Pole Con Growth

8/12/2019 Pole Con Growth

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This revision: August 2012

Growth and fiscal policy: a positive theory

Abstract

We present a political economy theory of growth in which the government affects the growth rate both di-rectly through public investments in infrastructure, and indirectly through the effect of taxation on learningby doing. Policy choices are made by a legislature consisting of representatives elected by geographically-defined districts. The legislature can raise revenues via a discretionary income tax and by issuing public

debt. We study the equilibrium relationship between the dynamics of debt and the growth rate of theeconomy. We use the model to study the impact of an austerity program! in which a country is forcedto reduce the debt"#$P ratio. To quantify these effects, the model is calibrated to the %.&. economy.

'evon (arseghyan$epartment of )conomics*ornell %niversity+thaca /012

lb3/45cornell.edu

6arco (attaglini$epartment of )conomicsPrinceton %niversityPrinceton 7 801//mbattagl5princeton.edu

For useful comments and discussions we thank Alberto Alesina, Marco Bassetto, Stephen Coate, Guido Tabelliniand the participants to the 2012 emmers pri!e conference, the "th CS#F$%G%#& S'mposium on #conomics and%nstitutions, and 2012 B#& Summer %nstitute(


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1 Introduction

The rapid deterioration of the fiscal position of the U.S. federal government in the aftermath of the

great recession of 2008 has brought the spotlight on the long term effect of public debt on the real

econom. !ederal debt in the U.S. is currentl its highest level since the decade follo"ing #orld

#ar $$. %oncerns over the gro"th of public debt has led to the &udget %ontrol Act of 2011 that

"ill trigger automatic across'the board cuts in spending if a deficit reduction bill of at least 1.2

trillions is not passed b (anuar 201). !or the U.S. *and for all other countries "ith high levels

of debt1 + the ,e -uestions are: To "hat etent do high levels of public debt permanentl reduce

the gro"th potential of the econom/ Are austerit programs effective in reducing debt3

and in increasing gro"th potential and "elfare/ 4o" should the be designed/

To ans"er these -uestions "e need a theor in "hich gro"th and fiscal polic are 5ointl de'

termined in e-uilibrium. The literature on gro"th6 ho"ever6 has traditionall been more focused

on the private sector6 emphasi7ing the role of entrepreneurial innovation and technological ad'

vancement. #ith fe" notable eceptions6 fiscal polic has been ignored or assumed as eogenous.

ven in the research that has eplicitl considered a role for the government6 public polic is

assumed to balance the budget in ever period and public debt is not studied. 9et6 fiscal polic

has changed in important "as during last four decades6 "ith potentiall significant implicationsfor macroeconomic outcomes *see !igure 1+. $n the post ##$$ era6 after bottoming at around

2; of 3 during the seventies6 the debt level in the U.S. has been steadil increasing over time6

surpassing


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1970 1980 1990 2000 2010

30

40

50

60

70

80Federal Debt, % of GDP

actual

estimate

1970 1980 1990 2000 2010

1

2

3

4

5

Public Investment and R&D, % of GDP

Public Investment

Public R&D

1970 1980 1990 2000 20108

10

12

14

16

18

20

Tax Revenue, % of GDP

Total

Net of Social Security

1970 1980 1990 2000 2010

4

6

8

10

12

Public Goods, % of GDP

Total

Net of Defense

!igure 1: !iscal trends in the U.S. econom.

representatives in the legislature have incentives to vote for policies that favor their o"n con'

stituencies and citi7ens benefit onl partiall from local public goods provided to constituencies

to "hich the do not belong. The level of public debt and the level of productivit in the econom

are state variables and create a dnamic lin,age across polic'ma,ing periods. #e use the model

to provide a positive theor of gro"th and fiscal polic and to evaluate the normative effects of

austerit programs that limit the abilit of the government to issue debt. Since our theor is

designed as a model for a large closed econom6 "e calibrate it to the U.S. econom to assess its

predictions -uantitativel.

Starting from an initial state6 the econom in our model converges to"ard a balanced gro"th

path in "hich consumption6 public investment6 public good provision6 public debt and productivit

gro" at the same constant rate. Under standard assumptions6 on the balanced gro"th path the

debt'to'3 ratio is positive and the gro"th rate of the econom is ine?cientl lo". The

transition to the balanced gro"th path is characteri7ed b "hat "e call the shrinking government

2


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effect: public debt gro"s faster than 36 provision of public goods and infrastructure gro"s

slo"er than 36 and the ta rate declines. ffectivel6 as the econom converges to its balancedgro"th path6 a decreasing fraction of 3 is devoted to providing public services. These findings6

along "ith our calibration results6 are in line "ith the U.S. *!igure 1+.

The shrin,ing government effect is a conse-uence of the political distortion and its effect on the

interest rate. 3olitical distortions induce the ruling coalition@the coalition in the legislature that

controls fiscal polic@to use debt to shift the burden of taation to the future. $n ever period

the ruling coalition trades off an etra increase in public goods toda for their o"n districts6 "ith

a more than proportional reduction in public goods in the follo"ing period for all districts. The

former option is al"as more appealing because the ruling coalition can better target current e'

penditures to their o"n districts rather than the future ependiture. %onse-uentl6 debt increases6

forcing legislators to increase the primar surplus to service its cost. egislators find it optimal to

do this b reducing ependitures rather than increasing taes: #hen ependitures are reduced6

disposable income and savings increase6 and so the interest rate is held do"n. To the contrar6

"hen taes are increased6 disposable income and savings decline6 so the interest rate goes up.

An interesting implication of the shrin,ing government effect is that6 as debt3 increases6

the gro"th rate of the econom does not necessaril go do"n. This occurs because the decline in

taation ma induce an increase in labor suppl and6 hence6 in learning'b'doing. This finding

ma help eplain the evidence suggesting a non monotonic relationship bet"een debt and gro"th.3

The fact that there is not necessaril a monotonic relationship bet"een public debt and gro"th6

ho"ever6 should not be interpreted as a sign that debt has a limited impact on "elfare. $n our

model debt al"as reduces "elfare6 even if it does not reduce gro"th: the reduction in "elfare is

induced b the reduction in public services.

To stud ho" countries can limit the ine?ciencies in gro"th highlighted above6 "e stud

a simple but plausible tpe of an Bausterit program.C The program is characteri7ed b t"o

features6 a target level for debt and a time hori7on: The countr is re-uired to bring do"n debt

to a given target level over a given number of ears. Three findings emerge from this eercise.

!irst6 in our calibration6 austerit programs tpicall increase "elfare if the are not ecessivel

ambitious. Second6 there is no Bone'si7e'fits'allC austerit program: the optimal plan depends

on the fundamentals and on the initial state of the econom. The higher is the accumulated

3 See for e4ample &einhard and &oo5 620117, 8umar and 9oo 620107 and Checherita and &other 620107(

)


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level of debt6 the less aggressive the programs should be6 both in terms of the debt target and

in terms of duration. The third finding is that the gro"th rate is a poor measure of the successof the program. Dn the transition path of the optimal austerit program6 gro"th is belo" the

pre'austerit level6 but "elfare is increasing.

Dur paper is related to t"o strands of literature. !irst the literature on endogenous gro"th.

Eost of this research is normative and focused on evaluating the effects of taation on the capital

accumulation process rather than at eplicitl modelling polic ma,ing *Febelo G1HH0I6 Jing and

Febelo G1HH1I6 &arro G1HH1I6 Sto,e and Febelo G1HH)I6 (aimovich and Febelo G2012I+. 3ositive

theories of gro"th have been presented in the contet of the research studing the political econom

of redistribution. The basic idea developed in these papers is that income ine-ualit determines

ta polic and therefore gro"th *&ertola G1HH)I6 3erotti G1HH)I6 Saint'3aul and Kerdier G1HH)I6

Alesina and Fodri, G1HHLI6 3ersson and Tabellini G1HHLI6 Jrusell and Fios'Full G1HHHI6 &enabou

G2000I6 Saint 3aul G2001I+. A common trait of these theories *both normative and positive+ is

that fiscal polic is assumed to balance the budget in ever period and so public debt is ruled

out b assumption.4 Dur paper contributes to this endogenous gro"th literature in t"o "as.

!irst6 "e allo" for a richer polic space "ith public debt. Second6 "e propose an eplicit dnamic

model of political decision ma,ing in "hich rational for"ard loo,ing polic'ma,ers bargain for the

polic outcome. To do this6 "e focus on a smmetric model in "hich there is no redistribution

of "ealth bet"een citi7ens. Dur focus is on the e?cienc of policies.

