Distribution of Distribution of responsibilities is a multi-responsibilities is a multi-

task problemtask problem

Sanjit Dhami (2005) “Optimal Distribution of Powers In Sanjit Dhami (2005) “Optimal Distribution of Powers In A Federation: A Simple, Unified Framework.”, A Federation: A Simple, Unified Framework.”, University of Leicester, UK. Working Paper No. 05/24, University of Leicester, UK. Working Paper No. 05/24, July 2005.July 2005.Two levels, four tasks: regional insurance, coarseness Two levels, four tasks: regional insurance, coarseness of federal information, internalisation of spillovers and of federal information, internalisation of spillovers and “raiding of commons”.“raiding of commons”.

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

TheoryTheory

Distribution of Distribution of responsibilities is a multi-responsibilities is a multi-

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

Planned ExperimentsPlanned Experimentsof the Ministryof the Ministry

1.1. Organization of the County Governor Organization of the County Governor andand the county authority in a singlethe county authority in a single administrative body – the single administrative body – the single administration county authorityadministration county authority

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

Testing the alternative models:Testing the alternative models:

Y = 0,4884 x 2,0305

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 x 0,6265

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 x 0,2772

0

1000

2000

3000

A Federal State emerges by variety of reasons. Some of the reasons come from a general problem of control in complex multidimensional systems.

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.

Historically a Federal State appeared in a process of unification of relatively small states to be more powerful (militarily, politically economically) together.

For example, there are Germany, Canada, USA. The opposite top – down process takes place too. It based on keeping multinational state sustainable.

A fundamental problem for the necessity of federal state’s structure arises in relation with efficiency of provision of local and national public goods.

See 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.

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 countryWhat 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

Total number of citizens in a country

Optimal number of government’s levels (tiers)

100 316 104 105 106 107 108 109 1010$

$

$ $ $

$

$

$

$

0,060

0,11

0,024

0,015

0,015

0,012

0,010

0,009

9

0,008

5

Head

tax

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

5247

41

World government is efficient if federal structure

Greater population – local government closer to people

PopulationPopulation Number of the Number of the bottom governmentsbottom governments

100100 11

316316 22

10 thousand10 thousand 9696

100 thousand100 thousand 1 5211 521

1 million1 million 16 94016 940

10 millions10 millions 186 340186 340

100 millions100 millions 2 332 8002 332 800

1 billion1 billion

10 billions10 billions

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 21095. Townships 448006. Villages 737400

Federal level

Three tiers:1. Central government 12. Provincial regions 313. Prefectures 331

Russian FederationFormally according to the Constitution of Russian Federation

there are three levels:Federal government 1Subjects of Federation 89Municipalities 11429

In fact Russia has or will have soon five (six) levels:Federal government 1Federal districts 7Subjects of Federation 89 (87)Municipal districtsTownshipsVillages

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.

AreasAreas 18661866

CitiesCities 10971097

City areas and districtsCity areas and districts 330330

Settlements of city typeSettlements of city type 17931793

Rural administrationsRural administrations 2442724427

Quantity of local governments in USA is greater thenQuantity of local governments in USA is greater then 82000 82000 (Year (Year 19851985)). . SeeSee. . RosenRosen, , HarveyHarvey, , SS. (1988). (1988)3130 3130 countiescounties Из них 17 вообще не имеют локальных правительств, 5 Из них 17 вообще не имеют локальных правительств, 5 княжеств имеют более 200 локальных правительств, княжеств имеют более 200 локальных правительств, Cook County Cook County в штате в штате Иллинойс имеет 513 локальных юрисдикций.Иллинойс имеет 513 локальных юрисдикций.Под локальными юрисдикциями понимаются муниципалитеты (города, Под локальными юрисдикциями понимаются муниципалитеты (города, большие и малые, поселения, главный признак многоцелевое назначение), большие и малые, поселения, главный признак многоцелевое назначение), школьные округа и специальные округа (одно-целевое назначение). школьные округа и специальные округа (одно-целевое назначение). В периоде с 1962 по 1972 годы число юрисдикций значительно В периоде с 1962 по 1972 годы число юрисдикций значительно уменьшилось с 91186 до 78218 за счет сокращения числа школьных уменьшилось с 91186 до 78218 за счет сокращения числа школьных округов, число которых сократилось на 54,5%. При этом число княжеств, округов, число которых сократилось на 54,5%. При этом число княжеств, городов и городских поселений осталось примерно на том же уровне, а городов и городских поселений осталось примерно на том же уровне, а число специальных округов, наоборот, выросло на 30,4%. После 1972 года число специальных округов, наоборот, выросло на 30,4%. После 1972 года процесс замедлился и число юрисдикций в целом понемногу возрастало. процесс замедлился и число юрисдикций в целом понемногу возрастало. Основной вывод, который делает автор, состоит в следующем. Большая Основной вывод, который делает автор, состоит в следующем. Большая фрагментация (больше юрисдикций) приводит к фрагментация (больше юрисдикций) приводит к greater competitiongreater competition andand redundancyredundancy. Соответственно, меньшая фрагментация приводит к большей . Соответственно, меньшая фрагментация приводит к большей эффективности и большей монопольной власти (силе). То – есть можно эффективности и большей монопольной власти (силе). То – есть можно говорить об оптимальном числе юрисдикций. говорить об оптимальном числе юрисдикций. Следует отметить, что автор ничего не говорит о механизме образования Следует отметить, что автор ничего не говорит о механизме образования юрисдикций.юрисдикций.

