Chapter 1. Estimating the Incidence of Indirect Taxes in Developing Countries. David E. Sahn and Stephen D. Younger 1

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1 Chapter 1 Estimating the Incidence of Indirect Taxes in Developing Countries David E. Sahn and Stephen D. Younger Introduction The distributional impact of the public sector s budget is a topic of enduring interest for economists and policymakers. The more recent literature on developing countries has focused almost exclusively on the expenditure side of the budget, as discussed in Chapter 2 But the few available studies on tax incidence in developing countries show that some tax policies have redistributive impacts both positive and negative of a size comparable to the effects of the more commonly studied social sector expenditures, ustifying more equal attention from analysts interested in understanding the distributional consequences of public policies. The methods that we describe for tax incidence analysis are intuitive and computationally straightforward. They have practical limitations, which we address in the final section to this note. But it is important to include one conceptual limitation up front: these methods are only useful for analyzing the equity consequences of public policy, yet good policy analysis requires consideration of both the equity and efficiency consequences, not necessarily in that order. Consequently, the type of analysis that we describe here is only one input to a complete analysis of tax policy The technique and theoretical background The MIT Dictionary of Modern Economics defines tax incidence as describing...those who suffer a reduction in their real income resulting from the imposition of a tax. (p.192, Pearce, 1986). To accomplish this description, we use survey data to determine individual households loss, and then describe how that loss is distributed across the households in the sample. To 1 The authors wish to thank Rutshia Bhattamishra for her research assistance. Tool Kit Chapter 1 page 1-1

2 measure each household s loss from a tax, we rely on basic duality theory. A household s expenditure function, y = e(p,u), is the minimum amount of money that it must spend to generate utility level u given a vector of prices p for all goods and services consumed. A household s compensating variation for a tax increase is the amount of income that it would need to ust keep its utility constant in the face of any price changes caused by the tax: CV 0 = e( p1, u ) e( p0, u) (1) where a 0 indicates the initial state and a 1 indicates the state after the tax change. Clearly, if we could estimate the household s expenditure function, we could easily calculate the compensating variation, and thus know how much real income declines as a result of the tax. Unfortunately, that is a difficult task, both in terms of data and analysis, and the methods that we use avoid it entirely by approximating the compensating variation. Consider for the moment the case in which the tax change affects only one price, p i. Recalling that, by Shepard s lemma, the derivative of the expenditure function with respect to p i is the compensated demand function for good i, the Taylor expansion of equation (1) is CV c 0 0 c xi ( p, u ) 2 xi ( p, u ) pi + pi 2 p + K (2) where x c ( p 0, u 0 i ) is the compensated demand function and i is the change in the price of p i caused by the tax increase. The first term in the Taylor expansion is the change in expenditure that the household would have to undertake to keep utility constant without changing its demand for good i (or any other), that being the initial quantity consumed times the price change. This is a first-order approximation to the compensating variation. Put otherwise, the compensating variation of a marginal change in the price of a good is simply the change in the consumption budget that is necessary to keep the consumption basket constant. In other words, the demand response to the tax may be ignored as a first approximation. p We can graph this approximation by noting that the difference in expenditures noted in equation (1) is equal to the integral of the compensated demand function from p0 to, again by Shepard s lemma. CV 0 = e( p, u ) e( p, u) = 1 i 0 i p1 p0 x c i 0 ( p, u ) dpi (3) Tool Kit Chapter 1 page 1-2

