Digitized by the Internet Archive in 2011 with funding from Boston Library Consortium Member Libraries http://www.archive.org/details/governmentdomestOOaghi HB31 .M415 Wo 54l working paper department of economics GOVERNMENT DOMESTIC DEBT AND THE RISK OF DEFAULT: A POLITICAL- ECONOMIC MODEL OF THE STRATEGIC ROLE OF DEBT Philippe Aghion Patrick Bolton No. 541 October 1989 Massachusetts institute of technology 50 memorial drive Cambridge, mass. 021 39 GOVERNMENT DOMESTIC DEBT AND THE RISK OF A POLITICAL- ECONOMIC MODEL OF THE STRATEGIC ROLE OF DEBT DEFAULT: Philippe Aghion Patrick Bolton No. 541 October 1989 1 t • flCBSjlWIFS DEC2 11989 GOVERNMENT DOMESTIC DEBT AND THE RISK OF DEFAULT : A Political-Economic Model of the Strategic Role of Debt.* by Philippe AGHION** and Patrick BOLTON*"* (forthcoming in "Capital Markets and Debt Management" edited by Rudiger Dornbush and Mario Draghi) MIT and DELTA, Paris. **** Harvard University and Laboratoire .** d' Econometrie de l'Ecole Poly technique, Paris. We are particularly grateful to Alberto Alesina for introducing us into the field of Macroeconomics and Politics and for many useful comments. We would also like to thank Olivier Blanchard, Jean-Pierre Dan thine, Rudiger Dornbusch, Pietro Reichlin and Philippe Weil for very helpful discussions. "Government Domestic Debt and the Risk of Default: A Political-Economic Model of the Strategic Role of Debt" By Philippe Aghion and Patrick Bolton ABSTRACT This paper focuses on the question of how differences in income and asset-holdings give rise to differences in preferences concerning fiscal policy and investigates how democratic political institutions, within a two-party system, solve the social choice problem of what fiscal policy to It is assumed that the implement when voters have conflicting preferences. party power its own constituency; in political in pursues the interests of particular the left-wing party identifies with the interests of low- income voters, and the right-wing party represents the high income voters. These party objectives give rise to fiscal policies where the left-wing party favours large government expenditures on public goods with concomitant high levels of taxation, and the right-wing party favours low levels of expenditure and low taxes. The party winning the elections implements the fiscal policy it favours most. It is shown that if default on public debt is costly for the government, then left-wing administrations may overaccumulate public debt. But if default on public debt is a real possibility, then right-wing administrations may overaccumulate public debt to ensure their re-election. Large outstanding debt changes the view of moderate voters about the left-wing party: they become more concerned about the government preserving the real value of their bond holdings than about maintaining expenditure on public goods. This is why they switch their votes from left-wing to conservative. I. INTRODUCTION of the research and controversy on macro fiscal recently, most Until was about when and whether debt-financed government deficits have policies real effects on aggregate output and employment. This problem has typically studied been in generations interacting agents) overlapping (or with a (such as policy in of fiscal the role benevolent a limited favouring optimal accumulation or in minimizing the deadweight loss of distortionary capital taxation) addressed within can be this framework (see Blanchard-Fischer for an extensive discussion of this approach). Thus, a particularly important fiscal policy aspect of generational) political suppressed in this model is the (intra redistributive effect of fiscal policy and the consequent conflicts arising from these distributional concerns. Behind the representative income agent maximizing a Social Welfare Function. Naturally, only of issues (1989) representative a representative of government set of model a and question a in preferences heterogeneity whether in terms of of lot preferences. or differences how differences lurks holdings asset of democratic agent in income paper focusses on the and asset-holdings give rise to concerning fiscal political institutions This policy and investigates how solve the social choice problem of what fiscal policy to implement, when agents have conflicting preferences. Our model is much inspired by the experience of public debt management and the political during conflicts surrounding the mid-war confronting the debt-overhang it in several European countries period. This was a time when one of the major problems various governments was how to deal with the huge problem inherited from World War I. Very broadly, in several countries there was a clear conflict about fiscal policy between right-wing parties representing the interests of the rentiers (among others) and thus favoring conservative fiscal policies aimed at preserving the real value of government parties debt and other forms of nominal domestic savings, and left-wing representing the interests of the workers and unemployed and who policies as well as increased expenditure on reflationary fiscal favoured goods. In several instances when left wing parties were elected (as public instance the "Cartel des gauches" in 192^ and the "Front Populnirc" in for shortly there France) in 1936 followed a period of more