Food Expenditure and GST in New Zealand

Ball, Christopher; Creedy, John; Ryan, Michael Working Paper Food Expenditure and GST in New Zealand New Zealand Treasury Working Paper, No. 14/07 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Ball, Christopher; Creedy, John; Ryan, Michael (2014) : Food Expenditure and GST in New Zealand, New Zealand Treasury Working Paper, No. 14/07, ISBN 978-0-478-42162-0, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205662 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/ Food Expenditure and GST in New Zealand Christopher Ball, John Creedy and Michael Ryan New Zealand Treasury Working Paper 14/07 April 2014 NZ TREASURY Food Expenditure and GST in New Zealand WORKING PAPER 14/07 MONTH/YEAR April 2014 AUTHORS Christopher Ball Treasury No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: ++64 +4 890 7206 John Creedy Victoria University of Wellington 23 Lambton Quay Wellington New Zealand Email: [email protected] Telephone: ++64 +4 917 6893 Michael Ryan Treasury No. 1 The Terrace Wellington New Zealand Email: [email protected] Telephone: No author defined ISBN (ONLINE) 978-0-478-42162-0 URL Treasury website at April 2014: http://www.treasury.govt.nz/publications/research-policy/wp/2014/wp-14-07 Persistent URL: http://purl.oclc.org/nzt/p-1645 ACKNOWLEDGEMENTS We are grateful to Matt Benge, Angela Mellish, Alastair Thomas and Martin Wong for their comments on an earlier draft of this paper. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email: [email protected] Telephone: +64 4 472 2733 Website: www.treasury.govt.nz DISCLAIMER Access to data used in this paper was provided by Statistics New Zealand under conditions designed to give effect to the security and confidentiality provisions of the Statistics Act 1975. The graphs presented in this report are the work of staff at the New Zealand Treasury and not Statistics New Zealand. The views, opinions, findings and conclusions are strictly those of the authors and do not necessarily reflect the views of the New Zealand Treasury. Abstract This paper has two main aims. First, the poor targeting of a policy of zero-rating food in a goods and services tax (GST) is illustrated in a simple model where the revenue lost from zero-rating food is instead devoted to a universal transfer payment, with a larger effect on progressivity. Second, the paper investigates the welfare effects on New Zealand households of zero-rating food. The detailed effects, for a range of household types, are then investigated using Household Economic Survey data. Demand responses to consumer price changes are estimated and welfare changes, in terms of equivalent variations, are obtained. Comparisons are made across ‘clusters’, consisting of groups of households with similar characteristics. The reform is seen to produce a very small amount of progressivity in the GST, with redistribution from richer households without children to poorer households with children, and older households. JEL Classification: H31; I3; D11 Keywords: Goods and services tax; tax progressivity; budget shares; welfare changes. WP14/07 Food Expenditure and GST in New Zealand i Executive Summary The New Zealand Goods and Services Tax (GST) is unusual in having a very broad base which includes food. This is usually defended on grounds of efficiency and there is often a presumption in favour of uniformity on the grounds of the large administrative and compliance costs of differentiation. These arguments are combined with the important point that equity objectives can be met using the nonlinear structure of income taxes and transfers. Nevertheless, other countries use the zero-rating of food (and other goods) for redistributive reasons. The issue is periodically raised in New Zealand, and it is sometimes suggested that if the GST rate becomes much higher than its current level, there is likely to be further pressure, on equity grounds, for the exemption of some goods. Hence, despite the limitations to any analysis of only one part of the complete tax and transfer system, since it is the overall effect that matters, a separate analysis of GST is warranted. A consumption tax imposed at a uniform rate on all goods and services has no redistributive effect since the real value of total expenditure of all households are reduced by the same proportion. A consumption tax is most progressive, or inequality