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Regional welfare weights for the UK: England,Scotland, Wales and Northern IrelandD. Evans a , E. Kula b & H. Sezer ca The Business School , Oxford Brookes University , Wheatley, Oxford, OX33 1HX, UK E-mail:b School of Economics & Politics , University of Ulster , Jordanstown, Belfast, BT37 0QB,UK E-mail:c The Business School , Oxford Brookes University , Wheatley, Oxford, OX33 1HX, UK E-mail:Published online: 18 Aug 2010.

To cite this article: D. Evans , E. Kula & H. Sezer (2005) Regional welfare weights for the UK: England, Scotland, Walesand Northern Ireland, Regional Studies, 39:7, 923-937, DOI: 10.1080/00343400500289937

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Regional Studies, Vol. 39.7, pp. 923–937, October 2005

Regional Welfare Weights for the UK: England,Scotland, Wales and Northern Ireland

D. EVANS*, E. KULA† and H. SEZER**The Business School, Oxford Brookes University, Wheatley, Oxford OX33 1HX, UK. Emails: djevans@brookes.ac.uk

and hsezer@brookes.ac.uk†School of Economics & Politics, University of Ulster at Jordanstown, Belfast BT37 0QB, UK. Email: ie.kula@ulster.ac.uk

(Received August 2003: in revised form November 2004)

E D., K E. and S H. (2005) Regional welfare weights for the UK: England, Scotland, Wales and NorthernIreland, Regional Studies 39, 923–937. In relation to public spending and regional policy, the importance of distributional issuesis stressed, and regional welfare weights are derived from an appropriate underlying social welfare function. Estimates of theseweights are then provided for the four countries comprising the UK. Welfare weights now have a very high policy profilefollowing the special emphasis placed by the UK Treasury, in its recently revised guidance on appraisal and evaluation ingovernment, on the assessment of the distributional impacts of social projects and policies. From an empirical perspective, thecritical component of each welfare weight measure is the elasticity of marginal utility of income (e). Alternative estimationapproaches based on demand analysis and income tax data are used to determine e, and a preferred measure of 1.60 emerges.The resulting regional welfare weights are then compared with recent patterns of per-capita regional public expenditure in theUK. The paper concludes by emphasizing the scope for further empirical work on welfare weights and regional policy inrelation to both the UK and the European Union.

Welfare weights Marginal utility UK

E D., K E. et S H. (2005) Les ponderations regionales et la protection sociale au Royaume-Uni: l’Angleterre,l’Ecosse, les pays de Galles et l’Irlande du Nord, Regional Studies 39, 923–937. On souligne l’importance des questions dedistribution par rapport aux depenses publiques et a la politique regionale et, a partir d’une fonction de protection sociale sous-jacente appropriee, on produit des ponderations regionales. On fournit des estimations de ces ponderations pour ce qui est desquatre pays qui constituent le Royaume-Uni. A l’heure qu’il est, les ponderations relatives a la protection sociale sont tres envue dans le domaine politique, etant donne l’importance accordee par le ministere des Finances au Royaume-Uni, dans sesconseils recemment modifies sur l’evaluation par le pouvoir, a l’evaluation des impacts sur la distribution des projets et despolitiques sociaux. Du point de vue empirique, la composante critique de chaque ponderation relative a la protection sociale estl’elasticite de l’utilite marginale du revenu (e). On emploie d’autres approches a l’estimation fondees sur l’analyse par la demandeet les donnees de l’impot sur les revenus afin de determiner e. Il en resulte une mesure preferee de 1,6. On compare lesponderations relatives a la protection sociale qui en resultent a des distributions recentes des depenses publiques regionales partete au Royaume-Uni. Pour conclure, l’article souligne les possibilites pour la recherche empirique ulterieure sur les ponderationsrelatives a la protection sociale et a la politique regionale par rapport et au Royaume-Uni, et a l’Union europeenne.

Ponderations relatives a la protection sociale Utlilite marginale Royaume-Uni

E D., K E. und S H. (2005) Regionale Wohlfahrtslasten fur das UK: England, Schottland, Wales und Nordirland,Regional Studies 39, 923–937. Es wird die Bedeutung von Verteilungsfragen im Verhaltnis zu offentlichen Ausgaben undRegionalpolitik betont, und regionale Wohlfahrtslasten von geeigneten zugrundliegenden Sozialeinrichtungen abgeleitet. Dannwerden Veranschlagungen dieser Lasten fur die vier Lander des UK vorgelegt. Nachdem das Finanzministerium des UK inseinen kurzlich uberarbeiteten Richtlinien zur Einschatzung und Beurteilung von Regierungsangelegenheiten besonderesGewicht auf die Beurteilung der Verteilungsauswirkungen von Sozialvorhaben und-bestrebungen gelegt hat, werden Wohfahrts-kosten jetzt bei politischen Bestrebungen sehr stark beachtet. Aus empirischer Perspektive gesehen ist die kritische Komponentejeder Wohlfahrtsmaßnahme die Elastizitat der Grenznutzung von Einkommen (e). Alternative, auf Nachfragenanalysen undEinkommenssteurraten gestutzte Einschatzungsansatze werden zur Bestimmung von e benutzt, und ergeben ein bevorzugtesMaß von 1,6. Die resultierenden Wohlfahrtslasten werden dann mit neueren Mustern der regionalen offentlich pro-Kopfausgabenim UK verglichen. Der Aufsatz schließt mit einem Hinweis auf Spielraum fur weitere empirische Arbeit uber Wohlfahrtslastenund Regionalpolitik sowohl im Bezug auf das UK, als auch die EU.

Wohlfahrtslasten Grenznutzung UK

0034-3404 print/1360-0591 online/05/070923-15 ©2005 Regional Studies Association DOI: 10.1080/00343400500289937

http://www.regional-studies-assoc.ac.uk

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924 D. Evans et al.

E D., K E. y S H. (2005) Indices regionales de bienestar social en el Reino Unido: Inglaterra, Escocia, Paıs deGales e Irlanda del Norte, Regional Studies 39, 923–937. Este artıculo enfatiza la importancia de cuestiones de tipo distribucionalcon relacion a los gastos publicos y la polıtica regional, y se extraen ındices regionales de bienestar social a partir de una funcionde bienestar social subyacente. A continuacion, se ofrecen estimaciones de estos ındices para los cuatro paıses que integran elReino Unido. Los ındices de bienestar social gozan de un alto perfil polıtico a raız del enfasis que el Departamento del Tesorodel Reino Unido les ha otorgado en la revision de las directrices sobre los procesos de evaluacion adoptados por el gobierno, enlo que respecta a la evaluacion del impacto de caracter distribucional de proyectos y polıticas sociales. Desde un punto de vistaempırico, el componente crıtico de cada una de las medidas de los ındices de bienestar social es la elasticidad de la utilidadmarginal de los ingresos (e). Se utilizan metodos de estimacion alternativos basados en el analisis de la demanda y datos sobreimpuestos salariales con objeto de determinar e, dando como resultado una medida preferente de 1,60. Subsiguientemente, losındices regionales de bienestar social resultantes se comparan con los patrones recientes de gastos publicos regionales per capitaen el Reino Unido. El artıculo concluye enfatizando el margen que existe para llevar a cabo mas trabajo empırico sobre losındices de bienestar social y sobre cuestiones de polıtica regional en el ambito del Reino Unido y la Union Europea.

