Taxation, Reranking and Equivalence Scales

van de Ven, Justin; Creedy, John Working Paper Taxation, Reranking and Equivalence Scales New Zealand Treasury Working Paper, No. 03/11 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: van de Ven, Justin; Creedy, John (2003) : Taxation, Reranking and Equivalence Scales, New Zealand Treasury Working Paper, No. 03/11, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205516 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Taxation, Reranking and Equivalence Scales Justin van de Ven and John Creedy N EW Z EALAND T REASURY W ORKING P APER 03/11 J UNE /2003 [473620-1] NZ TREASURY WORKING PAPER 03/11 Taxation, Reranking and Equivalence Scales MONTH / YEAR June 2003 AUTHOR / S Justin van de Ven National Institute of Economic and Social Research London, UK Email [email protected] John Creedy New Zealand Treasury 1 The Terrace Wellington NZ Email Telephone Fax [email protected] 64-4-472-5009 64-4-473-1151 NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz DISCLAIMER The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate. WORKING PAPER TITLE i Abstract This paper considers whether an equivalence scale implicit in transfer policy can be inferred from summary measures of reranking (whereby the rank order of pre-tax incomes is different from that of the post-tax distribution). It is conjectured that, if the government has a distributional objective and formulates tax policy with a view to equitable treatment of income units, then adopting the scale that is implicit in government transfer policy should identify only the reranking that has no equity foundation. This motivates the question: Is the incidence of reranking associated with a transfer system minimised by the equivalence scale that is implicit in the transfer system? The analysis presented in this paper suggests that the equivalence scale which minimises reranking, while not necessarily equal to the closest approximation to the one that is implicit in transfer policy, is nevertheless in its vicinity. JEL CLASSIFICATION D63 KEYWORDS Adult equivalence scales; reranking; horizontal equity WP 02/## | 1 Introduction The use of adult equivalent scales, to allow for non-income-relevant differences between income units, is widespread in the empirical analysis of inequality. A wide variety of scales exists and it is known that they can have substantial effects on income distribution comparisons; see Coulter et al. (1992b). While it is recognised that the choice of scales involves value judgements, surprisingly little attention has been given to the question of the value judgements implicit in the tax and transfer system. The aim of this paper is to examine whether information about such judgements can be obtained from the analysis of changes in the rank order of pre-tax incomes compared with that of the post-tax-and-transfer distribution, referred to as reranking. One explanation for the reranking observed in survey data is that the order based on income gross of taxes and benefits (pre-tax income) is ‘unfair’ because it fails to take into consideration the differing ‘needs’ of a heterogeneous population. Most transfer systems adjust for household need by basing tax and benefitpaymentsonthenumber,ageandhealthstatusof household members, and these adjustments can affect the post-tax order of households. However, it is unlikely that all rank reversals are attributable to an unfair distribution of pre-tax income.1Reranking can also arise as the result of government policy that is tangential to equity objectives. For example, unemployment benefits may be designed to encourage labour market participation, or certain types of income may be treated differently on efficiency grounds. Any reranking that arises as a result of these non-equity based considerations is an issue of concern for studies that consider the redistributive effects of taxation. This is because such reranking opposes the extent to which a transfer system reduces inequality of pre-tax incomes, and thus contradicts a progressivity objective. Adult equivalent incomes are commonly used to focus on reranking that is perceivedashavingnoequityjustification (hereafter referred to as inequitable 1Shoup (1969, p.23) made a similar point in the context of unequal treatment of pre-tax equals, or horizontal inequity. The relationship between horizontal inequity and reranking is discussed in Section 2. 