3 This integral is the area to the left of the compensated demand function in Figure 1, shown as ABDE. The first term in the Taylor expansion in equation (2) is equal to the area ACDE, the original quantity consumed times the price change. The second term is the triangle BCD. Higher order terms would capture the curvature of the demand curve. The only information that generally used in incidence analysis is the first-order approximation, area ACDE. As such, behavioral changes that the tax change might induce are not accounted for. 2 We simply observe the existing pattern of demand, multiply it by a hypothesized price change, and use the result as an estimate of each household s loss in real income. Finally, if a change in tax policy changes more than one price, all the first-order terms in equation (2) for goods whose price changes are summed together. While such an approach cannot tell us anything about the efficiency consequences of the tax change they depend entirely on its behavioral consequences it has been found it to be a reasonably satisfactory short-cut for the study of a policy s distributional impact. How to do a tax incidence analysis Most analyses of indirect tax incidence are concerned with the share of taxes paid by different groups. As such, the only data necessary are (1) a variable that defines the groups, and (2) an estimate of the taxes paid by each group, where we understand taxes paid to be the loss in real income described above. The most common source of these data is a nationally representative household survey such as a Living Standards Measurement Survey (Glewwe and Grosh, 2000) or a household income and expenditure survey, although summaries of these surveys, as published by national statistical agencies, might suffice if they are disaggregated according to the grouping of interest. Usually, the groups are defined by welfare levels poor vs. non-poor or each quintile of the welfare distribution so we require a variable that ranks people by welfare, and the preferred choice in the vast maority of studies is household expenditures per capita or per adult equivalent. But other groupings are possible, such as geographic location (political region or urban/rural), gender, ethnicity, or age cohort. In all cases, these variables are almost always readily available in the survey data. It is also increasingly the case that individual observations rather than groupings are used. 2 The second term in equation (2) does account for induced behavioral changes, the move up the demand curve. Including it in our calculation would yield an improved, second-order approximation to the compensating variation, but it requires estimating a demand system. Tool Kit Chapter 1 page 1-3

4 Estimates of the taxes paid by each group are more difficult, and it is actually helpful to explain first what to do once we have such an estimate, returning to the question of how to get it later. The simplest sort of comparison notes that group A pays so much of tax, group B so much, etc. For the most common case, where we want to group people by welfare status, the groups might be poor and non-poor, or people in each quantile of the welfare distribution. But in fact, it is easy to make a much more attractive comparison based on the theory of welfare dominance, which also offers the advantage of involving individual agents rather than groups of agents. The theory of welfare dominance provides general criteria that allow us to conclude that one distribution of welfare is better than another for broad classes of social welfare functions (Saposnik, 1981; Shorrocks, 1983; Foster and Shorrocks, 1988; Yitzhaki and Slemrod, 1991; Lambert, 1993). One particular application of this theory is particularly useful for tax incidence analysis. Shorrocks (1983) shows that if the generalized Lorenz curve 3 for one distribution of welfare is everywhere above the generalized Lorenz curve for another, then the first distribution is preferable to the second under any social welfare function that is (1) increasing in the welfare variable, (2) anonymous, and (3) equality-preferring. By increasing we mean that a larger value of the welfare variable, w i, is better than a smaller one for each individual i, i.e. there is no satiation. By anonymous we mean that the welfare function does not pay attention to who each person in the ordering is or whether a person changes position from one ordering to another. By equality preferring we mean that if we generate a distribution by taking an existing distribution and transferring a small amount of welfare from a better-of individual and transfer it to a worse-off one, the new distribution is preferred to the old. The generality of this comparison makes it quite attractive. To carry it out, we need only construct two generalized Lorenz curves, one pre-tax and one post-tax, and check to see if one is clearly above another. In practice, however, we have found it useful to use a slightly more restrictive condition. The Lorenz curves tend to be quite close together, even for maor tax changes, so that visually, it is more attractive to work with concentration curves, defined as 3 The generalized Lorenz curve is defined by L( i) = i k= n k= wk 1 µ ( w) wk 1 where L(i) is the generalized Lorenz ordinate and µ (w) the mean of the distribution W. In words, the generalized Lorenz curve plots the cumulative share of individuals in the sample (indexed by i) on the x-axis against the cumulative share of the welfare variable multiplied by its mean on the y-axis. The Lorenz curve is identical, but not scaled by the mean. Tool Kit Chapter 1 page 1-4