reducing, when it taxes most heavily those goods which form a systematically higher proportion of the budgets of high-expenditure households. This lies behind the argument that food should be exempt, given the long-established empirical relationship of a declining budget share for food as total expenditure increases. But there is a cost of such redistribution because since, to raise the same revenue, the tax rate imposed on other goods must be higher than in the uniform structure. Rational debate requires information both about the costs and benefits of such differentiation. The present paper contains two analyses of the effects of zero-rating. First, the poor targeting of such a policy is illustrated in general terms in a simple model where the revenue lost from zero-rating food is instead devoted to a universal transfer payment. It is shown that the universal transfer payment has a larger effect on tax progressivity than does zero-rating. The second analysis computes the detailed effects on New Zealand households of zero-rating food, for a range of household types. The effects were obtained using Household Economic Survey data. Demand responses to consumer price changes were estimated and welfare changes were obtained. Comparisons were made across ‘clusters’, consisting of groups of households with similar characteristics, as well as for households in total expenditure decile and age groups. A revenue neutral reform was found to produce a very small amount of progressivity in the GST, with welfare losses for higher decile groups and welfare gains for the lower deciles. Furthermore, redistribution is from richer households without children to poorer households with children, and older households. The value of allowing for demand responses was demonstrated by the fact that the use of tax WP14/07 Food Expenditure and GST in New Zealand ii changes, with an assumption of no responses to price changes, overstates the degree of progressivity achieved. The analysis thus supports earlier studies suggesting that indirect tax exemptions and zero-rating provide a poor redistributive instrument compared with the use of direct taxes and transfers. WP14/07 Food Expenditure and GST in New Zealand iii Contents Abstract i Executive Summary ii 1 Introduction 1 2 Budget Shares and Tax Structures 3 2.1 Elasticities and Liability Progression . . . . . . . . . . . . . . . . . 3 2.2 A Simple Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Demand Responses and Categories 6 3.1 The Clustering Technique . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Cluster Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4 Welfare Effects of GST Changes 9 5 Conclusions 14 List of Tables Table 1 – Cluster 2010 Demographic and Income Information . . . . . . . 8 Table 2 – Welfare Changes and Budget Shares for Clusters . . . . . . . . 10 Table 3 – Welfare Changes and Budget Shares for Deciles . . . . . . . . 11 Table 4 – Welfare Changes and Budget Shares for Various Groups . . . . 12 Table 5 – Ratio of Tax Change to Equivalent Variation: Revenue Neutral . . 13 WP14/07 Food Expenditure and GST in New Zealand iv Food Expenditure and GST in New Zealand 1 Introduction The New Zealand Goods and Services Tax (GST) is unusual in having a very broad base, which includes food. 1 This is usually defended on grounds of efficiency – that the broad base makes it possible to keep the GST rate relatively low. This keeps the excess burden, which approximately increases with the square of the rate, low. In an optimal tax framework there is no presumption in favour of uniformity; the conditions under which the maximisation of a social welfare function gives rise to uniform indirect taxes are strong and unlikely to hold. 2 However, faced with the enormous difficulty of computing a set of optimal taxes, there is often a presumption in favour of uniformity on the grounds of the large administrative and compliance costs of differentiation. 3 These arguments are combined with the important point that equity objectives can be met using the nonlinear structure of income taxes and transfers. Nevertheless, other countries have used the zero-rating of food and other goods, along with differential rates, for redistributive reasons. 