2 reranking).2This methodology requires the selection of an equivalence scale that is used to adjust incomes for differences in unit need. Despite a considerable research effort, however, no compelling criteria have been identified for selecting an equivalence scale. This problem is important for applied studies of reranking because observed reranking typically depends upon the equivalence scale adopted. Hence applied studies of reranking are commonly criticised for failing to differentiate between reranking that is attributable to assumed value judgements, and reranking that arises due to inequities of the tax and benefitsystem. 3 The question considered here is whether it is possible to infer a set of equivalence scales that are implicit in tax and transfer policy, by identifying the equivalence scale specification that minimises observed reranking.4Unlike estimation methods that have been suggested elsewhere5, this approach does not depend on an assumed tax function for reference units. It is based on the premise that, if the government has a distributional objective and formulates tax policy with a view to equitable treatment of income units, then adopting a scale that is implicit in government transfer policy should only identify inequitable reranking. Theconjecturethatthereexistsasingleequivalencescaleimplicitin transfer policy warrents some comment. Specifically, it is frequently assumed that the adjustments made by fiscal policy for household heterogeneity describe a range of equivalence scales, rather than a single set of relativities.6 It is possible, however, to show that the equivalence scale framework is sufficiently flexible to describe any redistributive system (see, for example, Muell2For recent literature that considers reranking, see Creedy and van de Ven (2001), Lambert and Ramos (1997a, b), Lerman and Yitzhaki (1995), Aronson et al. (1994), and Jenkins (1988a). 3On the scepticism that is associated with measures of reranking due to the equivalence scales assumed, see Lambert (2002, footnote 2). 4This suggestion was also mentioned briefly in Creedy and van de Ven (2001). A related issue concerns the aversion to inequality. Attempts to impute a value of inequality aversion implicit in government tax decisions include Christiansen and Jansen (1978) and Stern (1977); see also Mera (1969), Moreh (1981) and Brent (1984). 5See, for example, Muellbauer and van de Ven (2002a). 6See, for example, Coulter et al. (1992a). 3 bauer and van de Ven, 2002b).7In this paper we follow the methodology of Muellbauer and van de Ven (2002a), and define the equivalence scale implicit in transfer policy as the scale that minimises horizontal inequity.8 The issue of how reranking should be interpreted is discussed at greater length in Section 2. This discussion is extended in Section 3, where a formal model is used to identify the factors that determine the incidence of reranking. Section 4 considers whether the reranking observed for a transfer system is indeed minimised by the equivalence scale that is implicit in the transfer system. It is argued, based on a hypothetical population comprised of two income unit types, that reranking need not be minimised by the equivalence scale that is implicit in tax and benefit policy. It is, however, conjectured that, in practice, the scale that minimises reranking is likely to be closely related to the scale that implicitly underlies transfer policy. To test this conjecture, survey data are considered in Section 5. Previous work on the role of equivalence scales in distributional analyses has focused on inequality and poverty measurement.9A study that has examined the impact of equivalence scales on observed reranking is by Nolan (1987). He expressed surprise on finding that adult equivalent income showed more reranking than unadjusted incomes.10 Theobservationsbased on survey data that are presented in Section 5 suggest that Nolan’s findings (which appear to contradict the idea that an implicit equivalence scale can be identified by minimising observed reranking) are attributable to the focus of the equivalence scale that he used. Conclusions are in Section 6. 7See also Seneca and Taussig (1971). 8Horizontal equity requires ‘equal treatment of equals’. This is defined by Muellbauer and van de Ven (2002a) as the requirement that households with the same pre-tax equivalent incomes should have the same post-tax equivalent incomes. 9See, for example, Buhmann et al. (1988), Coulter et al. (1992a, b), and Banks and Johnson (1994). 10Nolan’s use of scales based on Supplementary Benefit rates followed the Royal Commission on the Distribution of Income and Wealth. 