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Why poor countries rely mostly on redistribution in-kind
Journal of Public Economics 75 (2000) 463–481 www.elsevier.nl / locate / econbase
Why poor countries rely mostly on redistribution in-kind P. Bearse a , G. Glomm b , *, E. Janeba c b
a Department of Economics, University of North Carolina, Greensboro, NC, USA Department of Economics, Michigan State University, 101 Marshall Hall, East Lansing, MI 48824, USA c Department of Economics, Indiana University, Bloomington, IN 47405, USA
Abstract We present a model in which the crucial distinction between rich and poor countries is that governments in rich countries have access to a more productive tax collection technology than governments in poor countries. Since the tax collection technology in poor countries is poor, the quality of the public service is low. Therefore many households at the top of the income distribution opt out of the public service. The median voter takes this into consideration and allocates a larger share of the public budget to redistribution in-kind (public service) than to redistribution in cash. 2000 Elsevier Science S.A. All rights reserved. Keywords: Public provision; Transfers; Redistribution; Majority voting JEL classification: H5; D72
1. Introduction Governments in most countries engage in some kind of redistributive activity. In rich countries social security and welfare payments exceed 10% of GDP and are larger than expenditure on public education (see Table 1). In middle income countries, social security and welfare budgets are smaller and roughly equal to public expenditures on education (see Table 2). In poor countries, social security *Corresponding author. Tel.: 11-517-355-7359; fax: 11-517-432-1068. E-mail address: [email protected] (G. Glomm) 0047-2727 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0047-2727( 99 )00076-6
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Table 1 Redistributive expenditures in rich countries (as percent of GDP)a
Education Health Social security and welfare Housing Number of observation a
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
4.9 4.3 10.3 1.0 4
5.7 5.2 14.1 1.4 15
5.4 4.6 13.5 1.6 24
5.3 4.8 12.8 1.6 26
5.4 5.0 13.4 1.6 24
5.6 4.9 13.5 2.0 23
5.4 4.8 13.7 1.7 24
5.3 4.8 13.7 1.7 24
5.2 4.9 13.3 1.7 21
5.5 4.7 14.0 1.9 18
Source: Author’s calculation from IMF Government Finance Statistics (1993).
Table 2 Redistributive expenditures in middle income countries (as percent of GDP)a 1981 1982 Education Health Social Security and welfare Housing Number of observations a
1983
1984
1985
1986
1987
1988
1989
1990
3.0 1.3
3.1 2.1
3.3 1.8
3.4 1.8
3.4 1.8
3.5 1.7
3.5 1.9
3.5 1.9
3.5 1.9
3.5 1.9
1.7 0.7 7
4.6 0.6 14
4.2 0.6 19
3.6 0.6 23
3.6 0.6 24
3.7 0.7 25
3.9 0.8 22
3.8 0.7 22
3.7 0.7 23
3.9 0.7 20
Source: Authors’ calculation from IMF Government Finance Statistics (1993).
and welfare payments take up a much smaller fraction of GDP; they are roughly a fourth of public education expenditures (see Table 3). The list of countries used in Tables 1–3 is given in Table 4. These countries are broken down into rich, middle income and poor using real per capita income in 1980 from the Summers and Heston (1988) data set. Redistribution, however, does not only take the form of social security and welfare payments; often redistribution is carried out in the form of subsidizing housing and health care for the poor or in the form of public
Table 3 Redistributive expenditures in poor countries (as percent of GDP)a
Education Health Social security and welfare Housing Number of observation a
1981 1982 1983 1984
1985
1986
1987
1988
1989
1990
4.5 1.6 1.3 0.9 9
4.5 1.6 1.1 0.8 21
4.5 1.6 1.2 0.9 21
4.3 1.7 1.1 1.2 22
3.9 1.5 1.1 0.9 21
4.2 1.6 1.3 1.1 17
4.1 1.6 1 1.1 14
5.1 1.8 1.2 1.2 13
4.7 1.7 1.5 1.1 19
4.3 1.6 1.1 1.4 22
Source: Authors’ calculation from IMF Government Finance Statistics (1993).
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Table 4 Poor, middle income and rich countries in 1980 with per capita GDP a Poor countries income # 1551 1. Bolivia 2. Botswana 3. Cameroon 4. Egypt 5. El Salvador 6. Ethiopia 7. Gambia 8. Ghana 9. India 10. Kenya 11. Lesotho 12. Liberia 13. Madagascar 14. Malawi 15. Morocco 16. Mauritius 17. Nepal 18. Papua New Guinea 19. Philippines 20. Sierra Leone 21. Sri Lanka 22. Swaziland 23. Yemen 24. Zambia 25. Zimbabwe 26. – a
Middle income countries 1529 1477 875 995 1410 325 556 421 614 662 694 680 589 417 1199 1484 490 1528 1551 512 1119 1079 957 716 930
Argentina Barbados Brazil Chile Colombia Costa Rica Cyprus Dominican Republic Ecuador Fiji Guatemala Iran Jordan Korea Malaysia Mexico Panama Paraguay Peru Portugal Syria Thailand Tunisia Turkey Uruguay Venezuela
Rich countries income #4630 4342 4454 3356 2552 2552 3031 4282 1868 2607 3005 1952 2944 1885 2369 3112 4333 2810 1979 2456 3733 3071 1697 1845 2319 4502 4242
Australia Austria Bahrain Belgium Canada Denmark Finland France Germany Iceland Ireland Israel Italy Kuwait Luxembourg Malta Netherlands New Zealand Norway Oman Singapore Spain Sweden Switzerland U.A.E. U.S.
8349 8230 9185 9228 11 332 9598 8393 9688 9795 9285 4929 6145 7164 19 454 10 173 4630 9036 7363 11 094 6209 5817 6131 8863 10 013 25 646 11 404
Source: Summers and Heston (1988).
education which is financed by a proportional or progressive income or wealth tax and made available to all school age children at an almost zero price.1 A glance at Tables 1–3 reveals that rich and poor countries treat transfers in cash (social security and welfare payments) and transfers in-kind (public expenditures on education, housing and health) differentially. Rich countries rely predominantly on transfers in cash in their redistribution policies, while in poor
1
While it is true that social security redistributes income between generations, it also is a tool for intragenerational redistribution. Rosen (1995), for example, documents that a low income earner who retires in 1995 makes a net gain out of social security of 21.7%, while for a high income earner there is a net loss of 27.8% from social security.
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countries the lion’s share of redistribution is through transfers in-kind.2 Burgess and Stern (1993) also document this fact, although their data are restricted to expenditures by central governments. This differential use of transfers in-kind vs. transfers in cash by rich vs. poor countries is the heart of this paper. We want to explain why poor countries use different redistribution policies than rich countries. In Section 2 we present a model which can deliver this differential treatment of in-kind vs. cash transfers as an equilibrium outcome. In the model a government raises an income tax at a uniform rate. A portion of tax revenue is used for uniform lump-sum transfers and the remainder is used for public provision of a good such as education, health or housing. For ease of reference we often refer to this good as education. Public education is made available to all households at a zero price. Public provision is ‘‘uniform and universal’’ in the sense of Besley and Coate (1991). Households are free, however, to opt out of public education and choose a private alternative. Choosing the private alternative entails paying the full marginal resource requirement. Public policies are determined endogenously through majority voting.3 Since public policy here is two dimensional (the size of the government budget and its split between transfers in-kind and transfers in cash), the voting problem is solved in two stages. In the first stage, the size of the government is determined while the composition of the government budget is determined in the second stage.4 The crucial distinction between poor and rich countries in this model is the government’s ability to raise revenue. We specify a tax revenue collection function similar to the one used by Perotti (1993). According to this revenue collection technology, the revenue raised is a strictly concave function of the (uniform) tax rate for exogenously given incomes. This technology is intended to capture tax evasion and tax avoidance activities of taxpayers and / or tax collection costs on the part of the government. As Easterly and Rebelo (1993) point out, these costs are not small. According to Vaillancourt (1989), total private and public costs associated with the income tax system and social security payments in Canada are about 7% of the revenue collected. For the U.K. a study by Sandford et al. (1989) contains an estimate of these costs of about 5% of revenue collected. Acharya (1985) estimated that in India income declared for tax purposes was 53.3% of the total income assessable. Herschel (1978) reports that in Argentina in the 1950s 2
Poor countries often receive foreign assistance for capital expenditures in health or in education. Even if foreign aid amounts of half of education or health expenditure, poor countries still use redistribution in kind more than redistribution in cash. 3 Using a majority voting model for all countries is a somewhat restrictive assumption. Note, however, that not all rich countries are democratic (UAE, Kuwait) and many poor / middle income countries are not dictatorships (Egypt, India). It is also interesting to notice that the expenditure composition in Tables 1–3 is quite stable over the whole period despite the fact that more and more countries have started liberalization both economically and politically in the late 1980s. 4 We use the two-stage voting procedure to avail well know issues of existence of a majority voting equilibrium (see, for example, Enelow and Hinich, 1984).