or less high inflation (fed by sharp increases in government spending) which amounted to a de facto default on public debt. Conservative governments on the contrary practiced severe fiscal Alesina (1987) endeavoured to curb inflation (see restraint and an illuminating survey of the mid war debt policies in for Europe) construct a model where these conflits about fiscal policy clearly We emerge as analyze be party in constituency restrict identifies pursue the interests of its own rather than a general Social Welfare Function. In this paper, attention These to a two-party interests of with the left-wing assumed to power is the right-wing average. incomes between agents. We then in hands of a political party elected through majority voting. The in the while differences of policy is determined when the government is assumed to how fiscal political we result a system : left-wing the party agents having incomes below the average party represents those agents with incomes above the party-objectives party favours give rise to fiscal policies where the large government expenditure on public goods with concomitant high levels of taxation and/or high levels of indebtedness, and the right-wing party levels favours low levels of expenditure, low taxes and low of outstanding debt. The fiscal policy that is implemented is the one of the party who wins the elections. Within if this model we address two sets of questions : first, what role any does public debt play in the dynamic political game between the two parties what future in constraining the actions of future administrations extent does elections? outstanding current fiscal Concerning debt constrain policy have the first future governments ? Second, to an impact on the outcome of question, both in large levels of terms of limiting future expenditure on public goods and in forcing higher levels of taxation to victory while redistribution Surprisingly, to however, exploit the government debt in order to both and increase public goods imposing higher future by in the of next elections finds it worth- provision of intertemporally" the "substitute in the levels large accumulate left-wing government anticipating the a conservative rival of its to show that debt. We repay the levels of taxation.' 1 this is the only instance where a government wishes commitment effect of debt. Conservative governments do not to constrain future left-wing governments by excessively accumulating wish Our debt. results are the commitment extensively with precise with earlier the work of (1988)] and Persson-Svensson (1989). Section IV Alesina-Tabellini [(1987a), deals contrast in thus effect of debt . It discusses the connections between these papers and ours. It also points out that the commitment value of debt disappears when future governments are allowed to default on question have inherited outstanding debt. Section V deals with the second the strategic role of debt : impact an administrations inflation outcome the on contemplate or explicit . We show that current fiscal policies future of possibility the default) . Our elections of only if future default (either through model is one of complete information with forward looking agents, where current fiscal policy only matters if it changes agents' preferences about future fiscal policies. It turns out that preference-reversals can only basic point is as follows large levels of debt can occur if there is a risk of default. The A current conservative government accumulating : swing the outcome of future elections in its favour because its left-wing rival is rationally expected to default on the debt while the conservative party is rationally expected to repay the debt. The larger maintaining they change are the outstanding the real towards value of the debt the more voters become concerned with debt and thus the more favourably inclined conservative administration. Large levels of debt the outcome of elections to the extent that they shift the conflict about fiscal policy away from issues of more or less expenditure on public goods to issues of more or less monetization of the debt. Interestingly, left-wing may parties described in section THE MODEL economy At closed economy beginning government. agent way as the V. is composed of a the same the in . consider a We debt use to government above. The circumstances in which this happens are conservative II. able be elections period, are held to appoint a new but different incomes .Each identical preferences Agents have is identified foreign debt or lending. This continuum of agents who all live for two periods. each of with no parameter a by a which measures his income in each period (agents earn the same income in both periods). The source of agents' is not modelled. The economy's income distribution in the absence earnings of intertemporal transfers given is by f(a) support [0,1]. The with individual voters' preferences are assumed to be represented by the utility function : U(c t ;g L where is cc consumption is log(c 1 + consumption special ' debt p log(c 2 + of the ; + (2.1) .