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Public goods and levels of federation

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Distribution of responsibilities is a multi-task problem

Theory

Sanjit Dhami (2005) “Optimal Distribution of Powers In A Federation: A Simple, Unified Framework.”, University of Leicester, UK. Working Paper No. 05/24, July 2005.

Two levels, four tasks: regional insurance, coarseness of federal information, internalisation of spillovers and “raiding of commons”.

The paper examines six regimes of distribution of powers: autarky, centralization, unregulated devolution, regulated devolution, direct democracy, and revenue maximizing leviathan.

More theory

- Besley T., Coate S. (2003) Centralized versus decentralized provision of local public goods: a political economy approach. Journal of Public Economics 87, 2611-2637.
- The centralization in provision of public goods is preferable if a degree of spillovers is large.
- Lockwood B. (2004) Decentralization via Federal and Unitary Referenda. Journal of Public Economics Theory, 6,(1) pp. 79 – 108. The paper investigates the trade – off between local provision of a project (good for local political authorities) and centralized provision (less cost because of economy of scale, for example, R&D).

Evidence

- Zax J. S. (1988). “The Effects of Jurisdiction Types and Numbers on Local Public Finance”. In: Fiscal Federalism: Quantitative Studies. (1988). Edited by Harvey S. Rosen. The University of Chicago Press. 1988.
- Variety of population’s tastes & number of types of jurisdictions.
- Number of tiers
- Jin H., Qian Y., and Weingast B. R. (2005)“Regional Decentralization and Fiscal Incentives: Fedelalism, Chinese Style” Journal of Public Economics, v.89, #9-19 September 2005.
- Citation from the paper: “China’s fiscal system has five hierarchical levels of government: (1) central; (2) provincial; (3) prefecture; (4) county; and (5) township. Below the township level, the village is an informal level of government. A municipality can be of the levels of a province, prefecture, or county; most municipalities are at the prefecture level. “

How Chinese Jurisdictions are defined

Federal level

Three tiers:

1. Central government 1

2. Provincial regions 31

3. Prefectures 331

Local level

More three tiers:

4. Counties 2109

5. Townships 44800

6. Villages 737400

1500

McGuckin R. and Dougherty S. (2003) “Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance”. The Conference Board Research Report R-1311-02-RR.

- Quantity of local governments in USA is greater then 82000 (Year 1985). See. Rosen, Harvey, S. (1988)
- 3130 counties. Among them 17 have no local governments. 5 countiescontain more then 200 local governments.Cook County at the State of Illinoishas 513 of local jurisdictions.
- The local jurisdictions aremunicipalities, school districts and special districts.
- In the period from 1962 to 1972 the number of local jurisdictions fell down from 91186 to 78218. School districts shrank 54,5%.
- More jurisdictions - greater competitionandredundancy. Less jurisdictions – greater efficiency and monopoly power. Where is optimum?

Distribution of responsibilities is a multi-task problem

Practice

- Geistlinger M. «Federalism and Distribution of Powers. The distribution of competences in the field of education» University of Salzburg, Department of Public Law.
- Survey across Federalist countries, including Russia.
- Ministry of Local Government and Regional Development (Norway). «The Government’s recommendations»
- Responsibilities should be placed at the lowest effective level.
- The county authority should not be developed into a superordinate authority.
- Changes in the distribution of responsibilities should help to reduce bureaucracy.
- The central government should have the responsibility for standardized and rule – oriented responsibilities and for supervisory responsibilities.

Planned Experimentsof the Ministry

Testing the alternative models:

- Organization of the County Governor andthe county authority in a singleadministrative body – the single administration county authority
- Differentiation of municipal responsibilities, which means that certain municipalities are assigned one or more county or state responsibilities.

Hierarchical Structure & Distribution of Responsibilities

- Commission of Mr. Kozak.
- The law on local governments’ responsibilities, to be introduced at I-st of January, 2006.
- The dead line for the reform of the local governance is year 2009.

Formally according to the Constitution of Russian Federation there are three levels:

Federal government 1

Subjects of Federation 89

Municipalities 11429

In fact Russia has or will have soon five (six) levels:

Federal government 1

Federal districts 7

Subjects of Federation 89 (87)

Municipal districts

Townships

Villages

Russia

The reform of the local governance considers creating 24000-30000 townships and villages in total. The townships and villages are at the same level but with a little bit different status.

