Central and Local Tax Auditing David Bartolini∗

Fabio Fiorillo

U NIVERSIT A` P OLITECNICA DELLE M ARCHE March 12, 2010

Abstract In a federal state the process of fiscal decentralisation assigns to local jurisdictions the provision of public goods/services along with the power to impose taxes. Little is said, however, about the enforcement of such local taxes. In particular, we focus on the following question: should the enforcement of a local tax be assigned at the local or central level? We propose a model where local and central tax authorities need to enforce tax compliance through a costly monitoring and auditing policy. We show that the assignment of tax enforcement may not follow the same criteria as tax assignment, whenever tax bases are correlated. JEL Classification: H26, H71 Key words: fiscal federalism, tax auditing

1

Introduction

The process of fiscal decentralisation has been widely investigated by the economic literature providing an accurate analysis of the benefits and costs of assigning the provision of public goods and tax power at the local level (Oates, 1999). As regards taxation a key factor is the mobility of agents across jurisdictions, which, on the one hand, can help matching public goods to preferences (Tiebout, 1956), but on the other hand makes the application of local taxes more complex (fiscal externality, tax competition, etc.). As a consequence, Wellisch (2000) maintains that a complete (optimal) tax system should finance the efficient level of public goods without distorting locational patterns. This approach, however, does not take into account the possibility of people evading taxes, most works implicitly assume that tax revenue is fully and costlessly raised. Obviously this is not the case, in reality tax authorities engage in expensive auditing activities. Since the objective of the optimal tax system is to raise revenues minimising distortions, the possibility to evade ∗ Contact: Deptment of Economics, Universit` a Politecnica delle Marche, p.zzale Martelli 8, 60121 Ancona (Italy). Email: [email protected] Tel.: 0039 071 220 7176 Fax.: 0039 071 220 7102

1

would undermine the whole tax structure because citizens would face a marginal tax rate which is not the intended one. In this framework tax revenue can be increased either by raising the legal tax rate or tightening the enforcement of the existing tax system (Kaplow, 1989). The literature dealing with the effect of evasion on the optimal tax system, however, do not considered the problem of tax enforcement in a decentralised setting.1 When we consider a federal state the question of who should enforce taxes, naturally arise. In a scenario in which taxes are assigned to the central and local level according to the standard principles of fiscal federalism, what rules should be followed regarding tax enforcement? In particular, should the central government enforce all taxes? Should a local tax be enforced at the local level? In other words, the objective of this work is to investigate the best assignment of auditing functions — centralised, decentralised or separate — in order to raise tax revenue at the lowest cost. We consider a federal state organised in a central government and local jurisdictions. Citizens in every jurisdictions face a central and a local tax. The amount of tax base reported by citizens depends on the probability of being audited, and the penalty incurred.2 In order to enforce taxation, the authority in charge uses some resources for monitoring and auditing activity. Therefore the amount of taxes collected is gross of the cost of enforcement. Since our aim is to investigate the distribution of enforcement powers between the central and local level, we consider the vertical interaction between the central authority and a representative local authority.3 In this setting information plays a crucial role. The “productivity” of resources devoted to the enforcement activity depends on the availability of information. We consider two types of information: direct information and information spillovers. The former stems from the possibility to directly observe citizens’ characteristics (e.g. standard of living, number of children, housing etc.). This information would impact on the enforcement cost of the central and local level according to the degree of mobility of the tax base, we assume that a mobile tax base is better monitored by the central level, while a less mobile tax base is better audited at the local level. This is because the advantage of a close observation of the citizens’ characteristics at the local level is hindered by the possibility to move the tax base in another jurisdiction. Information spillovers arise across tax bases when they are correlated, so that the auditing activity on the local tax can bear useful information about the central tax base, or viceversa. The magnitude of this externality depends on the connection between tax bases, for instance income and wealth tax bases are strictly linked. Looking at the correlation among per capita tax bases of the Italian Regions, we obtain a rough indication of the relevance of informative spillovers. Actually, as shown in table 1, several Italian tax bases (IRPEF, IRES, VAT, IRAP) are highly correlated. The same correlation can be also found among some components of the personal 1 As a reference for the study of optimal taxation with tax evasion, see Sandmo (1981) for income taxation, and Cremer and Gahvari (1993) for commodity taxation. 2 We model citizens behaviour as utitlity maximisers with no moral consideration about paying taxes, as in the seminal papers of Becker (1968) and Allingham and Sandmo (1972). 3 We acknowledge the importance of the horizontal distribution of enforcement powers among local jurisdictions, but we leave this issue for future research.