4 2 Interpretations of Reranking The appropriate interpretation of reranking depends on the importance that is assigned to the rank order of pre-tax incomes, which is reflected in alternative views regarding distributive justice.11 In the absence of a widely accepted principle of redistributive justice, some guidance may be obtained by relating reranking to horizontal equity, which was described by Musgrave (1959, p.160) as ‘perhaps the most widely accepted principle of equity in taxation’. The relation between reranking and horizontal equity is defined here with the use of a simple analytical framework. Assume that the redistributive objectives of tax policy designers are framed in terms of income per equivalent adult. Values in adult equivalent terms, as measured by the government, are denoted by a * superscript. Let x∗ iand y∗ idefine the pre-tax and post-tax equivalent income of unit i. Given the distribution of x∗ ifor a population, the government is considered to impose an ‘equivalised tax function’, T(x∗ i),sothat: y∗ i=x∗ i−T(x∗ i)+εi(1) where εiallows for the possibility of horizontal inequity, and assume that T0(x∗)≤1.This restriction prohibits an explicit reranking objective of government in terms of adult equivalent incomes: it was formulated by Feldstein (1976), and adopted by Kakwani and Lambert (1998) as one of their three axioms of equity in taxation.12 Add to this framework the following three assumptions. First, the population is sufficiently large such that there are several individuals with the same pre-tax income as any other individual. Second, that the government specifies taxation policy to minimise the individual-specificeffect, εi.Third, suppose the government’s objective is achieved on average such that E(εi)=0for all i. 11For example, with a Rawlsian view involving a maximin strategy behind a ‘veil of ignorance’, emphasis is on the minimum income level and no significance is attached to the rank order of incomes. 12Fei (1981) called this restriction ‘incentive preservation’, referring to the fact that an individual who is subject to a marginal tax rate in excess of 100 per cent has an incentive to reduce pre-tax income. 5 Under these conditions, any reranking that arises must also be identified as horizontal inequity. This conclusion, combined with the fact that precise pre-tax equals are seldom observed in survey data, explains why many applied studies of horizontal inequity focus upon reranking.13 To consider the interpretation of reranking it is consequently useful to focus on the concept of horizontal equity. Hence, if horizontal inequity is deemed to be undesirable under any view of distributive justice, it is reasonable to suppose that the same can be said for reranking, given the direct correspondence between the two concepts.14 However, this conclusion applies only to reranking that has no explicit equity justification. Furthermore, in practice it is important to weigh the undesirable implications of observed reranking against alternative issues of concern, such as those mentioned in the introduction. 3 Equivalence Scales and Reranking In terms of observed incomes, equation (1) translates to:15 yi=xi−a∗ iTµxi a∗ i¶+a∗ iεi(2) To explore the sources of observed reranking, assume that the government’s desired redistributive policy involves the linear function: T(x∗ i)=tx∗ i−G(3) where the same marginal tax rate, t<1, is applied to all income units irrespective of their characteristics, and there is a single transfer payment, 13See the definition of horizontal equity suggested by Feldstein (1976, p.83), and Plotnick (1985, p.241). Jenkins (1988b, p.308) refered to the ‘no-reranking’ condition as ‘strong horizontal equity’, and the ‘equal-treatement-of-equals’ condition as ‘weak horizontal equity’. 14See Musgrave (1990) for a brief survey of the relationship between alternative concepts of redistributive justice and horizontal equity. The concept of horizontal equity is not universally accepted. Gordon (1972) suggested that the initial ordinal ranking of individuals merits no normative emphasis. Also, horizontal equity may not be satisfied by the solution that maximises a utilitarian social welfare function (see, for example, Atkinson and Stiglitz, 1980). 15The derivation of equation (2) assumes that the same equivalence scale is applicable for pre-tax and post-tax income. 