5 C i) = i k= 1 n k= 1 T T k k ( (4) which is the same formula as the Lorenz curve with the total tax paid substituted for welfare. Note that observations remain ordered by welfare, not by taxes paid, so that C(i) gives the share of taxes paid by the poorest i/n households or individuals in the sample. If the concentration curve for a tax is everywhere below the Lorenz curve of income/welfare, then increasing that tax by a small amount and refunding the proceeds in proportion to welfare (the Lorenz curve) will increase social welfare for all social welfare functions that are increasing, anonymous, and equalitypreferring. Similarly, if tax a s concentration curve is everywhere below tax b s, then increasing tax a slightly and reducing tax b such that total tax revenue is unchanged will improve social welfare for the same class of social welfare functions - see (Younger, et.al., 1999). Note that it is possible to make poor/non-poor comparisons based on Lorenz and concentration curves, and also comparisons of each quantile s share, but the use of the entire distribution is more general than either of these comparisons, and equally easy to calculate. Standard errors for these curves are more difficult to calculate (Davidson and Duclos, 1997), but a specialized software package, DAD, is now available to do this. Calculating households or groups taxes paid We now return to the question of evaluating the cost to a given household of an ad valorem tax. Economists since David Ricardo have recognized that the statutory incidence of tax those who have to transfer the tax to the government is not the same as the economic incidence of the tax those whose real purchasing power declines because of the tax. Much of public economics involves understanding exactly how different statutory taxes are shifted among various agents, based on models of their behavioral responses to the taxes. The type of empirical tax incidence study that we describe here ignores all but the simplest of this theory. Typically, we assume that indirect taxes on goods are shifted entirely to consumers, a standard result if markets are competitive and the taxes apply to final sales (or value added) only. This ignores any effect that the taxes may have on firms welfare (or rather, their owners welfare) and, more importantly, any cascading of taxes through the economy s production structure. For import duties, we usually assume that all prices, including those for domestically produced goods of the same type, rise in proportion to the duty rate. Again, this is true in the simple case where markets Tool Kit Chapter 1 page 1-5

6 are competitive and the country is small. Although in this case we should note that some of the benefits of the tax go to domestic producers rather than the government. 4 In addition to deciding whose purchasing power actually declines when a tax is increased, we also need to calculate how much they lose. In the simplest of cases, where taxes are collected according to the letter of the law, this calculation is straightforward for ad valorem taxes. The tax paid is ust the tax rate times the pre-tax value of expenditures: T i, = t p xi, = ei, 1+ t t (4) where T i, is household i s total loss in purchasing power for a tax on good ; p x i, is household i s pre-tax amount of expenditure on good ; t is the ad valorem tax rate; and e i, is the post-tax amount of expenditure on good. The fact that T i, is proportional to e i,, the expenditure that would be reported in a household survey, is convenient, for reasons that we will come to shortly. Unfortunately, taxes are not paid according to the letter of the law, both because of corruption and because many transactions in developing countries occur in informal markets not subect to the government s tax handles, which are almost always formal sector firms or good passing through the port. In Madagascar, for example, we found that actual VAT collections were about eight percent of formal sector value added in 1995, even though the official VAT rate was 25 percent. And of course, formal sector value added is relatively small in Madagascar. Even if we assume that tax evasion and avoidance occur in such a manner that the result is an equiproportional increase in market prices for all consumers that is something less than the statutory tax rate, we face the practical problem of deciding what tax rate to use in equation (4). Our sense is that the best one can do without expending considerable resources probably is to gather information on tax revenues and tax bases from the authorities and use the ratios as estimates of the effective tax rate for that particular tax. There is one case in which this problem can be avoided. If we assume that a tax s incidence is proportional to expenditures, whatever the proportion, for all households, then we can simply use observed expenditures in equation (4), because the proportion cancels out of the numerator and denominator. This will only work, however, for one tax rate. Any attempt to combine two or more items with different tax rates will require that we make the calculation of taxes paid. 4 We are not aware of an analysis that tries to calculate this aspect of an import duty s incidence across households Tool Kit Chapter 1 page 1-6

