The marginal social valuation of income for the UK

The Authors

David Evans, Business School, Oxford Brookes University, Oxford, UK

Acknowledgements

JEL classification: D60, D61, H24

Abstract

Purpose – The British government takes equity issues formally into account in its appraisal of social projects and policies. However, evidence on which the measured distributional welfare weights are based is neither broad enough nor sufficiently reliable. This paper seeks to address these issues by considering a wider body of evidence.

Design/methodology/approach – An important component of the welfare weight measure advocated by HM Treasury is the elasticity of marginal utility of consumption (e). A critical review of existing evidence on e is provided with a view to establishing priority areas for further research. New measures of e are presented based on revealed social values as indicated in specific government policies relating to both foreign aid and proposed income-related fines for offences. Behavioural evidence based on demand analysis using a co-integration approach is also presented.

Findings – The results for e are sensitive to the estimation approach adopted. While the evidence based on a revealed social values approach including modified tax-based results suggests that e is close to unity, the measure currently used by HM Treasury, demand analysis suggests an e value close to 1.5. The evidence based on lifetime consumption behaviour is sensitive to model specification and needs updating.

Originality/value – Modified tax-based findings on e are presented along with new evidence based on alternative revealed social values approaches. The new evidence from demand analysis is based on an Autoregressive Distributed Lag (ARDL) approach to co-integration. This paper will be of interest to academics specialising in welfare economics and to practitioners involved in social project appraisal.

Article Type:

Research paper

Keyword(s):

Welfare; Social values; Social behaviour; United Kingdom.

Journal:

Journal of Economic Studies

Volume:

Number:

Year:

2008

pp:

26-43

Copyright ©

Emerald Group Publishing Limited

ISSN:

0144-3585

I. Introduction

It is clear that the British government is now concerned to assess directly the distributional impacts of its spending policies in cost-benefit analysis. In its latest guidance on appraisal and evaluation in government, HM Treasury states that distribution issues should be assessed in relation to policy proposals wherever it is practical to do so. See HM Treasury (2003, Annex 5, pp. 91-6). So, both equity and efficiency objectives are to be addressed in proposed spending plans with projected costs and benefits weighted according to their impact on different socio-economic groups. In its guidance, HM Treasury (2003, Annex 5, p. 91) identifies a number of specific distributional dimensions that are worthy of attention; these include income, gender, age, ethnicity and geographical location.

In an inter-temporal context, the interests of future generations must be weighed against those of the present generation with the choice of discount rate in social project appraisal determining the present value weighting of assessed costs and benefits. Clearly, from a societal perspective, an assessment of how the marginal valuation of income changes with the level of equivalised income is required. HM Treasury (2003, Annex 6, p. 97) recommends the application of the social time preference rate (stpr) which includes an element known as the elasticity of marginal utility of consumption (e). So, in an inter-temporal context or otherwise, a suitable measure of e is crucial for the construction of appropriate welfare weights to address equity issues in cost-benefit analysis.

The underlying theory concerning the different approaches to the measurement of welfare weights has been covered thoroughly by Stern (1977) and, more recently, Cowell and Gardiner (1999). These approaches include direct and indirect methods of assessing the value of e with the latter interpreting this welfare measure as either an income inequality aversion or risk aversion parameter. The empirical evidence on e based on these different approaches is often presented selectively and uncritically in order to defend a particular value for the purpose of policy application. For example, HM Treasury selects a unitary e value and does this on the basis of surveys of evidence provided by both Pearce and Ulph (1995) and Cowell and Gardiner (1999). However, a close reading of this evidence, as presented especially by the latter, does not offer any clear support for a unitary e value; see, for example, Evans (2005).

One clear objective of this paper is to provide a critical review of past empirical evidence on welfare weight measures with a particular view to suggesting empirical refinements for the purpose of new work. Behavioural evidence, drawn from lifetime household consumption models and demand analysis, is considered along with a revealed social values approach. A second objective is to conduct new empirical work relating to both of these approaches in order to identify a defensible value range for e. In section II, two new possible revealed social values approaches based on foreign aid policy and proposed income-related fines for minor offences are considered. Also, a revised interpretation of tax-based evidence on e is presented. These three approaches yield similar results. In section III, the results from an autoregressive distributed lag (ARDL) co-integration approach to the estimation of a demand for food model are presented and discussed. These results are very similar to those obtained for e using alternative co-integration techniques. The main conclusions and policy recommendations are covered in section IV.