2

income tax base, such as labour, house and capital (see table 2). This strong correlation suggests that informative spillovers may exist and should be considered in tax enforcement assignment. Table 1: Correlation among regional per capita tax bases (values in percentage) ’ IRPEF

I.C. IRAP

S. IRAP

I.C. VAT

S. VAT

IRES

100

83

83

82

72

83

Individual company IRAP

83

100

97

97

48

66

Society IRAP

83

97

100

98

42

65

Individual Company VAT

82

97

98

100

42

58

Society VAT

72

48

42

42

100

85

IRES

83

66

65

58

85

100

IRPEF

Table 2: Regional correlation among per capita components of the individual tax base (values in percentage) Labour income

Property income

Capital income

100

80

90

Property

80

100

79

Capital

90

79

100

Labour

The theory of optimal tax assignment relies on the degree of mobility in order to assign taxes to the different levels of government. It seems reasonable to follow the same principles also for the assignment of the enforcement power. However, the presence of spillovers among tax bases may lead to a different assignment of auditing responsibilities. For instance, it might be that an immobile tax base is strongly linked to a more mobile tax base, so that, even though the optimal allocation of taxes is achieved by decentralisation, it might be optimal to have a centralised tax enforcement. Our analysis does not exhaust all the issues related with tax enforcement. For instance, we do not consider agency problems that may arise when functions are delegated to agents with different objectives. Furthermore, we do not touch the problem of fiscal competition4 among local jurisdictions. Our analysis, however, by considering a very simple model shows that the 4 Cremer and Gahvari (2000) propose a two-state model in which fiscal competition is on the degree of effort put in tax auditing.

3

assignment of the enforcement powers between the central and the local level, might follow different rules than tax assignment.

1.1

Related literature

The economic literature has mostly focused on fiscal decentralisation assuming away any issue related to tax enforcement. A partial exception is Cremer and Gahvari (2000) which focus on a two-country model where the enforcement activity is conducted independently by the two countries. They consider fiscal integration taking into account that countries have another instrument to conduct fiscal competition: tax enforcement. Our model is substantially different since we look at a federal system where citizens face both a central and a local tax, and where there is less scope for tax competition. A work closer to our paper is Esteller-Mor´e (2004) which considers a model with two interrelated taxes. The idea is that auditing one tax base provides information on the other tax base. The author assumes that the possibility to check congruence in tax reports is limited by imperfect collaboration between tax administrations. Indeed, if collaboration were perfect, congruity would be the optimal tax payer’s strategy. This model differs from ours in two main aspects: firstly, in our model, the magnitude of the externality between the two tax bases depends on their similarity (irrespective of collaboration), and, secondly, we consider costly auditing.

2

Structure of the model

Let us consider a federal state with two levels of government: central and local. There are two types of taxes, a central and a local one. The objective of the central and local governments is to raise tax revenue in the most efficient way, i.e. at the lowest cost. Since there is an information problem tax authorities need to enforce compliance through costly policies, such as monitoring and auditing activities. Therefore, given the tax rate, each tax authority decides the amount of resources to devote to the enforcement of the assigned tax base. In this environment information plays a crucial role for monitoring technology. We distinguish between direct information and spillovers. Direct information stems from direct observation of the characteristics of the tax base, whereas information spillovers arise from the correlation between different tax bases (central and local). If we consider one tax in isolation, mobility would be the determinant characteristic for the assignment of tax enforcement, as each authority benefits from specific direct information depending on the mobility of the tax base. In particular, we assume that local authorities can exploit their proximity to citizens in order to observe income indicators as long as the tax base is not mobile. By contrast, the central authority can better cope with mobile tax bases, as it can track them across jurisdictions. We model this direct information structure as an iceberg cost on tax revenues. For simplicity we consider dichotomous mobility: a tax base is either mobile or immobile. Thus the central authority which monitors an immobile tax base incurs the cost b ≥ 0, while the local authority which monitors a mobile tax base incurs the cost B ≥ 0. The structure of such iceberg costs is described in table ??. 4