7 1.3. Examples of application There is an emerging body of literature examining household tax incidence in developing countries that follows the framework presented above. Most recently, using data on expenditures from the 1992 Integrated Household Survey, Chen et al (2001) conduct a welfare dominance analysis of tax incidence in Uganda. They find that the tax structure was progressive before reforms, and remained so after reforms. This indicates that the burden of tax reforms has not fallen disproportionately on the poor. Most individual tax categories were also progressive before reforms, with the exception of the excise tax on paraffin (kerosene), which is heavily consumed by poor households. Export taxes on coffee, one of Uganda s main exports, remained highly regressive, as the burden of the tax is shifted to relatively poorer rural farmers. Petroleum taxes (except paraffin) remained progressive. 5 The study concludes that reducing export taxes on coffee and taxes on paraffin will benefit the poor. Other tax reforms implemented in the 1990s were generally pro-poor. The pay-as-you-earn tax remains the most progressive tax, as it applied to the formal sector where the non-poor are employed. The study also finds that substituting value-added taxes for sales taxes does not necessarily worsen the welfare of the poor, since most goods consumed by the poor were zero-rated. A similar study by Younger et al (1999) examines household tax incidence in Madagascar. The study finds that most taxes are progressive, with the exception of kerosene taxes and export duties on vanilla. It proposes that a movement away from trade taxes and towards broadly-based value-added or income taxes would be both more equitable and efficient, since these would apply to the formal sector where the non-poor are employed. It also concludes that taxes on petroleum products (except kerosene, which is used heavily by the poor) are highly progressive and also provide a good tax handle for the government. Thus, it proposes concentration of duties on gasoline and reduction of duties on kerosene. Similar to the finding on export duties on coffee in Uganda, this study also finds that export duties on vanilla are more regressive than may other taxes, since the burden is passed on to vanilla producers who are rural farmers and not as wealthy as the population in general. Thus, it concludes that a movement away from export duties will have a positive distributional impact. Using data from the 1988 Ghana Living Standards Survey, Younger (1993) presents a tax incidence analysis from Ghana. Its findings are similar to those from the studies conducted in Uganda and Madagascar -- that broad-based taxes are either proportional (sales taxes) or progressive (income and property taxes), and that a greater reliance on broad-based taxes will 5 Taking into account the intermediate effects of petroleum tax diminished the progressivity of this result. Tool Kit Chapter 1 page 1-7

8 improve both equity and efficiency. Petroleum taxes are proportional or slightly progressive, even after taking into account the intermediate effects (such as on the cost of the public transit sector). However, the tax on kerosene, used heavily by poorer households, is regressive. As in the above-mentioned cases, this study also finds that the export duty on cocoa in Ghana is regressive and places an undue burden on rural farmers, and should be reduced to address equity considerations. In the context of ongoing tax-reforms in Papua New Guinea, Gibson (1998) discusses the impact of introducing VAT on consumer welfare. The paper uses a variant of the proposed technique, where the distributional characteristic of each good is defined as a measure of how heavily its consumption is concentrated among the poor. 6 Gibson argues that instead of removing existing distortions by virtue of being a uniform consumption tax, VAT will introduce new distortions through the proposed merit good exemptions: on financial services, health and educational services and public road transport. Using data from the 1996 Papua New Guinea Household Survey, Gibson also finds that the proposed exemptions rank lower than other items whose consumption is concentrated among the poor, including axes, bush-knives, and garden tools; school fees and children s clothing; pots and pans; salt, rice and tinned fish. He proposes that exemptions on rice and tinned fish fulfill both merit-good and poverty alleviation obectives and may be better candidates for VAT exemptions. Using data from the 1993 Living Standards and Development Survey for South-Africa, Alderman and del Ninno (1999) employ a similar methodology to assess how well VAT exemptions have been targeted and also rank commodities in terms of tax efficiency and equity, as well as the impact of exemptions on household food consumption. They estimate the ratio of the welfare cost to the revenue benefit, which gives a cost-benefit ratio to assess commodityspecific exemptions. 7 A ratio larger than one indicates that the welfare cost is greater relative to the revenue generated, which indicates that the commodity is a good candidate for tax exemption. They find that maize, which is currently exempted from VAT, is the best choice for low tax rates from the standpoints of equity, efficiency and the impact on the nutritional intake of the poor. In contrast, they find that lower tax rates on fluid milk, which is currently exempted from VAT, and meat, for which an exemption has been proposed, are not good instruments for 6 The welfare effect of a marginal price change is given by the weighted sum of each household s consumption of the taxed good(s). The weights reflect the social marginal value of consumption by each household, with higher weights given to consumption by the poor. 7 The welfare cost is based on the change in the unit cost of the commodity multiplied by a welfare weight (with more weight being put on the cost to poorer consumers) aggregated across all households. The revenue benefit is based on the change in revenue from the new tax, aggregated across all goods and all households. Tool Kit Chapter 1 page 1-8