I take into account one important factor: the cost to provide public goods by assigning the responsibilities to a certain level of hierarchy of governments.

- How many levels?
- What size (in terms of population) of a jurisdiction?
- How many governments are under control of upper government?
- Which level is to place the provision of a certain public good?

Russian heterogeneity provide public goods by assigning the responsibilities to a certain level of hierarchy of governments.

- According to Truman Bewley’s classification (democratic & entrepreneurial):
- Going to entrepreneurial governments:
- Abramovich (Chukotka), Khloponin (Krasnoyarsk), Zelenin (Tver), Boos (Kaliningrad), Prussak (Great Novgorod)
- Sizable number of municipalities (See Russian Journal “Municipal Power”, Successful Stories).
- There is an idea to declare a region be bankrupt as a cause to introduce a control from above.

Среднедушевые доходы населения provide public goods by assigning the responsibilities to a certain level of hierarchy of governments.

(тыс.рублей)

12

раз

Ингушетия

г.Москва

С.-Петербург

Татарстан

Башкортостан

Ямало-

Ханты-

Самарская

Свердловская

РОССИЯ

Московская

Новгородская

Саратовская

Ленинградская

Ненецкий АО

Мансийский АО

Тюменская

область

область

область

область

область

область

область

ВРП на душу населения provide public goods by assigning the responsibilities to a certain level of hierarchy of governments.

36

раз

Ингушетия

г.Москва

С.-Петербург

Татарстан

Башкортостан

Приморский край

Краснодарский край

Самарская

РОССИЯ

Ленинградская

Московская

Свердловская

Новгородская

Саратовская

Тюменская

область

область

область

область

область

область

область

Инвестиции в основной капитал на душу населения

(тыс.рублей)

281

раз

Ингушетия

Ненецкий АО

г.Москва

С.-Петербург

Татарстан

Башкортостан

Ямало-

Ханты-

РОССИЯ

Самарская

Московская

Новгородская

Свердловская

Саратовская

Ненецкий АО

Мансийский АО

Тюменская

область

область

область

область

область

область

Удельный вес общего объема денежных доходов,

приходящихся на 20% группу населения

с наименьшими доходами

Приморский край

С.-Петербург

Татарстан

Башкортостан

г.Москва

Ленинградская

Московская

Свердловская

РОССИЯ

Самарская

Ямало-

Ханты-

область

область

область

область

Ненецкий АО

Мансийский АО

Тюменская

область

Удельный вес общего объема денежных доходов,

приходящихся на 20% группу населения

с наибольшими доходами

г.Москва

Башкортостан

С.-Петербург

Татарстан

Приморский край

Ханты-

Самарская

Ямало-

РОССИЯ

Свердловская

Московская

Ленинградская

Тюменская

область

Мансийский АО

область

Ненецкий АО

область

область

область

Types of public goods денежных доходов,

- Extremes:
- (1) Public services on a lowest local level:
- cost = cN2
- (2) Pure public good (Samuelson):
- cost does not depend on N
- All other public goods are between and should be placed to appropriate level.

Rural municipalities денежных доходов,

Expenditures of budgets of rural municipalities

(mln. roubles)

Population

(thousand person)

Russia regions денежных доходов,

Expenditures of budgets of regions

(bln. roubles)

Population

(millions person)

Moscow districts денежных доходов,

Expenditures of budgets of Moscow districts

(mln. roubles)

Population

(thousand person)

Rural municipalities денежных доходов,

2,0305

Russia regions

Value of power

0,6265

Moscow districts

0,2772

Social Planner’s Problem денежных доходов,

- Given: Amount of public goods to provide.
- Objective: To minimize the total cost of public goods’ provision plus the expenditures on maintaining of all governments (head tax minimization).
- Variables to find: Number of hierarchical levels, size of all types of jurisdictions, what level to place a provision of a given public good

Optimal hierarchical structure (number of tiers and subordinates) as trade off between two parameters: efficiency of control bodies & cost to maintain its functioning.

