A Second-Best Theory of Local Government Policy

International Tax and Public Finance, 7, 5–22 (2000)c© 2000 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

A Second-Best Theory of Local Government Policy

DIETMAR WELLISCH [email protected] Universitat Dresden, Fakultat Wirtschaftswissenschaft, 01062 Dresden, Germany

JORG HULSHORSTTechnische Universitat Dresden, Fakultat Wirtschaftswissenschaft, 01062 Dresden, Germany

Abstract

This paper provides a model where a large number of small jurisdictions compete for mobile firms and householdsby supplying local public goods and factors. Jurisdictions only have an incomplete set of tax instruments at theirdisposal to achieve an efficient allocation. We derive second-best behavioral rules for local governments andextend optimal taxation results to the local level. Local governments distort locational decisions of mobile firmsand households by taxing them above marginal congestion costs so as to balance relative locational distortionsbetween taxes. The analysis also reveals that there is a systematic difference between the provision of local publicgoods and factors. While local public goods are provided according to the Samuelson rule in most situationsconsidered, local public factors are undersupplied relative to this rule.

Keywords: optimal taxation, local government finance

JEL Code: H21, H71

1. Introduction

In a unitary state, a benevolent government achieves a first-best allocation if it can financepublic goods and factors by raising lump-sum taxes. At the local level, however, theexistence of a non-distortive revenue source like a tax on land rents is not sufficient tosupport efficiency if public goods and factors are congestible. A complete tax instrumentset additionally requires location-based taxes on mobile firms and households in order tointernalize marginal crowding costs. If these taxes are available at the local level and iflocal governments maximize net land rents generated within their jurisdictions, they havethe correct instruments and the correct incentives to realize an efficient allocation. In thissituation, we will speak of afirst-bestpolicy at the local level.

However, a complete set of tax instruments rather serves as a theoretical benchmark casefor existing tax policies. Private property like land, for example, is legally protected againstheavy taxation in almost all countries of the European Union (EU), as in Germany by thewritten constitution.1 Distributional considerations may serve to explain these institutionalrestrictions since land and wealth endowments differ significantly among individuals. Butmost of all, high administrative costs might by the important reason for making little useof land taxation as a revenue source. Since site or market values of land are difficult toobserve and landowners have incentives to understate these values, the land tax entailscostly informational requirements (see Skinner, 1991a).2 Consequently, as Slemrod (1990)argues, although a land tax is anoptimal tax, it need not be part of anoptimal tax system

6 WELLISCH AND HULSHORST

if administrative costs are taken into account. In this case, local public goods and factorsmust be financed with distortionary taxes on mobile firms and households.

Othersecond-bestsituations arise if local governments are unable to tax either mobilefirms or households in order to internalize marginal congestion costs.3 In fact, location-based taxation plays a rather unimportant role in many federal states. For example, localgovernments in EU member countries have very limited access to location-based taxes onhouseholds and firms.4 Moreover, existing local income and property taxes cause distortionsin labor, capital, and housing markets and are thus second-best instruments even in a situationwithout household and firm mobility. Consequently, whenever local governments cannottax mobile firms and households directly, they have incentives to distort the allocation soas to charge firms and households indirectly for crowding costs they cause.

Since locational distortions are specific to the local (or regional) level and cannot befound in a unitary state, it is worth developing a second-best theory of local governmentpolicy—the basic purpose of the present analysis. Building on a model developed by Richterand Wellisch (1995), local governments supply impure local public goods and factors toperfectly mobile firms and households.5 Second-best situations considered in the presentpaper are characterized by the absence of either a tax on local land rents, a direct tax onmobile households, or a direct tax on mobile firms. In deriving the design of a second-besttax structure, the Ramsey (1927) taxation rule plays an important role (see e.g. Mirrlees,1986, and Persson and Tabellini, 1990). We use modified versions of the Ramsey rule tointerpret the second-best behavior of local governments. In particular, if a tax on local landrents is not available, local governments balance locational distortions caused by directfirm and household taxes relative to their impacts on land rents between these taxes. Thisrule also applies to the provision of local public factors. However, a remarkable result isthat even in the absence of land taxation, local governments provide public goods in linewith the Samuelson rule. Hence, migration does not only reveal the preferences for localpublic goods, as suggested by Tiebout (1956). Rather, local governments have incentives toconsider these preferences in a socially efficient way even if they only rely on distortionarytaxes. Moreover, there is a systematic difference between the provision of local public goodsand factors. While local governments have incentives to provide public goods efficientlywhenever they have a direct household tax at their disposal, the supply of public factors isalways distorted. The crucial point to explain this asymmetry is that local public factorsdirectly influence land rents, profits, and wages, whereas local public goods affect thesevariables only indirectly via locational responses of firms and households.