The second strand of literature to "hich our paper is related is the research on the political

econom of public debt *3ersson and Svensson G1H8HI6 Alesina and Tabellini G1HH0I6 &attaglini

and %oate G2008I among others+. These models are specificall aimed at modelling public debt6

but the do not allo" for gro"th and ma,e assumptions that simplif the determination of the

e-uilibrium interest rate. These t"o issues are intimatel connected. The ,e assumption in

this literature is that preferences are -uasi'linear: in this case the e-uilibrium interest rate is

constant and independent of the chosen policies.5 &alanced gro"th6 ho"ever6 is not consistent

4 An e4ception is Saint$.aul 61::27 where the o*ernment can issue debt( The main result of this paper is thatdebt is not welfare impro*in( The paper is normati*e and does not present a theor' of public debt(

5 %n the conte4t of normati*e models in which policies are chosen b' a bene*olent planner, the strateic interac$tion between /scal polic' and interest rates has been /rst studied b' Stoke' and ;ucas 61:"


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"ith these preferences: this is "h modelling endogenous gro"th and the endogeneit of interest

rates simultaneousl is necessar. As "e sho" in this paper6 the endogeneit of interest rates iscrucial to understanding the dnamics of fiscal polic in large closed economies. A neoclassical

gro"th model in "hich the government can epropriate capital in the presence of political econom

frictions is presented b Aguiar and Amador G20106 2012I. ifferentl from our "or,6 this research

focuses on the case of a small open econom for "hich the interest rate is eogenous: because of

this it does not stud the interaction bet"een fiscal polic6 interest rates and political distortions

that is the primar ob5ective of our "or,. !inall6 there is a significant literature studing the

political econom of deficit reduction programs both theoreticall and empiricall.6 Mone of the

papers cited above has eplicitl studied the lin, bet"een debt6 fiscal polic and the endogenous

gro"th process.

The organi7ation of the remainder of the paper is as follo"s. Section 2 outlines the model.

Section ) characteri7ed the political e-uilibrium. $n Section L "e stud the dnamics of the model

using parameters calibrated to the U.S. econom. $n Section "e use the model to stud the

effect of an austerit program and "e stud ho" the optimal austerit program depends on the

environment. Section < concludes.

2 Model

The economy A continuum of infinitel'lived citi7ens live in n identical districts indeed b

iN 1,...,n. The si7e of the population in each district is normali7ed to be one. There is a single

nonstorable consumption good6 denoted bc6 that is produced using a single factor6 labor6 denoted

b l. There is also a set ofn local public goods6 denoted b N

ii6 that can be produced

from the consumption good. The variables at timet "ill be denoted "ith a subscriptt. #e "ill

stud e-uilibria in "hich all agents from the same district j ma,e the same economic choices.

The citi7ens en5o the consumption good6 benefit the local public goods6 and suppl labor.!or most of the paper "e assume that each citi7en=s preferences in district i are represented b

6 Amon theoretical contributions we ha*e Alesina and -ra!en 61::17, Grilli and -ra!en 61::


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the follo"ing per period utilit function:

u*ct, lt, t+ N log *ct*1 lt++ O 0 log

it

jjt1

, *1+

"here >06 0> 0 and G0, 1I. This utilit describes a situation in "hich district i en5os a

direct benefit from public good i6 but there ma also be an eternalit from *the sum of+ public

goods provided to other districts. The parameter measures the si7e of this eternalit: the

closer is to one6 the smaller are the eternalities and the more i benefits onl the citi7ens in

district i. Since *1+ is a variation of the standard Jing6 3losser6 Febelo G1H88I utilit function

augmented for public goods6 "e "ill refer to it as J3F.7 %iti7ens discount future per period

utilities at rate .

All local public goods are produced from the consumption good according to a linear technolog

"ith marginal rate of transformation e-ual to one. The consumption good at timet is produced

"ith the linear technolog ctN ztlt. The variable ztis interpreted as an econom "ide productivit

factor6 such as human capital. 3roductivit ma increase because of learning'b'doing in the

private econom and because of direct public investments6 It *such as ependiture on research

and development6 education6 public infrastructure6 and other productivit enhancing investments+.

Specificall6 "e assume:

zt+1N *lt+ *It/zt+ zt, *2+

"here lt Nj

ljt/n is the average labor suppl6 *lt+ N 0 *lt+1 and *It/zt+ N 0 *It/zt+

1

are concave functions "ith i6 i > 0 for i N 0, 1 and 16 1 < 1. The function describes

the process of learning'b'doing: the more citi7ens "or,6 the more the learn from each other

and more productive the "ill be in the future. The function describes the benefits of public

investment: The higher is public investment6 the higher is the net period productivit. The

scaling b 1zt is standard to ensure that public investment as a fraction of output does not

shrin, to 7ero over time: $n a gro"ing econom6 the higher is productivit6 the more epensive itshould be in absolute terms to improve it.8

There is a competitive labor mar,et: thus the "age rate at t is e-ual to zt. There is also

a mar,et in ris,'free6 one period bonds. &oth citi7ens and the government have access to this

7 9e will e4tend the anal'sis to alternati*e utilit' functions in Section >(2 where we stud' how wealth e5ectsshape the e?uilibrium beha*ior(

8 9ithout loss of eneralit' we could ha*e speci/ed the econom' wide le*el of producti*it' as a product ofhuman capital, h, and public infrastructure, @ zt+1 ht+1@t+1, with ht+1 lt3ht and @t+1 It/zt3 @t.


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mar,et. The assets held b an agent in district j in period t "ill be denoted ajt . The gross

interest rate is denoted t: a dollar "orth of bonds at time t ields t at time t O 1.

Public Policies The government provides local public goods6 public infrastructure and can

ma,e direct monetar transfers to the districts. Eonetar transfers are uniform across districts

and are interpreted as a "elfare program smmetricall targeted to all regions. Fevenues are

raised b leving a proportional ta on labor income and the can be supplemented b bor'

ro"ing and lending in the bond mar,et. overnment polic in an period t is described b

{t, t, it ,....,

nt,It, Tt}6 "heret is the income ta rateP

t is the amount of bonds soldP

it is the

amount of public good provided to district iP It is the level of infrastructure investmentP and Tt isthe uniform transfer. #hent is negative6 the government is buing bonds. $n each period6 the

government must also repa the bonds that it sold in the previous period "hich are denoted b

t. The government=s initial debt level in period 1 is 06 agents initial assets are aj0N a0N

0n

.

overnment policies must satisf three feasibilit constraints. !irst6 ta revenues and net

borro"ing must be su?cient to cover public ependitures. To see "hat this implies6 consider

a period in "hich the initial level of government debt is t and the interest rate is t. Total

ependiture is

jjt OItO TtO t6 ta revenue is tztj

ljt 6 and revenue from bond sales is

t/t. So the government budget condition is:

t t

tO

j

jt OItO Tt tztj

ljt

0. *)+

Second6 to ,eep the polic space compact in the legislator=s maimi7ation problem6 "e assume that

local public goods6 public investment and transfers as fractions of 3 can not be smaller than

some minimal levels: It/yt I6 it/yt g andTt/yt T for all i6 "here I06 g >0 and T0.

The lo"er boundTis interpreted as commitments on transfers ta,en in previous legislations that

are not directl modelled here *as for eample Social Securit6 Eedicare and Eedicaid+. Third6the feasible debt6 relative to 36 is bounded: t/yt

b, b

. This constraint rules out 3on7i

schemes and re>ects the fact that if debt6 relative to 3 is too high6 then the government "ill

not be able to repla it.

Market equilibrium and political decision making Using the first order necessar condi'

tions for a citi7en=s problem6 labor and consumption choices in district i at time t can be repre'

Q


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sented as functions of the policies and net savings ait ait+1/t. $n the follo"ing "e "ill stud a

smmetric e-uilibrium in "hich ai

t N at as "ell as ci

t N ct andli

tN lt for an district i. Since foran given government polic the interest rate must clear the mar,et for one period bonds6 in such

an e-uilibrium "e have at at+1/t N 1n

*t t+1/t+. Using *)+ and households= optimalit

conditions "ith respect to consumption and labor6 "e can therefore epress the citi7ens= choices

as functions of current public policies onl. $t is useful to epress all the variables in terms of

3. efine git Nit/yt6 It NIt/yt, Tt NTt/yt andpt N

,

gjt

j

, It, Tt

. abor suppl can

then be "ritten as l *pt+6 "here:

l*pt+ N 1 t

1 1n

ItO

jgjt

O 1 t. *L+

%onsumption can be "ritten as c*pt, zt+ N ztc*pt+6 "here:

c*pt+ N*1 t+

1 1

n

ItO

jg

jt

1 1n

ItO

jg

jt

O 1 t

. *+

These epressions allo" us to "rite citi7en i=s utilit function onl as a function of current public

policies and the level of productivit:

u*pt, zt+ N *1 O 0+log ztO U*pt+ O 0log git

jgjt

1

, *ict in the legislature.

