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    Journal of Public Economics 66 (1997) 173197

    Tax evasion in an open economy:Value-added vs. income taxation

    a b ,*Roger H. Gordon , Soren Bo Nielsena

    Department of Economics, University of Michigan, Ann Arbor, MI 48109-1220, USAbEconomic Policy Research Unit, Copenhagen Business School, Nansensgade 19,5, DK-1366

    Copenhagen K, Denmark

    Received 1 January 1996; received in revised form 1 October 1996; accepted 22 October 1996


    Ignoring tax evasion possibilities, a value-added and a cash-flow income tax have similar

    behavioral and distributional consequences. Yet the available means of tax evasion under

    each can be very different. Under a VAT, avoidance occurs through cross-border shopping,whereas under an income tax it can occur through shifting taxable income abroad. Given

    evasion, we show that a country would make use of both taxes in order to minimize the

    efficiency costs of evasion activity, relying relatively more on whichever tax is harder to

    evade. We then make use of aggregate Danish tax and accounting data from 1992 to

    measure the amount of evasion that occurred under the two taxes. While the estimates of

    evasion activity are small, the figures imply that Denmark could reduce the real costs of

    evasion activity by relying more on value-added taxes. 1997 Elsevier Science S.A.

    Keywords: Tax evasion; Value-added tax; Income tax

    JEL classification: H21; H26; F23

    1. Introduction

    Given the increasing economic interdependence among developed countries, tax

    competition between countries is a growing concern. Multinationals can quickly

    shift substantial amounts of taxable income out of countries with high corporate

    *Corresponding author. E-mail: sbn/[email protected]

    0047-2727/97/$17.00 1997 Elsevier Science S.A. All rights reserved.

    P I I S 0 0 4 7 - 2 7 2 7 ( 9 7 ) 0 0 0 4 4 - 3

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    174 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    tax rates into countries with low rates, while individuals can readily escape

    domestic taxation of their income from financial assets through shifting their

    savings abroad into countries providing them anonymity and low tax rates.

    Given these pressures from transfer pricing and capital flight, countries have anincentive to lower their income tax rates relative to those in competing countries

    so that taxable income is shifted into rather than out of their jurisdiction. The extra

    tax base they attract by lowering their tax rates, however, will in large part result

    from a relocation of reported earnings, causing a drop in the tax base abroad and

    thereby generating a fiscal externality and inducing destructive tax competition

    among countries. The lower effective tax rate on foreign-source activity also

    creates costly distortions to the financial structure of firms and the portfolio choice

    of individuals. What options do countries face to lessen the efficiency costs

    generated by tax evasion in an open economy?

    In theory there do exist tax systems that are free of these locational distortions

    and fiscal externalities. As noted for example by Razin and Sadka (1991a) or1

    Mintz and Tulkens (1996), if individuals are immobile across countries then

    residence-based income taxes in a small open economy do not impose externalities

    on other countries that use the same type of tax, and the Nash equilibrium2

    residence-based tax rates cannot be improved on through tax coordination.

    However, in practice, such pure residence-based taxes have not been feasible. The

    basic problem is the difficulty of monitoring earnings and expenditures of

    domestic residents that occur abroad. While a government has the power to collect

    information from domestic firms and domestic financial intermediaries in order toenforce taxes on the earnings and expenditures of domestic residents, it has no

    ability to collect comparable information from foreign sources. Even if a country

    by statute has a residence-based tax, foreign-source earnings and expenditures will3

    as a result frequently escape tax, resulting in a very different tax structure in


    Taxes on the return to capital income are particularly vulnerable to avoidance

    and evasion, given financial arbitrage, transfer pricing, and capital flight. Razin

    and Sadka (1991b), for example, forecast that these combined threats will lower

    effective capital income tax rates to zero in equilibrium. In fact, Gordon and

    Slemrod (1988) find that the U.S. loses tax revenue on net from its attempt to tax4the return to capital. But if capital income taxes both lose revenue and generate

    1When individuals are mobile, only benefit taxes are not vulnerable to tax competition, as argued by

    Buchanan and Goetz (1972).2When countries are large enough to affect the international rate of interest, further complications

    arise. See, e.g., Huizinga and Nielsen (1996).3Hines and Hubbard (1990), for example, document that U.S. multinationals pay little or no U.S.

    taxes on their foreign-source earnings.4Sorensen (1988) reports similar findings for Denmark. The loss of revenue results only in part from

    income shifting across borders domestic portfolio arbitrage also generates substantial revenue losses,

    as high income investors borrow heavily from tax exempt entities to invest in lightly taxed assets,

    generating tax losses in the process.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 175

    particularly large efficiency losses, then they have lost their role as an effective tax

    instrument. In this paper, we instead examine the degree to which taxes on income

    from labor are also vulnerable to evasion in an open economy.

    What opportunities for tax evasion remain if new real investments by domesticfirms can be expensed and the returns to financial assets and liabilities are made

    tax exempt, thereby eliminating any distortions to capital investments? The cash

    flow of foreign subsidiaries of Danish multinationals should in theory be subject to

    the same cash-flow tax, but monitoring their cash-flow remains very difficult.

    Given these difficulties, Denmark has instead in many bilateral treaties exempted

    the earnings of the foreign subsidiaries of Danish firms from domestic taxation.

    This approach is equivalent to a cash-flow tax treatment in present value only if

    the income of foreign subsidiaries simply reflects a normal return to funds invested

    abroad. The results in Gordon and Slemrod (1988), however, suggest that reported

    corporate income is far too high to represent the normal return to past real capital

    investments. The most plausible explanation for the observed excess profits is5

    that they represent the return to entrepreneurial effort and imagination. Exempting

    the income of foreign subsidiaries from tax therefore exempts the return earned

    abroad on the ideas and efforts of domestic entrepreneurs. Through use of transfer6

    pricing, they can avoid tax as well on domestic-source earnings.