There are some other related contributions to the literature dealing with the behavior oflocal governments in second-best situations. Wilson (1986) and Zodrow and Mieszkowski(1986) show that local governments undersupply public goods relative to the Samuelsoncondition if they must raise taxes on mobile capital. Hoyt (1991), Krelove (1993), and Hen-derson (1994) demonstrate that this result also holds if local governments have to rely onproperty taxes distorting locational decisions of mobile households.6 The theoretical litera-ture on local public factors is not equally well developed. While Zodrow and Mieszkowski(1986) argue that local public factors are undersupplied in the presence of interregionalcapital tax competition, Oates and Schwab (1991) demonstrate that local governments pro-vide an efficient level of public factors if the tax on mobile capital serves as perfect user

A SECOND-BEST THEORY OF LOCAL GOVERNMENT POLICY 7

fee. The present paper is more general than the mentioned contributions in that it assumestwo mobile source of taxation, mobile householdsand firms. This enables us to derive asecond-best tax structure. Moreover, there are two types of public services, public goodsand factors. This generalization reveals the systematic difference between both types oflocal public services.

There are also some limitations to the present study which should be discussed briefly.First, distortionary taxes on income, capital and property which can only serve as proxiesfor direct household and firm taxes are excluded from the model since the fundamentalreasons for the second-best nature of local government policies can best be elaborated bycomparing second-best situations to the first-best policy. Therefore, we only deal withthese taxes informally. Second, contrary to Hoyt (1991), Krelove (1993), and Henderson(1994), the present model does not include housing. However, we argue that such anextension does not change the results significantly provided that a tax on housing (that is aproperty tax) is introduced as well. Third, the present analysis does not deal with strategicbehavior of governments, as analyzed in Gordon (1983), Burbidge and Myers (1994) andWellisch (1994), (1995a), and (1995b). Since each land rent maximizing local governmenttakes profits and utility as given, an incomplete set of tax instruments is the only source ofinefficiency considered.7

The paper is organized as follows. Section 2 describes the first-best policy of a localgovernment. In the presence of perfect interregional competition land rent maximizingbehavior ensures an efficient allocation. Section 3 considers second-best policies when thelocal tax instrument set is incomplete. It begins with the case where no residence-basedhousehold tax is available, proceeds with the case where no location-dependent firm taxexists, and ends with the case where an undistortive tax on land rents is infeasible. Section 4summarizes the basic results.

2. First-Best Policy

Consider a federal state consisting of many small jurisdictions which may be interpretedas communities. We concentrate on a single jurisdictioni in order to discuss the efficiencyproperties of local government decisions. Since the local government has to take locationaldecisions into account, let us first describe the behavior of households and firms.

2.1. Private Behavior

There areN identical, perfectly mobile households in the federal state. LetNi denotethe number of mobile households in jurisdictioni . All households living in a jurisdictionderive utility from the consumption of a local public goodzi and the consumption of privategoods,xi . LetUi ≡ U (xi , zi ) denote the utility function of a representative household withUi

x ≡ ∂Ui

∂xi> 0,Ui

z > 0≡ ∂Ui

∂zi.8

Households are endowed with one unit of labor which they inelastically supply in theirjurisdiction of residence. Letwi denote a household’s wage income. Additionally, eachhousehold owns1N of total land endowment and firms in each jurisdiction. Hence, nonlabor


income I is identical for each household independent of the place of residence. Finally,each jurisdiction collects a direct taxτ H

i from its residents.9 The entire net income is usedfor private consumption,

xi = wi + I − τ Hi . (1)

Arbitrage behavior of perfectly mobile households requires that a migration equilibrium isgiven byU (xi , zi ) = U (xj , zj ), for all jurisdictionsi and j . Since each small jurisdictionfaces a perfectly elastic supply of mobile households, it can attract any population at theprevailing utility levelu,

U (xi , zi ) = u. (2)

In the federal state, there is an exogenously given large number ofM identical perfectlymobile firms.10 All firms produce the private numeraire good with the same productiontechnologyFi ≡ F(l i ,ni , gi ) wherel i andni stand for the private factors land and labor,respectively, andgi denotes the local public factor in jurisdictioni . Fi is a concave functionwith respect to the private factorsl i andni .11

Firms simultaneously have to make two decisions choosing their locations as well as theirfactor inputs. Firms select their locations so as to maximize profits. Letπ i denote theafter-tax profit of a firm locating in jurisdictioni . Then, a locational equilibrium is givenby π i = π j , for all jurisdictionsi and j . Given a perfectly elastic supply of mobile firms,a single small jurisdiction can realize any number of firms at the prevailing after-tax profitlevel π ,

π i = π . (3)

In equilibrium Mi mobile firms choose jurisdictioni as their location. The after-tax profitof a representative firm locating ini is

π i = F(l i ,ni , gi )− ri l i − wi ni − τ Fi , (4)

whereri andwi are factor prices of land and labor in jurisdictioni andτ Fi denotes a direct

tax on firms.12 Price taking firms maximize profits by choosing their factor inputsl i andni

so as to equate marginal productivities to factor prices,

Fil = ri , (5)

Fin = wi . (6)

Let Li denote the local land endowment. Then, a local land market equilibrium requires

Li = Mi li , (7)

and the local labor market equilibrium is characterized by

Ni = Mi ni . (8)


Let us now describe the public sector. The costs of providing local public goods and factorsareCi (zi , Ni ) andHi (gi ,Mi ), respectively, depending on the service levels,zi andgi , aswell as on the number of users,Ni andMi . Local government revenue is raised by directtaxes on households and firms, and a tax on local land rentsti ,

Ni τHi + Mi τ

Fi + ti r i Li = Ci (zi , Ni )+ Hi (gi ,Mi ). (9)

Throughout the following analysis we will assume that per capita costs of public servicesexceed marginal congestion costs,Ci

Ni> Ci

N and Hi

Mi> Hi

M . Hence, if direct taxes are

chosen so as to internalize marginal congestion costs,τ Hi = Ci

N andτ Fi = Hi

M , a completetax instrument set on the local level must additionally include an undistortive revenue sourcesuch as a tax on land rentsti in order to balance the budget.

