A Positive Theory of Unemployment Insurance and Employment Protection

Abstract

The objective of this paper is to provide a political economy explanation of the empirically observed negative correlation between employment protection and insurance. We study an economy composed of four groups of agents (capitalists, unemployed people, low- and high-skilled workers), each one represented by a politician. Politicians first form political parties and then compete in a winner-takes-all election by simultaneously proposing policy bundles composed of an employment protection level and an unemployment benefit. We first show that, in the absence of parties (i.e., in a citizen-candidate model), low-skilled workers are decisive and support a maximum employment protection level together with some unemployment benefit. We then obtain that, under some conditions, allowing for party formation results in all policy equilibria being in the Pareto set of the coalition formed by high-skilled workers together with unemployed people. Policies in this Pareto set exhibit a negative correlation between employment protection and unemployment benefit.

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No. 7333

A POSITIVE THEORY OF
UNEMPLOYMENT INSURANCE
AND EMPLOYMENT PROTECTION


Vincent Anesi and Philippe De Donder


LABOUR ECONOMICS

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ISSN 0265-8003
A POSITIVE THEORY OF
UNEMPLOYMENT INSURANCE
AND EMPLOYMENT PROTECTION
Vincent Anesi, University of Nottingham
Philippe De Donder, Toulouse School of Economics and CEPR

Discussion Paper No. 7333
June 2009
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Copyright: Vincent Anesi and Philippe De Donder

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CEPR Discussion Paper No. 7333
June 2009
ABSTRACT
A Positive Theory of Unemployment Insurance and Employment
Protection*
The objective of this paper is to provide a political economy explanation of the
empirically observed negative correlation between employment protection and
insurance. We study an economy composed of four groups of agents
(capitalists, unemployed people, low- and high-skilled workers), each one
represented by a politician. Politicians first form political parties and then
compete in a winner-takes-all election by simultaneously proposing policy
bundles composed of an employment protection level and an unemployment
benefit. We first show that, in the absence of parties (i.e., in a citizen-
candidate model), low-skilled workers are decisive and support a maximum
employment protection level together with some unemployment benefit. We
then obtain that, under some conditions, allowing for party formation results in
all policy equilibria being in the Pareto set of the coalition formed by high-
skilled workers together with unemployed people. Policies in this Pareto set
exhibit a negative correlation between employment protection and
unemployment benefit.
JEL Classification: D72, J65 and J68
Keywords: bidimensional voting, citizen-candidate, flexicurity, labor market
rigidities and party competition
Vincent Anesi
School of Economics
University of Nottingham
University Park,
Nottingham NG7 2RD
Email:
vincent.anesi@nottingham.ac.uk


For further Discussion Papers by this author see:
www.cepr.org/pubs/new-dps/dplist.asp?authorid=166361
Philippe De Donder
IDEI & GREMAQ-CNRS
Manufacture des Tabacs, Office:
MF418
21 Allée de Brienne
31000 Toulouse
FRANCE
Email: dedonder@cict.fr

For further Discussion Papers by this author see:
www.cepr.org/pubs/new-dps/dplist.asp?authorid=157241

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* We thank Gilles Saint-Paul for stimulating discussions, as well as seminar
participants in Rochester and Verona. This paper has been written while the
first author was visiting the W. Allen Wallis Institute of Political Economy at the
University of Rochester. He wishes to express his appreciation to the Institute
for its hospitality. All errors remain ours.

Submitted 11 May 2009

Page 5

Abstract
The objective of this paper is to provide a political economy explanation of the
empirically observed negative correlation between employment protection and in-
surance. We study an economy composed of four groups of agents (capitalists,
unemployed people, low- and high-skilled workers), each one represented by a politi-
cian. Politicians …rst form political parties and then compete in a winner-takes-all
election by simultaneously proposing policy bundles composed of an employment
protection level and an unemployment bene…t. We …rst show that, in the absence
of parties (i.e., in a citizen-candidate model), low-skilled workers are decisive and
support a maximum employment protection level together with some unemployment
bene…t. We then obtain that, under some conditions, allowing for party formation
results in all policy equilibria being in the Pareto set of the coalition formed by
high-skilled workers together with unemployed people. Policies in this Pareto set
exhibit a negative correlation between employment protection and unemployment
bene…t.
JEL Codes: D72, J65, J68
Keywords: bidimensional voting, party competition, citizen-candidate, ‡ex-
icurity, labor market rigidities

