Back Matter

Back Matter

Liam Ebrill, Michael Keen, and Victoria Perry
Published Date:
November 2001
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    Appendix I Data

    This appendix describes the nature and sources of the data used in the background chapter and in the regression analysis. Except where indicated, the analysis is based on the data available in early 2000.

    Aggregate Revenue Variables

    • General government total revenue and grants (GGTRG). This comes from the IMF’s World Economic Outlook (WEO), and is available for almost all countries. This is intended to include all levels of government, nontax revenues and grants (meaning aid). WEO does not have a breakdown of GGTRG into these various components.
    • General (GTX) and central (CTX) government tax revenue. These are collected from Recent Economic Developments (REDs) papers prepared by IMF staff, which typically report one or the other. The most recent data for each country were available from 1994–97 by calendar year and 1995/96–1996/97 by fiscal year. There is also variation in presenting data: 87 percent are by calendar year and 13 percent by fiscal year. (The countries in the latter category are: Bangladesh, Belize, Egypt, Indonesia, Jamaica, Kenya, Malawi, New Zealand, Pakistan, Samoa, South Africa, Tanzania, Thailand; and Uganda). The percentage of countries with data in each year are: 1994: 2 percent, 1995: 20 percent, 1995/96: 2 percent, 1996/97: 10 percent, and 1997: 15 percent.

    The RED fiscal data are based on information supplied by country authorities and Fund staff estimates. Reporting practices vary across countries: (for example, about 47 percent of the countries report central government and 53 percent of the countries report general government (including lower levels)).

    The definition of “tax” should follow that of Government Financial Statistics (GFS) and also include social security, though in practice this may be omitted in some cases.

    There are three definitions of fiscal years in this report, depending on the country: April 1 to March 31; July 1 to June 30; and October 1 to September 30. The data for trade, value of imports of goods, value of exports of goods, GDP per capita, population, and private consumption are presented in calendar years. To make these data consistent with the revenue data for the countries stated above, the fiscal year was constructed by averaging pieces of two calendar years. For example, if the fiscal year runs from April 1 to March 31, then the observation year is the year corresponding to April to December (75 percent of 1995) and from January to March (25 percent of 1996).

    VAT Variables


    Taken from Recent Economic Developments (REDs). Data are again for the most recent period. The definition is as for the GFS category “general sales, turnover, or VAT.” In some cases, countries that replaced a turnover tax with a VAT may continue to receive some lagged revenue from the former—this may therefore include taxes other than VAT. Information on VAT revenues has in some cases been corrected, on the basis of information provided by staff, to ensure that it includes all VAT collected on imports.


    The VAT rates have been taken mainly from internal IMF sources. The variable SR in the regressions is the standard rate, in percent. The rates used in the econometric work were for the most part those effective as of August 1998. The variable RANGE is the difference between highest and lowest nonzero VAT rate, in percentage point.


    Various sources, including FAD technical assistance reports and tax guides. The variable THRESH used in the regressions of Chapter 4 is the threshold for traders in goods, measured in US$10,000 (converted at the nominal exchange rate).


    This is taken from Cnossen (1998). The variable GS takes the value unity if coverage is broadly all goods and services, zero otherwise.


    This is also taken from Cnossen (1998). The variable RETAIL takes the value unity if the VAT extends to the retail stage, zero otherwise.


    Import and export values have been taken from the WEO. The value of foreign trade is derived from corresponding balance of payments values unless otherwise specified by desk economists. WEO data are for the same period as the fiscal data. In addition, for calculation purposes, GDP data are obtained from the same source (WEO).

    Gross domestic product (GDP) Data are directly from the same source as the revenues for most of the countries, which is the Recent Economic Developments (REDs). However, OECD Revenue Statistics, WEO, and unpublished IMF sources have been used when data are not available. Data are for the latest available year.

    Illiteracy rates have been taken from The World Bank database and from various miscellaneous sources. ILLRATE is the percentage of people over 15 years old who are illiterate. These data were not readily available for consecutive years for each country, so data for the latest available year was used.

    Agricultural output data are from the World Bank database. Data are for the latest available year and cover the same period as for tax revenues. The variable AGR is agricultural output relative to GDP, in percent.

    Population (POP) has been obtained mainly from the World Economic Outlook (WEO) for the same period as the fiscal data.

    Regional groupings used are shown in Table AI.1.

    Table AI.1.Country and State Groups
    European Union (EU)1Americas (AS)Sub-Saharan Africa (AF)Central Europe and BRO (CBRO)
















    United Kingdom







    Costa Rica

    Dominican Republic


    El Salvador












    Trinidad and Tobago

    United States





    Burkina Faso



    Central African Republic


    Congo, Rep. of

    Congo, Dem. Rep. of

    Côte d’Ivoire

    Equatorial Guinea




    Gambia, The


















    Sierra Leone


    South Africa











    Bosnia and Herzegovina



    Czech Republic








    Macedonia, former Yugoslavia Rep. of





    Slovak Republic





    Source: IMF, staff classification.

    Plus Norway and Switzerland.

    Island economies of under 1 million, plus San Marino.

    North Africa and Middle East (NMED)Asia and Pacific (AP)Small Islands (SI)2
    Afghanistan, Islamic State of





    Iran, Islamic Rep. of










    Saudi Arabia

    Syrian Arab Republic



    United Arab Emirates




    Brunei, Darussalam







    Lao People’s Dem. Republic





    New Zealand


    Papua New Guinea



    Sri Lanka

    Taiwan Province of China


    Antigua and Barbuda

    Bahamas, The


    Cape Verde










    Marshall Islands


    Netherlands Antilles



    San Marino

    Sâo Tomé and Príncipe


    Solomon Island

    St. Kitts and St. Nevis

    St. Lucia

    St. Vincent and the Grenadines


    Source: IMF, staff classification.

    Plus Norway and Switzerland.

    Island economies of under 1 million, plus San Marino.

    Source: IMF, staff classification.

    Plus Norway and Switzerland.

    Island economies of under 1 million, plus San Marino.

    Appendix II Effective Rates of VAT

    There are two quite distinct concepts and measures of the “effective rate of VAT” to be found in discussions of VAT policy. This appendix discusses these concepts and the relationship between them.

    As a common framework, consider a closed economy of N commodities. Denote by ti the ad valorem tax rate on commodity i, by pi the net price and by qi the tax-exclusive price paid by buyers: thus qi = pi(1 + ti). It will also prove useful to denote by δt the proportion of input tax that is recoverable in the production of commodity i. Thus commodity i is exempt if and only if ti = δt = 0.