6 the two-income-unit case examined earlier. Secondly, the intensity of reranking relative to mean population income is diminished in subgroups that are subject to larger equivalence scales, as is observed for the reranking between units Band Cwhen moving from Panel A to B. Depending on the populations considered, these effects may evidently reduce reranking even if the scale considered is quite different from the relativities implicit in transfer policy. This statement can be made clear by the following example. Suppose the income units of subgroup 1are subject to horizontally equitable tax burdens (so that no reranking is observed within the subgroup), but those of subgroup 2involve some horizontal inequity. In this case, reranking of equivalised incomes can be minimised by applying an infinite equivalence scale to subgroup 2, which would omit reranking between the subgroups (since x− 1>0) and minimise the intensity of any reranking observed within subgroup 2 (relative to average population income). In Section 1 it was suggested that identifying the equivalence scale implicit in transfer policy by minimising observed reranking could be useful because it does not rely on the assumption of a particular tax function for reference households. The analysis presented here reveals that omitting comparisons with the reference unit tax function can lead to a significant difference between the equivalence scale implicit in transfer policy and the scale that minimises observed reranking. It is possible, for example, for reranking to be minimised by a scale that shifts a subgroup of the population to a point in the equivalised income distribution that is otherwise scarcely populated, and also distorts the equivalised tax burden of the subgroup relative to the remaining population. In short, the equivalence scale that minimises reranking can trade decreased reranking for increased horizontal inequity (as it is defined by Muellbauer and van de Ven, 2002a). The equivalence scale that minimises the incidence of reranking does not therefore necessarily coincide with the scale that is implicit in transfer policy. However, it may be suggested that the two scales are related. Indeed, it may be conjectured that the equivalence scale which minimises the incidence of reranking, while not necessarily equal to the closest approximation to the one that is implicit in transfer policy, is nevertheless in its vicinity. The above 13 analysis suggests that this depends on the joint distributions of income and subgroup characteristics. This is examined in the following section. 5 Analysis of Survey Data This section uses survey data to consider the relationship between equivalence scales and the reranking effects of taxation. A brief description of the data is given before presenting the empirical results. 5.1 The Data The data were derived from the Confidentialised Unit Record Files (CURFs) of the 1997-1998 Survey of Income and Housing Costs (SIHC) for Australia, and the Family Expenditure Survey (FES) for the UK. Both surveys provide income and demographic data for individuals and households. The SIHC records annual household income measured in 1997 Australian dollars, whereas the FES provides ‘normal’ measures of weekly income denominated in 1997 British pounds. Both surveys attempt to account for all direct pecuniary flows. For the analysis undertaken here, no attempt is made to impute indirect taxes. The income unit adopted for analysis is the nuclear family, which comprises a single adult or married (registered or de facto) couple and any dependant children under the age of 17 years. After deleting income units with inconsistent data, negative income gross of taxes and benefits, or non-positive income net of taxes and benefits, the FES and SIHC were reduced, respectively, to 6,803 and 8,451 households. 5.2 Empirical Results Measures of household income were adjusted for family size and composition using: ai=(Φci+wi)θ(17) where ciand wirefer respectively to the number of children and adults in income unit i,and0≤(θ,Φ)≤1.Thecoefficient θdetermines the economies 14 of scale implied by the equivalence scale, and Φindicates the effect of children relative to adults. The equivalence scale described by (17) is defined with reference to single adults with no dependant children, for whom ai=1 regardless of the parameter values adopted. The specification assumes that the parameters θand Φare independent of income.18 When calculating summary measures of reranking, measures of equivalent income were weighted by the number of individuals in each household. The analysis presented here focuses upon the Atkinson (1979)-Plotnick (1981) summary measure of reranking, R.19 