Signaling in political budget cycles: How far are you willing to go?

Signaling in political budget cycles. How far

are you willing to go?

¤

Jorge Miguel St reb

November 2001

A b st r act

This paper analyzes how het erogeneity in two dimensions, com-petency and charact er, a¤ect s polit ical budget cycles. Comcom-petency is t he e¢ ciency i n running t he government . Character is the degree of opport unism. In t his expanded space, previous results in t he lit -erat ure on the separat ing nat ure of t he signaling equilibrium hold if het erogeneity in opport unism is low. Wit h high heterogeneity in op-port unism, no separat ing equil ibrium exists. Rat her, t he equilibrium is part iall y pool ing: only ext reme types can be dist inguished.

¤_{I t hank Delia Ferr eira Rubio, Je¤r y Frieden, Geor ge McCandless, Juan Pablo Nicolini,}

Federico Weinschelbaum, and, very especially, Ernest o St ein for t heir st imulat ing ideas and insight s. I appreciat e t he comment s by part icipant s at a seminar at UTDT , and at t he meet ings of t he A A EP in Rosar io, t he LA CEA in Rio de Janeiro, and t he Economet ric Society in Punt a Chica, B uenos A ir es.

y_{Jorge M. St reb, Universidad del CE MA , A v. Córdoba 374, 1054 Buenos A ires, A}

Key words: rat ional political budget cycles, two-dimensional asym-met ric informat ion, signaling, discret ion, adverse select ion.

JEL: D7, E6

The lit er at ure on opport unist ic polit ical cycles has est ablished t hat , wit h

rat ional vot ers, cycles can signal t he compet ency of t he incumbent . The

wor k-horse models by Rogo¤ (1990) and Lohmann (1998) show t here is a

separat ing equilibrium where compet ent incumbent s st and out from t he rest .

This opport unist ic polit ical cycle lit erat ur e assumes t hat rat ional vot ers can

…gure out just how far an incumbent is willing t o go t o get reelect ed.

The pr oblem wit h t he exist ing result s is t he implicit assumpt ion t hat

op-port unism is common knowledge. I n fact , opop-port unism is part of an

individ-ual’s ut ilit y funct ion. Since ut ility funct ions are not observable, opport unism

has t o be inferred from t he act ions of t he incumbent , just like compet ence.

This is t he t heoret ical mot ivat ion t o explore t he consequences of asymmet ric

informat ion on opport unism.

Asymmet ric informat ion on opport unism can be relevant only if polit ical

candidat es are su¢ cient ly het erogeneous in t his dimension. T he fact t hat

polit icians di¤er in opport unism is recognized by Tuft e (1978) in his classic

st udy of polit ical cont rol of t he economy. He draws a clear-cut cont rast

between Ford, who was not willing t o t ake t he short view before elect ions,

and Nixon, who was willing t o exploit pre-elect oral engineering t o it s ut most .

That individuals can di¤er bot h in compet ency and in charact er is also

arises not only because t her e are di¤er ent qualit y cars, but also because t here

are dishonest sellers who are willing t o misst at e t he qualit y of a used car .

The issue of lemons lit erally pert ains t o polit ics: in a polit ical campaign,

vot ers were asked if t hey would buy a used car from one of t he candidat es

pict ur ed running for o¢ ce.

I n relat ion t o opport unist ic cycles, Alesina, Roubini, and Cohen (1997)

can empirically reject syst emat ic opport unist ic cycles before elect ions implied

by Nordhaus (1975). However, t hey cannot reject t he implicat ions of t he

seminal Rogo¤ (1990) paper , namely t hat polit ical cycles occur frequent ly,

t hough not always, before elect ions. Alesina et al. (1997) object t he Rogo¤

approach on ot her grounds, namely t hat his r esult t hat only compet ent

in-cumbent s dist ort economic policy is t roublesome and unrealist ic. T his paper

builds on Rogo¤ t o show t hat t his result is not inherent t o t he opport unist ic

approach.

This paper proposes an ext ended framework for rat ional polit ical budget

cycle (RPBC) models wheret he consequencesof two-dimensional asymmet ric

informat ion can be analyzed. When opport unism is not common knowledge,

incompet ent incumbent s can also dist ort economic policy. This paper is

relat ed t o St ein and St reb (1999) , who model t he elect oral manipulat ion

of exchange rat es in a signaling game t hat is a special case of t he pr esent

framework.

Sect ion I spells out t he economy and t he polit y, focusing on t he pot ent ial

t he RPBC model under asymmet ric informat ion on opport unism and

com-pet ency, and looks at t he welfare implicat ions. Sect ion I I I looks at some

concept ual issues surr ounding t he model. Sect ion IV present s t he

conclu-sions.

I . Economy and Pol it y

This Sect ion describes t he ut ilit y funct ions of vot ers and polit icians, t he

gov-ernment budget const raint s and t he elect oral inst it ut ions. The model follows

t he Rogo¤ (1990) dist inct ion bet ween public consumpt ion and invest ment

goods, t hat gives rise t o more and less visible budget it ems, as t he key device

t o model budget cycles around elect ions.

A . U t ilit y Funct ions

The economy is reduced t o t he net provision of public goods. There are

a large number of represent at ive consumer s, who are also vot ers. Visible

budget it ems, gt, are observed by vot ers cont emporaneously, and less visible

budget it ems, °t+ 1, are observed wit h a one-per iod lag. The variables gt and

°_{t+ 1}refer t o t he provision of public goods net of t axes.

The repr esent at ive individual derives ut ility from t he consumpt ion of g_t

and °_t. Ut ilit y U is separable over t ime, and wit hin each period it isseparable

U =

T

X

t = 0

u(gt; °t+ 1)

(1 + ±)t ; u(gt; °t+ 1) = w(gt) +

v(°_{t+ 1})

1 + ± ;

(1)

where v,w are st rict ly concave, w0> 0,v0> 0, and v0(0) ! 1 (t o assure an

int erior solut ion in what follows).

The incumbent is select ed from among t he populat ion. An incumbent

has preferences similar t o vot ers. It enjoys a sat isfact ion K ¸ 0 from being

in o¢ ce, t he ego-rent or kick from being t he leader. T his will be t he source

of opport unist ic behavior. Let µt = 1 when t he individual is incumbent , and

0 when not . Z gives t he incumbent ’s lifet ime ut ilit y:

Z = U +

T

X

t= 0

µ_tK (1 + ±)t

(2)

The lit erat ur e implicit ly assumes t hat t he kick K is common knowledge.