Indices de bienestar social Marginal de los ingresos Reino Unido

JEL classifications: D60, D61, R10

INTRODUCTION distributional issues are now being taken very seriouslyat policy level in the UK (H . M. T, 2003,

The importance of distributional issues related to public especially annex 5, pp. 91–96). This governmentsector spending has long been a matter of debate in the emphasis on distributional welfare weights shows aeconomic literature especially in cost–benefit analysis, determination to take equity issues formally intowhich is an application of welfare economics whose account in cost–benefit analysis wherever it is judgedaim is the maximization of social well-being from a to be feasible. The government has identified severalseries of options. Some economists contend that cost– specific distributional dimensions that are worthy ofbenefit analysis should be conducted under the assump- attention in the appraisal of social projects and policies.tion that the existing income distribution is optimal These include income, age, gender, ethnicity, religion(M, 1969; H, 1972). Even if it is and region. This paper focuses on broad regional issuesnot optimal, income distribution should be handled in in the UK and the application of appropriate regionala variety of different ways, for instance through the tax welfare weights.system. However, if a particular project imposes a Welfare weights attached to different income groupsburden on a section of the community, then a Kaldor– can change by income levels, prices and taxation. Non-Hicks compensation scheme should be implemented. recognition of these factors on the well-being of diverseOther than that, there is no need to deal with wider groups is unlikely to be effective in achieving the sociallydistributional issues. desirable results in the community (R , 1980;

At the other end of the spectrum, some economists C , 1983; M and R, 1989). Thebelieve that distributional issues should form an integral present paper considers distributional weights from thepart of the public sector spending schemes, including viewpoint of regional incomes in the UK by focusing

on the four countries of the Union: England, Wales,the appraisal of communal projects, so that specificScotland and Northern Ireland. Regional expenditurewelfare weights can be used to achieve equity andhas always been an important issue in the UK as well asefficiency objectives simultaneously (P andin the European Union since its creation. In fact, variousT, 1965; L , 1972; S , 1972; S ,regions of the UK have received substantial aids in1977). Then one task for the economic profession is tovarious forms from the European Union as well as fromhelp the government in the estimation of various setscentral government. Recent enlargement of the Euro-of welfare weights so that they can, if desired, bepean Union to include less well-off countries on theused in the allocation of public funds. L andContinent has created a debate about Europe-wideG (1994) consider that distribution by way ofregional spending, which is likely to intensify in futuretaxation or subsidy may not happen, even if it shouldyears. After calculating welfare weights for the UK, ahappen. Then there may be a case for the use of welfarecomparison is made with recent regional spendingweights to decide whether or not public spendingpatterns on income and employment-generating activi-meets greater social objectives. According to Bties with a view to finding out to what extent theyand T (1997), a good number of mainstreammatch.economists in the past disregarded the equity criterion

by focusing exclusively on economic efficiency and theREGIONAL WELFARE WEIGHTStime is ripe for taking distributional issues seriously.

It is clear from the UK Treasury’s latest guidance on S (1989) argues that in order to achievemaximum welfare gain in the community, public moneyappraisal and evaluation in central government that

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Regional Welfare Weights for the UK 925

should be distributed between individuals based onSWó;

n

ió1Ui (2)marginal utility of income. W (1972) contends

that welfare weights can focus on a number of criteriasuch as gender, age, ethnicity, religion, family status where Ui is the utility of the ith region with utilityand regions. Uneven distribution of income between being a function of income.regions has always been an important concern for the According to S and V T (1975),UK and the European Union, partly for the purpose if one assumes that regional utility functions have theof reducing migration from the deprived areas towards same algebraic form with the rate at which marginalthe better-off regions. In this respect, individual govern- utility declines being constant, then one can havements, as well as the European Union as a whole, have the following representative iso-elastic regional utilitybeen especially supporting agriculture, fisheries and function:forestry in the rural sector where income levels tendto be low. Public support for relatively poor rural

Uió(Y1ñe

i ñ1)

(1ñe)(3)communities is even a constitutional objective in some

countries, e.g. the Republic of Ireland (Article 45 ofwhere Yi is the per-capita income in region i and e isthe Irish Constitution).the absolute value of the elasticity of marginal utility ofThe main theoretical rationale for giving greaterincome. This iso-elastic utility function has the standardweights to poor regions is the concept of diminishingproperties of monotonicity and diminishing marginalmarginal utility of income, which is one of the oldestutility. The reason the term ‘(1ñe)’ appears in thetheories in economics (D , 1844; G , 1854;denominator of equation (3) is to ensure that Ui risesJ, 1855). According to S (1972),with income, no matter whether e is above or belowdespite its great potential in economic analysis, thisunity (the value of e clearly being an empirical matter).concept has been seriously under used in the profession.The reason the term ‘ñ1’ appears in the numerator ofF (1927) was one of the earliest economists tothis same equation is simply to avoid implying thatuse this concept in a robust manner in an analysis ofutility is being measured on a negative scale in casesthe progressive income tax scheme.where e exceeds unity. Other than that, its inclusionConsider a social welfare (SW) function from aserves no practical purpose. For further details on theregional viewpoint:properties of this commonly applied ‘Atkinson utility

SWóf(UA, UB, UC, . . .) (1) function’, see, for example, S (1977) andC and G (1999).2

where U is utility (where a subscript refers to a region), While the choice of income (consumption) as a solewhich can be defined in a variety of ways such as determinant of utility is certainly open to question, thepolitical/administrative borders, broad geographical Treasury does in fact suggest the relevance of a utilityfactors or some other criteria. Each region can, of function in which consumption is the only determinantcourse, be divided into various sub-regions. In theory, of utility (H . M. T, 2003, annex 5, p. 93).the policy-maker can have as many regions as it wishes. Therefore, the utility function outlined in equationRegional income per capita is the most convenient and (3) has practical policy relevance in relation to thecommon criterion used to measure regional utility. calculation of distributional welfare weights for UK

One contentious issue here is that of interregional applications. Whatever its shortcomings, it is at a policycomparison of utility similar to that of interpersonal level perceived as either the ‘correct’ or, at least, theanalogy. However, it is clear that the Treasury believes most pragmatic function to employ for the purpose ofthat it is appropriate to compare the utilities of different calculating welfare weights. Perhaps in the case of thesocio-economic groups on the basis of equivalized European Union, for example, with current memberincome for the purpose of constructing suitable welfare countries being culturally diverse and at varying stagesweights to be specifically applied in cost–benefit analysis of development, the calculation of regional welfare(H . M. T, 2003, annex 5, pp. 91–93).1 To weights would need additionally to take into account ado so, of course, requires that reliable information range of other variables to reflect adequately social well-concerning net benefits and incomes can be obtained being in the different countries. Such variables mightat acceptable cost, so the scale of the impact of a project, include health, education and environmental indicators.or policy proposal, along with the likely robustness of Future research relating to the application of welfareany calculation of distributional impacts are important weights in a regional context should experiment in thispractical matters. Wherever it is practical to do so, the area and possibly try to make use of the humanTreasury expects distributional weights to be applied in development index (especially in the case of the Euro-the appraisal of social projects and policy options. pean Union). Of course, income must still be an

When there are n regions in the country, or a important determinant of well-being and the variablepolitical/economic unity such as the European Union, does at least benefit from data reliability!