Finally, we can specify nonlabor income of all households in the federal state, consistingof the sum of profits and after-tax land rents in all jurisdictions,

N I = Mπ +J∑

j=1

(1− tj )r j L j . (10)

Perfect competition ensures that local governments take the equilibrium utility levelu andthe equilibrium profit levelπ as given. Hence, the considered equilibrium is of Walrasiantype.

Let us, for convenience, reconsider the introduced variables.ri andwi are endogenousprices andl i , Mi , ni , Ni , andxi are endogenous quantities determined in jurisdictioni .ti , τ H

i , τ Fi , gi , andzi are policy instruments of the local government.Li , I , u, andπ are

exogenous from a single jurisdiction’s viewpoint whereI , u, andπ take on the same valuesin all jurisdictions.

Locational decisions of mobile households and firms cannot directly be controlled by localgovernments. Hence, they must consider locational responses to policy changes. Using (2)and (3),Ni andMi can be expressed as implicit functions ofτ H

i , τ Fi , zi , andgi ,

Q(Ni ,Mi , τHi , τ

Fi , zi , gi ) ≡ U

[Fn

(Li

Mi,

Ni

Mi, gi

)− τ H

i + I , zi

]= u, (11)

S(Ni ,Mi , τHi , τ

Fi , zi , gi ) ≡ F

(Li

Mi,

Ni

Mi, gi

)− Fl

(Li

Mi,

Ni

Mi, gi

)Li

Mi

− Fn

(Li

Mi,

Ni

Mi, gi

)Ni

Mi− τ F

i = π , (12)

where (1) and (4)–(8) have been inserted into (2) and (3) in order to eliminate the endogenousvariablesxi , ri , wi , l i andni . Sinceti does not appear in (11) and (12), it follows thatNi

andMi are independent of the tax on land rents.From (11), we can see how the marginal productivity of laborFi

n responds to a change inpolicy instruments at a given level of utilityu,

d Fin

dti= d Fi

n

dτ Fi

= d Fin

dgi= 0,

d Fin

dτ Hi

= 1,d Fi

n

dzi= −Ui

z

U ix

. (13)


2.2. Local Government Behavior

According to utility-taking assumption (2), local governments perceive that they cannotaffect the level of their residents’ satisfaction. However, they do consider policy effects onthe return of domestic landowners.13 To internalize this effect, we assume that each localgovernment chooses its policy so as to maximize after-tax land rent in the jurisdiction. Wewill now show that this objective is compatible with efficiency if utility-taking governmentshave a complete tax instrument set at their disposal (see e.g. Brueckner, 1983; Wildasin,1986; Wilson, 1987; Hoyt, 1991; Krelove, 1993).

The government of jurisdictioni has to solve the following problem:

maximize Wi ≡ (1− ti )ri Li (14)

by choosing the policy variablesτ Hi , τ F

i , zi , andgi where

(1− ti )ri Li = Mi

(Fi − Ni

MiFi

n − π)− Ci (zi , Ni )− Hi (gi ,Mi )+ Ni τ

Hi . (15)

ti does not appear as control variable of the local government in (14) since the budgetconstraint (9) has been inserted forti into (14).

First-order conditions of this problem are14

dWi

dτ Hi

= (τ Hi − Ci

N)∂Ni

τ Hi

+ (τ Fi − Hi

M)∂Mi

∂τ Hi

= 0, (16)

dWi

dτ Fi

= (τ Hi − Ci

N)∂Ni

∂τ Ti

+ (τ Fi − Hi

M)∂Mi

∂τ Fi

= 0, (17)

dWi

dzi= (τ H

i − CiN)∂Ni

∂zi+ (τ F

i − HiM)∂Mi

∂zi+ Ni

Uiz

U ix

− Ciz = 0, (18)

dWi

dgi= (τ H

i − CiN)∂Ni

∂gi+ (τ F

i − HiM)∂Mi

∂gi+ Mi F

ig − Hi

g = 0. (19)

(16) and (17) reveal that local governments have incentives to internalize marginal crowdingcosts, i.e. that they chooseτ H

i = CiN andτ F

i = HiM , provided that the matrix consisting

of the elements∂Ni

∂τ Hi

, ∂Mi

∂τ Hi

, ∂Ni

∂τ Fi

, and ∂Mi

∂τ Fi

has full rank which is proved in Appendix 5.1.

Considering this preliminary result in (18) and (19), respectively, it follows an efficient

provision of local public goods,NiUi

z

U ix= Ci

z, and factors,Mi Fig = Hi

g.The efficient allocation serves as reference situation for the following distortions associ-

ated with an incomplete tax instrument set.


3. Second-Best Policies

Let us now consider the distortions that arise if local governments only have an incompleteset of tax instruments at their disposal. In this model, there are three second-best situationsconceivable. Either jurisdictions cannot tax mobile households, they cannot tax mobilefirms, or they have no undistortive tax on land rents available.