Inst ead, we explore t he consequences of opport unism being a random

vari-able eK . We work wit h polar t ypes. The incumbent can eit her be

non-opport unist ic, wit h realizat ion K = 0, or highly non-opport unist ic, wit h r

ealiza-t ion K = K &gealiza-t; 0, where K will be characealiza-t erized in Secealiza-t ion I I . T he pr iors

are t hat wit h probability s t he incumbent is highly opport unist ic, while wit h

pr obabilit y 1 ¡ s it is non-opport unist ic. A non-opport unist ic incumbent

be-haves as a benevolent social planner, while an opport unist ic incumbent is

willing t o dist ort policy on behalf of it s personal int er est s. The dist ance

between bot h t ypes, given by d ´ K ¡ 0 = K , det ermines t he degr ee of

B . B udget Const raint s

The government is subject t o t he following per-per iod budget const raint ,

where "t denot es act ual compet ency:

gt +

°t+ 1

1 + ±= "t (3)

A more compet ent government can provide mor e of bot h gt and °_{t+ 1}. For

a given "t, a t rade-o¤ bet ween gt and °t+ 1 exist s: larger expendit ures on

visible public goods, and lower visible t axes, can be achieved at t he cost of

hikes in t axes, and r educt ion in expendit ures, t hat only become visible aft er

elect ions. This t rade-o¤ re‡ect s budget cycles around elect ions, by which a

larger pre-elect oral budget de…cit requires a larger post -elect oral surplus.

We assume t hat t he act ual compet ency of t he incumbent follows an

MA(1) pr ocess, as in Rogo¤ and Sibert (1988), according t o t he realizat ions

of current and lagged compet ency shocks:

"t = " + ®t + ®t¡ 1

(4)

The priors vot ers have about random variable e®t are t hat wit h probabilit y

r t he shock is posit ive (®t = ®, compet ent ), and wit h probability 1 ¡ r t he

shock is negat ive (®t = ¡ ®, incompet ent ).

Consequent ly, incumbent s di¤er in t wo dimensions: compet ency and

op-port unism. Compet ency shocks e®t are assumed t o be independent ly

C. V ot ing B ehavior

Let t he t ot al ut ilit y of a vot er i be given by Ut+ qt;i, where qt;i is t he personal

appeal of a candidat e t o vot er i . We assume t hat qt;i is t he realizat ion of a

random shock eqt;i which is whit e noise and has an uniform dist ribut ion over

t he int erval [¡ q; q], and t hat qt;i is independent acr oss individuals.

I n regard t o t he inst it ut ional set up, we assume an incumbent ’s t erm in

o¢ ce last s two periods. Furt hermore, we will rest rict t he analysis in t his

paper t o t hecase wheret heincumbent has a t wo-t erm limit , as in present U.S.

const it ut ional pract ice, so an incumbent can at most be reelect ed once (t his

allows t o abst r act from reput at ional consequences of opport unist ic behavior) .

I I . R at i onal Polit i cal B udget Cy cl es

Rogo¤ (1990) and Lohmann (1998) pr esent models of RPBC t hat di¤er in

t heir t iming. In Rogo¤ (1990) , t here is asymmet ric informat ion because

in-cumbent s decide policy aft er t hey obser ve compet ency. Since compet ency is

known ex-ant e, only compet ent incumbent s engage in budget cycles, while

incompet ent incumbent s do not . I n cont rast , Lohmann (1998) develops a

model wit h symmet ric informat ion, where incumbent s decide policy before

t hey observe compet ency. All incumbent s engage in monet ar y cycles before

elect ions, but , ex-post , compet ent incumbent s are able t o go fart her t han

incompet ent ones. Persson and Tabellini (1999) t reat t he di¤erence between

-ric informat ion on compet ency in Rogo¤ (1990), as t he di¤erence bet ween a

moral hazard problem and an adverse select ion problem. Once het er

ogene-it y in opport unism is int roduced, t he di¤erence bet ween bot h set ups fades.

Adverse select ion is present from t he st art .

This Sect ion reviews t he Rogo¤ (1990) result s as a benchmark. The

sig-naling model is t hen ext ended fr om t he one-dimensional asymmet ric

informa-t ion seinforma-t up, where oppor informa-t unism is common knowledge, informa-t o a informa-two-dimensional

asymmet ric informat ion set up. We show no separat ing equilibrium exist s

when t he degree of het erogeneit y d = K is su¢ cient ly large.

The t iming of t he game each per iod is as follows. T he incumbent

ob-serves t he compet ency shock "_t before it decides °_{t+ 1} and g_t. Visible g_t is

t hen observed by all individuals. This sequence implies t hat in an elect ion

period incumbent s have an informat ional edge over vot ers in relat ion t o t heir

compet ency, as depict ed in Figur e 1.

< please insert Figure 1 about here>

The MA(1) process in equat ion (4) implies t hat shocks in o¤-elect ion

pe-riods do not a¤ect performance aft er elect ions, so only compet ency shocks in

elect ion periods mat t er for for ward-looking vot ers. Since compet ency shocks

in o¤-elect ion periods do not a¤ect vot ing decisions in elect ion periods, t he

incumbent ’s decision problem is decomposable int o on- and o¤-elect ion

pe-riods. I n o¤-elect ion periods, budget decisions are not a¤ect ed by elect oral

A . O¤ -elect ion P er iods

Consider an o¤-elect ion period t . No signaling is involved becauset he cur rent

compet ency shock only a¤ect s performance before elect ions, so t his

informa-t ion is noinforma-t relevaninforma-t for informa-t he decisions of forward-looking voinforma-t ers. Since informa-t he kick

from being in o¢ ce is not at st ake, an incumbent will pick gt t o maximize

(1), subject t o budget const raint (3). The FOC is

w0(gt) = v0(°t+ 1)

(5)

This condit ion det erminesopt imal g¤_t( ®t¡ 1; ®t) and °¤_{t+ 1}(®t¡ 1; ®t). More

com-pet ent incumbent s deliver more visible and invisible public goods, and charge

lower visible and invisible t axes. This det ermines a level of indirect ut ilit y

u¤_t(®t¡ 1; ®t) ´ u(g¤_t(®t¡ 1; ®t) ; °¤_{t + 1}(®t¡ 1; ®t)) in o¤-elect ion periods which is

higher wit h compet ent incumbent s t hat have ®t = ®.