Therefore, focusing on income (consumption) andthe aggregate social welfare function can be expressed as:

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926 D. Evans et al.

with reference to equation (3), the policy-relevant 100 in each year. From this information, it is clear thatutility function in the case of the UK, the incremental Northern Ireland and Wales are noticeably less well offutility would be: than England and Scotland. They should therefore

benefit from the application of higher welfare weightsin the allocation of regional funds. Table 1 reveals a

dUi

dYi

óYñei (4)

very modest decline in the per-capita incomes of Wales,Scotland and Northern Ireland relative to EnglandThe elasticity of marginal utility with respect to incomebetween 1995 and 1999. However, since the relativeis therefore:position does not change much, it would seem reason-able to use the mean figures for the purpose of calculat-d2Ui

dY2i

Yi

dUi/dYi

óñe (5)ing Y*/Yj for each country. The results of thesecalculations are shown in the last column of Table 1.Empirical evidence lends support to the constancy of

Properly deflated income (consumption) figures forthe elasticity of the marginal utility of income (Bthe main regions of the UK cannot be obtainedand T , 1997).from any official data sources. Consequently, givenSince we are interested in comparing income andthe possibility of significant regional price variationscorresponding marginal utility levels between regions,between the countries, welfare weights based solely onthe relevant ratio between, say, regions i and j would be:comparisons of per-capita income (consumption) maybe misleading. For example, there is major variation inYñe

i

Yñej

ó�Yj

Yi�e

(6) regional house prices and so it may be appropriate todeduct housing costs from income or consumptionfigures before undertaking any calculations of welfareThen the distribution weight, w, for region j as com-weights. Such a deduction may be considered appro-pared with the national average, Y*, would be:priate providing the quantity and quality of the housingstock, relative to population size, are at least similar

wó�Y*

Yj �e

(7) across the regions. It is possible to obtain expenditurefigures on ‘housing’ as a share of household expenditurefor each country of the UK. Table 2 shows that onlyin the case of Northern Ireland is this share figure

ESTIMATION OF REGIONAL noticeably smaller. Therefore, at a national level thereWEIGHTS is not much to be gained by adjusting the consumption

data to exclude housing costs in the cases of England,It is clear from equation (7) that regional welfare weightsScotland and Wales. Even in the case of Northerndepend not only on relative income levels, but also onIreland, making an appropriate adjustment is far fromthe extent to which the marginal utility of incomestraightforward in view of the fact that the number ofdeclines as income rises. The lower a region’s per-persons per household clearly exceeds the correspond-capita income level, relative to per-capita income foring figures for England, Wales and Scotland (Table 2the country as a whole, and the greater the extent toand accompanying notes). The issue is, however, likelywhich marginal utility declines, then the larger the sizeto be more serious at an intra-regional level and is aof the welfare weight for that region. The rate ofpotentially important consideration for the regionaldecline of marginal utility is captured by the elasticitygovernments (the Scottish Executive, the Northernof the marginal utility of income.Ireland Executive and the National Assembly forWales).3

Per-capita income levels While intra-regional variation in housing costs iscertainly an important consideration for the calculationTable 1 shows indices of per-capita Gross Domesticof welfare weights for within-country application, it isProduct (GDP) over 5 years for the four countriesstill far from straightforward as to how the weightscomprising the UK. The indices measure regional per-

capita income relative to the UK with the latter set to should be adjusted. Suppose that the intra-regional

Table 1. Indices of Gross Domestic Product per head relative to the UK (UKó100.0)

1995 1996 1997 1998 1999 Mean (Y*/Yj)

England 101.4 101.8 102.3 102.4 102.4 102.1 0.979Scotland 101.9 99.8 96.3 96.6 96.5 98.2 1.018Wales 83.8 82.6 80.6 80.2 80.5 81.5 1.227Northern Ireland 81.5 80.1 80.1 77.7 77.5 79.4 1.259

Source: O N S (2001, information from table 12.1, p. 155).

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Regional Welfare Weights for the UK 927

Table 2. Expenditure on housing in relation to total consumer further investigation with a view to advising govern-ment on a practical solution to the problem. The nextspending: average weekly expenditure, £ per week, 1997–

2000 official guidance from the Treasury concerning theappraisal and evaluation of social projects and policies

Expenditure Expenditureis not due to be published until 2009, so there is stillExpenditure on all goods per person onplenty of time for economists to address the issue!on housing and services all goods and

Region by households by households services

UK 55.20 (16%) 348.20 148.30 Elasticity of marginal utility of incomeEngland 57.50 (16%) 354.30 151.20Wales 44.70 (14%) 315.60 131.70 S (1977) and C and G (1999)Scotland 46.70 (15%) 317.30 139.70 discuss different methods for measuring e, althoughNorthern Ireland 30.70 (10%) 312.10 117.30 some of these suffer from a lack of suitable data for

reliable empirical measurement. In the present study,Notes: Data source: O N S (2001,table 8.11, p. 112). two methods will be employed to cross-check forFigures in parentheses in the second column indicate the consistency of outcomes. One method is based onpercentage share of housing in the total consumer spending consumer demand analysis applied to preference inde-of households.

pendent product groups, while the second method isAverage number of persons per household can be obtainedbased on a government’s degree of aversion to incomefor each country by dividing the figures in column 3 by

those in column 4. For Northern Ireland, the relevant figure inequality as revealed through the progressiveness ofis 2.66, while for each of the other countries the average size income tax. Each approach, together with the mainof household is somewhat smaller and close to 2.30. While empirical findings, is considered in turn.it is the case that Northern Ireland has the highest proportionof households living in detached houses (33% as opposed toonly 21% in England, for example), it also has the lowest

Consumer demand approachproportion in semidetached dwellings and the highest propor-tion in terraced houses. For evidence of this, see O F (1967) explains in detail the method of N S (2001, table 6.5, p. 87).

estimating e based on consumer demand analysis. Theapproach develops the work of F (1927) andF (1932). An approximate estimate of e is

quantity and quality of the housing stock relative to obtained from the ratio of the income elasticity ofpopulation size were similar across counties. Merely demand for a want independent good to its compen-deducting housing costs, in the form of mainly mort- sated own-price elasticity.4 In fact, the Frisch elasticitiesgage payments and rent, from total consumption on a formula for calculating e (absolute value) is as follows:per-capita basis in order to recalculate welfare weightsmight still be a mistake! For example, homeowners

eóy(1ñsy)

p*(8)living in South East England enjoy a number of impor-

tant benefits relative to homeowners in much cheaperwhere y is the income elasticity of demand, s is theareas of the country, e.g. The North East. Those inshare of product expenditure in total consumer spendingwork have much better prospects of re-employment inand p* is the compensated price elasticity of demandthe same geographical area if they lose their jobs and,(absolute value).in this sense, have greater employment security. Also,

In the case of an additively separable utility functionthey will be close to a city that offers the widest choice(want independence) with respect to a particular pro-of entertainment and cultural activities. Apart fromduct group such as food, then it is possible to measurethese important externality benefits (and some conges-the extent to which the marginal utility of incometion-related costs, no doubt) that would need to bedeclines as income rises. Consider the optimality condi-taken into account, there is also the important prospecttions for consumers when maximizing utility subject toof homeowners in the South East being able to makea budget constraint. They can be expressed as follows:considerable capital gains following retirement by mov-

ing to areas of cheaper housing (indeed, this source of MUF

PF

óMUNF

PNF

ój (9)capital gain may permit early retirement).In relation to adjustments to income (consumption)

figures to allow for differential housing costs across where MUF is the marginal utility of food, MUNF isthe marginal utility of non-food, PF is the price of food,regions, it is interesting that the Treasury makes no

direct reference to this particular issue in its latest official PNF is the price of non-food and � is the marginalutility of income (consumption).guidance on appraisal and evaluation in government