4 The issue is periodically raised in New Zealand, and it is sometimes suggested that if the GST rate becomes much higher than its current level, there is likely to be further pressure, on equity grounds, for the exemption of some goods. Hence, despite the limitations to any analysis of only one part of the complete tax and transfer system, since it is the overall effect that matters, a separate analysis of GST is warranted. When looking at only one tax, it is important, when measuring tax progressivity, to look at tax 1 For international comparisons, using the concept of ‘C-efficiency’ (reflecting departure from a uniform system), see Keen (2013). He decomposes the efficiency measure into a ‘poverty gap’ and a ‘compliance gap’. 2 This is essentially a second-best problem in view of the impossibility of taxing endowments. For example, with identical preferences, a fixed wage rate distribution, and a linear income tax, uniformity is optimal if Engel curves are linear and the marginal rate of substitution between goods is independent of leisure; see Stern (1990). 3 Indeed, the configuration of tax rates is irrelevant only if judges are indifferent to the distribution of welfare and, in addition, if all own-price and cross-price elasticities of demand are zero. On optimal indirect tax reform in Australia, see Creedy (1999). 4 Reference is often made to the exemption of food from GST. However, such policies impose zero rating, whereby registered firms can claim tax credits on inputs purchased. This differs from the technical term ‘exemption’, where such credits cannot be claimed. WP14/07 Food Expenditure and GST in New Zealand 1 payments in relation to the particular tax base, in this case total expenditure for each household.5 A consumption tax imposed at a uniform rate on all goods and services has no redistributive effect since the real value of total expenditure of all households are reduced by the same proportion. A consumption tax is most progressive, or inequality reducing, when it taxes most heavily those goods which form a systematically higher proportion of the budgets of high-expenditure households. This lies behind the argument that food should be exempt from a general consumption tax, given the long-established empirical relationship (referred to as Engel’s Law) of a declining budget share for food as total expenditure increases. But there is a cost of such redistribution because since, to raise the same revenue, the tax rate imposed on other goods must be higher than in the uniform structure. Rational debate requires information both about the costs and benefits of such differentiation. The present paper has two main aims. First, the use of differential rates in order to introduce progressivity is discussed in Section 2. Exemptions are compared with the use of the same tax revenue, lost by zero-rating food, to finance a universal benefit. The second aim is to investigate the detailed welfare effects on households of a change to the indirect tax structure in New Zealand involving the zero-rating of food (except for meals consumed outside the home) from GST. 6 A feature of the present paper is that demand responses to consumer price changes are estimated: the approach is discussed in Section 3 and in the Appendix. The treatment of consumers’ behaviour makes it possible to estimate money measures of welfare changes arising from tax changes. Comparison of welfare effects are made for a range of household types. In addition, comparisons are made across ‘clusters’, consisting of groups of households with similar characteristics. The clustering method is also described in Section 3. The welfare changes arising from the current system and a reform involving the zero-rating of food are reported in Section 4. Section 5 briefly concludes. 5 Spurious results can be obtained if a different tax base, such as income, is used. Popular discussions often focus inappropriately on tax in relation to income. The difference between bases is affected not only by income taxation but, in a short-period framework, by savings. Since savings are ultimately spent, they can be ignored when using annual data. On progressivity and indirect taxes, see detailed treatments in Creedy (1998a, 2001). 