II. Revealed social values approach

Estimates of e can be obtained from the social values of governments as revealed in specific economic policy measures. One popular approach is to interpret e as an income inequality aversion parameter from the government's perspective and then measure its value according to the degree of progressivity in a country's income tax schedule. For example, see Stern (1977) and Cowell and Gardiner (1999). The relevant empirical evidence, along with due consideration of the qualifications and problems involved, is presented in section II(1).

Two new approaches to assessing the value of e will be considered, alongside the income tax approach. One of these is based on the long-standing international policy arrangements concerning foreign aid payments by developed countries in favour of the poorest countries in the world. The other approach is to consider the new arrangements in the UK for establishing appropriate fines for individuals in relation to a range of offences. A system of income-related fines is outlined in the Management of Offenders and Sentencing Bill introduced in January 2005 (Home Office, 2005). Both these approaches are considered in section II(2).

Subject to certain important qualifications regarding the interpretation of the data on income tax rates, it will be shown that each of the three approaches to assessing the marginal social valuation of income yields an e value for the UK that is close to unity. In fact, the British Treasury, drawing on evidence provided by both Cowell and Gardiner (1999) and Pearce and Ulph (1995), decided that a unitary e value is appropriate for the UK (see HM Treasury, 2003, p. 98). It should be stressed, however, that only Cowell and Gardiner specifically consider a revealed social values approach, one based on income tax rates. Their own empirical work using 1999/2000 tax rates produced a result of 1.4 for e, or just below 1.3 if employees' national insurance contributions are additionally included in the tax rates measures.

II(1). Income tax rates and e

Assuming that the structure of a country's income tax rates is at least loosely based on the principle of equal absolute sacrifice of satisfaction and that an iso-elastic utility function applies, then an expression for e can be derived from the model outlined below. From equation (7) of this model, e is given by a ratio of variables involving marginal and average rates of income tax.

The model:

Equation 1 and Equation 2 Equation (1) reflects equal absolute sacrifice in which the income tax taken from individuals involves the same sacrifice of utility (k) for all taxpayers regardless of income levels. Equation (2) is an iso-elastic utility function assumed to apply to all individuals. Y denotes pre-tax income and T(Y) is the income tax function. Substituting (2) into (1) gives the following equation: Equation 3 Taking the total differential of equation (3) gives: Equation 4 After re-arranging terms in (4) and simplifying, the relationship becomes: Equation 5 In equations (4) and (5) t equals the effective marginal tax rate. Taking logs in (5) gives: Equation 6 So: Equation 7 Equation (7) provides the focus for the estimation of e, where:

Y =pre-tax personal income;

T =marginal tax rate;

T =total income tax liabilities; and

T/Y =average tax rate.

The equal absolute sacrifice model features prominently in public finance; see, for example, Richter (1983), Vitaliano (1977) and Young (1987). Furthermore, according to Stern (1977) this model fits the data better than the more complex theories concerning tax structures. Both Blue and Tweeten (1997) and Evans (2005) found empirical support for constancy of e. In fact, this model was recently used by Sezer (2006) in order to help estimate a suitable set of regional welfare weights for possible policy application in social project appraisal in Turkey. The empirical approaches to the estimation of e, based on the equal absolute sacrifice model, employ different methods, varying tax rate definitions and differing measures of appropriate average tax rates. So, unsurprisingly, a summary of the main evidence for the UK, shown in Table I, indicates a good deal of variation in the results. These differences in estimated e values require some explanation.

The highest value of e in Table I is 1.97, and this was calculated by Stern (1977) for the tax year 1973/1974 when there were many different tax rate bands up to a top marginal tax rate of 75 per cent. In contrast, Cowell and Gardiner (1999) estimated an e value of only 1.41 for the tax year 1999/2000 when the highest marginal rate of income tax was only 40 per cent. These contrasting estimates were both based on regression analysis with the intercept suppressed in each case. Despite the apparent equivalence of the methods employed, the difference between the e values can be partly explained by the fact that Stern (1977) focused on families with two children, while Cowell and Gardiner (1999) considered single persons without dependants. So, tax allowances were of greater relative significance in the Stern study and this fact is further compounded by the additional availability of mortgage interest tax allowance in 1973/1974.