(H . M. T, 2003). Despite the considerable Suppose the price of food rises by x% and consumersare given sufficient additional income so they are justdifficulties involved in making appropriate adjustments

to regional welfare weights with respect to regional willing to consume the same amount of food as beforeat the new relative price. For this to be a new optimalprice variation, this is an important issue that merits

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928 D. Evans et al.

consumption level, then consumers will require more Organization for Economic Co-operation and Devel-opment (OECD) data and found that it was empiricallyreal income than before so that they can consume the

larger amount of non-food desired because of the acceptable.favourable relative price change. Given diminishingmarginal utility, this keeps equation (9) in balance. Most

Estimation of e based on the demand for foodimportantly, the assumption of preference independenceensures that the marginal utility of food must remain The Constant Elasticities Model (CEM) is one of the

simplest demand models that can be used for regressionunchanged in this new ‘higher price’ situation since thesame quantity of food is being consumed. It follows analysis. It has been widely used in other studies

concerned with the measurement of e and tends tofrom this that the decline in � corresponding to theincome rise involved (%�Yi) must reflect the percentage yield both plausible and statistically significant estimates

of income and price elasticities. In this study, it willrise in the price of food. Therefore:be tested against other demand model specifications,

%*jóñ%*PF (10) namely the Almost Ideal Demand System (AIDS)associated with D and M (1980)ñ%*j

%*Yi

óeó%*PF

%*Yiand the quadratic extension of this model (QUAIDS)that has added flexibility. All three models, togetherwith the relevant algebraic expressions for the incomeFinally, since by design, the same percentage demandand price elasticities, are detailed below, together withresponse occurs with respect to both the price andthe definitions of the variables and the data source used.income changes involved, it follows that the elasticityThe models are estimated using annual data for theof � (ñe), with respect to income, can be measuredUK and the sample data period covers 1963–2002,approximately by the ratio of the income elasticity ofinclusive.6demand for food to the compensated own-price elasti-

city. Dividing both the numerator and denominator inthe last expression for e in equation (10), by the CEM.common percentage demand response (%�F) gives:

F @óaòbC @òcREL@òdPNF@òe (13)

where b is income elasticity, c is compensated priceeó[%*PF/%*F]

[%*Yi /%*F](11)

elasticity, d (homogeneity restriction)ó0; and where aprime denotes the natural log of the variable and e is

where the numeratoró1/p* (reciprocal of absolute the error term.compensated price elasticity of demand, ped) and thedenominatoró1/y (reciprocal of income elasticity). So:

AIDS.

eó[1/p*]

[1/y]ó

y

p*(12) SFóaòbC @òcREL@òdPNF@òe (14)

where income elasticityó1òb/SF, compensatedprice elasticityóc/SFñ(1ñSF) and d (homogeneityHowever, as equation (8) reveals, this ratio of elasticities,

highlighted in equation (12), would give an upward restriction)ó0.biased estimate of e in cases where the budget share ofthe preference independent product group is non-

QUAIDS.trivial. Since the budget share of food is significant, theFrisch modification (equation 8) needs to be applied. SFóaòb1C @òb2C @2òc1REL@òc2(REL@)2 (15)

F (1967) focused on the product group food òd1PNF@òd2(PNF@)2òeas a suitable choice of want independent good and thissame selection is also made in this study. Justification where income elasticityó1ò(b1ò2b2C@)/SF, compen-

sated price elasticityó(c1ò2c2REL@)/SFñ(1ñSF) andfor the choice is based on a number of reasons. First,several researchers have focused on food in obtaining homogeneity restriction is d1ód2ó0.plausible estimates of e (e.g. F, 1967; K ,1984; S et al., 1991; E and S, 2002).

Variable definitions and data sourceSecond, Evans and Sezer considered alternative productgroups such as ‘clothing and footwear’ and found that FCU household expenditure on food expressed per

capita and measured at current prices,they yielded implausible results that were clearly inferiorto those obtained for food.5 Third, S and F household expenditure on food expressed per

capita and measured at constant 1995 prices,S (1993) argued that want independenceis plausible for broad product classifications such as food. CCU total household expenditure on goods and

services expressed per capita and measured atIn fact, S (1988) tested the preferenceindependence assumption for broad aggregates using current prices,

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Regional Welfare Weights for the UK 929

C total household expenditure on goods and are determined in world markets and that many firmsin the food industry may employ a simple mark-upservices expressed per capita and measured at

1995 prices, pricing policy, whereby the percentage mark-up oncosts remains relatively inflexible over time.SF budget share of food (FCU/CCU),

PF consumer price index for food (1995ó1.0), Given the constraint of constancy for the elasticitiesin the CEM, its superior performance, in statisticalPNF consumer price index for non-food product

groups (1995ó1.0), terms, does seem surprising. However, despite theextent of the sample data period, 1963–2002, it remainsREL relative price of food (1995ó1.0) (RELóPF/

PNF). a clear possibility that the income and price elasticitiesof demand for food have remained approximately cons-Annual UK data on each variable were supplied by

the Office for National Statistics (ONS). The sample tant in value. In fact, statistical testing conducted byE and S (2002), based on the use of dummydata period is 1963–2002.

CEM yielded the best results; in fact, it was the only variables, suggested constancy in the case of the UKover the slightly shorter data period 1967–97.model for which the hypothesis of a co-integrating

relationship between the variables could be accepted. Furthermore, as reported in MAFF (2000), the esti-mated income elasticity of demand for ‘all foods’ isTests for co-integration were conducted using Johan-

sen’s maximum likelihood procedure after first applying close to constant through time over the data period1979–2000 (MAFF, 2000, section 6, p. 98). This surveyAugmented Dickey Fuller (ADF) tests to each relevant

variable to confirm its unit root [I(1)] status and then combines very large samples of household data withtime-series information. Finally, the very fact that a co-testing for the appropriate model lag structures on the

basis of both the Schwarz Bayesian (SBC) and Akaike integrating relationship has been found only in thecontext of a constant elasticities model points to theInformation criteria (AIC). The results for the ADF

tests are shown in Appendix 1 and confirm that all empirical relevance of constant elasticities in the caseof food over the data period 1963–2002.variables in the models are I(1). The evidence on lag

length (see Appendix 2) suggests that a 1-year lag is The main regression results showing the maximumlikelihood (ML) estimates of the long-run income andoptimal in the case of all three models. For the CEM

and AIDS models, both the AIC and SBC criteria price elasticities of demand for food, for the data period1963–2002, are shown in Table 3. The estimates aresuggest a 1-year lag, while in the case of QUAIDS,

only the latter criterion suggests 1 year with AICindicating 2 years. On the grounds of parsimony, given

Table 3. Constant elasticities model (CEM) regression results:the modest sample size, the shorter lag length is selectedUK demand for food, 1963–2002, long-run elasticities andfor QUAIDS.

error correction model (ECM) summaryThe test results for the number of co-integratingrelationships, r, in the case of each model are shown in Long-run elasticitiesAppendix 3. The tests results based on both the maximal

Own-price Cross-priceeigenvalue of the stochastic matrix and the trace wereIncome elasticity elasticity elasticityconsistent for each model, and, as such, only the former

Unrestricted 0.318 (0.114) ñ0.212 (0.087) 0.229 (0.096)are shown in Appendix 3. In the case of CEM, it isHomogeneity 0.334 (0.110) ñ0.197 (0.074) 0.197 (0.074)clear that the hypothesis of just one co-integrating

relationship between the variables is supported. The Notes: Compensated price elasticities.null hypothesis of ró0 is clearly rejected at the 95% Standard errors are shown in parentheses.