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only 25.5% of taxable income was actually reported for tax purposes. Alternatively, there could be differential corruption across countries. Both Bardhan (1997) and Mauro (1995), for example, document that corruption is higher in poor than in rich countries. Easterly and Rebelo (1993) argue that it is plausible that collecting tax revenue requires fixed costs which governments in poor countries might not find worthwhile to bear. In this paper, we take as a crucial assumption that governments in rich countries have access to better revenue collection technologies and exhibit less corruption and / or less tax evasion than governments in poor countries. We show that these differences between rich and poor countries can give rise not only to different government size but also to a different composition of public expenditure. When the tax revenue collection technology is unproductive, for any given tax rate, total tax revenues will be small. When tax revenues are small, the quality of the publicly provided good is poor and a large fraction of the top end of the income distribution opt out of the public service and buy the service on the private market. There is some evidence for opting out of publicly provided services by the rich. van de Walle (1995) documents that in Indonesia people in the top income decile are almost 15 times as likely to consult a private physician than people in the bottom decile. For the U.S., Catteral (1988) reports that the fraction of children attending private school increases almost monotonically with income. In 1982, only 3.3% of children whose parents had income less than $7 500 attended a private school, whereas 31.0% of those families with incomes above $75 000 chose a private school for their kids. In our model, the median voter takes this opting-out-behavior into consideration when voting on the composition of the public budget. If tax collection is poor, the median voter (in the second stage of voting) tends to vote for more redistribution in kind. Since more people opt out and leave relatively more resources for public education, shifting resources to in kind transfers deliver a greater ‘‘bang for the buck.’’ In the first stage of voting, higher tax rates prevail in rich economies because there governments have productive tax revenue collection technologies. Both predictions are roughly consistent with the data. There is a large literature on the optimality of transfers in cash and in kind. Examples of this literature include Buchanan (1975), Bruce and Waldman (1991), Blackorby and Donaldson (1988), Gahvari (1995), Munro (1989, 1992), Blomquist and Christianson (1998) and Besley and Coate (1991). In most of these papers redistribution in kind may be used to overcome some private information problem. In this paper we use as a starting point another information problem. In poor countries the personal income tax system is much less developed, mostly because a sizable part of the population is illiterate and works in the agricultural and / or in the informal sector. This makes it difficult to accurately assess income for tax purposes. Behind the inability to collect income tax revenue lies an informational
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problem. In poor countries it is difficult for the government to assess individual incomes. There may, therefore, be more tax evasion in poor countries. Also, in poor countries it may be more difficult to monitor bureaucrats. Consequently, there may be more corruption in poor countries. We model these kinds of informational problems as a loss of tax revenue, which is greater in poor than in rich countries. Given this differential loss of tax revenue, we seek to explain the different patterns of redistribution. This paper is closely related to the growing literature on endogenous redistribution in (dynamic) general equilibrium models. A nice survey of this literature is Benabou (1996). Persson and Tabellini (1994) study endogenous redistribution through transfers in cash in an overlapping generations economy. They find that higher inequality generates higher redistribution which in turn generates lower growth. Alesina and Rodrik (1994) study distributive politics and growth in a model in which public revenue is used to finance investment in infrastructure. Perotti (1994) contains an empirical investigation of the relationship between income distribution and growth. These papers above allow for one kind of redistribution, usually redistribution in cash. In this paper here we allow for several type of redistributive policies and make predictions about the relative importance of each type. We solve the model numerically in Section 3. Our simulations reveal that the voting equilibrium is roughly consistent with the stylized facts pointed out in Tables 1–4. In the model in Section 2 the inefficiency arises because of public corruption. In Section 4 we address how a different inefficiency, namely tax evasion, influences our results. Section 5 contains a discussion of potential alternative explanations of the stylized facts. Section 6 concludes.
2. The model The economy is populated by a large number of individuals. Population size is normalized to one. Each individual lives one period. All individuals have identical preferences over a consumption good c, and a good e. The consumption good c is always provided privately, while the good e is provided both publicly and privately; good e is made available to all individuals by the public sector, but individuals are free to purchase the private alternative on the market. We will refer to good e as education, but healthcare, housing or transportation are other possible interpretations. The utility function is given by 1 s s ]] hc 12 1 d e 12 j, s . 0, d . 0 i 12s i where c i and e i denote the amounts of the two consumption goods consumed by individual i. We use specific functional forms from the start, because few analytical
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results are available and we rely therefore heavily on numerical solution techniques. All individuals have identical preferences. Individuals are differentiated by income. Let y i denote income (or wealth) of individual i. Let F be the c.d.f of income. We assume that the support of F is the non-negative real line and that the mean exceeds the median. The government collects an income tax at the uniform rate t.5 Due to tax evasion or corruption the tax revenue collected falls short of the tax rate times income. We capture this with a tax function R(t ) 5 t 2 at 2 , a . 0. For a ,1 / 2, this function peaks when t .1. For a .1 / 2, the function is consistent with a Laffer curve. Letting Y denote aggregate income, the total tax revenue for the government is R(t )Y. This type of a revenue collection technology has been used by Perotti (1993). The government uses a fraction D [ [1,0] of tax revenues to purchase educational services which are made available to all individuals at a zero price. If N is the fraction of the population which attends the public school, then public school expenditure per pupil are given by
DR(t )Y E 5 ]] N
(1)
We can think of Eq. (1) as a linear education production function. The part of the budget which is not allocated to education is allocated to uniform lump-sum transfers. Income of an individual can then be written as (1 2 t )y i 1 (1 2 D)R(t )Y.6 5 Developing and developed countries differ not only in the size of government and composition of expenditures, but also in terms of the mix of government revenues. Burgess and Stern (1993) report that developing countries rely more heavily on indirect taxes than developed countries do, usually for the informational reasons discussed above. In our theoretical model we nevertheless use a linear income tax in all countries. This is not as restrictive as it may seem at first glance. Note that the income tax in our model is progressive because of the constant marginal tax rate and the uniform lump sum subsidy. A progressive tax system can be implemented also in countries using consumption taxes. For example, in a model with two consumption goods, say food and all other goods, differential taxation of these goods is progressive when low-income individuals consume relatively more food and food is taxed at a lower rate. For simplicity, we adopt a common model with one consumption good beside education in order to make our point. They key question, both in developing and developed countries, is whether the tax system or the in-kind transfer is the better tool to redistribute in favor of the median voter, regardless of having differential consumption taxes or a linear progressive income tax. 6 Here individuals pay the full amount of the statutory tax, and keep (1-t ) y i . Tax revenue disappears after it has been collected from the household. This can be interpreted as corruption.
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The uniform lump-sum subsidy in connection with a constant marginal tax rate can be interpreted as a linear progressive income tax. If an individual with income y i chooses public school, the associated indirect utility function is
H
S
1 DR(t )Y v ui 5 ]] f(1 2 t )y i 1 (1 2 D)R(t )Yg 12 s 1 d ]] 12s N
D J. 12 s
If an individual with income y i chooses the private school alternative, he solves the problem 1 s s max ]] hc 12 1 d e 12 j i i hc i ,e i j 1 2 s s.t. c i 1 e i 5 (1 2 t )y i 1 (1 2 D)R(t )Y. We will refer to this as problem P. The solution to this problem is c i 5 (1 1 d 1 / s )21 [(1 2 t )y i 1 (1 2 D)R(t )Y] e i 5 d 1 / s (1 1 d 1 / s )21 [(1 2 t )y i 1 (1 2 D)R(t )Y] and the associated indirect utility function is 1 v ri 5 ]](1 1 d 1 / s )s [(1 2 t )y i 1 (1 2 D)R(t )Y] 12 s. 12s An individual will choose the public service over private provision iff v ui $ v ri
(2) 3
Condition (2) at equality determines a critical level of income y with the property 3 3 that if y i ,y the individual chooses public provision and if y i .y the individual chooses private provision. This follows directly from substituting the expressions for v u and v r into condition (2). Fig. 1 illustrates v u and v r as functions of ˆ individual income and shows the cut-off level y. Both the tax rate t (the overall size of the government) and the composition of the government budget D are determined through majority voting. We let individuals vote in two stages. In the first stage, they vote on the tax rate. In the second stage, they vote on D, taking the tax rate as given. Individuals are forward looking and therefore in the first stage take into account how a change in t affects D. This two-stage voting process corresponds to actual rules in some countries. An equilibrium for this economy is an allocation for each household who chooses the public alternative (c ui ,e ui ), an allocation for each household who 3 chooses the private alternative (c ir ,e ir ), a critical level of income y, a public school enrollment N, and public policies (t, D(t )) such that
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Fig. 1. Indirect utilities.
S
D
DR(t )Y (i) sc ui ,e ui d 5 (1 2 t )y i 1 (1 2 D)R(t ), ]] , N (ii) (c ri ,e ri ) solves problem P, 3 (iii) the income level y satisfies condition (2) with equality, 3 (iv) N 5 F(y ), (v) given D (t ), t wins in majority voting in the first stage, (vi) given t, D wins in majority voting in the second stage. Notice that according to this definition voters in the first stage take into consideration how the choice of government size t influences the composition of the government budget D in the second voting stage.