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1Introduction
In most countries, labor markets institutions such as employment protection, unem-
ployment bene…ts and minimum wage legislations prevent private parties from freely
setting prices or quantities, creating rigidities. These rigidities may be at least in
part socially e¢cient in a second-best sense. For instance, in a world where workers
could be hired and …red at a hat’s drop and at no cost for the employer, workers
would have little incentive to acquire …rm-speci…c skills. Employment protection
could then provide incentives for workers to increase their productivity. Similarly,
unemployment bene…ts provide insurance for risk-averse workers a¤ected by random
employability shocks.
Making the point that some rigidities may be optimal (see Blanchard and Tir-
ole, 2007, among others) of course does not mean that the current level of rigidities
is the optimal one, or that it is determined by a social planner maximizing some
measure of welfare. As for the …rst point, many economists blame rigidities for high
(long term) unemployment, especially in Europe, and have been advocating for a
long time making the labor market more ‡exible (see for instance OECD Job Study,
1995). Despite these recommendations, many governments have failed to success-
fully implement such plans (see Section 5.1 in Boeri et al., 2006, or Saint-Paul, 1996).
Part of the literature has then taken a turn towards political economy explanations
of both the emergence of labor market institutions and resistance against moves
towards more ‡exibility.
The seminal paper in the political economy literature is Wright (1986). He
assumes that workers di¤er both intrinsically (they exhibit di¤erent probabilities to
become unemployed and di¤erent durations of unemployment) and by the “luck of
the draw,” in the sense that at any point in time they are either employed or not.
He shows how current employment conditions, future employment opportunities and
risk aversion a¤ect the outcome of a vote on the size of the unemployment bene…t. He
shows, e.g., that “even in an economy with complete private markets the provision
of unemployment insurance may be socialized via the electoral process. (p 379)”
The same type of approach has been adopted by most papers studying the polit-
ical economy of labor market institutions. These papers have in common that they
adopt an insider-outsider view of the labor market, pitting currently employed work-
ers against currently unemployed agents, and that they build a unidimensional model
which focuses on a single institution. In these models, the decisive voter is usually
a (low-skilled) worker. If the institution studied is employment protection (as in
Saint-Paul (1999, 2000, 2002)), the decisive voter favors a generous protection re-
gime because he is currently employed while, if the institution studied is unemploy-
ment insurance (as in Wright (1986), Persson and Tabellini (2000) or Pallage and
Zimmermann (2001)), the decisive voter favors a rather small program (because his
probability of incurring the damage is lower than the economy’s average). Put to-
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gether, these results suggest that we should only observe equilibria with both large
employment protection levels and low unemployment bene…ts.
While certain countries (such as Italy) conform to this equilibrium, not all coun-
tries do. There is a large heterogeneity among OECD countries in terms of how
generous unemployment insurance is and how much jobs are protected. Boeri et al.
(2006) and Chung and Jeong (2008) show that there exists a negative correlation
between both dimensions, with countries exhibiting low employment protection and
large insurance programs, and vice versa. The objective of our paper is to provide
a political economy explanation of this negative correlation between employment
protection and insurance.
Addressing this question requires building a bidimensional voting model. More-
over, it is our opinion that a meaningful depiction of labor markets must allow
voters to di¤er in more than one dimension. We wish to distinguish three ways
in which voters may di¤er from each other. First, they di¤er in their main source
of income (workers vs capitalists). Second, at any point in time, workers may
be employed or not (the insider-outsider con‡ict). Third, employed workers may
di¤er in their ability. Given that agents di¤er on more than one dimension, the
decision making process should put a lot of emphasis on the political alliances that
these di¤erent groups of voters may strike with each others. This in turn means