9 achieving equity or nutritional obectives. They also find that tax exemptions for beans, sugar and kerosene have favorable rankings from the viewpoint of equity. Ahmad and Stern conducted much of the pioneering work on tax incidence during the 1980s for India and Pakistan. Using data, Ahmad and Stern (1984) show that taxes on cereals, fuel, and light are less socially desirable relative to a tax on clothing for social welfare functions that are averse to inequality. In one exercise, they show that raising the tax on cereals by one rupee and lowering the tax on sugar and gur by one rupee maximizes revenue, while holding the welfare of all households constant. In another, they show that holding revenues constant, reducing the tax on cereals and increasing the tax on sugar increases the welfare of the poorest rural household. In a later study on India, Ahmad and Stern (1987) examine the effect of replacing a number of direct and indirect taxes on consumption by a simple proportional value-added tax (VAT). Using data from , the authors find that switching to a VAT would be equivalent to reducing the real expenditures of the poorest rural households by as much as 6.8 percent and increasing those of the richest rural households by more than 3 percent. Similarly, the real expenditures of the poorest urban households are reduced by about 4.8 percent while those of the richest are increased by 4.2 percent. This indicates that the welfare of the poor would be reduced if a proportional VAT replaced existing indirect consumption taxes. Ahmad and Stern (1987, 1991) also use a marginal analysis to compare the distributional impact of taxes on income with that on commodities. 8 At higher levels of inequality aversion they find that an extra unit of revenue from a tax on income becomes socially much more desirable than from a tax on cereals. In addition, the authors conclude that at higher levels of inequality aversion, import duties are the most attractive form of indirect tax revenue. Ahmad and Stern (1990) conduct a similar study on marginal tax reform in Pakistan. First, under the assumption that shadow prices 9 are proportional to producer prices, the authors show that at higher levels of inequality aversion, wheat and pulses 10 are not desirable candidates for sources for additional tax revenue whereas housing, fuel and light are. After relaxing the assumption that shadow prices are proportional to producer prices, the authors similarly find that goods such as wheat and pulses are not desirable candidates for additional tax revenue at high levels of inequality aversion. However, for goods with high shadow prices, their desirability as candidates for taxation changes when shadow prices are incorporated. For 8 The commodities chosen for taxation are those with low demand elasticities. 9 A shadow price <concept needs to be explained > 10 These goods form a large proportion of poor households budgets. Tool Kit Chapter 1 page 1-9