    Given the difficulties governments face in taxing foreign-source earnings, tax

    evasion is an inherent part of an income tax system in an open economy, even if

    capital income is exempt from tax. One alternative approach to taxing labor

    income, however, is to tax the income when it is spent rather than when it isearned, as occurs with a value-added tax. Ignoring evasion, a cash-flow tax has the7

    same economic incidence and efficiency cost as a value-added tax. Once evasion

    is taken into account, however, the incidence and efficiency consequences of the

    two taxes can be very different. A governments inability to monitor transfer

    pricing used by multinationals has no effect on the value-added tax base, since the

    only price that matters for the value-added tax is the price paid by the final

    consumer. Similarly the inability to monitor foreign-source earnings is of no

    consequence for a VAT as long as the government can monitor consumption

    5Apparently, entrepreneurs, in part for tax reasons, choose to leave much of their earnings within thefirm rather than paying it out as wages and salaries, thereby paying tax primarily at corporate rather

    than personal tax rates on this income. See Gordon and MacKie-Mason (forthcoming) and Leamer

    (1996) for further discussion.6While the income earned abroad, or shifted abroad through transfer pricing, could be subject to

    corporate taxes in the host country, multinationals seem to be quite effective at shifting their taxable

    earnings to tax havens where they escape taxation entirely. See, e.g. Hines and Rice (1990) for

    evidence for U.S. multinationals.7A cash-flow tax is equivalent to an origin-based value-added tax, while a European-style value-

    added tax is destination-based. While the timing of tax payments differs under origin-based and

    destination-based VATs, at constant and identical rates the present value of the revenue they collect

    differs only to the extent that the present values of imports and exports differ. This difference simply

    equals the initial foreign asset position of the country, which for Denmark in 1992 equaled 35% of


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    176 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    expenditures. Monitoring consumption expenditures, however, generates its own

    and very different enforcement problems. In particular, destination-based value-

    added taxes require rebates of taxes paid in the origin country and imposition of

    taxes in the destination country when any goods cross borders. Yet it is verydifficult to detect all imports at the border the E.U. has found doing so

    sufficiently costly that it has in large part abandoned the attempt to monitor8

    cross-border shopping by individuals. Both income taxes and value-added taxes

    are therefore subject to evasion/avoidance, but the level and nature of the evasion9

    opportunities can be very different in the two cases.

    In Section 3, we explore theoretically the optimal use of cash-flow vs.

    destination-based value-added taxes, given cross-border shopping, income shifting,

    and underground activity. We find that both should be used in practice the less

    vulnerable one of these taxes is to evasion, the larger its tax rate should be relative10

    to the other tax rate.

    The key parameters in this model determining the optimal relative tax rates are

    the relative vulnerabilities of the two taxes to evasion. In Section 4, we use data

    from 1992 on the relative size of the value-added tax base vs. the income tax base

    (assuming expensing for domestic real investments) in Denmark to measure the

    relative amounts of evasion under the two taxes. If both tax bases are measured

    accurately, then reported labor income should equal reported expenditures plus net

    asset accumulation. To the degree to which the amount of evasion differs under the

    two taxes, however, the size of the tax base that is more subject to evasion will be

    smaller than would be forecast using this aggregate budget constraint, given theobserved size of the other tax base. The difference between the forecasted and the

    actual tax base equals the difference in the amounts of evasion under the two

    taxes. The Danish tax authorities have used survey data to estimate the extent of

    evasion of their value-added tax due to cross-border shopping. Using this estimate

    in addition, we can estimate the amount of evasion under the income tax.

    In particular, given the information the Danish government reported on

    consumption abroad by Danes, we estimate that 3.9 billion Danish kroner of

    value-added escaped taxation in 1992 because of cross-border shopping. Using this

    figure together with our results on relative evasion rates, we infer that 14.8 billion

    8In a few instances, for example alcohol brought into the U.K. and tobacco and spirits entering

    Denmark, some border controls remain. The end of border controls technically converts evasion into

    avoidance, just as occurs through the exemption from tax of the income from foreign subsidiaries.

    Since these exemptions seem to have been enacted simply in recognition of the impossibility of

    preventing evasion, we continue to refer to these activities as evasion even if enforcement efforts have

    been abandoned.9Some other forms of evasion, e.g. the underground economy, affect the two taxes equally. We show

    below that the underground economy does not affect the relative attractiveness of the two tax bases.10

    In a recent study examining the same question, Boadway et al. (1994) assume in contrast that only

    income taxes are vulnerable to evasion. Offsetting this advantage to consumption taxes, they assume

    that only income taxes can have a nonproportional rate structure. In our model, in contrast, both taxes

    can be evaded but for simplicity both taxes are proportional.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 177

    kroner of labor income escaped domestic taxes by being shifted abroad. While both

    numbers are small (the total labor income tax base was 535.6 billion kroner), our

    theoretical results imply given these figures that more weight should be put on the

    value-added tax relative to current law in order to minimize the efficiency lossesthat arise due to evasion activity. Over time, we expect to see greater use of the

    value-added tax, given the increasing vulnerability of the income tax to cross-

    border activity.

    2. Implied efficiency costs from evasion and implications for tax design

    In order to focus on the effects of evasion on the relative attractiveness of labor

    income vs. value-added taxes, we examine a setting in which the two taxes are

    otherwise equivalent. In particular, we assume that residents have no net assets

    abroad, so that the present value of the two taxes is the same. In addition, we

    assume that both taxes are proportional and comprehensive, so ignore both

    differential value-added tax rates by commodity and any non-linear rate structure

    under the income tax. The key difference between the two tax bases that we focus

    on is the difference in their vulnerability to evasion. We use a very simple model to

    measure the efficiency losses from evasion. Assume that the utility of domestic

    residents depends on their consumption, C, labor supply, L, and the supply of11

    government services, G, yielding utility of U(C,L ) 1 V(G). By statute, assume

    that the value-added tax rate ist

    while the labor income tax rate is t. Theindividuals collective budget constraint is then C(1 1t) 5 L(1 2 t), ignoring12

    evasion, where we have assumed that the wage rate equals one. The govern-

    ments budget constraint, ignoring evasion, is G 5tC1 tL.

    Assume initially that evasion of the value-added tax takes the form entirely of13

    cross-border shopping. By purchasing the fraction f of ones consumptionCabroad, tax payments fall by f C(t2t ), where t is the value-added tax rateC f facross the border. (By constraint, f $ 0.) This cross-border shopping generatesCnon-tax costs of N ( f )C, arising e.g. from extra travel expenses. When laborC Cincome taxes are evaded, we assume the income is shifted abroad, where it is


    taxed at the foreign rate t. Assume that evading the fraction f $ 0 of laborf L

    11The assumed separability in the utility function simplifies some of the steps below, but should have

    no fundamental effect on the results. Since neither tax distorts savings decisions, we omit savings

    decisions from the model.12

    We do not include any initial assets in this budget constraint, to assure that the present value of the

    two tax bases is the same.13

    We later introduce evasion through the underground economy as well.14

    A t equal to zero would indicate that income is shifted into a tax haven. This plausiblyfcharacterizes the tax evasion opportunities of a multinational, though would be less appropriate for

    individuals physically working abroad. The effective marginal tax on evaded labor income is difficult to

    assess; to the extent that it is set too low, we will underestimate the responsiveness of the income tax

    base to t, thereby overestimating the optimal labor income tax rate.

