Regionally Heterogeneous Preferences and Voting on an Unemployment Insurance: Proportional vs. Majority Vote

A C T A U N I V E R S I T A T I S L O D Z I E N S I S

Ivo Bischoff *, Stefan Schäfer**

REGIONALLY HETEROGENEOUS PREFERENCES AND VOTING

ON AN UNEMPLOYMENT INSURANCE:

PROPORTIONAL VS. MAJORITY VOTE

IN T R O D U C T IO N

One o f the m ost im portant questions in the field o f fiscal federalism is

how to account for regional heterogeneity in preferences. On the one hand,

O ates’ decentralization theorem makes a plausible recom m endation: “ the

level o f welfare will always be at least as high (and typically higher) if

Pareto-efficient levels of consum ption of the good are provided in each

jurisdiction than if any single, uniform level of consum ption is m aintained

across all jurisdictions” 1. In addition, Tullock points out that the frustration

cost o f those who are, in an election, outvoted by the m ajority will be

lower in the case of decentralization2. On the other hand, regional spillovers

and economies of scale strengthen the case of centralization. Whenever

economies of scale o r spillovers are large, centralization is recom mended3.

Yet a centralized solution can draw on different mechanism s - the

propor-tional and the m ajoritarian voting rule - to aggregate individual preferences.

This paper will show how the two mechanisms differ in the results they

produce when used to decide about the m ain param eters o f an

unemp-loym ent insurance (UI). Section 2 introduces the basic concept of an UI

and interregional heterogeneity in preferences. Section 3 compares the

* D r. A ssista nt Professor, D ep a rtm e n t o f E conom ics , U niv ersity o f G ie ße n, L icher Str. 74, 35394 G ie ß en /G erm a ny (c o rres pon ding a u th o r).

** S ch olar o f the „S tiftu ng d er deuts chen W irtsch aft“ , D e p a rtm e n t o f E conom ics, U niver-sity o f G ie ßen.

1 W. E. O a t e s , Fiscal Federalism, H a rc o u rt B race Jo van ov ich , N ew Y o rk -C h ic ag o 1972, p. 54.

2 G . T u l l o c k , Federalism: Problems o f Scale, “ Public C hoice” 1969, vol. 6 (1), p. 19-29. 3 E .g. I. B i s c h o f f , S. S c h a e f e r , U nemploym ent Insurance and M icro-level 1мЬог M a rk e t P olicy in a Federalist S ta te, P a pe r presented a t the U niversity o f L od z, Polan d A pril 23, 2004.

decisions m ade under the proportional and the m ajoritarian voting rule,

respectively. Section 4 illustrates im plications o f different voting rules for

different form s o f interregional heterogeneity in preferences.

1. U N E M P L O Y M E N T IN SU R A N C E AND H E T E R O G E N E IT Y IN PR E F E R E N C E S

1.1. Introducing the Basic Mcchanism of a Central Unemployment

Insurance

M ost countries have installed a scheme of unem ployment benefits to

cushion the loss of income that people face when losing their job. In order to

grant unem ployment benefits, an insurance premium m ust be collccted from

the employed. Let b denote the insurance premium the employed have to pay

(expressed in per cent of their income). A denotes the so called replacement

rate. It states the percentage of unit wage a person receives when he is

unemployed. Beyond this definition of the U l’s main parameters, let us assume

th at we have a very crude economy in which labor is the only source of

income. Let us furthermore assume that every individual earns the same wage

when he is employed. T hus the individuals are only different with respect to

the probability of having a job. Every individual i has an individual probability

p, to be employed and thus a probability to be unemployed of (1 — pt).