M ore relevant for elect oral decisions will be t he fact t hat indirect ut ilit y

u¤

t(®t¡ 1; ®t) is higher wit h ®t¡ 1 = ® t han wit h ®t¡ 1 = ¡ ®. This will imply

t hat vot ers are more likely t o reelect incumbent s t hat have high compet ence

in elect ion periods, as we now show.

B . Elect ion Per iods

Maximizing vot ers compar et he incumbent wit h an opposit ion candidat e

cho-sen at random from t he populat ion. Vot ers base t heir decision on t he

(superscript o denot es t he opposit ion candidat e; no superscript is used for

incumbent ). This implies t hat t here is probabilist ic vot ing.

An elect ion will be det ermined by t he median vot er. An incumbent will

be reelect ed if t he expect ed indirect ut ility of median vot er m in period t + 1,

condit ional on informat ion available in t , is higher wit h t he incumbent t han

wit h t he opposit ion candidat e:1

E [u¤_{t+ 1}(®t; ®t+ 1) j ½t] + qt;m > E[u¤ot+ 1(®t; ®t+ 1) j ½ot] + qot;m

(6)

The informat ion in (6) t hat condit ions expect at ions refers t o informat ion

on visibleexpendit ure, t hat can be used t o evaluat et he probabilit y ½_t t hat t he

incumbent is compet ent . In t he case of t he opposit ion candidat e, expect ed

compet ency is exogenously given at ½o

t = r .2 T here is no incumbency bias:

rule (6) followed by forward looking vot ers implies t hat if t he incumbent is

perceived t o be compet ent wit h t hesame probability as opposit ion candidat e,

t he incumbent ’s probability of reelect ion will be1

2.

Since indirect ut ilit y u¤

t+ 1(®t; ®t+ 1) aft er elect ions is increasing in cur rent

compet ency ®t, vot ing rule (6) implies t hat vot ers who maximize expect ed

1_{The MA (1) st ruct ure in (4) rest rict s t he fut ur e horizon t o one period, since elect or al}

decisions can only a¤ect t he expect ed value of out comes in t he next period. T he expr essions for expect ed indir ect ut ility in (6) t ake int o account t he pr obability ½t t he candidat e is

compet ent in t he curr ent period (e.g. E [u¤t + 1(®t; ®t + 1) j ½t] ´ ½tE u¤t + 1(®; ®t + 1) + (1 ¡

½t) E u¤t + 1(¡ ®; ®t + 1) ), and t he probabilit y r candidat es will be compet ent next period (e.g.

E u¤t + 1(®; ®t + 1) ´ r u¤t + 1( ®; ®) + (1 ¡ r ) u¤t + 1(®; ¡ ®)).

2_{I f none of t he candidat es had a t r ack r ecord, t he elect ion would solely hinge on t heir}

per sonal appeal. The winning candidat e would be det er mined by whet her qt ;m ¡ qot ;m is

ut ility are mor e likely t o r eelect an incumbent when t he probabilit y ½t it is

compet ent (®t = ®) is higher.

C. O ne-dimensional A sym m et r ic I nfor m at ion

We present a st ripped down version of t he Rogo¤ ( 1990) model. The model

implicit ly assumes t hat t he opport unism of incumbent s is observable.

Rogo¤ and Sibert ( 1988) showed t hat polit ical budget cycles can signal

compet ency t o rat ional forward looking vot ers. Rogo¤ (1990) reformulat ed

t he signaling game in a fully opt imizing framework wit h t wo types of

com-pet ency, high and low. The equilibr ium will be separat ing: incumbent s wit h

high compet ency choose high expendit ure and low t axes before elect ions,

while incompet ent incumbent s do not .

Say gs

t is t he level of visible public goods t hat a compet ent incumbent

picks in a separat ing equilibr ium, while an incompet ent incumbent picks t he

lower level g¤

t ´ gt¤(®t¡ 1; ¡ ®). Consequent ly, vot er’s beliefs will be given by:

(7) gt = gst ) ½t = 1

g_t = g¤_t(®_{t ¡ 1}; ¡ ®) ) ½_t = 0

I n equilibr ium, vot ers will infer t hat an incumbent who delivers g_ts is

compet ent . For ot her, out -of equilibrium, values of visible expendit ure, we

assume t he lower t hreshold of each int erval de…nes expect ed compet ency.

Thus, while t he separat ing signal gs

½t = 1, not signaling wit h at least t hat level of visible budget it ems leads t o

lose any such reput at ion, so ½t = 0.

For t his t o act ually be a Perfect Bayesian Equilibrium, compet ent and

incompet ent incumbent s must be willing t o pick t hese signals. I f t he

incum-bent is incompet ent , it s expect ed ut ilit y from picking t he separat ing signal

g_ts must not be larger t han it s expect ed ut ility from picking g¤_t(®t¡ 1; ¡ ®):

E[Zs j ®t = ¡ ®] E [Z¤j ®t = ¡ ®]

(8)

The di¤erence in expect ed ut ilit y between t he LHS and t he RHS of

equa-t ion (8) can be expressed as equa-t he equa-t empequa-t aequa-t ion equa-t o signal of an incompeequa-t enequa-t

incumbent . M ore generally, for an incumbent of t ype ®_t, t he t empt at ion

T(gs

t; g¤t( ®t¡ 1; ®t) j ®t) can be expressed, by algebraic manipulat ion, as t he

di¤erence between t he expect ed fut ure bene…t s – due t o t he increased

prob-abilit y of enjoying t he perks of being in o¢ ce t wo periods more – and t he

expect ed welfare cost s – due t o t he dist ort ion pr oduced by t he budget cycle

–, i.e.:

T (g_ts; g_t¤(®t¡ 1; ®t) j ®t) ´ B(gst; gt¤(®t¡ 1; ®t)) ¡ C(gts; gt¤(®t¡ 1; ®t) j ®t)

(9)

where

B(gs

t; g¤t(®t¡ 1; ®t)) ´ [p(gst) ¡ p(gt¤(®t¡ 1; ®t))] 2

X

i = 1

K (1 + ±)i

and

(11)

C(g_ts; g¤_t(®t¡ 1; ®t) j ®t) ´ u¤_t(®t¡ 1; ®t j ®t) ¡ us_t(g_ts; ("t ¡ gs_t)(1 + ±) j ®t)

+ [p( g_ts) ¡ p(g_t¤(®t¡ 1; ®t))]

E [u¤

t+ 1(®t¡ 1; ®t) j ½ot] ¡ E[u¤t+ 1( ®t¡ 1; ®t) j ®t]

1 + ±

The expect ed welfare cost s compr ise a current cyclical e¤ect and a fut ure

wealt h e¤ect . T he wealt h e¤ect is due t o t he fact t hat while an opposit ion

candidat e has a probabilit y ½o

t = r of being compet ent in t + 1, an incumbent

knows it s compet ency ®t will be eit her be high or low for sure. The wealt h

e¤ect is an added cost of signaling for an incompet ent candidat e, and a

bene…t for a compet ent candidat e.