3.1. Absence of a Direct Household Tax

The basic purpose of this subsection is to drive distortions when jurisdictions cannot taxmobile households and to explain the associated inefficiencies. The absence of a di-rect household tax is a typical restriction on the local level in many federal states. InGermany, for instance, direct taxation of households is entirely delegated to the federalgovernment.15

If jurisdictions have no direct tax on mobile households at their disposal,τ Hi ≡ 0,

the first-order condition (16) drops out. Usingτ Hi ≡ 0 in (17)–(19) and inserting the

migration responses∂Ni∂∗ and ∂Mi

∂∗ , ∗ ∈ {τ Fi , zi , gi }, from (A.7)–(A.12) in Appendix 5.1, it

follows

PROPOSITION1 Suppose that jurisdictions cannot tax mobile households,τ Hi ≡ 0. Then,

the competitive equilibrium among jurisdictions is characterized by the following necessaryconditions:

(i)τ F

i − HiM

UiM

= −CiN

UiN

,

(ii)Ni

Uiz

U ix− Ci

x

U iz

= −CiN

UiN

,

(iii)Mi Fi

g − Hig

U ig

= −CiN

UiN

,

where UiM ≡ ∂Ui

∂Mi= −Ui

xli Fi

nl+ni Finn

Mi, Ui

N ≡ ∂Ui

∂Ni= Ui

xFi

nnMi

, and Uig ≡ ∂Ui

∂gi= Ui

x Fing.

The competitive equilibrium is characterized by an inefficient allocation. Jurisdictionscannot directly internalize marginal crowding costs of supplying local public goods bylevying head taxes on mobile households. Hence, they take alternative measures to re-strict the inflow of households indirectly, thereby causing distortions. Let us interpretthe difference between direct taxes and marginal congestion costs of supplying publicfactors as distortions due to the inflow of mobile firms and households, respectively. De-viations from the Samuelson conditions are described as distortions caused by the pro-vision of public services. Then, according toProposition 1, local governments choosetheir remaining policy instruments so as to equate distortions caused by the inflow ofmobile firms and the provision of public services measured in terms of marginal utilityto relative congestion costs caused by immigration of mobile households. Condition (i)


shows that local governments tax mobile firms inefficiently high provided that wages

rise with an increasing number of mobile firms, i.e. if∂Fin

∂Mi= − l i F i

nl+ni Finn

Mi> 0. In this

case, the inflow of mobile households can be restricted by repelling mobile firms. An-other measure is to provide an inefficiently low level of public goods, as stated in con-dition (ii ). Since marginal utility of public goods is positive,Ui

z > 0, the attractive-ness of the jurisdiction decreases from the viewpoint of households. Finally, if wages

rise with an increasing supply of local public factors,∂Fin

∂gi= Fi

ng > 0, then, followingcondition (iii ), local governments undersupply public factors relative to the Samuelsonrule.

Incidentally, since distortions (i)–(iii ) depend onCiN , efficiency is achieved in case of

pure public goods,CiN = 0, where no marginal congestion costs have to be internal-

ized.The results derived in this subsection are similar to the conclusions drawn by Hoyt (1991)

and Krelove (1993). These authors show that local governments raise a distortionary taxon local property which serves a a proxy for a tax to cover marginal congestion costs.16

The property tax distorts the demand for housing, thereby affecting migration decisions.However, the present analysis reveals that instead of raising a property tax, local govern-ments can also use firm taxes, local public goods, and local public factors in order to chargemobile households indirectly for the crowding costs they cause. More generally, distortionsapply to all policy fields that have a direct impact on utility.

3.2. Absence of a Direct Firm Tax

Let us now assume that the set of local tax instruments is incomplete with respect to the directtax on mobile firms,τ F

i ≡ 0. In this case, first-order condition (17) vanishes. Insertingτ F

i ≡ 0 into (16), (18), and (19) and considering the migration responses∂Ni∂∗ and ∂Mi

∂∗ ,∗ ∈ {τ H

i , zi , gi }, from (A.5), (A.6), and (A.9)–(A.12) in Appendix 5.1, gives

PROPOSITION2 Suppose that jurisdictions cannot tax mobile firms,τ Fi ≡ 0. Then, the

competitive interregional equilibrium is characterized by the following necessary condi-tions:

(i)τ H

i − CiN

π iN

= −HiM

π iM

,

(ii) NiU i

z

U ix

− Ciz = 0,

(iii)Mi Fi

g − Hig

π ig

= −HiM

π iM

,

whereπ iN ≡ ∂π i

∂Ni= − l i F i

nl+ni Finn

Mi, π i

M ≡ ∂π i

∂Mi= l 2

i F i t

ll 2ni l i Filn+n2

i F inn

Mi, andπ i

g ≡ ∂π i

∂gi= Fi

g −ni Fi

ng− l i F ilg.