10 example, rice becomes a relatively more attractive candidate for taxation than in the case where shadow prices were not taken into consideration. The reason for this, as the authors explain, is that rice has a high shadow price relative to the market price (since it is an exportable) which implies that the government should discourage domestic consumption of this valuable commodity by taxing it. In conclusion, the authors say that a good whose consumption is concentrated among the poor, that has a low shadow price and is less responsive in terms of revenue increase, is a less desirable commodity for a tax increase, holding other things constant. Ahmad and Stern (1991) also discuss the use of introducing VAT in Pakistan for addressing distributional and revenue concerns. They state the inappropriateness of a singlerate VAT for developing countries, since a number of agricultural sectors cannot be covered under a uniform VAT. The authors discuss the introduction of a tiered-vat system with zero rating for exports, exemptions for the agricultural sector, a standard rate of 10 percent and a luxury rate of 20 percent, together with excises. Such a VAT could be revenue-neutral while having a progressive impact on income distribution General Evaluation and "operational" hints The great advantage of the method discussed here is its simplicity. With a standard household survey, an analyst who is familiar with the tax system and market structure of a country can usually obtain a sensible estimate of a tax s incidence in a few hours. The requisite programming skills are minimal, and there is a convenient software package, DAD 11 that calculates concentration curves and other summary measures of incidence easily, with standard errors. The simplicity of the results group k pays x percent of tax (change) is also attractive to a broad public interested in economic policy. Even those who find most economic analysis incomprehensible (or nonsensical) can easily understand the meaning and the relevance of this type of result. Of course, simplicity often comes with inaccuracy. There are several potential sources of inaccuracy in these methods. First, because the methods do not take into account behavioral responses to a tax change, they provide only a first-order approximation of a tax s true incidence. As such, they are more appropriate for the analysis of marginal changes what happens if we raise the VAT from 15 to 16%? than for large policy changes what happens if we eliminate 11 <where can it be obtained, what DAD does stand for? Tool Kit Chapter 1 page 1-10

11 import duties and substitute a VAT? We are not aware of a literature that tries to calibrate how inaccurate these methods might be in analyzing the incidence of large tax changes in developing countries, although Banks, Blundell, and Lewbel (1996) found that first-order approximations of a change in the United Kingdom s VAT from zero to 17.5 percent (the actual rate) were inaccurate. A second source of inaccuracy in these methods is the use of simple assumptions about how statutory taxes translate into economic incidence. Almost uniformly, markets are assumed to be competitive so that buyers bear the burden of all consumption taxes. More egregiously, questions of tax avoidance via informal markets or corruption are mostly ignored, even though the ratio of actual taxation to expenditures is often a small fraction of what the statutory rates suggests should be collected. Unfortunately, to address these limitations requires considerably more complex analysis of the behavior of both consumers and producers in the relevant markets. (see Chapter 12 on multi-markets). It also complicates the analysis of taxes which ostensibly have the same tax rate. If evasion differs across product, then even estimation of a uniform VAT faces the problems of aggregation across commodities with different effective tax rates that we discuss in Box 1. A third source of inaccuracy comes from the fact that many indirect taxes, even those like the VAT that are intended to fall only on final sales, are effectively levied on intermediate goods. In these cases, even with the simplifying assumptions of competitive markets, one must take into account the nature of production in the economy to understand the incidence of the tax for consumers. While it is possible to approximate this using only an input-output table (Raemison and Younger, 2000), most analyses use a computable general equilibrium model with the consequent increase in complexity and cost this issue is handled in detail in chapter 13 and 15 of this volume. An obvious recommendation, then, is that the methods are better applied to taxes whose burden clearly falls directly on consumers, advice that excludes taxes such as excise duties on petroleum products and import duties on production inputs that are important in developing countries. Given the uncertainty about effective tax rates in developing countries, another recommendation is that these methods are more likely to be accurate when considering taxes on individual goods, or on sets of goods where effective tax rates are likely to be similar. This is because, in these cases, we do not actually need to know the tax rate, ust that it is proportional to expenditures. We can then carry out most analyses using only the household expenditure information. Tool Kit Chapter 1 page 1-11