A fairer comparison of e values between “now” and “then” requires a re-calculation of average tax rates in relation to income after the deduction of tax allowances (as opposed to income before their deduction). This was, in fact, done by Evans (2005) for 20 OECD countries including the UK. The justification for this re-calculation of rates is that it is only reasonable to assume diminishing marginal utility for income in excess of the subsistence level. The re-working of Stern's data to calculate the revised average tax rates is shown in Table II. Direct calculation of e shows that the original value of 1.97 falls to 1.58. This latter figure can now be fairly compared with the estimate of 1.24 for the UK in 2002/2003, reported in Table I (see Evans, 2005).

Table I also shows e values based on tax rates that additionally include employees' national insurance contributions. Cowell and Gardiner (1999) now obtain a lower estimate for 1999/2000 of 1.28, once again based on regression analysis. In contrast, Evans and Sezer (2005) obtain an e value of 1.5 for 2001/2002, calculated directly at the average wage paid to full-time workers in manufacturing industries. However, these results are based on average tax rates calculated conventionally, rather than in relation to income after the deduction of personal tax allowances. Based on adjusted average tax rates, then these e values would be lower.

Estimates of e based solely on income tax rates do seem more in keeping with the principle of equal absolute sacrifice of satisfaction. From a government's perspective, the rationale for national insurance contributions is very different from “thoughts” concerning the optimum structure of income tax rates. The former are used largely to fund health-care and this is a needs- rather than an income-related benefit. As such, it can be argued that national insurance contributions should not really be included in the tax rate measures used to calculate e.

The tax-based results for e, presented in Table I, are calculated from un-weighted tax rate data. Stern (1977) suggested weighting the data according to the number of taxpayers in each income group. As most individuals are basic rate taxpayers, then this procedure would produce an e value close to unity, providing average tax rates are calculated in relation to income after the deduction of tax allowances, as discussed above. In fact, for the purpose of estimating e as a component of the stpr, which is now the official discount rate in the UK (see HM Treasury (2003)), then it is the circumstances of the average household that count. See, for example, Kula (1984) for clarification of this fact in relation to the assessment of welfare weights in an inter-temporal context. Using data on UK wage income for 2005, Table III shows that, for single person households, e is close to unity when measured at the average wage (AW) of adult, full-time workers.

Spackman (2004, p. 493) makes the point that progressivity in the income tax structure has for many years now been constrained by concerns about work incentives and the supposed supply-side boost to the economy from lower rates of income tax. As a result of these concerns, he feels that the schedule of tax rates can no longer be reasonably viewed as revealing the extent of a government's aversion to income inequality. However, it is possible to view this claim of promoting work incentives as essentially a cover for a rather relaxed view by the then Conservative government on the issue of income inequality. As people in the UK “enjoyed” low income tax rates under the Conservatives from 1979-1997, it would obviously be difficult now for any government to re-introduce tax rates in excess of 40 per cent in the near future. In this sense, Spackman is right. It can be argued, of course, that once account is taken of the relatively small proportion of individuals paying higher tax rates and adjustments are made to average tax rates, matters already discussed, then the re-estimation of e would produce a value close to unity both for recent years and years prior to 1979.

Before turning to other revealed social values approaches to the determination of e, some comment is in order regarding the new flat-tax regime being introduced by East European countries. The structure consists of a single low income tax rate, 20-25 per cent, combined with generous personal allowances, so that the poor pay nothing. Poland became the ninth East European country to adopt this flat tax system in March 2005. The major claims made for this simplified system are the removal of work disincentives, reduced administration costs and much lower compliance costs.

Whether or not economic growth is enhanced in countries adopting the new flat tax system remains to be seen. It is certainly possible that high-income earners, especially, may invest a significant proportion of their higher disposable incomes in pension-boosting savings schemes. To the extent that people decide to take early retirement on the strength of this, then a delayed income effect in favour of leisure will occur. This early retirement option may lead to some shrinkage in the size of the workforce. Whatever the merits and drawbacks of the flat tax structure, it is consistent with an e value of unity in the context of the equal absolute sacrifice model. This is provided, of course, that average tax rates are expressed in relation to income after the deduction of tax allowances.

