metadata: authors: 0: author: Auriol,Emmanuelle
1: author: Warlters,Michael Ian
count: Africa
docna: 0: docna: The marginal cost of public funds in Africa
docty: Policy Research Working Paper
subtopic: Tax Administration,Macro-Fiscal Policy,Taxation & Subsidies,Economic Adjustment and Lending,Tax Law,Labor Markets,Disability,Public Sector Economics,Services & Transfers to Poor,Economic Assistance,Access of Poor to Social Services,Public Finance Decentralization and
            Poverty Reduction
abstracts: cdata!: The authors use a computable general
            equilibrium model to estimate the marginal cost of public
            funds (MCF) for taxes on domestic goods, exports, imports,
            capital, and labor in 38 African countries. The resulting
            MCF estimates provide directions for tax reform in Africa.
            The authors investigate the MCFs of hypothetical taxes in
            the informal sector and the impact of administrative costs.
            Finally, they investigate the relationship between MCF
            dispersion and measures of tax system inefficiency.
repnme: repnme: The marginal cost of public funds in Africa
display_title: The marginal cost of public funds in Africa
listing_relative_url: /research/2005/08/6200534/marginal-cost-public-funds-africa
topicv3: Informal Sector m1326258 1168,Tax and Revenue Policy and Administration
            m1327008 720,Social Assistance m1327201 1466,Taxation m1327615 1121,Tax Simplification m1504614 2527
publishtoextweb_dt: 2010-07-01T00:00:00Z
no_of_pages: 39
author_keys: 0: author_key: 901922
1: author_key: 142680
model_extractions: WPS3679

# The Marginal Cost of Public Funds in Africa

Michael Warlters† and Emmanuelle Auriol‡

## JEL Classification Numbers: H21, H24, H25, H26, H29

## World Bank Policy Research Working Paper 3679, August 2005

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._ †World Bank, email: mwarlters@worldbank.org ‡ARQADE and IDEI, Toulouse.
# **1 Introduction**

What social rate of return should public infrastructure projects be required to achieve in Africa? What is the next challenge in the reform of African tax structures? The answers to these questions require knowledge of the marginal cost of public funds (MCF). If a project does not yield a social return greater than the MCF, it is not worth having. Holding revenue constant, welfare can be increased by reducing taxes with high MCFs and increasing taxes with low MCFs, so estimates of MCFs provide directions for reform of tax structures.

The central role of the MCF in these important public policy issues is well known. So it is surprising that there are few empirical estimates of MCFs. Table 1 summarizes existing estimates. We know of only three papers in which estimates of the MCF have been derived for developing countries. We know of only one African country, Cameroon, for which the MCF has been estimated. Moreover, for methodological reasons existing estimates are not all truly comparable.

Perhaps the major reason for this relative paucity of MCF estimates has been the amount of data required and the time expense of creating and calibrating the computable general equilibrium (CGE) models used for estimation. CGEs are required because real tax systems are complex, and because it is necessary to take account of multiple interactions within tax systems.<sup>1</sup> Thus, the challenge as we have conceived it is to develop a simple CGE model that can be calibrated with little more than national accounts data, and which can be used to provide consistent estimates comparable across countries. To be useful for tax policy analysis, the model should take account of the major classes of taxes in African countries: taxes on domestic goods, exports, imports, corporate income tax, and personal income tax. On average, in the Sub-Saharan African countries that we examine, these taxes represent respectively 25%, 3%, 35%, 13%, and 14% of tax revenue, with the remaining 10% coming from other sources.<sup>2</sup> A key requirement for realism is that the model should take account of the existence of informal sectors, which occupy a larger part of the economy in Africa than elsewhere. For example, Schneider & Enste (2000) report the shadow economy occupied on average 15% of GDP in OECD countries in 1990, but 27% in Botswana and 76% in Nigeria.<sup>3</sup> We might suspect that in countries with larger informal sectors, it is easier for economic agents to shift from formal to informal activity. Greater substitutability would lead to higher marginal costs of taxation on formal activity. The presence of an informal sector has been shown to have a noticeable

> 1To provide the intuition for the effects of key parameters, analytical models with minimal data requirements were used in initial development of the theory (e.g. Stuart (1984), Mayshar (1991), Snow & Warren (1996)). But there are limits to the complexity of models that can be solved analytically.

> 2Eighteen countries in our sample do not use export taxes. Among the twenty countries that do use them export taxes constitute 7% of tax revenue.

> 3These figures are estimated using physical input methods.

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effect on MCF estimates in Canada.<sup>4</sup> In addition to the economic effect of informal sectors, including informal sectors avoids a calibration problem. CGE models have sometimes applied ‘effective’ tax rates, calculated as tax revenues divided by sector size. This results in low modelled tax rates. Effective tax rates provide an average between taxpayers who pay tax at something like the legal rate, subject to some under-reporting, and informal producers or consumers who pay no tax. Effective tax rates underestimate the marginal tax rate incurred by those who actually pay tax. Models using effective tax rates are thus likely to underestimate MCFs.<sup>5</sup> Our paper makes several contributions to the literature on MCFs. The first is the development of a simple general equilibrium model that can handle taxes on the five major tax classes, takes account of the existence of informal sectors, can be calibrated with little more than national accounts data, and can be easily reproduced by other researchers for other countries. After a brief review of the existing literature in section 2, we present the model in section 3. It is inspired by the minimal data requirements of the ‘1-2-3 model’ of Devarajan, Go, Lewis, Robinson, & Sinko (1997). The basic 1-2-3 model has one country with two producing sectors and three goods: a domestic good, exports and imports. This model is extended to include production of an informal good, and four factors of production: formal capital, informal capital, formal labor and informal labor. Our definition of an informal good or factor is simply one on which no tax is paid.

Section 4 contains the paper’s second important contribution: application of the model to produce estimates of MCFs for taxes in 38 African countries, vastly increasing the number of developing countries for which MCF estimates exist. Sensitivity testing of the model reveals which elasticities are the most important in determining MCF magnitudes, and suggests that our base case estimates are reasonably robust for purposes of tax reform.

The paper’s third innovation, presented in section 5 is an investigation of the

> 4Fortin & Lacroix (1994) suggest the informal sector accounts for around 0.02-0.05 of their MCF estimates of 1.39-1.53 for labor taxation in Canada. They note that although small, the impact of the informal sector increases rapidly with the level of the marginal tax rate. The importance of the informal sector when analyzing taxation in developing countries is also emphasized in other settings in recent papers by García Peñalosa & Turnovsky (2005) and Emran & Stiglitz (2005).

5It seems that the models used by Devarajan, Suthiwart-Narueput & Thierfelder (2001) apply ‘effective’ tax rates. For example their Cameroon model applies tax rates of 0.7% for food and forestry, 2.5% for intermediate goods, 3.4% for construction, 6% for services, 7.4% for food and consumption, and 19.1% for cash crops. We do not have access to the legal tax rates in force at the time the Cameroon model was created, but the current VAT rate (which has replaced the previous system of sales taxes) is 18%, suggesting that effective tax rates were indeed used in their model. The relatively high effective tax rate for cash crops may be explained by noting that cash crops are largely exported. Exports tend not to escape taxation, so the effective tax rate approximates a revenue-weighted average of legal tax rates.

2
<u>Table 1: Selected MCF Estimates</u>

|Country|Tax type|Estimate|Source|
|---|---|---|---|
|Australia|Labor|1.19-1.24|Campbell & Bond (1997)|
|Australia|Labor|1.28-1.55|Findlay & Jones (1982)|
|Australia|Capital|1.21-1.48|Diewert & Lawrence (1998)|
|Australia|Capital|1.15-1.51|Benge (1999)|
|Bangladesh|Sales|0.95-1.07|Devarajan et al. (2001)|
|Bangladesh|Import|1.17-2.18|Devarajan et al. (2001)|
|Cameroon|Sales|0.48-0.96|Devarajan et al. (2001)|
|Cameroon|Import|1.05-1.37|Devarajan et al. (2001)|
|Canada|Commodity|1.25|Campbell (1975)|
|Canada|Labor|1.38|Dahlby (1994)|
|Canada|Labor|1.39-1.53|Fortin & Lacroix (1994)|
|China|Sales|2.31|Lafont & Senik-Leygonie (1997)|
|India|Excise|1.66-2.15|Ahmad & Stern (1987)|
|India|Sales|1.59-2.12|Ahmad & Stern (1987)|
|India|Import|1.54-2.17|Ahmad & Stern (1987)|
|Indonesia|Sales|0.97-1.11|Devarajan et al. (2001)|
|Indonesia|Import|0.99-1.18|Devarajan et al. (2001)|
|New Zealand|Labor|1.18|Diewert & Lawrence (1994)|
|Sweden|All taxes|1.69-2.29|Hansson & Stuart (1985)|
|United States|All taxes|1.17-1.33|Ballard, Shoven & Whalley (1985)|
|United States|Labor|1.21-1.24|Stuart (1984)|
|United States|Labor|1.32-1.47|Browning (1987)|
|United States|All taxes|1.47|Jorgenson & Yun (1990)|
|United States|Labor|1.08-1.14|Ahmed & Croushore (1994)|

3
marginal cost of raising funds in currently informal sectors, and the effect of administrative costs on MCF estimates. We find that quite high levels of administrative costs would be justified to extend taxation to currently exempt informal sectors. Finally, in section 6 we examine the relationship between dispersion of MCFs for different tax instruments and the scope for welfare improving tax reform. We conclude in section 7.

# **2 The Marginal Cost of Public Funds**

The MCF measures the change in social welfare associated with raising an additional unit of tax revenue using a particular tax instrument: where ∆ _W_ is a monetary measure of the change in social welfare and ∆ _R_ is the change in tax revenue arising from a marginal change in a tax instrument. The change in social welfare is a measure such as the equivalent variation or change in consumer surplus, rather than the marginal excess burden. Useful reviews of the theoretical and empirical literature on MCFs can be found in Ballard & Fullerton (1992) and Devarajan et al. (2001).

One possible measure of the MCF in the presence of goods taxation is illustrated in Figure 1, in a simple two good partial equilibrium setting with fixed producer prices. Quantity units for the two goods are chosen so that producer prices for the two goods are equal to one. A marginal change in the tax on good 1 reduces consumer welfare by area _a_ , and increases compensated tax revenue by _a − b_ + _d_ , giving an MCF of _a/_ ( _a − b_ + _d_ ). If all the income released by the reduction in demand for good 1 is spent on good 2, the MCF can be approximated by where _ε_ 1 _<_ 0 is the compensated elasticity of demand for good 1.<sup>6</sup> This simple formula highlights key determinants of the MCF, but it does not deal with the full complexity of the tax system. For example, it does not capture distortions arising from taxation of intermediate goods or factors, and it does not take into account how the marginal tax revenue is spent. Nor is the methodology underlying this formula the only, or indeed the most common, way of calculating the MCF.