We consider B and b as the difference in direct information costs between the central and local Figure 1: Structure of direct information costs. tax base

tax authority

mobile

immobile

central

0

b

local

B

0

tax authority. For instance, B is the difference in direct information costs of monitoring a mobile tax base, between the central and local authority, the latter authority being (by assumption) less efficient in monitoring a mobile tax base. A tax system, however, is a combination of several (possibly) correlated taxes, so that an information spillover between tax bases cannot be ruled out. Indeed, when tax bases are highly correlated, the information gathered monitoring a particular tax base can be useful for the enforcement of the others, therefore reducing the auditing costs.

2.1

Monitoring technology

We assume that a tax payer discloses the true level of tax base when audited. The auditing activity has a cost, which is reflected by the relationship between resources devoted to auditing and probability of being audited. We define the probability of being audited as an increasing function of the resources allocated. The effect of resources on the probability of being audited depends on the level of government which performs the task and on the information spillovers.5 For the sake of clarity, we consider only a unidirectional spillover, from local to central taxes. This means that auditing local taxes makes less costly to audit central ones. The auditing function for the national tax is (1)

P = P (R, p) with

∂P = γ > 0; ∂R

∂2P = γ0; ∂R2

∂P = ∂p

where P and p represent the likelihood of being audited by the central and the local authority, respectively. The parameter  represents the marginal spillover which we assume to be constant. The auditing function for local taxes is p = p(r) 5 Since

(2)

direct information is modelled as an iceberg cost on tax revenue, it does not directly influence monitoring.

5

with

∂p ∂2p = λ0 = λ > 0; ∂r ∂r2 In the current version of the paper we set γ 0 and δ 0 both equal to zero, therefore assuming a linear monitoring technology. The marginal productivity of resources on monitoring a central tax γ is positive and constant and it does not depend on the monitoring activity on the other taxes. The marginal productivity of resources on monitoring local taxes, λ, is positive and constant.6 The reduced form of equations 1 and 2 has the following Jacobian matrix: 



 γ J = 0

λ   λ

The elements in the diagonal represent the marginal productivity of resources, both for central and local taxes. Off the diagonal there is the spillover effect between tax bases: a positive effect of local resources on the auditing of the central tax, ∂P ∂r = λ. If we had considered also spillovers from the central tax to the local one, then the element in the lower left-hand corner of the Jacobian matrix would not be zero.

2.2

Auditing authority and tax revenue

All levels of government implement the auditing policy in order to maximise the (net) tax revenue, i.e. the total amount of tax revenue collected minus the amount of resources devoted to the auditing activity. The tax revenue collected depends on citizens’ choice on the amount of tax base to report. Given the probability of being audited (P and p, for central and local tax auditing, respectively), the tax rate (T and t) and the penalty (F and f ), each citizen optimally decides the tax base to report for the central tax, X ∗ (P, T, F ) and the tax base to report for the local tax, x∗ (p, t, f ). The net tax revenue equals the sum of the optimal citizens’ report plus the penalty that they pay when monitored (and found guilty) minus the resources allocated to monitoring. The net revenue from the central tax is denoted by G, while the net revenue from the local tax is denoted by g, G =

(1 − D)

X

[X ∗ (P, T, F ) + P · (S + T )(Y − X ∗ (P, T, F ))] − R

(3)

ι

g

=

(1 − d)

X

[x∗ (p, t, f ) + p · (s + t)(y − x∗ (p, t, f ))] − r

(4)

ι

where ι indicates citizens, Y and y are the true tax base of the central and local tax, respectively; D is the iceberg cost payed by the central authority; d is the iceberg cost payed by the local authorities. As in Allingham and Sandmo (1972) both an increase in the penalty (F and f ) and in the 6 Decreasing

marginal productivity would lead to similar results.