The average employment probability is denoted by p. This also represents

the level o f employment. Therefore (1 —p) is the unem ployment rate. The

total income achieved in our economy is given by

Y tot = p Y

(1)

where: Y = income at full employment, (hereafter Y = 1)

Due to the budget restriction, the following relationship between A and

b m ust hold:

p-b = ( l —p)A

(2)

1.2. Describing an Individual I‘s Attitude towards 1Ъе Basic Parameters

h and v

Individual i’s cxpected disposable income is:

in equation (3), the first summand describes the disposable income of

an employed individual weighed with this individual’s employment

proba-bility, while the second one describes an unemployed’s income weighed with

this individual’s probability o f being unemployed. Assuming that the

in-dividual’s utility is best described by a logarithmic function of his expected

disposable income, we get

Ut = Pt x ln (1 — b) + (1 — pt) x In Я

(4)

Applying the Lagrange--d\gox\{hm leads to the utility-maximizing

com-bination o f b and Я preferred by individual i:

L = pt x In (1 — b) + (1 — pt) x In Я- A [p x fc-( 1 — p) x Я]

(5)

Solving dL/db = 0, dL/d). = 0 and d L /d \ = 0 yields the combination o f b and

Я which maximizes individual i’s utility:

b = 1 ——

Я » --- - ---

(6)

p l - ”‘

( 1 _ , Х 1 + _ Л - )

1

- Pi

Individual i’s attitude towards the policy parameters b and Я crucially

depends on its individual employment probability pr The higher pt, the

lower the preferred values of b and Я. Due to individual differences in

skills or mobility, p{ and thus the preferred values o f b and Я can be

expccted to differ across individuals. The broader the spectrum o f p that

the individuals in one region are applied with, the m ore heterogeneous the

preferences for b and Я are within the region.

1.3. Integrating Interregional^ Differring Preferences into the Analysis

In an economy consisting of different regions, different types of

heterogene-ity in preferences can be identified. First, heterogeneheterogene-ity may be large within

regions (m/ra-regional heterogeneity), second, the regions may differ in their

average preferences (j'/j/er-regional heterogeneity). Given these two options,

4 different cases have to be considered. From a fiscal federalism point of view,

only the two cases with large inter-regional heterogeneity in preferences are of

importance. Figure 1 illustrates the remaining two cases that arc characterized

by low m/ra-rcgional heterogeneity (case A) or high ш/ra-rcgional heterogeneity

(case B), respectively - given high w/er-regional heterogeneity in each case.

— •— r eg io n A — •— r e g io n В — *— r e g io n С — □ — fe de ral ion

C as e A I sy m m e tric C ase В I sy m m etric

C ase A 2 asy m m etric C ase U2 asym m etric

C ase A 3 asy m m etric _{C ase B3 asy m m etric} — • — r eg ion D

r eg io n Л re g io n В r eg io n С fe der ation

Within cach region, a triangular distribution of prcfcrcnccs is assumed.

The param eters describing this form of distribution arc the minimum value

o f p (a), the length of the base segment (//) and a param eter for the

skewed ness (y). Th e value o f [i measures the intrarcgional heterogeneity in

preferences. Interregional differences can be described in terms o f differences

in all three parameters.

In case A, the preferences o f cach regional po pulation cover ap

-proximately one half the political spectrum; intrarcgional heterogeneity is

low. In contrast, the intrarcgional heterogeneity in case В ist very high: In

all three regions there arc individuals with values of p close to zero as

well as individuals with the maximum value of p close to 1. So in all

three regions the individuals* prcfcrcnccs covcr nearly the entire political

spectrum.

In addition, both eases arc characterized by different forms o f

inter-regional heterogeneity (sec figure 1). In case A, the bases of the triangular

distributions hardly overlap. Almost every person in region A is applied

with a lower value o f p than cach person in region В or C. The interregional

difference conccrns all inhabitants. Case В is more complicated, since in

all three regions the individual values of p cover almost the entire political

spectrum. Here, the от/er-rcgional hetcrcogcneity results from different forms

of /«/ra-rcgional heterogeneity due to different values of y. In region A,

the distribution of p is skewed to the left, while in region С it is skewed

to the right.

2. A G G R E G A T IO N O F P R E F E R E N C E S IN A R E P R E S E N T A T IV E D E M O C R A C Y

•

Whenever the unemployment insurance is a public institution, the

deci-sions conccrning its m ajor param eters arc m ade politically. In order to

benefit from economies of scale and cope with shocks in unemployment,

an unemployment insurance system should be provided by a central agency4.