Different measures of the MCF for the same tax instrument can be found occur according to: 6 See Browning (1976) for the approximation methodology for areas _a_ , _b_ and _c_ . The assumption that all income released from good 1 spending is spent on good 2 (eg. because there are only 2 goods) enables area _d_ to be measured as 1+ _<u>t</u>_ <u>2</u> _t_ 2<sup>(</sup><sup>_b_+</sup><sup>_c_).</sup> 4
Figure 1: Calculating the MCF <!-- Start of picture text --> @<br>@ @@<br>@@ D 1 0 @@@ D @2 1<br>@ D 2 0 @@<br>a @ @ @<br>1 + t 1 @ 1 + t 2 @<br>b @ d @@<br>@ @@<br>1 @ MC 1 1 @@ MC 2<br>c @ e @@<br>@ @@<br>q 1 1 q 1 0 q 2 0 q 2 1<br><!-- End of picture text --> A marginal increase in the tax on good 1, reduces compensated demand for good 1 from _q_ 1<sup>0to</sup><sup>_q_</sup> 1<sup>1.The consumer’s reduction in spending on good 1 liberates income to be spent on</sup> good 2, shifting the compensated demand curve for good 2, and increasing compensated demand for good 2 from _q_ 2<sup>0to</sup><sup>_q_</sup> 2<sup>1.The marginal change in welfare is (approximately) given</sup> by area _a_ , the change in compensated tax revenue is given by areas _a − b_ + _d_ . So a measure of the MCF of the tax on good 1 is _a/_ ( _a − b_ + _d_ ).

- The nature of the tax experiment conducted. Ballard & Fullerton (1992) identify two broad classes of theoretical analysis: ‘differential’ and ‘balanced budget.’ In differential analysis, one tax is marginally increased and another is decreased sufficiently to maintain the budget balance. The usual experiment is to increase a distortionary tax, and to reduce a lump-sum tax (return the revenue to consumers as a lump-sum). The income effects of the two tax changes cancel, leaving only substitution effects. Estimates of the welfare change, ∆ _W_ , depend on compensated elasticities, while the change in revenue, ∆ _R_ , can be equated with the actual lump-sum transfer. In balanced-budget analysis, one tax is marginally increased and the revenue is spent on a public project. Income effects are included in the analysis, and MCF estimates are derived using uncompensated elasticities. These are not the only possible measures. Wildasin (1984) proposed a measure in which the compensated change in welfare is divided by the compensated change in tax revenue rather than the actual change in tax revenue (the measure illustrated in Figure 1).

- The choice of numeraire. Håkonsen (1998) has proposed an alternative measure derived from the dual of the government’s optimal tax problem (maximize revenue subject to a given level of social welfare) that is invariant to the choice of numeraire.

- The attribution of some general equilibrium effects between benefit and cost. Consider a marginal tax increase that increases revenue by one dollar, before public spending occurs. Public spending could increase the tax base in

5
a second round effect (for example, building highways increases petrol tax revenue). If this second round effect is attributed to the MCF, the increase in revenue is greater than one dollar, and the MCF is accordingly reduced. But the second round effect could equally well be attributed to a measure of the marginal benefit of public spending. Mayshar (1991) proposed that all revenue effects of public spending should be incorporated in the benefits measure (MBF), rather than the MCF.

The consequence of this multiplicity of measures is that MCF estimates prepared using different methodologies are not comparable. Fortunately, Schöb (1994) has shown that standard MCF measures provide a valid basis for revenue-neutral tax reform, provided they are prepared using consistent methodologies (for example, with the same numeraire, with changes in welfare measured using the equivalent variation, and with public spending consisting only of lump sum transfers). For valid use in cost-benefit analysis, all revenue effects of public spending should be included in the MBF, and the MBF should be measured consistently with the MCF.

For tax reform analysis, estimates of the MCF for different tax instruments in the same country will commonly be prepared using consistent methodologies. For tax reform, the MCF can loosely be thought of as ordinal, rather than a cardinal measure. The levels of MCF estimates will depend on the estimation methodology, but these levels are not important in deciding directions for reform. What is important is which tax instruments have high MCFs and which have low MCFs.

Triest (1990) notes that MCF estimates are often made using producer prices as the numeraire, while benefits of public projects are usually calculated using consumer prices. Failure to adjust for the choice of numeraire could lead to wrong decisions. Care is required to ensure consistent comparisons when using the MCF in cost benefit analysis.

# **3 The Model**

Our model is formally set out in Appendix A. Setting aside investment for the moment, three final goods are produced in the country: _untaxed_ ( _U_ ), _domestic_ ( _D_ ), and _exports_ ( _E_ ). Four goods are consumed: _leisure_ ( _Z_ ), _untaxed_ , _domestic_ , and _imports_ ( _M_ ). Exports are not consumed directly. Instead they are used to purchase foreign exchange (at a constant exchange rate), which is used to purchase imports from the rest of the world. The representative consumer has endowments of leisure (which may be converted into labor), capital, and foreign exchange.<sup>7</sup> Investment occupies a large part of the economy in reality, so it needs to be incorporated somehow, although it serves no role in a static model. This is achieved

> 7The endowment of foreign exchange represents the trade balance. In Africa, this is financed by borrowing and foreign aid. In a static model borrowing has no purpose, so the endowment can be thought of as foreign aid.

6
in the model by creating an additional good, _investment_ ( _I_ ). In the model consumers derive utility by purchasing savings/investment. We set preferences as Cobb-Douglas over investment and all other goods, meaning that consumers devote a constant proportion of their incomes to savings/investment. On the production side of the economy, firms receive funds from sales of their production and from investment. These funds are spent on factors of production. Thus the production sectors are modelled as using factor inputs, to produce jointly a final good ( _untaxed_ , _domestic_ or _export_ ) together with _investment_ . Sector output is divided between the good and investment according to a constant elasticity of transformation function. By setting this elasticity equal to one (Cobb-Douglas), a constant proportion of each production sector’s total income is derived from investment.<sup>8</sup> The production goods use four factors of production: _formal capital_ ( _K_<sup>_f_</sup> ), _informal capital_ ( _K_<sup>_i_</sup> ), _formal labor_ ( _L_<sup>_f_</sup> ) and _informal labor_ ( _L_<sup>_i_</sup> ).<sup>9</sup> One consequence of including informal factors is that capital taxation results in a deadweight loss, even though the total supply of capital is fixed. Labor taxation also induces a deadweight loss as a result of substitution between formal and informal labor, in addition to the deadweight loss arising from substitution between labor and leisure.

Constant elasticity of substitution (CES) functions are used in all production and utility functions. The structure of these functions is set out in Figure 2. The first panel is the utility function, where utility ( _W_ ) is a CES function of _leisure_ , _investment_ , and a consumption good _C_ , and _C_ is a composite good produced by a CES function of _untaxed_ , _domestic_ , and _imports_ . The remaining panels are the production functions for _domestic_ , _export_ and _untaxed_ . The bottom parts of these diagrams represent the nested CES functions over the factors of production, with the top levels representing capital/labor substitution, and the bottom levels representing formal/informal substitution. The top parts of the diagrams represent the CET functions between the final good and investment. The relevant elasticities, used in robustness testing of the model, are labelled by sigma and tau and appropriate sub- and super-scripts.

Taxes are imposed on _domestic_ , _exports_ , _imports_ , _formal capital_ , and _formal labor_ . There are no untaxed traded exports or imports. This is not meant to imply that no smuggling occurs in African countries. Rather, the official figures for trade are based on customs data, which typically reflects taxed goods. An implication is

> 8The modelling differs from the standard 1-2-3 model. The standard model starts with the definition that _GDP_ = _C_ + _G_ + _I_ +( _E − M_ ) (see section 3.2), and combines _C_ + _G_ + _I_ into a single domestic good, giving _GDP_ = _D_ + _E − M_ . In the IMF figures used in this study government spending is already allocated to consumption or investment, so the original data are represented as _GDP_ = _C_ + _I_ + ( _E − M_ ). It would be simple to make the figures for investment disappear (since investment serves no role in a static model) by simply following the standard model. But it seems wrong to suppose that all investment goes toward domestic consumption goods, and that no investment goes into the production of export goods. We have thus included an explicit investment good, ensuring that the full value of GDP is reflected our model.

9 The _informal_ good uses only _informal capital_ and _informal labor_ .

7
Figure 2: Utility and Production Functions <!-- Start of picture text --> Utility Domestic Exports Untaxed<br>D ID E IE U IU<br>A A � � A A � � A A � �<br>A � τD A � τE A � τU<br>W A� A� A�<br>�A �A �A �A<br>�� AA σW �� AA σD �� AA σE �� AA σU<br>�� AA �� AA �� AA �� AA<br>Z C I KD LD KE LE KU i L i U<br>�A �C �C �C �C<br>�� AA σC �� CC σD K �� CC σD L �� CC σE K �� CC σE L<br>�� AA �� CC �� CC �� CC �� CC<br>U D M KD i K D f Li D L D f KE i K E f Li E L E f<br><!-- End of picture text --> that the _untaxed_ good is produced and consumed purely domestically.

Tax revenue received by the Government is transferred lump-sum to consumers. The experiment of increasing a distortionary tax rate and returning the revenue lump-sum can be interpreted in terms of both ‘differential’ and ‘balanced-budget’ analysis. Treating government expenditure as transfers rather than spending on public goods may approximate the reality of much government spending in Africa.<sup>10</sup> But as emphasized in section 2, for purposes of MCF estimates the realism of the modelled public expenditure is not as important as the fact that a consistent experiment is conducted across tax instruments.

The economic relationships in the model can be represented by a rectangular social accounting matrix (SAM) such as Table 2. The entries in the SAM are expressed as percentages of GDP at market value. All rows and columns sum to zero, reflecting a Walrasian equilibrium in which incomes equal expenditures. In the consumer’s column positive entries are endowments or factor incomes, negative figures are expenditures on goods, including investment. In the production columns, positive entries are the receipt of sales revenue or investment, and nega-

> 10In Uganda, Reinikka & Svensson (2002) found that schools received only 13% of the money paid by the central government for schools’ non-wage expenditures. Pritchett (1996) observes that growth accounting data can be reinterpreted supposing that total factor productivity growth is the same across all regions. Actual public investment in Africa could then be as little as 8.4% of the amount spent on capital. Rajkumar & Swaroop (2002) find that the effect on outcomes of marginal public spending on health and education is not significantly different from zero in countries rated as very corrupt or with ineffective bureaucracies. These studies suggest, by different means, that only a small portion of public spending in Africa arrives in projects with positive social rates of return.

8
<u>Table 2: SAM for Guinea-Bissau 2001</u>

|Co|nsumer|Untaxed|Domestic|Exports|Imports|Foreign|Govt|
|---|---|---|---|---|---|---|---|
|Untaxed|-48.20|48.20||||||
|Domestic|-5.67||4.93||||**0.74**|
|Exports||||24.60||**-27.21 **|**2.61**|
|Imports|**-57.71**||||53.41||**4.30**|
|Investment|**-18.92**|11.73|1.20|5.99||||
|Foreign Exchange|26.20||||-53.40|27.20||
|Formal Capital|2.36||-0.39|-1.97||||
|Informal Capital|48.36|-28.85|-2.93|-16.58||||
|Formal Labor|9.45||-1.58|-7.87||||
|Informal Labor|34.61|-31.08|-0.92|-2.61||||
|Capital Taxes|||-0.15|-0.77|||**0.92**|
|Labor Taxes|||-0.16|-0.79|||**0.95**|
|Transfers|9.51||||||-9.51|

Figures represent a percentage of GDP at market value. Positive figures are revenues received by the column from the row. Negative figures are payments made by the column to the row. Figures in bold are taken directly from national accounts, all others are calculated using the calibration process.

tive entries are payments to factors or factor taxes. In the government’s column, positive figures are tax revenues, the negative figure is the transfer to consumers. The ‘Foreign’ column represents the purchase of exports and the sale of imports by the rest of the world, using foreign exchange.