    Denoting by A the matrix whose typical element aik is the input of commodity k required per unit of output of commodity i, net output x ≡ (xi) is related to gross output as

    where IN is the N-dimensional identity matrix, and a prime indicates transposition. As a final preliminary, note that since tax revenue is raised on all gross sales y but credited to the extent that intermediate purchases Aʹ.y are to nonexempt sectors, the total tax revenue collected is

    where Δ = diag {δ1…, δn} and P = diag{p1,…, pN}.

    Input-Choice Distortion: The Type-I Effective VAT Rate

    A key attraction of the VAT is that it leaves firms’ input choices unaffected, so long as all input taxes are effectively recovered. And it is a central disadvantage of exemption that it undoes this effect and so potentially distorts production decisions. Moreover, and as emphasized in Chapter 8, this distortion arises not only in the input choices made by the exempt sector itself but also in the input choices of downstream sectors which use the output of the exempt sector as an input: for that exemption can be expected to lead to a tax-induced increase in input prices faced downstream.

    One concept of the effective rate of VAT—discussed and applied, for instance, by Gottfried and Wiegard (1991)—seeks to describe this potentially complex pattern of distortion. This concept of the effective VAT rate on a commodity i—which we refer to as the “type-I” effective rate—is defined to be the difference between its tax-inclusive selling price, qi, and the price at which it would sell if VAT were removed and factor prices remained unchanged.

    To calculate this, note first that, as a matter of definition

    where vi denotes the per unit value added in the production of i, defined as the difference between the net selling price (pi = qi- tipi) and the tax cost of material inputs (each unit of input k costing qk if good i is exempt (so that δi = 0) and qk - tkpk if it is not exempt (δi=1). Writing (II.3) in vector form and solving gives:

    At unchanged factor prices and input usage, selling prices in the absence of tax would thus be (IN - A)-1v. Type I effective tax rates—expressed (like the statutory rates) tax-exclusive relative to prices pi—are consequently:

    If there are no exemptions, so that Δ = IN, the type-I effective rate on each commodity k is thus precisely the statutory rate applied to sales of k. Exempting any commodity k, however, potentially distorts the effective tax rate on any other commodity j away from the statutory rate tj. So long as all tax rates are positive moreover, the direction of the effect is clear: the type-I effective rate on any commodity is always at least as large as the statutory rate,1 reflected in the increased input costs associated with exemption.

    Note too, combining (II.2) and (II.5), that revenue raised by the VAT can be written as

    In revenue terms, the outcome is thus equivalent to taxing all final sales at the type-I effective rate.

    Self-Supply: The Type-S Effective Rate

    A quite different definition of the effective VAT rate on commodity I is that developed and applied by Kay and Warren (1980) and Hemming and Kay (1981). Referred to here as the “type-S” effective rate of VAT, this is the net tax paid per unit of good i (output tax less input tax recovered) as a proportion of the value added in its production:

    This concept takes account only of VAT levied directly in relation to sector i. It is best thought of as indicating the strength of the incentive that an exempt person—most obviously, the final consumer, though the logic applies to exempt persons more generally—has to supply himself/herself with i rather than purchasing it directly: such self-supply avoids the need to pay output tax at ti but also removes the possibility of recovering input tax.

    The type-S effective rate on commodity i may be above or below the statutory rate.2 It coincides with the statutory rate if i is taxable and all inputs and outputs are all taxed at the same rate: for value added in producing i is then taxed at precisely the statutory rate, and it is this rate that therefore indicates the incentive that an exempt person has to self-supply.3 If, on the other hand, the production of i is taxable and output is taxed at a rate above the weighted average rate on inputs in the sense that4

    where wikaikpik / Σjaijpij, then the type-S effective rate exceeds the statutory rate. That is, the statutory rate understates the incentive to self-supply. For highly taxed outputs produced from lightly taxed inputs—the archetypal example being restaurant meals produced from zero-rated food—the type-S effective rate is higher than the statutory rate. Similar arguments would apply, for example, to home repair items, personal services and the like.

    For an exempt commodity, the type-S effective rate is zero: there is neither advantage nor disadvantage in producing i for oneself rather than buying it, since the seller would also be exempt.

    Note that in vector form (II.7) becomes

    where S is the diagonal matrix with kkth element pk - Σjakjpk. Comparing this with (II.2) gives

    so that, in revenue terms, the situation is as it would be if the type-S effective tax rate were charged on the value added associated with each gross sale.

    Relating the Two Effective Rates

    While the definitions of both effective rates are purely mechanical, with no behavioral content, the underlying rationale is in each case to derive some sense of how the VAT is likely to affect resource allocation. The two measures correspond to different dimensions of possible distortion.

    These dimensions are related: self-supply mitigates the distortion of input choices by eliminating the unrecovered output tax that would otherwise be borne on the exempted input. The two concepts are also related in a more formal sense. Comparing (II.5) with (II.9) gives:

    The two sets of effective rates thus coincide if either is uniform over commodities.5 It is sufficient for this that there be no exemptions and that statutory rates be uniform across commodities. In general, however, the two will evidently differ.

    Note too that, interpreted as guides to resource allocation effects, both measures are very partial ones. The type-I effective rate, for instance, rests on an assumption that factor prices are unaffected by the presence of the tax, which is thus shifted entirely to consumers.

    Appendix III Sources of Gain in Replacing Tariffs by a Consumption Tax

    Consider a small open economy inhabited by a representative individual whose preferences are characterized by an expenditure function E(q,g,u) defined over consumer prices q, public expenditure g and utility u. Suppose further that E(q,g,u) = e(q,u) -δg, where δ > 1 is the marginal social value of public funds. The production side is characterized by a revenue function r(p) defined on producer prices p. World prices are ρ.

    We compare two regimes. In one (indicated by superscript τ), only tariffs are levied, so that

    In the other, indicated by superscript c, only destination-based consumption taxes are levied, so that

    In either case, the national income-expenditure identity requires that

    It is also convenient to denote by

    the deadweight loss (defined as in Kay (1980)) from the distortion of consumer prices away from world prices under regime i.

    Adding and subtracting gτ+e(ρ, uτ) in (III.3) (evaluated for the tariff regime) one finds, on using (III.1) and rearranging, that

    Proceeding similarly for the consumption tax regime, adding and subtracting gc+e(ρ, uc), one finds

    Adding (III.5) and (III.6), rearrangement gives

    showing the welfare gain from moving to the consumption tax to consist of the three terms discussed in Chapter 16: the revenue effect, valued at the excess of the marginal social value of revenue over unity; the reduction in deadweight loss from distorted consumption decisions; and improvement in production efficiency (nonnegative by convexity of the revenue function).


