. For these reasons, we are confident that endogeneity biases in our participation model are likely to be small. Moreover, convincing analysis of a model endogenising pensions and assets (and, potentially, housing and education also) would require long-horizon longitudinal data that does not currently exist for the UK.

4.4. Identification

In general terms, the model is of the form

  • equation image(5)

where G is a function with range [0,1] and B(Y, X) represents the rules of the IS programme. If all the variables in (Y, X) can appear indirectly through a simple benefit rule B(Y, X) and also directly in their own right, then it is clear that the model is non-parametrically unidentified despite the fact that B(.) is a known function. However, changes in the rules of the IS system in 2000 and 2001 break the exact functional relationship between B and (X, Y) in the sample and give independent identifying variation. Moreover, there are further restrictions that help to resolve this identification problem. We are usually content to make a smoothness assumption about the direct effect on behaviour of personal characteristics such as age, income and wealth. There are several discontinuities and kinks built into the IS rules: (i) discontinuities in the guaranteed minimum at ages 75 and 80; (ii) several discontinuities in the guaranteed minimum related to the amount of disability benefit; and (iii) a kink in the definition of notional income related to capital (at £3000, rising to £6000 in 2001/2). A smoothness assumption on the direct impact of age, capital and the disability benefit element of income will theoretically suffice to ensure identification, provided the minimum acceptable degree of smoothness can be imposed appropriately. Exclusion restrictions can also be used to identify the model. If one or more of the variables determining B can be excluded a priori from the model, then the separate impacts of B and (Y, X) can be distinguished empirically. Our final specification embodies several such restrictions. Some are data-driven, but we assume a priori that financial capital has a direct effect on take-up behaviour only through the contribution of observed investment returns to net income, which does not affect the calculation of IS entitlement.

4.5. Implicit Claim Costs

We now estimate the compensating variation required to offset stigma and other barriers to participation. Once F(.), σ and α are known, estimates of individual claim costs can be constructed in various ways. It is not appropriate to use the unconditional mean Ziα as most other researchers have done, since this makes no use of information about the actual take-up decision of unit i. Instead we should condition the prediction of claim costs for claimants on the take-up event + V < lnB. A natural approach is to use a conditional expectation. For the ith IS recipient:

  • equation image(6)

In the probit case where F(.) = Φ(.) is the N(0,1) distribution function, this gives

  • equation image(7)

An alternative is to use a conditional median estimate, equation image, which satisfies

  • equation image(8)

and thus

  • equation image(9)

Analogous expressions for non-claimants are given by Hernandez et al. (2006).

Note that equation image and equation image always lie below the unconditional mean and median of exp(Ziα + V) for participants. Claimants will, on average, tend to be those who suffer lower than average levels of claim costs and conversely for non-claimants. The relationship between implicit claim costs and the coefficient of lnBi is important. As σ→∞, the impact of entitlement on take-up vanishes. If we adjust α to keep the take-up probability constant at some value P, then limσ→∞Zi(α/σ) = − F−1(P). Consider the median (9). Since equation image. This occurs because the leftward shift in the median induced by the truncation condition Ci < Bi is greater, the larger is σ. Conversely, equation image for non-claimants: as we increase σ, Ziα must increase towards lnBi in order to keep the take-up probability constant. Thus the entitlement coefficient is critical in this type of model. A small value will imply modest implicit claim costs for those who do take-up the benefit, but very much larger costs for those who do not. A large coefficient implies large claim costs for claimants and a weaker distinction between claimants and non-claimants.