# **3.1 Data**

The data are given in Appendix B. Country-specific data comprise values of exports, imports and investment as a percentage of GDP, tax revenues for each of the five taxes, and legal tax rates for domestic goods, capital and labor. These data were obtained from IMF country report statistical annexes, for the most recent years available. The data also include labor-output ratios for _untaxed_ , _domestic_ and _exports_ that are, by assumption, common for all countries. The labor-output ratios are the averages of ratios derived from SAMs prepared by IFPRI for Malawi 1998, South Africa 1999, Tanzania 2001, Zambia 1995, and Zimbabwe 1991.

Data for tax revenue from sales of _domestic_ are derived from tax revenues from domestic VATs. In the absence of a VAT, general sales tax revenues are used. Corporate income tax revenues are interpreted as tax revenues from _formal capital_ . Personal income tax revenues are equated with revenues from _formal labor_ . Data for tax revenues from _exports_ and _imports_ are taken directly from the national 9
accounts.<sup>11</sup> We ignore classes of tax revenue that do not fall into any of the five tax revenue classes of the model. For the countries in our sample, such other taxes represent on average 10% of total tax revenue. We suppose that these other tax revenues are unaffected by shocks to the model’s five tax rates, implicitly treating them as lump-sum taxes.

Our model has only a single tax instrument for each good or factor. This rate is treated as both the average and the marginal tax rate. The inclusion of an untaxed domestic good and informal factors allows us to suppose that the average tax rates for _domestic_ , _formal capital_ and _formal labor_ can be equated with the legal tax rates. We implicitly assume that either the legal tax bill is paid entirely or it is not paid at all.

For _domestic_ , the legal tax rate used is the standard VAT or sales tax rate on domestic goods. In countries without a VAT, tax rates on intermediate goods cascade in the taxed price of final output. In such cases, the tax rate applied in the model is likely to be an underestimate of the marginal tax rate on many domestic goods.

Progressive personal income tax schedules provide multiple legal marginal tax rates for the tax on _formal labor_ . Where the average public sector salary is known or can be calculated, this salary is treated as a proxy for the average wage paid to formal labor, and is used to determine the relevant marginal tax rate. If the average public sector salary is not known a marginal rate of income tax from the middle of the legally specified tax rates is chosen. To this rate is added the rate of any payroll tax. The standard rate of corporate income tax is used for the tax on _formal capital_ .

For taxes on _exports_ and _imports_ , there are usually multiple legal tax rates, and there is no simple method of choosing between them to provide a single tax rate for the model. Instead we used average tax rates calculated as tax revenues divided by the tax base. To the extent that informal traded goods are represented in the official statistics for exports and imports, this procedure underestimates the average of multiple marginal tax rates.

# **3.2 Model Calibration**

The calibration process is formally described in Appendix C. All quantities in the SAM can be derived from the data described above. Using the quantities in the SAM, and the assumed elasticities, the production and utility functions can be calibrated.

The calibration process starts with a standard definition of GDP, the sum of

> 11The countries of the Southern African Customs Union (Botswana, Lesotho, Namibia, South Africa and Swaziland) share imports tax revenue according to a formula that gives a reduced share of the revenue to South Africa. Our calibration method is inaccurate to the extent that the formula differs from the share of regional imports that is consumed by each country.

10
consumption, investment and net exports: _GDP_ = _C_ + _I_ + ( _E − M_ ). The figures for _C_ and _I_ incorporate government consumption and investment. This definition of GDP corresponds to the format usually given in IMF country reports.

In our model the goods that are consumed (ignoring leisure), can be divided between _imports_ and non-imports ( _N_ ), where non-imports comprise _domestic_ and _untaxed_ . Total consumption in the model is thus given by _C_ = _N_ + _M_ . Using the definition of GDP we calculate the amount of non-imports consumed as _N_ = _GDP − I − E_ . Consumption of non-imports is equal to production of non-imports. Production of _domestic_ , the taxed non-imported good in the model, is calculated by dividing VAT revenue by the tax rate, giving the tax base: _D_ =<sup>_<u>R</u>_</sup> _tD_<sup>_<u>D</u>_.</sup> Consumer expenditure on the _untaxed_ good (equal to the value of production) is thus the residual of non-imports: _U_ = _N −_ (1 + _tD_ ) _× D_ .

Funds received by firms are spent on factors. Allocation of firm revenue between capital and labor is achieved using assumed labor-output ratios. The amount of formal factor usage is determined by dividing factor tax revenues by their tax rates. Informal factor usage is then the residual of total factor expenditure less formal factor expenditure.

The calibration process can be illustrated with data from Guinea-Bissau and the SAM of Table 2. The value of _investment_ , as a percentage of GDP at market prices, is available directly from the national accounts: _I_ = 18 _._ 9. The producer value of exports is derived by subtracting export tax revenue from the market value of exports: _E_ = 27 _._ 21 _−_ 2 _._ 61 = 24 _._ 6. The producer value of _domestic_ is determined by dividing tax revenue for domestic goods (0.74% of GDP) by the standard sales tax rate (15%): _D_ =<sup><u>0</u></sup> 0<sup>_<u>.</u>_</sup> _._<sup><u>74</u></sup> 15<sup>=4</sup><sup>_._93.Thevalueof</sup><sup>_untaxed_isthentheresidualof</sup> GDP less investment and the taxed value of _domestic_ and _exports_ , all expressed as a percentage of GDP: _U_ = 100 _−_ ( _D_ + 0 _._ 74) _−_ ( _E_ + 2 _._ 61) _− I_ = 48 _._ 20.

Total funds received by the firms in a sector is the sum of sales and investment. For example, firms producing exports receive _E_ + _IE_ = 24 _._ 60 + 5 _._ 99 = 30 _._ 59. It is assumed that production is competitive, so that all funds received by firms are paid out to factors. Capital and labor requirements for production are determined using the labor-output ratios. Thus, for example, with a labor-output ratio of 0.37 for exports, total capital used to produce exports is _KE_ = (1 _−_ 0 _._ 37) _×_ ( _E_ + _IE_ ) = 18 _._ 55. Since _untaxed_ uses only _informal capital_ and _informal labor_ , this procedure is all that is required to determine the allocation of capital and labor to _untaxed_ .

For _domestic_ and _exports_ , factor usage must be divided between formal and informal factors. The amounts of formal capital and labor are determined by dividing tax receipts by the legal tax rate. With a 39% corporations tax, total _formal capital_ is _K_<sup>_f_</sup> = 00 _.._ 3992<sup>=2</sup><sup>_._36.</sup> Applying a personal income tax rate of 10% implies total _formal labor_ of _L_<sup>_f_</sup> =<sup><u>0</u></sup><sup>_<u>.</u>_</sup> 0<sup><u>945</u></sup> _._ 1 = 9 _._ 45. These amounts are divided between _domestic_ and _exports_ in proportion to output. For example, _formal capital_ in _exports_ is _KE_<sup>_f_=</sup><sup>_Kf ×_</sup> _E_ + _<u>ED</u>_<sup>= 2</sup><sup>_._36</sup><sup>_×_</sup> 24 _._ <u>2460+4</u> _<u>.</u>_ <u>60</u> _._ 93<sup>= 1</sup><sup>_._97.Informal capital and labor</sup> are then the residuals of total capital and labor for each industry less formal capital and labor and the taxes paid on these factors. For example _informal capital_ used 11
to produce _exports_ is _KE_<sup>_i_=</sup><sup>_KE −K_</sup> _E_<sup>_f×_(1+</sup><sup>_tK_) = 18</sup><sup>_._55</sup><sup>_−_1</sup><sup>_._97</sup><sup>_×_(1+0</sup><sup>_._39) = 16</sup><sup>_._58.</sup> The SAM of Table 2 does not show _leisure_ . The quantity of leisure is determined by the representative consumer’s endowment of time less the sum of formal and informal labor. To enable simple calibration of the elasticity of labor supply, the utility function is specified with unitary (Cobb-Douglas) elasticity of substitution between leisure and all other goods. This implies a labor supply elasticity of _η_ = _<u>T</u> −LL_ where _T_ is the time endowment and _L_ is total labor supply. The value of _L_ is fixed by the data – in the case of Guinea-Bissau _L_ = _L_<sup>_i_</sup> + _L_<sup>_f_</sup> = 9 _._ 45+34 _._ 61 = 44 _._ 06. The calibration approach is to choose a value for the labor supply elasticity, which then fixes the value of _T_ . There appear to be very few published estimates of the elasticity of labor supply in developing countries. For rich countries, estimates of the elasticity of labor supply are close to zero, when estimated for those who are employed. Nevertheless at the extensive margin, the decision whether or not to take a job, the elasticity of labor supply is positive. For our developing countries, we felt that some small responsiveness of labor supply to changes in taxation was appropriate, and thus chose an elasticity of 0.05, implying that _T_ = 1 _._ 05 _× L_ .

National accounts figures represent values: price _×_ quantity. Following the Harberger convention, units of aggregate goods are chosen such that quantities equal values. This implies that for untaxed goods or factors, benchmark prices are equal to one. For taxed goods and factors, we choose quantity units such that either the net of tax price or the gross of tax price is equal to one at the benchmark equilibrium. Specification of the tax rates allows calculation of the missing prices.

With all benchmark prices and quantities determined, calibration finishes with the selection of elasticities for the CES utility and production functions. Our base case uses unitary elasticities: constant returns to scale Cobb-Douglas functions. This appears to be reasonable for the elasticity of demand for imports (Senhadji 1998). But we do not have evidence on the empirical magnitude of other necessary elasticities. Faced with a data vacuum we preferred a simple functional specification, and performed sensitivity checks by changing elasticities.

While this account of the calibration process is straight-forward, it glosses over several problems with the calibration of informal sectors. It is likely that these problems affect all countries to some degree, but the issue is particularly acute in eight countries where, using the procedure described above, the calibrated values of sections of the informal economy are negative. The _untaxed_ good is negative in Equatorial Guinea (-74% of GDP), Gabon (-2 %), Mauritania (-3%), Namibia (-22%), and Swaziland (-3%). In addition, the calibration process gives negative values for _informal labor_ used to produce _domestic_ and _exports_ in Cape Verde (-5%), South Africa (-13%) and Zimbabwe (-13%).

The first problem is a general question about the reliability of GDP data in small developing economies. In particular, statisticians dealing with developing economies make efforts to incorporate the informal economy, but to the extent that some informal activities escape the measure of GDP, our calibrated informal sectors are too small. Data reliability may affect results for all countries, but it 12
does not give rise to negative calibrated values for _untaxed_ goods.