I n a separat ing equilibrium, condit ion (8) can be expressed as t he

con-dit ion t hat an incompet ent must not face a posit ive t empt at ion t o deviat e

from g_t¤(®t¡ 1; ¡ ®):3

T(gs_t; g_t¤(®t¡ 1; ®t) j ®t = ¡ ®) 0

(12)

For cyclest o exist , t he separat ing signal gs_t has t o belarger t han g_t¤(®t¡ 1; ®),

because ot herwise a compet ent can signal it s t ype choosing it s …rst best .

De-3_{We assume t hat when t he bene…t is equal t o t he cost of signaling, i.e.}

not e by Kmi n t he opport unism such t hat T(g¤_t( ®t¡ 1; ®); gt¤(®t¡ 1; ®t) j ®t =

¡ ®) = 0. We charact erize opport unism as high when t he following holds:

K > Kmi n (13)

Condit ion (13) assures t hat a compet ent incumbent has t o produce a

budget cycle t o di¤erent iat e it self. If opport unism were smaller t han Kmi n,

t he equilibrium would st ill be a separat ing, but t here would be no budget

cycle. I n t hat inst ance, t he compet ent would be able t o signal it s t ype by

picking g_t¤(®t¡ 1; ®), wit hout dist ort ing current expendit ure. Thus,

Pr op osit ion 1 Assume information on compet ency is asymmetric and

in-formation on oppor tunism symmet ric. The equilibr ium is separating. I f

op-por tunism is low, there is no political budget cycle. I f opop-portunism is high,

competent incumbents engage in a political budget cycle.

This is a rest at ement of Proposit ions 1 and 2 in Rogo¤ (1990).

No pooling equilibrium survives t he applicat ion of equilibrium dominance

argument s. To see t his, say t hat a pooling equilibrium exist s and t hat it is

given for example by t he level g¤_t(®t¡ 1; ®) t hat is opt imal for a compet ent

incumbent . In a pooling equilibrium, ½= r , so by vot ing rule (6) t he

proba-bilit y of reelect ion p(g¤_t(®t¡ 1; ®)) = 1₂.

To consider deviat ions from t he pooling equilibrium, it is convenient t o

condit ion T(g¤_t(®t¡ 1; ®t); gt¤ j ®t) = 0 wit h respect t o gt, one can …nd t he

pairs (gt; p(gt) ) t hat leave an incumbent of t ype ®t indi¤er ent :

p0(gt) =

v0(°_{t+ 1}) ¡ w0(g_t)

E [ut + 1j®t]¡ E[uot + 1j½ot]

1+ ± +

(2+ ±) K ( 1+ ±)2

(14)

I f K were so small for t he denominat or of (14) t o be negat ive, an

incom-pet ent incumbent would not be willing t o mimic g¤

t(®t¡ 1; ®) in t he …rst place

because t he bene…t of being reelect ed t o o¢ ce would not even compensat e

t he negat ive wealt h e¤ect . Thus, t he denominat or must be posit ive for a

pooling equilibrium t o exist ( condit ion (13) is su¢ cient for t he denominat or

t o be posit ive). By FOC (5), t he numerat or is zero at g¤

t(®t¡ 1; ®t). Due t o

t he concavit y of t he ut ility funct ions v and w, indi¤erence curves are convex.

The convexity of t he indi¤erence curves means t hat t hey reach a minimum

at g¤

t(®t¡ 1; ¡ ®) for an incompet ent , and at g¤t(®t¡ 1; ®) for a compet ent . The

indi¤erence curves t hrough g¤_t(®_{t¡ 1}; ®) are depict ed in Figure 2.

< please insert Figure 2 about here>

From Figure 2, one can see t hat t he indi¤erence curves of an

incompe-t enincompe-t incumbenincompe-t incompe-t o incompe-t he righincompe-t of g_t¤(®t¡ 1; ®) will best eeper t han t he indi¤erence

curves of a compet ent incumbent .4 Therefore, t he deviat ion t hat would leave

an incompet ent incumbent indi¤erent between t he pooling equilibrium and

est ablishing a reput at ion of compet ency ½_t = 1 would make t he compet ent

4_{For compet ent incumbent s, t he denominat or in (14) is larger because of posit ive wealt h}

e¤ect in t he fut ure, and t he numerat or is smaller because for any given gt t hey can pr ovide

bet t er o¤. Only t he compet ent is willing t o deviat e from t he pooling

equi-librium, so applying t he Cho-Kreps crit er ion vot ers will infer t he incumbent

is compet ent if t hat gt, or more, is observed. Applying t his same argument

t o ot her possible equilibrium point s, one can show no pooling equilibrium

survives.5

D . T wo-dim ensional A sy m m et r ic I nform at ion

We now ext end t he set up t o asymmet r ic informat ion on bot h compet ency

and opport unism. Inst ead of two t ypes of incumbent s, t here ar e now four

types: opport unist ic and non-opport unist ic, who can be eit her compet ent or

incompet ent . We will show t hat if het erogeneity is low, t here is a separat ing

equilibrium, as in Rogo¤ ( 1990). If het erogeneity is high, t he equilibrium is

inst ead semi-separat ing.

We posit t he following signals in t he Perfect Bayesian Equilibrium:

(15) g_t = gs

t ) ½= 1

gt = gt¤(®t ¡ 1; ®) ) ½=

(1 ¡ s)r (1 ¡ s)r + ¸ s(1 ¡ r )

gt = g¤t(®t¡ 1; ¡ ®) ) ½= 0

5_{One can replicat e t his analysis for t he model in chapt er 5 of Persson and Tabellini}

The variable ¸ in (15) st ands for t he probability t hat an incompet ent ,

opport unist ic, incumbent is willing t o mimic gt¤(®t¡ 1; ®). The value of gst will

be de…ned below. Out -of-equilibrium values of gt are assumed t o lead t o t he

same reput at ion of compet ency as t he lowest value in each int erval of ( 15).