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    The Authors

    Liam Ebrill is Assistant Director in the Policy Development and Review Department of the IMF. He was previously an Assistant Director in the Fiscal Affairs Department, where he served as head of the Tax Policy Division with his responsibilities including leading tax policy technical assistance missions and research in applied public economics. His previous positions in the IMF included both industrial country macroeconomic surveillance and economic program negotiations and monitoring. Prior to joining the IMF, Mr. Ebrill was an Associate Professor in the Department of Economics at Cornell University where his research was focused on tax policy issues. He received his PhD from Harvard University and his BA and MA (Economics) from University College, Dublin.

    Michael Keen is an Advisor in the Fiscal Affairs Department of the IMF, having been Professor of Economics at the University of Essex. He has published widely on the theory and practice of public finance, and is currently Executive Vice-President of the International Institute of Public Finance and Chair of the International Seminar in Public Economics. Founding co-editor of International Tax and Public Finance, he is also on the editorial boards of the Journal of Public Economics, Fiscal Studies, the Economics of Governance and the German Economic Review. He is a fellow of the Centre for Economic Policy Research, CESifo, and the Institute for Fiscal Studies, and has been a consultant for the European Commission, House of Lords, World Bank, and the private sector.

    Jean-Paul Bodin is Deputy Chief of the Revenue Administration Division of the IMF Fiscal Affairs Department. Since he joined the IMF in July 1991, he has been involved in numerous technical assistance missions in a broad range of countries, including a number of missions to support the preparations for, or to improve the operations of, a VAT. He is a former senior official of the French Ministry of Finance, Direction générale des impôts (DGI). Mr. Bodin was Assistant Director of the Tax Audit and Investigation Department of the DGI before joining the IMF, where he supervised the tax fraud investigation program. Prior to that, he had significant experience in the operations of the French tax system, including collection and enforcement activities. Mr. Bodin holds an advanced degree in law from the University of Rennes. He graduated from the French National Tax School in 1971.

    Victoria Summers is Deputy Chief of the Tax Policy Division of the IMF Fiscal Affairs Department. Prior to joining the IMF, she was the Deputy Director of the Harvard International Tax Program, where she taught comparative income taxation and value-added taxation. She previously practiced tax law with the Boston firm of Hale and Dorr. Ms. Summers has served as Chair of the VAT Committee of the American Bar Association Section of Taxation, and was a member of the Section of Taxation’s special task force on U.S. tax reform. She received her J.D. from the Harvard Law School and her B.A. from Yale University, in economics.

    Reviews of The Modern VAT

    “Despite the dramatic recent spread of the VAT, the literature on value-added taxation is very scarce. The authors of this book fill this gap in a most admirable manner. Drawing on the vast experience accumulated by the Fiscal Affairs Department of the IMF, they discuss matters of principle as well as all of the practical issues associated with implementing a VAT, covering both developing and developed countries. The book will be a standard reference on VAT for years to come and a most valuable source of information for practitioners and academics working in the area of Public Finance.”

    Professor Peter Birch Sørensen

    Director of Economic Policy Research Unit

    University of Copenhagen

    “Every once in a long while, an institutional innovation comes along that conquers the fiscal world. The value-added tax is such an innovation. Over the last few decades, VATs have been put into place all around the world. Those countries that do not yet have one seem usually to be considering adopting one soon. The IMF’s Fiscal Affairs Department has played an important role in assisting many developing and transitional countries to enter the brave new world of VAT. In the course of doing so, of course, FAD’s experts have learned a great deal about the design and administration of VATs. Much of this knowledge is on offer in this book, which thus updates and complements several valuable earlier IMF publications on the subject. In addition, however, and most intriguingly, this book also raises some very interesting questions about a number of aspects of VAT about which there is, it appears, still more to learn. It should be on the shelves not only of all those involved in VAT administration but also of those interested in tax policy and administration more generally.”

    Professor Richard M. Bird

    Rotman School of Management

    University of Toronto

    Value-Added Tax or VAT, first introduced less than 50 years ago, is now a pivotal component of tax systems around the world. The rapid and seemingly irresistible rise of the VAT is probably the most important tax development of the latter twentieth century, and certainly the most breathtaking. Written by a team of experts from the International Monetary Fund, this book examines the remarkable spread and current reach of the innovative tax, and draws lessons about the design and implementation of the VAT as experienced by different countries around the world. How efficient is it as a tax, is it fair, and is it suitable for all countries are among the questions raised in this highly informative and well-researched book that also looks at the likely future of the tax.

    “This book will be a standard reference on VAT for years to come and a most valuable source of information for practitioners and academics working in the area of public finance,” says Professor Peter Birch Sørensen, Director of Economic Policy Research Unit, University of Copenhagen.

    “Every once in a long while, an institutional innovation comes along that conquers the fiscal world. The value-added tax is such an innovation. The IMF’s Fiscal Affairs Department has played an important role in assisting many developing and transitional countries to enter the brave new world of VAT. In the course of doing so, of course, its experts have learned a great deal about the design and administration of VATs. Much of this knowledge is on offer in this book, which thus updates and complements several valuable earlier IMF publications on the subject,” says Professor Richard M. Bird of the University of Toronto.


    The Fiscal Affairs Department has as one of its main functions the provision of technical advice in taxation and government expenditure matters to IMF member countries.


    Here and below, “tax revenue” includes compulsory social contributions.


    The Baltic countries, Russia, and other countries of the former Soviet Union.


    Bangladesh affords an example of the former, Pakistan an example of the latter.


    Malawi is a striking example. It was deemed by the Fiscal Affairs Department (FAD) of the IMF to have a VAT by 1994, though the tax did not extend to the retail stage. The adoption of a VAT—meaning extension to the retail stage—was then part of IMF program conditionality in 1996. In addition, many countries choose to call by some other name—a general sales tax, or a goods and services tax—what is clearly a VAT. The label chosen is of no importance for this report.


    Since a turnover tax is levied on turnover irrespective of value added, the tax collected on a given good will reflect the number of taxable stages in its chain of production. See the discussion of “cascading” in Chapter 2.


    Instances of limited crediting of taxes on inputs date back to at least the 1930s. Sullivan (1965) describes such arrangements in Greece (1933), Argentina (from 1935), and the Philippines (1939); but crediting was in the first case limited by sector, and seems under the latter two to have been limited to items physically incorporated into output.