The second problem arises in countries with considerable re-exportation of imports. The problem can be seen when we consider the definition _GDP_ = _C_ + _I_ + ( _E − M_ ). Suppose that initially there are no re-exports, and then an additional $100 of goods is imported and immediately re-exported without any value-added. The GDP figure, which is the sum of value-added, is unchanged. But the increase in measured exports reduces our measure of non-imports by $100, since _N_ = _GDP − I − E_ . With the size of _domestic_ calibrated independently, any re-export of goods results in a corresponding diminution of the _untaxed_ sector: _U_ = _N − D_ . With sufficient re-exportation, the _untaxed_ sector becomes negative. An extreme case is Equatorial Guinea, where exports constitute 106% of GDP. For most countries it seems likely that re-exports constitute a sufficiently small part of total exports that the calibration method is not seriously compromised. Unfortunately we did not have the necessary data to eliminate the problem by separating total exports between those of domestic origin and those of foreign origin.

The final problem in calibrating _untaxed_ arises from the method of calculating _domestic_ , by dividing sales tax revenue by the tax rate. Where the sales tax is a VAT, with full rebating of tax paid on inputs and a single rate, the calibration method probably gives a fairly accurate measure of the _domestic_ tax base. But if sales taxes cascade, without rebates for taxes paid on inputs, the effective marginal tax rate can be much higher than the standard sales tax rate. In such cases, the tax rate used for calibration purposes is too low, so the estimated _domestic_ tax base is too large. Then, noting that _U_ = _N − D_ , when the estimated size of _D_ is too large, the estimated size of the _untaxed_ sector is too small. The fact that Namibia and Swaziland do not have VATs may help to understand the small calibrated values of their _untaxed_ sectors. The further a country’s sales tax system departs from a perfect VAT with a single tax rate and no exemptions, the less accurate is the calibration methodology for identifying the _domestic_ tax base.

Similar issues arise in calibrating informal factor supplies. If the assumed laboroutput ratios are not sufficiently large, the total labor supply is less than the calibrated value of _formal labor_ . If the personal income tax rate used for calibration is too small, the calibrated value of _formal labor_ is too large. In principle the same problems could arise in calibrating _informal capital_ , but in practice the problem did not arise.

Our solution is pragmatic. The basic calibration methodology suggests ‘small’ values for the _untaxed_ good and _informal labor_ used to produce taxed goods. At the same time, strictly positive values are required for the experiments conducted in section 5.1. For the five countries with negative _untaxed_ , we set the value of _untaxed_ at 1% of GDP.<sup>12</sup> For the three countries with negative _informal labor_ requirements in _exports_ and _domestic_ , we adjusted the labor-output ratio to ensure that _informal labor_ constituted 1% of _formal labor_ . It should be emphasized that

> 12For these countries, the calibrated market value of the three produced goods thus exceeds 100% of GDP.

13
a process of adjustment of the values in the SAM is typical in the development of CGEs: real-world data rarely match the internal consistency requirements of a SAM. Nevertheless, our results should be interpreted with particular caution for the ‘problem’ countries, and for all countries lacking VATs (these are reported in the data appendix).

# **4 Results**

We calculated the MCFs associated with six different shocks to tax rates. In the first five experiments we increased each tax rate individually by 1% of the existing tax rate.<sup>13</sup> In the sixth experiment we increased all five tax rates simultaneously by 1%. In each case the additional tax revenue, ∆ _R_ , was redistributed to consumers as a lump sum transfer. The new equilibrium was established using a computable general equilibrium model written using GAMS MPSGE.

The welfare change induced by the combined tax and spend experiment was measured in terms of the numeraire using the equivalent variation ( _EV_ ).<sup>14</sup> The MCF of the experiment was calculated as _MCF_ = _−_ ( _EV −_ ∆ _R_ ) _/_ ∆ _R_ . The value of the additional transfer was subtracted from the consumer’s new welfare level because the MCF measures the cost of taxation and not the benefit of public spending.

## **4.1 Base Case Estimates**

The resulting MCF estimates are presented in Table 3. The estimates provide a basic blueprint for tax reform in each country. For any pair of tax instruments, the same total revenue could be achieved for lower deadweight loss by lowering tax rates associated with a high MCF and increasing low-MCF tax rates.

On average, the MCF associated with a marginal increase in all five tax rates is 1.17, indicating a required rate of return of 17% for African public projects. Among individual tax instruments, on average the lowest MCFs are associated with taxes on the two taxed consumption goods ( _domestic_ and _imports_ ), and the highest MCFs are associated with the two taxed factors ( _formal capital_ and _formal labor_ ). The _exports_ MCFs exhibit the greatest variation.

The high variance of _exports_ MCFs requires comment. Much of the variation comes from two countries: Burkina Faso and Rwanda. The _exports_ MCFs in these two countries are negative because the tax shock reduces tax revenue. The high absolute values occur because the exports tax rate shock induces a marginal change

> 13Where the tax rate was 0% we increased it to 1%.

> 14In theoretical papers on the MCF changes in utility are converted to a monetary measure by dividing by the marginal utility of income. When the utility function is linearly homogeneous (as is the case in our model) the equivalent variation gives the same measure of welfare change.

14
<u>Table 3: MCF Estimates</u>

|Country|Domestic|Exports|Imports|Capital|Labor|All|
|---|---|---|---|---|---|---|
|Benin|1.11|1.28|1.15|1.68|1.60|1.23|
|Botswana|1.03|1.02|1.03|1.07|1.05|1.05|
|Burkina Faso|1.15|-10.82|1.18|1.55|1.55|1.25|
|Burundi|1.10|0.76|1.10|1.66|1.88|1.22|
|Cameroon|1.10|1.08|1.07|1.53|1.27|1.14|
|Cape Verde|1.11|1.96|1.21|1.72|1.79|1.37|
|Central African Rep.|1.14|1.31|1.14|1.62|1.71|1.23|
|Chad|1.19|1.26|1.09|1.87|2.01|1.33|
|Dem. Rep. of Congo|1.01|1.02|1.01|1.43|1.38|1.10|
|Côte d’Ivoire|1.05|1.06|1.06|1.43|1.36|1.12|
|Eq. Guinea|1.05|1.00|1.00|1.24|1.10|1.13|
|Eritrea|1.02|0.63|1.03|1.20|1.14|1.09|
|Ethiopia|1.13|3.14|1.23|1.75|1.60|1.31|
|Gabon|1.03|1.02|1.05|1.39|1.35|1.10|
|Gambia|0.98|1.12|1.08|1.45|1.21|1.12|
|Ghana|1.03|1.17|1.10|1.50|1.26|1.17|
|Guinea|1.11|1.01|1.00|1.49|1.43|1.12|
|Guinea-Bissau|1.09|1.35|1.13|2.03|1.49|1.26|
|Kenya|1.02|1.20|1.06|1.30|1.11|1.08|
|Madagascar|1.13|1.16|1.11|1.58|1.32|1.17|
|Malawi|1.20|1.04|1.01|1.39|1.43|1.23|
|Mali|1.11|1.27|1.14|1.66|1.64|1.21|
|Mauritania|1.08|0.97|0.98|1.24|1.22|1.10|
|Mozambique|1.04|1.17|1.07|1.60|1.22|1.11|
|Namibia|0.97|1.10|1.06|1.39|1.09|1.10|
|Niger|1.17|1.29|1.15|1.90|1.80|1.24|
|Nigeria|0.99|1.02|1.02|1.30|1.19|1.08|
|Rwanda|1.14|-92.74|1.14|1.87|1.80|1.28|
|São Tomé|1.27|1.21|1.07|1.54|1.31|1.15|
|Senegal|1.07|1.27|1.13|1.55|1.80|1.19|
|South Africa|1.09|1.02|1.00|1.29|1.11|1.12|
|Sudan|1.09|1.92|1.23|1.87|1.57|1.26|
|Swaziland|1.11|1.01|1.01|1.34|1.30|1.09|
|Tanzania|1.17|1.59|1.20|1.76|1.73|1.27|
|Togo|1.06|1.11|1.07|1.40|1.50|1.12|
|Uganda|1.10|0.82|0.97|1.40|1.30|1.11|
|Zambia|1.06|1.09|1.03|1.44|1.14|1.09|
|Zimbabwe|1.08|1.10|1.03|1.28|1.10|1.11|
|Average|1.09|-1.58|1.08|1.52|1.42|1.17|
|Max|1.27|3.14|1.23|2.03|2.01|1.37|
|Min|0.97|-92.74|0.97|1.07|1.05|1.05|
|Std. Dev.|0.06|15.32|0.07|0.22|0.26|0.08|

15
in total tax revenue that is close to zero.<sup>15</sup> Excluding these two countries, the remaining countries can be divided into two groups. There are 16 countries with zero exports taxes (see the data in Appendix B), that as a group have a low average _exports_ MCF of 1.07. The remaining 20 countries have positive exports taxes, and have an average _exports_ MCF of 1.32. The relatively high MCF associated with positive exports taxes can be understood by noting that _exports_ is effectively an input into _imports_ , so that distortions introduced in the market for _exports_ amplify distortions in the market for _imports_ .

The general equilibrium interactions between tax instruments are illustrated in Figure 3 for the case of Guinea-Bissau. MCFs for different tax instruments are plotted as a function of the import tariff. The diagram provides various insights into the interactions within the system.

- The _imports_ MCF increases with the import tariff.

- The MCFs for _exports_ , _capital_ and _labor_ are greater than the _imports_ and _domestic_ MCFs, and they increase at a faster rate than the _imports_ MCF. _Exports_ , _capital_ and _labor_ are inputs into the production of the taxed consumption goods, _imports_ and _domestic_ , that enter directly into the consumer’s welfare function. Increases in taxation of these inputs causes increased distortion of the taxed prices of the outputs, in addition to substitution of informal factors for formal factors.

- The _domestic_ MCF decreases as _tM_ increases. When _tM ≥_ 34% the _domestic_ MCF is less than one, indicating that marginally increasing the _domestic_ tax helps to correct the distortions induced by high import tariffs, thereby increasing welfare. _Domestic_ and _imports_ are substitutes in consumption, so as _import_ tariffs increase, consumption of _domestic_ increases, helping to offset the effect of existing _domestic_ taxation.

- Reflecting the conflicting effects of the individual taxes, the MCF obtained by simultaneously varying _all_ tax rates decreases for values of _tM <_ 4% and increases for _tM >_ 4%. One implication is that this measure of the MCF does not necessarily increase with total tax revenue. (The illustrated values of _tM_ are on the ‘good’ side of the Laffer curve: total revenue is increasing in _tM_ .)

The diagram also illustrates that over wide ranges of the import tariff rate the ordering of MCFs for individual taxes is unchanged.

15Although not apparent in the reported results, the exports tax shock also reduces total tax revenue in Burundi and Eritrea. In these countries, which have zero exports tax rates, the marginal reduction in tax revenue is associated with a positive _exports_ MCF, because the marginal welfare change is positive.