To est ablish t hat t his is indeed t he equilibrium, we have t o make sure

t hat no t ype of incumbent want s t o deviat e fr om t he proposed solut ion. The

t empt at ion t o signal depends on t wo fact or s, compet ency ®t and opport unism

K :

T(gs_t; g¤_t(®t¡ 1; ®t) j ®t; K ) ´ B (gst; gt¤( ®t¡ 1; ®t) j K ) ¡ C(gst; g¤t(®t¡ 1; ®t) j ®t)

(16)

The cost C(g_ts; g_t¤(®t¡ 1; ®t) j ®t) is as de…ned in (11) above. The bene…t

of reelect ion B(gs_t; g¤_t(®t¡ 1; ®t) j K ) is as in (10) for opport unist ic incumbent s

wit h K = K , but zero for non-opport unist ic incumbent s wit h K = 0.

The problem under t wo-dimensional asymmet ric informat ion is t hat , if

het erogeneit y in opport unism is su¢ cient ly high, an incompet ent incumbent

may be willing t o go fart her t han a compet ent incumbent t o produce a

po-lit ical budget cycle.

To est ablish t his, we…rst int roducesome not at ion. Let gex t_t denot e t he

vis-ible budget it ems for which t he t empt at ion t o signal of a non-opport unist ic,

compet ent , incumbent becomes zero (and beyond which ext reme t he t

emp-t aemp-t ion becomes negaemp-t ive), T (gext

t ; g¤t(®t¡ 1; ®t) j ®t = ®; K = 0) = 0.

an incompet ent , opport unist ic incumbent t o pick g_tex t and gain a reput at ion

of compet ency ½ = 1 is exact ly zero, T( gtext; gt¤(®t¡ 1; ®t) j ®t = ¡ ®; K =

Kex t_{) = 0.}

The following condit ion will imply t hat het erogeneit y d = K is high:

K > Kext (17)

For high het er ogeneit y K > Kext, we now show t hat only a part ially

pooling equilibr ium exist s. There is a simple int uit ion behind t he solut ion:

a non-opport unist ic incumbent is not willing t o dist ort economic policy for

elect oral gain. I n part icular, a non-opport unist ic incumbent t hat is

compe-t encompe-t accompe-t s compe-t o maximize social welfare, so icompe-t is only willing compe-t o signal as far as

t he cyclical dist ort ion is smaller t han t he posit ive wealt h e¤ect .

Let t he signal gs

t in (15) be de…ned by t he condit ion t hat T(gst; gt¤(®t¡ 1; ®t) j

¡ ®; K ) = 0. Consider …rst t he non-opport unist ic t ypes. A compet ent

incum-bent will prefer g¤

t(®t¡ 1; ®) t o gst because it s t empt at ion t o signal is negat ive

at gs

t > gtext. On t he ot her hand, an incumbent who is incompet ent never

deviat es from g¤

t(®t ¡ 1; ¡ ®).

Consider now opport unist ic t ypes. A compet ent incumbent will be willing

t o signal gs

t, while an incompet ent will by const ruct ion prefer not t o signal. I t

remainst o show what an incompet ent , opport unist ic, incumbent will act ually

do. Given assumpt ion (17), one can always assure t hat t here is a probabilit y

g_t¤(®t¡ 1; ®) .6 Moreover, for a large enough K one can assure t he equilibrium

will be in pure st r at egies (¸ = 1).

For low het erogeneity K Kext_{, a separat ing equilibrium exist s. At t he}

separat ing signal gs

t where an incompet ent , opport unist ic, incumbent is just

indi¤erent between t hat and g_t¤(®t¡ 1; ¡ ®), compet ent incumbent s are willing

t o send separat ing signal. Behavior in (15) collapses t o signals in (7) , where

compet ent incumbent s pick g_ts¸ g_t¤(®t¡ 1; ®).7 Consequent ly,

Pr op osit ion 2 Assume infor mation on competency and on oppor tunism is

asymmet ric. I f heterogeneit y in oppor tunism is low, a separating equilibr ium

exists. I f heterogeneity is high, a separating equilibr ium does not exist . The

equilibr ium is par tially pooling, and opport unistic incumbents engage in a

political budget cycle.

I t is not problemat ic t o just ify t hat opport unism may be high, since t he

idea t hat t he driving force of polit icians is t o win elect ions is a classic in

polit ical science (Schumpet er, 1942; Downs, 1957). What may be

problem-at ic is t he idea t hproblem-at some incumbent s are non-opport unist ic. Nevert heless,

t he crucial point for t he result s in Proposit ion 2 is not t hat t here be

nonopport unist ic incumbent s, but rat her t hat nonopport unism be su¢ cient ly het

-6_{The gain from signaling can be made arbit rarily close t o B (g}s t; g

¤

t(®t ¡ 1; ®t) j K ) if ¸ is

su¢ cient ly low, because ½will t end t o 1, while t he cost C(g¤_t( ®t ¡ 1; ®); g_t¤(®t ¡ 1; ¡ ®) j ¡ ®)

is lower t han C(gst; gt¤(®t ¡ 1; ¡ ®) j ¡ ®).

7_{There is a separat ing equilibrium over t he int er val K 2 [0; K}ex t_{] , but over a cert ain}

int erval of kicks t o t he left of Kex t _{t here is also a part ially pooling equilibr ium (det ails}

erogeneous.8

No pooling equilibrium is possible, because a non-opport unist ic,

incom-pet ent , incumbent which will always choose g¤

t(®t¡ 1; ¡ ®) . By applicat ion of

t he Cho-Kreps int uit ive crit erion, one can also rule out a part ially pooling

equilibrium where all ot her t ypes of incumbent s pick g_t¤(®t¡ 1; ®). To est ablish

t his, Figur e3 depict s t he indi¤erence curves t hat go t hrough g_t¤(®t¡ 1; ®). The

indi¤erence curves are derived by di¤er ent iat ion of T (g_ts; g_t¤(®t¡ 1; ®t) j ®t; K ) ,

for incumbent s of t ypes (®; 0) , (®; K ), and (¡ ®; K ).