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    178 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    15income taxes generates non-tax costs of N ( f )L. In addition, assume that each ofL L

    2these cost functions is quadratic, so that N ( f ) 5 0.5 Cf /c and N ( f ) 5 0.5C C C L L

    2Lf /d, where c and d are parameters measuring the ease of evasion. The extraLexpenses incurred in evading value-added taxes we presume take the form oftransportation and other expenditures abroad, which would be taxable at rate t,fwhile the costs incurred from evading labor income taxes we presume simply

    result from a lower return to labor supplied abroad. As a result the budget

    constraint becomes:

    2C(1 1t) 2 f C(t2t ) 1 0.5C(1 1t )f /c 5 L(1 2 t)(1 2 f )C f f C L

    1 L(1 2 t )f (1 2 0.5f /d), (1)f L L

    16whereas the governments budget constraint becomes

    G 5tC(1 2 f ) 1 tL(1 2 f ).C L

    Under these assumptions, it immediately follows that the utility-maximizing

    levels of evasion for individuals are f 5max(d9(t2t ), 0) and f 5max(c9(t2t ),L f C f 0), where d95 d/(1 2t ) and c95 c /(1 1t ). In addition, the individual choosesf f

    17how much to work. The first-order condition for L equals

    21 2 t1 0.5d9(t2 t )U fL

    ] ]]]]]]5 2 . (2)2U 1 1t2 0.5c9(t2t )C f

    In designing its tax policy, the government chooses the two tax rates in order to

    maximize individual utility, taking as given how individuals respond to these tax

    rates. At the optimal policies, any minor perturbations in tax rates must leave

    individual utility unaffected. In particular, consider the implications of a marginal

    increase in t accompanied by a marginal decrease in t chosen to leave the

    right-hand side of Eq. (2) unaffected, so that

    21 2 t1 0.5d9(t2 t ) 1 2 c9(t2t )f f]]]]]] ]]]]t/t 5 2 . (3)S D2S D 1 2 d9(t2 t )1 1t2 0.5c9(t2t ) ff

    By design, this policy change will have no effect on individual labor supply

    decisions or on individual consumption levels, so will affect utility only through

    15We assume here that these evasion costs consist of lost real resources rather than fines. When fines

    do exist, we redefine t and t to represent all payments to the government, while f and f representC Lsuccessful evasion.

    16For simplicity, we ignore any tax revenue generated from cross-border activity undertaken by

    foreign residents. For an attempt to model explicitly the simultaneous choice of value-added taxes by

    two neighboring countries, see Kanbur and Keen (1993).17

    We confine ourselves in the following to the case where both optimal tax rates exceed the

    respective foreign tax rates.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 179

    its implications for G. Maximizing G with respect to t and allowing t to respond

    according to Eq. (3), we find after a bit of simplification that

    c9t(1 1 d9t ) 5 d9t(1 1 c9t ). (4)f f

    When, for example, income taxes become more costly to evade, d9 is smaller

    implying that t rises relative to t. Similarly, when t rises, t also rises sincefevasion of the VAT has become less of a threat.

    If in the empirical work we can estimate the fraction of each tax base that is lost

    due to evasion, then we can infer the values of c9 and d9 knowing the statutory tax

    rates. This information, when combined with Eq. (4), in principle gives us

    information about the optimal tax structure. In particular, if the current tax rates are t, t, t, and t, and the observed evasion rates are f and f , then the optimal taxf f C L

    rates t* and t* satisfy

    t2t(1 2 f )ft* f CL] ] ]]]]5 . (5)S DS Dt* f t2 t(1 2 f )C f L

    This derivation makes a number of simplifying assumptions which deserve

    mention. For one, the functional form used to describe the non-tax costs of evasion

    imposes a tight link between the total amount of evasion, which we hope to

    measure, and the marginal change in this amount as tax rates increase, which is

    what matters in the optimal tax rate calculation. A general functional form for NCand N would lead to a more complicated link between observed amounts ofLevasion and optimal tax rates, and a more complex optimal tax formula. More

    limited generalizations are possible, however. For example, unreported consumer

    expenditures abroad consist in part of cross-border shopping, which is motivated

    primarily by tax differences, and in part of tourist expenditures which are likely to

    be much less responsive to tax differences. Below we report data on both

    cross-border shopping and tourist expenditures. For purposes of discussion in this

    paper, we will assume that the fraction of pretax consumption expenditures

    allocated to foreign tourism is entirely unaffected by t, while the amount of18

    cross-border shopping is proportional to the value-added tax savings. As seen inAppendix A, with this modification to our assumptions optimal tax policies

    continue to satisfy Eq. (4).

    In addition, the above model ignores the underground economy, and more

    generally the possible evasion of both income and value-added taxes on domestic

    transactions. The basic theoretical question is the degree to which a shift in the

    relative use of a VAT vs. a labor income tax in collecting a given amount of

    18In particular, if tourist expenditures abroad equal aC for some exogenous value a, then

    2value-added tax payments equal t(1 2a)C(12f ), while the costs of tax evasion equal 0.5(12a)Cf /C Cc.

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    180 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    revenue affects the extent of tax evasion through underground activity. A major

    component of the underground economy is activity that is totally unobserved by

    the tax authorities, e.g. cash transactions in the service sector. Here, no taxes

    would be paid, regardless of whether income or value-added taxes are used. Theincentive to become a part of this sector depends on the total amount of taxes

    owed if taxes are not evaded, and this would be unaffected by a shift in tax base if

    total tax revenue is left unaffected. Therefore, the presence of such underground

    activity does not affect the choice between the two tax bases, regardless of its19

    importance. In Appendix A, we generalize our initial model to incorporate

    underground activity as well as tourism abroad. This is the version of the model

    we will use in interpreting the data we report below.

    Our conclusions about optimal tax rates very much depend on the specific20

    model used, yet this model cannot possibly capture all forms of tax evasion. In

    the empirical work reported below, our measure of the relative amounts of evasion

    under the two taxes is valid regardless of the source of evasion. However, our use

    of this information to infer something about optimal tax policy does depend on the

    specific assumptions we make about the characteristics of this evasion activity.

    The above model also ignores a variety of other complications that make one

    tax or the other more attractive. For example, both taxes allow for redistribution

    based on aggregate income or expenditures, but only the consumption tax allows

    for redistribution as well based on the relative amounts that individuals consume

    of different goods. While Sandmo (1974) demonstrated conditions under which

    this variation in tax rates by good would not be desired, these conditions may or21may not hold.

    In contrast, a labor income tax can much more easily accommodate a

    progressive rate structure. However, this progressivity need not be affected by a

    shift towards more use of value-added taxes. For example, McLure (1991)

    proposes a modified value-added tax in which wage and salary payments are

    deductible from the VAT base but in which each individuals wage and salary

    income is then taxed separately using a progressive rate structure with a maximum


    In a similar vein, Kesselman (1993) demonstrates that a revenue-preserving change in the mix ofdirect income and indirect consumption taxes has no effect on (domestic) evasion activity, if the

    below-ground sector evades both taxes.20

    For example, one form that evasion may take is that some sales to consumers are unreported for

    purposes of both the cash-flow tax and the value-added tax. Now, the amount of tax evasion equals

    (t1t)U, where U measures the amount unreported. If we assume that the cost of succeeding at this

    evasion is a quadratic function of U, the chosen value of U will be proportional to t1t. Holding

    government revenue fixed, however, t1t will be minimized when only labor income taxes are used,

    since the income tax base L is larger than the consumption tax base: C5L(1 2t)/(11t).21

    Being able to vary the consumption tax rate by good also provides an indirect means of introducing

    tariffs, particularly if production taxes can be introduced that vary by good, as noted for example by

    Gordon and Levinsohn (1990). Use of a labor tax, in contrast, provides a means of precommitting not

    to make use of indirect tariffs.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 181

    22rate equal to the VAT rate. This approach to adding progressivity to a destination-

    based VAT is equivalent to supplementing a proportional VAT with a wage23

    subsidy with declining subsidy rates as an individuals income rises.