II(2). Alternative approaches

The proposed income-related fines for minor offences, introduced in the Management of Offenders and Sentencing Bill will be considered first of all. The other approach to be covered is based on foreign aid policy. In both cases, suitably adapted versions of the equal absolute sacrifice model, introduced in section II(1), are assumed to apply. So, proportionality involving constant rates of fines or foreign aid contributions, respectively, must according to equation (7) imply a unitary value for e.

a) Income-related fines for minor offences

The Management of Offenders and Sentencing Bill, January 2005, proposes a new system of income-related fines for five classes of minor offences in the UK. The most minor of these, such as a child passenger in a car not wearing a seat belt, incurs a fine of ten times an offenders' daily disposable income, subject to a maximum fine of £750. This compares with the current fine of £200 for this type of offence. For the most serious of these crimes the income multiple is 200 subject to a maximum fine of £15,000. An example of this class of offence would be driving without insurance.

In the context of these fines, disposable income is defined as after-tax income less average outgoings on food, housing and utilities. This definition of income builds in a welfare-based equivalisation element covering basic living costs. Such costs vary according to household size, type of dwelling and geographical location. It is only after basic living costs have been met that it becomes reasonable to assume diminishing marginal utility of income. This condition, in turn, makes the definition of disposable income employed suitable for use in an adapted equal absolute sacrifice model.

Examples of the fines incurred at various levels of disposable income are shown for contrasting offences in Table IV. Proportionality of fine only applies up to a ceiling daily disposable income figure of £75, or an annual figure of £27,375. While only a relatively small percentage of individuals will have disposable income exceeding £75 per day, for these people the marginal rate of fine is zero and thus e equals 0. For the vast majority of adult offenders however, the implied e value is clearly unity and therefore a weighted average e value for society would only fall marginally short of this value.

If the Bill becomes law, then it will be possible to record how the public responds to these income-related fines. If, for example, this new scale of fines reduces the number of offences to a lesser extent in the case of richer individuals, then this may inform the government that a progressive scale is required, one that is consistent with a higher value of e.

b) Foreign aid policy

In an international policy context, the long-standing agreement that developed countries should set aside a certain proportion of their gross domestic product (GDP) to finance foreign aid for the poorest countries, could be viewed as indicating a revealed social value of e. The current target for developed countries is to donate 0.7 per cent of GDP in foreign aid by 2014. The actual percentage figure is not important as far as revealing an appropriate value of e is concerned, just the fact that developed countries should aim to contribute the same percentage figure. This proportionality factor clearly indicates a unitary e value for these countries providing the principle of equal absolute sacrifice is assumed to apply. Reference to equation (7) in a suitably adapted version of the tax-based equal absolute sacrifice model, see section II(1), makes this clear.

There is a substantial degree of dispersion in per capita real GDP amongst developed countries. For selected countries, Table V shows this fact clearly with reference to average per capita real GDP over the period 2000-2004. As the policy intention is that countries should pay the same proportion of GDP in foreign aid, then a unitary e value is appropriate for the purpose of calculating distributional welfare weights for application in the appraisal of regional social policy initiatives in developed countries. At least, this is the case given that policy-makers have the principle of equal absolute sacrifice of satisfaction in mind.

A target percentage foreign aid contribution, established for developed countries, also supports the appropriateness of a unitary e value in the calculation of present value welfare weights in an inter-temporal context. So, this thinking would support the choice of a unitary e value in the calculation of any developed country's stpr. Of course, HM Treasury (2003) already employs an e value of unity in the calculation of its official discount rate of 3.5 per cent, based on social time preference. However, the evidence it draws on in choosing this figure, mainly supplied by Cowell and Gardiner (1999) and Pearce and Ulph (1995) in their surveys of relevant empirical work, does not actually support the choice. See Evans (2005) for discussion of this evidence.