< please insert Figure 3 about here>

This part ially pooling equilibrium would not resist t he deviat ion by an

opport unist ic, compet ent incumbent , t hat would be willing t o go beyond t he

signal g_t t hat assures an opport unist ic, incompet ent incumbent a reput at ion

of compet ency ½_t = 1. Figure 3 shows t he speci…c case where het er ogeneit y

is high, so an opport unist ic incumbent t hat is incompet ent is willing t o go

fart her t o signal high compet ency t han a non-opport unist ic incumbent t hat is

compet ent . This implies t hat no separat ing equilibrium exist s eit her. Rat her ,

t her e is a part ially pooling equilibrium as charact er ized in Proposit ion 2.

8_{Unlike t his paper , wher e elect ions are probabilist ic so t he incumbent has an incent ive}

E. W elfar e E¤ ect s of Cy cles

The welfare propert ies of budget cycles under twodimensional asymmet

-ric informat ion can be charact erized very neat ly when one of t he types is

non-opport unist ic. The sign of t he welfare e¤ect s revolve around whet her a

separat ing equilibrium exist s or not .

Pr op osit ion 3 Assume there is two dimensional asymmetric infor mat ion.

I f there is a separating equilibrium, political budget cycles are welfare

enhanc-ing. I f no separating equilibr ium exist s, political budget cycles are welfare

reducing.

Pf. (i) A non-opport unist ic, compet ent incumbent behaves like a

benev-olent social planner. T his type signals in t he range where signaling cost s

are negat ive (t he posit ive fut ure wealt h e¤ect s for vot ers out weigh t he

cur-rent cyclical dist ort ion), so cycles are welfare enhancing. This only holds

for signals g_ts t hat correspond t o K Kext, t he int erval where a separat ing

equilibrium exist s. (ii) If K > Kex t, no separat ing equilibrium exist s. There

is a part ially pooling equilibrium where opport unist ic incumbent s dist ort t he

pr ovision of visible public goods. In case t hey are compet ent , t his dist ort ion

reduces welfare because signaling cost s are posit ive (t he posit ive wealt h

ef-fect is smaller t han t he cyclical dist or t ion). I n case t hey are incompet ent ,

signaling cost s are posit ive because a negat ive wealt h cost is added t o t he

According t o Pr oposit ion 3, cycles reduce welfare when no separat ing

equilibrium exist s. This is not equivalent t o demonst rat ing t hat elect ions

as such reduce welfare. Elect ions comprise bot h a policy bias and a

selec-t ion e¤ecselec-t (Lohmann, 1998). T he currenselec-t welfare loss selec-t haselec-t opporselec-t unisselec-t ic

incumbent s produce t hrough cycles is t he policy bias, t hat is not present in

o¤-elect ion per iods.9 However, elect ions have a select ion e¤ect , since t hey

pr ovide t he opt ion of changing t he incumbent . I n expect ed value, t he

elec-t oral opelec-t ion has a posielec-t ive wealelec-t h e¤ecelec-t , since ielec-t allows elec-t o replace incumbenelec-t s

t hat are incompet ent .10 The policy bias may be dominat ed by a select ion

e¤ect , so t he net welfare e¤ect of elect ions is ambiguous (Lohmann, 1998,

Proposit ion 4). Since t he policy bias is increasing in t he degree of het

ero-geneit y in opport unism, t he posit ive e¤ect of elect ions is less likely t he higher

t he degree of het erogeneit y.

9_{Opport unist ic incumbent s produce t he bias, which amount s t o an expect ed}

wel-fare loss of sf r [u¤t (®t ¡ 1; ®) ¡ ut(gs; ("t ¡ gs) (1 + ±) j ®)] + (1 ¡ r )[u¤t (®t ¡ 1; ¡ ®) ¡

ut(g¤( ®t ¡ 1; ®); ("t ¡ g¤(®t ¡ 1; ®))(1 + ±) j ¡ ®) ]g.

1 0_{Expect ed ut ilit y in period t + 1 aft er elect ions in a part ially pooling equilibrium depends}

on t hree possible scenarios: t here is a separat ing signal gst t hat leads t o probabilit y p(1) of

reelect ing a compet ent in sr of t he cases; t here is an int er mediat e signal g¤t( ®t ¡ 1; ®) t hat

wit h probabilit y p(x ), where x = _{( 1¡ s) r + ¸ s( 1¡ r )}( 1¡ s) r , leads t o r eelect a compet ent in (1 ¡ s)r of t he cases, and an incompet ent in s(1¡ r ) of t he cases; and t her e is a low signal g¤

t(®t ¡ 1; ¡ ®)

t hat wit h probabilit y p(0) leads t o reelect an incompet ent in (1 ¡ s)(1 ¡ r ) of t he cases. Expect ed ut ility in period t + 1 if t her e ar e no elect ions is based on t he probabilit ies (r ; 1 ¡ r ) t hat incumbent is compet ent or not . Doing t he algebra, t he expect ed ut ilit y next per iod of t he elect or al opt ion of reelect ing t he incumbent is posit ive because of t he higher probabilit y of replacing incumbent s wit h below average compet ency: ( 1 ¡ r ) r f E [u¤

t + 1 j

I I I . C oncept ual Fr am ewor k

We now brie‡y review some of t he concept ual aspect s underlying t he model.

A . A sym m et r ic I nfor m at ion on O ppor t unism

Het er ogeneit y along t he dimensions of compet ency and charact er is quit e

widespread. For inst ance, Covey et al. ( 1995, pp. 240-1) focus on t he

import ance of bot h compet ency and charact er for business organizat ions.

They also give more homely examples, such as want ing physicians t o be

compet ent , t o give us t he right t reat ment , and honest , t o not prescribe a

cost ly t reat ment we do not need. T he issue of het erogeneity in honesty has

been alr eady explored, among ot her areas, in t he lit erat ure on corrupt ion

(e.g. Weinschelbaum, 1998) and governance (e.g. Dixit , 2001).

The assumpt ion about asymmet ric informat ion on opport unism springs

nat urally from t he fact t hat opport unism charact erizes preferences.

Prefer-ences are subject ive. As argued at t he beginning of t he paper, opport unism

is not direct ly observable. One has t o infer an individual’s charact er from

t he act ions t he individual t akes. Act ions reveal preferences.

B . Signaling in Sp ence

The pr esent signaling model is a variat ion of Spence (1973). The

princi-pals here are vot ers, r at her t han …rms. T he agent s are polit icians, rat her

educat ion.