16
<!-- Start of picture text --> 3.5<br>3<br>2.5<br>Capital<br>Labour<br>2 Exports<br>All<br>Imports<br>Domestic<br>1.5<br>1<br>0.5<br>0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4<br>Import tariff rate<br>MCFs<br><!-- End of picture text --> Figure 3: MCFs in Guinea-Bissau as a Function of the Import Tariff 17
Table 4: Sensitivity Testing

|Experiment|D|E|M|K|L|All|(1)|(2)|(3)|
|---|---|---|---|---|---|---|---|---|---|
|_σC_ = 2|1.19|1.88|1.17|1.93|1.89|1.31|29|25|35|
|_σD_ =_σE_ =_σU_ = 2|1.09|-0.26|1.08|1.50|1.45|1.17|33|33|38|
|_σC_ =_σD_ =_σE_ =_σU_ = 2|1.19|2.02|1.18|1.93|1.98|1.32|29|25|36|
|_σ_<sup>_K_</sup><br>_D_ <sup>=</sup><sup>_σL_</sup><br>_D_ <sup>=</sup><sup>_σK_</sup><br>_E_ <sup>=</sup><sup>_σL_</sup><br>_E_ <sup>= 2</sup>|1.09|-1.58|1.08|2.53|1.89|1.24|35|34|37|
|_σ_<sup>_L_</sup><br>_D_ <sup>=</sup><sup>_σL_</sup><br>_E_ <sup>= 2</sup>|1.09|-1.58|1.08|1.52|1.89|1.19|22|20|37|
|_σC_ = 0_._5|1.05|1.15|1.05|1.40|1.29|1.11|35|32|35|
|_σD_ =_σE_ =_σU_ = 0_._5|1.09|1.13|1.08|1.52|1.39|1.17|36|34|37|
|_σC_ =_σD_ =_σE_ =_σU_ = 0_._5|1.05|1.14|1.04|1.41|1.28|1.11|34|32|35|
|_σ_<sup>_K_</sup><br>_D_ <sup>=</sup><sup>_σL_</sup><br>_D_ <sup>=</sup><sup>_σK_</sup><br>_E_ <sup>=</sup><sup>_σL_</sup><br>_E_ <sup>= 0</sup><sup>_._5</sup><br><br>|1.09|-1.58|1.08|1.29|1.28|1.14|31|28|37|
|_σ_<sup>_L_</sup><br>_D_ <sup>=</sup><sup>_σL_</sup><br>_E_ <sup>= 0</sup><sup>_._5</sup>|1.09|-1.58|1.08|1.52|1.28|1.16|31|27|38|

Columns D, E, M, K, L, and All report average MCFs for the 38 countries. Columns (1), (2) and (3) indicate the number of countries that are ‘close’ to the base case estimates in the sense of giving the same recommendations for tax reform. In column (1) the tax instruments found to have the highest and lowest MCFs are the same as in the base case. In column (2) all five individual MCFs are ranked in the same order as in the base case. In column (3) at most one pairwise comparison of MCFs gives a different recommendation from the base case estimates.

# **4.2 Robustness of Results**

Our results are dependent on the specified elasticity parameters. We experimented with alternative elasticities to see the effect on our estimates. The notation for the relevant elasticities is set out in Figure 2.

In testing different elasticities we maintained the following values equal to one: _σW_ , _τD_ , _τE_ , and _τU_ . This ensures that the representative consumer invests a constant proportion of income, and that each production process receives a constant proportion of its total funds from investment.

We tested several combinations of elasticities, and the results are set out in Table 4. For each experiment, any unmentioned elasticity is equal to 1. The first five experiments increase elasticities. The first experiment increases the consumer’s elasticity of substitution between consumption goods. The second increases the elasticity of substitution between capital and labor in all goods. The third increases the elasticity of substitution between consumption goods and between capital and labor. The fourth increases substitution between formal and informal factors. The fifth increases substitution between formal and informal labor, but leaves unchanged the degree of substitution between formal and informal capital. The final five experiments perform corresponding reductions in the elasticities of substitution.

Changing elasticities had the expected effect on the magnitude of our MCF estimates: higher substitutability results in higher MCFs. The MCF associated with a simultaneous shock of all five taxes, _MCF_ ( _All_ ), varied between 1.11 and 1.32. _MCF_ ( _All_ ) is more sensitive to variation in the consumer’s elasticity of substitution 18
between consumption goods than the producers’ elasticity of substitution between capital and labor. On the production side, MCF estimates are more sensitive to changes in the elasticity of substitution between between formal and informal factors than the elasticity of substitution between capital and labor. It is clearly important to have a good estimate of the relevant elasticities if MCF estimates are to be used for cost-benefit analysis.

But for partial revenue-neutral tax reform, it is the ordering of MCF estimates that is important, not their magnitudes. For such reform, the aim is to compare two tax instruments, increase the tax rate on the low MCF tax, and decrease the tax rate on the high MCF tax. Table 4 reports the number of countries in which the ordering of MCFs is robust to changes in elasticities. Three measures of robustness are used. The first measure supposes that reform is concentrated on the most extreme MCFs. The two tax instruments with the highest and lowest MCFs are identified. If these two instruments are the same as in the base case, the ordering is considered robust. Among the five tax instruments there are ten pairwise comparisons that are possible, identifying for each pair the high and low MCF instruments. The second measure of robustness requires that all ten such comparisons report the same pairwise ordering. This implies that all five instruments follow the same order as in the base case. The third measure of robustness permits just one pairwise comparison to give a different ordering from the base case. On the basis of the third measure the ordering of MCF estimates was robust to variations in elasticities in a minimum of 35 out of 38 countries. That is, we can be reasonably confident of the recommendations for tax reform that are implied by our base case estimates.

# **5 Informal Sectors and Administrative Costs**

Analysis of African tax systems quickly confronts two salient features: the significance of informal sectors and the relatively high cost of tax administration:

- Excluding countries in which our basic calibration method gave a negative _untaxed_ good, the value of _untaxed_ production represents on average 30% of GDP, with a maximum of 61% in Niger. Adding in the value of untaxed factors used to produce _domestic_ and _exports_ , the average informal economy in these countries represents 69% of GDP, with a maximum of 90% in the Democratic Republic of Congo.

- Table 5 provides an international comparison of administrative costs, measured by dividing the expenses of tax collection agencies by the revenue collected. The average for rich countries is 1.36%, 1.88% for Latin American countries, and 2.35% for African countries.<sup>16</sup>

- 16Not all of the tax agencies represented in these figures collect all types of taxes. Since

19
<u>Table 5: Tax Administration Costs</u>

|Country|Year(s)|Cost/Collections|
|---|---|---|
|Australia|2001-2002|1.2%|
|Canada|2001-2002|2.3%|
|New Zealand|2001-2002|1.2%|
|UK|2001-2002|1.6%|
|US|2002|0.5%|
|Guatemala|1999-2001|1.9%|
|Mexico|1995, 1997-98|1.7%|
|Peru|1996-1998|1.9%|
|Venezuela|1995-1998|2.0%|
|Ghana|1993|2.8%|
|Kenya|1995-2000|1.2%|
|Namibia|2001-2002|1.3%|
|South Africa|1998-2001|1.1%|
|Tanzania|1996-1997|3.0%|
|Uganda|1991-2000|3.6%|

The cost/collections ratio reports the annual cost of tax collection agencies divided by the amount of money collected. For data sources, see Appendix B.

In this section we examine the impact of the informal economy on the MCF in the formal economy, and then measure MCFs of potential taxes in different parts of the informal economy, ignoring any administrative costs. We then examine how the presence of administrative costs affects our estimates for taxes in the formal economy, and we consider the level of administrative costs that could be justified to impose taxes in the informal economy.

# **5.1 The Informal Economy**

The simple partial equilibrium formula 2 suggests that the magnitude of the MCF, and in particular whether the MCF is greater or less than one, is determined in part by the difference between 1+ _<u>t</u>_ <u>1</u> _t_ 1<sup>and</sup> 1+ _<u>t</u>_ <u>2</u> _t_ 2<sup>.If we think of good 2 as a composite</sup> for all goods other than good 1, the average rate of taxation on good 2 falls as the proportion of untaxed goods in the economy increases. This suggests that economies with large informal sectors are likely to have high MCFs.

Figure 4 plots our base case estimates of _MCF_ ( _All_ ) against the calibrated value of _untaxed_ , suggesting the strength of this intuition. A simple regression of our 38 estimates of _MCF_ ( _All_ ) on _untaxed_ and a constant has an adjusted _R_<sup>2</sup> of the costs of collection vary by tax type, this may give a distorted impression of the efficiency of some agencies.

20
<!-- Start of picture text -->
1.40<br>1.35<br>1.30<br>1.25<br>1.20<br>1.15<br>1.10<br>1.05<br>1.00<br>0 10 20 30 40 50 60 70<br>Untaxed Output (% GDP)<br>MCF(All)<br><!-- End of picture text -->

Figure 4: MCF(All) as a Function of the Value of the Untaxed Good 0.75. Some of the unexplained variation in MCF values in the diagram is due to variation in tax structures. To capture this in a simple way, we created a variable, _structure_ , which measured the proportion of exports and factor tax revenue in total tax revenue (using the same figures used for calibration of the model). Adding this variable to the regression we obtained: The adjusted _R_<sup>2</sup> of this regression is 0.78. Standard errors are reported in brackets, with the coefficients on the constant and untaxed significant at 1% and the coefficient on _structure_ significant at 2.5%. In contrast a regression of _MCF_ ( _All_ ) on just _structure_ and a constant gives no statistically significant results. These results suggest that, at least for the African countries we have studied, the magnitude of an economy’s average MCF is dominated by the size of the informal economy, with the tax structure playing only a relatively small role.

The logic of the simple partial equilibrium formula 2, suggests that if a good is more lightly taxed than goods in the rest of the economy, it will have a low MCF. Thus, taxes imposed on parts of the informal economy should have very low MCFs. We confirmed this intuition by imposing hypothetical taxes on informal parts of the economy in our model.

21
We supposed it was possible to impose a tax in these sectors, and marginally increased the tax from an initial rate of zero. We calculated MCFs when 1% taxes were imposed on: production of the _untaxed_ good ( _U_ ); _informal capital_ used anywhere in the economy ( _K_<sup>_i_</sup> ); _informal capital_ used to produce _domestic_ or _export_ goods ( _KDE_<sup>_i_);</sup><sup>_informallabor_usedanywhereintheeconomy(</sup><sup>_Li_);and</sup> _informal labor_ used to produce _domestic_ or _export_ goods( _L_<sup>_i_</sup> _DE_<sup>).Wedistinguished</sup> between taxing a factor wherever it is used and taxing a factor when it is used to produce _domestic_ or _export_ goods because the latter seems more plausible. It seems more likely that the administration will be able to tax a firm’s accounting profits (returns to capital) and labor inputs in cases where the firm’s output is already taxed. The results of these experiments are reported in Table 6.

In all countries the MCF of a tax on the _untaxed_ good is less than 1. The negative welfare shock suffered by households (before the revenue is returned lump-sum) is smaller than the increase in government revenue. Once lump-sum redistribution of the revenue occurs, households are better off than before the tax shock. Increasing taxes in the informal sector helps to counteract existing taxes in other sectors, moving relative prices towards their undistorted levels.

When taxation of informal factors is restricted to inputs to _domestic_ and _export_ goods, the MCF is higher than when informal factors are taxed wherever they are used: _MCF_ ( _KDE_<sup>_i_)</sup><sup>_>MCF_(</sup><sup>_Ki_)and</sup><sup>_MCF_(</sup><sup>_Li_</sup> _DE_<sup>)</sup><sup>_>MCF_(</sup><sup>_Li_).</sup> Two effects operate. Taxing an untaxed factor helps to restore prices to their undistorted levels, tending to lower the MCF. When the untaxed factors are inputs to taxed goods, the relative costs of these goods rise, the distortion associated with goods taxation increases and the MCF tends to be higher. The second of these effects is relatively stronger when the tax shock is concentrated on inputs to _domestic_ and _export_ goods.