    Changes in tax rates over time in response to changes in the desired level ofgovernment expenditures introduces very different types of intertemporal distor-

    tions in the two cases. Changing labor tax rates distort the relative wage rates at

    different dates and so the timing of work effort, whereas changing consumption

    tax rates distort the desired timing of consumer purchases and therefore of desired


    If the entry of new firms generates positive externalities by providing in-

    formation to others about the potential viability of new products, new forms of

    organization, or even just new locations, then a labor tax can be used to help

    correct this externality. For example, new owners can easily convert their labor

    income into capital gains through leaving profits within the firm and later selling

    their ownership rights in the firm. Such subsidies to new firms are not so easily

    arranged under a consumption tax.

    One further factor is the desired tax treatment of non-residents. If a country is

    small relative to world markets so that it is a price taker in the relevant market,

    then it is easy to show that the optimal tax rate on activity by foreign residents is

    zero. When the country is not a price taker, however, e.g. it has unique tourist

    attractions, then it does have an incentive to set tax policy to take advantage of this

    market power. The extent of market power can easily differ with respect to

    consumer markets and labor markets.For these reasons and others, any conclusions about the nature of optimal tax

    policy must be subject to qualifications. But evidence on the relative vulnerability

    of consumption vs. income taxes to evasion remains an important consideration in

    the relative attractiveness of the two taxes.

    3. Evidence on the extent of evasion of VAT vs. labor income taxes

    3.1. Conceptual approach

    To measure the relative amounts of evasion under the two taxes, we make use of

    the aggregate cash-flow constraint for the country, linking current earnings, current

    22Given the specific design of this proposal, however, existing GATT rules would likely prevent

    border corrections when goods are exported and imported, so the proposal does not include such

    corrections. If GATT rules allowed it, however, border corrections could easily be appended to the

    proposal by allowing a deduction at the top rate when goods are exported and imposing a tax at the top

    rate when goods are imported.23

    For example, a nonlinear income tax function T(L) can replaced by T(L)2LD t when a

    proportional labor income tax is reduced in favor of more use of a value-added tax.

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    182 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    expenditures, and the current accumulation of assets. With accurate accounting

    data, accounting earnings would exactly equal accounting expenditures plus asset

    accumulation. Using tax data, however, the figures for both earnings and

    expenditures will be understated due to evasion. If evasion of the income tax isrelatively larger, then the observed earnings reported for tax purposes will be

    smaller than the value forecast based on observed expenditures reported for tax

    purposes and accounting information on asset accumulation. This difference then

    gives us a measure of the relative amounts of evasion under the two tax bases.

    We will implement this approach using detailed tax and accounting data for

    Denmark for the calendar year 1992.

    To facilitate this estimation of the relative amounts of evasion under the two tax

    bases, we define the income tax base and the value-added tax base to minimize the

    differences between the two other than differences in timing of payments and in

    evasion rates. To begin with, we compare a value-added tax not with the current

    income tax but with a proportional cash-flow tax on business earnings from real24

    assets along with a personal tax at the same rate on wage income.

    Such a cash-flow tax does not distort investment decisions, and ignoring evasion

    and transition issues should have the same incidence as a comprehensive value-

    added tax. The current value-added tax in Denmark, in contrast, exempts or

    imposes a zero rate on a variety of expenditures. In many cases, this more25

    favorable tax treatment seems to be justified by distributional considerations.

    While distributional considerations are normally pursued in different ways under a

    VAT vs. a labor income tax, in order to minimize the differences between the twotax bases we standardize for distributional characteristics by examining a uniform-

    rate value-added tax. We estimated the value added that would be reported under

    such a uniform VAT by adding to the observed tax base an accounting measure of

    the value-added in each of the exempt sectors and consumption in each of the26

    zero-rated sectors. In so doing, we ignore any potential evasion in these sectors.

    We decided to make one exception, however, for the financial services sector. The

    exemption here we viewed to exist not because of any distributional considerations

    but because of administrative difficulties in enforcing a value-added tax on this

    sector. Individuals can easily make use of banks and insurance companies in

    foreign countries, even foreign branches of domestic firms, when prices are

    24Our procedure for modifying the existing income tax data to estimate the tax base for this

    cash-flow tax follows closely the procedure described in Gordon and Slemrod (1988).25

    The specific exempt sectors at issue are education, medical care, personal transportation, social

    services (e.g. nursing homes), rental housing, and financial services, while the zero-rated sectors are

    sales of ships, airplanes, and newspapers.26

    Of these exempt or zero-rated sectors, other than financial services, the only one where cross-

    border shopping seemed plausible was sales of ships and airplanes. However, given the conspicuous

    nature of ships and airplanes, enforcing domestic taxes at import of these goods should be straight-

    forward, so we proceed under the assumption that the amount of evasion does not change if these

    sectors are not exempt or zero-rated.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 183

    cheaper abroad, so the amount of cross-border shopping should be particularly

    sensitive to the tax treatment of this sector. As a result, we decided to operate

    under the assumption that no value-added taxes on this sector are feasible. To

    maintain consistency with this assumption, we also eliminated any cash-flowincome or wage payments from the financial services sector in our measure of

    labor income.

    Given these definitions of the alternative tax bases, we use the countrys

    aggregate cash-flow constraint to forecast how the two should compare if they

    were reported accurately. Given the special treatment of the financial sector in our

    analysis, we keep explicit track of this sector in the following derivation. Start

    with the cash-flow constraint of the household sector, where

    (W 1 W 1 W) 1 S 1 rA 1 r D 1 (p1p ) 5 (C1 C 1 H) 1 F 1 Te f h h d h e f h h

    ~ ~1 A 1 E. (6)h

    Here, W, W , and W equal wage income from the taxed sector, from the tax-exempte f(financial) sector, and from abroad, respectively. S equals government subsidieshto households, while T equals all personal income tax and value-added taxhpayments by the household sector. The terms C, C, and H consist of non-durablefconsumption expenditures at home, non-durable expenditures abroad, and durable

    (primarily housing) expenditures; F represents consumption expenditures in thehexempt financial sector. (p1p ) equals the residual cash-flow of both the taxedeand the tax-exempt sectors by convention, all earnings net of real investment

    expenditures are paid out to households. D equals the household sectors depositshin the financial sector, earning a monetary rate of return of r plus perhaps variousdnon-cash service benefits. A in contrast represents holdings of domestic govern-h

    d fment bonds, B , and foreign financial securities, B , net of loans from theh h

    d ffinancial sector, L : A 5B 1B 2L these holdings earn an average pre-taxh h h h h

    ~rate of return of r. Finally, E represents net purchases from foreigners of corporate27

    equity issued by domestic firms.