that we wish to depart from the usual two party approach adopted in a large part
of the political economy literature. It seems to us very di¢cult to state ex ante
which party represents which voters. Saint-Paul (1996, p.281) discusses this point
at length, criticizing the idea that left wing parties represent “labor” while right-
wing parties are biased against it. We consider it much more fruitful to allow voters
to be represented by politicians who decide which alliances to strike with each other
and which political parties to form. In such a framework, both the number of parties
and their constituents are endogenous at equilibrium.
We adapt the economic model from Pagano and Volpin (2005) to …t our purpose.
The economy is populated with capitalists and workers. A subset of workers are hired
in the initial stage and can invest in …rm-speci…c human capital in order to increase
their productivity. They di¤er in their ability to become more productive, which
can be either low or high. Productivity is observable by all but non contractible.
The …rm then tries to …re low-productivity workers (those who have not invested or
for whom the investment has not paid o¤) in order to replace them with lower-paid
currently unemployed workers. This attempt to …re people may be voided in court
with a probability that increases with the degree of employment protection. The
public policy consists of both this employment protection level (EPL thereafter)
and a tax which …nances an unemployment bene…t (UB thereafter). The vote is
taken at an interim stage, when workers have already invested in human capital but
before the investment has proved fruitful or not. We assume that no group forms a
majority by itself, that unemployed workers form the largest group, and that they
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form a majority when they join forces with either the high-skilled workers or the
unemployed.
Our modelling of political competition is based on Levy (2004). Her approach
is particularly well suited to our problem, since (i) unlike the traditional Downsian
model, equilibria in pure strategies do exist with multidimensional policy spaces and
(ii) both the number and the constituency of political parties are endogenous. At
the voting stage, there are four groups of citizens (capitalists, unemployed agents,
low- and high-skilled workers), each represented by one politician. These politicians
…rst form coalitions (parties) and then compete in a winner-takes-all election by
simultaneously proposing policy bundles composed of an EPL and an UB. The
incentive to form a party resides in the ability to enlarge the set of credible proposals:
while individual politicians are restricted to proposing their most-favored policy (no
other proposal would be considered as credible by voters), parties can propose any
policy that is in the Pareto set of their constituents (i.e., any policy that may be the
result of e¢cient bargaining between party members is deemed credible by voters).
The equilibrium of this game is then composed of a partition of politicians into
parties and of the vector of policies proposed by these parties.
Our results run as follows. Both capitalists and unemployed agents prefer no
EPL while workers (both low- and high-skilled) prefer maximum EPL. In terms of
UB, capitalists want none while unemployed agents would like a very large one.
Employed workers are in between, with low risk workers preferring a larger bene…t
than high risk workers. Preferences of unemployed and (especially high-skilled)
workers are thus very much opposed. As a result, the Pareto set of these two
groups trades-o¤ a lower protection level against a larger employment bene…t – i.e.,
it exhibits a negative correlation between those two dimensions.
In the absence of political parties (i.e., when each group is represented by a
citizen-candidate restricted to either running with his most-favored policy or not
running in the elections), the unique equilibrium policy consists of the most-preferred
package of the low-skilled workers: a very large EPL together with a moderate UB.
We then show that allowing for the formation of political parties drastically changes
the set of equilibrium policies. We obtain that, provided that high-ability workers
and unemployed agents can agree on some policy that both strictly prefer to the
most-favored policy of the low-ability workers, there exists an equilibrium where
high-ability workers and unemployed coalesce in a party and win by proposing a
policy with some positive UB and EPL. We then state two other conditions (on
the preferences of agents) that, if satis…ed, jointly insure that the only policies that