3. Solving the model We solve the model backwards. For a given public policy, each household decides whether or not to opt out of the publicly provided3 service. Imposing equality on condition (2) determines the level of income y which makes the household just indifferent between opting out or not. This critical income level is given by
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H
J
d 1 / 12 s D R(t )Y y 5 ]]]]]] 1 ] 2s1 2 Dd ]] (1 2 t ) fs1 1 d 1 / sd s 2 1g 1 / 12s N
3
(3)
whenever that expression is non-negative. We then have Result 1: A household with income y i opts out of the public service if and only 3 if y i .y. 3 Since the critical level of in y in Eq. (3) is a declining function of participation in the public service N, we have Result 2: Given D and t, there exists exactly one solution to the equilibrium 3 condition N 5 F(y ) if the c.d.f. F is continuous and strictly increasing. For a given t, which is determined in the first stage, the share D is chosen by majority voting. The voting problem on D is very similar to the one analyzed by Epple and Romano (1996). They prove, under a particular single-crossing property of indifference curves in tax-expenditure space, that a majority voting equilibrium exists. Their existence proof relies on the assumption that the government only finances educational expenditures. (Bearse et al., 1998) show that this particular single-crossing property does not arise when the government also finances uniform lump-sum transfers and when the voting decision is made on the composition of the government budget. Even when t is held fixed, there are no known conditions sufficient for an equilibrium when voting on the government budget composition D. Furthermore, we study here a two-dimensional voting problem, which is solved sequentially. For these reasons we are forced to rely heavily on numerical solution techniques. We pick a sample of 101 households which are drawn from a lognormal distribution, that is lny | N(m 5 3.606, s 5 0.615). If income is measured in $1000 this distribution roughly corresponds to the U.S family income distribution in 1992. We pick a grid of 101 points for values for t between zero and one and do likewise for D and N. For each value of t, we solve the voting problem on D by running a tournament between all possible values of D. This step generates the composition of the public budget D as a function of the size of the public budget t. We then run a tournament of all the 101 values of the size of the public budget. In general there is no guarantee that we will avoid cycles. Our computations reveal that for some tax rates t there are cycles when voting on the composition D. In order to avoid complications arising from the presence of cycles, we eliminate all tax rates t which generate cycles when voting over D in the second stage.7 In the first stage, when voting over t, we allow only those tax rates which do not generate cycles. Table 5 contains the first results. There we keep the utility function and the income distribution constant and vary the tax collection productivity parameter a. As the tax collection parameter a rises, the share of the
7
In our companion paper we characterize existence of cycles in more detail.
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Table 5 Composition and size of Government in economics with varying tax collection productivity Preference parameters
Tax collection productivity a
Government size t
Government budget composition D
Participation in public service N
Public service quality E
s 50.9 d 50.1
0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5
0.950 0.460 0.300 0.230 0.180 0.950 0.430 0.290 0.260 0.250 0.950 0.370 0.360 0.250 0.160 0.950 0.350 0.360 0.260 0.230
0.000 0.000 0.190 0.220 0.280 0.000 0.210 0.270 0.310 0.330 0.000 0.370 0.390 0.390 0.510 0.000 0.870 0.870 0.950 0.950
0.000 0.000 0.964 0.942 0.936 0.000 0.970 0.934 0.932 0.932 0.000 0.934 0.932 0.817 0.754 0.000 0.932 0.932 0.854 0.810
0.000 0.000 2.385 2.162 1.172 0.000 3.772 3.393 3.435 3.433 0.000 6.017 5.957 4.760 4.412 0.000 13.469 13.287 11.485 10.690
s 51.1 d 50.1
s 51.5 d 50.1
s 51.5 d 50.5
public budget going to transfers in kind generally rises. Surprisingly, we obtain this result for high and low elasticities of substitution in utility. In order to provide some intuition for this result we consider an economy with a fixed tax rate t. For this economy we vary a and study (i) how preferences over D of a voter with fixed income change with a and (ii) how the identity of the decisive voter changes. Consider Fig. 2. If D 50, the consumer who chooses public education attains point A where c i 5 (1 2 t )y i 1 R(t (a )Y and e i 5 E 5 0. If D 51, the individual attains point B where c i 5 (1 2 t )y i and e i 5 E 5 [R(t (a ))Y] /N. Letting D vary over [0,1] traces out the line segment AB. This line segment borders the feasible set for the individual. Now suppose that the tax collection parameter a rises. As a rises, R(t (a )) falls (for fixed t ; the point A moves down along the c-axis to point A9. Similarly, the point B moves left to point B9. However, as a rises, the quality of the publicly provided good falls, more individuals opt for the private alternative and N falls. Since N falls the decline in [R(t (a ))] /N is smaller than the decline in R(t (a )). Thus the new border of the feasible set, the line segment A9B9, is flatter than the border AB. This is like a change in a relative price. As a rises, the good e (publicly provided) becomes cheaper relative to good c.
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Fig. 2. Comparative statistics on tax collection parameter a.
Now there are two cases to consider. In the first case s ,1. Then the substitution effect associated with this relative price change dominates the income effect. Each voter would like to shift resources from c to e, that is each voter prefers a higher D. As a rises, opting out increases for a given D. High income individuals opt out and desire D 50. If the most preferred D is an increasing function of own income, which is the case for fixed N,8 having more people opt out at the top of the distribution implies that the decisive voter has lower income. We have three effects: The direct or substitution effect raises D. A second effect, i.e. changing the identity of the decisive order, lowers D. The third effect arises because at higher a, more people opt out of public provision and the median voter gets more bang for the buck when funds are allocated to public education. Our simulations reveal that the first and the third effect are dominant. The second case, s .1 is a bit trickier. Here the income effect associated with this change in the relative price dominates the substitution effect. As a rises, each voter would prefer a lower D. The identity of the median voter also changes. Here the most preferred D is an increasing function of income for all individuals who
8
When N is endogenous the indirect utility function may not even be concave in D.
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use the publicly provided service. Those who opt out and use the private service have a most preferred D of zero. As a rises, the identity of the decisive voter changes. With higher a, the income of the decisive voter is lower. Since the most preferred D is rising in income, the decisive voter now has a lower most preferred D. The third effect raises opting out with an increase in a and thus induces the median voter to shift public funds from cash transfer to public education. As long as the third effect is dominant, an increase in a is consistent with higher D. This is confirmed in Table 5. In Table 6 we fix the preference parameters at s 51.1 and d 50.1, but allow the mean income to vary, holding s, the measure of inequality constant. The range of a we consider is the same as before. Average incomes are allowed to decrease by factors of 10, 20 and 30. A ratio of 30 corresponds roughly to the income ratio between the richest and poorest countries. As average income drops, the voting equilibrium stays unaffected. The intuition here is that technologies exhibit constant returns to scale and that preferences are homothetic. Changing the measure of average income is therefore a change in scale which has no economic effect. In Table 7 we study mean preserving spreads of the income distribution. We increase s and adjust m to keep mean income exp[m 1 ]21 s 2 ] constant. In this experiment we set s 51.1 and d 50.1. The results in Table 7 are robust with respect to changes in the preference parameters. Evidently, as the income distribution undergoes a mean preserving spread, the tax rate generally (not universally) rises and the fraction of the government budget going to the public Table 6 Changing average income Income distribution parameters
Average income
Tax collection Productivity a
Tax rate t
Government budget composition D
m51.303 s50.615
4.433
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
m50.61 s50.615
2.217
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
m50.205 s50.615
1.478
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
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Table 7 Mean preserving spreads Income distribution parameters
a
t
D
N
E
m53.606 s50.615
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.00 0.210 0.270 0.310 0.330
0.000 0.970 0.934 0.932 0.932
0.000 0.377 0.339 0.343 0.343
m53.475 s50.8
0.1 0.2 0.3 0.4 0.5
1.00 0.75 0.470 0.340 0.270
0.110 0.140 0.170 0.180 0.200
1.000 0.988 0.434 0.855 0.812
4.424 4.036 3.283 2.764 2.570
m53.295 s51.0
0.1 0.2 0.3 0.4 0.5
1.00 1.00 0.700 0.560 0.430
0.110 0.110 0.130 0.150 0.140
1.000 1.000 0.964 0.932 0.847
4.489 3.991 3.381 3.171 2.530
service falls. For most of the income distributions we tried, the fraction of the government budget going to the public service rises as a rises.
4. An alternative interpretation of tax evasion So far we assumed that the post-fisc income of an individual i is (1 2 t )y i 1 (1 2 D)R(t )Y. In this specification each household pays taxes in amount t y i but the amount of revenue actually available for redistribution is R(t )Y , t Y. Our interpretation here is that there is some government waste: Some bureaucrats siphon off tax revenue and use it to go skiing in Davos, Switzerland. An alternative formulation for the individual’s budget constraint is (1 2 R(t ))y i 1 (1 2 D)R(t )Y. According to this alternative budget constraint, a household with income y i is taxed at the rate t so that the assessed tax payment would be t y i . However, the household can hide some income from the tax authority and gets away with paying only
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R(t )y i , t y i . We repeat the analysis of the previous section for this alternative budget constraint. The results are similar to the previous case: As the tax collection technology worsens (a rises), participation in the public service N falls, the share of the public budget going to redistribution in-kind rises and government size falls.