    The cash-flow of the taxable domestic business sector can be represented by:

    Q 1 r D 1 S 5 (W 1 W ) 1 F 1 rL 1 I1 T 1 (p1p 1 p 2p ). (7)d d d d f

    Here, Q represents cash sales, S measures government subsidies to firms, while

    r D equals earnings on bank deposits. The payroll, W1W , consists of wage andd droyalty payments, W, to domestic residents and payments W to foreign residents.dAs before, F represents expenditures on financial services, L equals loans from the

    financial sector, and T equals cash-flow and other business tax payments. I

    represents all real investments made that period. The residual profits, p1p 1p 2d dp, consists of the profits accruing to the domestic household sector, p, the profitsfgoing to foreign owners due to their direct investment, p , payments to foreignersd

    27Corporate bonds are virtually unknown in Denmark.

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    184 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    on their portfolio investment in domestic firms, p , minus the profits received byddomestic firms on their subsidiaries abroad, p.f

    28The cash-flow of the financial sector equals:

    d fr(B 1 B 1 L 1 L ) 1 (F1 F ) 5 r (D 1 D ) 1 W 1 R 1 T 1 Ie e h h d h e e e e

    1 (p 1p 2p ). (8)e de fe

    Here, R and I equal non-durable and durable purchases of real inputs from thee etaxable sector, while T refers to unrebated value-added taxes paid on theseepurchases. The definitions of the other variables correspond to those above, with

    the subscript e referring to the exempt sector.

    Finally, the cash-flow constraint of the government equals:

    d d~T 1 T 1 T 1 T 2 T 1 B 5 (S 1 S ) 1 r(B 1 B 1 B ) 1 G 1 I . (9)h e d f h h e d g

    As defined above, T 1T1T equals all tax payments by domestic households andh efirms. But some of these tax payments, T go to foreign governments, while somefforeign firms and individuals make tax payments, T , to the domestic government.d

    Similarly, B represents foreign holdings of domestic government bonds. FinallydG 1I equals current government expenditures on non-durables and investmentggoods.

    Combining all of these cash-flow constraints, we find that

    (Q 2 I1p 1p 1 W) 2 (p 1p 1 W ) 5 (C1 C 1 H1 R 1 I 1 Gf fe f d de d f e ef f f~ ~ ~1 I ) 2 [r(B 1 B 2 B ) 2 p ] 1 (T 2 T ) 1 (B 1 E2 B ). (10)g h e d d f d h d

    The first term in parentheses on the left-hand side of Eq. (10) in theory equals the

    tax base under a cash-flow income tax on firms combined with a personal tax on

    payments deductible under the cash-flow tax (e.g. wage and royalty payments).

    Note that foreign-source as well as domestic-source earnings accruing to domestic

    residents should in principle be included in this tax base.

    The second term on the left-hand side is a correction term for reported taxable

    earnings going to foreigners due to their direct investment in the domestic

    economy these funds are not available to finance domestic consumption. Thereis some question, though, how to interpret the observed cash flow of the domestic

    subsidiaries of foreign multinationals. This cash flow can in principle include not

    only the earnings of foreign owners but also the non-wage compensation of

    domestic employees that is retained within the firm and paid out later in deferred

    compensation or stock options. Only the former component is unavailable to

    28For notational simplicity, new purchases/sales of financial assets are all listed in the household

    sector, and foreign portfolio investment in the domestic financial sector is ignored.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 185

    finance domestic consumption. For simplicity, we will assume that the observed

    cash-flow of domestic subsidiaries of foreign firms results entirely from the

    non-wage compensation of domestic employees, in which case any earnings of

    foreign residents has been paid out in a deductible form, e.g. through royalty29

    payments or transfer pricing.

    The first term on the right-hand side of Eq. (10) should approximate the tax30

    base under a destination-based value-added tax. Some purchases of domestic

    consumer goods will be done by non-residents, however, and are not financed by

    the income flows included in this equation. We will subtract off estimates of the

    size of these purchases by non-residents, in order to focus on the activity of

    domestic residents. In theory, the observed value-added tax base should include

    purchases abroad by domestic residents, C. Since the financial sector is assumedfto be exempt, inputs it purchases from other sectors (R 1I ) remain subject to tax.

    e eGovernment expenditures, G 1I , in Denmark are sometimes subject to VAT andgsometimes not. Where such expenditures are not included in the observed tax base,

    they will be added in separately.

    Ignoring evasion, the tax base for an income tax and a destination-based VAT

    differ because of the three residual terms. First, consumption expenditures can be

    financed in part from the return to financial assets owned abroad by domestic

    residents, whereas part of the return taxable under an income tax is income

    accruing to foreign portfolio investors in domestic business and government

    financial assets so is not available to finance domestic consumption. Second,

    earnings of domestic individuals can be used in part to finance increasedownership of foreign assets or the purchase of domestic assets currently owned by

    foreigners, rather than for current consumption. Finally, some domestic earnings

    are lost through tax payments to foreign governments so are no longer available to

    finance domestic consumption, while some government revenue arises from

    domestic taxes paid by foreign residents.

    Evasion activity implies, however, that Eq. (10) will not be satisfied in the data.

    To begin with, the observed cash-flow tax base will likely be smaller than the

    theoretically correct measure due to avoidance of taxes on foreign-source income.

    Similarly, the observed tax base for the destination-based VAT will be smaller than

    the theoretically correct measure due to cross-border shopping, while undergroundactivity will affect both measures.

    29To the extent that the reported cash-flow of foreign subsidiaries does include income accruing to

    foreign residents, we overestimate the reported amount of labor income and so underestimate the

    relative amount of evasion under the income tax.30

    Note that housing and consumer durables can be treated in either of two ways under such a tax.

    Either consumption services arising from use of these goods can be taxed period by period or else

    expenditures on the purchase of these goods can be taxed at the purchase date. In present value, the two

    methods are equivalent. Denmark uses the latter method.

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    186 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    3.2. Measurement of the income tax base

    The tax base described above for the income tax consists of taxable wage and

    salary income from all but the financial sector plus a measure of the cash-flow ofDanish non-financial firms (measured net of wage and salary payments). We

    collected data from a wide variety of sources to measure the size of this tax base

    for 1992. Details of the calculations are in Appendix B.