are proposed in all equilibria belong to the Pareto set of the coalition made of
high-ability workers together with unemployed agents. Our model does not allow
us to make a speci…c prediction as to which point of the Pareto set will emerge (we
typically have multiple equilibria), but is precise enough to tell us that equilibria
exhibit a negative correlation between job protection and insurance, which is what
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we observe empirically. In particular, our model is consistent with the emergence of
policies that contradict the intuition from standard median voter approaches.
Before embarking on the description and solving of the model, let us brie‡y
review the related literature. To the best of our knowledge, there are only two papers
dealing with the political economy of job market institutions in a multidimensional
setting. Pagano and Volpin (2005) analyze the political determinants of investor
and employment protection. We have simpli…ed the part of their model that deals
with the capital …nancing of the …rm while we have introduced an UB. Observe
that, in our model, the UB is driven by two competing logics (see saint-Paul (1996),
p.274): an “insurance logic” (since the bene…t provides income in case workers
are …red) and a “wage formation logic” (the UB is the outside option of workers
– increasing their outside option also increases the competitive wage paid by the
…rm). We di¤er totally from Pagano and Volpin (2005) in the setting of the political
choice mechanism, since they adopt a probabilistic voting setting with two parties
and obtain results that crucially depend (as always within the probabilistic voting
approach) on assumptions regarding the distribution of ideological bias among the
di¤erent categories of voters.
The other close paper is Boeri et al. (2006), whose objective is the same as ours:
explaining why political-economy equilibria exhibit a negative correlation between
UB and EPL. While we share the same objective, we di¤er in both the economic
and the political modelling. Their economic model is an extension of Wright (1986),
with workers varying in their skill levels. Both EPL and UB are set up in such a way
that they redistribute in favor of low-skilled workers. The modelling of the public
decision making process assumes that people vote separately on the two dimensions,
and a (so-called Shepsle or induced) equilibrium is such that each instrument is set at
its majority-favored level given the other instrument. Low-skilled voters are decisive
in both votes and there is substitution between EP and UB since “a higher level of
unemployment insurance for the low-skills reduces the cost, in terms of consumption,
of being unemployed; thus leading a low-skill insider to require a lower degree of EPL
(p. 15)”. Whether low-skilled voters prefer a large EPL or UB very much depends
on the amount of redistribution associated to each instrument. The authors show
that “more earning inequality or a more progressive UB system involve more cross-
skill redistribution (...) thereby making unemployment bene…ts more appealing to
low skill types (p.15)”. The driving force for the negative relationship between UB
and EPL in our model is di¤erent and comes from the fact that the Pareto set for
high-skilled workers and unemployed exhibits such a relationship, with unemployed
preferring a large UB and a small EPL while (high-skilled) employed have opposite
preferences.
We now turn to our model.
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2The Economic Environment
2.1Basic Setting
We consider an economy populated by a continuum of citizens of measure 1 + ?,
? 2 (0;1), which is partitioned into two economic classes: workers and capitalists.
Workers own labor and no capital; capitalists own capital, but no labor. The measure
of workers is one, so that the measure of capitalists is ?.
There are three goods in the economy: labor, capital, and a consumption good
(the numeraire) produced by a single …rm using labor and capital as inputs. Its
Leontie¤ production technology exhibits a labor-capital ratio equal to~`. All workers
have the same labor endowment, normalized to 1, that they rent to the …rm in
exchange of a wage. Each capitalist has the same capital endowment, k, which is
o¤ered to the …rm in exchange for a share in its ownership. Capitalists then share
equally the pro…t (revenue minus wage bill) of the …rm.
The total stock of capital is ?k so that the …rm initially hires a mass ` ? ?k~`
of workers in exchange of a promise of a wage wI (where the subscript I stands
for initial). We assume that ` < 1 so that there is some unemployment in the