9 See Appendi4 )(2 for details(

10 ote that from 23 we ha*e z l3 I/z3 z, so normali!in Ib'y , we ha*ez Zp3z as noted in the te4t(

8


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overnment polic decisions are made b a legislature consisting of representatives from each

of the n districts. Dne citi7en from each district is selected to be that district=s representative.Since all citi7ens have the same polic preferences6 the identit of the representative is immaterial

and hence the selection process can be ignored. The legislature meets at the beginning of each

period. To describe ho" legislative decision'ma,ing "or,s6 suppose the legislature is meeting at

the beginning of a period in "hich the current level of public debt is bt. The process has t"o

phases: government formation and bargaining in the government.11 $n the first phase6 one of the

legislators is randoml selected to form a government6 "ith each representative having an e-ual

chance of being recogni7ed. A government is a cabinet ofG representatives and a polic platform

{bt, t, "t, It, Tt}, "here "t is the aggregate amount of public goods. $n the second phase6 the

cabinet members allocate the local public goods. The initial government formateur proposes

a provisional distribution of the local public goods

gjt

j

. $f the first proposal is accepted b

# G cabinet members6 then it is implemented and the legislature ad5ourns until the beginning

of the net period. At that time6 the legislature meets again "ith the difference being that the

initial level of public debt is bt and productivit is given b *2+. $f6 on the other hand6 the first

proposal is not accepted6 another member of the government is chosen to propose an alternative

redistribution ofgjtj . The process continues until a proposal is approved b the cabinet. #e

assume that each proposal round ta,es a negligible amount of time.12

3 The political equilibrium

&efore "e characteri7e the political e-uilibrium in the econom described in the previous section6

it is useful to highlight the ,e determinants of gro"th in our econom. Dn a balanced gro"th

path "e should epect income6 consumption6 investment to gro" at the same constant rate $ and

per capita productivit and the real interest rate to remain constant. $n an econom "ith a non

trivial public sector "e should also epect public ependiture to gro" at the same rate as the11 A similar barainin process in which /rst a formateur selects the o*ernment and then the cabinet members

barain o*er the allocation of taretable transfers is presented b' Baron and -iermeier 620017( %n Baron and-iermeier 620017 the barainin phase consists in a take it or lea*e it o5er with a status ?uo polic' in case a?uali/ed maorit' in the o*ernment is not reached(

12 =ur barainin process i*es as special cases man' barainin processes used in the political econom' literature(9hen G 1 the polic' is chosen b' a randoml' selected dictator who ma4imi!es his own utilit' as in Alesina andTabellini 61::07( As we will show, whenG > 1 and q G the polic' is chosen to ma4imi!e the areate utilit' ofa coalition of si!e G as in Battalini and Coate 620127( 9hen G q n, the polic' coincide with the utilitarianoptimal polic'(

H


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private econom6 and ta revenues to be a constant fraction of income:13

R

NRII

NRTI

N$6 RN 0. *8+

Using these conditions6 it is eas to see that in our econom *L+'*Q+ impl that the gro"th rate of

all the ,e variables is determined b the gro"th rate of productivit: $ N Rz/z. ven before

"e start studing political decision ma,ing6 "e can see the role of fiscal polic on $. !rom *2+6

in the stead state "e have:

$NRz

z N!*p+ 1, *H+

"here6 as defined above6!*p+ N*l*p++ *I nl*p++. The gro"th rate is a function of the primitivesof the econom and of public policies. This is not in itself a ne" observation6 since it has been

long recogni7ed that in endogenous gro"th models public policies have a long term effect on the

gro"th rate *see Febelo G1HH1I+. The interesting point is that6 in our model6 eplaining fiscal

polic is necessar to obtain anendogenoustheor of gro"th.

%ondition *H+ leaves t"o open -uestions. !irst6 "hat determines the long run fiscal polic6 and

hence the gro"th of the econom on the balanced gro"th path/ As it can be seen from *H+6 this

econom ma have either positive or negative gro"th in the stead state6 since there is no a prior

reason to epect $ >0. Second6 "hat are the dnamics of the polic variables/ An econom

ma reach the stead state "ith an increasing ta rate and decreasing public investment6 or "ith a

decreasing ta rate and decreasing investment6 or the reverse. Studing the path of the econom

to"ards the balanced gro"th path is one "a to shed light on the long run trends of fiscal polic

variables. To ans"er these -uestions "e need an eplicit theor of public polic ma,ing. #e

address these issues in the net t"o sections. $n Section ).1 "e characteri7e e-uilibrium behavior.

$n Section ).2 "e derive the implications for the balanced gro"th rate and for the transition path

converging to it.

3.1 Equilibrium behavior

To characteri7e behavior "hen policies are chosen b a legislature6 "e loo, for a smmetric Ear,ov

perfect e-uilibrium *SE+ in "hich plaers= strategies depend onl on the level of public debt per

unit of human capital6 i.e. bt N t/zt. As "e formall sho" belo" there is no loss of generalit in

13 =b*iousl' these conditions need not be satis/ed on the path of con*erence( The predictions of the modelfor the con*erence path will be discussed in Section


12/44

adopting bt as a state variable.14 A smmetric Ear,ov e-uilibrium can be formall defined b a

collection of polic functions p*b+ N{*b+, I*b+, T*b+, b

*b+, g*b+, gc

*b+}. 4ere *b+6 I*b+ and T*b+are the ta rate and the share of 3 spent on public investment and transfers proposed in state

b. The function b*b+ is the ne" level of debt normali7ed b the future level of human capital6 i.e.

/z "here z N!*p*b++z.15 The remaining t"o functions describe ho" local public goods are

distributed in the econom. $n a SE the proposer randoml selectsG 1 legislators to form a

governmental cabinet6 choosing them from the remainingn 1 legislators "ith e-ual probabilit.

The proposer provides su?cient local public goods to #cabinet members to guarantee their vote6

and as little as possible to the others *in the cabinet or outside+. The functions g*b+ and gc*b+

are the shares of 3 of the public good proposed for6 respectivel6 the proposer=s district and

the other districts in the minimal "inning coalition. All the other representatives ecluded from

the minimal "inning coalition receive the minimal share of 3 possible6 g.

As standard in the theor of legislative voting6 "e focus on "ea,l stage undominated strate'

gies6 "hich implies that legislators vote for a proposal if the prefer it *"ea,l+ to continuing on

to the net proposal round. #e focus6 "ithout loss of generalit6 on e-uilibria in "hich6 at each

round6 proposals are immediatel accepted b at least # legislators so that6 on the e-uilibrium

path6 no meeting lasts more than one proposal round. #e sa that an e-uilibrium is smooth if

the polic functions are continuousl differentiable in b. $n the reminder of the paper "e focus

the analsis on smooth e-uilibria. This propert is satisfied b construction in all e-uilibria

computed in Section L.

To characteri7e the e-uilibrium strategies consider the problem faced b the proposer. The

proposer chooses the policies to maimi7e the utilit of his o"n district under t"o sets of con'

straints. !irst6 the budget constraint and the feasibilit constraints that "e have described in the

previous section. Second6 an incentive compatibilit constraint that guarantees that the proposal

is voted b a -ualified ma5orit. To be approved6 the policies must be such that:

U*p+ O 0 log

*gc+

jg

j1

O %*b, z+ N%G*b, z+, *10+

14 Strateies can not depend on the current le*el of debtDG-. since G-. is itself a function of current policies(The debtDG-. ratio at time t is t/ztnlpt3( 9hile t/zt is a state inherited from the past, pt is a control *ectorchosen at t (

15 The future le*el of debt in absolute terms can therefore be e4pressed in terms of the current policies asZpb33z bb3( The future debt in terms of future G-. depends on future policies so it is indeterminate at thetime bb3 is chosen( %n e4pectation it isbb3/nlbb33 where lbb3 is future labor suppl' in state bb3(

11


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"here z N!*p+z is the epected productivit level after polic p is implemented and %G*b, z+ is

the outside option of a cabinet member. The left hand side of this constraint is the epectedutilit of accepting the proposal for a member of the minimal "inning coalition "ho receives a

levelgc*b+ of local public good. The outside option of a cabinet member6%G*b, z+6 is the epected

utilit of voting no and therefore moving to the stage of the bargaining game in "hich a ne"

government member is randoml selected.16 The net result sho"s that *10+ imposes a precise

relationship bet"eeng*b+ andgc*b+:

Lemma 1. In equilibrium, the incentive compatibility constraint (10) is satisfied if and only if

gc*b+ N g*b+Q(G,q) g(1Q(G,q)), where&*G, #+ N 1Gq+1

*0, 1I.

emma 1 sho"s that the bargaining process forces the proposer to provide a level of por, to the

members of the minimal "inning coalition e-ual to a geometric average of the level he assigns to

his o"n district and the level he assigns to the districts outside the coalition6 g. Total ependiture

in public goods6 moreover is a function ofg onl: "*g+ N g O *# 1+gQ(G,q) g(1Q(G,q)) O *n #+g.