    The basic approach we used is as follows: To begin with, we collected data on

    the wage and salary income received by Danish residents from the non-financial

    sector that was paid out it a form deductible that year from the measure of

    business income. On net, we found that individuals received 427.9 billion Danish

    kroner in wages and salaries in 1992.

    To measure the cash-flow of Danish non-financial firms, we started with the

    reported taxable profits of these firms, and replaced depreciation deductions with a

    deduction for new investment, replaced the current deductions for goods with-

    drawn from inventories with a deduction for new purchases added to inventories,

    and eliminated all deductions/ income from financial assets, primarily consisting of31

    deductions for interest payments. After several further corrections described in

    the Appendix, our measure of the cash flow of non-financial Danish firms equals

    107.7, implying that aggregate taxable labor income in Denmark in 1992 equaled

    535.6 billion kroner.

    3.3. Measurement of the value-added tax base

    Given that the 25% VAT collected 81.1 billion Danish kroner in 1992, we

    started with an estimate of the value-added tax base of 324.4. In Appendix B, we

    describe a variety of corrections we needed to make, given the differences between

    the actual tax base and the comprehensive base described in Eq. (10). The key

    corrections were the inclusion of value-added in the currently exempt sectors and

    the inclusion of currently exempt forms of government expenditures. After these

    various corrections, we end up with an estimate of 488.7 for a comprehensive

    value-added tax base.

    3.4. Measurement of the three correction terms

    According to Eq. (10), labor income will differ from value-added because of

    three separate correction terms. To begin with, individuals can finance consump-

    tion in part from their net holdings of assets abroad. According to the current

    account statistics provided by the Danish Central Bank, net interest and dividends

    receipts in Denmark in 1992 equaled 234.2 billion kroner.

    31As a result, though, we do eliminate the return to some forms of labor income, e.g. sales of ideas to

    foreigners, that show up in the data as capital gains on financial assets.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 187

    In addition, current income can be spent not only on current consumption and

    investment in productive assets but also on the net acquisition of financial assets

    abroad. According to data from the Danish Central Bank, in 1992 there was a net

    capital outflow (ignoring net foreign direct investment, which is included in otherterms in Eq. (10)) of 10.2 billion kroner.

    Finally, we need to measure the tax payments made by foreigners to the

    domestic government minus the taxes paid abroad by domestic residents. We32

    calculated, using an average VAT and excise tax rate for Denmark of 33.1%, that

    foreign consumers paid about 5.7 billion kroner in VAT and excise taxes out of

    total tourist expenditures in Denmark of 22.9 billion. In 1992 Danish consumption

    expenditures (gross of VAT) abroad equaled 23.0 billion kroner. Taking a

    weighted average of the VAT and excise tax rates in those countries that are

    destinations for Danish tourists and cross-border shoppers, we estimate that they

    faced an average VAT and excise tax rate similar to the German one of 21.1%,

    implying tax payments abroad equivalent to 4.0 billion kroner. On net, therefore,

    Danes receive an extra 1.7 billion kroner due to cross-border tax payments.

    Danish subsidiaries abroad and foreign subsidiaries in Denmark will also be

    paying some taxes. As noted earlier, however, their reported taxable income could

    include income accruing but not yet paid out to domestic employees as well as

    income accruing to foreign residents. We have presumed that the bulk of the

    income accruing to foreign residents has been paid out in a tax-deductible form,

    e.g. through transfer pricing, so make no further correction for taxes paid by these33

    firms.Taken together, the three correction terms imply that the accounting figure for

    labor income should exceed that for value-added by 42.7 billion kroner.

    3.5. Implications for evasion of income vs. value-added taxes

    As shown above, the base for a comprehensive value-added tax, net of sales to

    foreigners, would have equaled 488.7 billion kroner in 1992. Given this figure and

    given the data on the three correction terms in Eq. (10), ignoring evasion the

    reported labor income should have equaled 488.7142.75531.4 billion kroner. In

    contrast, the actual figure for labor income that we calculate would have beenreported for tax purposes under a cash-flow tax equaled 535.6 billion kroner. The

    difference between these two figures is 4.2 billion kroner, so evasion under the

    32In Lassen and Nielsen (1996) the average effective tax burden on consumption in Denmark and

    other EU countries is calculated, using the method suggested by Mendoza et al. (1994). The result of

    this calculation is a tax burden in 1992 of 33.1% in Denmark and 21.1% in Germany. These figures are

    used in the following.33

    We did attempt to calculate the difference in the size of the corporate and withholding tax

    payments by foreign subs in Denmark relative to those paid by Danish subs abroad, to see how

    important this assumption was. The difference in the two figures was essentially zero, eliminating any

    ambiguity from this source.

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    188 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    income tax is estimated to be 4.2 billion kroner less than the sum of tourist

    expenditures and evasion under the value-added tax.

    What are the implications of the above calculations for the optimal relative tax

    rates on income vs. value-added, given the model described in Appendix A?According to this model, observed labor income should equal L(12f )(12f),Lwhere f is the evasion rate through underground activity. Given our data on labor

    income, this implies that

    L(1 2 f )(1 2 f) 5 535.6. (11a)L

    Also according to the model, observed consumption should equal [C20.5 fL(1 1

    N)] (12a)(1 2f ), implying given the data on consumption thatC



    f )[C2



    488.7, (11b)C

    where the tax factor N is defined in Eq. (A2) in Appendix A.

    As mentioned above, in 1992 Danish tourist expenditures abroad, including

    cross-border shopping, amounted to 23.0 billion kroner (19.0 billion net of foreign

    taxes). In addition, the Danish Institute of Border Region Research estimated that

    cross-border shopping in 1991 on the part of Danes in Germany amounted to some

    4.1 billion kroner, including German indirect taxes. Updating this figure to 1992,

    having in mind a stronger pressure on the DanishGerman border a year later, one

    may set the figure at 5.0 billion kroner. These two estimates imply that

    a(1 1t ) C2 0.5fL(1 1 N) 5 18.0, (11c)f gf


    (1 2a)f C2 0.5fL(1 1 N) [1 1 (t1t )/2] 5 5.0. (11d)f gC f

    Given that 19.0 billion kroner escapes domestic value-added tax by being spent

    abroad, and that evasion under the value-added tax exceeds that through income

    shifting under the income tax by 4.2 billion kroner, we infer that evasion of labor

    income through income shifting must equal 14.8 billion kroner. Using Eq. (A1) in

    Appendix A, and simplifying, this implies that

    (1 2 f)f L[1 2 (t1 t )/2] 5 14.8. (11e)L f

    Finally, the Rockwool Foundation Research Unit in Denmark has estimated (cf.