Thismeasureisaffected by both the incidence and intensity of reranking and captures the area between the Lorenz curve and the concentration curve of the post-tax income distribution. The Lorenz curve is obtained by ranking individuals according to post-tax income, while the concentration curve orders individuals by pre-tax income. Since the Gini coefficient, Gy, measures the area between the Lorenz curve and the 450line of equality, and the concentration index Cymeasures the area between the concentration curve and the 450line of equality, Ris calculated by: R=Gy−Cy(18) where; Gy=2 ¯ycov (y,F (y)) (19a) Cy=2 ¯ycov (y,F (x)) (19b) The variables xand ydenote pre-tax and post-tax income respectively, F(.) is the respective cumulative distribution function, cov(.)is the covariance operator, and ¯yis the arithmetic mean of y. When the ordering of individuals by post-tax income is the same as the ordering by pre-tax income, F(y)= F(x),Gy=Cy,andR=0. 18This formulation was used by, for example, Cutler and Katz (1992), Banks and Johnson (1994), Jenkins and Cowell (1994), and Citro and Michael (1995). Furthermore, Buhmann et al. (1988) show, using a simplification where children are given the same weight as adults, that adjusting θprovides an approximation to a wide range of equivalence scales. 19For alternative summary indices of reranking see, for example, King (1983), Cowell (1985), and Jenkins (1988b). 15 The reranking measure, R, incorporates the same aggregation that is associated with the Gini coefficient. To explore different value judgements associated with the aggregation, the analysis has been repeated using the extended Gini coefficient. Since similar results are obtained for all of the measures considered, the discussion presented below focuses upon the Atkinson-Plotnick statistic, and results for alternative statistics are presented in Appendix A. To obtain a detailed picture of the effect on reranking of using different values of θand Φ, the unit square including all combinations of θand Φ was divided into a grid of 31 intervals per coefficient. Varying the equivalence scales affects redistribution, V, measured as the reduction of the Gini coefficient from the pre-tax to the post-tax equivalent income distribution.20 This effect is not the focus of interest here, so the measures of reranking are reported as percentages of redistribution. These percentages are plotted as surface projections for the Australian and UK survey data in Figures 2 and 4 respectively. Figures 3 and 5 provide the associated topographic maps, which divide the observed variation into fifty equally spaced iso-reranking lines. The surface plot and topographic map of Figures 2 and 3 indicate that reranking based on the Australian data is highly dependent upon the parameter values selected for the equivalence scale. The Atkinson-Plotnick measure of reranking ranges between 5.677 and 10.184 per cent of associated redistribution. A similar range is observed for UK data, where Rvaries between 7.304 and 13.722 per cent of V. Comparing Figures 2 and 3 with 4 and 5, indicates that data from the two countries produce a similar profile for the relation between reranking and the equivalence scale parameters. In each case, the corners of the unit square form local maxima, with an elongated basin around the minimum incidence of reranking.21 Taking cross-sections with respect to the Φaxis of the profiles of reranking indicates a U-shaped relationship with θthat is similar to the findings for inequality and poverty statistics obtained by Banks and Johnson 20See, for example, Banks and Johnson (1994), for a consideration of the effect of equivalence scale parameters on inequality. 21The profiles are driven by variation in Rrather than V:similar conclusions are obtained when profiles of Rrather than R/V are considered. 16 Figure 2: Reranking by Equivalence Scale Parameters - Surface Profile: Australia Figure 3: Reranking by Equivalence Scale Parameters - Topographic Map: Australia 17 Figure 4: Reranking by Equivalence Scale Parameters - Surface Profile: UK Figure 5: Reranking by Equivalence Scale Parameters - Topographic Map: UK 18 (1994) and Coulter et al. (1992b).22 The reranking minimising scale parameters may be compared with econometric estimates of the scale implicit in transfer policy, based on the use of an explicit tax function following Muellbauer and van de Ven (2002a). For Australia, a quadratic polynomial equivalent tax function and a logarithmic specification for tax function heteroscedasticity were used