Again, the competitive equilibrium is characterized by an inefficient allocation. Juris-dictions have no direct instrument to internalize marginal crowding costs of providinglocal public factors. Hence, they use the remaining instruments to restrict the inflow ofmobile firms indirectly. Proposition 2reveals that local governments choose their pol-icy instruments so as to equate distortions caused by immigration of mobile householdsand the provision of public factors relative to their marginal effects on profits to rel-ative congestion costs caused by the inflow of mobile firms. Following condition (i),local governments tax mobile households above marginal crowding costs if profits in-crease with an additional household in the jurisdiction,π i

N > 0.17 Since firms avoidlocating in a jurisdiction if profits decrease, their inflow can be restricted by using in-efficiently high taxes on households. According to condition (ii ), the provision of lo-cal public goods is in line with the Samuelson rule. Local governments have no in-centives to distort this policy field since the supply of local public goods has no directimpact on profits,∂π

i

∂zi= 0. Public good provision affects profits only indirectly via

migration decisions of households. However, as stated in condition (i), locational de-cisions of households are already distorted by use of direct taxation. Finally, condi-tion (iii ) suggests that local governments undersupply local public factors compared tothe Samuelson condition if profits of local firms increase with a higher provision level,π i

g > 0.Notice again, that distortions in (i) and (iii ) depend onHi

M . Hence, efficiency is achievedin case of pure public factors,Hi

M = 0.A comparison of the results derived in 3.1 and 3.2 reveals that there is an important

difference between the provision of local public goods and factors. If local governmentshave no direct household tax, they undersupply local public factors in order to restrict theinflow of households. However, if no firm tax is available, local public goods are providedin line with the Samuelson condition and are not used to limit the inflow of mobile firms.The basic reason for this difference is that local public factors directly influence marginalproductivity of labor, thereby affecting utility, while local public goods affect profits onlyindirectly via their impact on the size of the local work force.

Does this asymmetry vanish if households consume land? Let us deal with this probleminformally. Following Krelove (1993), we assume for this purpose that firms producehousing and that all households are equally endowed with an exogenously given amount ofa private numeraire good. Then, profits do not only depend onNi , Mi , andgi , but also onthe producer price of housing, saypi . Suppose that local governments additionally have atax on housing (that is a property tax) at their disposal and letqi be the consumer price ofhousing. Then, we can express the property tax rate asqi − pi . Since local governmentshave incentives to distort all policy fields that directly affect profits, they will drive a wedgebetween the households’ marginal willingness to pay for housing and marginal social costs.More specifically, raising the property tax is the direct measure to reduce the producer priceof housingpi , thereby restricting the inflow of mobile firms. A more indirect measurewould be to reduce housing demand by distorting the provision of public goods. However,our analysis implies that if a tax on housing exists, the local government will use thisdirect instrument to affect profits and it will still supply local public goods according to theSamuelson condition.


Finally, let us briefly discuss what happens to the results if a tax on (perfectly mobile)capital used by firms exists as a proxy for the direct firm tax. A capital tax drives a wedgebetween the marginal productivity of capital and the common interest rate in the federalstate. Intuitively, local governments will tax capital whenever this measure induces mobilefirms to stay away. In terms of the present model, they will equate the capital tax raterelative to the marginal impact of capital on profits to relative congestion costs caused bymobile firms. Hence, if profits increase (decrease) with an additional unit of capital, localgovernments will tax (subsidize) this factor of production.

3.3. Absence of a Nondistortionary Tax

Now suppose that jurisdictions have no undistortive tax available,ti ≡ 0. Hence, they haveto finance local public goods and factors entirely with taxes on mobile households and firmsthat distort locational choices. This situation is very similar to a second-best problem in aclosed economy where public funds cannot be financed with lump-sum taxes.

In the absence ofti , there are four policy instruments left,τ Hi , τ F

i , zi , andgi . We assumethatτ F

i adjusts endogenously in order to balance the budget of the local government.18

Then, the problem of a local government is to

maximize Wi ≡ Li ri (20)

by choosingτ Hi , zi , andgi where

Li ri = Mi

(Fi − Ni

MiFi

n − π)− Ci (zi , Ni )− Hi (gi ,Mi )+ Ni τ

Hi . (21)

The first-order conditions of this problem are again given by (16), (18), and (19). How-ever, the locational responses∂Ni

∂∗ , ∂Mi∂∗ , ∗ ∈ {τ H

i , zi , gi }, differ from the responses useduntil now sinceτ F

i (instead ofti ) adjusts endogenously for budget clearing purposes. Lo-cational responses are now derived from the two locational equilibrium conditions (11)and

P(Ni ,Mi , τHi , zi , gi ) ≡ F

(Li

Mi,

Ni

Mi, gi

)− Fl

(Li

Mi,

Ni

Mi, gi

)Li

Mi

− Fn

(Li

Mi,

Ni

Mi, gi

)Ni

Mi− Ci (Ni , zi )

Mi

− Hi (Mi , gi )

Mi+ Ni τ

Hi

Mi= π . (22)

Since condition (11) still holds, responses of marginal productivity of labor,Fin, to changes

in τ Hi , zi , andgi continue to be given by (13). (22) follows from (12) by substituting the

government’s budget restriction (9) (withti = 0) for τ Fi . Locational responses derived

from (11) and (22) are stated by (A.16)–(A.21) in Appendix 5.2. Inserting (A.16)–(A.21)into first-order conditions (16), (18), and (19) allows us to state


PROPOSITION3 Suppose that jurisdictions have no undistortive tax available, ti ≡ 0. Then,the competitive equilibrium is characterized by the following conditions:

(i)τ H

i − CiN

RiN

= τ Fi − Hi

M

RiM

,

(ii) NiU i

z

U ix

− Ciz = 0,

(iii)Mi Fi

g − Hig

Rig

= τ Fi − Hi

M

RiM

,

where RiN ≡ ∂(Li Fi

l )

∂Ni= l i F i

ln, RiM ≡ ∂(Li Fi

l )

∂Mi= −(l 2

i F ill + ni l i F i

ln), and Rig ≡ ∂(Li Fi

l )

∂gi=

Li Filg.