5. ESTIMATES

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

5.1. The Binary Take-up Model

We use two different estimators of the binary take-up model: the probit technique which assumes normality; and the semi-parametric estimator of Klein and Spady (KS) (1993), which, in its simplest form, maximises the following quasi-log-likelihood:

  • equation image(10)

where summations are over the set of n pensioner households for whom Bi > 0, τi is the dependent variable equal to 1 for IS participation and 0 for non-participation, and equation image is a non-parametric kernel estimate of the regression function of τi on lnBiZiα. We use the Gaussian kernel:

  • equation image(11)

where ϕ(.) is the standard normal density function. Note that equation image is not normalised to have zero mean and unit variance. Scale and location are normalised by fixing the coefficient of lnBi at unity and excluding the intercept term from the linear form . This choice of normalisation does not affect the construction of implicit cost estimates. We experimented with fixed and adaptive bandwidths (the latter using the Breiman et al., 1977, method), with remarkably little effect on the results; those reported here are based on a fixed bandwidth h = 0.6.

Table II gives estimates of the stigma/claim cost coefficients α. Precise definitions and summaries of the variables are given by Hernandez et al. (2006). For the probit model the estimates are calculated as minus the coefficients of the relevant variables divided by the coefficient of lnBi. The estimates are the outcome of an extensive process of specification search. The chosen form is superior (in likelihood terms) to other models with alternative functional forms for income and entitlement. There has been some attention paid by sociologists to neighbourhood influences on welfare participation behaviour, with the conclusion that high local rates of poverty, welfare dependency and density of population lead to higher rates of take-up, because of lower social stigma and better local information and support, reducing claim costs (Hirschl and Rank, 1999). We are only able to match survey respondents to large regions rather than neighbourhoods and there are, consequently, no locational effects detectable. We are also able to accept our specification against models with fuller demographic structure and a more general specification involving the ages and education levels of both members for two-person households. Annual dummy variables were also included and found to be insignificant with χ2 statistics of 3.33 and 5.50 for samples 1 and 2, respectively, and a 5% critical value of 9.488. To guard against pre-test bias, we have worked from ‘general’ models to ‘specific’ ones, using a conservative criterion, retaining explanatory variables with asymptotic t-ratios in excess of 1.0. Besides log entitlement, the main factors generating high claim costs emerge as income per head, education, status as a recipient of disability benefit, owner-occupation and newly entitled status.

Table II. Parametric and semi-parametric coefficient estimates (scaled coefficients equation image)
VariableSample 1aSample 2b
ProbitKSProbitKS
 equation image |t|equation image |t|equation image |t|equation image |t|
  • a

    n = 4003;

  • b

    n = 4129.

Single male household− 2.267− 2.809− 1.064− 1.232
(3.104)(2.770)(2.702)(2.371)
Single female household− 3.528− 3.688− 1.947− 2.026
(4.328)(3.431)(4.960)(4.022)
Age/108.746− 1.9856.029− 0.738
(2.056)(0.386)(2.235)(0.220)
(Age/10)2− 0.4810.183− 0.3310.092
(1.800)(0.561)(1.946)(0.435)
Income per person0.1020.1220.0410.047
(4.422)(3.542)(4.649)(3.865)
Head educated past 141.3891.3250.9300.918
(3.627)(2.757)(4.084)(3.088)
Disability benefit0.8320.6000.7150.634
(2.289)(1.210)(3.037)(1.951)
Registered disabled− 1.248− 1.028− 0.840− 0.872
(2.735)(1.769)(3.006)(2.293)
Owner-occupier3.4412.9162.2572.140
(5.968)(4.605)(8.144)(6.343)
Rent-free2.2992.2831.2571.383
(2.638)(2.164)(2.384)(2.089)
Newly entitled2.2811.7751.5851.500
(4.047)(2.726)(4.480)(3.359)

The estimated effect of income is always significant at the 5% level but varies considerably over the two samples. For the probit model estimated on sample 1 data, the coefficient implies a large 11% increase in expected claim costs for each additional £1 of original income. This falls to just over 4% when the data from sample 2 are used. For the KS estimates the range is similar: a 13% impact on sample 1 data but under 5% for sample 2 data. Housing tenure is closely linked to social status as well as wealth. Being a home-owner greatly increases the barriers to IS take-up, increasing estimated mean claim costs as much as eightfold. This is likely to reflect the relatively poor access that home-owners have to information and advice, which is available (through housing associations and local authority housing offices) to most renters.6