LR-test for homogeneity restriction:critical value in favour of the alternative hypothesis�2 (1)ó0.3321 (0.564).ró1, while the hypothesis that ró1, as opposed to

ró2, can be accepted at the 90% critical value. It isECM summary (homogeneity restriction imposed)

equally clear that the hypothesis of no co-integrating ecm1 (ñ1)ñ0.504 (0.104) calculated tóñ4.85; adjustedrelationships (ró0) is supported in the cases of both R2ó0.553; Durbin–Watson statistic (DW)ó1.88, where

ecm1óFñ0.334Cò0.197RELñ5.081.the AIDS and QUAIDS models since the calculatedtest statistics are below the relevant 90% critical values.

Diagnostic testsTherefore, on the strength of these particular results,the AIDS and QUAIDS models are rejected in favour Lagrange multiplier

Test statistics (LM) version F-statistic versionof CEM in which a long-run relationship between thedemand for food variables has been identified. The Serial correlation �2 (1)ó0.123 (0.726) F1,37ó0.116 (0.735)single co-integrating relationship for the demand for Functional form �2 (1)ó0.171 (0.679) F1,37ó0.162 (0.690)

Normality �2 (2)ó1.097 (0.578) not applicablefood means that other variables in the model can beHeteroscedasticity �2 (1)ó0.233 (0.630) F1,37ó0.221 (0.641)treated as ‘long-run forcing’ variables. For example, this

finding is consistent with weak endogeneity of the Notes: Figures in parentheses are likelihoods, i.e. the likelihood ofprice variable. Possible economic reasons for weak no serial correlation, correct functional form, normality and

homoscedasticity.endogeneity may include the fact that some food prices

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930 D. Evans et al.

sensible and statistically significant with food demand as food (e.g. S , 1988), many economistshave felt that this condition is too strong an assumptionclearly both income and price inelastic. The estimated

income elasticity of 0.32 is quite close to the estimate and that the approach is therefore questionable ontheoretical grounds (e.g. S , 1977; D andof 0.34 obtained by E and S (2002) over a

similar but shorter data period using a simple Engle– M, 1980). Therefore, despite the plausibleand statistically well-determined estimates of e obtainedGranger error-correction model. Also, the compensated

own-price elasticity of ñ0.212 almost coincides with from this consumer demand approach, there is a needto cross-check results with those obtained from athe estimate of ñ0.208 in this latter study. In fact, the

compensated own- and cross-price elasticities associated completely different theoretical method. One suchmethod is based on the social values of a governmentwith food and non-food, respectively, are very similar

in value and so the model is re-estimated after imposing as revealed through the structure of income tax rates.In this approach, e is interpreted as an income inequalitythe theoretically expected homogeneity condition. The

absolute value of the price elasticity falls marginally to aversion parameter, so the more progressive the taxstructure, the greater is the degree of income inequality0.197, while the income elasticity is now 0.334. These

results are also shown in Table 3 and the reported chi- aversion (e) from the policy-maker’s perspective.This tax-based approach to the estimation of esquare test clearly supports this theoretically expected

homogeneity restriction. A summary of the associated depends on two important assumptions; first, thatincome tax structures reflect to an important extent theerror correction model (ECM) results for the restricted

model (homogeneity imposed) is shown in the lower principle of equal absolute sacrifice of satisfaction; and,second, that an iso-elastic social utility function ishalf of Table 3, and it can be seen from these that the

coefficient of ñ0.504 is statistically significant, thus relevant. The theory concerning the second assumptionhas already been addressed above and is largely anconfirming the validity of the co-integrating relation-

ship. This finding suggests that following a market empirical matter. B and T (1997) providedempirical evidence to support the approximate con-disturbance, equilibrium would be re-established after

approximately 2 years. The diagnostic tests associated stancy of e. The equal absolute sacrifice of satisfactionassumption implies that in any given tax year thewith the ECM clearly indicate an absence of heterosc-

edasticity and serial correlation problems in the under- government’s tax structure is designed in such a waythat the tax taken from each taxpayer represents thelying model. Also, and rather importantly, both the

Lagrange multiplier (LM) and F-statistic versions of same sacrifice of utility or satisfaction. Therefore, if agovernment has a high degree of income inequalityRamsey’s regression specification test (RESET) are

very clearly passed (Table 3). aversion reflecting a high e value, then this would beconsistent with a view that marginal social utilityFrom the preferred estimates of the income elasticity

(0.33) and the absolute value of the compensated own- declines relatively quickly as personal incomes rise.This, in turn, would be consistent with a highlyprice elasticity (0.19) of demand for food, an appropriate

e value can be derived using the Frisch elasticities progressive structure of income tax rates in countrieswith a high degree of personal income inequalityformula (equation 8). The average share of food in total

consumer spending over the sample data period is 16%. with respect to pre-tax incomes. Of course, differentgovernments may have rather different views on incomeTherefore, the term ‘(1ñsy)’ in equation (8) equals

[1ñ0.16(0.33)], a figure of approximately 0.95. Apply- inequality so that tax-based e measures can differ acrosscountries and change through time. Some empiricaling this adjustment factor to the ratio of the income

and price elasticities yields an estimate for e of 1.60. support for the validity of the ‘equal absolute sacrificemodel’ was provided by S (1977) who showedThis same result was obtained by E and S

(2002) using a more basic co-integration approach for that it provided a better fit to the data than was thecase for more complex models of tax structures.the shorter data period 1967–97.

The equal absolute sacrifice model can be set outformally as follows:

Tax-based approach to the estimation of eU(Y)ñU(YñT(Y))ók (16)

The F (1967) approach to the estimation of eis based on utility under certainty and this is generally

U(Y)ó(Y1ñeñ1)

(1ñe)(17)regarded as an ordinal rather than a cardinal concept.

Given ordinal utility, then e cannot be sensibly measuredusing this method since each different monotonic trans- Equation (16) reflects equal absolute sacrifice in which

the income tax taken from individuals involves the sameformation of the utility function would produce adifferent and completely meaningless value of e ! Only sacrifice of utility (k) for all taxpayers regardless of

income levels. Equation (17) is an iso-elastic utilityin the case of preference independence can e be mea-sured via the Frisch elasticities formula (equation 8). function assumed to apply to all individuals. Y is pre-

tax income and T(Y) is the income tax function.Despite the empirical evidence supporting preferenceindependence in the case of broad product groups such Substituting (17) into (16) gives:

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Regional Welfare Weights for the UK 931

2002/03 are shown in Table 4. In fact, apart from(Y1ñeñ1)

(1ñe)ñ

[(YñT(Y))1ñeñ1]

(1ñe)ók (18) alternative weighted regressions based on numbers of

taxpayers and amounts of income, respectively, resultsTaking the total differential of equation (18) gives: are also presented for unweighted data. In each case,

intercepts are initially included in the estimated equa-Yñeñ[(YñT(Y)]ñe(1ñt)ó0 (19)tions to test whether the underlying assumptions

After rearranging terms in (19) and simplifying, the embodied in equation (21) are supported by the data.relationship becomes: Only where intercepts are statistically insignificant can

it be claimed that the assumptions of equal absolute(1ñt)ó�1ñ

T(Y)

Y �e

(20) sacrifice and constancy of e receive empirical support.Both S (1977) and C and G(1999) impose the underlying theory from the outsetIn equations (19) and (20), t is the effective marginalby suppressing the intercept in the regression equations.tax rate. Taking logs in (20) gives:It is a good idea to see if the data support the theory.