$t should be noted that the "eight on g*b+ is increasing function of#: the larger is #6 the more

the proposer is forced to internali7e the "elfare of the other government members. $ndeed6 "hen

the voting rule is unanimous and so #N G6 "e have gc Ng.17

As seen in Section 26 the citi7ens= per period indirect utilit function is separable in z andp*see *


14/44

moreover6 the proposer=s problem can be "ritten as:

mab,,g,I,T

U*p+ O 0log gO V*b+

'.t. !*b+b/ *b, p+ Gb O "*g+ O IO T nl*p+I N 0

b b6 g g6 II6 TT , G0, 1I

*12+

The representation in *11+'*12+ highlights the role of the political process on ho" policies are

chosen in e-uilibrium. #hen N 0 policies have a uniform effect on the citi7ens= "elfare. $n this

case there is no political con>ict and the proposer chooses policies to maimi7e the "elfare of the

representative citi7en. #hen > 06 districts value local public goods differentl. $n this case

the proposer overestimates the "elfare effect ofg. The magnitude of the overestimation depends

on Gn

&*G, #+. #hen#N G N n6 "e have&*G, #+ N 1 and full alignment of interest across districts

is re'established. #henG < n andor #


15/44

the compensating variation for a marginal increase in ta revenues.19 $t is6 therefore6 a measure

of the distortion introduced b the government into the econom. To see the importance of thisconcept6 consider the marginal cost of public funds associated "ith the policies {t, b

t , I

t, T

t, g

t }

that "ould be chosen b a benevolent planner "ho can commit to the optimal polic plan. Under

standard assumptions6 the planner aims at smoothing the cost of taation over time as much as

possible. This implies that polices are chosen so that the marginal cost of public funds is e-uali7ed

over time: )*+t N )*+t+1 for an t > 0.

20 A constant marginal cost of public funds

implies that fiscal polic and the gro"th level of the econom are all constant for an t >0. $s

this result still valid in a political e-uilibrium/ $f not6 "hat are the implications for the dnamics

of the econom/

To ans"er these -uestions6 let us define *b, b+ as the interest rate in state b "hen the ne"

level of debt isb *and the other policies are at the e-uilibrium level+. The elasticit of the interest

rate "ith respect to b evaluated at the e-uilibrium level b Nb*b+ in state b is:

-*b+ N*b, b+

bb

*b, b+. *1)+

This elasticit has a clear empirical interpretation since it measures the relationship bet"een t"o

observable variables6 debt and the interest rate. et us also define-g*b+ as the elasticit ofg "ith

respect to debt6 -g*b+ N g(b)b

bg(b) . #e have the follo"ing characteri7ation of the uler e-uation

in a political e-uilibrium:

Proposition 2. In equilibrium$

G1 -*bt+I )*+*bt+ N

1 0

G

n&*G, #+ 1+

*bt+1+ -g*bt+1+

)*+*bt+1+,

*1L+

where *b+ is a nonnegative function of debt&

This representation of the uler e-uation has a straightfor"ard interpretation that clarifies the

forces shaping the dnamics of fiscal polic. The left hand side is the marginal benefit of debt:

b increasing debt b a unit6 ta revenues can be reduced b a unit at t6 inducing a net "elfare

19 %n intuiti*e terms, the MCPF is the marinal monetar' compensation necessar' to compensate an aent fora marinal increase in ta4 re*enues(

20 A formal anal'sis if the plannerEs problem is a*ailable from the authors upon re?uest( See also ;un?*istand Sarent 6200>7 for the anal'sis of a similar problem in a model with no endoenous rowth(

1L


16/44

gain e-ual to)*+*bt+. This term is corrected b *1 -*bt++ to account for the fact that the

government is not a price ta,er in the bond mar,et. #hen6 for eample-*bt+>06 an increase indebt implies an increase in the interest rate: the corresponding reduction in resources limits the

benefit of an increase inb. The right hand side can be interpreted as the marginal cost of debt. An

increase in debt generates t"o effects: it reduces future resources *"ith a "elfare effect measured

b the first term6 )*+*bt+1++6 and changes the polic mi b affecting policies *this second

effect is represented b the term

1 0Gn&*G, #+ 1+

*bt+1+ -g*bt+1++

+. #hen policies are

chosen b a utilitarian planner6 the second effect is irrelevant: policies are al"as optimal6 so b

the envelope theorem6 a marginal change from the optimal level has no "elfare effect. Since in

the model described above policies are ine?cient6 ho"ever6 the change in the polic mi induced

b b has a first order impact that can not be ignored. The first term of the right hand side

of *1L+6 therefore6 incorporates the political distortion. Mot surprisingl6 the si7e of the political

distortion depends on and Gn

&*G, #+: the larger is6 the more severe is political con>ict because

citi7ens internali7e little of the benefit of local public goods provided to districts to "hich the do

not belongP the smaller is Gn

&*G, #+6 the less the ruling coalition is forced to internali7e the "elfare

of the remaining districts. #hen N 0 andor Gn

&*G, #+ N 16 it is as if policies "ere chosen b a

utilitarian decision ma,er6 so the political distortion is 7ero.21

Dn a balanced gro"th path debt gro"s at the same rate as income6 so bt remains constant at

b. #e sa that balanced gro"th path isstableif there is a neighborhood ofb such that the debt

ratiob converges tob for an initial state in the neighborhood. $n general it is hard to establish

analticall the properties of the e-uilibrium policies and of a stable stead state. $n the net

sections "e "ill use propositions 1 and 2 to stud a calibrated version of the model numericall.

4o"ever6 in the reminder of this section "e can use *1L+ to sho" that6 in the model described

above6 political distortions are necessar to eplain t"o stli7ed empirical facts about developed

countries and to characteri7e the ,e properties of the convergence path.

#e sa that a balanced gro"th path is regularif it stable and t"o conditions are met: *1+ debt

is positive on the path6 i.e. b > 0P and *2+ the interest rate elasticit is positive at the stead

state: i.e.6-*b+> 0 *or*b, b+/b >0 atb+. !rom a theoretical point of vie" neither of these

t"o properties need to necessaril hold in e-uilibrium. There is ho"ever evidence that these t"o

21 9e obtain an interestin interpretation of 1>3 b' di*idin both sides b' 1 bt3( The o*ernment acts asa standard monopolist debt is chosen to e?uali!e the marinal bene/t to the marinal cost of debt weihted b' astandard markup factor that depends on the elasticit' of the demand 1/ 1 bt33(

1


17/44

bt,bt+1

MCPF(b) MCPF(b)

Fig 2.A Fig 2.B

b*

MCP F(b*)

( ) ( )0 1 1 11 1 ( ) ( )

t g t t Q q b b MC PF b

n

+ + +

G

( )1 ( ) ( )t tb MC PF b

1( )tMCPF b +

( )1 ( ) ( )t tb MC PF b

bt,bt+1

!igure 2: The uler e-uation for G N #N n and # < n.

properties are satisfied in most economies.22 $ndeed6 the are al"as satisfied in the calibrations

"e present in the net section. #e sa that there is political conictin the econom if >0 and

# < n. #e have:

Proposition 3. stable steady state is regular only if there is political conict&

The intuition behind 3roposition ) is illustrated b !igure 2. %onsider first !igure 2.A

"here "e represent an e-uilibrium in an environment "ith no political con>ict *so Gn

&*", #+ N 1

andor N 0+. The red dotted line represents the left hand side of the previous e-uation6

*1-*b++)*+*b+P the blue solid line represents the right hand side6 )*+*b+.23 #e have a

stable stead state "hen the blue solid line intersects the red dotted line from belo". At the stead

state6)*+*bt+1+ N)*+*bt+6 so the onl "a to satisf the e-uilibrium condition is to have

-*b+ N 0: as it is apparent from *1)+6 in a regular econom this is possible onl if b N 0 "hen

there is no political distortion *i.e. N 0 andor G

n

&*G, #+ N 1+. The onl "a to haveb >0 on

the balanced path is to shift )*+*b+ Bdo"n"ard6C so that the intersection moves to the right.

As illustrated in !igure 2.& this is possible onl if0

1 Gn

&*G, #++

*bt+1+ -g*bt+1+> 06 i.e.6

onl if there is a political distortion: Gn&*G, #+< 1 and >0.

22 The re?uirement of a positi*e le*el of debt at the stead' state seems natural( For e*idence on the interestrate see, for e4ample, Ardana, Caselli and ;ane 6200)7 and ;aubach 6200:7(

23 %n the Fiure, MCPFb3 intersects the oriin, but it is not necessar' to ha*e MCPF03 0( The actualle*el ofMCPF03 is irrele*ant for the anal'sis(

1


18/44

$t is interesting to note that the positive interior level of debt in the model is the result

of t"o contrasting forces: on the one hand6 political econom distortions push debt upP on theother hand6 the attempt to manipulate the interest rate pushes debt do"n. #e "ould not have

positive debt at the stead state "ithout the first effectP "e "ould not have an interior level of

debt "ithout the second effect: politicians "ould al"as have an incentive to shift the financing

of ependiture to the future and accumulate more debt. At the stead state the t"o incentive

eactl counterbalance each other.

The net result characteri7es the dnamics of the public sector on the convergence path to a

regular stead state.