- ). private good period in t and g is 3 is the discount factor. Of course,. this function. utility g2 We adopt mainly it to make . , is provided by the government' 3 ' . In fact, in our the government's role is limited to determining the level of current expenditure period ) 2 The public good, g t model gj tractable. Our results hold for a much wider class of utility calculations functions' = of the public good rather a ) 1 on the public good as well as the method of financing. In the government can choose between various combinations of tax and financing. In period 2 only taxes are available to finance both the debt repayments and the expenditure on the public good. most Throughout of (i) taxes are not distortionary (ii) the equal by t government the paper Later in and r 2 ] the : rate of transformation between the private and the public good is to one. denote assume that income-tax rates are we we shall make the additional assumptions that to begin with, uniform and, paper the rates in the tax the latter assumption' ''. we relax periods 1 and 2 respectively. The can choose any tax rate between zero and one' tax rate public goods g[ period one in t. ' . Finally, given and given the government's expenditure on by the government's budget constraint 1 is given : JjT ia f(a)da. - d = gl ^ the amount of public debt accumulated in period , We (2.2) The interest rate at which the government can borrow, r, will be determined endogenously in the model. an agent Now, the public good, with income a, anticipating government expenditures on g t and g2 , financed with tax rates Tj and t 2 solves the following intertemporal consumption problem' max C *- 1 " i C2 log(c 1 + ) + p log(c 2 + g 2 \ ) * Cj + c2 s < a(l-Tj < a(l-r 2 ) + (2.3) s.p . We model the political process as follows each At elected power : period a left-wing it has : * <1 s. t. where p = 1+r gj > there are two : political parties party and a right-wing party' total control over t and g t . 7) . competing to be Once a party is in Prior to the election, a party To pursuing a particular fiscal policy if it is elected' commit to cannot we ideas, fix time-line below represent sequence the of and events in the moves : t = 2 incumbent administration new elections chooses parties cannot chooses g 2 and t 2 commit to future and how much of policies during the campaign the public debt to be repaid. gj ' and Tj (d and p are then implicitly determined) Figure new government : 1 The party which gets at least fifty percent of the votes is elected. How do we distinguish between a left-wing and a right-wing party ? We assume that the left-wing party represents primarily the interests of those individuals whose income is party represents primarily the interest of those whose income is above the average. Average income below the More specifically, we suppose that the left-wing party maximizes the interests of some income group a L maximizes exogenously the interests given, and in the economy. The right-wing of some < Ea ; and that the right-wing party income group o^ > Ea. Both a and a are we do not consider the question of how a party may wish to choose a in order to maximize the probability of being elected. We shall be interested in the subgame perfect-equilibria of this game. As usual, one solves for these equilibria backwards. This is particularly straight-forward uncertainty <9) . in this model since there is perfect information and no The only potential difficulty arises from the endogeneity The individual the interest-rate. of interest rate equilibrium ; savings decisions depend on future policy well as as on the the latter simultaneously influences and and on future policy. Before solving for the perfect equilibria of the depends described above, we shall consider various scenarios which will serve game helpful as about expectations (rational) their agents' We benchmarks. begin solving for the optimal government by policies when the government is respectively a social planner, a right-wing dictator in period public debt on outstanding default assuming that the government does not left-wing dictator, and a Then 2. we solve for the political equilibrium, first assuming no default and secondly, allowing the period-2 governments to default on outstanding public debt. OPTIMAL POLICY III. A SOCIAL DECISIONS OF PLANNER AND OF RIGHT-WING AND LEFT-WING DICTATORS. Throughout paper this These are political equilibrium. interests of 2 (1 ' representative call a dictator time-consistent compare with the dynamic government a pursuing the clientele and who remains in power in periods his own A social . We optimal benchmarks to the relevant policies. consider only we planner, on 1 the other hand, maximizes the utility of a average consumer. We are particularly interested in finding out how much debt each type of government wants to accumulate in period To income and 1. begin with, consider the optimal savings behavior of an agent with a. Solving savings function the maximization problem (2.3) yields the following : pp(g,+ a(l-T, ))-(g 2 + a(l-T 2 s(a;p;T ;g ) 1 ' = —— )) . (3-1) (1 + P)p The equilibrium interest rate p is then given by the following equation : Jjs(a,p;T t ;g t )f (a)da The gj Using equation TjEa = Lemma savings and the RHS the demand for an d dp - the two government budget-constraints, (where Ea denotes the average income in one easily solves for the equilibrium interest-rate , equilibrium In : (3-2) supply of (3-1) T 2 Ea = d. have we p = 1/(3 for levels all : of debt Obvious level outstanding of debt exceed cannot Ea.p , for otherwise the government is