The regression results shown in Table 4 includeLog(1ñt)óe log�1ñ

T(Y)

Y � (21) equations specifying a reversal of the implied dependentand independent variables in equation (21). This reversalproduces estimates of the reciprocal of e, and from theseSo:the appropriate e values can be compared with thedirect estimates. This precaution reflects the lack of aeó

log(1ñt)

log�1ñT(Y)

Y �(22)

proper causal relationship in the equation, although itwould seem to make more sense to argue that a variablereflecting the variation in average tax rates depends onone reflecting variation in marginal tax rates, ratherthan vice versa. If this line of thinking is accepted, then

Tax-based estimates of e the indirect estimates of e should be preferred.Table 4 shows that the unweighted data in equationEquation (21) provides the focus for the estimation of

(1) reject the underlying theory since the intercept ise, where Y is the pre-tax personal income, t is thenon-trivial and statistically significant. However, whenmarginal tax rate, T is the total income tax liabilitiesweighted data by numbers of taxpayers are employedand T/Y is the average tax rate.

Estimates of e based mainly on weighted data for (equation 2), the estimated intercept is statistically

Table 4. Estimates of e based on personal tax data for 2002/03

Durbin–WatsonIntercept Log (1ñT/Y ) Log (1ñt) R2 (%) statistic (DW)

1 Log (1ñt) ñ0.127 1.03 92.2 2.00(unweighted data) (ñ5.52) (9.07)2 Log (1ñt) ñ0.0066 1.54 85.9 0.92(weighted by numbers of taxpayers) (ñ1.55) (6.54)3 Log (1ñt) 1.83 0.78(weighted by numbers of taxpayers) (11.96)4 Log (1ñt) ñ0.0073 1.37 90.9 1.48(weighted by income) (ñ1.56) (8.35)5 Log (1ñt) 1.57 1.26(weighted by income) (13.81)6 Log (1ñT/Y) 0.0028 0.664* 90.9 1.47(weighted by income) (0.79) (8.35)7 Log (1ñT/Y) 0.613* 1.28(weighted by income) (13.81)

Notes: *Estimates of the reciprocal of e.Data used in the regressions are based on November 2002 Inland Revenue projections for personal income tax liabilities by incomerange, 2002/03. They are extracted from Table 2.5, Income Tax Statistics and Distributions. Source: http://www.inlandrevenue.gov.ukThe statistical package used does not produce R2 statistics for equations in which the intercept is suppressed.Weights using numbers of taxpayers: the group weights (nine income groups in total) for the weighted least-squares regressions arebased on numbers of taxpayers in each group or income range. The intra-group weights for computation of the ‘average’ marginal taxrates for each group are based on the numbers of taxpayers liable to pay tax at each relevant marginal tax rate.Weights using amounts of income: inter-group weights are based on group income liable to tax. The intra-group weights used tocalculate marginal tax rates for each group are based on amounts of income liable at the relevant marginal tax rates.

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932 D. Evans et al.

insignificant. An even better result is obtained when Based on the preferred case, the least well off country(Northern Ireland) has a regional welfare weight ofincome weights are used (equation 4): the intercept is

insignificant, R2 is higher than for equation (2) and the 1.45 that is 50% higher than the corresponding weightfor England. By comparison, Wales has a welfare weightDurbin–Watson statistic suggests a greater degree of

error independence. Dropping the insignificant inter- that is 43% higher than the weight for England. If themid-value of e (1.30) is used in the calculation ofcept produces a well-determined e estimate of 1.57 in

equation (5). It is an estimate that almost coincides welfare weights, then the regional weight for NorthernIreland falls from 1.45 to 1.35. For Wales, the weightwith the result obtained in the present paper, and by

E and S (2002), using the FFF (F, falls from 1.39 to 1.30. It is clear that the higher welfareweights for the less well off countries in the UK,1927; F , 1932; and F, 1967) model.

Finally, taking the indirect estimate of e (equation 6), namely Wales and Northern Ireland, could be used tojustify generous financial assistance from official sourcesa highly insignificant intercept is obtained. Suppressing

the constant produces an estimated e value of 1.63. in the form of regional investment grants and subsidies.Such assistance can provide an important stimulus to theThese preferred results are substantially higher than the

unitary e value assumed by the Treasury, In fact, they local economies and help to restrict outward migration.are close to the Treasury’s previous view of 1.50.

UK welfare weights REGIONAL ECONOMIC POLICY ANDSPENDING IN THE U K

The preferred estimate of e is 1.60 and this is based onevidence from different methods: the demand for want- Is there any match between welfare weights calculated

here and regional economic policy and public sectorindependent goods and the progressiveness of incometax. Thus, the closeness of the e estimates, around 1.60, spending in the UK? The UK’s regional economic

policy has been evolving since the inter-war periodderived from these entirely different approaches suggeststhat the decision by H . M. T (2003) to revise largely in response to changing national and inter-

national conditions. The level of expenditure allocateddownwards its estimate of e to unity may have been amistake. For example, a close consideration of empirical to regional development, the type and range of policy

instruments introduced, and the geographical distribu-evidence presented by C and G (1999)does not suggest an e value as low as this! In fact, H . M. tion of assisted areas within the UK have changed

noticeably over the last 70 years. What has not changedT (1997) reported that for the UK, a valueof around 1.50 for the elasticity of marginal utility of is the commitment of the government towards improv-

ing economic conditions in all underprivileged areas.income is fairly widely accepted. The Treasury refersto evidence mainly drawn from savings behaviour but The Treasury divides public spending into two

groups: identifiable and non-identifiable (H . M.acknowledges a lack of precision in the estimate of ebased on savings data. The present empirical work T, 1996). The former can be identified from

official records as having been incurred on behalf of abroadly supports the Treasury’s old position.The full set of welfare weight results for each country particular population. The latter is deemed to be

incurred on behalf of the UK as a whole, or whichis shown in Table 5. Column 1 gives the ratio of per-capita GDP for the UK to per-capita GDP for the cannot be separated between the individual territories

from the existing record. One group of identifiablecountry in question. This information, taken fromthe last column of Table 1, yields weights that are expenditure is for trade, industry, energy and employ-

ment. Table 6 provides a comparison of identifiableconsistent with the current Treasury view on e, i.e.unity. Column 2 presents the preferred welfare weights public expenditures for the four regions of the UK. It

is clear that Northern Ireland benefits from the highestfor each country. Using equation (7), eó1.60 is appliedto each figure in column 1. In column 3, the mid- per-capita expenditures. This is appropriate since, being

the least well off of the four countries, it has the highestrange value of 1.30 is used to calculate the relevantwelfare weights. regional welfare weight (Table 5).