    Sources differ: Shoup (1973, p. 15) places introduction in 1966; Tait (1988) sees it as a process beginning in 1960.


    Then called the Business Activities tax.


    Shoup (1973) cites this as the first consumption-type VAT; it is not clear why he does not so regard the 1954 French VAT.


    Södersten (1999) provides an account of the introduction of the VAT in Europe.


    The 183 members of the IMF, Netherlands Antilles, and Taiwan Province of China.


    The category “other” is of course especially diverse: the high average per capita GDP reflects the adoption of the VAT during the 1990s by a few developed countries, including Canada and Switzerland, while the large average population reflects its adoption by China.


    State-level VATs are, however, scheduled for introduction in India in April, 2002. How these difficulties will be dealt with remains unclear.


    The data in Table 1.3 relate variously to central or general government tax revenue, depending on data available, and include social charges.


    Based on data available in the summer of 1999.


    India’s Maharashtra state removed a state-level VAT.


    Venezuela renamed and reformed its VAT structure in 1994, but on the definition above the tax remained a VAT throughout.


    The absence of any tax on intermediates does not, however, guarantee production efficiency. For instance, imperfect competition can result in firms facing different marginal costs in equilibrium, which would imply a production inefficiency.


    To see the difference between production inefficiency and cascading, assume that there are no substitution possibilities between inputs. Then an input tax gives rise to no production inefficiency; but there will be cascading if output is also taxed. Conversely, an input tax may give rise to a production inefficiency even if there is no taxation of output and, consequently, no cascading.


    The Times, January 16, 2000.


    See Shoup (1973, 1990) for a more complete treatment.


    The discussion here draws especially on Cnossen (1993), McLure (1987), Mintz (1995), Old-man and Schenk (1995), and Summers and Sunley (1995).


    The Philippines used the subtraction method before switching to invoice crediting (McLure, 1987). Vietnam uses the subtraction method for individual entrepreneurs.


    Summers and Sunley (1995), Bird (1995). FAD has strongly recommended against the subtraction/gross margin method; among other things, being difficult to administer, it facilitates evasion.


    As described in Kenyon (1996), the Michigan variant is a consumption-type VAT (capital expenditures being deductible in arriving at the definition of profits used in the addition), whereas that in New Hampshire is of the income type.


    Oldman and Schenk (p. 74, 1995) see this as an advantage for the subtraction method, presumably on the grounds that this unsuitability helps amass opposition to rate proliferation.


    Under the subtraction-based VAT in Japan, credit is indeed available in respect of purchases from exempt traders.


    Another natural comparison is with a turnover tax: but here the key merit of the VAT, at least in its pure form, in avoiding cascading and production inefficiency is clear enough. A formal comparison between RST, VAT, turnover tax, and manufacturer level taxes is provided by Das-Gupta and Gang (1996).


    Lent, Casanegra, and Guerard (1973) provide an early recognition of the limits to self-enforcement.


    There have been a few exceptions (Bosnia-Herzegovina, for example has a retail sales tax of 20 percent) but generally in contexts of unusually tight control by the tax authorities.


    For a longer-term perspective, one should compare the revenue performance of the VAT with the broad set of possible alternative taxes to the VAT rather than with just sales taxes. Recall from the discussion of equivalencies in Chapter 2, for example, that a VAT is equivalent to a wage tax combined with a profit tax at the same rate. Once the VAT is in place, the similarity between increasing the rate of VAT and increasing the tax on labor income, in particular, will be evident to taxpayers.


    The extensive empirical literature comparing taxes on income and on consumption (for example, Auerbach and Kotlikoff, 1987) does not address the issue here since the consumption tax considered there need not be a VAT.


    Stockfisch (1985) in a related piece compared the growth of revenues between OECD members who did and did not adopt a VAT between 1964 and 1981. He performs no formal tests, but sees no significant difference in revenue growth performance. However, the hypothesis here concerns the level, rather than the growth of revenues.


    Panel data would be preferable to enable some control for country-specific effects. A time series of VAT revenues, however, is not available for a wide set of countries. Informal accounts of experience over time in some African countries are given in Chapter 5.


    These revenue data relate variously to years between 1994 and 1997; other variables in the regressions reported here and elsewhere in the book are contemporaneous with those revenue data.


    That is, the dependent variable is ln(θ/1-θ), where θ is the ratio of general government revenue and grants to GDP: the logistic transformation is employed to ensure a dependent variable with range (—∞, +∞). This approach is adopted throughout, but the qualitative results prove insensitive to this choice.


    Broadly similar results are obtained if, as in many studies, the ratio of imports to GDP is used instead of OPEN.


    Taking account of the length of time a VAT has been in place did not add insight.


    Multicollinearity problems arise if the replacement is made in Column C.


    Note that the picture that emerges from the regressions is quite different from that implied by the simple averages in Table 1.5. No significant association between the VAT and general tax revenue emerges from the analysis here. The fact that the earlier tabulations point to general tax revenue being higher in countries with a VAT, thus, presumably reflects the tendency for countries with a VAT to be richer, and for richer countries to have higher tax ratios. The reconciliation between the significant effect found in the regressions for general government revenue and grants and the similarity of conditional means between the two sets of countries might be explained in terms of those countries with a VAT tending to rely less on international trade (as also shown in Table 1.5), a disadvantage in terms of raising revenue that counteracts the effect of their greater real income, and which the VAT goes some way to offset.


    Sometimes also referred to as the “productivity ratio.”


    Data on VAT revenues as such are not available. As described in the Appendices, the GFS category “general sales, turnover or VAT” is used; while some of the sample countries may receive some belated revenue from a sales or turnover tax that it replaced, this seems unlikely to be a significant source of bias. More important, the measure may not in all cases include VAT collected on imports, though additional information has been used to correct for this wherever possible.


    We leave aside the question of whether public consumption should be subject to VAT (discussed in Chapter 8). In practice, only data on private consumption are available for a reasonably broad sample; this is used here in calculating the C-efficiency ratios.


    Zee (1995) describes how potential VAT revenue can be estimated from national accounts data, given an assumption on “leakage.” Pellechio and Hill (1996) show that estimation from consumption and production sides of the accounts, while equivalent in principle, can give quite different results in practice.


    More formally, denoting derivatives by subscripts, the distinction is between the direct effect Rα and the indirect effect Rττu.


    These 99 are the “with-VAT” countries of the empirical exercise in the previous chapter.