See, for example:

Qian Yingyi (1994) “Incentives and Loss of Control in an Optimal Hierarchy”. Review of Economic Studies, 61(3):527-544.

The paper considers an commercial organization that owns a capital stock an uses a hierarchy to control the production.

The optimal problem is to find number of tiers in the hierarchy and optimal quantity of workers is in each tier.

The objective function is a revenue generated from production activity.

The trade off is between the two parameters: the number of bureaucrats to control workers and efficiency of working activity under the control.

There is sizable literature devoted to optimal design of technical devices, like memory for computers and others.

See, for example:

Jacob B. L., Chen P. M., Silverman S. R. and Mudge T. N. (1996) “An Analytical Model for Designing Memory Hierarchies”. IEEE Transactions of Computers, vol. 45, # 10, October 1996.

In my case: (1) More tiers, more jurisdictions on the bottom – less expenditures to provide public services (cN2)

(2) Less tiers, less jurisdictions – less expenditures to keep functioning of governments.

(3) Responsibility to provide a certain public good should be assigned to a tier with maximal efficiency to produce. (Depends on power a in cNa)

In the presentation I formulate and solve relatively simple optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of population.

Notations:

N - total number of citizens in a country;

с - costs of a government to provide one unit of a public good (actually public service) per a person;

q - number of a hierarchical level (a tier) for a given government;

q = 0,1, 2, …;

kq - costs for keeping functioning of the government on hierarchical level q, under condition that the level is lowest;

nq - quantity of governments under subordination of the level’s q government;

fq - total costs for provision of a public service (quantity is equal to one) for the whole population plus costs to keep all governments functioning;

Then if optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of q = 0, one has total costs to provide one unit of public good and costs to keep the government functioning as

f0= k0+ c*N2.

Here the first term is costs of government’s functioning (central one) and the second one is costs to provide public good for the whole population.

Objective function – total costs

(under conditions: (1) all citizens are equal to each other, (2) everybody receives a unit of the public service.)

c*n2 - costs for provision of a unit of public good (service) for n people;

kq*ln(nq)- costs to keep government of the level q functioning, under condition that the government controls nq governments of lower level

If optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of q >= 1 to calculate total costs is a little bit more difficult.

It is easy to do under assumption that all governments of a given level control the same number of governments.

The number nq indicate exactly that condition.

The number does not depend on particular copy of the level’s q government.

Namely,

f1= k0*ln(n0) + n0*(k1 + c*(N/n0)2) =

k0*ln(n0) + n0*k1 + c*N2 / n0

Under optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of q = 2 total costs are:

f2 = k0*ln(n0) + n0*k1*ln(n1) + n0*n1*k2 + c*N2 / n0*n1

Going along the induction one obtains the total costs for arbitrary number of levels q:

fq = k0*ln(n0) + n0* k1*ln(n1) + n0*n1* k2*ln(n2) +…+

n0*n1*…*nq-2*kq-1*ln(nq-1) + n0*n1*…*nq-1*kq +

c*N2 / n0*n1*…*nq-1

Optimal number of government’s levels (tiers) optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

The problem consists of finding the q*, which provides minimal total costs for provision of public good in quantity 1. In other words:

q* = arg Min(fq)

Here Min is taken over q. But it is clear that functions fq depend on the other parameters participating in the definition of the function, that is on N, с, kq, nq . Hence the number q* depends on the named parameters.

Optimal quantity of inhabitances in a country optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

What is more effective from the point of view of total costs to provide public goods?

To be in large Federal State or to create smaller state (probably federal one too).

Much depends on relation between the numbers kq. The population has to compare the total costs (and hence amount of taxes) under staying in the initial Federation or secession in a certain stake.

Namely, one has to compare

{Min(fq)/n},

where n runs from 1 to N. The N can be equal to infinity. Min is taken over nand q. Here Min(fq)/n is a head tax in the case of the size of population is equal to n. The country has “federal” structure if q*>0.

Optimal size of a country with a fixed number of ties optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

Let us suppose that q is given. Then optimal size of population n*(q) is going to be dependent on the given q.

The problem makes sense in some practical issues as we see below.