12 Finally, we reiterate our caution from the introduction: these methods are about equity, but tax policy analysis must also consider both economic and administrative efficiency. It must be clear in particular that if demand responses may be ignored as a fist approximation when evaluating the welfare effects of a change in indirect taxation, this is not the case for total tax receipts. Examining the impact of such a change on the budget of the government thus requires going beyond that approximation or possibly using some aggregate model of demand References Ahmad, Ehtisham and Nicholas Stern (1984). The theory of reform and Indian indirect taxes. Journal of Public Economics 25(3): Ahmad, Ehtisham and Nicholas Stern (1987). Alternative sources of government revenue: Illustrations from India, In Newbery, David and Nicholas Stern, eds. The Theory of Taxation for Developing Countries. Oxford: Oxford University Press. Ahmad, Ehtisham and Nicholas Stern (1990). Oxford Economic Papers 42(1): Tax reform and shadow prices for Pakistan. Ahmad, Ehtisham and Nicholas Stern (1991). The Theory and Practice of Tax Reform in Developing Countries. Cambridge: Cambridge University Press. Alderman, Harold and Carlo del Ninno (1999). Poverty issues for zero rating VAT in South Africa. Journal of African Economies 8(2): Banks, James, Richard Blundell, and Arthur Lewbel, 1996, "Tax Reform and Welfare Measurement: Do We Need Demand System Estimates?" The Economic Journal, v.106, pp Bourguignon, Francis, Luiz A. Pereira da Silva and Nicholas Stern (2002). Evaluating the Poverty Impact of Economic Policies: Some Analytical Challenges. Mimeo, World Bank. Chen, Duanie, John Matovu and Ritva Reinikka (2001). A quest for revenue and tax incidence. In Ritva Reinikka and Paul Collier, eds., Uganda s Recovery: The Role of Farms, Firms and Government. Washington, DC: World Bank. Chu, Ke-young, Hamid Davoodi and Saneev Gupta (2000). Income Distribution and Tax and Government Social Spending Policies in Developing Countries. International Monetary Fund Policy Working Paper: WP/oo/62. Washington, DC: International Monetary Fund. Davidson, Russell, and Jean-Yves Duclos, 1997, " Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, v.65, pp Foster, James E.; Shorrocks, Anthony F., 1988, Poverty Orderings, Econometrica 56, pp Gibson, John (1998). Indirect tax reform and the poor in Papua New Guinea. Pacific Economic Bulletin 13(2): Tool Kit Chapter 1 page 1-12

13 Grosh, Margaret; Glewwe, Paul, eds., 2000, Designing household survey questionnaires for developing countries: Lessons from fifteen years of the Living Standards Measurement Study. Washington, D.C.: World Bank. Lambert, Peter, 1993, The Distribution and Redistribution of Income: 2 nd Edition, Manchester University Press. A Mathematical Analysis, Newbery, David and Nicholas Stern (1987). Oxford: Oxford University Press. The Theory of Taxation for Developing Countries. Pearce, David W., 1986, The MIT Dictionary of Modern Economics, 3 rd edition, Cambridge, MA: The MIT Press. Raemison, Harivelo and Younger, Stephen D., 2000, Indirect Tax Incidence in Madagascar: Estimations Using the Input-Output Table, CFNPP working paper #106. Saposnik, Rubin, 1981, "Rank-Dominance in Income Distributions," Public Choice, 36, pp Shoven, John B. and John Whalley (1984). Applied General Equilibrium models of taxation and international trade: An introduction and survey. Journal of Economic Literature 22(3): Slack, Enid and Richard M. Bird (2002). Land and Property Taxation. Mimeo, World Bank. Shorrocks, Anthony F., 1983, Ranking Income Distributions, Economica, 50, pp Yitzhaki, Shlomo, and Slemrod, Joel, 1991, " Welfare dominance: taxation," American Economic Review, 81, pp An application to commodity Younger, Stephen D., Sahn, David E., Haggblade, Steven, and Dorosh, Paul A., 1999, Tax Incidence in Madagascar: An Analysis Using Household Data, World Bank Economic Review, 13, pp Younger, Stephen (1993). Estimating Tax Incidence in Ghana: An Exercise using Household Data. Cornell Food and Nutrition Policy Program Working Paper 48. Tool Kit Chapter 1 page 1-13

14 Figure Compensating variation for an ad valorem tax on good i P i P i 1 A B C P i 0 E D X ic (P,u 0 ) X i 0 <Box 1.1 missing > Tool Kit Chapter 1 page 1-14