5. Discussion and alternative explanations Our explanation of the observed difference in government transfer policies across countries is based on three elements: (1) Agent heterogeneity in terms of income which leads to conflicting political interests, (2) the government’s ability to effectively provide the good differs across countries for any given tax rate, and (3) the possibility to opt out and to purchase the good in the private market. We have indicated in the introduction that there is empirical evidence for these assumptions. Yet it is not clear whether all three elements are necessary for explaining the observed puzzle. In this section we discuss this issue in more detail. In particular, one may conjecture that the possibility to opt out is not essential. We argued in the previous section that one reason for element (2) is the higher degree of tax evasion in poor countries. In this sense we deal with an informational issue because the government’s ability to obtain information about private income is limited. Such limited ability to observe private types also is at the heart of papers by Buchanan (1975), Bruce and Waldman (1991), Blackorby and Donaldson (1988), Gahvari (1995), Munro (1992) and Blomquist and Christianson (1998). In all of these papers transfers in cash only are not efficient due to some hidden information or hidden action problem. In Blackorby and Donaldson (1988), for example, the government cannot costlessly distinguish between the types of individuals who are to receive transfers. They show that ‘‘second-best optima,that are not first-best, occur when the first-best distribution is not compatible with the self-selection constraints.’’ In such a world transfers in kind may be feasible and useful for optimality. A government which optimizes subject to self-selection constraints may thus rely on a mixture of transfers in cash and transfers in kind. It is possible that the nature of private information in poor countries relative to rich countries is such that optimal redistribution schemes in poor countries rely more on transfers in kind than on transfers in cash. This is a possible alternative explanation. We have found no empirical evidence for this explanation however. Similarly, the Samaritan’s dilemma (see Buchanan, 1975 and Bruce and Waldman, 1991) might be exacerbated in poor countries. Poverty in poor countries may be much more devastating than poverty in rich countries and thus elicit larger cash transfers. If the probability of becoming impoverished is endogenous and depends on actions by the potential recipient, it might be optimal in poor countries to have a larger
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share of transfers in kind than in cash. Again this might provide an alternative explanation for our stylized facts, although it is difficult to falsify. Another alternative which does not require assumptions on information asymmetries is a model involving non-homothetic preferences. Suppose all individual’s preferences are given by the semi-linear form ln e 1 c. The government collects an income tax at the rate of t, a fraction of the public revenue, D, goes to fund public education and the remainder goes to financial transfers. There is no opting out; all individuals attend public schools. In order to determine the fraction of the public budget going to education, each individual solves the problem Max ln Dt Y 1 (l 2 t )y 1 (1 2 D) t Y D
Where y is individual income and Y is average income. The solution to this problem is
D 5(t Y)21 . Notice that all individuals, regardless of individual income, prefer the same share D. The budget share is thus independent of income inequality. Notice also that D is declining in average income. This result is consistent with our stylized fact that in poorer societies governments allocate a larger share of the public budget to education. According to our data, the fraction of the national income allocated to in kind transfers rises as income rises. This model with semi-linear preferences does not deliver this second result since E /Y 5 1 /Y falls with income.
6. Concluding remarks In this paper we have presented a model to explain why poor countries have smaller governments than rich countries and why governments in poor countries, unlike governments in rich countries, rely mostly on redistribution in-kind and not on redistribution in cash. In the model the crucial distinction between rich and poor countries, apart from differences in average income, is that governments in rich countries have access to better tax collection technologies than governments in poor countries. The model is successful in the sense that redistribution in-kind, as a fraction of the overall government budget, falls as the tax collection productivity rises. Differences in mean income, holding inequality constant, generate no differences in redistribution policies. Mean preserving spreads of
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income increase government’s share of GNP and typically decrease redistribution in kind relative to redistribution in cash. Comparing a rich economy such as Switzerland, for example, with high average income, low income inequality and good tax collection technology with a poor economy such as Columbia with low average income, high income inequality and a poor tax collection technology, entails consideration of two effects, which work in opposite directions. The model we have used relies on a number of assumptions / abstractions. First, both the financial transfer and the provision of the public service are uniform and universal. Such uniform and universal provision of public services was thought of as a great equalizer. Tawney (1964) argued that it makes it ‘‘possible for a society . . . to abolish . . . the most crushing of disabilities, and the most odious of the privileges which drive a chasm across it.’’ LeGrand (1982) documents that uniform and universal provision of public services is actually a means toward greater inequality since rich individuals take advantage of the publicly provided services at greater rates than the poor. The rich are more likely to use public train services than poor individuals, for example, and are thus more likely to benefit from public provision of rail services. Second, many transfer programs in both rich and poor countries are targeted to a specific group of recipients. This is true for transfers in cash and transfers in kind. Such targeting can involve substantial administrative costs and errors. For a survey of such targeted programs see Grosh (1995). The uniform and universal public provision scheme in our paper potentially avoids such targeting costs. Third, our model abstracts from productivity differences between the public and the private sector. European experience with privatization in recent years suggests that there may be sizeable productivity differences between the public and the private sector. If such productivity differences are reflected in a lower price for the private alternative, there may be more opting out. Finally, we used a model of direct democracy in this paper. In this framework, the non-existence issue seems difficult to avoid. Using models of representative democracy following Besley and Coate (1997) or Osborne and Slivinski (1996) might be one way to solve the non-existence problem. We plan to take up these issues in future work. The result in this paper is obtained in a model with a limited set of instruments. It is an open question whether the results survive in a model where there is a progressive income tax or where cash transfers are capped at some level of income. Cremer and Gahvari (1977), show that in-kind transfers are part of Pareto optimal policy, even when non-linear income taxes are available. Existence of an equilibrium in such an enriched model might be problematic. We also plan an empirical project to complement the simulation approach in this paper. In this empirical paper we plan to use statistical inference to study the relationship between measures of in kind, in cash redistribution, measures of tax avoidance, and the income distribution. For the tax avoidance we can use the data from Stotskey and Wolde Mariam (1997) for Sub-Saharan Africa. For the income distribution we can use the new data set from Deininger and Squire (1996).
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Acknowledgements The authors wish to thank Tim Besley, Robin Burgess, Michael Smart, John Strauss, and seminar participants at MSU and at the ISPE conference in Oxford, December 1997 for helpful comments and suggestions.
References Acharya, S., 1985. Aspects of the Black Economy in India, Government of India, New Delhi. Alesina, A., Rodrik, D., 1994. Distributive politics and economic growth. Quarterly Journal of Economics 109, 465–490. Bardhan, P., 1997. Corruption and development: A review of issues. Journal of Economic Literature (September), 35, 1320–1346. Bearse, P., Glomm, G., Janeba, E., 1998. Composition of government budget, non-single peakedness and majority voting. Manuscript. Benabou, R., 1996. Inequality and growth. Manuscript. Prepared for the NBER Annual Macroeconomics Conference. Besley, T., Coate, S., 1997. An economic model of representative democracy. Quarterly Journal of Economics 112 (February), 85–114. Besley, T., Coate, S., 1991. Public provision of private goods and the redistribution of income. American Economic Review 81 (September), 979–984. Blackorby, Ch., Donaldson, D., 1988. Cash versus kind, self-selection, and efficient transfers. American Economic Review 78 (September), 691–700. Blomquist, S., Christianson, V., 1998. Price subsidies versus public provision. International Tax and Public Finance 5 (July), 283–306. Bruce, N., Waldman (, M., 1991. Transfers in-kind: why they can be efficient and nonpaternalistic. American Economic Review 81 (December), 1345–1351. Buchanan, J., 1975. The Samaritan’s dilemma. In: Phelps, E.S. (Ed.), Altruism, Morality and Economics Theory, Russell Sage Foundation, New York, pp. 71–85. Burgess, R., Stern, N., 1993. Taxation and development. Journal of Economic Literature 31 (June), 762–830. Catteral, J.S., 1988. In: James, T., Levin, H.M. (Eds.), Private School Participation and Public Policy in Comparing Public and Private Schools, vol. 1, The Falmer Press, Philadelphia, pp. 46–66. Cremer, H., Gahvari, F., 1977. In-kind transfers, self-selection and optimal tax policy. European Economic Review 41 (January), 92–114. Deininger, K., Squire, L., 1996. A new data set measuring income inequality. The World Bank Economic Review 10, 565–591. Easterly, W., Rebelo, S., 1993. Fiscal policy and economic growth: an empirical investigation. Journal of Monetary Economics 32 (November), 417–458. Enelow, J., Hinich, M., 1984. The Spatial Theory of Voting: An Introduction, Cambridge University Press, Cambridge. Epple, D., Romano, R., 1996. Ends Against the Middle: Determining Public Sector Provision When There Are Private Alternatives. Journal of Public Economics 62, 297–325. Gahvari, F., 1995. In-kind versus cash transfers in the presence of distortionary taxes. Economic Inquiry 33 (January), 45–53. Grosh, M.E., 1995. Toward quantifying the trade-off: administrative costs and incidence in targeted programs in latin america. In: van de Walle, D., Nead, K. (Eds.), Public Spending and the Poor, The Johns Hopkins University Press, Baltimore.