6 For a detailed analysis of zero-rating of food from a legal and administrative point of view, see van Klink (2012). WP14/07 Food Expenditure and GST in New Zealand 2 relative budget share on luxury items, such as international air travel, audio-visual and computing equipment and major cultural and recreational equipment but the lowest budget share of any cluster on food (11 per cent). Households in Cluster F, on average, are roughly the same age as L, slightly less qualified and on lower incomes, and have a food budget share of 12.73 per cent compared with 10.99 per cent. The lowest income cluster of these, D, a beneficiary cluster, with relatively large average payments of unemployment, invalid and sickness benefit, relatively low wage and salary income, and a food budget share of 15.94 per cent. 4 Welfare Effects of GST Changes The welfare effects reported here are for two policy changes. The first change simply eliminates GST on food, so that all households are expected to gain. The second policy involves the zero-rating of food while at the same time keeping total GST revenue constant by raising the GST rate imposed on all other goods. The measure of welfare change is the equivalent variation ( EV ), defined as the maximum amount an individual would be prepared to pay (after the tax policy change) to return to the old prices. Hence a negative value of EV indicates a welfare gain rather than a loss. The method of calculation is described in the Appendix. For comparisons among households with differing compositions, parametric adult equivalent scales are used such that the adult equivalent size, s , of a household with na adults and nc children is given by s = (na+θnc)α , with θ = 0 . 6and α = 0 . 8. The latter reflects the assumed extent of economies of scale within the household. The data used are obtained from the Household Economic Survey for 2010. The empirical results are presented in Table 2 for the clusters and in Table 3 for the deciles of the distribution of household expenditure per adult equivalent person. 12 Consider first the section of the table for deciles of household expenditure per adult equivalent person. The final column shows the average budget share for food within each decile. 13 This decreases systematically as total expenditure 12 The unit is the household: that is, 10 per cent of households are in the lower decile of household expenditure per adult equivalent. 13 All values reported are averages within the designated groups, obtained as weighted averages using the HES sample weights used to aggregate to population values. In the case of the budget shares, these are obtained as the ratio of the (weighted) average household expenditure on food, divided by average total expenditure. This is in line with Statistics New Zealand calculations of budget shares (though of course the ratio of averages is not the same as the average of ratios). WP14/07 Food Expenditure and GST in New Zealand 9 Table 2: Welfare Changes and Budget Shares for Clusters No GST on food Revenue neutral Food EV EV/y EV EV/y share Clusters A -534 -1.68 -15 -0.05 13.82 B -1028 -2.19 -292 -0.62 19.38 C -696 -1.53 59 0.13 12.27 D -486 -1.88 -70 -0.27 15.94 E -456 -2.16 -125 -0.59 17.62 F -733 -1.54 55 0.12 12.73 G -936 -1.32 260 0.37 11.13 H -663 -1.92 -112 -0.32 16.18 I -1418 -1.66 -22 -0.03 14.05 J -1026 -1.51 105 0.15 12.31 K -1011 -1.56 63 0.10 13.71 L -1139 -1.36 267 0.32 10.99 increases, consistent with Engel’s Law. The first policy change considered is the simple zero-rating of food. With a Goods and Services tax-exclusive rate of 0.125, or 12.5 per cent (consistent with the use of the 2009/10 Household Expenditure Survey), this implies a reduction in the price of food, while the prices of other goods remain constant in this partial equilibrium setting. 14 Hence it is expected that all households are better off as a result of this change, as indicated by the fact that all values of EV in the second column of the table are negative: the convention in the public finance literature that a welfare loss is indicated by a positive EV is followed here. Although all households gain, it is clear that those in the top decile gain considerably more than those in the lower decile in absolute terms. This reflects the poor ‘target efficiency’ of this kind of policy change where it is intended to generate greater equality: it is impossible to exempt food from indirect taxation for only those in specific categories defined by personal characteristics. Nevertheless, in relative terms, the lower deciles gain relatively more than the higher deciles: the ratio EV/y declines systematically as y increases, from − 2 . 