6

probability of auditing (P and p) increases the reported tax bases; the effect of the tax rate is ambiguous since it depends on the attitude towards risk. It is possible to prove that when the elasticity of the report (X and x) with respect to the probability of auditing is positive and less than one, the tax revenue increases less than  proportionally with P and p,  ∂g ∂2g ∂2G ∂G ∂P > 0; ∂P 2 < 0 and ∂p > 0; ∂p2 < 0 . Moreover, if F + T < 1 (and f + t < 1) the tax revenue increases with the penalty,   ∂g ∂G ∂F > 0; ∂f > 0 . This set up is consistent with tax revenue functions of the following type G(P )

=

A(P, Ω)H(T, F )(1 − D) − R

(5)

g(p)

=

a(p, ω)h(t, f )(1 − d) − r

(6)

where Ω and ω represent the propensity to declare central and local tax base, respectively. The derivatives of equations 5 and 6 are the same as equations 3 and 4, when we impose AP > 0; AP P < 0; AΩ > 0; ap > 0; app < 0; aω > 0; HF > 0; hf > 0 We remark that A(P, Ω)H(T, F ) represents the central tax gross revenue, given the citizens’ optimal choice. Analogously, a(p, ω)h(t, f ) is the tax gross revenue from local taxes.

3

Equilibrium

We consider the equilibrium outcome according to the assignment of the enforcement function between the local and the central tax authorities: (S) separate (decentralised), perfect correspondence between tax assignment and enforcement powers; (C) centralised auditing, i.e. the central authority enforces compliance on both taxes. The strategy space of the tax authority and the monitoring technology changes according to the institutional scenario. We derive an equilibrium for each of the institutional scenario, in order to compare the results in terms of net tax revenue.

3.1

Separate enforcement

The central government is concerned with the enforcement of the central tax, while the local government is responsible for the enforcement of its local tax. The tax authorities simultaneously, and independently, chose the level of resources which maximise their net tax revenue. We assume that both governments levy taxes in the same area.7 7 Our model represents the special case of symmetric jurisdictions and no informational spillover among local authorities, where the analysis can be conducted considering a representative jurisdiction.

7

The local tax authority behaves according to, max g(r)

=

a(p, ω)h(t, f )(1 − dS ) − r

(7)

∂g ≡ gr ∂r

=

ap [p(r), ω]λ · h(t, f )(1 − dS ) − 1 = 0

(8)

r

The local authority chooses r∗ which solves equation 8. Note that r∗ is a dominant strategy for the local authority, for the action chosen by the central authority does not influence its optimal choice. Analogously, the central government maximises its net total revenue choosing the resource for auditing the national tax, max G(R)

=

A(P, Ω)H(T, F )(1 − DS ) − R

∂G ≡ GR ∂R

=

AP [P (R, r), Ω]γ · H(T, F )(1 − DS ) − 1 = 0

R

(9) (10)

In this case the optimal response of the central authority, R∗ , depends also on local resources r. Proposition 1 An increase in resources devoted to the enforcement of the local taxes produces a “crowdingout” effect on the resources for the central tax. Proof. We have GRr = γλAP P H(T, F )(1 − DS ) < 0 thus

GRr λ dR∗ =− =− 0 γ

Local resources influence the tax revenue of the central authority through two channels: the information spillover and the crowding out effect. The former has a positive impact on revenues, the larger is , the larger is the effect on the revenues of the central tax. This effect is magnified by the productivity of the local resources, λ. On the contrary, the productivity of the central resources, γ, reduces the impact of r on G, as the larger is γ the larger is the negative impact of the crowding-out on G. 8

The equilibrium of the sequential game is given by the strategy profile {xe , X e , re , Re }, where re and Re are the solutions to the system of equations given by conditions 8 and 10. Given the equilibrium choice of the citizens and the tax enforcement authorities, we can now conduct some comparative statics, to investigate how the allocation of resources to tax enforcement changes with some parameters of the model. Firstly, the authorities’ choice depend on the cost of the enforcement which is mainly due to the direct information costs (d, D) they face. Proposition 3 The amount of equilibrium resources devoted to local tax enforcement decreases with the information direct cost d. The amount of equilibrium resources devoted to the central tax decreases with the information direct cost D, and increases with the information direct cost d. Proof. Since grr = λ2 app · h(t, f )(1 − dS ) < 0 and grd = −λap h(t, f ) < 0 we get

dre grd =− 0 as

dR dr

< 0 and

dr dd

< 0.