Ignoring distributional issues, on average among the fictional tax instruments for taxing the informal sectors, the best way of raising money is by increasing taxes on _untaxed_ goods. The average _MCF_ ( _U_ ) is 0.87, lower than the average MCF elsewhere in the informal economy.

But governments may hesitate to increase taxes of the informal sector if they care about distributional issues and poor households are concentrated in production of _untaxed_ goods or they consume a lot of _untaxed_ goods. When distributional issues are considered, a promising part of the informal economy is _informal capital_ used to produce taxed goods: average _MCF_ ( _KDE_<sup>_i_) is 1.05.That is, imposing taxes</sup> on companies that produce taxed goods but do not pay company tax generally offers a lower cost of public funds than increasing existing taxes elsewhere in the formal economy. In many cases such companies have legal tax exemptions, which can be removed with low administrative expense.<sup>17</sup> Removing such exemptions has the 17In a survey of 197 businesses in Cameroon, Gauthier & Gersovitz (1997) report that 4 were legally exempt from sales tax, while 30 were legally exempt from the business profits tax. In Gauthier & Reinikka (2001) a similar survey of 158 businesses in Uganda reports 17 exemptions from sales tax and 41 exemptions from the corporate income tax. Both 22
<u>Table 6: MCFs in the Informal Sector</u>

|Country|_U_|_K_<sup>_i_</sup>|_K_<sup>_i_</sup><br>_DE_|_L_<sup>_i_</sup>|_L_<sup>_i_</sup><br>_DE_|
|---|---|---|---|---|---|
|Benin|0.87|0.95|1.07|0.94|1.12|
|Botswana|0.86|0.90|0.91|0.92|0.95|
|Burkina Faso|0.89|0.94|1.21|0.92|1.19|
|Burundi|0.83|0.95|1.05|0.87|0.99|
|Cameroon|0.89|0.97|1.02|0.97|1.06|
|Cape Verde|0.81|0.79|1.22|0.80|1.26|
|Central African Republic|0.92|0.98|1.15|0.97|1.16|
|Chad|0.93|0.97|1.12|0.97|1.15|
|Democratic Republic of Congo|0.97|0.99|1.00|0.99|1.00|
|Côte d’Ivoire|0.83|0.95|0.98|0.95|1.00|
|Equatorial Guinea|0.98|0.98|0.98|1.00|1.00|
|Eritrea|0.87|0.88|0.92|0.93|0.99|
|Ethiopia|0.87|0.89|1.17|0.92|1.21|
|Gabon|0.85|0.97|0.97|0.99|0.99|
|Gambia|0.84|0.95|0.99|0.93|1.01|
|Ghana|0.87|0.95|1.03|0.92|1.04|
|Guinea|0.93|1.00|1.05|0.98|1.06|
|Guinea-Bissau|0.89|0.97|1.22|0.92|1.26|
|Kenya|0.81|0.92|0.94|0.87|0.93|
|Madagascar|0.91|0.97|1.07|0.96|1.11|
|Malawi|0.96|0.98|1.03|0.98|1.05|
|Mali|0.89|0.96|1.10|0.96|1.15|
|Mauritania|0.89|0.96|0.97|0.94|0.95|
|Mozambique|0.86|0.98|1.02|0.95|1.03|
|Namibia|0.79|0.92|0.92|0.85|0.86|
|Niger|0.94|0.98|1.16|0.98|1.19|
|Nigeria|0.92|0.98|0.98|0.97|0.97|
|Rwanda|0.90|0.94|1.14|0.96|1.18|
|São Tomé|0.84|0.95|1.08|0.80|1.14|
|Senegal|0.83|0.95|1.03|0.93|1.05|
|South Africa|0.78|0.89|0.92|0.71|0.77|
|Sudan|0.95|0.97|1.18|1.00|1.21|
|Swaziland|0.78|0.96|0.96|0.89|0.89|
|Tanzania|0.91|0.98|1.21|0.93|1.21|
|Togo|0.89|0.96|1.02|0.98|1.05|
|Uganda|0.92|0.98|1.03|0.98|1.05|
|Zambia|0.82|0.97|1.00|0.81|0.92|
|Zimbabwe|0.76|0.88|0.91|0.69|0.76|
|Average|0.87|0.95|1.05|0.92|1.05|
|Max|0.98|1.00|1.22|1.00|1.26|
|Min|0.76|0.79|0.91|0.69|0.76|
|Std. Dev.|0.06|0.04|0.09|0.07|0.12|

23
potential for a low marginal cost of taxation, without obvious major effects on the poorest households.<sup>18</sup>

# **5.2 Costs of Tax Administration**

A taxpayer paying a dollar of taxes suffers the same loss of utility regardless of whether the administration has paid 2 cents or 50 cents to enforce the collection. Further, the administration costs are not lost to society. They are paid to civil servants and other providers of goods and services. Thus, tax administration costs do not alter ∆ _W_ in our MCF formula 1.<sup>19</sup> Administration costs do, however, alter ∆ _R_ in our MCF formula, by reducing the net revenue available for government spending. If we suppose that administration costs constitute _μ_ % of tax revenue collected, a tax shock that changes gross revenue by ∆ _R_ changes net revenue by 1<sup><u>∆</u></sup> _−_<sup>_<u>R</u>_</sup> _μ_<sup>%.Incorporatingadministrativecosts</sup> in our MCF estimates is thus a simple matter of multiplying by 1 _−_ <u>1</u> _μ_<sup>.</sup> Table 5 indicates that on average _μ_ = 2 _._ 35% in Africa. On this evidence, our base case results should be multiplied by 1.024. Incorporating administration costs increases the average _MCF_ ( _All_ ) for African countries from 1.17 to 1.20. Although Africa has more costly tax administrations than other regions, this alone is unlikely to result in substantially higher marginal costs of public funds.

One explanation for the failure to tax the informal sector may be large administrative costs associated with taxing the first marginal unit of the tax base. For example, there may be high lump sum costs associated with identifying taxpayers. Thus _μ_ may be higher for taxes on the informal sector than for taxes in other sectors.

We do not have data on the magnitude of administrative costs for the informal sector ( _μ_<sup>_i_</sup> ). However, noting that in an optimized tax system the MCF of all tax instruments would be equal, we can calculate the _μ_<sup>_i_</sup> that would equate the MCF of a tax in the informal sector, _MCF_<sup>_i_</sup> , with the base case _MCF_ ( _All_ ) when administrative costs are considered, according to the following formula: studies found that exemptions tended to be granted to large firms, while smaller firms were more likely to evade tax illegally. Legal tax exemptions may be the result of corruption. Fjeldstad (2002) reports that in the mid 1990s senior Tanzanian officials accepted bribes in return for tax exemptions: “within the Ministry of Finance, the _Revenue Department_ went under the nickname of the ‘Tax Exemption Department.’ ”

> 18An alternative means of increasing capital taxation may be to encourage firms to move from the informal to the formal sector by lowering licence fees and time costs for establishing formal enterprises (Auriol & Warlters 2005).

> 19We treat as negligibly small the marginal change in consumer surplus forgone on goods that could have been produced using the factors of production involved in tax administration.

24
Using _μ_ =0.0235, we calculated the threshold administrative costs, _μ_<sup>_i_</sup> for the parts of the informal economy discussed in section 5.1. Table 7 reports the averages across our sample of countries. On average, increased efforts to enforce taxes on the _untaxed_ good would be justified up to the point where administrative costs consume 27% of the revenue collected. Taxing currently untaxed profits of businesses that produce taxed goods would be justified with administrative costs of 13%.

|Table 7: A|dministrative|Cost|Thresholds|
|---|---|---|---|
|_U_|_K_<sup>_i_</sup><br>_K_<sup>_i_</sup><br>_DE_|_L_<sup>_i_</sup>|_L_<sup>_i_</sup><br>_DE_|
|0.27|0.21<br>0.13|0.23|0.12|

# **6 MCF Dispersion & Tax System Inefficiency**

When only distorting taxes are available, the MCFs of optimal taxes are all equal. This suggests that MCF dispersion could be used as a measure of tax system inefficiency. In fact, high variance of the MCFs does not necessarily indicate great scope for welfare-enhancing revenue-neutral tax reform.

To assess the potential benefits of tax reform, we derived optimal taxes to achieve each country’s existing revenue. We iteratively reduced high MCF taxes and increased low MCF taxes until MCFs were equalized or remaining high MCF taxes had zero rates. The resulting tax structure involves zero taxes on _exports_ , _capital_ and _labor_ . The only taxes are on the taxed goods that are consumed: _domestic_ and _imports_ . This is an illustration of the Diamond & Mirrlees (1971) production efficiency result. We calculated the welfare gain from moving to optimal taxes (subject to the limited set of distorting tax instruments), and calculated the resulting MCFs of the taxes on _domestic_ and _imports_ . For comparison, we also measured the welfare gain from entirely removing all distorting taxes, or equivalently, only using lump-sum taxation.

The results are reported in Table 8:

- Countries are listed in order of the potential welfare gains from moving to optimal taxes to achieve the same tax revenue using only distorting taxes. The column ‘∆ _W_ (optimal)’ reports these welfare gains in percentage terms, where the change in welfare is measured using the equivalent variation. The average potential welfare gain is 0.44%.

- The column ‘∆ _W_ (zero taxes)’ reports the total welfare cost of the tax system. On average, replacing all taxes by a lump sum tax (or equivalently in the model, eliminating all taxes), welfare could be increased by 0.8%. This suggests that more than half of the deadweight loss of African tax systems is due to the tax structure, rather than the revenue target.

25
- The column ‘Std. Dev. MCFs’ reports the standard deviation of the base case MCF estimates for the five tax instruments. To examine the correlation between this measure of inefficiency and the potential welfare gains of optimal distortionary taxes we performed a simple regression of the form ∆ _Wi_ = _aσi_ + _b_ , where ∆ _Wi_ is the deadweight loss of current taxes relative to optimal taxation, _σi_ is the standard deviation of base case MCFs, and _a_ and _b_ are coefficients to be estimated. The result was statistically insignificant. We conclude that the standard deviation of MCFs is not a good predictor of the potential benefits of tax reform. The reason is that the marginal cost of taxation can greatly exceed the average social cost.<sup>20</sup>

- The column ‘MCF’ reports the MCF associated with optimal taxation. The average figure is 1.07. This is well below the average figure for _MCF(All)_ reported in the base case estimates (1.17). Tax reform can potentially lower the cost of public funds by a significant amount. If the MCF were actually used as a criterion for project approval, moving to optimal taxes would permit many more public projects to go ahead.

- The ‘Revenue’ column reports tax revenue as a percentage of GDP. We explored the relationship between tax revenue and tax system inefficiency using simple regressions of the form _Yi_ = _aXi_ + _b_ , with tax revenue as the single explanatory variable. We found tax revenue to be a significant determinant of the two deadweight loss measures, but not significant in explaining the MCF measures nor the dispersion of MCFs.<sup>21</sup> Revenue only explains part of the differences in the efficiency cost of taxation, even when the effects of tax structure are removed (by finding optimal imports and domestic taxes to achieve the given revenue), because differences remain in the structure of each economy.