    Recall that the variable used is somewhat wider than VAT revenue alone.


    Specifically, the trade variable (“OPEN”) appears rather less significant.


    It is also possible that such imperfections in the refunding of input taxes to exporters could bolster revenues in economies with more extensive trade.


    To make the point more formally, assume revenue from the VAT is v(m, β) while revenue from other taxes is r(m, β), where m denotes the significance of trade in the economy and β a vector of policy instruments. Denoting the choice of instruments with and without the VAT by β+ and β-, the finding that revenues increase with the significance of trade corresponds to v(m)≡v(m, β+(m)) being increasing in m. This is consistent with the fact that the gain from adopting a VAT, Δ ≡ v(m, β+(m))+r(m, β+(m))-r(m, β-(m)), decreases with respect to trade so long as the fall in other sources of revenue induced by the policy changes made when adopting the VAT—such as a reduction in trade taxes—increases with respect to trade sufficiently rapidly.


    The effect, moreover, seems to be robustly linear: additional nonlinear terms in age prove insignificant.


    An interesting first-hand account of the accumulation of experience in introducing and operating a VAT is provided by the Chairman of H.M. Customs & Excise in Strachan (1998).


    The detailed survey data described in Chapter 6 are unfortunately no help for this purpose, since sufficient information was only obtained for a very small numbers of countries. In only 15 cases, for example, did the survey indicate whether or not a large taxpayer unit was in place. Attempts were made to correlate residuals from regressions of the kind reported here with more detailed tax information for subsets of countries from the survey, but no useful results were obtained.


    Additional variables used were measures of the variation in rates, the number of rates, and the number of IMF missions related to VAT. None were significant.


    In addition, the negative coefficient of RETAIL is counter-intuitive, as extension to the retail stage implies a wider base and so should imply greater revenues.


    The data reported are for all countries included in the survey exercise described in Chapter 6 for which responses to the relevant question were obtained.


    This simply says, in the jargon of public finance, that the marginal cost of public funds generally exceeds unity.


    The calculation of administration costs depends in addition on such matters as whether the full amount of capital purchases is included or whether there is an allowance for annual amortization; how the costs of tax office accommodations in state-owned buildings should be calculated; how pension funds are handled. And taxpayers’ compliance costs for individual taxes are not easy to separate in the face of common accounting and invoicing obligations.


    It will, though, generally be a matter of opinion whether this reflects an inequitable compliance burden or, to the contrary, the very effectiveness of the VAT in exposing such traders to tax. And again, if small traders are to be subjected to any taxation, they will presumably experience some compliance costs.


    Broadly speaking, the six Anglophone countries examined fall into three groups in terms of the origins of their consumption tax systems: the systems of Kenya and Uganda evolved from the old East African Common Market system, the domestic indirect tax structure of which in turn had been based upon the British system of excise taxes. Malawi, though not one of the three members of the Common Market, had a similar British-based system. Zambia, until the mid-1970s, had relied primarily on abundant revenues from the mineral sector, and had a much less developed domestic tax system. That country adopted a quite limited sales tax after mineral revenues declined sharply. The revenue systems of Swaziland and Lesotho are based around the Southern African Customs Union (SACU) and are intimately tied to South Africa.


    As the name suggests, LTUs are mechanisms that allow the tax administration to focus efforts on the largest entities in the country, where the revenue yield is naturally the greatest.


    Since not all questions were completed for all survey countries, the sample size can vary by question.


    That is, an organization where tax officers are specialized by function (for example, registration, collection, and audit) instead of being specialized by tax.


    A simple regression of the current number of rates, NT, against the number of rates at the time of introduction, NO, the AGE of the VAT and regional dummies gives (with t-ratios in parenthesis):


    This result is related to the inverse elasticity result since, for example, the tax-induced price increase for an elastically demanded commodity will tend to significantly reduce the value of consumer expenditure and so, taking account of the consumer’s budget constraint, will tend to have a particularly depressing effect on the incentive to earn income, aggravating the unavoidable distortion of labor-leisure decision.


    For example, it can be seen from Atkinson and Stiglitz (1980) that it is sufficient for the optimality conditions to be satisfied with two distinct nonzero rates of indirect taxation that preferences be of the form U[F(X0,L)]+A(X1α+X2α,L)+B(X1β+X2β,L), where the sets of goods superscripted by 0, α, and β are disjoint. The solution applies identical nonzero rates to goods that are perfect substitutes for one another.


    Results from such models are limited, not least because they presume forms of preferences that may to some degree prejudge the potential gain from departures from uniformity. Moreover, the conclusions drawn may be sensitive to the precise exercise considered. In Ballard and Shoven (1987), for example, the effects of differentiation in mitigating the impact of the VAT on the poorest decile depend very much on whether the VAT is used to reduce marginal rates of income tax by the same proportion for all taxpayers or by the same absolute amount. In the latter case, differentiation reduces the adverse impact on the poorest by 0.4 percent of the present value of their lifetime income (Table 6.8), which is larger than the mitigating effect on the poorest groups found by Hossain (1995).


    The argument is developed by Sah (1983).


    And of course rate differentiation will do nothing for equity concerns if poorly designed: Liberati (1999), shows that, conversely, a recent reform in Italy involving a reduction in the number of VAT rates in Italy actually improved the distribution of real income.


    In the simplest case, incidence—the extent to which the burden of the tax is split between consumers and producers—depends on relative elasticities of demand and supply. Kotlikoff and Summers (1985) and Boadway and Keen (2000) review the literature on tax incidence.


    The importance of indirect tax effects operating through the sources of income, rather than the uses to which it is put, is emphasized, and analyzed in a CGE model of a developing country, by Bovenberg (1987).


    There may be some very specific exceptions. The sale of a business as a going concern, for example, should in principle be subject to VAT (with a credit for the purchaser); but difference in the timing of the purchase and subsequent credit may create cash flow problems for the purchaser that can be avoided by simply zero-rating such transactions.


    Unfortunately, there are no data allowing a comparable analysis in relation to exemptions, an area in which the effects at issue may be even more important.


    An exemption may be defined either in terms of particular commodities or in terms of particular traders. An example of the latter kind is the exclusion of small traders from the VAT system through use of a threshold below which registration for the VAT is not required. This kind of exemption is discussed separately below.


    Some countries impose an excise on cement.


    This will be so however many taxable stages occur after the exemption: even if the immediate purchaser from the exempt sector sells to a registered trader, who is therefore able to reclaim the increased tax charged by that supplier, the increase in output prices throughout the chain will at some point be reflected in sales to unregistered persons (including final consumers).