Proposition 4. *tarting from any b0 in a left neighborhood of a regular steady state, both

infrastructure and the e+pected level of local public goods grow at a slower rate than -".

An interesting implication of 3roposition L is that despite the fact that in this econom the

polic'ma,er has ecessive incentives to spend in local public goods6 the epected suppl of public

goods declines over time6 and so the public sector becomes smaller and smaller as a fraction of

3. This phenomenon is a conse-uence of the political distortion in the presence of endogenous

interest rates. As debt increases6 the proposer finds it optimal to increase the primar surplus b

reducing ependitures rather than b increasing taes: reducing ependitures rather than raisingtaes forces up disposable income and savings6 and so it holds interest rates do"n. To the contrar6

an increase in taes forces do"n disposable income and savings6 and6 hence6 puts up"ard pressure

on the interest rate. 3roposition L sho"s that the legislators al"as find it optimal to shrin,

the provision of public services *both in terms of public goods and infrastructure+. 4o"ever6 the

proposition does not establish that the find it optimal to decrease taation. This finding "ill be

established in the net section "hen "e solve numericall a version of the model calibrated after

the U.S. econom.

#hat is the implication of this converging path for productivit/ #hen there is no learning'

b'doing6 this -uestion can be easil ans"ered.

Proposition 5. If1 N 0, then starting from any b0 in a left neighborhood of a regular steady

state, the growth rate in productivityRzt/zt gradually declines on the convergence path&

!igure ) illustrates the last part of 3roposition L and 3roposition . As b converges to b

infrastructure declines: in this case the gro"th rate of productivit *I+ shifts to"ards the L

1Q


19/44

( )tI

( )1tI + ( )I 45o

zt zt+1 zt+Tz

z

!igure ): ro"th namics

degree line andz gro"s at a decreasing pace *or potentiall ma even decline if *I+ is lo"er than

one+.

3roposition does not necessaril hold in the presence of learning'b'doing. The reason

is that the ta rate ma decline on the transition path. $f this decline implies an increase in

labor suppl6 then "e have t"o forces pushing in opposite directions. A decline in the ta rate6

ho"ever6 does not generall impl that labor suppl increases. The reason for this is that6 as debt

increases6 agents hold more financial "ealth. The "ealth increase implies higher marginal utilit

for leisure: this ma more than counterbalance the effect of the decrease in taation. $n the net

section "e sho" that "ith J3F preferences labor suppl tpicall declines on the transition path6

so productivit is decreasing also "ith learning'b'doing.

" # calibrated solution o$ the model

".1 %ositive analysis

$n this section "e stud the model presented above b numerical methods6 calibrating it to the

U.S. econom. The ,e parameters describing preferences and technolog are chosen to minimi7e

the differences bet"een the stead state values of the ,e aggregate variable predicted b the

18


20/44

model and the corresponding average values in the U.S. econom in the 2001'2010 period. These

variables include public spending6 public investment and debt6 as fractions of 3. $mplicit isthe assumption that fiscal variables have been6 on average6 at their balanced gro"th levels during

this time period. The details on the calibration are presented in the appendi. #e "ill discuss

alternative scenarios in Section L.2 and . #ith fe" eceptions that "e discuss belo"6 all of the

-ualitative results presented here are robust to specific details of the calibration.

!igure L sho"s that the model has no di?cult in achieving the calibration targets *note that

the ta revenue3 ratio is not eplicitl targeted in the calibration+. !igure describes the

dnamics of the model sho"ing the transition to the balanced gro"th path and compares it to the

data.24 A number of interesting features of the e-uilibrium dnamics emerge.

!irst6 consistentl "ith the theoretical analsis of the previous sections6 in the model debt gro"s

faster than 3 during transition to"ard the balanced gro"th path. Although the empirical time

series are naturall more volatile6 the lo" fre-uenc behavior of fiscal variables appears consistent

"ith the U.S. evidence.

Second6 both ta revenues and ependiture in public goods and in infrastructure gro" slo"er

than 3 on the transition path. The numerical solution therefore reinforces the analtic results

presented in the previous section b sho"ing that not onl do ependitures over 3 decline6

but the ta revenues over 3 decline as "ell. This is the same shrin,ing government effect

discussed in 3roposition L. As debt increases6 the government has to increase the primar surplus

b either increasing taes or reducing ependitures. Feductions in ependitures6 ho"ever6 tend

to be more effective as the increase citi7ens= savings and6 hence6 reduce the e-uilibrium interest

rate. & reducing ependiture the government relaes the budget constraint in t"o "as: directl

b reducing ependituresP and indirectl6 b reducing the e-uilibrium interest rate. The effect of

an increase in taation is different. 4igher taes reduce disposable income and therefore6 ceteris

paribus6 reduce savings and increase the e-uilibrium interest rate. As the stoc, of debt increases6

the interest rate effect becomes increasingl significant6 ma,ing ta increases even less attractive.

The third feature regards labor suppl and provides some insight about the mechanics of the

model. The right panel of !igure < sho"s that despite the reduction in taation6 labor suppl

declines over time. This phenomenon is due to the fact that as debt increases6 households hold

24 %n our comparison of the model with the data we focus on the period from 1:)1 to 2010( 9e do not considerearlier data because we would like to abstract from the conse?uences of 99%% and the 8orean 9ar, which hadsini/cant /scal impacts not related to the speci/c issues we are stud'in in this paper(

1H


21/44


22/44

1970 1980 1990 2000 20100

10

20

30

40

50

60Public debt, % of GDP

1970 1980 1990 2000 2010

10

15

20

25Taxes (net of SS contributions), in %

1970 1980 1990 2000 2010

10

15

20

25(Total) Public good, % of GDP

Year1970 1980 1990 2000 2010

1

1.5

2

2.5

Public Investment, % of GDP

Year

Model

No Pol. Distortions

Data

!igure : !iscal 3olic namics: data6 political e-uilibrium6 and e-uilibrium "ith no politicaldistortions.

-uite remar,able. #e should also stress that modest response of the gro"th rates to the rise in

debt along the transition path is a conse-uence of our conservative calibration strateg. Mamel6

in the calibration the gro"th elasticit "ith respect to public investment is positivel related to

the specific definition of public investment used as target value.25 !or the latter "e use a narro"

definition6 BFesearch and evelopmentC component of federal outlas. Using a broader measure6

such as BTotal $nvestment Dutlas for Ea5or 3ublic 3hsical %apital6 Fesearch and evelopment6

and ducation and TrainingC component of federal outlas "ould amplif the effect of political

econom distortions on the gro"th rates of productivit and output.

25 As we detail in Appendi4, the calibrated *alue of the parameter1 is tin' 0(001"1(

21


23/44

1970 1980 1990 2000 20103

2

1

0

1

2

3TFP Growth, in %

Model

Data

1970 1980 1990 2000 2010

5

4

3

2

1

0

1

2

3

4

5

GDP Growth, in %

1970 1980 1990 2000 20108

6

4

2

0

2

4

6

8Labor Supply, in %

!igure


24/44

0 0.2 0.4

5

10

15

20

25

30

35

40

Public debt, % of GDP

0 0.2 0.4

22

24

26

28

30

32

Tax rate, in %

0 0.2 0.4

10

12

14

16

18

20

22

(Total) Public good, % of GDP

0 0.2 0.4

100

100.05

100.1

100.15

100.2

100.25

Labor supply

0 0.2 0.40

0.05

0.1

0.15

Growth rates, in %

Cumulative

Due to LBD

Due to g

0 0.2 0.4

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Public investment, % of GDP

!igure Q: 3ublic ood ternalit6 !iscal 3olic and conomic Dutcomes.

06 as discussed in Section ).

Second6 a decrease in political con>ict induces a higher level of investment in public infrastruc'

ture and local public goods. As decreases the proposer internali7es more of the benefit of all

local public goods and heshe internali7es less of the benefit of the local public good provide to

hisher o"n district. This reduces the political bias: indeed6 "hen N 0 the proposer chooses

policies in the same "a as a utilitarian decision ma,er.

The third effect is perhaps more surprising: a decrease in political con>ict induces an increase

in the ta rate and it has a non'monotonic effect on labor suppl and gro"th. As decreases6

the ta rate increases to finance higher provision of public good "ithout increasing debt *for the

reasons discussed in Section ).2+. As decreases6 stead state labor suppl initiall increases.

This phenomenon is due to the "ealth effect: the decrease in induces a decline in public debt

and6 hence6 in privatel held "ealth6 so it induces a decline in the marginal utilit of leisure as

2)


25/44

"ell. !or lo"er levels of6 ho"ever6 the higher ta rate tends to counterbalance the "ealth effect6

and labor suppl decreases in response to a decline in . Monetheless6 the effects of taation and"ealth roughl offset each other@the differences in labor suppl across different =s do not eceed

0.2 percent.

The non monotonicit in labor suppl eplains "h the gro"th rate is non monotonic in .