# **7 Conclusion**

Our results suggest that a reasonable estimate of the average MCF in Africa is 1.17 (the average of _MCF(All)_ across the 38 countries). Among the various sensitivity tests that we conducted, this figure varied between 1.11 and 1.32. The estimate was most sensitive to changes in the consumer’s elasticity of substitution between _imports_ , _domestic_ and _untaxed_ . Senhadji’s (1998) estimates of the elasticity of demand for imports supports our assumption of unitary elasticity of substitution between _imports_ and other goods. So the major uncertainty concerning our base case estimates is the elasticity of substitution between _domestic_ and _untaxed_ .

> 20Note the convexity of the MCF functions for _exports_ , _capital_ and _labor_ in Figure 3.

> 21Significant results are: ∆ _W_ ( _optimal_ ) = 0 _._ 02(4 _._ 05) _Revenue_ + 0 _._ 16(2 _._ 05), _R_ 2 = 0 _._ 31; and ∆ _W_ ( _zero taxes_ ) = 0 _._ 04(4 _._ 26) _Revenue_ +0 _._ 31(2 _._ 42), _R_<sup>2</sup> = 0 _._ 34. Figures in parentheses are t-statistics.

26
Table 8: Measures of Tax System Inefficiency

||∆_W_|∆_W_|Std. Dev|MCF|Revenue|
|---|---|---|---|---|---|
|Country|(optimal)|(zero taxes)|MCFs|(optimal)||
|Botswana|0.02|0.38|0.02|1.05|12.50|
|Eq. Guinea|0.11|0.11|0.10|1.00|3.42|
|Dem. Rep. Congo|0.12|0.13|0.21|1.01|2.57|
|Guinea|0.19|0.39|0.23|1.06|6.96|
|Madagascar|0.25|0.73|0.20|1.11|9.40|
|Uganda|0.26|0.41|0.24|1.04|8.88|
|Nigeria|0.28|0.33|0.13|1.01|6.45|
|Sudan|0.28|0.59|0.37|1.14|5.23|
|Malawi|0.29|0.33|0.19|1.03|3.78|
|Mozambique|0.29|0.50|0.22|1.05|11.18|
|Eritrea|0.29|0.38|0.22|1.02|13.96|
|Niger|0.30|0.69|0.36|1.14|6.69|
|Cameroon|0.33|0.75|0.20|1.08|10.43|
|Togo|0.34|0.66|0.21|1.06|11.30|
|Gabon|0.36|0.75|0.19|1.06|10.20|
|Mauritania|0.36|0.42|0.13|1.01|10.52|
|C.A.R.|0.37|0.72|0.27|1.11|7.75|
|Zambia|0.38|0.72|0.17|1.05|17.30|
|Tanzania|0.41|1.05|0.28|1.16|9.40|
|São Tomé|0.43|0.70|0.17|1.05|15.18|
|Kenya|0.43|0.76|0.11|1.04|19.48|
|Mali|0.43|0.96|0.27|1.12|11.19|
|Gambia|0.44|0.88|0.18|1.06|16.57|
|Zimbabwe|0.45|1.05|0.10|1.06|23.34|
|Burkina Faso|0.47|0.93|5.45|1.12|10.00|
|Ghana|0.48|0.79|0.18|1.06|11.86|
|South Africa|0.50|1.09|0.11|1.06|21.17|
|Côte d’Ivoire|0.52|0.98|0.19|1.06|15.74|
|Guinea-Bissau|0.56|0.78|0.38|1.07|9.51|
|Chad|0.58|0.78|0.42|1.08|6.22|
|Benin|0.59|1.27|0.26|1.12|12.90|
|Swaziland|0.60|0.86|0.15|1.03|22.69|
|Rwanda|0.63|1.03|42.14|1.11|9.66|
|Namibia|0.72|0.96|0.16|1.03|25.19|
|Ethiopia|0.75|1.47|0.81|1.14|13.28|
|Senegal|0.76|1.49|0.31|1.10|17.23|
|Cape Verde|1.12|1.79|0.38|1.12|18.32|
|Burundi|1.13|1.74|0.46|1.08|18.04|
|Average|0.44|0.80|1.48|1.07|12.25|

27
On average, taxes on factors have high MCFs and taxes on imports and domestic goods have low MCFs. This outcome follows from the Diamond & Mirrlees (1971) result for optimal taxation, that production decisions should not be distorted. A major focus of tax reform in recent years has been the introduction of VATs. Our results suggest that welfare could be improved by increased reliance on these VATs, and reduced reliance on exports and factor taxes.

An important finding is the strong relationship between the size of the untaxed sector and the value of MCF(All). Auriol & Warlters (2005) suggest that governments could reduce the size of their informal sectors by reducing red tape barriers to business entry into the formal sector. The results here suggest that such a policy would not only help to enhance revenue by enlarging the tax base, but would also reduce the marginal cost of public funds.

The existence of MCFs lower than one in the informal sector suggests scope for increasing welfare and tax revenue simultaneously. Measures to bring currently informal activities within the tax base would be justified even if a large proportion (up to 27%) of the additional revenue were consumed in enforcement and administration. Alternative measures to enlarge the tax base by reducing barriers to entry into the formal economy also seem like high priorities.

An obvious question is whether MCFs in Africa are higher or lower than in rich countries. It is beyond the scope of this paper to estimate the MCF in rich countries,<sup>22</sup> but we suggest that differences in the MCF are probably not strongly related to the wealth of the country. Our results suggest that _MCF_ ( _All_ ) tends to be greater with higher tax revenue, greater use of corporate and personal income taxes, higher administrative costs, larger informal sectors and greater use of export taxes. The first two of these factors tend to occur in rich countries, while the final three factors tend to occur in poor countries.

The potential extensions of this paper are numerous. Extensions to take account of the dynamic effects of taxation on savings, investment and growth; or distributional considerations; or non-tax distortions such as labor-market rigidities or regulated prices<sup>23</sup> would all be useful. We hope, however, that in the first instance the model we have presented can be applied to further countries and across time periods, to provide a panel of MCF estimates. These estimates would not only be useful for public policy analysis, but also for the testing of numerous economic theories in which the MCF plays a role.

> 22There are several difficulties in adapting our model to rich countries. For example, the European customs union must be modelled to examine import tariffs, and in the United States, state level taxes vastly complicate the analysis. Social security taxes also need to be taken into account. These difficulties are not insurmountable, but we leave them for future research.

> 23Devarajan et al. (2001) have empirically shown that tax and non-tax distortions are cumulative. Taxes in sectors with less total distortions tend to have lower MCFs because they push resources towards highly-distorted sectors. The relative importance of tax and non-tax distortions is a subject for further research.

28
# **Appendices**

# **A Model Specification**

The single representative consumer maximizes a CES utility function with five goods: _leisure_ ( _Z_ ), _untaxed_ ( _U_ ), _domestic_ ( _D_ ), _imports_ ( _M_ ), and _investment_ ( _I_ ) subject to the income constraint.

̃ _Max W_ = _W_ ( _Z, U, D, M, I_ ) _subject to PLZ_ + _puU_ + _P_<sup> ̃</sup> _DD_ + _P_<sup> ̃</sup> _M M_ + _P_<sup> ̃</sup> _I I ≤ Y_ A tilde over a price indicates that it is tax-inclusive: Consumer income is the value of the endowments of foreign exchange ( _a_ ̄), time ( _T_<sup> ̄</sup> ), and capital ( _K_<sup> ̄</sup> ) plus the transfer received from the government ( _R_ ).

Leisure plus labor supply equals the time endowment.

The consumer’s order conditions are: Factors are combined by CES production functions to produce intermediate goods for _untaxed_ ( _ψU_ ), _domestic_ ( _ψD_ ), and _exports_ ( _ψE_ ). The factors used are capital and labor, each of which may be formal (taxed) or informal (untaxed). The notation for factors is _s_<sup>_q_</sup> _r_<sup>:theamountoffactor</sup><sup>_s∈{K, L}_usedtoproducegood</sup> _r ∈{U, D, E}_ , where _q ∈{i, f }_ indicates whether the factor is informal or formal.

The 10 first order conditions determining factor usage in production are given by: The intermediate goods are divided between final goods and investment using CET production functions.

29
The value of imports is equal to the value of exports plus the endowment of foreign exchange.

Factor demand equals factor supply: Factors receive the same after-tax return wherever employed: Taxes are zero for the informal good and factors: Formal factors face the same tax rates whether producing _exports_ or _formal_ goods. This permits simpler notation: The numeraire is foreign exchange: Goods supply equals demand.

The transfer to the consumer is equal to tax revenue.

Parameters in the model are: production and utility function parameters; endowments of time, capital and foreign exchange; and tax rates. Parameter values are determined by the calibration process.

30
# **B Data**

The data required for the model are:

- _E_ exports (% of GDP)

- _M_ imports (% of GDP)

- _RD_ tax revenue from VATs and sales taxes (%GDP)

- _RE_ tax revenue from export taxes (% GDP)

- _RM_ tax revenue from import taxes (% GDP)

- _RK_ tax revenue from capital taxes (% GDP)

- _RL_ tax revenue from labor taxes (% GDP)

- _TD_ tax rate on domestic goods and services

- _TK_ tax rate on capital (corporate tax rate)

- _TL_ tax rate on labor

- _αi_ labor-output ratio in production of _untaxed_

- _αf_ labor-output ratio in production of _domestic αe_ labor-output ratio in production of _exports_

Country-specific data are set out in Table 9. All country-specific data were obtained from IMF Statistical Annexes to country reports, available on the internet at www.imf.org. Table 9 also reports the year for which the data apply, and whether the country had a VAT in that year.

In the absence of data on labor-output ratios for all countries, the model uses the average ratios for the five countries of Table 10, supposing that the ratios are constant across all countries. These data are derived from social accounting matrices prepared by the International Food Policy Research Institute. Among other data, the SAMs provide for each commodity: the value-added by each factor; exports of each commodity; domestic demand for the commodity; and goods taxes paid. Let _Li_ denote the labor share of value added for each commodity _i_ . Let _Ei_ denote exports of each commodity. The first row in the table, the labor-output ratio <u>�</u> _<u>i</u>_<sup>(</sup><sup>_Li×Ei_)</sup> for exports is then . Commodities are classified as _untaxed_ if the taxes <u>�</u> _i_<sup>_Ei_</sup> paid on the commodity constitute less than 5% of the value of domestic output of the commodity, and _domestic_ if more than 5% is taxed. Let _Uj_ be the valueadded of untaxed goods. The labor-output ratio for _untaxed_ is then calculated <u>�</u> _<u>j</u>_<sup>(</sup><sup>_Lj×Uj_)</sup> as . The same procedure is used to calculate the labor-output ratio for <u>�</u> _j_<sup>_Uj_</sup> _domestic_ .