    The usage here and below is loose: gains of this sort would typically be shared between supplier and purchaser.


    The gain will be somewhat greater than this, since the exemption of A leads, as a consequence of unrecovered input tax, to an increase in the price B pays for its inputs, the effects of which are multiplied by any tax levied on B’s sales. This consideration also implies that firm B will have some countervailing incentive to lobby against the granting of exemption to its supplier (so long as it expects to remain taxable itself).


    The discussion here focuses mainly on simple loan transactions. Similar issues apply to insurance contracts with a savings component and to other more complex forms of financial intermediation. See also Schenk and Zee (2001).


    Profits for this purpose should in principle be defined on a cash flow basis, with investment immediately expensed.


    Some algebra may be helpful. Denote the amount of the loan by L, the borrowing and lending rates by rB and rL respectively, and the tax rate by τ. Also define λB and λL to take the values 1 and 0 as the borrower (lender, respectively) is registered or not; thus the example in the text has λB = 1 and λL = 0. In the first period of the loan (assumed for simplicity to last only two periods), the net liability of the bank is zero; that of a registered borrower is τL; and a registered lender receives a credit of τL. In period 2, the net liability of the bank is τ(rB-rL)L; a registered borrower is due a credit of τ(1+rB)L, and a registered lender is liable for tax of τ(1+rL)L. Assuming that the government obtains a rate of return p on its net receipts in the first period of λBτL - λLτL, net revenue in period 2 is:

    (1+p)(λB –λL)τL+τ(rB–rL)L–λBτ(1+rB)L+λLτ(1–rL)L = τL[(1–λB)(rB–p)+(1–λL)(p–rL)]

    Thus, tax is ultimately collected only on that part of the margin that reflects the value added enjoyed by nonregistered traders.


    New Zealand, however, has signaled its intention to review the exemption of financial services: see New Zealand Inland Revenue Department (1999).


    This is a simplification: revenue will be less than this to the extent that financial services are exported (hence zero-rated) and greater to the extent that a higher price of financial services leads to higher prices of taxed commodities produced with their help.


    Cnossen (1995) provides a very useful account of both the issues in this area and current practice in the EU and some OECD countries.


    This is the essence of the “S-tax” (“s” for “stock”) proposed by Conrad (1990).


    To the extent that the property is used to provide traded services, which can be subject directly to VAT, prepayment is not strictly necessary. But the operation of the credit ensures that there is no net tax due on resale, and treatment in this way serves as a safeguard.


    The survey was not well designed to elicit information on the extent of zero rating of agricultural inputs.


    These problems are likely to be less marked for VAT, or other sales taxes, than for income tax.


    More fundamentally, it may quite plausibly be the case that the overall distribution of tax payments under the optimal tax system is not progressive, in the sense that the average rate of tax may fall over some range of income. Edwards, Keen, and Tuomala (1994) show that the marginal rate of direct and indirect taxes combined is optimally zero for the taxpayer with the highest income; over some range of income the overall tax system must therefore be regressive, in the (usual) sense that the ratio of all taxes paid to income falls as income rises.


    This issue is complicated, moreover, by the possibility of bequests, which imply that not all wealth is consumed over a lifetime. Inheritance taxes have a potentially important role in this context.


    See, for example, Poterba (1989).


    This argument focuses upon the shift toward a VAT from a system that previously relied more heavily on income taxation. To the extent that a VAT explicitly replaces some other tax(es) bearing on consumption, these distributional effects would be mitigated.


    There are of course many methodological and data issues associated with such studies, including not least the allocation of unrecovered VAT on intermediate purchases. These issues are left aside here.


    Or nearly: the proportion of consumption taken in VAT actually falls slightly between the poorest (in terms of consumption) and the next poorest decile.


    This is implied by, but does not imply, the VAT being progressive in the sense that the proportion of consumption taken in VAT rises with the level of consumption.


    It is a further merit of the VAT—but one shared with other forms of indirect tax—that it ensures that those who manage to stay outside the income tax system at least pay some tax on their final consumption.


    For this reason, and because of exchange rate changes, figures shown as “actual” in Table 11.1 may differ from the current figures in Table 1.3.


    See Terkper (1996) for a considered account of this episode.


    HM Customs & Excise, for example, launched a review of the VAT threshold in July 1998.


    Excluding China, which has a particularly complex threshold structure. Figures are for thresholds and exchange rates at the time of the survey.


    For countries with multiple thresholds, it is that for goods which enters this calculation.


    In addition to those noted in the main text, there are other respects in which threshold provisions vary. In Bolivia, the threshold is specified not in terms of turnover but in terms of income or assets. Countries also differ in the existence and nature of provisions to avoid rapid movements in and out of registration: some, such as the United Kingdom, set different thresholds for registration and deregistration, others set minimum periods for registration (until liquidation, in Belgium and Spain). Some countries (for example, Germany) set different thresholds for retrospective and prospective turnover.


    But some countries—including Côte d’Ivoire and Niger—set a higher threshold for services.


    Less frequent filing, for example, or the use of cash accounting. Some countries (including the Netherlands and Sweden) set a zero threshold in the sense that all firms must register but exempt the smallest traders from VAT. In Sweden, specifically, the very small (turnover less than Skr 30,000) are entirely exempt while the less small (turnover between Skr 30,000 and Skr 1 million) report their VAT declarations on their income tax return.


    In China, there is another threshold determining liability to the turnover tax.


    OECD (1994) indicates that in 1992 Norway, Spain, Sweden, and Turkey did not allow voluntary registration.


    If turnover follows a Pareto distribution with parameter θ > 1, the share of turnover accounted for the largest n percent of firms is (n/100)θ/(θ-1). Table 11.1 suggests, however, that distributions are too variable to construct any very general rules from this.


    For the United Kingdom, the National Audit Office (1994) puts the compliance costs for small traders at about $480, a figure broadly comparable to Cnossen’s, but administration costs rather higher, at about $190. (Cnossen’s figures, it should be noted, are averages over all taxpayers; what is relevant to the rule in (11.1) is rather the collection costs in relation to the marginal taxpayer, which are likely to be higher.)


    See Lahiri and Ono (1988). In a dynamic context, however, smaller firms may be especially important for longer-term growth.


    Avoidance can, though, also go the other way, toward the artificial aggregation of companies (through tax-induced vertical integration) in response to the incentives for exempt firms to self-supply (as discussed in Chapter 8).


    More precisely, (11.1) becomes

    where t is the rate of turnover tax and a prime refers to the sales tax regime.