$t is important to stress that "elfare is monotonicall increasing in : hence6 the gro"th rate is

not necessaril a good measure of "elfare in this model. As political distortions are reduced6 the

public goods share of output increases: public goods increase "elfare6 but the do not increase

gro"th. The result is that "ith higher "e ma have more BconsumptionC in the form of public

goods6 but a lo"er gro"th rate. $n these situations6 the econom gro"s at a slo"er rate6 but it

has a superior balance *as measured b "elfare+ bet"een the private and the public sector.

Since debt is monotonicall decreasing in 6 the non monotonicit of the gro"th rate "ith

respect to ma eplain "h there is evidence suggesting a non monotonic relation bet"een debt

and gro"th.26 !igure Q suggests that "e should epect the relationship bet"een gro"th and

debt to be negative for countries "ith a high 6 and positive for countries "ith lo" .

4.2.2 ealth e!ects

As "e have described above6 "ealth effects pla an important role in the dnamics of the econom.

ven "ith a declining ta rate6 labor suppl declines over time because of the accumulation of

private "ealth necessar to finance the stoc, of public debt. To stud the role plaed b "ealth6

"e compute the e-uilibrium "ith an alternative utilit function in "hich "ealth effects are absent.

The comparison bet"een economies "ith and "ithout "ealth effect "ill help to better understand

the role of the "ealth effect on gro"th and the polic'ma,ing process.

To this end "e assume that the citi7ens= preferences are described b a version of reen"ood6

4erco"it7 and 4uffman *446 1H88+ utilit function. As is "ell ,no"n6 44 preferences need

to be ad5usted to be consistent "ith balanced gro"th path. #e do this in spirit of (aimovich and

Febelo *2008+. $n particular6 "e assume that the utilit function from consumption and labor is

26 For e*idence on the relationship between debt and rowth see, for e4ample, &einhart and &oo5 620107, 8umarand 9o 620107 and Checherita and &other 620107(

2L


26/44

given b

U*ct, lt+ N log

ct t l

1+

t

1 O 0

!. *1+

$n this definition the variable t depends on aggregate *or average+ consumption and labor in

periodt: the higher aggregate consumption is6 the higher is labor disutilitP the higher is aggregate

labor suppl6 the lo"er is labor disutilit. Eore precisel:

tN *ctO gt+

lt,

"here is a constant and the upper bar on the other variables indicates their respective average

values *"hich are ta,en as eogenous b the individual citi7ens+. !igure 8 illustrates the dnamics

of an econom calibrated in the same "a as in the baseline model. The behavior of fiscal variables

is ver similar to that described in the previous section "ith eception of taes. 4ere the ta rate

decline is less pronounced. As before6 the gro"th rates decline over time *see !igure H+. Since

"ith 44 utilities "e do not have "ealth effects6 labor suppl is no" driven b the reduction in

taes6 and so it is increasing over time.27

' Growth and austerity pro!rams

As the analsis of the previous section has highlighted6 the political e-uilibrium is ine?cient: itleads to an ecessive accumulation of debt relative to 3 and ma result in a lo"er than e?cient

gro"th rate. %an "e improve "elfare b forcing the government to run a larger primar surplus/

And if es6 ho" does the econom react to such an imposition/ Ans"ering these -uestion ma

help better understand the li,el effects on "elfare of austerit measures of the tpe passed b

the U.S. congress "ith the &udget %ontrol Act of 2011.28 $n this section "e use the political

econom model described above to stud the effects of these tpes of programs and the "a the

should be designed. !irst6 "e consider a simple tpe of austerit program: starting from the

balanced gro"th path6 a countr is re-uired to permanentl reduce the debt to 3 ratio to a

target level1 in Tears.29 Second6 "e then rela the assumption that the austerit program can

27 ote that dependin on the parameteri!ation, it is possible to ha*e positi*e rowth on the transition pathe((, shuttin down public in*estment in this e4ample will impl' that rowth depends onl' on learnin$b'$doin,and hence increases as the debt rises(

28 The Budet Control Act of 2011 establishes o*er :00 billions in budet cuts in 10 'ears and triers automaticacross$the board cuts in spendin if a de/cit reduction bill of at least 1(2 trillions is not passed b' anuar' 201


27/44

1970 1980 1990 2000 201020

30

40

50


1970 1980 1990 2000 20107

8

9

10

11

12

13

14Taxes (net of SS contributions), in %

1970 1980 1990 2000 20107

8

9

10

11

12

13


Year1970 1980 1990 2000 2010

0.6

0.8

1

1.2

1.4

1.6Public Investment, % of GDP

Year

ModelData

!igure 8: 44: !iscal 3olic namics

last forever: #e consider the case in "hich austerit can onl be imposed for a limited amount

of time6 after "hich legislators are free to choose fiscal polic "ith no constraints.

The e!ects o" an austerity plan #ith commitment. !igure 10 illustrates the evolution of

the e-uilibrium studied in the previous section "hen6 starting from the stead state6 the econom

is forced to reduce the level of debt relative to 3 b 0; of its current level in Q ears. #e

consider this plan because6 as "e "ill sho" belo"6 it is the optimal austerit plan for the specific

econom assumed in the calibration *the design of the optimal plan is discussed in greater detail

in the net subsection+.30

3erhaps not surprisingl6 after the introduction of the program the ta rate and government

ependiture in public goods and infrastructure respectivel spi,e up and do"n. There is ho"ever

30 %n the ne4t subsection we consider alternati*e calibrations of the econom'( All the ?ualitati*e feature of thed'namics of the econom' after an austerit' proram discussed here are robust to the speci/c calibration(

2


28/44

1970 1980 1990 2000 20103

2

1

0

1

2

3TFP Growth, in %

Model

Data

1970 1980 1990 2000 2010

5

4

3

2

1

0

1

2

3

4

5

GDP Growth, in %

1970 1980 1990 2000 20108

6

4

2

0

2

4

6

8Labor Supply, in %

!igure H: 44: ro"th and abor Suppl namics

a ,e difference in their reaction: the ta rate ,eeps increasing for the entire period of the program

and it settles at a permanentl higher stead stateP b contrast6 public good provision dips belo"

the pre'program period stead state level for t"o ears6 it then recovers and ,eeps increasing until

the higher stead state is reached. $n the seven ears of the program6 the ta rate increases b

L percentage points and total public ependiture as a share of 3 increases b percentage

points.31 uring the austerit program6 the gro"th rate of 3 remains belo" the pre'program

level b about 0.;. &ecause of the fall in the gro"th in 36 the debt3 ratio initiall

increases6 but then it graduall falls until it reaches the ne" stead state.

The transition process ehibits a number of interesting features. !irst6 as the econom con'

verges to"ard a ne" balanced path6 the gro"th rate is belo" its pre'program level. The gro"th

rate6 ho"ever6 is a poor measure of "elfare and a poor "a to measure the success of the program.

The last panel of !igure 10 illustrates the dnamics of the per period epected indirect utilit *i.e.

the epected value of *


29/44

0 2 4 6 815

20

25

30

35

40


0 2 4 6 821

22

23

24

25

26

27Tax Rate, in %

0 2 4 6 88

9

10

11

12

13

14


0 2 4 6 897.5

98

98.5

99

99.5

100

100.5

Labor supply

Time Period0 2 4 6 8

0.6

0.4

0.2

0

0.2

Time Period

Growth Rate, in %

0 2 4 6 80.05

0

0.05

Utility

Time Period

!igure 10: volution of the econom during the austerit program.

utilit starts increasing6 and it continues to increase until the end of the program.

The second interesting feature of the transition is that although the program imposes to run

a fiscal surplus6 the si7e of the public sector over 3 increases over time. This process is

the reverse of the shrinking government effectthat "e have highlighted in the previous sections.

As "e have eplained6 the endogeneit of the interest rate ma,es reduction in ependitures a

more effective "a to increase the budget surplus than increases in taation "hen debt is high a

reduction in ependiture lo"ers the interest rate. As debt is forced to decline6 therefore6 this bias

in the polic mi is reduced.

The optimal austerity plan. #e no" discuss ho" to chose the optimal austerit plan6 and ho"

it changes "ith the environment. !igure 11 compares the "elfare effects of alternative austerit

programs for the baseline calibration. The ro"s of the table list alternative target reductions in

28


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Target DurationLevel 1 2 3 4 5 6 7 8 9 10 15 20

35 0.52 0.81 0.84 0.85 0.85 0.84 0.83 0.82 0.80 0.79 0.72 0.66

30 0.45 1.35 1.46 1.5 1.51 1.5 1.49 1.47 1.45 1.43 1.32 1.21

25 -0.50 1.56 1.81 1.92 1.95 1.96 1.96 1.94 1.92 1.9 1.77 1.64

20 -3.24 1.39 1.84 2.04 2.12 2.16 2.18 2.18 2.17 2.15 2.04 1.91

15 0.70 1.46 1.78 1.94 2.03 2.08 2.1 2.12 2.12 2.08 1.99

10 -0.69 0.51 1.01 1.27 1.43 1.53 1.61 1.66 1.7 1.79 1.79

5 -3.1 -1.28 -0.53 -0.12 0.14 0.33 0.48 0.60 0.70 1.02 1.2

0 -7.12 -4.4 -3.32 -2.69 -2.26 -1.94 -1.67 -1.45 -1.25 -0.53 -0.04

!igure 11: ong term austerit programs. An entr in the table is empt "hen the correspondingreduction in debt is unfeasible.

the debt relative to output. The columns of the table list alternative hori7ons of the program. The

entrij in columni and entrj is the e-uivalence variation associated to the austerit program

epressed as a percentage of consumption in each period.32 T"o interesting observations can be

dra"n from this table. !irst6 ecept for the cases in "hich the program is etremel ambitious

*both in terms of debt reduction andor in terms of time hori7on+6 austerit is "elfare improving.