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Herschel, F., 1978. Tax evasion and its measurement in developing countries. Public Finance 33, 232–268. LeGrand, J., 1982. The Strategy of Equality Redistribution and the Social Services, George Allen and Unwin, London. Mauro, P., 1995. Corruption and growth. The Quarterly Journal of Economics, August, 681–711. Munro, A., 1992. Self-selection and optimal in-kind transfers. Economic Journal 102 (September), 1184–1196. Munro, A., 1989. In-kind transfers, cash grants, and the supply of labor. European Economic Review 33 (October), 1597–1604. Osborne, R.J., Slivinski, A., 1996. A model of political competition with citizen candidates. Quarterly Journal of Economics 111 (February), 65–96. Perotti, R., 1993. Political equilibrium, income distribution, and growth. Review of Economic Studies 60 (September), 755–776. Perotti, R., 1994. Income distribution and growth: an empirical investigation. Manuscript. Persson, T., Tabellini, G., 1994. Is inequality harmful for growth? Theory and evidence. American Economic Review 84, 600–621. Rosen, H.S., 1995. Public Finance, 4th ed. Irwin. Sandford, C., Godwin, M., Hardwick, P., 1989. Administrative and Compliance Costs of Taxation, Fiscal Publications, Bath, U.K. Stotskey, J.G., Wolde Mariam, A., 1997. Tax Effort in Sub-Saharan Africa. IMF Working Paper [107. Summers, R., Heston, A., 1988. A new set of international comparisons of real product and price levels: estimates for 130 countries, 1950–1985. Review of Income and Wealth 34, 1–25. Tawney, R.H., 1964. Equality. London Unwin Books. van de Walle, D., 1995. The distribution of subsidies through public health services in indonesia, 1978–1987. In: van de Walle, D., Nead, K. (Eds.), Public Spending and the Poor, The Johns Hopkins University Press, Baltimore. Vaillancourt, F., 1989. The Administrative and Compliance Costs of Personal Income Taxes and Payroll Taxes, Canadian Tax Foundation, Toronto.
Why poor countries rely mostly on redistribution in-kind P. Bearse a , G. Glomm b , *, E. Janeba c b
a Department of Economics, University of North Carolina, Greensboro, NC, USA Department of Economics, Michigan State University, 101 Marshall Hall, East Lansing, MI 48824, USA c Department of Economics, Indiana University, Bloomington, IN 47405, USA
Abstract We present a model in which the crucial distinction between rich and poor countries is that governments in rich countries have access to a more productive tax collection technology than governments in poor countries. Since the tax collection technology in poor countries is poor, the quality of the public service is low. Therefore many households at the top of the income distribution opt out of the public service. The median voter takes this into consideration and allocates a larger share of the public budget to redistribution in-kind (public service) than to redistribution in cash. 2000 Elsevier Science S.A. All rights reserved. Keywords: Public provision; Transfers; Redistribution; Majority voting JEL classification: H5; D72
1. Introduction Governments in most countries engage in some kind of redistributive activity. In rich countries social security and welfare payments exceed 10% of GDP and are larger than expenditure on public education (see Table 1). In middle income countries, social security and welfare budgets are smaller and roughly equal to public expenditures on education (see Table 2). In poor countries, social security *Corresponding author. Tel.: 11-517-355-7359; fax: 11-517-432-1068. E-mail address: [email protected] (G. Glomm) 0047-2727 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0047-2727( 99 )00076-6
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Table 1 Redistributive expenditures in rich countries (as percent of GDP)a
Education Health Social security and welfare Housing Number of observation a
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
4.9 4.3 10.3 1.0 4
5.7 5.2 14.1 1.4 15
5.4 4.6 13.5 1.6 24
5.3 4.8 12.8 1.6 26
5.4 5.0 13.4 1.6 24
5.6 4.9 13.5 2.0 23
5.4 4.8 13.7 1.7 24
5.3 4.8 13.7 1.7 24
5.2 4.9 13.3 1.7 21
5.5 4.7 14.0 1.9 18
Source: Author’s calculation from IMF Government Finance Statistics (1993).
Table 2 Redistributive expenditures in middle income countries (as percent of GDP)a 1981 1982 Education Health Social Security and welfare Housing Number of observations a
1983
1984
1985
1986
1987
1988
1989
1990
3.0 1.3
3.1 2.1
3.3 1.8
3.4 1.8
3.4 1.8
3.5 1.7
3.5 1.9
3.5 1.9
3.5 1.9
3.5 1.9
1.7 0.7 7
4.6 0.6 14
4.2 0.6 19
3.6 0.6 23
3.6 0.6 24
3.7 0.7 25
3.9 0.8 22
3.8 0.7 22
3.7 0.7 23
3.9 0.7 20
Source: Authors’ calculation from IMF Government Finance Statistics (1993).
and welfare payments take up a much smaller fraction of GDP; they are roughly a fourth of public education expenditures (see Table 3). The list of countries used in Tables 1–3 is given in Table 4. These countries are broken down into rich, middle income and poor using real per capita income in 1980 from the Summers and Heston (1988) data set. Redistribution, however, does not only take the form of social security and welfare payments; often redistribution is carried out in the form of subsidizing housing and health care for the poor or in the form of public
Table 3 Redistributive expenditures in poor countries (as percent of GDP)a
Education Health Social security and welfare Housing Number of observation a
1981 1982 1983 1984
1985
1986
1987
1988
1989
1990
4.5 1.6 1.3 0.9 9
4.5 1.6 1.1 0.8 21
4.5 1.6 1.2 0.9 21
4.3 1.7 1.1 1.2 22
3.9 1.5 1.1 0.9 21
4.2 1.6 1.3 1.1 17
4.1 1.6 1 1.1 14
5.1 1.8 1.2 1.2 13
4.7 1.7 1.5 1.1 19
4.3 1.6 1.1 1.4 22
Source: Authors’ calculation from IMF Government Finance Statistics (1993).
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Table 4 Poor, middle income and rich countries in 1980 with per capita GDP a Poor countries income # 1551 1. Bolivia 2. Botswana 3. Cameroon 4. Egypt 5. El Salvador 6. Ethiopia 7. Gambia 8. Ghana 9. India 10. Kenya 11. Lesotho 12. Liberia 13. Madagascar 14. Malawi 15. Morocco 16. Mauritius 17. Nepal 18. Papua New Guinea 19. Philippines 20. Sierra Leone 21. Sri Lanka 22. Swaziland 23. Yemen 24. Zambia 25. Zimbabwe 26. – a
Middle income countries 1529 1477 875 995 1410 325 556 421 614 662 694 680 589 417 1199 1484 490 1528 1551 512 1119 1079 957 716 930
Argentina Barbados Brazil Chile Colombia Costa Rica Cyprus Dominican Republic Ecuador Fiji Guatemala Iran Jordan Korea Malaysia Mexico Panama Paraguay Peru Portugal Syria Thailand Tunisia Turkey Uruguay Venezuela
Rich countries income #4630 4342 4454 3356 2552 2552 3031 4282 1868 2607 3005 1952 2944 1885 2369 3112 4333 2810 1979 2456 3733 3071 1697 1845 2319 4502 4242
Australia Austria Bahrain Belgium Canada Denmark Finland France Germany Iceland Ireland Israel Italy Kuwait Luxembourg Malta Netherlands New Zealand Norway Oman Singapore Spain Sweden Switzerland U.A.E. U.S.
8349 8230 9185 9228 11 332 9598 8393 9688 9795 9285 4929 6145 7164 19 454 10 173 4630 9036 7363 11 094 6209 5817 6131 8863 10 013 25 646 11 404
Source: Summers and Heston (1988).
education which is financed by a proportional or progressive income or wealth tax and made available to all school age children at an almost zero price.1 A glance at Tables 1–3 reveals that rich and poor countries treat transfers in cash (social security and welfare payments) and transfers in-kind (public expenditures on education, housing and health) differentially. Rich countries rely predominantly on transfers in cash in their redistribution policies, while in poor
1
While it is true that social security redistributes income between generations, it also is a tool for intragenerational redistribution. Rosen (1995), for example, documents that a low income earner who retires in 1995 makes a net gain out of social security of 21.7%, while for a high income earner there is a net loss of 27.8% from social security.