    The Japanese structure is similar but slightly more complex than this because the marginal rate on entry is structured so as to ensure that all firms beyond some size pay VAT at the same rate on all their value added.


    A point emphasized by Godwin (1998).


    In a few cases, FAD successfully advised against assigning these collections to the internal revenue department during the preparations for the VAT.


    The United Kingdom, Israel, Malawi, and Belize (until that country repealed the VAT in April 1999).


    Cyprus, Dominican Republic, Jamaica, Ghana, Kenya, Luxembourg, Tanzania, Uganda, Zambia, Mauritius, China, Egypt, Pakistan (since 1996) and Belgium (prior to the creation in 1999 of a single administration for VAT, income, and other taxes).


    In Europe, France merged the income tax and VAT offices in the early 1970s and Italy has also done so.


    The Canadian Taxation Department and the Customs and Excise Department were merged in a single department reporting to a deputy minister in 1994. However, while VAT and income tax headquarters and field offices have been successfully merged, there are still separate headquarters and field offices for the customs administration.


    Others, such as Mauritius and Rwanda, have also taken steps to establish revenue authorities.


    The most noticeable steps taken in this direction are in Uganda, which recently established a large taxpayer unit, in which VAT, excises, and income tax operations are fully integrated, and in Ghana, where a single taxpayer identification number was introduced.


    As explained by Tait (1988), “the United Kingdom case is unusual. The customs administration was assigned responsibility for the operations of the purchase tax that was introduced during World War II, when the tax administration was overburdened and when the Customs was less busy than usual. Because of this accident of timing, the Customs gained in experience in dealing with the purchase tax, and when the time came to introduce the VAT, this experience was a deciding factor in allocating responsibility for VAT administration.”


    One advantage of an integrated VAT and customs administration is that it should facilitate exchanges of information on imports and exports, a requirement for effective processing of refunds. However, this is essentially an information technology issue—not an organizational one—that should be resolved by the implementation of appropriate computer systems using a single taxpayer identifier for both tax and customs administration purposes.


    For example, Côte d’Ivoire in 1960, Morocco and Niger in 1986, and Tunisia in 1988.


    There has been a subsequent improvement in many of these countries—for example, Côte d’Ivoire and Senegal now have only two VAT rates, and all other WAEMU countries have a single VAT rate; moreover, businesses below the registration threshold are now exempted. In recent years, most of these countries have also embarked on reforms to improve their tax administration (including the establishment of large taxpayer units, simplified collection procedures, and more effective collection enforcement programs).


    When describing VAT payments and refunds, Tait (1988) indicated that “the VAT is basically a self-assessed tax.” He did not consider this to be an issue for discussion.


    These complicated procedures were also applied in Uganda until 1998. Uganda, however, began implementing simple VAT filing and payment procedures through the banks in early 1999.


    The schedule for fulfilling these tasks is tight. In one of the countries surveyed, for example, taxpayers must file the VAT return before the 10th of the following month and pay the tax due before the 25th of the same month based on a tax notice issued by the tax offices. To cope with this schedule, tax offices must process and issue the tax notice within 10–12 days.


    In the country mentioned in the preceding footnote, studies prepared to support the tax administration computerization program showed that the cost (staff and computer equipment) was 2.5 times higher than would be expected if self-assessment procedures had been implemented. The additional cost resulted from the requirement to issue assessment notices for all returns.


    Alternative solutions would focus on measures to reduce the tax administration workload due to the lack of self-assessment. For example, VAT returns and payments could be made once or twice a year to limit the number of returns and payments to be processed. Alternatively, the VAT could be applied only above a threshold (higher than that which would otherwise be recommended). The first solution, however, would have serious drawbacks for revenue collection. The second makes little sense since taxpayers above a very high threshold are precisely those most capable of self-assessing their liabilities.


    Under the new system, customs clearance is no longer needed on trade between EU countries. The purchase of goods and services from EU businesses is no longer treated as an import but as a domestic transaction and VAT on intra-European transactions must be declared and paid monthly (or quarterly), along with the domestic transactions, using the same VAT return form.


    This is especially true when the disparity between salaries for the private and public sectors is substantial. A common approach to deal with the risk of collusion is to organize auditors into teams (at least two auditors for each audit); however, there is little evidence that this approach helps address the problem of corruption.


    There are often concerns in the business communities of developing countries and transition economies that the tax system is not always applied in a transparent manner and that objections and appeals are costly and complicated. In these countries, taxpayers are sometimes presented with large tax bills, which are intended to provide a basis for negotiation of a settlement of increased liabilities resulting from audits. In a number of cases, little explanation is provided to justify the reasons for these additional liabilities and auditors are not always interested to discuss technical issues.


    Most modern tax administrations have developed case selection systems (usually computer based) to select VAT returns for audits. The more effective systems utilize taxpayer profiles and criteria to identify the highest risks for the revenue. These systems are frequently based on the crosschecking of internal information—for example: comparing return information with basic ratios (markup ratio), comparing information from different taxes (VAT and income tax), and using information from previous audits. Most systems also use information from other sources, for example: comparing customs information on tax paid on imports with input tax credit claims in the VAT returns; comparing customs information on exports and amount of zero-rated sales in the VAT return; and cross-checking of information on sales and purchases (information collected from large enterprises and government suppliers).


    For example, replacing the checking of 100 percent of invoices by selective programs (ranging from the cross-checking of sample quantities of purchase and sales invoices in the course of VAT audits to intensive cross-checking of invoices within specific industries or among major taxpayers).


    Excess credits can also arise even with positive value added if the rate of tax on inputs is sufficiently in excess of that on outputs. More precisely, excess credits arise whenever the proportionate excess of the average rate of tax on inputs exceeds that on output by more than the ratio of value added to input costs.


    Tax administrations that are not operating effectively often build up a large stock of refund liabilities. By turning off the “refund tap,” weak tax administrations can make current collection look better, so long as no one is tracking unpaid refund claims. In effect, current tax collections are inflated. Although in a number of countries the law usually provides that interest should be paid to the taxpayer in the event of publicly stated commitments being broken, it is not clear that tax authorities of these countries consistently apply these provisions.


    Silvani and Brondolo (1996) provide a detailed discussion of some of the methods used to control refunds to exporters.


    In cases where the investment is in a start-up or rapidly expanding enterprise, exemption for imported capital goods would even give a tax incentive to import rather than purchase domestically.


    Recall from Chapter 1 that these are defined here as islands with populations under 1 million, plus San Marino.