Given the crowding out effect the amount of resources devoted to the central tax is influenced by both costs, while the amount of resources devoted to the local tax is influenced only by the local information cost. The optimal choice is also influenced by the tax payers’ choice on the amount of tax base to report. The latter is influenced by parameters such as the level of the penalty, and the sensitivity to the risk of being audited. Also in this case the equilibrium level of the resources for the central tax depends on the parameters affecting local tax enforcement. Proposition 4 The amount of resources devoted to the enforcement of the local tax increases with the sensitivity of tax payers to the probability of being audited, ω, and with the level of the penalty f . The equilibrium resources for the central tax increases with the sensitivity of tax payers to the probability of being audited by central authority, Ω, and with the penalty F . It, also, decreases with ω and with f . Proof. Since grω = λapω h(t, f )(1 − dS ) > 0 with apω > 0, then grf = λap hf (1 − dS ) > 0; the e grf grω dr e same holds for central tax revenue dr dω = − grr > 0, df = − grr > 0, ; the same for central tax e e e dR dr revenue. Moreover , dR df = dr e df < 0. Proposition 5 The equilibrium level of R increases with the marginal productivity of resources in monitoring central taxes, γ; the equilibrium level of r increases with the marginal productivity of resources in monitoring local taxes, λ. 9

Proof. e

dRe dγ

G

Rγ > 0 if GRγ > 0, thus if = − GRR

P γRe

> − AAPPP P , since P is linear in Re and in p,

γR +p γRe

p AP P = 1 + γR P . The LHS is always higher than 1, while the RHS is always lower e > − A P e than 1. The proof for r is similar.

3.2

Centralised enforcement

In this setting the central tax authority is responsible for the enforcement of both central and local taxes,8 therefore the objective is the maximisation of W , that is the sum of the central and local tax revenue.

max W

{R,r}

∂W ∂R ∂W ∂r

=

[A(P, Ω)H(T, F )(1 − DC ) − R] + +[a(p, ω)h(t, f )(1 − dC ) − r]

(11)

=

AP [P (R, r), Ω]γ · H(T, F )(1 − DC ) − 1 = 0

(12)

=

ap [p(r), ω]λ · h(t, f )(1 − dC ) − 1 + +AP [P (R, r), Ω] · H(T, F )(1 − DC )λ = 0

(13)

The equilibrium level of resources is determined by the solution of the following system of tow equations in two unknowns,

AP [P (R, r), Ω]γ · H(T, F )(1 − DC ) = 1 λ ap [p(r), ω]λ · h(t, f )(1 − dC ) +  = 1 γ

(14) (15)

Note that condition (15) does not depend on R, therefore the equilibrium level of local resources is the solution of equation (15). Also in this case the choice of the local resources is not affected by the choice of the resources for the central tax.

4

Optimal Tax and Enforcement assignment

In this section we use our model to compare the two scenarios. We stard by considering the extreme case in which all parameters are the same in the two scenarios, in particular the direct information costs are the same (DC = DS and dC = dS ). The suffixes, C and S represent the centralised and the separate institutional scenario, respectively. Proposition 6 The equilibrium level of local resources in the centralised case is greater (or equal) than e the equilibrium level in case of separate enforcement, rC ≥ rSe . Given 3, the equilibrium level of central e resources is lower (or equal) than the equilibrium level in the separate scenario, RC ≤ RSe . 8 The

analysis is analogous in case of enforcement implemented by the local authority on both local and central tax.