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countries the lion’s share of redistribution is through transfers in-kind.2 Burgess and Stern (1993) also document this fact, although their data are restricted to expenditures by central governments. This differential use of transfers in-kind vs. transfers in cash by rich vs. poor countries is the heart of this paper. We want to explain why poor countries use different redistribution policies than rich countries. In Section 2 we present a model which can deliver this differential treatment of in-kind vs. cash transfers as an equilibrium outcome. In the model a government raises an income tax at a uniform rate. A portion of tax revenue is used for uniform lump-sum transfers and the remainder is used for public provision of a good such as education, health or housing. For ease of reference we often refer to this good as education. Public education is made available to all households at a zero price. Public provision is ‘‘uniform and universal’’ in the sense of Besley and Coate (1991). Households are free, however, to opt out of public education and choose a private alternative. Choosing the private alternative entails paying the full marginal resource requirement. Public policies are determined endogenously through majority voting.3 Since public policy here is two dimensional (the size of the government budget and its split between transfers in-kind and transfers in cash), the voting problem is solved in two stages. In the first stage, the size of the government is determined while the composition of the government budget is determined in the second stage.4 The crucial distinction between poor and rich countries in this model is the government’s ability to raise revenue. We specify a tax revenue collection function similar to the one used by Perotti (1993). According to this revenue collection technology, the revenue raised is a strictly concave function of the (uniform) tax rate for exogenously given incomes. This technology is intended to capture tax evasion and tax avoidance activities of taxpayers and / or tax collection costs on the part of the government. As Easterly and Rebelo (1993) point out, these costs are not small. According to Vaillancourt (1989), total private and public costs associated with the income tax system and social security payments in Canada are about 7% of the revenue collected. For the U.K. a study by Sandford et al. (1989) contains an estimate of these costs of about 5% of revenue collected. Acharya (1985) estimated that in India income declared for tax purposes was 53.3% of the total income assessable. Herschel (1978) reports that in Argentina in the 1950s 2
Poor countries often receive foreign assistance for capital expenditures in health or in education. Even if foreign aid amounts of half of education or health expenditure, poor countries still use redistribution in kind more than redistribution in cash. 3 Using a majority voting model for all countries is a somewhat restrictive assumption. Note, however, that not all rich countries are democratic (UAE, Kuwait) and many poor / middle income countries are not dictatorships (Egypt, India). It is also interesting to notice that the expenditure composition in Tables 1–3 is quite stable over the whole period despite the fact that more and more countries have started liberalization both economically and politically in the late 1980s. 4 We use the two-stage voting procedure to avail well know issues of existence of a majority voting equilibrium (see, for example, Enelow and Hinich, 1984).
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only 25.5% of taxable income was actually reported for tax purposes. Alternatively, there could be differential corruption across countries. Both Bardhan (1997) and Mauro (1995), for example, document that corruption is higher in poor than in rich countries. Easterly and Rebelo (1993) argue that it is plausible that collecting tax revenue requires fixed costs which governments in poor countries might not find worthwhile to bear. In this paper, we take as a crucial assumption that governments in rich countries have access to better revenue collection technologies and exhibit less corruption and / or less tax evasion than governments in poor countries. We show that these differences between rich and poor countries can give rise not only to different government size but also to a different composition of public expenditure. When the tax revenue collection technology is unproductive, for any given tax rate, total tax revenues will be small. When tax revenues are small, the quality of the publicly provided good is poor and a large fraction of the top end of the income distribution opt out of the public service and buy the service on the private market. There is some evidence for opting out of publicly provided services by the rich. van de Walle (1995) documents that in Indonesia people in the top income decile are almost 15 times as likely to consult a private physician than people in the bottom decile. For the U.S., Catteral (1988) reports that the fraction of children attending private school increases almost monotonically with income. In 1982, only 3.3% of children whose parents had income less than $7 500 attended a private school, whereas 31.0% of those families with incomes above $75 000 chose a private school for their kids. In our model, the median voter takes this opting-out-behavior into consideration when voting on the composition of the public budget. If tax collection is poor, the median voter (in the second stage of voting) tends to vote for more redistribution in kind. Since more people opt out and leave relatively more resources for public education, shifting resources to in kind transfers deliver a greater ‘‘bang for the buck.’’ In the first stage of voting, higher tax rates prevail in rich economies because there governments have productive tax revenue collection technologies. Both predictions are roughly consistent with the data. There is a large literature on the optimality of transfers in cash and in kind. Examples of this literature include Buchanan (1975), Bruce and Waldman (1991), Blackorby and Donaldson (1988), Gahvari (1995), Munro (1989, 1992), Blomquist and Christianson (1998) and Besley and Coate (1991). In most of these papers redistribution in kind may be used to overcome some private information problem. In this paper we use as a starting point another information problem. In poor countries the personal income tax system is much less developed, mostly because a sizable part of the population is illiterate and works in the agricultural and / or in the informal sector. This makes it difficult to accurately assess income for tax purposes. Behind the inability to collect income tax revenue lies an informational
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problem. In poor countries it is difficult for the government to assess individual incomes. There may, therefore, be more tax evasion in poor countries. Also, in poor countries it may be more difficult to monitor bureaucrats. Consequently, there may be more corruption in poor countries. We model these kinds of informational problems as a loss of tax revenue, which is greater in poor than in rich countries. Given this differential loss of tax revenue, we seek to explain the different patterns of redistribution. This paper is closely related to the growing literature on endogenous redistribution in (dynamic) general equilibrium models. A nice survey of this literature is Benabou (1996). Persson and Tabellini (1994) study endogenous redistribution through transfers in cash in an overlapping generations economy. They find that higher inequality generates higher redistribution which in turn generates lower growth. Alesina and Rodrik (1994) study distributive politics and growth in a model in which public revenue is used to finance investment in infrastructure. Perotti (1994) contains an empirical investigation of the relationship between income distribution and growth. These papers above allow for one kind of redistribution, usually redistribution in cash. In this paper here we allow for several type of redistributive policies and make predictions about the relative importance of each type. We solve the model numerically in Section 3. Our simulations reveal that the voting equilibrium is roughly consistent with the stylized facts pointed out in Tables 1–4. In the model in Section 2 the inefficiency arises because of public corruption. In Section 4 we address how a different inefficiency, namely tax evasion, influences our results. Section 5 contains a discussion of potential alternative explanations of the stylized facts. Section 6 concludes.
2. The model The economy is populated by a large number of individuals. Population size is normalized to one. Each individual lives one period. All individuals have identical preferences over a consumption good c, and a good e. The consumption good c is always provided privately, while the good e is provided both publicly and privately; good e is made available to all individuals by the public sector, but individuals are free to purchase the private alternative on the market. We will refer to good e as education, but healthcare, housing or transportation are other possible interpretations. The utility function is given by 1 s s ]] hc 12 1 d e 12 j, s . 0, d . 0 i 12s i where c i and e i denote the amounts of the two consumption goods consumed by individual i. We use specific functional forms from the start, because few analytical
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results are available and we rely therefore heavily on numerical solution techniques. All individuals have identical preferences. Individuals are differentiated by income. Let y i denote income (or wealth) of individual i. Let F be the c.d.f of income. We assume that the support of F is the non-negative real line and that the mean exceeds the median. The government collects an income tax at the uniform rate t.5 Due to tax evasion or corruption the tax revenue collected falls short of the tax rate times income. We capture this with a tax function R(t ) 5 t 2 at 2 , a . 0. For a ,1 / 2, this function peaks when t .1. For a .1 / 2, the function is consistent with a Laffer curve. Letting Y denote aggregate income, the total tax revenue for the government is R(t )Y. This type of a revenue collection technology has been used by Perotti (1993). The government uses a fraction D [ [1,0] of tax revenues to purchase educational services which are made available to all individuals at a zero price. If N is the fraction of the population which attends the public school, then public school expenditure per pupil are given by
DR(t )Y E 5 ]] N
(1)
We can think of Eq. (1) as a linear education production function. The part of the budget which is not allocated to education is allocated to uniform lump-sum transfers. Income of an individual can then be written as (1 2 t )y i 1 (1 2 D)R(t )Y.6 5 Developing and developed countries differ not only in the size of government and composition of expenditures, but also in terms of the mix of government revenues. Burgess and Stern (1993) report that developing countries rely more heavily on indirect taxes than developed countries do, usually for the informational reasons discussed above. In our theoretical model we nevertheless use a linear income tax in all countries. This is not as restrictive as it may seem at first glance. Note that the income tax in our model is progressive because of the constant marginal tax rate and the uniform lump sum subsidy. A progressive tax system can be implemented also in countries using consumption taxes. For example, in a model with two consumption goods, say food and all other goods, differential taxation of these goods is progressive when low-income individuals consume relatively more food and food is taxed at a lower rate. For simplicity, we adopt a common model with one consumption good beside education in order to make our point. They key question, both in developing and developed countries, is whether the tax system or the in-kind transfer is the better tool to redistribute in favor of the median voter, regardless of having differential consumption taxes or a linear progressive income tax. 6 Here individuals pay the full amount of the statutory tax, and keep (1-t ) y i . Tax revenue disappears after it has been collected from the household. This can be interpreted as corruption.