69 in the first decile to −1.04 in the top decile.15 This kind of tax policy change is not, however, revenue neutral. In practice it would be necessary to raise tax revenue in other ways or reduce expenditure, in order to avoid debt increases. Suppose that the extra revenue (in aggregate) is obtained 14 It could be argued that, since food may enter as an intermediate input into some goods and services which are still subject to GST, those other goods will not have constant prices. This kind of effect cannot be considered here but can reasonably be expected to be small. 15 There is an exception in that the average ratio for decile 4 is slightly higher than that for decile 3. WP14/07 Food Expenditure and GST in New Zealand 10 Table 3: Welfare Changes and Budget Shares for Deciles No GST on food Revenue neutral Food EV EV/y EV EV/y share Equivalised expenditure deciles Decile 1 -472 -2.69 -206 -1.18 24.16 Decile 2 -619 -2.38 -216 -0.83 20.09 Decile 3 -620 -1.95 -108 -0.34 17.12 Decile 4 -759 -1.99 -147 -0.38 16.79 Decile 5 -796 -1.78 -65 -0.15 15.47 Decile 6 -899 -1.74 -52 -0.10 15.39 Decile 7 -966 -1.59 40 0.07 13.45 Decile 8 -998 -1.52 99 0.15 12.66 Decile 9 -1003 -1.32 292 0.38 11.19 Decile 10 -1188 -1.04 803 0.70 7.87 by increasing the GST rate applied to taxed goods and services. It is found, by a process of trial and error, that the rate would need to increase by 2 percentage points. This is the rate obtained after all households adjust their consumption pattern as a result of the relative price change between taxed and untaxed goods. The effects of this revenue neutral change are shown in the two columns under the heading ‘Rev neutral’ in the table. For the first six decile groups the EV is still negative, reflective a welfare gain, but for the higher-decile groups there is a welfare loss. When converting to the ratio, EV/y , the revenue neutral policy change is progressive in that the absolute value of the ratio, EV/y , decreases as y increases. However, the relative gains to the lower-decile groups are much smaller than with the first (revenue decreasing) policy change. Turning to the results for the clusters, whose characteristics are summarised in Table 1, all groups gain from the aggregate revenue-reducing policy of simply zero-rating food. Those with the largest gains from this policy, clusters A, B, D, E, H and I, continue to gain from the revenue-neutral policy. However, as before, their relative gains are much lower. Clusters D and E are the older households with few, if any, children and low average incomes, with relatively large food budget shares. Clusters B and I are households with relatively more children and, as expected, relatively high budget shares for food. The biggest losers from the revenue-neutral policy are clusters G and L, consisting of high-income households with few children and hence lower food budget shares. Table 4 shows results for various other groups distinguished by age, household WP14/07 Food Expenditure and GST in New Zealand 11 Table 4: Welfare Changes and Budget Shares for Various Groups No GST on food Revenue neutral Food EV EV/y EV EV/y share Age <25 -720 -1.45 133 0.27 11.56 25-34 -852 -1.55 79 0.14 13.01 35-44 -977 -1.71 -21 -0.04 13.56 45-54 -1011 -1.55 101 0.15 12.77 55-64 -850 -1.50 116 0.20 12.61 65+ -622 -1.98 -109 -0.35 16.21 Household structure Single -409 -1.53 43 0.16 12.07 Single with children -693 -1.77 -46 -0.12 14.64 Couple only -912 -1.54 89 0.15 12.66 Couple with children -1222 -1.78 -89 -0.13 14.33 Other: no children -1086 -1.67 2 0.00 14.63 Other: with children -841 -1.43 162 0.28 12.25 Housing tenure Mortgage -892 -1.61 45 0.08 13.12 Renting -737 -1.66 8 0.02 13.79 Other -1020 -1.61 47 0.08 13.13 structure, and housing tenure. 16 In particular it is seen that, with the groups classified by household structure, those with children are generally the only ones to experience welfare gains from the revenue neutral policy change. Consistent with this finding, the age group 35-44 – the prime child-rearing age bracket – experience welfare gains from the revenue neutral change. Again, not surprisingly, those in the age group 65 and over also gain, on average, from the revenue neutral policy. These results demonstrate clearly that the absolute and relative gains and losses from a revenue neutral policy of zero-rating food in a GST are small relative to total expenditure, despite the fact that the policy can achieve some progressivity. Such exemptions