Education has a large effect. Having schooling past age 14 is estimated to quadruple expected claim costs on the basis of models estimated from sample 1 data. The expected claim costs are lower when sample 2 is used; nevertheless, having schooling past the age of 14 more than doubles claim costs. Although better-educated people may have greater capacity to negotiate the intricacies of the benefit system, on this evidence they must also typically be more vulnerable to stigma or tend to be in circumstances entailing greater costs of claiming. The two disability variables reflect the household's status as a recipient of a (medically assessed but non-means-tested) disability benefit or as one containing a registered disabled person. These have respectively positive and negative impacts on expected claim costs. Note that registering as a disabled person is voluntary and has no direct implications for benefit entitlement, but may bring other benefits such as unrestricted car parking. These two variables summarise a combination of factors. One might interpret the coefficient of the former variable as an indicator of physical impairment which increases the physical difficulty of coping with the IS claims process and thus increases implicit claim costs (roughly twofold). The latter might be interpreted as an indicator of low vulnerability to stigma: those who are willing to seek formal recognition of disability may also tend to be more willing to accept an IS-dependent status and thus have lower expected claim costs (by around 58%). In the absence of direct information on physical capacity, such interpretations are necessarily speculative.

The probit and KS estimates have similar qualitative implications in the samples considered here. However, there is an important difference for age. Using the probit model, claim costs are estimated to increase with age, although at a decreasing rate. If accepted, this result would be hard to rationalise. It seems unlikely that people who claim benefit when younger would cease to do so when they reach a critical age. If the age effect arises through the acquisition of information through time, one would expect the take-up rate to be increasing. Adjustment models based on random durations of periods of need (see Anderson and Meyer, 1997) are inappropriate here and again suggest rising take-up rates. Another interpretation would be that the age variable reflects a cohort effect implying a gradual upward drift in take-up rates over time but this conflicts with the absence of a trend in IS take-up among pensioners at the macro level (DWP, 2004a, and earlier). The issue is resolved once the more flexible semi-parametric approach is used, since age becomes insignificant for all samples. This last finding provides a good illustration of the often-neglected proposition that misspecification of distributional form can cause serious biases in binary response models.

Finally, we have included in the model a dummy variable to reflect the possibility that there is some delay in adjusting to changes in the rules of the benefit system. In April 2001 there was a major revision in the IS rules, which significantly extended entitlement. A dummy variable is used to identify cases of individuals who are entitled in the year they are interviewed but who would have been non-entitled (with unchanged circumstances) under the previous year's rules. This variable has a strongly significant coefficient, implying the existence of adjustment lags.

Figure 2 shows the distribution functions (.) for the probit and KS models in sample 2. To make these comparable, the probit probability, Φ(.), is plotted against the standardised KS estimate. The most striking difference between the two distributions is the fatter upper tail of the KS estimate and a local concentration at around − 1 standard deviations in the lower tail.

thumbnail image

Figure 2. Estimated distribution functions for the probit and KS models

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5.2. Estimates of the Implicit Stigma/Claim Costs

Table III shows estimated claim costs for the subsample of pensioners receiving IS, constructed using (6) and (9). Means and medians differ substantially but the semi-parametric estimates give much higher estimated claim costs than the probit model, whatever method is used to construct implicit costs. Results are sensitive to the choice of sample, with larger costs estimated in sample 2, where recorded rather than simulated benefit receipt is used when possible. For the preferred KS estimates, the average estimated claim cost for IS recipients is around £4 per week in sample 2 and £3.40 in sample 1 (15% and 13% of mean entitlement, respectively).

Table III. Summary measures of estimated stigma/claim costs for IS recipients (£ per week)
 MeanMedian
  • a

    n = 2527;

  • b

    n = 2653; standard errors in parentheses.