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The uniform lump-sum subsidy in connection with a constant marginal tax rate can be interpreted as a linear progressive income tax. If an individual with income y i chooses public school, the associated indirect utility function is
H
S
1 DR(t )Y v ui 5 ]] f(1 2 t )y i 1 (1 2 D)R(t )Yg 12 s 1 d ]] 12s N
D J. 12 s
If an individual with income y i chooses the private school alternative, he solves the problem 1 s s max ]] hc 12 1 d e 12 j i i hc i ,e i j 1 2 s s.t. c i 1 e i 5 (1 2 t )y i 1 (1 2 D)R(t )Y. We will refer to this as problem P. The solution to this problem is c i 5 (1 1 d 1 / s )21 [(1 2 t )y i 1 (1 2 D)R(t )Y] e i 5 d 1 / s (1 1 d 1 / s )21 [(1 2 t )y i 1 (1 2 D)R(t )Y] and the associated indirect utility function is 1 v ri 5 ]](1 1 d 1 / s )s [(1 2 t )y i 1 (1 2 D)R(t )Y] 12 s. 12s An individual will choose the public service over private provision iff v ui $ v ri
(2) 3
Condition (2) at equality determines a critical level of income y with the property 3 3 that if y i ,y the individual chooses public provision and if y i .y the individual chooses private provision. This follows directly from substituting the expressions for v u and v r into condition (2). Fig. 1 illustrates v u and v r as functions of ˆ individual income and shows the cut-off level y. Both the tax rate t (the overall size of the government) and the composition of the government budget D are determined through majority voting. We let individuals vote in two stages. In the first stage, they vote on the tax rate. In the second stage, they vote on D, taking the tax rate as given. Individuals are forward looking and therefore in the first stage take into account how a change in t affects D. This two-stage voting process corresponds to actual rules in some countries. An equilibrium for this economy is an allocation for each household who chooses the public alternative (c ui ,e ui ), an allocation for each household who 3 chooses the private alternative (c ir ,e ir ), a critical level of income y, a public school enrollment N, and public policies (t, D(t )) such that
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Fig. 1. Indirect utilities.
S
D
DR(t )Y (i) sc ui ,e ui d 5 (1 2 t )y i 1 (1 2 D)R(t ), ]] , N (ii) (c ri ,e ri ) solves problem P, 3 (iii) the income level y satisfies condition (2) with equality, 3 (iv) N 5 F(y ), (v) given D (t ), t wins in majority voting in the first stage, (vi) given t, D wins in majority voting in the second stage. Notice that according to this definition voters in the first stage take into consideration how the choice of government size t influences the composition of the government budget D in the second voting stage.
3. Solving the model We solve the model backwards. For a given public policy, each household decides whether or not to opt out of the publicly provided3 service. Imposing equality on condition (2) determines the level of income y which makes the household just indifferent between opting out or not. This critical income level is given by
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H
J
d 1 / 12 s D R(t )Y y 5 ]]]]]] 1 ] 2s1 2 Dd ]] (1 2 t ) fs1 1 d 1 / sd s 2 1g 1 / 12s N
3
(3)
whenever that expression is non-negative. We then have Result 1: A household with income y i opts out of the public service if and only 3 if y i .y. 3 Since the critical level of in y in Eq. (3) is a declining function of participation in the public service N, we have Result 2: Given D and t, there exists exactly one solution to the equilibrium 3 condition N 5 F(y ) if the c.d.f. F is continuous and strictly increasing. For a given t, which is determined in the first stage, the share D is chosen by majority voting. The voting problem on D is very similar to the one analyzed by Epple and Romano (1996). They prove, under a particular single-crossing property of indifference curves in tax-expenditure space, that a majority voting equilibrium exists. Their existence proof relies on the assumption that the government only finances educational expenditures. (Bearse et al., 1998) show that this particular single-crossing property does not arise when the government also finances uniform lump-sum transfers and when the voting decision is made on the composition of the government budget. Even when t is held fixed, there are no known conditions sufficient for an equilibrium when voting on the government budget composition D. Furthermore, we study here a two-dimensional voting problem, which is solved sequentially. For these reasons we are forced to rely heavily on numerical solution techniques. We pick a sample of 101 households which are drawn from a lognormal distribution, that is lny | N(m 5 3.606, s 5 0.615). If income is measured in $1000 this distribution roughly corresponds to the U.S family income distribution in 1992. We pick a grid of 101 points for values for t between zero and one and do likewise for D and N. For each value of t, we solve the voting problem on D by running a tournament between all possible values of D. This step generates the composition of the public budget D as a function of the size of the public budget t. We then run a tournament of all the 101 values of the size of the public budget. In general there is no guarantee that we will avoid cycles. Our computations reveal that for some tax rates t there are cycles when voting on the composition D. In order to avoid complications arising from the presence of cycles, we eliminate all tax rates t which generate cycles when voting over D in the second stage.7 In the first stage, when voting over t, we allow only those tax rates which do not generate cycles. Table 5 contains the first results. There we keep the utility function and the income distribution constant and vary the tax collection productivity parameter a. As the tax collection parameter a rises, the share of the
7
In our companion paper we characterize existence of cycles in more detail.
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Table 5 Composition and size of Government in economics with varying tax collection productivity Preference parameters
Tax collection productivity a
Government size t
Government budget composition D
Participation in public service N
Public service quality E
s 50.9 d 50.1
0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5
0.950 0.460 0.300 0.230 0.180 0.950 0.430 0.290 0.260 0.250 0.950 0.370 0.360 0.250 0.160 0.950 0.350 0.360 0.260 0.230
0.000 0.000 0.190 0.220 0.280 0.000 0.210 0.270 0.310 0.330 0.000 0.370 0.390 0.390 0.510 0.000 0.870 0.870 0.950 0.950
0.000 0.000 0.964 0.942 0.936 0.000 0.970 0.934 0.932 0.932 0.000 0.934 0.932 0.817 0.754 0.000 0.932 0.932 0.854 0.810
0.000 0.000 2.385 2.162 1.172 0.000 3.772 3.393 3.435 3.433 0.000 6.017 5.957 4.760 4.412 0.000 13.469 13.287 11.485 10.690
s 51.1 d 50.1
s 51.5 d 50.1
s 51.5 d 50.5
public budget going to transfers in kind generally rises. Surprisingly, we obtain this result for high and low elasticities of substitution in utility. In order to provide some intuition for this result we consider an economy with a fixed tax rate t. For this economy we vary a and study (i) how preferences over D of a voter with fixed income change with a and (ii) how the identity of the decisive voter changes. Consider Fig. 2. If D 50, the consumer who chooses public education attains point A where c i 5 (1 2 t )y i 1 R(t (a )Y and e i 5 E 5 0. If D 51, the individual attains point B where c i 5 (1 2 t )y i and e i 5 E 5 [R(t (a ))Y] /N. Letting D vary over [0,1] traces out the line segment AB. This line segment borders the feasible set for the individual. Now suppose that the tax collection parameter a rises. As a rises, R(t (a )) falls (for fixed t ; the point A moves down along the c-axis to point A9. Similarly, the point B moves left to point B9. However, as a rises, the quality of the publicly provided good falls, more individuals opt for the private alternative and N falls. Since N falls the decline in [R(t (a ))] /N is smaller than the decline in R(t (a )). Thus the new border of the feasible set, the line segment A9B9, is flatter than the border AB. This is like a change in a relative price. As a rises, the good e (publicly provided) becomes cheaper relative to good c.
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Fig. 2. Comparative statistics on tax collection parameter a.
Now there are two cases to consider. In the first case s ,1. Then the substitution effect associated with this relative price change dominates the income effect. Each voter would like to shift resources from c to e, that is each voter prefers a higher D. As a rises, opting out increases for a given D. High income individuals opt out and desire D 50. If the most preferred D is an increasing function of own income, which is the case for fixed N,8 having more people opt out at the top of the distribution implies that the decisive voter has lower income. We have three effects: The direct or substitution effect raises D. A second effect, i.e. changing the identity of the decisive order, lowers D. The third effect arises because at higher a, more people opt out of public provision and the median voter gets more bang for the buck when funds are allocated to public education. Our simulations reveal that the first and the third effect are dominant. The second case, s .1 is a bit trickier. Here the income effect associated with this change in the relative price dominates the substitution effect. As a rises, each voter would prefer a lower D. The identity of the median voter also changes. Here the most preferred D is an increasing function of income for all individuals who
8
When N is endogenous the indirect utility function may not even be concave in D.