Second6 the effect of a program is neither monotonic in its si7e nor in its time hori7on. $f6 for

eample6 "e fi the time hori7on atTN Q periods6 austerit implies a gain of 0.8); in per period

consumption for target level of ); of 3P as "e reduce the target to 20; of 36 the benefit

increases to 2.18;P but for targets belo" 20;6 the benefit declines6 reaching a negative value of

'1.HL; for a complete reduction of debt to 7ero. Similarl6 if "e fi1 at 20;6 achieving the goal

in one period is e-uivalent to a permanentreduction in consumption of ').2L;P achieving it in

Q periods induces a permanent increase in consumption b 2.18 percentP achieving it in 20 ears

induces an increase b 1.H1;.

32 %n particular, letct,lt,t andct,lt,t be the path of consumption, labor and public oods pro*ided before andafter austerit' proramij implemented at t0( The *ariablexij is is chosen so that

t=t0t 6uct1 xij3, lt, t37

is e?ual to

t=t0tuct,lt,t3(

2H


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The fact that an austerit program forcing fast debt repament improves "elfare ma appear

surprising at first sight. Although the debt level is ine?cientl high at the e-uilibrium steadstate6 it ma appear that the best "a to pa it bac, is 5ust to evenl spread its cost over time b

servicing its cost and ,eeping the principal constant. To see "here the problem "ith this reasoning

is6 "e should note that although at the stead state the legislators ,eep policies constant6 the polic

mi is ine?cient. !irst6 political distortions induce a biased distribution of ependitures to"ard

local public goods for the districts of the ruling coalitionP second6 the lac, of commitment induces

legislators to use fiscal polic to ,eep the interest rate ine?cientl lo". !orcing legislators do run

a primar surplus is not directl beneficial because it reduces public debtP it is beneficial because it

induces them to change the polic mi. This could be seen b comparing the e-uilibrium stead

stateb "ith the stead state that "ould be reached b a benevolent planner "ith commitment

*the first best+ and "ith the stead state reached after the austerit plan6 in both cases starting

fromb0N b.33 The benevolent planner "ould increase the ta rate from the e-uilibrium stead

state level from 21.1; to ).);6 g from H.); to 2).);6 and I from 0.H; to 2.L;. $mposing the

austerit plan atb does not induce such a large long term change in the polic mi6 but it brings

it closer to this optimal levels6 inducing the intermediate levels N2.2;6gN1L.2; and IN1.L;.

4o" does the design of the optimal austerit program depend on the stead state level of debt

before the plan is implemented/ $n the baseline calibration presented above the parameters are

chosen so that the stead state level of debt3 is L0.;. !igure 12 illustrates alternative

calibrations "ith higher values 6 the measure of the eternalit and therefore of the political

con>ict in the econom *and ,eeping all the remaining parameters constant+. !or each level of

6 the corresponding ro" illustrates the ,e variables of the ne" political e-uilibrium: the first

column sho"s the stead state level of the debt'to'3 ratio "ith no austerit planP the follo"ing

t"o columns describe the associated optimal austerit program in terms of its time hori7on and

final debt3 target *calculated assuming the econom starts at the stead state level of debt+.

!igure 12 illustrates that there is no Bone'si7e'fits'allC optimal austerit program. As increases6

and therefore the stead state level of debt3 increases as "ell6 the time hori7on of the optimal

program becomes longer and the target level less demanding6 ranging from a debt to 3 level

of 20.1 for the benchmar, econom *"ith N .)+ to a target of 2.Q for an econom in "hich

33 The computation of the stead' state when policies are chosen b' a bene*olent planner with commitment isomitted to sa*e space( The details are a*ailable from the authors(

)0


32/44

Value Implied SS of Optimal Austerity Measureof debt/GDP ratio Years Target Level

.53 40.5 7 20.1

.55 47.0 9 20.3

.57 55.7 9 22.8

.59 63.1 10 23.7

.61 70.1 10 24.5

.62 78.9 11 25.7

!igure 12: Dptimal austerit for different =s.

is .


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0 10 2015

20

25

30

35

40


0 10 2021

22

23

24

25

26

27

28Tax Rate, in %

0 10 208

9

10

11

12

13

14


0 10 2096

97

98

99

100

101

102

Labor supply

Time Period0 10 20

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

Time Period

Growth Rate, in %

0 10 200.06

0.04

0.02

0

0.02

0.04

0.06

Utility

Time Period

!igure 1): volution of the econom during the austerit program.

period consumption.

( &onclusion

This paper develops a political econom theor of gro"th and fiscal polic. $n the theor6 the

gro"th rate of the econom depends on public investment and6 through learning'b'doing6 on

labor suppl. !iscal polic affects citi7ens= incentives in t"o "as: taation distorts labor suppland deficits distort consumptionsavings decision through their effect on the interest rate. 3olic

choices are made b a legislature consisting of elected representatives. 3olitical con>ict arises

because representatives in the legislature have incentives to vote for policies that favor their o"n

constituencies and citi7ens benefit onl partiall from local public goods provided to constituencies

to "hich the do not belong.

)2


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Target Duration

Level 1 2 3 4 5

35 -0.04 0.29 0.34 0.37 0.39

30 -0.58 0.39 0.54 0.63 0.68

25 -1.89 0.29 0.59 0.76 0.85

20 -4.88 -0.02 0.50 0.76 0.91

15 -0.56 0.26 0.64 0.85

10 -1.38 -0.15 0 .38 0.68

5 -2.55 -0.76 -0.03 0.35

0 -4.18 -1.60 -0.64 -0.14

!igure 1L: Short term austerit programs. An entr in the table is empt "hen the correspondingreduction in debt is unfeasible.

The model predicts that the econom converges to a balanced gro"th path in "hich consump'

tion6 public investment6 public good provision6 public debt and productivit gro" at the same

constant rate. The transition to the balanced gro"th path is characteri7ed b "hat "e call the

shrinking government effect: public debt gro"s faster than 36 provisions of public goods and

infrastructure gro" slo"er than 3 and the ta rate declines. These findings are consistent "ith

the U.S. eperience over the past fe" decades6 both from a -ualitative point of vie" and6 in our

calibrated solution6 from a -uantitative point of vie".

#e use the model as a laborator to stud the impact of a simple Bausterit programC in

"hich a countr is re-uired to bring do"n the debt3 ratio. #e sho" that austerit programs

ma be used to limit political distortions and increase "elfare. The analsis ho"ever sho"s that

there is no Bone'si7e'fits'allC optimal austerit program: the higher is the accumulated level of

debt6 the less aggressive the optimal program should be *in terms of both the debt target to

reach and timing+. The analsis also sho"s that the gro"th rate and the short term dnamics of

debt3 are poor measures of "elfare and a poor "a to measure the success of the program.

Dn the transition path of the optimal austerit program6 gro"th is belo" the pre'austerit level6

but "elfare is increasing.

))


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There are man different directions in "hich the ideas presented here might usefull be devel'

oped. To focus on public policies6 "e have made a number of simplifing assumptions both onthe description of the econom and on the political process: there is no private capital6 no shoc,s6

"e are restricting attention to a smmetric econom "ith no redistribution6 and "ith a relativel

simple political decision ma,ing process. tending the model to rela these assumption "ould

certainl provide a richer frame"or, for analsis and improve the model=s predictive abilit. #e

are confident that these assumptions can be relaed in future research.

)L


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)e$erences

Aguiar6 E. and E. Amador6 2011. Bro"th under the Shado" of propriation6C .he /uarterly ournal of 2conomics& 12


37/44

%hecherita %. and 3. Fother6 2010. BThe impact of 4igh and ro"ing ebt on conomicro"th.C uropean %entral &an, #or,ing 3aper Mo. 12)Q.

e &ortoli . and ! Munes6 2012. Bac, of %ommitment and the evel of ebt6C ournalof the 2uropean 2conomic ssociation6 forthcoming.

ra7en A.6 20016 "olitical 2conomy in 'acroeconomics6 3rinceton Universit 3ress.

ra7en6 A. and K. rilli6 1HH). BThe &enefit of %rises for conomic Feforms6C merican2conomic #eview6 vol. 8)*)+6 pp. H8'


38/44

3erotti6 F.6 1HH). B3olitical -uilibrium6 $ncome istribution6 and ro"th6C #eview of2conomic *tudies6 vol.