III. Behavioural evidence

Two contrasting approaches based on underlying preference functions are considered. First, e is measured indirectly as a relative risk aversion parameter from evidence on the inter-temporal elasticity of substitution in consumption, drawn from estimated models of lifetime consumption behaviour. Then, a more direct approach based on the demand for a preference-independent good is considered, one in which e can be measured from estimates of income and price elasticities of demand. Weaknesses of both approaches are considered together with the consistency, or otherwise, of the empirical evidence produced in different studies. Finally, a new estimate of e is provided for the UK using an autoregressive distributed lag approach (ARDL) to co-integration in the context of a demand for food model. The sample data period is 1963-2002.

III(1). Lifetime consumption behaviour

Both Cowell and Gardiner (1999) and Pearce and Ulph (1995) regard this approach to the estimation of e in an especially favourable light. They highlight the main empirical evidence obtained from lifetime consumption models, which suggests average e values for developed countries that are close to unity. See Blundell et al. (1994), Attanasio and Browning (1995) and Besley and Meghir (1998). HM Treasury (2003), in its selection of a unitary e value for policy application in social cost-benefit analysis, has been heavily influenced by this evidence, especially by that of Blundell et al. (1994). A succinct account of the theory concerning the inter-temporal elasticity of substitution in consumption and its relationship with e is given by Cowell and Gardiner (1999, Appendix A.3, pp 40-41). Specifically, the approach of Blundell et al. (1994) is followed.

There are dangers in taking results from the Blundell et al. study for the purpose of policy application “today”. The relevant data period finished nearly 20 years ago and the years 1970-1986 pre-date the de-regulation of retail financial markets. Furthermore, this period saw record inflation, supply-side shocks and major macroeconomic policy changes. See Evans (2005) for further detail on these important points.

The results obtained for e, interpreted as the reciprocal of the inter-temporal elasticity of substitution in consumption, are very sensitive to model specification. When Blundell et al. (1994) added a dummy variable to capture the effect of high UK real rates of interest in the early 1980s, the results for households with average family characteristics changed completely. Without the inclusion of a dummy variable, e estimates ranged from 1.2 at the first decile income level to 1.4 at the ninth decile. With the inclusion of a dummy variable then e increases steeply with income, ranging from 0.35 to 1.05 at the corresponding deciles. Averaging the mid-range estimates, 1.3 and 0.7, gives the unitary value of e selected by HM Treasury (2003). However, in relative terms, these are seriously over-arching estimates and they do not inspire confidence in the appropriateness of unitary e for policy application.

An important weakness concerning the specification of the empirical lifetime consumption model is that only a single rate of interest is included, a long-term government bond rate. Since borrowing rates for households were much higher than saving rates over the data period 1970-1986 and these rates did not always move closely together, then estimates of e obtained from the empirical model are likely to be misleading.

If lifetime consumption models for the UK were estimated over a more recent data period, say 1988-2004, then at least this would cover years of relatively low inflation and de-regulated financial markets. However, it would still be important to specify appropriate saving and borrowing rates, especially as it is only in recent years that the latter have fallen more into line with saving rates for purposes other than house purchase. Indeed, a failure to take into account sharply falling borrowing rates at a time, for example, when saving rates are only falling gradually, would lead to an over-estimation of the inter-temporal elasticity of substitution in consumption and consequently an under-estimation of e.

Even if borrowing and saving rates are taken into account, problems still remain. Competitive market pressures and technology have combined to produce a bewildering array of saving and loan products marketed aggressively by financial institutions – e.g. fixed rate mortgage options. This product differentiation and marketing drive may have resulted in on-going changes in consumer preferences for financial products since de-regulation in 1986. Indeed, the sharp fall in the savings ratio in recent years, see Table VI, can be partly accounted for by both the increased availability and diversity of intensively marketed credit, and the sizeable reduction in loan rates relative to saving rates in more recent years. Taking all the relevant factors into account in a lifetime consumption model poses a formidable challenge. So, despite the theoretical merits of this approach to the estimation of e, the considerable empirical difficulties involved make it advisable to also consider an alternative behavioural model, one that poses fewer empirical problems. One such model is based on consumer demand for preference-independent goods.