are a ‘poor redistributive instrument’. As demonstrated above using a simple illustration, a policy of raising transfer payments – even where these are received by everyone – is capable of producing more progressivity. The above results may be compared briefly with those obtained by a simple comparison of tax payments in relation to total expenditure, with no allowance 16 Values for ‘Other households’ are omitted from the table. These two groups (with and without children) are extremely heterogeneous, and in the case of those without children the EV is negligible, making the ratio of the change in tax to the equivalent variation extremely high. WP14/07 Food Expenditure and GST in New Zealand 12 for demand responses to price changes, instead of using equivalent variations. Table 5 shows the ratio of the reduction in GST to the equivalent variation, for the revenue neutral policy change which, as explained above, involves an increase in GST of 2 percentage points. Where this ratio has a positive sign, the tax changes and welfare changes are in the same direction. A negative sign indicates that the use of tax changes, with no demand responses, suggests a change in the opposite direction from that of the welfare change. In all the cases where there is a negative sign, the use of tax changes indicates a gain, whereas the use of equivalent variations indicates a welfare loss. Even where the two measures agree about the direction of change, it is clear that there are substantial differences in relative orders of magnitude. Table 5: Ratio of Tax Change to Equivalent Variation: Revenue Neutral Age ∆Tax/EV <25 0.85 25-34 0.28 35-44 0.85 45-54 0.45 55-64 0.44 65+ 1.07 Household structure Single 0.99 Single with Children 1.44 Couple Only 0.57 Couple with Children 0.99 Other: no children -45.50 Other: with children 0.50 Tenure Mortgage 0.32 Renting -3.15 Other 0.32 Clusters ∆Tax/EV A 1.34 B 1.25 C 1.05 D 1.25 E 0.93 F 0.65 G 0.77 H 1.13 I 3.67 J 0.84 K -0.52 L 0.94 Deciles Decile 1 1.18 Decile 2 1.05 Decile 3 1.43 Decile 4 1.16 Decile 5 1.89 Decile 6 2.63 Decile 7 -0.25 Decile 8 0.56 Decile 9 0.71 Decile 10 1.00 WP14/07 Food Expenditure and GST in New Zealand 13 5 Conclusions This paper has investigated the detailed welfare effects on households of a change to the indirect tax structure in New Zealand involving the zero-rating of food in the GST. Such a policy is typically motivated by a desire to introduce some progressivity into the GST structure, in view of the well-established property that the share of household expenditure devoted to food declines as household income increases. As mentioned in the introduction, it is sometimes argued that the case for zero-rating is greater, the higher is the uniform GST rate. However, richer households benefit more in absolute terms. The poor targeting of such a policy is illustrated in a simple model where the revenue lost from zero-rating food is instead devoted to a universal transfer payment, with a larger effect on progressivity. The detailed effects of zero-rating food, for a range of household types, were then investigated using Household Economic Survey data. Demand responses to consumer price changes were estimated and welfare changes, in terms of equivalent variations, were obtained. Comparisons were made across ‘clusters’, consisting of groups of households with similar characteristics, as well as for households in decile and age groups. A revenue neutral reform is seen to produce a very small amount of progressivity in the GST, with welfare losses for higher decile groups and welfare gains for the lower deciles. Furthermore, redistribution is from richer households without children to poorer households with children, and older households. It was also shown that the use of tax changes, with an assumption of no responses to price changes, somewhat overstates the degree of progressivity achieved. The analysis supports earlier studies suggesting that indirect tax exemptions and zero-rating provide a poor redistributive instrument compared with direct taxes and transfers. WP14/07 Food Expenditure and GST in New Zealand 14 Appendix A: Utility, Demand Elasticities and Welfare This appendix describes the method used to obtain demand elasticities and welfare changes using the linear expenditure system (LES), applied separately for a range of demographic groups (though the following notation generally