Riley (2001) consider s an ext ension of t he original Spence model from two

types of agent s t o four types of agent s. This resembles our two-dimensional

asymmet ric informat ion framework, wher et here also are four t ypes of agent s:

compet ent and incompet ent incumbent s, which can be opport unist ic or not .

However, t heresult s of our t wo-dimensional asymmet ric informat ion

frame-wor k di¤er sharply from Riley’s analysis of Spence. Riley considers t he e¤ect

of “ noise” . He shows t hat t he separat ing equilibrium of t he Spence signaling

model breaks down if some unproduct ive workers have low signaling cost s

(in t erms of years of formal educat ion) , while some product ive workers have

high signaling cost s. He shows t hat , in t hat case, no obvious alt ernat ive

equilibrium exist s. Unlike t he Riley model, here t here is a sharply de…ned

part ially pooling equilibrium. The reason is t hat t he signaling cost s of t he

four t ypes of agent s di¤er.

I f one were t o apply t he present framework t o t he case of labor mar ket s,

it would roughly run as follows. T he di¤erences in charact er imply t hat

t he t ast e for st udy, or perhaps t he desire t o achieve social recognit ion, can

vary (in our discret e example, t hey would be eit her high or low). This t rait

is independent from t he fact t hat highly compet ent individuals have lower

cost s of complet ing formal educat ion. An applicat ion of t hisframework t o t he

Spence signaling model, in t he presence of high het erogeneity in charact er ,

will lead t o a part ially pooling equilibrium where very compet ent individuals

t her e will be t ypes wit h low compet ence and low mot ivat ion. In t he middle,

t he mix of compet ent individuals, and of hard-dr iven individuals t hat want

t o succeed, would be di¢ cult t o t ell apart . Ext reme t ypes would st ill send

unequivocal signals.

C. L ow V isibilit y as D iscr et ion

In t he paper, t he incumbent can successfully manipulat e t he budget because

of t he fact t hat some budget it ems are not visible before elect ions.

A possible int er pret at ion of low visibilit y is as a measure of t he

discre-t ionar y power vesdiscre-t ed in discre-t he execudiscre-t ive branch. Decisions discre-t hadiscre-t need discre-t he audiscre-t

ho-rizat ion of congress can be expect ed t o be much more visible t han decisions

t hat can be solely decided by t he execut ive power. I f low visibility is a

measure of t he discret ion enjoyed by t he execut ive in unilat erally deciding

…scal policy, a variable ® 2 ( 0; 1] can be used as an index for t he degree of

discret ion:

gt +

1 ¡ ® ®

°_{t+ 1} 1 + ±= "t (18)

I n t he paper, we assumed t hat less visible it em °_{t+ 1} fell by 1 + ± when

visible it ems gt incr ease by one unit , which would correspond t o ® = 1=2.

As ® approaches one, on t he ot her hand, all budget it ems t end t o become

visible, so d°_{t + 1}=dgt = ¡ [®=(1 ¡ ®)](1 + ±) t ends t o minus in…nit y, and t he

t her efore be t o reduce t he discret ion of t he execut ive.11

The degree of discret ion depends on t he inst it ut ional framework. The

discret ion of t he U.S. president is small and subject t o a large cont rol of

congress, when compared t o t he parliament ary syst em in Europe where t he

execut ive has quasi-legislat ive powers (cf. Carey and Shugart , 1998).

The di¤erences in t hediscret ion t hat t heexecut ive enjoys can help explain

why Alesina, Roubini, and Cohen (1997, chaps. 4 and 6), observe t here is no

recent evidence of opport unist ic cycles in t he U.S., specially aft er 1980 when

many federal t ransfer programs in t he U.S. have become mandat ory by act s

of Congress so t hey cannot be easily manipulat ed for shor t r un purposes. In

cont rast , opport unist ic cycles are present in ot her OECD count ries.

Lat in America st ands in even st arker cont rast t o t he U.S. experience.

Lat in America followed t he lead pioneered by t he U.S. of a division of powers

à la M ont esquieu, but in pract ice t here has been a concent rat ion of

quasi-legislat ive powers in t he hands of t he pr esident . The degree of execut ive

discret ion is subst ant ial (Carey and Shugart , 1998). Since t he st udy by

Ames (1987), t here is also ample evidence of budget cycles in Lat in America.

M ore generally, budget cycles are especially st rong among developing

count ries (Drazen, 2001). These di¤erences in out comes may re‡ect

dif-ferences in inst it ut ional st ruct ures of t he type out lined here.

1 1_{A not her is t o impose t erm limit s. However, t er m limit s t hat rule out reelect ion not}

D . A dver se Select ion in Polit ics

It is somet imes said t hat t he worst , least scrupulous people are select ed by

t he polit ical process. However, t he issue of lemons in polit ics, like lemons in

market s, can be expect ed t o depend on t he inst it ut ional st ruct ure.

I n t he speci…c case of RPBC, if one int erpret s low visibilit y as high

discre-t ionalidiscre-t y, more oppordiscre-t unisdiscre-t ic incumbendiscre-t s increase discre-t heir chances of polidiscre-t ical

survival when t he execut ive is given a lot of short -run leeway on budget ary

mat t ers. T his is det riment al because it leads t o reward t he wr ong t ype of

incumbent s. I f t here were no room for cycles, vot ers would be able t o t ell

compet ent and incompet ent incumbent s perfect ly apart , cont rary t o what

happens in t he part ially pooling equilibrium of Proposit ion 2.

Polit ical hist ory oft en seems t o be a long succession of dominance by t he

most rut hless individuals. For inst ance, t he assassinat ions carried out by

feudal lords and princes in Europe t o impose t heir power, or cont emporary

rulers like Sadam Hussein, who dist inguished himself by his violent charact er ,

wor king his way up t o head t he secret police in I rak before st aging a coup

t hat put him in power. These cases of adverse polit ical select ion would

almost cert ainly not have not made it t o t he t op in a syst em wit h more

rest rict ive rules such as t he U.S., or, for t hat mat t er, in most any of t oday’s

const it ut ional democr acies.

The Federalist not es t hat we are governed by men, not angels, so we must

design polit ical inst it ut ions t aking t hat int o account . This paper marks t he

cases. I nst it ut ions can in fact det ermine which t ypes ar e most successful in

t he polit ical arena.12

I V . Conclusions

Previous lit erat ure on RPBC implicit ly assumes t hat vot ers know t he

in-cumbent ’s exact degree of opport unism, so as t o …gure out just how far t he

incumbent is willing t o go t o get reelect ed. T his paper considers a more

general set up wher e t here is het erogeneit y and asymmet ric informat ion on

opport unism.