III(2). Consumer demand for a preference-independent good

This demand analysis approach to the estimation of e is based on the work of Fisher (1927), Frisch (1932) and Fellner (1967). It is commonly referred to as the FFF model. It can be demonstrated, to good approximation, in the case of a preference independent good that the model yields an e value equal to the ratio of income elasticity of demand (y) to the compensated price elasticity (p) providing the good has a relatively small budget share (w). For products with more significant budget shares then an adjustment to this ratio is required using the following formula (Frisch, 1959) that takes budget share specifically into account: Equation 8 Numerous demand studies relating to broad product groups have been conducted for many different purposes; for example, demand forecasting and tax policy simulations. From these models, estimates of e can be obtained providing the product groups in question can be regarded as preference-independent. This condition requires that these products enter a consumer's utility function in additively separable fashion. If additive separability does not apply then equation (8) is no longer appropriate and calculated e values would now be meaningless changing with each monotonic transformation of the utility function. See Evans et al. (2005) for a concise explanation of why additive separability is required in order for e to be calculated from estimates of income and price elasticities of demand.

While Stern (1977) and Deaton and Muellbauer (1980a) are among those who regard preference independence as an unreasonably strong condition, others including Fellner (1967), Selvanathan and Selvanathan (1993), and Evans and Sezer (2002) have argued that preference independence is plausible in relation to broad product groups such as food. In fact, based on data for 15 OECD countries, Selvanathan (1988) tested the want-independence assumption for broad aggregates and found it to be empirically valid. So, the FFF approach, whilst controversial, is worthy of consideration and as noted by Spackman (2004, p. 495) has the great merit of providing a direct measure of e. It should be stressed that the method requires only one product group to be preference independent and in empirical work the focus has generally been on food.

A consideration of the empirical evidence on e is based on contrasting selected studies conducted since the major survey of consumer behaviour reported by Brown and Deaton (1972). Some of this work involves the estimation of complete demand systems while other studies are based on single equation demand models. The main results from these studies are highlighted in Table VII with elasticities and e values shown only for the UK. The survey by Brown and Deaton (1972), covering different countries and data periods, showed a very wide variation in e values with an average value close to 2. From their own work for the UK covering the period 1900-1970, a preferred value of 2.8 was obtained for e. The Linear Expenditure System (LES) was the typical choice of model, although it often yields rather low estimates of compensated price elasticities and thus large values of e. For clear evidence of this, see Table VII and the results obtained by Parks and Barten (1973). This same study also produced e values in excess of 7 for both France and The Netherlands.

Improvements in demand models and especially the development of the Almost Ideal Demand System (AIDS) by Deaton and Muellbauer (1980b) mean that more attention should be given to later empirical work as far as complete demand systems are concerned. Examples of good work include Blundell (1988), Blundell et al. (1993) and Banks et al. (1997). The results for e based on each of these studies are reported in Table VII. In each case, seven broad product groups are covered and data from UK Family Expenditure Surveys (FES) over an extensive time period involving more than 65,000 non-pensioner households are used. In the 1988 and 1993 studies, the time-series data run from 1970-1984. The longer time-series of 1970-1986 is used by Banks et al. (1997). The results presented in Table VII vary according to whether an AIDS or quadratric extension of AIDS (QUAIDS) model is employed. In the case of Blundell (1988), the compensated price elasticity of demand (p) is, at −0.24, substantially lower than the corresponding value of −0.35 in the QUAIDS model of Blundell et al. (1993). Since the income elasticities are close to 0.6, the two models produce contrasting e values: 1.37 in the QUAIDS model as opposed to the AIDS model result of 1.97. The greater flexibility of the QUAIDS model means that the lower e value should be preferred.

An interesting feature of the QUAIDS results produced by Blundell et al. (1993) is that the OLS estimates for the micro-model agree with the Generalised Method of Moments (GMM) results for the aggregate model to yield an e value only marginally in excess of unity. This can be clearly seen from inspection of Table VII. However, it is more appropriate to compare the unbiased GMM estimates, in which case the micro-model result of 1.37 is somewhat higher. This latter result should perhaps be preferred because of the disaggregation of the household data. Banks et al. (1997) also employ the QUAIDS model for the extended data period 1970-1986, and from Table VII their results are seen to be in close agreement with those from the aggregate model of Blundell et al. (1993). So, only the demand for food results from the aggregate QUAIDS model yield e values that are consistent with the choice made by HM Treasury (2003). The preferred micro-model of Blundell et al. (1993) suggests a higher value of almost 1.4.