Numerical optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

calculations

Optimal number of government’s levels (tiers) optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

one level

two levels

three levels

four levels

Total number of citizens in a country

five levels

Optimal quantity of inhabitances in a country optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

$

$

$

$

$

$

$

$

$

0,11

1

2

3

4

5

0,060

0,024

0,015

0,015

Head tax

0,012

0,010

0,0099

0,0085

Total number of citizens in a country

100

316

104

105

107

108

109

1010

106

Number of inhabitances in a municipality optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

1

2

3

4

5

158

100

104

72

66

60

52

47

41

Total number of citizens in a country

100

316

104

105

107

108

109

1010

106

1 optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

Each government has

its appropriate public good

2

Greater population –

local government closer to people

How many mayors? optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

Literature optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

- Alesina Alberto and Spolaore Enrico (1997), On the Number and Size of Nations, The Quarterly Journal of Economics, CXII, #4, November 1997, pp1027-1056.
- McGuckin R. and Dougherty S. (2003) “Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance”. The Conference Board Research Report R-1 311-02-RR

From the social planner to a realistic mechanism optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

- 1. Generating projects.
- 2. Public choice: which project?
- 3. Who chooses, people in which
jurisdictions?

- 4. Referendum,…

Literature (cont...) optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

- Besley T. and Coate Stephen (2003) “Centralized versus decentralized provision of local public goods; a political economy approach” Journal of Public Economics, 87 2611-2637
- Bewley Truman F. (1981) “A Critique of Tiebout’s Theory of Local Public Expenditures”. Econometrica, vol. 49, #3, May, 1981.
- McGuckin R. and Dougherty S. (2003) “Restructuring Chinese Enterprises: The Effect of Federalism and Privatization Initiatives on Business Performance”. The Conference Board Research Report R-1311-02-RR.

Literature (cont...) optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

- Samuelson, P. A. (1954) The Pure Theory of Public Expenditure. Review of Economics and Statistics, 37, 4.
- Муниципальная власть №1 (2004).
- Иноземцев В. Л. (2004) «Специфические особенности европейской социальной модели». Журнал Института Европы РАН Современная Европа, №1. Стр. 87-99.
- Казаков А. И. (2004) Российский этнический федерализм: угроза целостности страны? ж. Федерализм, №1.
- Евсеенко Т. Солопова Н. (2004) Конфедерация как форма государственного устройства.
- ж. Федерализм, №1.
- Boerzel T. A. and Hosti M. O. (2002) “Brussels between Bern and Berlin: Comparative Federalism meets the European Union”. Constitutionalism Web-Papers, Con WEB No. 2/2002. http://les1.man.ac.uk/conweb/
- В работе Boerzel T. A. and Hosti M. O. (2002) приводится ряд аргументов в пользу того, что Европейский Союз идет в сторону Федеративного устройства согласительного (а не конкурентного) типа.

Literature (cont...) optimization problem where the only factor for Federal State’s existence matters. Namely, it is size of

- Qian Yingyi (1994) “Incentives and Loss of Control in an Optimal Hierarchy”. Review of Economic Studies, 61(3):527-544.
- Winter Eyal “Scapegoats and Optimal Allocation of Responsibility” Hebrew University of Jerusalem, The Economic Department and the Center for Rationality.
- Jacob B. L., Chen P. M., Silverman S. R. and Mudge T. N. (1996) “An Analytical Model for Designing Memory Hierarchies” IEEE Transactions of Computers, vol. 45 NO 10 October 1996.
- Rosen, Harvey, S. (1988) Introduction to “Fiscal Federalism: Quantitative Studies” Edited by Harvey S. Rosen. Pp. 1 – 4. The University of Chicago Press.
- Zax, Jeffrey S. (1988) “The Effects of Jurisdiction Types and Numbers on Local Public Finance”. In “Fiscal Federalism: Quantitative Studies” Edited by Harvey S. Rosen. Pp. 79 – 106. The University of Chicago Press.
- Численность населения Российской Федерации по городам, поселкам городского типа и районам на 1 января 2004г.» (2004). Федеральная служба государственной статистики, Москва 2004г.

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