As expected, the competitive equilibrium is characterized by an inefficient allocation ifjurisdictions have no tax on land rents available. However, assuming that per capita costsof supplying public services exceed marginal congestion costs,Ci

Ni> Ci

N and Hi

Mi> Hi

M ,requires the existence of such an undistortive revenue source to balance the budget.Propo-sition 3shows that local governments choose their remaining policy instruments so as toequate distortions caused by the inflow of mobile households and firms and the provision oflocal public factors relative to their impacts on the local land rent. Condition (i) can be con-sidered as a second-best taxation rule. The denominator on the LHS reflects the change inthe land rent due to a change in the number of mobile households, while the denominator onthe RHS describes the impact of an additional mobile firm. Let us assume that the marginalproductivity of land increases with the number of mobile workers as well as with the numberof mobile firms,Ri

N, RiM > 0. Then, both tax rates must exceed marginal crowding costs in

order to balance the budget. Since household and firm taxes directly influence the numberof mobile residents and firms locating in the jurisdiction, condition (i) can be interpretedas Ramsey taxation rule for distortionary taxes at the local level. The ordinary Ramseyrule requires to equate distortions caused by taxes relative to their induced changes in taxrevenues among taxes. Here, jurisdictions balance distortions relative to the impacts oftaxes on land rents among taxes. Condition (ii ) reveals that local governments again haveno incentives to distort the supply of local public goods since public good provision affectsmarginal productivity of land (that is the price of land) only indirectly via migration deci-

sions of households,∂(Li Fi

l )

∂zi= 0. However, as stated in condition (i), the trade-off between

the distortion caused by the inflow of households and its impact on the local land rent isdelegated to the direct household tax which is already chosen optimally. Finally, followingcondition (iii ), the distortion caused by the provision of local public factors measured interms of the associated change in the land rent must be equal to relative distortions causedby the inflow of mobile firms and households, respectively. Hence, if the marginal productof land rises with an increasing supply of public factors,Ri

g > 0, there is an inefficientlylow supply of local public factors relative to the Samuelson rule.

It is again important to notice that the introduction of housing into the analysis does notaffect the efficient supply of public goods provided that a tax on housing is available. As


argued before, such a tax directly affects the price of housing, thereby changing the landrent, while public goods affect the price of housing only indirectly.

The asymmetric incentives concerning the supply of local public goods and factors, asderived in 3.1–3.3, can be summarized in

PROPOSITION4 Whenever an incomplete tax instrument set consists of a direct householdtax and another tax, local governments provide local public goods in line with the Samuelsonrule. Local public factors, on the other hand, are always supplied inefficiently relative tothe Samuelson condition when the tax set is incomplete.

It is well known that decentralized provision of public goods reveals the preferences ofmobile households (Tiebout, 1956) and that local governments internalize these preferencescorrectly if their tax instrument set is complete (Wildasin, 1986). However, the novel insightof Proposition 4is that local governments have incentives to internalize the preferences ofmobile households in a socially efficient way even when they must rely on distortionarytaxes. This holds regardless of whether local governments provide local public factors ornot. The important condition for this result to hold is that jurisdictions must have a secondrevenue source aside from the direct tax on mobile households.

4. Conclusions

The basic purpose of this paper has been to gain insights into second-best policies at thelocal level. We have assumed that jurisdictions are competitive net-rent maximizers and thatlocal public services are congestible. Second-best situations have been modelled throughthe non-availability of direct taxes on mobile households and mobile firms as well as throughthe absence of a tax on land rents. Depending on whether a direct household tax, a directfirm tax, or a tax on land rents is not available, local governments distort all policy fieldsthat directly affect utility, profits, or land rents. In particular, if there is no undistortivetax on land rents, the optimal taxation structure at the local level can be described by amodified Ramsey rule which requires to equalize locational distortions caused by directtaxation relative to the impact of taxes on the local land rent. Moreover, the existence of aresidence-based tax on households releases local governments from distorting the provisionof local public goods even if their tax instrument set is incomplete.

Richter and Wellisch (1995) derive a similar conclusion in a model with both immobileand mobile households. If local governments cannot avoid the outflow of local land rentsby taxing them confiscatorily, they use the remaining instruments to restrict the outflowindirectly. However, in the presence of direct household taxes which are used to repelmobile households, thereby reducing the outflow of land rents, local governments have nofurther incentives to distort the provision of local public goods. Burbidge and Myers (1994)show that strategic behavior of regions is also compatible with an efficient supply of localpublic goods provided that a residence-based tax on mobile households and/or a capitaltax exists. Since these instruments are used to increase the own income share of a region,there is no need to distort the supply of public goods as well. Finally, as suggested byHulshorst and Wellisch (1996), there are also important differences between the provisionof local public goods and local environmental policy. Since emissions are a local public


bad as well as a public production factor, local governments distort the choice of localemission standards in second-best situations just as they distort the provision of ordinarypublic factors.