economy. Workers hired at this stage can make a costly e¤ort in order to improve
their productivity (such as investing in …rm-speci…c human capital for instance). If
they choose not to make this e¤ort, their productivity is y. If they choose to make the
e¤ort, they incur a disutility cost ? > 0 but have a probability xiof increasing their
productivity to y +? (if the e¤ort fails to prove fruitful, their productivity remains
y): There are two groups of workers di¤ering in their ability to transform e¤ort into
higher productivity: 0 < xL< xH < 1: The proportion of high-ability workers is
denoted by ?, with a majority of low-ability people among workers (? 2 (0;1=2)).1
Individual productivity is observable, but not contractible.2
After having observed individual productivities, the …rm may try to …re some
workers in order to replace them with cheaper unemployed individuals, who are
o¤ered a wage wR(where R stands for restructuring). However, every attempt to
lay o¤ a worker can be voided by a court with probability ?(?) 2 (0;1), where
?0> 0, ?(0) = 0 and ?(1) < 1. We assume that it is too late at this stage for
unemployed people joining the …rm to invest in speci…c human capital, so that their
1Saint-Paul (1996) reckons that “unskilled and semi-skilled workers (...), including workers
without a college degree, make up more than 70% of the workforce in most European coun-
tries.”(p.275)
2The noncontractibility of individual productivity may be viewed as a characteristic of the pro-
duction technology. We refer the reader to Pagano et al. (2005, foonote 10) for further justi…cations
of this assumption.
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productivity is y.
At the end of the game, payo¤s are distributed according to the status of indi-
viduals at that time. The individuals who are unemployed at the end of the game
receive an unemployment bene…t, denoted by ?. The wage paid to people working
in the …rm depends upon their seniority: people employed since the initial stage are
paid wI(irrespective of their –non contractible– productivity) while people hired at
the restructuring stage are paid wR. Capitalists share equally the pro…t of the …rm.
Everybody pays the same lump sum tax ? ? 0, whose proceeds …nance the unem-
ployment bene…t. The unemployment bene…t ? is obtained using the government
budget constraint
(1 ? `)? = ?(1 + ?):
The tax ? forms the …rst component of the public policy. The second component
is the degree of employment protection, ? 2 [0;1]. Public policy is decided, by
majority voting, after the workers hired at the initial stage have invested in speci…c
human capital, but before the result of this investment is observed (by workers and
the …rm). Observe that the unemployment level 1 ? ` does not depend on the
unemployment bene…t ? nor on the job protection policy ? in our model.
We now summarize the timing of the game:
(1)
Stage 1 (Initial hiring) Capitalists invest all their capital in the …rm. The …rm
hires a measure ` ? ?k~` < 1 of workers in exchange of the promise of a wage
wI.
Stage 2 (Workers’ investment) Employed workers decide whether to invest in
…rm-speci…c human capital.
Stage 3 (Voting) A government is democratically elected to implement a policy
vector (?;?), with the unemployment bene…t ? determined by the budget
constraint (1).
Stage 4 (Restructuring) Employed workers and the …rm learn about employees’
individual productivities. The …rm may try to replace some of them with cur-
rently unemployed agents in exchange of a wage wR. However, every attempt
to lay o¤ a worker can be voided by a court with probability ?(?) 2 (0;1).
Stage 5 (Production and consumption) Output is produced, capitalists receive
the …rm’s pro…t, employed workers are paid their wage (wIor wRdepending
on their seniority), and unemployed workers obtain the unemployment bene…t.
All pay the lump sum tax ?.
All agents care only for the amount of consumption good consumed (they derive
no bene…t from leisure and so no disutility from working) and use their entire after-
tax income to purchase that good. They all have the same preferences over private
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consumption, which are represented by a von-Neumann-Morgenstern utility function
U : R+! R, with U(0) = 0, U0> 0, U00< 0, and limc!0U0(c) = 1.
2.2Wage setting
The …rm is a monopsonist on the market for labor. In the absence of any trade
union, the …rm would o¤er the smallest wage that is acceptable to the workers (the
competitive wage). We rather assume, as in Lee and Roemer (2005), that workers’
interests are defended by a trade union that bargains for a higher wage than the
competitive one. Let ? ? 1 stand for the gross mark-up on the competitive wage