    Mogensen (1994), p. 140) that the number of hours in the black economy

    corresponds to about 4.6 percent of the total registered number of hours in

    Denmark. This implies that

    f/[(1 2 f)(1 2 f )] 5 0.046 (11f)L

    The six equations (11af), along with the definition of N and data on the tax rates

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 189

    Table 1

    Estimates of the extent of tax evasion in Denmark, 1992

    t 50 t 50.25f f

    f 0.042 0.042

    f 0.037 0.045Lf 0.008 0.008CL 581.1 585.5

    C 523.8 523.8

    a 0.029 0.029

    N 0.325 0.322

    X 1.724 3.529

    Note: X stands for the optimal ratio of value-added to income tax rates, divided by the actual ratio, i.e.

    X;[((t* /t*)/(t/t))].

    34t, t, t, and t are sufficient to solve for the six values: L, C, f, f , f , and a. Thef f L C resulting estimates are reported in Table 1.

    It is normally assumed that the shadow economy has a smaller size in Denmark

    than in most other countries. According to the estimates in Table 1, evasion of

    consumption and labor income taxes through international channels likewise is a

    limited phenomenon.

    The estimates for the extent of evasion can then be used to infer the optimal

    relative use of value-added vs. income taxes in Denmark, using Eq. (5). Based on

    the figures in Table 1, we find thatt* t] ]5 1.72S D,t* t

    suggesting that more weight should be put on the value-added tax relative to the35

    income tax given the existing evasion opportunities in Denmark. This result is

    driven solely by the implications of the tax structure for evasion, and does not take

    into account many other considerations affecting the choice of income vs.

    value-added taxes.

    4. Conclusions

    In recent years, there has been substantial concern about increasing income tax

    evasion as economies become more open, due in particular to the greater ease of

    34As mentioned in fn. 32 above, the VAT and excise tax burden in Denmark and Germany are

    estimated in Lassen and Nielsen (1996) to be 33.1% and 21.1%, respectively. Further, we calculate that

    the average marginal tax rate on labor income, weighting by individuals labor income, equaled 58%,

    while we initially set t equal to zero. Below, an alternative value of t of 25% is also investigated.f f35

    Inserting the alternative value of t of 25% reinforces the conclusion that more weight should bef

    put on value-added taxes. See Table 1.

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    190 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    capital flight and transfer pricing. Similarly, use of the value-added tax has been

    limited by fears that domestic consumers will evade the tax by shopping abroad.

    The main objective of this paper has been to measure the amounts of evasion that

    occur under each tax using detailed data from Denmark for 1992. The analysis isbased on comparing the observed labor income tax base with the figure that would

    be forecast based on the economys aggregate cash-flow constraint given observed

    consumption expenditures under the VAT and observed accounting figures for asset

    accumulation. While true accounting data on income and consumption would

    satisfy this accounting identity precisely, the figures on income and consumption

    reported for tax purposes will each be too small due to evasion. This procedure

    allows us to measure the difference in the amounts of evasion under the two taxes.

    The Danish government has measured directly the amount of evasion of the

    value-added tax due to consumption expenditures abroad, allowing us to combine

    their figure with our estimate to infer the amount of evasion under the income tax

    due to income being shifted abroad.

    The data suggest that evasion rates under each tax were relatively modest.

    Despite much focus on cross-border shopping between Denmark and Germany,

    especially before the launching of the Internal Market in EU, only about 0.8% of

    consumption evaded tax through cross-border shopping. In contrast, we estimate

    that about 4% of labor income was lost due to income shifting. For purposes of

    comparison, the size of the underground economy seems to be about 4.2% of the

    overall economy.

    In the paper, we also develop a theoretical model to examine the choice ofincome vs. value-added tax rates that would minimize the excess burden resulting

    from evasion activities. Based on this theory in conjunction with computed

    evasion rates, we forecast that evasion costs could be reduced by increasing the

    VAT rate relative to the income tax rate, at least given the situation prevailing in

    1992 in Denmark.


    An earlier draft of this paper was presented at a conference in Munich on

    Competition or Harmonization? during October 30November 2, 1995. The

    first author would like to thank the Economic Policy Research Unit at the

    Copenhagen Business School and N.S.F. Grant No. SBR-9422589 for financial

    support during the writing of this paper. We would like to thank the participants at

    the conference, Pierre Pestieau, Chi-Wa Yuen, Esben Dalgaard, Emil Sunley,

    seminar participants at NYU and the University of Michigan, and the referee of

    this paper for helpful comments, and David Dreyer Lassen for very able research

    assistance. The activities of EPRU are financed by a grant from The Danish

    National Research Foundation.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 191

    Appendix A

    Optimal taxes in the presence of underground activity and tourism

    In the underground economy, the use of cash transactions facilitates the evasion

    of both income and value-added taxes. While a dollar of pre-tax labor income

    otherwise generates less than one dollar of consumption, in the underground

    economy we assume no taxes are due so that a dollar of labor income generates a

    full dollar of consumption.

    Denote the fraction of labor effort which individuals allocate to the underground

    economy by f. This underground activity imposes real costs on evaders of 0.52

    Lf /e. As a result, only fL (1 20.5 f/e) on net is available for shadow

    consumption. We assume that tourism abroad is unaffected by domestic tax rates

    and constitutes a fixed share a of remaining consumption C2fL(1 20.5 f/e). The

    residual, (12a)[C2fL (1 20.5f/e)], is split between cross-border shopping and

    consumption at home in the same way as in the text.

    With this information, the individuals budget constraint now equals

    [C2 fL(1 2 0.5f/e)][a(1 1t ) 1 (1 2a)((1 2 f )(1 1t)f C

    1 f (1 1t )(1 1 0.5f /c))]C f C

    5 (1 2 f)L[(1 2 f )(1 2 t) 1 f (1 2 t )(1 2 0.5f /d)] (A1)L L f L

    The individuals optimal values of f and f remain the same as before, whereasC Ltheir optimal value of f equals (12N)e, where

    21 2 t1 0.5d9(t2 t )f

    ]]]]]]]]]]]]N; . (A2)2(1 2a)[1 1t2 0.5c9(t2t ) ] 1a(1 1t )f f

    We may use this to rewrite the budget constraint in a simpler way as

    C5 NL(1 2 f) 1 fL(1 2 0.5fL /e), (A19)

    As seen from collecting the tax payments in Eq. (A1), the governments budget

    constraint now equals2

    G 5t(1 2 f )(1 2a)[C2 ( f2 0.5f /e)L] 1 t(1 2 f )L(1 2 f). (A3)C L

    As before, consider the effects of an increase in t and a decrease in t chosen so as

    to leave the individuals incentives (and behavior) unchanged. Substituting the

    optimal value of f into equation (A19), we see that the individuals choice of labor

    supply depends solely on N. The combined tax change is therefore designed to

    leave N unchanged, so the drop in t needed to offset a rise in t satisfies

    1 2 c9(t2t )t f] ]]]]5 2 (1 2a)N . (A4)

    t 1 2 d9(t2 t )f

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    192 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    At the optimal tax rates, this combined change in tax rates should leave

    government revenue unchanged. Differentiating revenue with respect to t, and

    allowing t to adjust according to Eq. (A4), we find that

    t2](1 2a)(1 2 2c9t1 c9t )[C2 L( f2 0.5f /e)] 1 (1 2 2d9t1 d9t )L(1 2 f)f f t

    5 0.