Thus citizens o f all regions pay the same premium and - in the case of

unemployment - receive the same unemployment benefits. Regional

dif-ferences in predif-ferences cannot be accounted for by regionally differing

parameters of the UI. Consequently, the param eters are set by the federal

parliament - usually by a simple majority vote. In order to derive predictions

conccrning the outcome o f the political decision making process, the

fol-lowing passages draw on a broader discussion th at focusses on how different

№

institutional settings affect the political design o f a IJ15. N cugart’s analysis6

is m otivated by the empirical observation according to which proportional

voting and the replacement rate arc positively related; on average, in

countries with a m ajoritarian electoral system the replacement rate is lower

than in countries with a proportional electoral system. The question Ncugart

poses is whether the differences in the voting system cause the observed

differences in the UI. As a complete form alization of these aspects would

exceed the confined spatial limits o f this paper, we have to concentrate on

the intuition that lies behind Ncugart’s reasoning. The cardinal question is:

W hat characterizes the decisive voter in case of a proportional election or,

respectively, in case o f a m ajoritarian election?

2.1. The Median Voter Approach

Anthony Downs7 has provided a simple yet powerful model which can

derive the param eter values set by the parliament from the distribution of

preferences o f the underlying electorate. This model became known as the

median voter m odel“. The median voter model assumes that two parties

compete for the majority of votes of a given electorate. The voters arc

fully informed a bout all relevant issues and will certainly make use of their

right to vote. There is only one political issue - in our case the param eters

of the UI. Due to the budget restriction, the voters and politicians arc left

with only one degree o f freedom when setting these param eters. Hereafter,

we will assume tha t the replacement rate is the variable param eter. The

voters differ in their preferences concerning this param eter - depending on

their individual value of p: Following (6), the relationship is strictly

anti-proportional. Each voter has a so-called bliss point which describes the

value of ). which maximizes his individual utility, lie will vote for the party

which offers a value of A that is closest to this bliss point.

5 R . W r i g h t , The Redistributive Roles o f U nemployment Insurance a nd the D ynamics o f Voting, “ J o u rn a l o f Public E conom ics” 1986, vol. 31, p. 377-399; G . S a i n t - P a u l , Exploring the P olitic al E cono m y o f Labour M a rk e t Institutions, “ E c on om ic Policy” 1996, vol. 23, p. 265-315; T . P e r s s o n , G. T a b e l I i n i , F ederal F iscal Constitutions: R isk Sharing and R edistribution, “ Jo u rn a l o f Political E cono m y” 1996, vol. 104, p. 979-1009; T . P e r s s o n , G . T a b e 11 i n i, C onstitutional Rules and Fiscal Policy Outcomes, “ A m erican E conom ic Review” 2004, vol. 4, 94, p. 25-45.

6 M . N e u g a r t , Unemployment Insurance: the Role o f E lectoral S ys tem s a nd Regional Labor M ark ets, Pap er presented a t the E PC S-C onference in Berlin, 2004.

7 A. D o w n s , A n E conom ic Theory o f Democracy, H arper and R ow, New Y o rk 1957. * D . M u e l l e r , Public Choice III, C am bridge U niversity Press, C am bridge 2003; I. B i s -c h o f f , P arty C om petition in a Heterogeneous Ele-ctorate: the Role o f Dominant Issue Voters, “ Public C ho ice” , forthco m ing .

I'hc parties can he assumed to differ in the preferred replacement rates.

During the election race, they arc forced to change the replacement rates

offered to the voters in order to attract the m ajority of votes. In this race

for political power, the party offering a low replacement rate will be forced

to increase the latter, while the party initially offering a high replacement

rate has to reduce it. Thereby their policy platform s converge until, finally,

they arc identical. Both parties offer the replacement rate which is favored

by the voter with the m edian value o f p. Regardless of which party finally

wins the election, it will set the param eter values for the UI in accordance

with the prcfcrcnccs o f the m edian voter.