A comparison between the welfare weights and theactual per-capita public expenditure figures can beTable 5. Regional welfare weights: England, Scotland, Walesmade for 1996–2000. According to the weights shownand Northern Irelandin Table 5, per-capita expenditure for Northern Ireland

Region W1 (eó1.0) W2 (eó1.6) W3 (eó1.3) is too high. However, this is no longer the case if totalidentifiable expenditure (all functions) is considered:England 0.979 0.967 0.973

Scotland 1.018 1.029 1.023 the per-capita index averages 134, which is close to theWales 1.227 1.387 1.305 appropriate welfare weight for Northern Ireland. TableNorthern Ireland 1.259 1.446 1.349 6 suggests excessive per-capita expenditure for Scotland

but appropriate expenditure for Wales between 1996Note: The formula for the regional welfare weight is given byequation (7). and 2000. This finding also extends to total identifiable

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Regional Welfare Weights for the UK 933

Table 6. Index of per-capita identifiable expenditure on trade, such as e changes. In the UK, the Treasury publishesdetailed guidance on social appraisal and evaluationindustry, energy and employment, 1988–2000 (UKó100)every 6 years. It is therefore advisable to use, for

Northernexample, the most up-to-date data on regional indicesYears England Scotland Wales Irelandof per-capita income or consumption (relative to

1988/89 77 155 173 494 UKó100) taking an average position over, say, 5 years.1989/90 76 160 177 507

The latest empirical evidence on the value of e should1990/91 80 172 171 340also inform the policy-maker concerning the need for1991/92 81 162 157 355

1992/93 83 158 157 314 any adjustments to the values of the regional welfare1993/94 84 158 145 329 weights.1994/95 83 158 138 3131995/96 87 168 116 322Average 81 161 154 372

CONCLUSIONS1996/97 86 165 131 2621997/98 84 169 144 276

Regional welfare weights, derived from an appropriate1998/99 84 168 148 275social welfare function, can be expressed as ratios of1999/2000 89 148 114 252

2000/01 87 154 108 315 national to regional per-capita real incomes raised toAverage 86 161 129 276 the power of e. Empirical measures of these weights

depend critically on estimates of e. Using the FFFSource: H. M. T (1996) for 1988/89–1995/96; H. M.demand analysis approach, the results, based on aT (2002) for 1996/97–2000/01.consideration of alternative demand models, yield sens-ible and well-determined elasticity estimates, fromwhich an e value of approximately 1.6 is derived. Theexpenditure. Of course, differences in relative income

dispersion across the regions may have a bearing on this result is confirmed by analysis of income tax data andcompares favourably with the measure of 1.5 reportedand investigation of the issue may suggest an adjustment

of welfare weights based on per-capita regional income by H . M. T (1997), but not with the latestpreferred Treasury measure of unity that lacks anylevels.

It is important to recognize that the calculated welfare obvious empirical support (H . M. T, 2003).Our preferred welfare weight measures are comparedweights should only be applied to income-related

benefits and costs associated with social projects and with the weights implied if e takes, first, the Treasury’scurrently preferred value of unity and, second, thepolicy options. Needs-related benefits and costs associ-

ated, for example, with much of the expenditure on midpoint value of 1.3. As is to be expected, the regionalwelfare weights for the less well off regions of Waleseducation, health, and law and order should not be

weighted. Provision for social projects yielding these and Northern Ireland are considerably lower if an evalue of unity is used as opposed to our estimated valuelatter types of benefits and costs should clearly be based

on demographic factors, most obviously population size. of 1.6 (Table 5).Comparison of the preferred measured welfareThe identifiable income-related benefits and costs

associated with regional social projects and policy weights with regional indices of per-capita identifiablepublic expenditure does suggest some degree of corres-options should be weighted according to the relative

representative income levels of the target groups wher- pondence, with Northern Ireland being the main bene-ficiary. However, while per-capita expenditure figuresever it is practicable to do so. In relation to decisions

regarding funding levels from official sources for coun- for Wales match well, there does appear to be animportant discrepancy in the case of Scotland wheretries, such as central government and the European

Union, then with regard to income and employment the relevant welfare weight is consistent with a lowerlevel of per-capita expenditure relative to the UK.generating social investments, per-capita funding should

be reasonably consistent with a set of welfare weights The focus on per-capita incomes for the regions tohelp decide the relative welfare weights is only strictlybased, as far as possible, on economic criteria. At least

this is the case if it is anticipated that countries will, on appropriate if the relative dispersion of income (e.g. byhousehold) in each of the countries comprising the UKaverage, make equally productive use of the funds from

a social perspective! is at least similar. In focusing on per-capita incomeratios, we have implicitly assumed that this is the case.It is important that the values of welfare weights are

updated periodically in line with the availability of new To the extent that income dispersion does differ, thenso the government would need to make adjustments toand better quality information, e.g. improved statistics

relating to cost of living indices, better quality regional the distributional welfare weights. For example, if thedistribution of income by county, on a per-capita basis,data relating to the distribution of income and changes

in relative living standards across regions. It is also differed significantly in the four countries, then thecountries with most dispersion (in relative terms) wouldnecessary to revise these weights if new research con-

vincingly reveals that the value of a key component need to have their welfare weights adjusted upwards.

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934 D. Evans et al.

How the weights might be adjusted for funding pur- A third priority relates to the measure of e, since ithas been shown clearly here that its numerical valueposes would then depend on how project/policy

benefits are likely to be distributed across the counties, has a major influence on the calculated values ofregional welfare weights. While two entirely differentat least insofar as this matter is predictable.

In comparing income distributions, care must be approaches to the estimation of e adopted in this papergave consistent results that agreed approximately withtaken to ensure that properly equivalized incomes (by

household size and age composition) are considered. the value deemed appropriate by the Treasury in its oldappraisal guidance (H . M. T, 1997), it mustFurthermore, given the regional differences in housing

costs, should these be deducted before calculating the still be a matter of some concern that the latest officialguidance suggests only a unitary value of e! There isrelative dispersion figures? Further research on regional

welfare weights, both in the cases of the UK and the a definite need for further research concerning theappropriate value of e, i.e. research based on differentEuropean Union, needs to focus on these important

income dispersion issues so that weights based simply methods, improved estimation techniques and coveringas many countries as possible.on per-capita income ratios can, where necessary, be

adjusted accordingly. Furthermore, this work should besupplemented by an investigation into the use of official

Acknowledgements – The authors thank the referees forfunds by the various regional governments, e.g. Thehelpful comments on an earlier draft of this paper.Welsh Assembly in the case of Wales. Distributional

welfare weights, on the lines discussed here, can beapplied at this intra-regional level as well focusing onthe representative incomes of the target groups.

H . M. T (2003), in its latest guidance onappraisal and evaluation in central government, has

APPENDIX 1: UNIT ROOT TESTSfurther raised the policy profile of distributional impactsFOR CONSTANT ELASTICITIESof social projects and policies. Considerable emphasis isMODEL (C E M), ‘ALMOST IDEALnow placed on welfare weights (H . M. T,DEMAND SYSTEM’ (A I D S) AND2003, annex 5, pp. 91–96). Looking beyond the UK,

QUADRATIC EXTENSION OF THISthe issue of regional public expenditure is set to becomeMODEL (Q U A I D S) VARIABLESeven more important in Europe given the large number

of countries that have recently become members of the The tests were based on the following autoregressiveEuropean Union. There is rich scope for further work models, one of which includes a time trend term:in relation to European regional policy and welfare

�Ytóaò(pñ1)Ytñ1òvtweights. In fact, three clear priorities for the futureassessment of welfare weights have emerged from the

�Ytóaò(pñ1)Ytñ1ò�tòvtwork reported here and each will be highlighted inturn with a view to pinpointing important areas for where p is the first-order autocorrelation coefficientfuture research. and the rejection of non-stationarity in the levels data

One important matter concerns taking proper require this coefficient to be significantly less than unity.account of interregional variations in the cost of living. In both equations, this is equivalent to (pñ1) beingHousing costs are especially a problem here, but any significantly less than zero. If the null hypothesisadjustment to welfare weights depends not only on the (pñ1)ó0 is accepted, then Y is subject to first-orderavailability of better quality data, but also on a proper non-stationarity.assessment of any external benefits and costs associated Lagged values of �Y, up to the fourth order, werewith living in ‘high’- and ‘low’-cost housing areas. added to both equations to conduct Augmented

The second priority concerns taking proper account Dickey–Fuller (ADF) tests. The optimal lag lengths inof any significant interregional differences in the relative the autoregressive equations were selected according todispersion of income. In its latest appraisal guidance, the Schwarz Bayesian criterion (SBC) and for eachthe Treasury focuses on the distribution of equivalized variable the optimum lag structure is shown below.net household income by quintile group and gives an The critical ADF t* values were as follows:example for the UK as a whole. The example only

For nó35relates to income before the deduction of housing costsand it would be better if it were by decile group.