that the union is able to enforce for all workers.
We now solve the game backward, starting with the restructuring stage (since
there is no decision to be taken at the last stage). Agents have no disutility from
working, so that the competitive wage for newly hired workers is equal to their
outside option, the unemployment bene…t ?. After (unmodelled) bargaining between
the …rm and the union, the wage o¤ered to new workers at this stage is
wR= ?? = ??1 + ?
1 ? `
(2)
where the second equality is obtained from the budget constraint (1). The after-tax
income of these workers is
?? ? ? = ??1 + ?
1 ? `? ?:
The before-tax income of unemployed agents is the unemployment bene…t ? = ?1+?
with the corresponding after-tax income ? ?? = ?`+?
of (2) is that the …rm has an incentive to …re low productivity workers (in order to
replace them with unemployed agents) as soon as the competitive wage in the …rst
stage is larger than the unemployment bene…t (i.e., as soon as wI> ??).
The rest of the paper will be devoted to the study of the third, majority voting,
stage. In order to solve that stage, we need to construct individuals’ preferences for
the policy options ? and ?. This in turn requires to solve for workers’ decision to
invest or not in human capital, and for the wage wIthat is o¤ered to them in the
…rst stage. To do this, we assume for the moment that a policy pair (?;?) has been
chosen and we move to the second stage, where voters choose whether to invest or
not in human capital.
Making the e¤ort of investing in human capital has a sure cost, ?, and an uncer-
tain return. This return takes the form not of a higher wage (because productivity is
not contractible), but rather of a larger probability of remaining employed. Hence,
for workers to choose to make this e¤ort, it must be the case that (i) their wage if
1?`
1?`. Observe that a consequence
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they remain employed is larger than the employment bene…t they would receive if
…red, and (ii) the …rm tries to …re workers of low productivity, and only them (if
the …rm’s decision to …re did not depend on the productivity of the worker, then no
worker would have an incentive to make the e¤ort, and thus no one would exhibit a
high productivity at equilibrium).
We then look at the case where the …rm’s owners (the capitalists) bene…t when
the workers of type i choose to make the e¤ort of trying to be more productive. This
in turn means that the …rms tries to …re all workers with low productivity (and only
them). Anticipating this, workers of type i make this e¤ort only if the expected
payo¤ from making the e¤ort is larger than the expected payo¤ if they do not make
the e¤ort:
[xi+ (1 ? xi)?(?)]U(wI? ?) + (1 ? xi)[1 ? ? (?)]U(? ? ?) ? ?
? ?(?)U(wI? ?) + [1 ? ? (?)]U(? ? ?):
The payo¤ when investing (the left-hand side of (3)) increases with ability (because
the investment has a larger chance to succeed) while the payo¤ when not investing
(the right-hand side of (3)) does not depend on ability, so that if the constraint
is satis…ed for low ability workers, it is also satis…ed for high ability workers. We
assume that the …rm’s pro…t is larger when all workers are induced to invest in
human capital.3We then solve for wI in (3) and we obtain the competitive wage
wc— the minimum wage o¤ered in the initial stage that would induce all employed
workers to invest in human capital — as
?
Let us now move to the …rst stage and to the setting of the wage wI. The …rm’s
owners (the capitalists) set the wage just high enough to induce workers to invest.
This wage level is given by (4) and would be o¤ered by the …rm in the absence of
trade union. Thanks to the (unmodelled) intervention of the trade union, a worker
hired in the initial stage and keeping his job until the end of the game will receive
a wage of wI= ?wc: His …nal after-tax income is then ?wc? ?. Finally, we assume
that individuals have a larger expected payo¤ if they get hired in the initial stage
than if they were to remain unemployed at that stage. We show in the next section
that this assumption is satis…ed provided that the e¤ort cost ? is low enough.
We are now in a position to study the preferences of agents at the voting stage.
(3)
wc= ? + U?1
U(? ? ?) +
?
[1 ? ?(?)]xL
?
> ?:
(4)
3This assumption is satis…ed when ? is large enough, as this leaves su¢cient room for the …rm
to pay a large wage (enticing even low ability workers to make an e¤ort) while leaving more pro…t
to the …rm than if it did not entice all workers to be more productive. Observe also that a large
value of ? guarantees that the payo¤ of capitalists is strictly positive at equilibrium.