2.2. Median Voter under Proportional and Majoritarian Vote

U nder proportional vote, the entire national electorate is regarded as

one unit. W ithin this electorate, the person with the m edian value of p is

the decisive voter. Both political parties’ policy platform s will propose

param eter values which suit this national median voter (A = /(/>*?«))• Thus,

proportional voting completely neglects ш/er-regional heterogeneity of

prc-fcrcnccs. The median voter is characterized according to his individual

unem ploym ent risk, not according to his hom e region.

With m ajority voting, the interregional heterogeneity o f prcfcrcnccs

m atters. The analysis requires a three-stage consideration. First, within each

election district all voters have to be lined up according to their individual

em ploym ent probability. This procedúre allows for the identification of

each district’s m edian voter. Second, all election regions have to be lined

up in asccnding order o f the individual employm ent probability of the

region’s m edian voter. T his leads us to the determ ination of the m edian

region, i.e. the district whose representative is the decisive one in the

parliam entary vote. Finally, in order to determ ine the outcom e of the

election, the preferences of the median region’s median voter have to be

identified. The m ain difference between the proportional voting system and

the m ajoritarian one is quite obvious: While in the latter the political

decision follows the preferences o f the m edian region’s m edian voter

(Л = f(P M eedree)), the form er results in the whole nation being considered as

one voting region and thus (1

=/(р"мел))-Returning to the question posed by N cugart: how can the m ajoritarian

electoral system’s bias tow ards higher replacement rates be accounted for?

N c uga rt’s formal fram ework does not offer a definite answer9. Instead, the

result depends on the underlying assum ptions conccrning the relative level

oľ the national m edian voter’s em ployment probability com pared with that

o f the m edian voter in the decisive region. If риы пв > Рм'ел, a m ajoritarian

electoral system yields lower replacement ratios than a proportional one ct

vice versa.

3. H E T E R O G E N E IT Y IN PR E F E R E N C E S AN D T H E R O L E OK V O T IN G R U L E S: S O M К IL L U S T R A T IO N S

1 he triangular distribution of preferences put forth in section 3 provides

a valuable framework to show under which conditions рм ы "0 > Рм'ы- Due

to the lack ol space, the following illustrations can merely give some

intuition. F o r this purpose, consider the six hypothetical scenarios in figure

1. F or three regions А, В, С of identical size, there arc three scenarios for

case A (small intra-regional heterogeneity, ß = small, different a) and three

for case В (large m /ra-rcgional heterogeneity, // = large, similar a). Within

these cases, scenario 1 assumes that region A and С arc - in terms of

m odus and у - symmetric in their differences to region B, while the other

scenarios assumes region В to be closer to region A (scenario 2) respectively

region С (scenario 3). In the symmetric cases, Рмыгсд > Ршл and thus both

voting rules lead to the same param eter values of the UI. T he same result

holds for the asymmetric cases A2 and A3. T hus, only in the case of

asym metric distribution o f preferences across regions A N D large inlra-

rcgional heterogeneity docs the voting rule m atter. The relationship between

voting rule and replacem ent rate postulated by Neugart will only occur if

the distribution of preferences across and within regions resembles case B2.

The opposite is true in case of scenario B3. Empirical research has to be

conducted to determine which o f the described distribution is given in reality.

Ivo Bischoff \ Stefan Schäfer

R E G IO N A L N IE N IK .IK IÍN O R O D N E P R E F E R E N C J E I G L O S O W A N IE N A D U B E Z P IE C Z E N IE M PR Z E D B E Z R O B O C IE M :

G L O S O W A N IE P R O P O R C J O N A L N E A W IĘ K S Z O Ś C IO W E

W artyk ule p rze ds taw io no problem atykę politycznych decyzji, dotyczą cych podstaw ow yc h p a ram e tró w us ta la nia ubezpieczenia od be zrob ocia n a poziom ie c entralny m . Po ró w n an o skutk i, w ynikające z większościowego i p rop o rcjon aln eg o g losow ania. W yniki s top y z as tąp ien ia bez-ro b oc ia zależą od bez-roz łożenia indyw idualnych preferencji w ra m a c h i pom iędz y okręgam i w yborczym i.