omits the additional subscript). The first stage is to obtain, for each household type, a set of average budget shares, wki , for each consumption category, i, and a range of total expenditure groups, k . The total expenditure elasticities are obtained using the variations in budget shares for each commodity group. However, the observed variability in budget shares gives rise to some negative total expenditure elasticities. This can be overcome by smoothing the data. The approach used was first to carry out a series of ordinary least squares regressions of the form: wki =ai+bilog yk+ci(1/yk)(A.1) for each commodity group (and household type), where the values of yk correspond to the arithmetic mean values of total expenditure in each group, k . The form in ( A.1 ) provides a reasonably good fit for most groups and ensures that the predicted weights add to unity. The second stage is to compute ownand cross-price elasticities, eii and eij, (again for each total expenditure group and household type) using Frisch’s (1959) results for additive demand systems. The expressions require the use of the elasticity of the marginal utility of total expenditure with respect to total expenditure, ξ, often referred to as the ‘Frisch parameter’. If δij denotes the Kronecker delta, such that δij = 0 when i6 = j, and δij = 1 when i = j , Frisch showed that the elasticities can be written as: eij =−eiwj1 + ej ξ+eiδij ξ(A.2) It is necessary to make use of extraneous information about the way in which the Frisch parameter varies with total expenditure. In view of the role played by the Frisch parameter and the lack of a really firm foundation for the values used, it is important to carry out a range of sensitivity analyses. WP14/07 Food Expenditure and GST in New Zealand 15 The third stage involves obtaining parameters of the LES direct utility function (again for each total expenditure group and household type): U=Y i (xi−γi)βi(A.3) with 0 ≤βi≤ 1; γi is the committed consumption of good i, and Pβi = 1 . The own-price elasticity, eii,is given by: eii =γi(1 −βi) xi −1(A.4) The total expenditure elasticity of good i, ei,is: ei=βiy pixi (A.5) Having obtained the total expenditure elasticities from the smoothed budget shares, the corresponding values of βi at each total expenditure level were obtained using ( A.5 ), whereby βi = eiwi. Using the values of own-price elasticities as described in the second stage above, equation ( A.4 ) can be used to solve for piγi, the committed expenditures for each good. As before, the various parameters vary with y, but the additional subscript is suppressed for convenience. Defining the terms A and B respectively as Pipiγi and Q(pi/βi)βi,the indirect utility function for the LES, V(p, y), is: V= (y−A)/B (A.6) The expenditure function, E(p, U), the minimum expenditure required to achieve Uat prices p, is found by inverting (A.6) and substituting Efor yto get: E(p, U) = A+BU (A.7) If the vector of prices changes from p0 to p1, the equivalent variation, EV , is EV =E(p1, U1)−E(p0, U1).Substituting for Eusing (A.7) gives: EV =y−(A0+B0U1)(A.8) Substituting for U1,using equation (A.6) into (A.8) and rearranging gives: EV =y−A01 + B0 B1y A0 −A1 A0 (A.9) The term A1/A0 is a Laspeyres type of price index, using γi s as weights. The term B1/B0 simplifies to Q(p1i/p0i)βi, which is a weighted geometric mean of price relatives. These two terms can be expressed in terms of the ˙p s. 17 If all prices change by the same proportion, ˙pi = ˙p for all i, and ( A.9 ) becomes EV/y = (1 −B0/B1)+(A0/y){(B0/B1) (A1/A0)−1},with B1/B0=A1/A0= 1 + ˙p. 17 Since p1i = p0i(1 + ˙pi), and defining si = p0iγi/Pip0iγi, it can be shown that A1/A0 = 1 + Pisi˙piand B1/B0=Qi(1 + ˙pi)βi. WP14/07 Food Expenditure and GST in New Zealand 16 References Ball, C. and M. Ryan (2014). New Zealand households and 2008/09 recession. New Zealand Economic Papers 48(1). Creedy, J. (1998a). Are consumption taxes regressive? Australian Economic Review 31(2), 107–116. Creedy, J. (1998b, June). Measuring the Welfare Effects of Price Changes: A Convenient Parametric Approach. Australian Economic Papers 37(2), 137–51. Creedy, J. (1999). Marginal indirect tax reform in australia. Economic Analysis and Policy 29, 1–14. Creedy, J. (2001). Indirect tax reform and the role of exemptions. Fiscal Studies 22(4), 457–486. Creedy, J. (2002). 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