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use the publicly provided service. Those who opt out and use the private service have a most preferred D of zero. As a rises, the identity of the decisive voter changes. With higher a, the income of the decisive voter is lower. Since the most preferred D is rising in income, the decisive voter now has a lower most preferred D. The third effect raises opting out with an increase in a and thus induces the median voter to shift public funds from cash transfer to public education. As long as the third effect is dominant, an increase in a is consistent with higher D. This is confirmed in Table 5. In Table 6 we fix the preference parameters at s 51.1 and d 50.1, but allow the mean income to vary, holding s, the measure of inequality constant. The range of a we consider is the same as before. Average incomes are allowed to decrease by factors of 10, 20 and 30. A ratio of 30 corresponds roughly to the income ratio between the richest and poorest countries. As average income drops, the voting equilibrium stays unaffected. The intuition here is that technologies exhibit constant returns to scale and that preferences are homothetic. Changing the measure of average income is therefore a change in scale which has no economic effect. In Table 7 we study mean preserving spreads of the income distribution. We increase s and adjust m to keep mean income exp[m 1 ]21 s 2 ] constant. In this experiment we set s 51.1 and d 50.1. The results in Table 7 are robust with respect to changes in the preference parameters. Evidently, as the income distribution undergoes a mean preserving spread, the tax rate generally (not universally) rises and the fraction of the government budget going to the public Table 6 Changing average income Income distribution parameters
Average income
Tax collection Productivity a
Tax rate t
Government budget composition D
m51.303 s50.615
4.433
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
m50.61 s50.615
2.217
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
m50.205 s50.615
1.478
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.000 0.210 0.270 0.310 0.330
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Table 7 Mean preserving spreads Income distribution parameters
a
t
D
N
E
m53.606 s50.615
0.1 0.2 0.3 0.4 0.5
0.950 0.430 0.290 0.260 0.250
0.00 0.210 0.270 0.310 0.330
0.000 0.970 0.934 0.932 0.932
0.000 0.377 0.339 0.343 0.343
m53.475 s50.8
0.1 0.2 0.3 0.4 0.5
1.00 0.75 0.470 0.340 0.270
0.110 0.140 0.170 0.180 0.200
1.000 0.988 0.434 0.855 0.812
4.424 4.036 3.283 2.764 2.570
m53.295 s51.0
0.1 0.2 0.3 0.4 0.5
1.00 1.00 0.700 0.560 0.430
0.110 0.110 0.130 0.150 0.140
1.000 1.000 0.964 0.932 0.847
4.489 3.991 3.381 3.171 2.530
service falls. For most of the income distributions we tried, the fraction of the government budget going to the public service rises as a rises.
4. An alternative interpretation of tax evasion So far we assumed that the post-fisc income of an individual i is (1 2 t )y i 1 (1 2 D)R(t )Y. In this specification each household pays taxes in amount t y i but the amount of revenue actually available for redistribution is R(t )Y , t Y. Our interpretation here is that there is some government waste: Some bureaucrats siphon off tax revenue and use it to go skiing in Davos, Switzerland. An alternative formulation for the individual’s budget constraint is (1 2 R(t ))y i 1 (1 2 D)R(t )Y. According to this alternative budget constraint, a household with income y i is taxed at the rate t so that the assessed tax payment would be t y i . However, the household can hide some income from the tax authority and gets away with paying only
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R(t )y i , t y i . We repeat the analysis of the previous section for this alternative budget constraint. The results are similar to the previous case: As the tax collection technology worsens (a rises), participation in the public service N falls, the share of the public budget going to redistribution in-kind rises and government size falls.
5. Discussion and alternative explanations Our explanation of the observed difference in government transfer policies across countries is based on three elements: (1) Agent heterogeneity in terms of income which leads to conflicting political interests, (2) the government’s ability to effectively provide the good differs across countries for any given tax rate, and (3) the possibility to opt out and to purchase the good in the private market. We have indicated in the introduction that there is empirical evidence for these assumptions. Yet it is not clear whether all three elements are necessary for explaining the observed puzzle. In this section we discuss this issue in more detail. In particular, one may conjecture that the possibility to opt out is not essential. We argued in the previous section that one reason for element (2) is the higher degree of tax evasion in poor countries. In this sense we deal with an informational issue because the government’s ability to obtain information about private income is limited. Such limited ability to observe private types also is at the heart of papers by Buchanan (1975), Bruce and Waldman (1991), Blackorby and Donaldson (1988), Gahvari (1995), Munro (1992) and Blomquist and Christianson (1998). In all of these papers transfers in cash only are not efficient due to some hidden information or hidden action problem. In Blackorby and Donaldson (1988), for example, the government cannot costlessly distinguish between the types of individuals who are to receive transfers. They show that ‘‘second-best optima,that are not first-best, occur when the first-best distribution is not compatible with the self-selection constraints.’’ In such a world transfers in kind may be feasible and useful for optimality. A government which optimizes subject to self-selection constraints may thus rely on a mixture of transfers in cash and transfers in kind. It is possible that the nature of private information in poor countries relative to rich countries is such that optimal redistribution schemes in poor countries rely more on transfers in kind than on transfers in cash. This is a possible alternative explanation. We have found no empirical evidence for this explanation however. Similarly, the Samaritan’s dilemma (see Buchanan, 1975 and Bruce and Waldman, 1991) might be exacerbated in poor countries. Poverty in poor countries may be much more devastating than poverty in rich countries and thus elicit larger cash transfers. If the probability of becoming impoverished is endogenous and depends on actions by the potential recipient, it might be optimal in poor countries to have a larger
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share of transfers in kind than in cash. Again this might provide an alternative explanation for our stylized facts, although it is difficult to falsify. Another alternative which does not require assumptions on information asymmetries is a model involving non-homothetic preferences. Suppose all individual’s preferences are given by the semi-linear form ln e 1 c. The government collects an income tax at the rate of t, a fraction of the public revenue, D, goes to fund public education and the remainder goes to financial transfers. There is no opting out; all individuals attend public schools. In order to determine the fraction of the public budget going to education, each individual solves the problem Max ln Dt Y 1 (l 2 t )y 1 (1 2 D) t Y D
Where y is individual income and Y is average income. The solution to this problem is
D 5(t Y)21 . Notice that all individuals, regardless of individual income, prefer the same share D. The budget share is thus independent of income inequality. Notice also that D is declining in average income. This result is consistent with our stylized fact that in poorer societies governments allocate a larger share of the public budget to education. According to our data, the fraction of the national income allocated to in kind transfers rises as income rises. This model with semi-linear preferences does not deliver this second result since E /Y 5 1 /Y falls with income.
6. Concluding remarks In this paper we have presented a model to explain why poor countries have smaller governments than rich countries and why governments in poor countries, unlike governments in rich countries, rely mostly on redistribution in-kind and not on redistribution in cash. In the model the crucial distinction between rich and poor countries, apart from differences in average income, is that governments in rich countries have access to better tax collection technologies than governments in poor countries. The model is successful in the sense that redistribution in-kind, as a fraction of the overall government budget, falls as the tax collection productivity rises. Differences in mean income, holding inequality constant, generate no differences in redistribution policies. Mean preserving spreads of
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income increase government’s share of GNP and typically decrease redistribution in kind relative to redistribution in cash. Comparing a rich economy such as Switzerland, for example, with high average income, low income inequality and good tax collection technology with a poor economy such as Columbia with low average income, high income inequality and a poor tax collection technology, entails consideration of two effects, which work in opposite directions. The model we have used relies on a number of assumptions / abstractions. First, both the financial transfer and the provision of the public service are uniform and universal. Such uniform and universal provision of public services was thought of as a great equalizer. Tawney (1964) argued that it makes it ‘‘possible for a society . . . to abolish . . . the most crushing of disabilities, and the most odious of the privileges which drive a chasm across it.’’ LeGrand (1982) documents that uniform and universal provision of public services is actually a means toward greater inequality since rich individuals take advantage of the publicly provided services at greater rates than the poor. The rich are more likely to use public train services than poor individuals, for example, and are thus more likely to benefit from public provision of rail services. Second, many transfer programs in both rich and poor countries are targeted to a specific group of recipients. This is true for transfers in cash and transfers in kind. Such targeting can involve substantial administrative costs and errors. For a survey of such targeted programs see Grosh (1995). The uniform and universal public provision scheme in our paper potentially avoids such targeting costs. Third, our model abstracts from productivity differences between the public and the private sector. European experience with privatization in recent years suggests that there may be sizeable productivity differences between the public and the private sector. If such productivity differences are reflected in a lower price for the private alternative, there may be more opting out. Finally, we used a model of direct democracy in this paper. In this framework, the non-existence issue seems difficult to avoid. Using models of representative democracy following Besley and Coate (1997) or Osborne and Slivinski (1996) might be one way to solve the non-existence problem. We plan to take up these issues in future work. The result in this paper is obtained in a model with a limited set of instruments. It is an open question whether the results survive in a model where there is a progressive income tax or where cash transfers are capped at some level of income. Cremer and Gahvari (1977), show that in-kind transfers are part of Pareto optimal policy, even when non-linear income taxes are available. Existence of an equilibrium in such an enriched model might be problematic. We also plan an empirical project to complement the simulation approach in this paper. In this empirical paper we plan to use statistical inference to study the relationship between measures of in kind, in cash redistribution, measures of tax avoidance, and the income distribution. For the tax avoidance we can use the data from Stotskey and Wolde Mariam (1997) for Sub-Saharan Africa. For the income distribution we can use the new data set from Deininger and Squire (1996).
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Acknowledgements The authors wish to thank Tim Besley, Robin Burgess, Michael Smart, John Strauss, and seminar participants at MSU and at the ISPE conference in Oxford, December 1997 for helpful comments and suggestions.
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