10

If there are spillovers the solution of the separate scenario differs from the solution of the centralised scenario. Indeed, only if all direct costs and spillover are zero we have total indifference between the two scenarios. We, now, consider the general case of different information costs and positive spillovers. The economic theory on tax assignment suggests that taxes should be assigned to the central or local level in order to minimise inefficiencies due to mobility. Accordingly, mobile taxes are assigned to the central level, while immobile taxes are assigned to the local level. If we follow the same principles for the assignment of the enforcement powers, there would be no direct information costs (DS = dS = 0), in the separate scenario. By contrast, assigning the enforcement of a mobile tax at the local level and the enforcement of an immobile tax at the central level would result in the maximum direct information costs (DS = b and dS = B). Remark 1 In the separate scenario the enforcement should be assigned according to mobility, the local level should enforce the immobile tax base, while the central level should enforce the mobile tax base. Proof. The proof can be derived by proposition 3 In the centralised scenario the enforcement of the immobile (local) tax has a direct information cost (DC = 0, dC = b). The comparison, in terms of tax revenue, between the two scenarios depends on the level of spillovers between the local and the central tax base, , with respect to the level of b, the direct cost the central authority incurs in because of the lack of information on the local tax base. Given the level of the spillover, the higher is b the smaller is the revenue in the centralised scenario with respect to the separate case. On the other hand, given b the higher is  the greater is the revenue of the centralised scenario with respect to the separate case. Therefore, the optimal enforcement assignment suggest to centralise when spillovers are high and direct information costs are lower. We remark that when spillovers do not exist and direct information costs equal zero, the centralised tax revenue is the same as the revenue of the separate scenario. In this case, we can consider a second-order Taylor expansion9 of the tax revenue function in the initial condition D = 0, d = 0,  = 0. For the centralised scenario we have 1 0 0 W = W 0 + WD dD + Wd0 dd + W0 d + (dD dd d)HW (dD dd d)0 2

(16)

where W 0 represents the value computed in the initial condition; and HW is the Hessian matrix of W ,   0 0 0     HW =  0 Wd   0    0 Wd W 9 All

derivatives in the appendix.

11

After some algebra we get the following equation for the centralised scenario, W

=

1 0 2 0 W 0 + gd0 b + G0  + Wd b + W  2

(17)

In the separate scenario the Taylor expansion looks like, 1 Γ = Γ0 + G0D dD + gd0 dd + G0 d + (dD dd d)HΓ0 (dD dd d)0 2

(18)

where Γ = G + g, and HΓ is the Hessian matrix of Γ, which is a matrix of zeros in the initial point. After some algebra we get Γ = Γ0 + G0  (19) Starting from the case when scenarios coincides (D = 0, d = 0 and  = 0) and assuming that the parameters change from separate to centralised scenarios are small, we can argue that the centralised scenario produces a greater tax revenue if W > Γ. Proposition 7 The total revenue in the centralised scenario is greater than in the separate scenario, 1 λ ( )( 1 ) W ≥ Γ if and only if b ≤ ¯b, where ¯b = 2 aγpp γ 1 . −a

Proof.

ap

h+ γ 

1 0 2 0 W 0 + gd0 b + G0  + Wd b + W  ≥ Γ0 + G0  2

simplyfing 1 0 2 0 gd0 b + Wd b + W  ≥0 2 substituting out −ahb + and

1 ap 1 λ 1 ap 2 b −  ≥0 γ app 2 γ γ app

  1 ap 1 λ 1 ap 2  ≥ ah +  b 2 γ γ −app γ −app

hence, b≤

1 2





λ γ app −a ap h



1 γ + γ1 

This proposition means that the policy maker should centralise the enforcement only when the loss in terms of direct information costs is lower than a positive threshold, ¯b. This threshold increases with the magnitude of the spillover, i.e. the larger the benefit in terms of spillovers the larger is the direct information cost that the policy maker is willing to incur. Perhaps, more interesting is the fact that the threshold depends negatively on a measure of the relative risk   a aversion of evading local taxes, −a app . The higher the level of risk aversion the lower is p the threshold. The economic intuition is that an increase in risk aversion results in a large 12

opportunity cost of choosing the centralised solution, for high risk aversion is associated with a large local tax revenue. Thus, the total direct information cost (bg) is larger, and the policy maker would centralise only for low values of b.