as follows: T∗(x∗ i)=β0+β1x∗ i+β2x∗2 i+εTi (20) εTi ∼N¡0,σ2 Ti¢,σ2 Ti =exp(e1+e2xi)(21) For the UK, a third-order polynomial with homoscedastic errors was found to provide a better fit for the tax function. The estimates are displayed in Table 1.23 Table 1: Econometric Estimates of Tax Policy Implicit Scale Australia UK Φ 0.36536 0.15512 (0.0189) (0.0141) θ 0.70962 0.71991 (8.5E-03) (1.1E-02) β 0-7283.08 -86.1408 (70.896) (1.1093) β 10.43645 0.52920 (2.6E-03) (1.5E-02) β 23.71E-08 -2.63E-04 (1.5E-08) (3.4E-05) β 36.76E-08 (1.1E-08) e1 / std error (tax fn) 14.836 31.778 (0.1417) (0.5733) e2 4.26E-06 (1.4E-06) std error (eqiv scale) 0.30261 0.09304 (0.0262) (0.0244) R-Squared 0.94992 0.94422 Standard Errors in Parentheses It can be seen that the equivalence scale parameters that minimise R/V displayed in Figures 2 to 5 are in the vicinity of the estimates in Table 1, 22However, the results considered here correct for the effect of the equivalence scale relativities on inequality per se. Furthermore, unlike the profiles of inequality and poverty reported by Banks and Johnson (1994), the profiles of reranking displayed in Figures 2 to 5 exhibit a global minimum with Φ>0. 23The estimation method involved searching for parameter values that minimise deviations from horizontal equity. Given a close association between reranking and horizontal inequity, it is likely that the values also minimise observed reranking. 19 although the differences are statistically significant. However, the measures of R/V associated with the regression estimates are within the 95 per cent confidence interval about the global minimum observed for R/V using both Australian and UK data. For Australia, the R/V measure calculated at the parameter estimates in Table 1 is equal to 5.728, and for the UK the respective R/V measure is equal to 7.520. These compare with a minimum R/V of 5.677 with a 95 per cent confidence interval of 5.340-6.039 for Australia, and a minimum of 7.304 with a 95 per cent confidence interval of 6.945-7.719 for the UK.24 These results suggest that the reranking-minimising equivalence scales may provide a conservative basis for scales implicitly used by policy makers. Figures 4 and 5 for the UK also help to explain the observations reported by Nolan (1987), who found more reranking for equivalised than unequivalised incomes. Consideration of Figure 5 reveals that combinations of θand Φon the upper-diagonal spanning between (θ=1,Φ'0.2) to (θ'0.65,Φ=1)are associated with a higher measure of R/V than the value obtained when θ=0(for which the equivalence scale is unresponsive to household size). The equivalence scale parameter combinations defined within this upper-diagonal consequently imply the same ordinal relation observed by Nolan for equivalised and unequivalenced incomes. Hence, it is possibletoconcludethattheresultsreportedbyNolanareattributableto the specific relativities of the scale that he imposed, rather than a conclusion that holds more generally. The parameters that minimise R/V imply larger economies of scale (a smaller value for θ) and a larger adjustment for children relative to adults (a larger value of Φ) compared with the associated regression estimates for both countries. This finding can be explained with reference to the analysis in Sections 3 and 4. The survey populations considered in Figures 2 to 5 can be divided into three groups; income units for which a larger equivalence scale is associated with the parameter estimates derived using the two-stage regression displayed in Table 1 (households comprised predominantly of adults), 24Standard errors were calculated using the Bias Corrected and Accelerated Bootstrap following Efron and Tibshirani (1993). 20 income units for which a larger equivalence scale is associated with the parameter values that minimise the incidence of reranking (households with children), and income units for which the equivalence scale is unaffect by the parameters adopted (reference households). Australian and UK data reveal that the average pre-tax equivalent income (adjusted by the scales associated with the regression estimates) of income units in the first of these three groups is greater than the average pre-tax equivalent income in the second group ($24,648 compared with $10,261 for Australia, and £ 269.04 compared with £78.36 for the UK). Thus, raising equivalence scales above those from regression estimates for a subgroup of income units that have, on average, low pre-tax equivalent incomes tends to reduce the R/V observed, and