5% Significance levelHowever, this is a step in the right direction and what

Constant, no trend ñ2.9558is now required are more comprehensive data of reliableConstant plus trend ñ3.5562quality, additionally including income after the deduc-

tion of housing costs, not only for the countries com-prising the UK, but also for the member countries of Calculated t* values for all variables entering the

demand models were as follows:a rapidly expanding European Union.

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Regional Welfare Weights for the UK 935

APPENDIX 3: TESTING FOR THEConstant, no trend Constant plus trend

NUMBER OF CO-INTEGRATINGF@ (DF) 1.25 ñ1.80 RELATIONSHIPS IN MODELSSF@ (DF) ñ0.79 ñ1.13C@ (ADF(1)) 0.24 ñ2.89 (A) Constant elasticities model (CEM)PF@ (ADF(1)) ñ2.49 ñ1.66 (0.84792 0.38371 0.15445 0.02529)PNF@ (ADF(1)) ñ2.31 ñ1.02REL@ (ADF(1)) ñ0.55 ñ2.84 Null Alternative Statistic 95% Critical 90% CriticalC@2 (ADF(1)) ñ0.58 ñ3.23

ró0 ró1 67.80 27.42 24.99(REL@)2 (ADF(1)) ñ0.94 ñ2.36ró1 ró2 17.43 21.12 19.02(PNF@)2 (ADF(1)) ñ2.28 ñ3.24ró2 ró3 6.04 14.88 12.98ró3 ró4 0.92 8.07 6.50

For both sets of equations, excluding and including atime trend variable, all variables are clearly I(1). (B) Almost ideal demand system (AIDS)

(0.45290 0.19289 0.10512 0.021345)

Null Alternative Statistic 95% Critical 90% CriticalAPPENDIX 2: CRITERIA FORSELECTING THE LAG ORDER IN ró0 ró1 21.67 27.42 24.99

THE ALTERNATIVE DEMAND ró1 ró2 8.51 21.12 19.02ró2 ró3 4.04 14.88 12.98MODELSró3 ró4 0.73 8.07 6.50

(A) Constant elasticities model (CEM)

Adjusted (C) Quadratic almost ideal demand system (QUAIDS)Lag order AIC SBC LR-test (0.44028 0.17859 0.11609 0.03332 0.01479

0.00537 0.00247)4 352.15 301.27 ñ3 354.62 315.71 �2 (16)ó13.12 (0.664)

Null Alternative Statistic 95% Critical 90% Critical2 355.51 328.57 �2 (32)ó27.77 (0.681)1 358.06 343.10 �2 (48)ó40.81 (0.760) ró0 ró1 36.92 45.63 42.700 154.98 151.98 �2 (64)ó253.26 (0.000) ró1 ró2 25.89 39.83 36.84

ró2 ró3 17.08 33.64 31.02ró3 ró4 4.44 27.42 24.99(B) Almost ideal demand system (AIDS)ró4 ró5 1.22 21.12 19.02ró5 ró6 0.36 14.88 12.98Adjustedró6 ró7 0.15 8.07 6.50Lag order AIC SBC LR-test

Notes: LR-test applied: unrestricted intercepts and no trends.4 405.08 354.20 ñFigures in parentheses for each model are eigenvalues in descend-3 407.20 368.29 �2 (16)ó13.46 (0.639)

ing order.2 408.04 381.10 �2 (32)ó28.16 (0.661)1 410.82 395.86 �2 (48)ó40.98 (0.754)0 193.95 190.95 �2 (64)ó266.80 (0.000)

NOTES(C) Quadratic almost ideal demand system (QUAIDS)

1. Equivalized income involves the adjustment of householdAdjusted income according to household size and composition by

Lag order AIC SBC LR-testmeans of the McClements equivalence scale. For details

4 566.83 488.27 ñ of this scale see, for example, O N3 563.53 503.67 �2 (25)ó20.59 (0.715) S (2001, p. 256).2 566.98 525.83 �2 (50)ó36.26 (0.927) 2. Equation (3) can be expressed as follows: (a) Uió1 560.49 538.04 �2 (75)ó59.16 (0.910) [Yi

(1ñe)/(1ñe)]ñ1/(1ñe). If e exceeds unity, then the0 390.97 387.23 �2 (100)ó200.63 (0.000) expression ‘ñ1/(1ñe)’ in (a) must be positive and

therefore as Yi increases, so utility rises on a positiveNotes: AIC, Akaike information criterion; SBC, Schwarz Bayesianscale towards this positive term approaching it in valuecriterion; LR, log-likelihood ratio test.asymptotically. For example, if eó1.5, then the secondterm in (a) would equal 2. In the case of eóunity, then(a) collapses and needs to be replaced by the following‘special case’ equation: (b) Uiólog Yi. Differentiating Ui

with respect to Yi in (b) then gives the followingexpression for marginal utility: (c) MUióYi

ñ1. Thesignificance of this special case is that H. M. Treasury(2003, annex 5, p. 93) currently applies a unitary e valueand therefore specifies this ‘special case’ utility functionin its current guidance on social project appraisal andevaluation.

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936 D. Evans et al.

should not materially influence the utility derived from3. According to the notes and definitions relating to tableconsuming any specific quantity of food!8.3 (Income distribution of individuals 1999/2000) in

5. In the case of ‘clothing and footwear’, the implausibleO N S (2001, p. 255),results may well have been due to a failure to capturesensitivity testing against the alternative cost of livingadequately the underlying model dynamics and associ-regimes suggests that estimates of income before housingated lag structure. Also, for this product group andcosts are deducted are not sensitive to regional priceothers, a constant elasticities demand model may well bedifferentials, but results after deduction of housing costsinappropriate.are sensitive. In particular, for London, living standards

6. The use of quarterly data involves a more complex lagmay be overstated, while in the North East and Wales,structure in the model and the possibility of multi-living standards may be understated.collinearity problems due to the additional lagged4. Want or preference independence in relation to a productexplanatory variables entering the demand equation.group such as food is consistent with the following addi-Also, the seasonal variation in the quarterly data istively separable utility function: UióU1(X1)òU2(X2), unlikely to exhibit regularity over a suitably lengthy data

etc. Therefore, for food (X1) to be a want independentperiod and there is therefore a danger that the estimated

good in relation to all other goods (X2), then the utility regression model would not properly capture the seasonalderived by consumers from any given amount of food effects. In fact, the standard treatment of seasonal vari-consumed must be independent of the amount of non- ation in regression models consists of specifying deter-food (for any combination of non-food goods) con- ministic seasonal dummy variables, but if the seasonalsumed. In the case of food, this property of want pattern changes during the data period, then this standardindependence does appear to be reasonable since while approach must result in biased estimates of the regressionthe consumption of food may be considered to be coefficients. This particular problem has only beencomplementary to many different ‘activities’ (e.g. enter- recently addressed in the literature (e.g. A andtainment) in the general sense, there do not seem to be P , 1998; F and M , 2002). For a veryany important specific complementary goods to food. recent attempt to deal with the problem by letting theConsumers will eat in many different contexts and thus data determine the seasonal structure (in relation to the

demand for apples), see A et al. (2004).the consumption of less entertainment, for example,

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