Probit: conditional mean method equation imageSample 1a1.701.20
  (0.26)(0.19)
 Sample 2b2.781.96
  (0.27)(0.19)
Probit: conditional median method equation imageSample 1a0.100.04
  (0.01)(0.00)
 Sample 2b0.530.29
  (0.17)(0.11)
Klein–Spady: conditional mean method equation imageSample 1a3.402.20
  (0.08)(0.25)
 Sample 2b3.972.61
  (0.08)(0.19)
Klein–Spady: conditional median method equation imageSample 1a1.850.95
  (0.05)(0.23)
 Sample 2b2.071.20
  (0.05)(0.17)
Entitlement to IS among IS recipientsSample 1a25.5115.19
  (0.48)(0.60)
 Sample 2b26.7415.95
  (0.47)(0.61)

Figure 3 shows the empirical distribution of these estimated claim costs for the subset of pensioners in sample 2 observed receiving IS. The KS estimates imply greater dispersion, especially using the conditional mean method to construct implicit costs.

thumbnail image

Figure 3. Kernel estimates of the claim costs distribution

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How do these estimates compare with others in the literature? There are no directly comparable figures available, since other researchers have not taken account of the conditioning on observed take-up. For example, Duclos (1995, p. 409) gives expected costs of claiming Supplementary Benefits (SB) in Britain in 1985. Among the pensioner cases, take-up costs range from over £3 per week for single pensioners to over £20 for couples. However, these are not conditioned on the take-up event. The analysis closest to our own is the work on Housing Benefit (HB) by Blundell et al. (1988), who estimated claim costs by finding the level of entitlement at which the unconditional take-up probability is 0.5. From the published probit coefficients and sample means relating to retired/unoccupied respondents (Blundell et al., 1988, pp. 73–74), we can apply (7) and (9) to estimate implicit claim costs for the average 1984 HB-entitled pensioner. These are £1.79 and £1.08 (updated to 2002 prices) using the conditional mean and median methods. These are lower than our 1997–2002 estimates for IS, which has a lower take-up rate and, presumably, higher claim costs than HB.

The claim costs faced by those who do not participate in the IS programme cannot be estimated reliably. For participants, claim costs are bounded by the amount of entitlement B, but for non-participants they are unbounded. The conditional mean method is particularly unstable since it is heavily influenced by the tail behaviour of the function F(.), which is not well-determined statistically. Good estimates of the upper tail of the claim costs distribution would require sample cases with large entitlements, but this is prevented by the design of the benefit system.

6. IMPLICATIONS FOR POVERTY MEASUREMENT

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

How much difference do claim costs make to the empirical measurement of pensioner poverty? A satisfactory answer requires the whole distribution of claim costs, rather than its mean or median. Ignoring implicit claim costs, a pensioner unit is in poverty if total net income Y + B falls below a poverty line T(X), where B is actual IS receipt. Let S be the size of the benefit unit. The FGT poverty measure of Foster et al. (1984) weights poor individuals by their distance below the poverty threshold:

  • equation image(12)

where (using a poverty aversion parameter of 2):

  • equation image(13)

and Q = 0 otherwise. A baseline estimate of FGT replaces the expectations in (12) by sample averages:

  • equation image(14)

A crude adjustment for claim costs replaces Q(Y, B, X) by

  • equation image(15)

and Q* = 0 otherwise. Alternatively, we can use an analytical adjustment, which is preferable since it gives a consistent estimate. For those receiving benefit, log claim costs are lnC = + V, conditional on the event + V < lnB. Thus we estimate the numerator of (12) as the sample average of equation image where

  • equation image(16)

and Q** = 0 otherwise, where Y is net income excluding benefits. The poverty line, T(X), is a percentage of the IS guaranteed minimum for the benefit unit M. Results are given in Table IV. The effects of adjusting for claim costs are moderate: depending on the sample, threshold and estimator used, measured poverty is 4–13% higher when claim costs are taken into account. This is a non-negligible impact that could have a significant effect on the outcome of a welfare analysis (see Pudney et al., 2006, for an example of this).