    As defined and discussed in Chapter 4.


    A simple linear regression for 173 countries gives In(OPEN) = 3.46 - (0.122)In(POP), with a (White-adjusted) t-statistic on the slope coefficient of -4.8 and R¯2 of 0.14.


    To the extent, for example, that the tax administration may be able to put pressures on recalcitrant taxpayers by phoning their parents.


    For a small economy, maximizing social welfare subject to a revenue constraint requires zero tariffs if destination-based consumption taxes can be deployed. This result is a corollary of the Diamond-Mirrlees (1971) theorem on the desirability of production efficiency (described in Box 2.1).


    Keen and Ligthart (2001) show that this can be done, in the simplest case, merely by increasing consumption taxes by exactly the same amounts that tariffs are cut.


    Setting the consumption tax at a rate equal to that of the initial tariff, consumption is unaffected by the switch; but revenue is now collected not only on imports but on all consumption, a base that will be wider to the extent that there is any domestic production.


    While differences in the size of these bases might be addressed by setting different tax rates, higher rates are themselves likely to induce more distortions through the encouragement of evasion and avoidance.


    Writing C/M for the ratio of private consumption to imports, one finds for a sample of 156 countries that In(C/M) = 0.44 + (0.18)In(POP), with (White-adjusted) t-statistic on the slope coefficient of 6.9 and R¯2 of 0.25.


    As discussed in Chapter 7, this will typically not be fully optimal. Insofar as excises deal with the important deviations from uniformity, the benchmark is nevertheless a natural one.


    Calculated as the sum of the revenue gain from moving to the VAT (relative to GDP), (0.1) (0.5) (0.2) valued at 1.25 per unit, and the efficiency gain of 0.005.


    Though, of course, any WTO obligations will need to be met.


    In the EU, the term origin taxation has come to be used to refer to a system in which tax is collected by the country of origin even if that revenue is later channeled to another jurisdiction. Thus the Commission refers to its clearinghouse system, described later, as an origin system. This is important because of the EU’s long-standing intention (laid down in the preamble to the sixth Directive, issued in 1977) of ultimately “… abolishing the imposition of tax on importation and the remission of tax on exportation in trade between member states….”


    Questions concerning how VAT revenue should be shared lie in the realm of fiscal federalism proper, and are not pursued here.


    A number of Indian states have also operated systems with similarities to a VAT.


    Canada’s experience in superimposing a federal VAT on preexisting provincial sales taxes shows, however, that this difficulty is not always insuperable.


    The most general equivalence results are in Lockwood, de Meza, and Myles (1994); see also Genser (1996).


    It might seem enough (Fratiani and Christie, 1981) that (ad valorem) tax rates be collinear across countries, so that an exchange rate adjustment can move one from a situation in which producer prices are equated across countries (under the destination basis) to one in which consumer prices are equated (as under the origin basis). Unless taxes are fully uniform within each country, however, such a realignment will change the real allocation of resources because it will typically affect tax revenues (Keen and Smith, 1996).


    See, for example, Bovenberg (1994).


    See Keen and Lahiri (1998). Consider, for example, a situation in which two firms, located in different countries, survive in equilibrium, with one less efficient than the other (but able to survive, nevertheless, behind a price above the competitive level). First best policy is to eliminate the less efficient firm and subsidize the output of the other to the level at which price equals marginal cost. This can be achieved under origin taxation simply by setting a large enough origin tax in the country of the inefficient firm to drive it out of business and an appropriate origin subsidy in the other.


    A point first noted by Cnossen and Shoup (1987).


    See Genser and Schultze (1997) for further discussion.


    For the EU, Cecchini (1988) puts the gain at 1.7 percent of the value of intracommunity trade.


    The classic statement of the argument is Cnossen and Shoup (1987).


    Practice varies, but “goods” are commonly defined in terms of tangibility and “services” then as all that remains (except, perhaps, land): see Williams (1996), pp. 184–88.


    The European Commission (1998) proposed that refund claims be made to the jurisdiction in which the purchaser is registered rather than the jurisdiction of the supplier.


    We do not discuss issues related to the corporate tax, though there are clearly links with those affecting VAT, a key issue in each case being how to establish tax nexus in the circumstances of the new technologies.


    Described and discussed in McLure (1999).


    The treatment of telecoms is discussed in Ogley (1997, 1998) and Rainer and Claeys (1997).


    European Commission (1996, p. 14).


    A further alternative, recently proposed by Satya Poddar, is for goods to be released for export once confirmation has been received of payment of import VAT by the importer.


    See the discussion in Lee, Pearson, and Smith (1988).


    In its less widely noted proposal concerning the recovery of input tax charged in other member states, the European Commission (1998) envisages replacing the current system, which requires traders to approach the authorities in the jurisdiction in which tax was charged, by a form of clearing between national authorities (traders then dealing only with their own authorities), and, moreover, a form of clearing based on invoices.


    The “viable integrated VAT” proposed by Keen and Smith (1996) in the context of the EU debate on VAT. Keen (2000) provides a detailed comparison between CVAT and VIVAT. See also the symposium on sub-national VAT in International Tax and Public Finance, with contributions from Bird and Gendron (2000), Keen and Smith (2000) and McLure (2000).


    Summers and Sunley (1995) describe the difficulties with VAT in the CIS.


    This is a generalization, as treatment was by no means uniform (Baer, Summers, and Sunley, 1996). From early on, Ukraine applied the destination principle to all its trade. Some others give credit on imports from other CIS countries at the rate of the exporting country: the aggregate tax collected would thus be as under the destination principle, but its allocation in line with value added in the two countries.


    Summers and Sunley (1995).


    See Guerard (1973). A more recent detailed account is also provided by Longo (1991).


    Recall that origin taxation for the VAT, as defined here, requires the importing state to give credit not for tax actually paid but for the hypothetical amount that would be paid at the rate of that state.


    This follows on noting from (II.5) that tI-t = P-1(IN-A-1.A.P. (IN-Δ).t, the product of nonnegative matrices and a vector whose elements are all nonnegative.


    This is in contrast to the type-I rate, which, recall, is always at least as large as the statutory rate.


    This again is in contrast to the type-I rate, which coincides with the statutory rate even if multiple rates of VAT are applied (so long as there are no exemptions).


    Assuming value added at net prices to be strictly positive.


    Uniformity of type-I rates, for example, implies that tI*=τe where e is an N-vector of ones, and the result then follows on observing that, from the definition of S, S-1(IN - A).P.e=e.

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