5

Conclusions

The tax assignment theory usually ignores compliance problems and the issue of tax enforcement is usually not considered in a federal framework, neither theoretically nor empirically. Moreover, it is not a relevant part of the political agenda. In fact, roughly speaking, tax enforcement powers are assigned following the principle that the level of government who has the power to levy the tax will also be responsible for the enforcement. We showed that this practice is correct only when there are no information spillovers among tax bases. Even if the collaboration among enforcement authorities were so close to cancel out any direct information cost, the presence of information spillovers among tax bases should be taken into account. Since internalising the externalities at the central or at the local level may result in direct information costs, the governments (both local and central) face a trade off between direct information and spillovers. In Italy, although the law assigns the enforcement power to the level of government which levies the tax, local governments delegate to a national agency the enforcement task, so as to keep the political decision on the enforcement, while delegating the actual enforcement to a central agency. According to our model this solution can allow the internalisation of informative spillovers, but incurs in comparatively larger information costs the less mobile is the local tax base. To sum up, the main message of our paper is that the allocation of tax enforcement powers may follow a different pattern than tax assignment whenever information spillovers are important.

13

A

Derivatives

GD (D = 0; d = 0;  = 0)

=

WD (D = 0; d = 0;  = 0)

=

−A[P (Re , re ,  = 0)]H

gd (D = 0; d = 0;  = 0)

=

Wd (D = 0; d = 0;  = 0)

=

−a[p(re )]h

GDD (D = 0; d = 0;  = 0)

=

WDD (D = 0; d = 0;  = 0)

=

0

gdd (D = 0; d = 0;  = 0)

=

=

0

G [∀(D; d; )]

=

Wdd (D = 0; d = 0;  = 0) h i ∗ dR∗ AP H(1 − D) γ dR d + λr − d

=

− λγ r

dR∗ d

with W [∀(D; d; )]

=

  e dr e e AP H(1 − D) γ dR d + λr + λ d −

with(Re ; re )

AP H(1 − D) =

W [∀(D; d; )]

=

− λγ r  e ap h(1 − d) λ dr d −

= dRe d

+

1 γ

ap h(1 − d) =

and

G [∀(D; d; )]

− λγ re

=

In the centralised scenario λ

Wr 1 dre γ =− =− =− 2 d Wrr λ app h(1 − d) γλapp h(1 − d) dRe WR λ =− = − re d WRR γ Thus WD (D = 0; d = 0;  = 0)

  e dr e e = −AP H γ dR = d + λr + λ d

Wd (D = 0; d = 0;  = 0)

=

e

−λap h dr d

=

0 1 ap γ app

and after some algebra W (D = 0; d = 0;  = 0) = −

1 1 λap 1 λ ap λ =− 2 =− = − Wd (D = 0; d = 0;  = 0) γ 2 h app γ λap h app γ γapp γ G (D = 0; d = 0;  = 0) = 0

14

1 λ

dr e d

− γ1 

References A LLINGHAM , M. G. AND S ANDMO , A. 1972. Income tax evation: a theoretical analysis. Journal of Public Economics 1:323–338. B ECKER , G. S. 1968. Crime and punishment: An economic approach. Journal of Political Economy 76:169–217. C REMER , H. AND G AHVARI , F. 1993. Tax evasion and optimal commodity taxation. Journal of Public Economics 50:261–275. C REMER , H. AND G AHVARI , F. 2000. Tax evasion, fiscal competition and economic integration. European Economic Review 44:1633–1657. E STELLER -M OR E´ , A. 2004. Tax evasion in interrelated taxes. Public Economics 0401001, EconWPA. K APLOW, L. 1989. Optimal taxation with costly enforcement and evasion. NBER Working Paper n. 2996. O ATES , W. E. 1999. An essay on fiscal federalism. Journal of Economic Literature 37:1120–1149. S ANDMO , A. 1981. Income tax evasion, labour supply, and teh equity-efficiency tradeoff. Journal of Public Economics 16:265–288. T IEBOUT, C. M. 1956. A pure theory of local expenditure. Journal of Political Economy 64:416–424. W ELLISCH , D. 2000. Theory of Public Finance in a Federal State. Cambridge University Press.

15