Table IV. Foster–Greer–Thorbecke poverty measures (probit model)
 Poverty linea
1.2 M1.1 MM0.9 M
  • a

    M is the IS guaranteed minimum for the benefit unit.

Probit estimates      
  equation image0.01480.00820.00450.0028
Sample 1n = 17, 089equation image (mean)0.01540.00860.00450.0028
  equation image (median)0.01490.00820.00450.0028
  equation image0.01560.00880.00470.0029
  equation image0.01540.00880.00490.0031
Sample 2n = 17, 081equation image (mean)0.01620.00930.00510.0031
  equation image (median)0.01550.00890.00500.0031
  equation image0.01650.00960.00540.0033
Klein–Spady estimates      
  equation image0.01480.00820.00450.0028
Sample 1n = 17, 089equation image (mean)0.01600.00900.00470.0028
  equation image (median)0.01540.00860.00460.0028
  equation image0.01620.00920.00490.0029
  equation image0.01540.00880.00490.0031
Sample 2n = 17, 081equation image (mean)0.01660.00960.00520.0031
  equation image (median)0.01600.00920.00500.0031
  equation image0.01690.00990.00550.0033

7. CONCLUSIONS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

This paper studies the take-up of Income Support by UK pensioners using data on the financial years 1997/8–2001/2 from the British Family Resources Survey. Two binary choice models of IS take-up are estimated: a probit model and a more flexible semi-parametric model. In addition to the (log) level of entitlement, the main factors contributing to high claim costs are income per head, education, status as a recipient of disability benefit, owner-occupation and newly entitled status. Using a revealed preference approach we consider the implicit costs of claiming Income Support. These costs might arise from the onerous nature of the claims process, from social stigma associated with being on welfare and from the difficulty of acquiring information about the benefit system. We develop a new technique of constructing individual-specific estimates of claim costs, allowing for the self-selection effect of the take-up process. Implicit costs are found to be moderate for most IS recipients, typically around £3–4 per week (or about 13–15% of entitlement) for the average benefit recipient, and consequently the degree of measured poverty among pensioners increases by a modest but non-negligible amount (up to 13% for the Foster–Greer–Thorbecke index) when these claim costs are taken into account.

The revealed preference approach argues that non-participants judge themselves to be better off foregoing than claiming their entitlements because of these costs. It does not follow from our results, however, that non-participation is no cause for concern. The fact that some eligible individuals choose not to participate in means-tested programmes simply indicates that they find living below the poverty line preferable to living on welfare. If governments want to use means-tested welfare programmes to prevent poverty, they need to find ways to reduce the size of the costs involved relative to the size of the benefits paid out.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

We are grateful to participants in seminars at the universities of Essex, Leicester and Southampton and at the RES conference, Warwick and ESEM Stockholm for helpful discussion. Comments from the Editor and referees have improved the paper enormously. We are grateful to the Economic and Social Research Council for financial support of this research, under contracts R000239105 and RES518285001. Thanks are also due to other project team members Geraldine Barker and Holly Sutherland and to members of the project's advisory group. Material from the Family Resources Survey, made available by the Office for National Statistics via the UK Data Archive, has been used with permission. All responsibility for the analysis and interpretation of the data presented here lies with the authors.

