TOP - DOWN Coming from

a central government and

theory

Distribution of responsibilities is a multi-task problem

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.

Theory

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

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.

Local level

More three tiers:

4. Counties 2109

5. Townships 44800

6. Villages 737400

Federal level

Three tiers:

1. Central government 1

2. Provincial regions 31

3. Prefectures 331

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 counties contain more then 200 local governments. Cook County at the State of Illinois has 513 of local jurisdictions.

The local jurisdictions are municipalities, 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 competition and redundancy. 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 Experiments of the Ministry

1. Organization of the County Governor and the county authority in a single administrative body – the single administration county authority

2. Differentiation of municipal responsibilities, which means that certain municipalities are assigned one or more county or state responsibilities.

Testing the alternative models:

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 was year 2009.

After that: two opposite processes

Hierarchical Structure &

Distribution of Responsibilities

Districts 1866

Towns 1097

Districts with towns 330

Townships 1793

Villages 24427

Russian Federation Formally according to the Constitution of Russian Federation

there are three levels:

Federal government 1

Subjects of Federation 89

Municipalities 24500

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

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.

1. How many levels?

2. What size (in terms of population) of a

jurisdiction?

3. How many governments are under

control of upper government?

4. Which level is to place the provision of a

certain public good?

16

,8

16

,0

12

,9

10

,6

6,9

5,8

5,3

5,2

4,4

4,3

4,2

3,7

3,3

3,0 1

,4

0

5

10

15

20

29

4

23

2

80

73

70

66

62 57

54

52

48

47

45

39 8

0

50

100

150

200

250

300

43

6

32

1

11

9

10

9 25

20

18

15

14

14

13

13

12

8 1,5

5

0

100

200

300

400

500

7,8

7,1

6,6

6,1

5,9 5,9

5,8 5,6

4,9

4,9

4,6

4,5

2,5

0

2

4

6

8

62,7

50,2

49,6

48,5

48,5

46,1

45,3

45,0

45,0

44,4

42,8

41,3

39,2

0

10

20

30

40

50

60

70

Types of public goods

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.

Y = 0,4884 x2,0305

0

30

60

90

120

0,42 1,7 2,53 5 5 5,3 6,1 5,2 17,5 18,8 31,1

Y = 0,7478 x0,6265

0

100

200

300

400

0,05

0,36

0,69

0,85

0,95

1,04

1,21

1,36

1,49

2,06

2,59

2,87

3,78

6,62

Y = 586,58 x0,2772

0

1000

2000

3000

215,

70

697,

10

783,

40

1109

,30

1058

,30

1122

,40

1188

,20

1239

,10

1389

,80

1588

,20

Social Planner’s Problem

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;

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

Then if 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.

If 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 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

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 number of government’s levels (tiers)

Optimal quantity of inhabitances in a country

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 n and 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

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.

100

316

10 000

100 000

1 000 000

10 000 000

100 000 000

1 000 000 000

10 000 000 000

one level

two levels

three levels

four levels

five levels

Optimal number of government’s levels (tiers)

100 316 104 105 106 107 108 109 1010

He

ad

ta

x

Total number of citizens in a country

Optimal quantity of inhabitances in a country

100 316 104 105 106 107 108 109 1010

Total number of citizens in a country

Number of inhabitances in a municipality

100

158

104

66 72

60

52 47

41

Each government has its appropriate public good

Greater population – local government closer to people

Population Number of the bottom governments

100 1

316 2

10 thousand 96

100 thousand 1 521

1 million 16 940

10 millions 186 340

100 millions 2 332 800

1 billion

10 billions

• 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

• 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.

• 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.

• 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.

BOTTOM - UP Numerical experiments

Agent – based model of a country

Each level should invent its appropriate

public good.