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2.3Voter preferences
Policy preferences in the third stage depend upon voters’ type ?. Voters can be
i-ability employed workers (? = ei;i 2 fL;Hg), unemployed (? = u), or capitalists
(? = c). Recall that, at the voting stage, all currently employed agents have already
incurred the cost associated to their e¤ort to be more productive, but are yet to
know whether this e¤ort will prove fruitful. Workers as well as currently unemployed
individuals form expectations as to their status in the …nal stage of the game, and
thus as to their …nal payo¤.
Let p : [0;1] ? feL;eH;ug ! (0;1) be the probability for a voter of type
? 2 feL;eH;ug to be employed at the production phase when the EPL is ?. This
probability is given by
?xi+ (1 ? xi)?(?) if ? = ei;i 2 fL;Hg
where x ? ?xH+ (1 ? ?)xLis the average proportion of high productivity workers
(equal to the expected proportion by the law of large numbers). We de…ne the policy
space as P ? [0;? ?] ? [0;1] for some exogenous value of ? ?.4
Voters’ policy preferences over P are then given by:5
8
:
where ? w(?;?) denotes the average wage paid in the production stage and is given
by
? w(?;?) ? ?f[x + (1 ? x)?(?)]wc+ (1 ? x)[1 ? ?(?)]?g:
We make the following reasonable assumptions on the distribution of voters’
types:
> (1 ? ?)` > max??;1 ? ` +?
(b) 1 + ? < 2minf`;1 ? ?`g:
4We need to impose an exogenous value of ? as upperbound because tax proceeds are increasing
p(?;?) ?
(1?x)[1??(?)]`
1?`
if ? = u;
V(?;?;?) ?
<
p(?;?)U (?wc? ?) + [1 ? p(?;?)]U??`+?
U?[y + x? ? ? w(?;?)]`
1?`
?
if ? 2 feL;eHg;
if ? = u;
if ? = c;
p(?;?)U???1+?
1?`? ??+ [1 ? p(?;?)]U??`+?
1?`
?
?? ??
(5)
Assumption 1 (a)
1+?
22
?.
with ? in the absence of preference for leisure.
5Recall that the e¤ort cost ? has already been sunk at that stage, and thus does not appear
in policy preferences. Also, the wage wI has already been set by the …rm in the initial stage. As
we focus on subgame perfect equilibria, we assume in the rest of the paper that wcis given by (4)
where ? and ? are set at their equilibrium value (i.e., the value that the …rm has anticipated at
the initial stage of the game).
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(c) ` <
xL
1??(xH?xL):
Assumption 1(a) guarantees that the low-ability employed form the largest group
but fall short of the majority. It also implies that the capitalists form an electorally
small group of voters.6
Assumption 1(b) states that employed people constitute
a majority of voters, as well as low-ability employed together with unemployed.
Observe that we make no assumption on whether low-ability workers together with
capitalists form a majority, or whether the complement made of high ability workers
together with unemployed forms a majority – i.e., we allow for ? + (1 ? ?)` 7
?`+1?`: As for Assumption 1(c), it guarantees that the probability for an individual
unemployed (at the voting stage) of …nding a job is lower than the probability for a
worker employed (at the same stage) of remaining so (given that s/he has invested
in human capital):
p(?;?) > p(?;u) for ? 2 feL;eHg and any (?;?) 2 P:
Observe that this inequality, together with wc> ?, implies that, at the third stage,
employed workers are better o¤ (in expectation) than unemployed workers:
V(?;?;?) > V(?;?;u) for ? 2 feL;eHg and any (?;?) 2 P:
This does not imply that the initial stage expected welfare is larger for employed
workers than for unemployed agents, since employed workers anticipate that they
will have to subtract the e¤ort cost ? from V(?;?;?). We then assume that ? is
low enough that individuals have a larger expected payo¤ in the initial stage if get
hired than if they were unemployed at that initial stage.7
We now introduce our de…nition of the political equilibrium concept.
3Voting
The main di¢culty when voting over multidimensional policy spaces is the absence
of Condorcet winner (i.e., of a policy bundle that is preferred by a majority of voters
to any other feasible bundle). This in turn means that a classical Downsian political
competition model with two parties interesting only in winning elections has no
6The addition of half the capitalists to the unemployed on the right hand side of assumption
1(a) is not strictly necessary to obtain our results, but it allows to simplify the proof of Proposition
1 below. It does not imply that capitalists play no role in the election, as will be clear in section 4.
7It is straightforward to see that agents are better o¤ when employed in the initial stage if
? = 0. By continuity this is also true for small values of ?.
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