vice versa for a subgroup of income units with high pre-tax equivalent incomes. Consider two representative individuals drawn from the first and second population subgroups referred to above, and denote them Aand Brespectively. Let a∗denote the equivalence scale defined by the parameter estimates in Table 1, and assume that the respective pre-tax incomes of Aand Bare such that 0<x A/a∗ A=x∗ A<x ∗ B=xB/a∗ B. Suppose that the equivalence scale used for analysis is ˜a,where˜aA>a ∗ Aand ˜aB<a ∗ B. Hence: 0<x A/˜aA=˜xA<x ∗ A<x ∗ B<˜xB=xB/˜aB(22) The pre-tax equivalent incomes of Aand Bexhibit greater disparity based on the equivalence scale ˜athan on a∗. Thissuggestsitislesslikelythat reranking is observed between Aand B. Indeed, assuming that the marginal rate of the equivalent tax function is strictly less than one, the left hand side of equation (15) opposes the inequality condition required for reranking. This is offset by uncertainty regarding the effectontherighthandsideof equation (15), which depends upon the equivalent tax function parameters and the heteroscedastic application of taxation in addition to the alteration considered for the equivalence scale. Assuming the same equivalence scale is applicable for pre-tax and post-tax income, ˜yA<y ∗ Aand ˜yB>y ∗ B,which supports the conclusion that it is less likely that reranking between Aand Bis observed using equivalence scale ˜athan a∗. These effects are consistent with 21 the discussion in Section 4 regarding Figure 1, where the relative increase considered for the equivalence scale of subgroup 2 resulted in the omission of observed reranking between income units Aand Band a reduced area in which reranking between subgroups could occur. 6 Conclusions Rerankingcanhaveasignificant effect on the progressivity achieved by a tax-transfer system, and is closely related to concepts of equity and redistributive justice. However, empirical analyses of reranking are typically subject to criticism on the basis of the value judgements that they exogenously impose. This paper examined the implications for reranking of different value judgements regarding the needs of heterogeneous income units. It was conjectured that an appropriate estimation strategy for the equivalence scale implicit in transfer policy is to seek the relativities that minimise reranking. This strategy does not require an assumed specification for the tax function of reference units. Analytical results showed that the equivalence scale that minimises observed reranking can differ from the scale that is implicit in transfer policy. Nevertheless, analysis of survey data from Australia and the UK revealed no significant difference between the minimum measure of reranking, and the reranking observed for regression-based scales that minimise horizontal inequity using an explicit tax function. Hence, the reranking-minimising equivalence scales may provide a conservative basis for scales implicitly used by policy makers. The analysis presented here consequently provides the analyst with a framework for selecting the parameters of a given equivalence scale specification. It does not, however, provide an adequate response to criticism that observed reranking may be due to horizontal inequity ‘imposed from the outside’; selection of an equivalence scale specificationcanhaveanimportant effect on the measures of reranking obtained. Clearly, the practitioner must continue to exercise care when selecting an equivalence scale, and when interpreting associated distributional observations. 22 Nolan, B. (1987), “Direct taxation, transfers and reranking: some empirical results for the UK”. Oxford Bulletin of Economics and Statistics,49, pp. 273-290. Plotnick, R. (1985), A comparison of measures of horizontal inequity. In Horizontal Equity, Uncertainty, and Economic Well-Being. Edited by M. David and T. Smeeding. Chicago: Chicago University Press. Plotnick, R. (1981), “A measure of horizontal inequity”, Review of Economics and Statistics, 63, pp. 283-288. Seneca, J.J. & Taussig, M.K. (1971), “Family equivalence scales and personal income tax exemptions for children”, Review of Economics and Statistics, 53, pp. 253-262. Shoup, C.S. (1969), Public Finance, London: Weidenfeld and Nicolson. Stern, N. (1977) Welfare weights and the elasticity of the marginal valuation of income. In Artis, M. and Nobay,R. (eds.) Studies in Modern Economic Analysis. Oxford: Basil Blackwell. Yitzhaki, S. (1983), “On an extension of the Gini inequality index”, International Economic Review, 24, 617-628. 29