5. Appendix

5.1. First-Order Conditions and Migration Responses

Let us first derive the necessary conditions (16)–(19). The optimal choice ofτ Hi will

be explained in detail. The remaining first-order conditions (17)–(19) can be derivedanalogously. Inserting (15) into (14), it follows with the help of the envelope theoremas a necessary condition for choosingτ H

i :

dWi

dτ Hi

= −CiN

∂Ni

∂τi H− Hi

M

∂Mi

∂τ Hi

+ τ Hi

∂Ni

∂τ HI

+ Ni

+ ∂Mi

∂τ Hi

(Fi − Ni

MiFi

n − π)− Mi

(Fi

l

Li

M2i

∂Mi

∂τ Hi

+ Ni

Mi

d Fin

dτ Hi

)= 0. (A.1)

We now substitute (5)–(8) into (4) and then (4) into (3). It follows thatFi − ni Fin − π =

l i F il + τ F

i . Furthermore, (13) yieldsd Fin

dτ Hi= 1. Inserting both expressions into (A.1) and

collecting terms yields the necessary condition (16).The migration responses∂Ni

∂∗ and ∂Mi∂∗ , ∗ ∈ {τ H

i , τFi , zi , gi }, can be derived from (11) and

(12). Total differentiation yields in matrix form

(QN; QM ;SN; SM ;

)(d Ni

d Mi

)=(−Qτ H ; −Qτ F ; −Qz; −Qg;−Sτ H ; −Sτ F ; −Sz; −Sg;

)dτ H

idτ F

idzi

dgi

, (A.2)

with

QN = UixFi

nn

Mi, QM = −Uix

(Li

M2i

F iln +

Ni

M2i

F inn

),

SN = − Li

M2i

F iln −

Ni

M2i

F inn, SM = L2

i

M3i

F ill + 2

Ni Li

M3i

F iln +

N2i

M3i

F inn,

Qτ H = −Uix, Qτ F = 0, Qz = Ui

z, Qg = Uix Fi

ng,

Sτ H = 0, Sτ F = −1, Sz = 0, Sg = Fig −

Li

MiFi

lg −Ni

MiFi

ng. (A.3)

Let A denote the matrix on the LHS of (A.2), it follows that

|A| = Uix

L2i

M4i

[Fi

nnFill − (Fi

nl)2]. (A.4)


The determinant|A| is positive due to strict concavity ofFi with respect tol i andni . Thefollowing analysis will use the abbreviation

a ≡ Uix

Mi |A| ,

Solving (A.2) with the help of Cramer’s rule and making use of (A.3) yields

∂Ni

∂τ Hi

= a[l 2i F i

ll + 2l i ni Filn + n2

i Fnn]< 0, (A.5)

∂Mi

∂τ Hi

= a[l i F

inl + ni F

inn

], (A.6)

∂Ni

∂τ Fi

= a[l i F

inl + ni F

inn

] = ∂Mi

∂τ Hi

, (A.7)

∂Mi

∂τ Fi

= aFinn < 0, (A.8)

∂Ni

∂gi= −ali F

ing

[l i F

ill + ni F

iln

]− a[Fi

g − l i Filg][ l i F

inl + ni F

inn

], (A.9)

∂Mi

∂gi= −a

[Fi

nn(Fig − l i F

ilg)+ l i F

iln Fi

ng

], (A.10)

∂Ni

∂zi= −Ui

z

U ix

a[l 2i F i

ll + 2ni l i Filn + n2

i F inn

] = −Uiz

U ix

∂Ni

∂τ Hi

> 0, (A.11)

∂Mi

∂zi= −Ui

z

U ix

a[ni F

inn+ l i F

iln

] = −Uiz

U ix

∂Mi

∂τ Hi

. (A.12)

Using the migration responses (A.5)–(A.8), we can now verify that

det

∂Ni

∂τ Hi

∂Mi

∂τ Hi

∂Ni

∂τ Fi

∂Mi

∂τ Fi

= am> 0. (A.13)

Hence, the matrix consisting of the elements∂Ni

∂τ Hi

, ∂Mi

∂τ Hi

, ∂Ni

∂τ Fi

and ∂Mi

∂τ Fi

has full rank.


5.2. Distortionary Taxation and Locational Responses

In the absence of a land rent tax, the migration responses∂Ni∂∗ and∂Mi

∂∗ ,∗ ∈ {τ Hi , zi , gi }, set out

in the first-order conditions (16), (18), and (19) can be derived by implicitly differentiatingthe two-equation system (11) and (22). Note thatτ F

i is assumed to adapt endogenouslyfor budget clearing purposes. Sinceτ F

i does not appear in (11), the derivationsQ∗, ∗ ∈{N,M, τ H , z, g}, set out in (A.3) are still valid. Differentiating the modified condition fora locational equilibrium of firms (22) yields

PN = − Li

M2i

F iln −

Ni

M2i

F inn−

CiN − τ H

i

Mi,

PM = L2i

M3i

F ill + 2

Ni Li

M3i

F iln +

Ni

M3i

F inn−

HiM − τ F

i

Mi,

Pτ H = Ni

Mi, Pz = −Ci

z

Mi, Pg = Fi

g −Li

MiFi

lg −Ni

MiFi

ng−Hi

g

Mi. (A.14)