I n t he Rogo¤ vein, we model t he polit ical cycle in t erms of …scal policy.13

This paper considers only two t ypes of compet ency and of opport unism. Wit h

high het erogeneity in opport unism, t wo-dimensional asymmet ric informat ion

dest roys t he separat ing equilibrium charact er ist ic of earlier models. I n it s

place, t here is a part ially pooling equilibrium wher e cycles are caused by

highly opport unist ic incumbent s, regardless of t heir compet ence. T he welfare

implicat ions of RPBC are less favorable because t he informat iveness of cycles

is r educed.

Empirically, t here is a cr it erion t o dist inguish whet her cycles lead or not

t o a separat ing equilibrium. The observat ional di¤erence is t hat in a

par-1 2_{Caselli and Morelli (2001) endogeneize t he ent r y int o polit ics, st udying precisely t he}

issue of what det er mines t he mix of compet ency and honest y of elect ed o¢ cials.

1 3_{The st or y in t erms of act ive monet ary policy would be quit e similar. However, Drazen}

t ially pooling equilibrium vot ers can be surprised aft er elect ions, while in a

separat ing equilibrium t hey always foresee t he correct level of compet ency.

Though indeed vot ers are apt t o be disappoint ed by whom t hey vot ed, t he

reason for developing t his ext ended set up is t heoret ical: t he fact t hat t he

incumbent ’s preferences, t he springs and wells of act ion, are not direct ly

observed by vot ers.

This signaling model implies a variant of Spence ( 1973). Though t he

equilibrium is no longer separat ing, signaling is resilient t o t heint roduct ion of

asymmet ric informat ion in t wo dimensions. I n t hemiddle ground it is di¢ cult

t o t ell di¤erent types apar t , but going t o ext r emes leads t o single oneself out .

The probabilit y of high compet ency is t hus monot onically increasing in t he

signal.

The dist inct ion between visible and non-visible budget it ems t hat is at t he

root of t he budget cycle can be relat ed t o t he degree of discret ion enjoyed

by t he execut ive. I n t his sense, t he U.S. Congress st ands out for having

subst ant ially curbed t he discr et ion of t he President , which may help explain

why t he impact of opport unist ic cycles seems t o have disappeared in recent

years. The inst it ut ional st ruct ure can be specially import ant t o det ermine

R efer ences

[1] Akerlof, George. “ The market for ‘Lemons’: Qualit y uncert ainty and

t he market mechanism.” Quar ter ly Jour nal of Economics, August 1970,

84( 3), pp. 488-500.

[2] Alesina, Albert o; Roubini, Nouriel and Cohen, Gerald. Political Cycles

and the Macroeconomy. Cambridge: MI T Press, 1997.

[3] Ames, Barry. Political Sur vival. Polit icians and Public Policy in Latin

Amer ica. Berkeley: University of California Press, 1987.

[4] Carey, John M . and Shugart , Mat t hew S., eds. Executive Decree

Au-thor it y. Cambridge: Cambridge University Pr ess, 1998.

[5] Caselli, Francesco, and Morelli, M assimo. “ Bad polit icians.” Working

Paper, NBER, Oct ober 2001.

[6] Covey, St ephen; Merill, Roger and M er ill, Rebecca. Fir st T hings Fir st .

New York: Simon and Schust er, 1995.

[7] Dixit , Avinash. “ On models of economic governance.”

Pr esident ial Addr ess t o t he Economet ric Society Meet ings

(ht t p:/ / www.princet on.edu/ ~dixit ak/ home/ govmodes.pdf ), 2001.

[8] Downs, Ant hony. An Economic Theor y of Democracy. New York:

[9] Drazen, Allan. “ The polit ical business cycle aft er 25 years.” NBER

Macroeconomics Annual. Fort hcoming, 2001.

[10] Lohmann, Susanne. “ Rat ionalizing t he polit ical business cycle: A

workhorse model.” Economics and Politics, March 1998, 10(1), pp. 1-17.

[11] Nordhaus, William. “ The polit ical business cycle.” Review of Economic

Studies, April 1975, 42(2), pp. 169-90.

[12] Persson, Torst en, and Guido Tabellini. Macroeconomic Policy,

Credibil-ity and Politics. Chur: Harwood Academic Publishers, 1990.

[13] Persson, Torst en, and Guido Tabellini. “ Polit ical economics and

macroe-conomic policy,” in John B. Taylor and Michael Woodford, eds.,

Hand-book of Macroeconomics, 1C. Amst erdam: Nort h Holland, 1999.

[14] Riley, John. “ Silver signals: 25 years of signaling and screening.” Journal

of Economic Literature, June 2001, 39(2), pp. 432-78.

[15] Rogo¤, K ennet h. “ Equilibrium polit ical budget cycles.” Amer ican

Eco-nomic Review, March 1990, 80(1), pp. 21-36.

[16] Rogo¤, Kennet h and Sibert , Anne. “ Elect ions and macroeconomic policy

cycles.” Review of Economic Studies, Januar y 1988, 55(1), pp. 1-16.

[17] Schumpet er, Joseph A. Capitalism, Socialism and Democracy. New

[18] Spence, Michael. “ Job market signaling.” Quar ter ly Jour nal of

Eco-nomics, August 1973, 87(3), pp. 355-379.

[19] St ein, Ernest o and St r eb, Jorge. “ Elect ions and t he t iming of

devalua-t ions.” Working paper, Universidad del CEMA, 1999.

[20] Tuft e, Edward. Polit ical Control of the Economy. Princet on: Princet on

Universit y Press, 1978.

[21] Weinschelbaum, Federico. The Tr iangle of Cor ruption. Ph.D. dissert

γγt+1 gt

Timing with asymmetric information on competency

εεt gt elections observed

Figure 1:

Deviations from Pooling Equilibrium gt(ααt-1,αα)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4

Visible expenditure gt

p(gt)

incompetent

competent

gts

g_t(α_t-1,α)

Deviations from Partially Pooling Equilibrium gt*(ααt-1,αα)

0 0.2 0.4 0.6 0.8 1 1.2 1.4

5.2 5.6 6 6.4 6.8 7.2 7.6 8

Visible expenditure gt

p(gt)

incompetent opportunistic

competent opportunistic

competent non-opportunistic

gts

gt*(αt-1,α)