The administrative costs of tax collection presented in Table 5 are derived from various sources. For the United States: IRS Data Book, FY2002, available at: www.irs.gov/pub/irs-soi/02db30cs.xls; For other OECD countries – authors’ calculations based on the following tax agency annual reports: Australia – ATO Annual Report 2002, available at www.ato.gov.au; United Kingdom – Inland Revenue, Annual Report for the year ending 31st March 2002, available at www.inlandrevenue.gov.uk/pdfs/report2002.pdf; New Zealand – Inland Revenue 31
Table 9: Country-Specific Data

|Country|year|_E_|_M_|_I_|_RD_|_RE_|_RM_|_RK_|_RL_|_TD_|_TK_|_TL_|_VAT_|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Benin|2001|27.69|35.40|19.18|2.76|0.14|6.54|1.90|1.57|0.18|0.38|0.28|*|
|Botswana|2001|56.20|33.20|15.70|2.07|0.00|2.95|5.00|2.48|0.10|0.15|0.10|*|
|Burkina Faso|2001|9.34|23.38|19.50|3.66|0.42|3.32|1.28|1.32|0.18|0.20|0.15|*|
|Burundi|2000|7.79|21.23|8.39|9.16|0.00|3.40|1.57|3.91|0.20|0.40|0.50|-|
|Cameroon|2001|31.80|29.20|17.80|3.96|0.08|3.91|1.46|1.03|0.19|0.39|0.17|*|
|Cape Verde|2001|30.82|65.35|17.36|0.58|0.78|9.78|3.59|3.59|0.10|0.20|0.20|-|
|CAR|1999|16.78|23.83|14.41|2.76|1.12|2.36|0.52|1.00|0.18|0.30|0.31|-|
|Chad|2000|16.58|32.03|17.02|1.88|0.22|1.85|1.13|1.15|0.18|0.45|0.48|*|
|Congo|1999|21.90|25.59|24.10|1.03|0.05|0.74|0.27|0.49|0.03|0.40|0.35|-|
|Côte d’Ivoire|1999|44.33|37.46|16.30|4.82|2.56|4.60|2.08|1.68|0.20|0.35|0.27|*|
|Eq. Guinea|2001|106.02|125.60|56.79|0.63|0.45|0.28|1.67|0.39|0.06|0.25|0.10|-|
|Eritrea|2000|5.26|67.37|18.50|2.77|0.00|4.37|4.84|1.98|0.05|0.25|0.12|-|
|Ethiopia|2001|15.36|31.18|18.04|2.66|0.18|6.22|2.90|1.32|0.15|0.30|0.15|-|
|Gabon|2000|66.96|32.65|21.84|1.99|0.79|5.16|1.54|0.72|0.18|0.35|0.30|*|
|Gambia|1998|50.53|61.32|18.30|1.46|0.00|11.18|2.09|1.85|0.10|0.35|0.15|-|
|Ghana|1998|34.27|46.66|24.67|1.62|2.32|4.30|1.85|1.77|0.10|0.35|0.15|*|
|Guinea|1998|21.60|23.40|17.10|4.65|0.02|1.45|0.20|0.65|0.18|0.35|0.29|*|
|Guinea-Bissau|2001|27.21|57.71|18.92|0.74|2.61|4.30|0.92|0.95|0.15|0.39|0.10|-|
|Kenya|2000|26.47|36.39|15.55|6.62|0.00|5.96|3.45|3.45|0.15|0.30|0.15|*|
|Madagascar|2001|28.59|31.75|15.50|2.65|0.00|4.79|0.99|0.97|0.20|0.35|0.15|-|
|Malawi|1999|27.04|49.32|17.08|1.61|0.00|0.61|0.71|0.86|0.20|0.30|0.32|-|
|Mali|2000|25.50|37.50|20.60|2.32|0.22|6.22|1.31|1.12|0.18|0.35|0.29|*|
|Mauritania|2002|38.54|66.93|33.04|3.87|0.00|2.34|2.01|2.30|0.14|0.25|0.26|*|
|Mozambique|2001|21.90|38.50|41.64|3.99|1.98|3.22|0.73|1.27|0.17|0.45|0.15|*|
|Namibia|1997|52.62|58.17|19.75|4.54|0.00|9.62|5.03|6.00|0.10|0.40|0.20|-|
|Niger|2000|17.80|25.33|10.78|1.61|0.18|3.61|0.56|0.73|0.19|0.43|0.34|*|
|Nigeria|2000|53.27|37.54|17.70|1.37|0.00|2.77|1.22|1.09|0.05|0.30|0.20|*|
|Rwanda|2001|9.30|25.80|18.40|3.16|0.00|3.41|1.91|1.19|0.15|0.40|0.30|-|
|São Tomé|2000|35.32|82.44|43.49|0.41|0.05|10.20|1.81|2.71|0.35|0.30|0.13|-|
|Senegal|2000|30.50|39.60|19.10|4.64|0.00|8.48|1.91|2.20|0.20|0.35|0.44|*|
|South Africa|1999|25.70|24.40|16.50|5.87|0.00|1.00|3.60|10.70|0.14|0.30|0.30|*|
|Sudan|1999|8.11|15.13|16.70|1.29|0.07|2.85|0.90|0.12|0.10|0.40|0.20|-|
|Swaziland|2001|70.20|83.30|18.10|3.55|0.00|13.20|2.15|3.78|0.32|0.30|0.33|-|
|Tanzania|2002|15.90|24.50|17.00|2.51|0.00|4.67|0.66|1.55|0.20|0.30|0.25|*|
|Togo|1998|33.72|40.39|14.20|3.20|0.00|5.60|1.60|0.90|0.14|0.30|0.33|*|
|Uganda|1998|11.78|28.48|17.65|6.56|0.01|1.00|0.66|0.66|0.17|0.30|0.20|*|
|Zambia|1998|29.30|38.40|14.40|6.60|0.00|4.60|1.40|4.70|0.18|0.35|0.20|*|
|Zimbabwe|2000|29.81|31.00|15.55|6.00|0.00|2.59|3.89|10.86|0.15|0.30|0.30|-|

|||Table 10: Lab|or-Output|Ratios (%|)||
|---|---|---|---|---|---|---|
||Malawi|South Africa|Tanzania|Zambia|Zimbabwe|Average|
|export|38.08|56.14|33.58|19.39|37.09|36.86|
|domestic|48.34|48.28|33.59|39.37|46.82|43.28|
|untaxed|58.66|53.99|43.79|53.15|49.70|51.86|

32
Annual Report 2001-2002, available at: www.ird.govt.nz/ aboutir/reports/annual02.pdf; and Canada: Canada Customs and Revenue Agency, 2001-2002 Annual Report to Parliament, Financial Statements, available at www.cra-arc.gc.ca/agency/ annual/2001-2002/. For Guatemala: simple average of adjusted figures from Mann (2002). Ghana: revenue-weighted average of figures cited by Terkper (1995). Namibia: statistics provided by Klaus Schade of the Namibian Economic Policy Research Unit. Tanzania: statistics provided by Odd-Helge Fjeldstad of the Chr. Michelsen Institute. Remaining countries: Taliercio (2004). We are very grateful to Klaus Schade, Odd-Helge Fjeldstad and Robert Taliercio Jr. for their assistance in obtaining these data.

# **C Model Calibration**

Benchmark quantities of goods and factors (entries in the SAM) are calculated using the following equations: 33
_L_<sup>_i_</sup> _D_<sup>=</sup><sup>_αD_(</sup><sup>_XD_+</sup><sup>_ID_)</sup><sup>_−_(1 +</sup><sup>_TL_)</sup><sup>_Lf_</sup> _D informal labor_ used to produce _domestic L_<sup>_i_</sup> _E_<sup>=</sup><sup>_αE_(</sup><sup>_XE_+</sup><sup>_IE_)</sup><sup>_−_(1 +</sup><sup>_TL_)</sup><sup>_Lf_</sup> _E informal labor_ used to produce _exports L_<sup>_i_</sup> _U_<sup>=</sup><sup>_αU_(</sup><sup>_XU_+</sup><sup>_IU_)</sup> _informal labor_ used to produce _untaxed KD_<sup>_i_= (1</sup><sup>_−αD_)(</sup><sup>_XD_+</sup><sup>_ID_)</sup><sup>_−_(1+</sup><sup>_TK_)</sup><sup>_K_</sup> _D_<sup>_f_</sup> _informal capital_ used to produce _domestic KE_<sup>_i_= (1</sup><sup>_−αE_)(</sup><sup>_XE_+</sup><sup>_IE_)</sup><sup>_−_(1 +</sup><sup>_TK_)</sup><sup>_K_</sup> _E_<sup>_f_</sup> _informal capital_ used to produce _exports KU_<sup>_i_= (1</sup><sup>_−αU_)(</sup><sup>_XU_+</sup><sup>_IU_)</sup> _informal capital_ used to produce _untaxed_ ̄ _K_ = _KE_<sup>_f_+</sup><sup>_K_</sup> _D_<sup>_f_+</sup><sup>_K_</sup> _E_<sup>_i_+</sup><sup>_K_</sup> _D_<sup>_i_+</sup><sup>_K_</sup> _U_<sup>_i_</sup> total capital endowment _TL_ ̄ == 1 _L._<sup>_f_</sup> _E_ 05<sup>+</sup> _L_<sup>_Lf_</sup> _D_<sup>+</sup><sup>_L_</sup> _E_<sup>_i_+</sup><sup>_Li_</sup> _D_<sup>+</sup><sup>_Li_</sup> _U_ totalendowmentlabor supplyof time Tax rates on _exports_ and _imports_ are calibrated, rather than being drawn directly from the legal tax rates: tax rate on _exports_ tax rate on _imports_ We do not observe price or quantities of goods, but we do observe the total amount of money spent on each good (values as a percentage of GDP). Following the Harberger convention we choose units of the aggregate goods such that quantities equal values. This implies that initial prices equal one. Where goods are taxed, goods units can be chosen such that either the gross of tax or net of tax price equals one. We chose units such that the agent supplying the good or factor received a price of one, with remaining prices implied by tax rates: _P_<sup>_w_</sup> _M_<sup>= 1</sup> _PI_ = 1 _PU_ = 1 _PL_ = 1 _PK_ = 1 world price of imports (and foreign exchange) price of _investment_ price of _untaxed_ wage received by labor (formal or informal); also the wage paid by producers for _informal labor_ wage received by capital (formal or informal); also the wage paid by producers for informal capital _PD_ = 1 _PE_ = 1 producer price of _domestic_ producer price of _exports_ 34
<u>1</u> An n-factor CES production function, _F_ = _A_ (<sup>�</sup><sup>_n_</sup> _j_ =1<sup>_θjX_</sup> _j_<sup>_ρ_)</sup> _ρ_ , with factors _Xj_ , share parameters _θj_ , scale parameter _A_ , and elasticity of substitution _σ_ = 1 _−_ <u>1</u> _ρ_<sup>, can</sup> be rewritten in calibrated form as where a bar over a variable indicates the observed benchmark level. The benchmark factor demands, factor prices and product outputs, combined with the elasticities of substitution fully specify the three production functions. The same methodology can be used for the CES utility function, where the _Xi_ s represent goods consumed, the _pi_ s are goods prices, and the benchmark utility level is normalized to unity.

The calibration process is completed with the selection of substitution elasticities for production and utility functions. In the absence of reliable evidence on the magnitude of these elasticities for Africa we chose a base case of _σ_ = 1 for all four functions, and then ran sensitivity checks with different values for _σ_ .

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