• 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 Besley T. and Coate Stephen (2003) “Centralized versus decentralized provision of local public goods; a political decentralized provision of local public goods; a political economy approach” Journal of Public Economics,economy approach” Journal of Public Economics, 87 87 2611-26372611-2637

• Bewley Truman F. (1981) “A Critique of Tiebout’s Bewley Truman F. (1981) “A Critique of Tiebout’s Theory of Local Public Expenditures”. Econometrica, Theory of Local Public Expenditures”. Econometrica, vol. 49, #3, May, 1981.vol. 49, #3, May, 1981.

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

• Samuelson, P. A. (1954) The Pure Theory of Public Expenditure. Review of Samuelson, P. A. (1954) The Pure Theory of Public Expenditure. Review of Economics and Statistics, 37, 4.Economics and Statistics, 37, 4.

• Муниципальная власть №1 (2004). Муниципальная власть №1 (2004). • Иноземцев В. Л. (2004) «Специфические особенности европейской Иноземцев В. Л. (2004) «Специфические особенности европейской

социальной модели». Журнал Института Европы РАН Современная социальной модели». Журнал Института Европы РАН Современная Европа, №1. Стр. 87-99. Европа, №1. Стр. 87-99.

• Казаков А. И. (2004) Российский этнический федерализм: угроза Казаков А. И. (2004) Российский этнический федерализм: угроза целостности страны? ж. Федерализм, №1.целостности страны? ж. Федерализм, №1.

• Евсеенко Т. Солопова Н. (2004) Конфедерация как форма государственного Евсеенко Т. Солопова Н. (2004) Конфедерация как форма государственного устройства.устройства.

• жж. . ФедерализмФедерализм, №1., №1.• Boerzel T. A. and Hosti M. O. (2002) “Brussels between Bern and Berlin: Boerzel T. A. and Hosti M. O. (2002) “Brussels between Bern and Berlin:

Comparative Federalism meets the European Union”. Constitutionalism Web-Comparative Federalism meets the European Union”. Constitutionalism Web-Papers, Con WEB No. 2/2002. Papers, Con WEB No. 2/2002. http://les1.man.ac.uk/conweb/http://les1.man.ac.uk/conweb/

• В работе В работе Boerzel TBoerzel T. . AA. . and Hosti Mand Hosti M. . OO. (2002) приводится ряд аргументов в . (2002) приводится ряд аргументов в пользу того, что Европейский Союз идет в сторону Федеративного пользу того, что Европейский Союз идет в сторону Федеративного устройства согласительного (а не конкурентного) типа. устройства согласительного (а не конкурентного) типа.

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

• Winter Eyal “Scapegoats and Optimal Allocation of Responsibility” Winter Eyal “Scapegoats and Optimal Allocation of Responsibility” Hebrew University of Jerusalem, The Economic Department and the Hebrew University of Jerusalem, The Economic Department and the Center for Rationality.Center for Rationality.

• Jacob B. L., Chen P. M., Silverman S. R. and Mudge T. N. (1996) “An Jacob B. L., Chen P. M., Silverman S. R. and Mudge T. N. (1996) “An Analytical Model for Designing Memory Hierarchies” IEEE Analytical Model for Designing Memory Hierarchies” IEEE Transactions of Computers, vol. 45 NO 10 October 1996.Transactions of Computers, vol. 45 NO 10 October 1996.

• Rosen, Harvey, S. (1988) Introduction to “Fiscal Federalism: Rosen, Harvey, S. (1988) Introduction to “Fiscal Federalism: Quantitative Studies” Edited by Harvey S. Rosen. Pp. 1 – 4. The Quantitative Studies” Edited by Harvey S. Rosen. Pp. 1 – 4. The University of Chicago Press.University of Chicago Press.

• Zax, Jeffrey S. (1988) “The Effects of Jurisdiction Types and Zax, Jeffrey S. (1988) “The Effects of Jurisdiction Types and Numbers on Local Public Finance”. In “Fiscal Federalism: Numbers on Local Public Finance”. In “Fiscal Federalism: Quantitative Studies” Edited by Harvey S. Rosen. PpQuantitative Studies” Edited by Harvey S. Rosen. Pp. 79 – 106. . 79 – 106. The The University of Chicago PressUniversity of Chicago Press..

• Численность населения Российской Федерации по городам, Численность населения Российской Федерации по городам, поселкам городского типа и районам на 1 января 2004г.» (2004). поселкам городского типа и районам на 1 января 2004г.» (2004). Федеральная служба государственной статистики, Москва 2004г.Федеральная служба государственной статистики, Москва 2004г.