    Substituting for C from equation (A19), for t/t from Eq. (A4), using the

    equilibrium condition that f5(1 2N)e, and simplifying we find that the optimal

    tax rates continue to satisfy Eq. (4).

    Appendix B

    Details of the measurement of labor income

    The Ministry of Taxation reports the following figures for personal labor income36

    for 1992:

    Net wages, transfers, and pension benefits 579.5

    Other labor income 10.0

    Minus employee pension contributions 214.1]]

    Wages plus transfers and net pension receipts 575.4

    The intended measure of wage income includes as wage income the same figure

    reported by firms that year as a wage deduction. As a result, the deferral of

    reported personal income that occurs through pension plans needs to be undone.

    We therefore add to the above figure the total pension contributions (by employers

    as well as by employees), compiled from various financial institutions:

    Employee and employer pension contributions 29.7

    and subtract

    Total pension benefits 14.8]]

    to give

    Wages plus transfers 590.3

    36All figures represent billions of 1992 Danish kroner.

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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 193

    To measure wage income alone, we exclude taxable government transfers:

    Minus transfers 2137.7

    In order to impose the same tax treatment of the financial sector under both the

    income tax and the value-added tax, we also need to subtract off the wage income

    from the financial sector:

    Minus wages in the financial sector 2 24.7]]]

    to yield a measure of total taxable wage income.

    Taxable wages 427.9

    We next measured the real cash-flow of Danish firms. Given the available Danish

    data, this process turned out to be somewhat complicated. The central source of

    data comes from the company form which is issued by the Department of

    Taxation, Central Customs, and Tax Administration, and is filled out by about

    78,000 Danish firms. These forms are not filed by firms traded on the Danish stock37

    exchange, by firms with low enough revenue, or by firms in several selected38

    industries. Within each of seventy different sectors among the covered industries,

    we used data on the ratio of aggregate accounting depreciation in that sector to

    accounting depreciation among the 78 000 firms within that sector to forecast thecash-flow figures for the covered industries as a whole. The first column reports

    the resulting figures for corporations and partnerships, whereas the last column

    reports equivalent figures for personally owned firms:

    Corp1Part Other

    Taxable income 31.8 33.2

    Plus net financial expenditures 17.1 14.8

    Plus depreciation deductions 27.1 12.4

    Plus inventory depreciation 3.0 0.6]] ]]

    Cash flow1I (covered) 79.0 61.0

    These figures measure the cash-flow only from the industries covered by the

    company form. For the remaining industries, we used accounting data to

    measure accounting surplus (or gross operating surplus) before depreciation

    37Only 240 firms had shares traded on the Danish stock exchange and the vast majority of these firms

    were small or medium-sized.38

    The main uncovered sectors are agriculture, horticulture, fur farming, agricultural services,

    forestry, fishing, fish farming, lignite/ oil/ natural gas production, electricity and gas supply, district

    heating, water supply, mail services, and telecommunications.

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    194 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    deductions, yielding an estimate for the cash-flow of these uncovered industries39


    Cash flow1I (uncovered) 55.9

    The observed cash flow is measured net of expenditures on financial services,

    whereas the tax base appearing in Eq. (10) does not include a deduction for F.

    Undoing this deduction:

    Expenditures on financial services 6.3

    One complication is that these reported cash-flow figures are net of production

    taxes of 12.4, labor market contributions of 1.9, and include production subsidiesof 23.7. Yet as seen in Eq. (10) the desired measure of labor income is before any

    taxes and subsidies. We therefore include the following correction:

    Minus net government subsidies 29.4

    Finally, we need to subtract off new investment expenditures in the non-financial

    business sector. According to the National Accounts, fixed gross investment in the

    private non-financial sector equals 87.3, while inventory net investment equals


    Minus new investment 2 85.1]]

    Combining the above figures we find that aggregate business cash flow equals

    Cash flow 107.7.

    This measure should in principle include the cash-flow of foreign subsidiaries of

    domestic firms. However, Denmark by law generally exempts this foreign-sourceincome, and we assume that little if any revenue could be collected from these

    subsidiaries in any case. There is also a question of how to treat the income

    reported by subsidiaries of foreign firms located in Denmark. We assume that this

    income represents the earnings of Danish residents not paid out in wages and40

    salaries, in which case no correction is needed.

    39This figure includes a correction for value-added taxes paid on purchases of intermediate inputs,

    amounting to 3.8 billion kroner.40

    The aggregate income of these subsidiaries was 1.8 billion kroner, so this assumption makes little


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    R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197 195

    Details of the measurement of value-added

    The actual value-added tax base under 1992 law was 324.4 billion kroner. Our

    desired measure of value added differs from the measure under 1992 for fourdifferent reasons.

    (1) The actual tax base is measured gross of excise taxes.

    We therefore needed to subtract off

    Excise taxes 32.6

    (2) The actual base omits value-added in tax-exempt sectors and omits consump-

    tion expenditures in zero-rated sectors.

    Based on Ministry of Taxation data, we estimate that including all of these

    sectors other than the financial sector in the tax base would result in an increase in

    the base of

    Value-added in exempt1output in zero-rated sectors 22.2

    (3) The current figure does not include all government expenditures on goods and


    The initial figure for the value-added tax base includes 57.1 billion kroner of

    expenditures on goods and services by the government, but only a few selectedunits of the government are subject to value-added tax under current law. In order

    to include appropriately all government expenditures on goods and services, we

    measured total government expenditures on goods and services and then added to

    the value-added tax base the difference between this figure and 57.1. Available

    data report the following figures for government expenditures:

    Wages 158.0

    Purchases of intermediate goods 67.3

    Gross investment 13.8

    Transfers abroad (net of subsidies from the EU) 9.9Minus included government expenditures 257.1


    Correction for exempt government expenditures 191.9

    (4) Expenditures by foreigners in Denmark are included in the observed figure.

    According to the Central Bureau of Statistics, foreigners spent 22.9 billion

    kroner on goods and services in Denmark, expenditures that include value-added

    and excise tax payments. Given an average effective VAT and excise tax rate of

    33.1% (cfr. fn. 32 above), foreign consumption expenditures net of tax payments

    equaled 17.2 billion kroner. Since our desired measure would include only

    expenditures by domestic residents, we need the following correction:

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    196 R.H. Gordon, S.B. Nielsen / Journal of Public Economics 66 (1997) 173197

    Minus consumer purchases by foreigners 2 17.2]]

    Collecting terms, we find that the base for a comprehensive value-added tax wouldequal:

    Value-Added 488.7


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