REFERENCES

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information
  • Anderson PM, Meyer BD. 1997. Unemployment insurance take-up rates and the after-tax value of benefits, Quarterly Journal of Economics CXII: 913937.
  • Blundell R, Fry V, Walker I. 1988. Modelling the take-up of means-tested benefits: the case of housing benefits in the United Kingdom. Economic Journal 98: 5874.
  • Bollinger CR, David MH. 1997. Modeling discrete choice with response error: Food Stamp participation. Journal of the American Statistical Association 92: 827835.
  • Breiman LW, Meisel A, Purcell E. 1977. Variable kernel estimates of multivariate densities, Technometrics 19: 135144.
  • Duclos J-Y. 1995. Modelling the take-up of state support. Journal of Public Economics 58: 391415.
  • DWP. 2001. Income Related Benefits: Estimates of Take-Up in 1999/2000. Government Statistical Service: London.
  • DWP. 2004a. Income-Related Benefits: Estimates of Take-Up in 2001/2002. DWP Information and Analysis Directorate: London.
  • DWP. 2004b. The Pensioners' Income Series 2002/3. DWP Pensions Analysts Division: London.
  • DWP. 2004c. State Pension: Summary of Statistics, March 2003. www.dwp.gov.uk/asd/asd1/state_pension/SP_ summ_stats_Mar04.asp [17 September 2006].
  • Foster J, Greer J, Thorbecke E. 1984. A class of decomposable poverty measures. Econometrica 52: 761766.
  • Hancock R, Barker G. 2005. The quality of social security benefit data in the British Family Resources survey: implications for investigating income support take-up by pensioners. Journal of the Royal Statistical Society Series A 168(1): 6382.
  • Halpern J, Hausman JA. 1986. Choice under uncertainty: a model of applications for the social security disability insurance program. Journal of Public Economics 31: 131161.
  • Hernandez M, Pudney SE, Hancock RM. 2006. The welfare cost of means-testing: pensioner participation in Income Support. ISER Working Paper no. 2006/12, University of Essex: Colchester, UK.
  • Hirschl TA, Rank MR. 1999. Community effects on welfare participation. Sociological Forum 14: 155174.
  • Keane M, Moffitt R. 1998. A structural model of multiple welfare program participation and labor supply. International Economic Review 39: 553589.
  • Kim M, Mergoupis T. 1997. The working poor and welfare recipiency: participation, evidence and policy directions. Journal of Economic Issues 31: 707728.
  • Klein RW, Spady RH. 1993. An efficient semiparametric estimator for binary response models. Econometrica 61: 387421.
  • Moffitt R. 1983. An economic model of welfare stigma. American Economic Review 73: 10231035.
  • Pudney SE, Hancock RM, Sutherland H. 2006. Simulating the reform of means-tested benefits with endogenous take-up and claim costs. Oxford Bulletin of Economics and Statistics 68: 135166.
  • 1

    Income Support for pensioners became known as the Minimum Income Guarantee during the course of our sample period. We retain the older name.

  • 2

    In our sample period only around 1.36% of IS recipients received neither HB nor CTB. Only 0.26% of those receiving IS + HB did not also receive CTB; among renters, only 1.08% of those receiving IS + CTB did not also receive HB.

  • 3

    FRS interviewers encourage respondents to consult bank records, payment books, etc., to give accurate figures. We tried substituting recorded IS, where available, for simulated entitlement provided it did not exceed the guaranteed minimum. Results were similar to those for sample 2.

  • 4

    Few FRS respondents (around 0.8% of the sample) had claims pending; we include these and treat them as recipients. Their omission from the sample makes no detectable difference.

  • 5

    The approximation is exact if U1 = U0(Y + Be + V). If subjective claim costs are proportional to the amount received, then U1 = U0(Y + BBe + V) and the take-up condition is + V < 0, and take-up is unrelated to the scale of entitlement. This is rejected empirically.

  • 6

    Since renters who are entitled to IS are also entitled to both HB and CTB and owners entitled to IS are also entitled to CTB, we also estimated two additional models: one using total entitlement to all benefits as the variable B; the other using total entitlement only for renters and IS entitlement for owner-occupiers. Both models gave a poorer fit.

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. THE STATE PENSION-BENEFIT SYSTEM IN BRITAIN
  5. 3. THE 1997–2002 FAMILY RESOURCES SURVEY
  6. 4. THE COMPENSATING VARIATION APPROACH
  7. 5. ESTIMATES
  8. 6. IMPLICATIONS FOR POVERTY MEASUREMENT
  9. 7. CONCLUSIONS
  10. Acknowledgements
  11. REFERENCES
  12. Supporting Information

The JAE Data Archive directory is available at http://qed.econ.queensu.ca/jae/datasets/hernandez001/ .

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.