The remaining studies reported in Table VII are single equation models of the demand for food, estimated for the specific purpose of calculating e values. Kula (1985), using regression analysis, obtained an e value of only 0.71 for the UK although this result is based on only a small data sample. Furthermore, Kula (1984) using the same methodology estimated much higher values of e for the USA and Canada; 1.89 and 1.56, respectively. More recent UK estimates of e using co-integration analysis suggest that a value of about 1.6 is appropriate. See, for example, Evans and Sezer (2002), Evans (2004) and Evans et al. (2005). For India, Kula (2004) also obtained an e value of 1.6 using co-integration analysis.

Evans et al. (2005) cover the data period 1963-2002 for the UK and, based on a co-integrating VAR approach, only found evidence of a co-integrating relationship between demand for food variables in the case of the constant elasticities model (CEM). A single co-integrating relationship was found with the demand for food specified as the dependent variable. Both the AIDS and QUAIDS models failed to yield any co-integrating relationships between the variables. Further support for the relevance of the CEM comes from analysis of repeated cross-section data from the National Food Survey over the data period 1979-2000. It was found that the income elasticity of demand for “all foods” remained broadly constant, see MAFF (2000).

III(3). ARDL model of the demand for food and e

As only a single co-integrating relationship between demand for food variables was found in the Evans et al. (2005) study, an ARDL approach to co-integration is appropriate in this particular case. The advantages of adopting such an approach are its lag structure flexibility and its ability to handle both I(0) and I(1) regressors. Although all variables are I(1) on the basis of conventional ADF tests in Evans et al. (2005, Appendix 1), a reformulation of such tests under the null hypothesis of stationarity can sometimes give conflicting results. This is especially the case when using only modest-sized data samples. Because of this doubt the ARDL model, developed by Pesaran and Pesaran (1997) and Pesaran et al. (2001), is applied to the same data set used by Evans et al. (2005). This model has not previously been used for the purpose of estimating e although it has been employed in other economics contexts. For example, see Karfakis (2004) in relation to testing the quantity theory of money in Greece, De Vita and Abbott (2004) in relation to real exchange rate volatility and US exports and Narayan and Narayan (2005) in relation to Fiji's import demand function.

The single equation demand for food model used by Evans et al. (2005) can be expressed as follows: Equation 9 where:

F = household expenditure on food expressed per capita and measured at constant 1995 prices;

C = household expenditure on all goods and services expressed per capita and measured at constant 1995 prices;

REL = an index of the relative price of food (price of food relative to the price of non-food), 1995=1.0;

PNF = consumer price index for non-food product groups, 1995=1.0; and

v = error term.

(Note: annual UK data on these variables were supplied by the Office for National Statistics. The data period is 1963-2002.)

This constant elasticities model (CEM) out-performed both the AIDS and QUAIDS models in the co-integrating VAR approach used by Evans et al. (2005). In fact, the CEM was the only model to yield a co-integrating relationship between the demand for food variables (Evans et al., 2005, Appendix III). As a precaution, the non-standard F-tests for co-integrating relationships in the ARDL approach were applied to the CEM and the results confirmed the single co-integrating relationship between the variables in equation (9) with C, REL and PNF as the long-run forcing variables. This finding confirms the relevance of the ARDL approach to co-integration in the context of estimating a long-run demand for food relationship using recent UK data. The reason for including PNF in equation (9) is to provide a direct test for homogeneity. Theoretically, the coefficient d should be 0, but it is useful to see whether or not the data offer support for homogeneity.

The optimal lag structure in the ARDL model of equation (9), for the sample data period, is ARDL (1,1,0,0) taking the variables in the order in which they enter this equation. The first order lags for F and C, in the context of annual data, were found to be optimal on the basis of different selection criteria: the Schwarz Bayesian (SBC), the Akaike Information (AIC) and the Hannan-Quinn (HQC) criteria.