39/44

* #ppendi+

$n this appendi "e first detail the statements and propositions presented in Sections 2 and ). #e

then discuss our data sources and the calibration presented in Sections L and . As a preliminar

result6 "e start sho"ing that the citi7ens= indirect utilit functions can be represented as in (8)&

Lemma %1. .he per period indirect utility function is given by (8) where

U*pt+ N log

"#$n0 *1 t+1+0

1

1

n

ItO

jg

jt

1+ 1

1 1n

ItO

jg

jt

O 1 t

1++0

%&'

*1


40/44

%t N 1 O 01

log ztO

O=t

t

U*p+ O (1+0)

1

1 log*I+ O *1O 1+log lO log 00n

1

O03log

gi

jgj

1 ,

"hich6 in turn6 using the epression for 3log gi can be "ritten as

%tN A log ztO

j=tjt

U*pt+ O 0

G

n&*G, #+log gt

,

"here A N 1+01 and

U*pt+ N (0O U*pt+ O*1 O 0+

1 G1log *It+ O *1O 1+log ltI *1Q+

O0 *1 +log

gtO *# 1+gQ(G,q)t g

(1Q(G,q)) O *n #+g

,

"ith(0N (1+0)

1 log

00n1

O 0Gn

GqGq+1O

nGn

log g.

$f "e define VtN

=t tU*p+ O 0

Gn

&*G, #+log g

or6 in a recursive form6

Vt N U*pt+ O 0G

n&*G, #+log gtO Vt+1 *18+

condition *1Q+ can be "ritten as %t NA log ztO Vt. The epected value of a citi7en "ho ,no"s

to be a government formateur %pt can be represented in the same. The onl difference is that

the proposer receives log gt for sure instead than 3log

git

jgjt

1. As it can be easil

proven6 "e have:

%pt NA log*zt+ OU*pt+ O 0 log gtO Vt+1. *1H+

"here Vt+1 is defined b *18+.

The proof of the proposition no" follo"s immediatel. Since A log z is a constant6 if p*b+

solves *12+ givenV*b+6 then it must be an optimal reaction function given the true value function

A log*z+ OU*p+ O0 log gO V*b

+P moreover if V*b+ satisfies *11+ given p*b+6 then %*b, z+ N

A log zO V*b+ is the epected value in the game. Dn the contrar6 ifp*b+ is an e-uilibrium6 then

"e must have %*b+ N A log zO V*b+ and the proposer must maimi7e *12+.

*.3 %roo$ o$ %roposition 2

$t is first convenient to define the marginal cost of public funds *described informall in Section

)+. et 1*b, p+ N *b, p+ Gb O "*g+ O IO T nl*p+I. !rom the proposer=s budget constraint

)H


41/44

in *12+6 "e have N z1*b, p+. $n order to reduce nominal debt b one marginal unit the

re-uired increase in taes must be 4 N Gz1*b, p+I

1

. The net marginal reduction in utilitb an increase in taes is given b V*b, p+6 "here V is the indirect utilit function defined in

*11+.35 The reduction in utilit in absolute value is therefore V(b,p)zB(b,p)

. Eoreover the marginal

utilit of consumption is 1zc(p(b)) . The marginal cost of public funds6 then is:

c(p)V(b,p)B(b,p)

. Mote

that the agrangian multiplier 5 from *12+ can be "ritten as: 5*b+ N V(b,p)B(b,p)

. #e conclude

that the marginal cost of public funds "hen policies are p and the agrangian multiplier is 5 is

)*+*b+ N 5*b+c*p+.

#e no" prove *1L+. %onsider the first order condition "ith respect tob of *12+:

5*b+!*p+

*b, p+

1

b

*b, p+

*b, p+

b

N V*b+,

#e have

5*b+!*p+

*b, p+ *1 -*b++ N V

*b+, *20+

"here - *b+ is the elasticit of the interest rate as defined in *1)+. et Vp*b+ be the ob5ec'

tive function of *12+. Adding and subtracting 0log *g*b++6 "e can "rite: V*b+ N Vp*b+ O

0 Gn&*G, #+ 1+ log g*b+. !rom the envelope theorem applied to *12+6 at an point of differ'entiabilit "e have Vp*b+ N5 *b+6 so "e can "rite:

V*b+ N5 *b+ O 0

G

n&*G, #+ 1+

g*b+/b

g*b+ . *21+

Using *20+ and "e have:

*1 -*b++5!*p+

*p+ N5 *b+ 0

G

n&*G, #+ 1+

g*b+/b

g*b+ . *22+

Dbserve no" that *Q+ can be "ritten as: *b, p+ N c*p*b++!*p+/c*p+. #e can therefore "rite:

*1 - *b++ c*p+ 5 *b+ Nc*p*b++ 5 *b+

1 15 *b+

0

Gn

&*G, #+ 1+

g*b

+/b

g*b+

*2)+

efine: *b+ N 1/ *b 5 *b++6 and let-g*b+ N g(b)b

b

g(b) be the elasticit ofg*b+ "ith respect to

b. Using the fact that)*+*b+ N5*b+c*p+6 "e obtain *1L+.

35 The indirect utilit' is e*aluated at the e?uilibrium polic' pb3, where b is the state( For simplicit' we omitthe state form the e4pression of the polic' when it does not create confusion(

L0


42/44

*." %roo$ o$ %roposition 3

$fG N#Nn andor N 0& "e have

1 Gn&*G, #++

N 0. $n this case6 at the stead state b

"e must have: (b,b)

bb

(b,b) N 06 "here the derivative is evaluated at b. Since)*+*b+> 0

and (b,b)

b >0 at b Nb6 a stead state is possible onl ifb N 0.

*.' %roo$ o$ %roposition "

$n a regular stead state b "e have:

-*b+ N 0

1

G

n&*G, #++

*b+ -g*b

+. *2L+

"here -*b+> 0 and *b+> 0. #e conclude that -g*b+< 0 and so g*b+ is decreasing in b in

a neighborhood of the stead state in an smooth e-uilibrium. Since the stead state is stable6

starting from b0 in a left neighborhood6 bt+1 > bt6 and so t+1/t < yt+1/yt for an t > 0. &

emma 16 "e must have and ct+1/ct < yt+1/yt6 "here

ct N g

ctyt is the dollar value of public

goods allocated to the districts in the minimal "inning coalition. !rom the first order conditions

of *12+ it is also eas to sho" that It is monotone in gt6 so "e have It+1/It < yt+1/yt as "ell.

*.( -ata and &alibration

'ata $n this section "e provide information on the sources of the data used to construct !igures

16 L6 on the U.S. econom. #e also brie> discuss the statistical significance of the trends

illustrated in the !igures.

ata on output and the ta revenue'to'3 ratio is obtained from &A=s Mational $ncome

and 3roduct Accounts (M$3A6 Tables Q.1 and 1L.26 respectivel+.36 Ta revenues are measured

net of Social Securit contributions. ata on productivit is obtained from (ohn !ernald=s series

on utili7ation ad5usted T!3 based on &asu6 !ernald and Jimball G200


43/44

*Table ).1+.39 Dur definition of public investment comes from !ederal Dutlas6 M$3A6 Table H.1.

#e have loo,ed at t"o measures: BFesearch and evelopment6C and BTotal $nvestment Dutlasfor Ea5or 3ublic 3hsical %apital6 Fesearch and evelopment6 and ducation and Training.C $n

our baseline calibration "e conservativel use the former.

Dver the period of 1HQ1'2010 "e observe that !ederal debt *as a fraction of 3+ sho"s

positive statisticall significant time trend. 3ublic goods *as a fraction of 3+ sho" negative

statisticall significant time trend. This fact is robust to the inclusioneclusion of 4ealth and to

inclusioneclusion of Mational efence in the definition of public goods. 3ublic investment *as a

fraction of 3+6 defined either "a6 sho"s negative statisticall significant time trend. This fact

is robust to the inclusioneclusion of the defence share. Ta revenues *as a fraction of 3+6

sho" negative statisticall significant time trend.

)alibration The ,e parameters describing the fundamentals$, 0 and are chosen follo"ing

the F&% literature. #e choose log'utilit function for consumption "ith$ N 1 as in (aimovich

and Febelo G2008I and Ecrattan and 3rescott G2010I. #e set N 1.)Q, "hich ields labor

elasticit of about 1. at the stead state of the model and is in a mid'range of the parameters

used in the literature. #e setto 0.HL6 so that "e match the real interest rate of


44/44

similar results.40 The remaining parameters are chosen to fit the ,e moments. $n particular6 "e

choose, 0and1to match the debt'to'3 ratio6 the share of total public good and investmentin 3. This ields values of 0.)6 0.LH and 0.001816 respectivel.

40 #((, increasin or decreasin it b' a factor of two lea*es the ?uantitati*e results of the paper *irtuall'unchaned(

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