Substituting nextP∗ for S∗, ∗ ∈ {N,M, τ H , z, g} into (A.2) and recalling that the localgovernment has no freedom to choose the firm tax,dτ F

i ≡ 0, yields

(QN; QM ;PN; PM ;

)=(−Qτ H ; −Qz; −Qg;−Pτ H ; −Pz; −Pg;

)dτ Hi

dzi

dgi

. (A.15)

Let B denote the matrix on the LHS of (A.15). Solving (A.15) with the help of Cramer’srule and using the abbreviation

b ≡ Uix

Mi |B|yields the locational responses used to deriveProposition 4:

∂Ni

∂τ Hi

= b[l 2i F i

ll + ni l i Filn + τ F

i − HiM ], (A.16)

∂Mi

∂τ Hi

= b[l i Finl − τ B

i + CiN ], (A.17)

∂Ni

∂zi=b

[Ci

z

Mi(l i F

iln + ni F

inn)−

Uiz

U ix

(l 2i F i

ll + 2ni l i Filn + n2

i F inn+τ F

i −HiM)

], (A.18)

∂Mi

∂zi= b

[Ci

z

MiFi

nn−Ui

z

U ix

(l i Filn + ni F

inn− τ H

i + CiN)

], (A.19)


∂Ni

∂gi= b

(Hi

g

Mi− Fi

g + l i Filg

)(l i F

iln + ni F

inn)

− bFing(l

2i F i

ll + ni l i Filn + τ F

i − HiM), (A.20)

∂Mi

∂gi= b

[(Hi

g

Mi− Fi

g + l i Filg

)Fi

nn− Fing(l i F

iln − τ H

i + CiN)

]. (A.21)

Acknowledgments

The authors would like to thank Jack Mintz and three anonymous referees for helpfulcomments and suggestions.

Notes

1. Only in Anglo-Saxon countries land taxation via theproperty taxis supposed to be of quantitative importancefor local public budgets. In most EU member countries, revenues from land taxation are rather small becausetax rates are low and/or tax bases are narrow (see Mennel, 1994, for a comprehensive overview of tax systemsin the EU).

2. Skinner (1991b) also mentions that there is a strong downward historical trend in land taxation.3. Third-best scenarios where two taxes are institutionally infeasible are excluded from the following analysis.4. Only in Scandinavian countries like Denmark and Sweden income taxes on residents are well-known revenue

sources at the local level. In Austria and Germany local governments can raise income taxes on firms — theso-calledGewerbesteuer. A comparable tax does also exist in Italy, and in the UK, there is the well-knowntax on local property.

5. Richter and Wellisch (1995) derive distortions due to the outflow of land rents. This problem is ignored byassuming immobile land owners away.

6. These findings strongly correspond to the literature on marginal costs of public funds where authors like Pigou(1947), Stiglitz and Dasgupta (1971), Atkinson and Stern (1974), Browning (1976), Wildasin (1984), andWilson (1991), among others, show that benevolent governments do not provide public goods efficiently ifthey have to finance them with distortionary taxes.

7. In the presence of strategic behavior, there are alternative objective functions such as profit-maximization orutility-maximization conceivable. Henderson (1994) demonstrates that not only optimal government policy,but also revenue instruments chosen depend on the underlying objective function.

8. Since all households are identical, the utility function does not carry a jurisdiction-specific index in thefollowing. Partial derivatives are expressed by subindeces throughout this paper.

9. Such a tax can also be interpreted as a direct user charge for local public goods. Of course, the followingresults do not change either if we replace the direct tax on households by a tax on labor income since there isno labor-leisure decision.

10. To exclude market entry, we assume that there are fixed set-up costs for establishing a new firm which just coverprofits in equilibrium (see Wellisch, 1995a, for a detailed discussion). Moreover, there are no location-specificand firm-specific fixed factors of production.

11. Fi can also be a linear-homogeneous function with respect to all factors including the public inputgi . Theresults derived in this paper do not depend on the degree of homogeneity.

12. A direct firm tax can also be interpreted as user fee for local public factors. The results remain unaltered, too,if a tax on profits is considered instead. Such a tax does not distort the factor demand of firms, it only affectstheir locational decisions.

13. This implies that Arrow-Debreu separation occurs. Although mobile residents and land owners are identical,the linkages between their activities as consumers and their interests as land owners are so minimal at the


margin that they can be ignored. However, the behavior of consumers and land owners can also be separatedby assuming that landowners are completely absentee, or, as in Hoyt (1991), by postulating that immobile landowners choose policy instruments so as to maximize their net wealth.

14. Appendix 5.1 provides a detailed derivation.15. Zoning arrangements might substitute for a direct taxation of households (see e.g. Wildasin, 1986). However,

since zoning is not observable in many federal states including the EU, this possibility is excluded in thefollowing.

16. The property tax is equivalent in its effects to a direct tax on households if housing and private consumptionare perfect complements (see Krelove, 1993). This case shall be excluded from our discussion.

17. The sign ofπ iM is positive due to strict concavity ofFi with respect tol i andni .

18. It can be shown, however, that all results remain unchanged ifτ Hi adapts endogenously for budget clearing

reasons. A proof is available from the authors upon request.

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A Second-Best Theory of Local Government Policy

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