The long-run income and price elasticities of demand for food consistent with ARDL (1,1,0,0) are shown, together with supporting statistics, in Tables VIII and IX. The elasticities are of sensible magnitude and well-determined. They are much the same as those reported in Evans et al. (2005) and after applying equation (8) yield the same e value of 1.6. The diagnostic tests for the underlying ARDL model are also shown in Table IX. Both the LM and F-test results clearly indicate the absence of serial correlation and heteroscedasticity problems. However, the tests for appropriateness of functional form give conflicting results. Testing at the 5 per cent significance level, the F-test suggests model adequacy while the LM test marginally rejects the regression model specification. The estimated long-run coefficient on PNF (d in equation (9)) is relatively small in value and not statistically different from zero at the 5 per cent level, thus offering empirical support for homogeneity of the demand function.

Annual data were used in the estimation of the ARDL model of the demand for food and in the alternative co-integration approaches used by Evans (2004) and Evans et al. (2005). While the use of quarterly data would increase the number of sample observations fourfold, it would not increase the effective sample size to the same extent. One reason for this qualification regarding sample size is the fact that in at least some successive quarters there will be very little price variation, especially during periods of relatively low inflation. Another reason is the loss of degrees of freedom due to the higher order lag structure associated with quarterly data. Furthermore, the inclusion of more lagged variables in a quarterly model may lead to multicollinearity problems and the seasonal variation in the data may not exhibit regularity over a lengthy data period meaning that the specification of deterministic seasonal dummy variables would be inappropriate. A flexible approach letting the data determine the pattern of seasonality would be better. Attempts to capture changing seasonal patterns in demand data represent an important recent development in empirical work. See, for example, Arnade et al. (2004).

Estimates of e and the component elasticities, based on UK demand for food analysis, are consistent regardless of the level of sophistication in the co-integration analysis. Simple Engle-Granger error correction models along with co-integrating VAR and ARDL models all yield e estimates of around 1.6. Furthermore, for each approach taken, the CEM emerges as the appropriate specification, whereas both AIDS and QUAIDS models fail to yield any co-integrating relationships between the variables. For evidence of this consistency with respect to the Engle-Granger and co-integrating VAR approaches, see Evans (2004) and Evans et al. (2005). The results are much the same as for the ARDL model considered in this paper.

IV. Concluding comments

Evidence on UK welfare weights based on a revealed social values approach does suggest the appropriateness of a unitary e value for policy application in the appraisal of social policies and projects. The evidence presented in this paper is based on income tax data, foreign aid policy and proposed income-related fines for crimes. While this evidence suggests that HM Treasury selected an appropriate value of e in its latest policy guidance, it did so despite the fact that the evidence on which it drew, principally Cowell and Gardiner (1999), did not support the choice. Further work on revealed social values can extend the ideas introduced here for the UK to other countries. In particular, if the principle of “equal absolute sacrifice of satisfaction” is invoked, then consideration of policy on foreign aid contributions suggests the relevance of a unitary e value for all developed countries.

In relation to behavioural evidence, results based on lifetime consumption models have produced e values close to unity. This work needs updating to cover the period following the de-regulation of UK financial markets and the models used need to be modified in order to capture the changing relationship between the rates of interest that savers and borrowers face. Account should also be taken of possible preference shifts prompted by the product differentiation and aggressive marketing policies of financial institutions. These are formidable empirical problems that need to be addressed in future work.

Results from behavioural evidence based on demand models vary according to the sophistication and type of model, the level of aggregation in the data, the sample data period and the choice of estimator. Single equation work based on the UK demand for food, using both elementary and more complex co-integration techniques, suggests that the CEM is relevant and an e value of 1.6 appropriate. While this e estimate seems robust, it does differ sharply from the unitary value suggested by evidence based on a revealed social values approach. There is a need for updated work based on complete demand systems using household data over time. Furthermore, on grounds of preference independence, the focus should be placed on results for the demand for food and the CEM should be tested against AIDS and QUAIDS model specifications. Finally, a flexible approach to seasonality, as suggested for example by Arnade et al. (2004), should be adopted rather than the standard deterministic dummy variable approach. Hopefully, such refinements will yield estimates of e that are more in keeping with the unitary value suggested by the revealed social values approach.

Equation 1