unable to pay back all the public debt in period 2 Consider periods of : [0;Ea.p]. Proof The 1 and g 2 d + the economy) d e the net LHS represents savings. = 1 first and optimal the policy chosen by ( l ' ' a social planner in We suppose that the social planner maximizes the utility 2. a representative The main reason for selecting this average consumer. social welfare function is that it allows us to characterize a point on the Pareto-frontier abstracting from distributional issues between high- and low-income agents. This is not the case, for instance, with the utilitarian welfare function which corresponds to maximizing the sum of the utilities. The latter welfare function leads to perfect equality as the social optimum in our model* X2) . Thus, in period 2 the social planner chooses t 2 and g 2 utility of the consumer with income Ea s(Ea;p;T t ;g t log g 2 where g, = + T,Ea Ea(l-T 2 ) : ) + (3-3; d - — p . (Recall p to maximize the = 1/p from lemma 1) Substituting for g 2 it is clear that the social planner is in (3-3) d indifferent rate t, 1 e ' 31 and since the rate of transformation between , the public private and equal to good is one, the social planner is indifferent between any feasible level of expenditure on public goods similar result A planner chooses t logtc^ period holds in d and g ; [ max Since . (3Ea are non-distortionary taxes the second-period tax between any to solve the social In the first period, 1. . : { g )+ plog(c 2 + g2 t ) Tj ;d subject to Ea(l-T s(Ea,p,T t ,g t - ) 1 t, notice Now, Ea d + c,2 = Ea(l-T 2 g2 = r 2 Ea d(c. + g. that - = dT ) (3-M s(Ea;p,T t ;g t - ) ) dp ; = (i Consequently, 1.2) planner is indifferent between any level of taxation t. d(Cj+ gj = straightforward to see that (i = 1,2) ; planner is indifferent between any feasible result that the governments' individuals' government dd between any level of is reminiscent feasible level period 1 e , [0,1]. It is also so that the social of debt and therefore expenditure on public goods of the Ricardian equivalence theorem , . This to the extent financial structure is indeterminate as a result of intertemporal arbitrage deficit social the : increases today, behaviour. That agents ds(a,p,T t ;g t is to say, when the save more to pay future ) increases in taxes (note that = 1 so that one extra dollar of dd deficit today is exactly offset by an extra dollar of savings). However our result is government not only in government more general than the Ricardian equivalence theorem, since expenditure decisions here are endogenous. The indeterminacy is the financial structure, but also in the optimal level of expenditure. One might refer to this result as "Ricardian super 10 To complete our characterization of the social optimum note indeterminacy" social planner that if the debt in period to default on public oustanding were allowed it is easy to show that he would be indifferent between 2, and no default. This is altogether not surprising given that taxes default are assumed to be nondistortionary clear become will As below, social the planner's optimal policy differs from that of a left-wing or right-wing dictator. Consider first the fiscal policy of a dictator of type a in period 2 (in other words, optimal the optimal policy income-group a ) : The government then chooses t 2 and g 2 to solve max log(c 2 T 2 ;g 2 subject to government which represents the interests of the of a : and + g2 : ) c2 = a(l-T 2 +p.s(a,p;r t ;g t g2 = t 2 Ea ) dp - . (3-51 ) (where s, p, d are taken as given) Solving government chooses the chooses and = g,' obtains dp easily one (3-5) t,d = result the — Ea maximizes t2 expenditure on = and g 2 1 = Ea - dp log(Cj+ g, + ) Ea, the ; Vice-versa, if a < Ea, that is, the government the public good. In period 1, a dictator of type a chooses Tj max > In other words, the government . to minimize expenditure on the public good. government chooses that if a and d to solve (3log(c 2 + g* Tj ;d subject to : c, = a(l-r,) - s(a,p.T ;g t (_ and c2 = a(l-T*) g, = T,Ea + d g, = T ? Ea - dp + ) s(a,p,T t ;g t )p (3-6) 11 and t" are the solutions to problem (3-5) k»here g 2 t, s(a,p.T t ;g t ) Ea+d+atl-Tj - ) where s^\d (-r*Ea-d/p+a( 1—rj ) ) = P One can easily if a < Ea, verify that then both + c g L defined in solution are is to t in + (as g, follows that the optimal It . c2 ( set Tj decreasing in t dictator increasing are (3-6)) and Y =1. Vice-versa, if a Ea, > then c 1 + g : and c 2 =0. Thus so that the solution then is to set Tj + g, if a maximize tax revenues (and expenditure on public goods) wants to he wants to do so in both periods. The same is true if he wants to minimize assumptions on Given our taxes. dictator a L and maximize expenditure wants to dictator wants to minimize expenditure o^ , this means that a left-wing on public goods and a right-wing , . It remains to determine how much debt each type of dictator is willing incur in to indifferent fact period 1. A left-wing dictator, who sets Tj between any that both cx + g l level of and c 2 + g2 debt below t2 = =1, will be Ea.p. This follows from the (as defined in remain constant as (3-6)) the level of debt is changed. The left-wing dictator is indifferent between debt and taxes, reduction since any in expenditure increase in debt today implies a corresponding on the public good tomorrow so that the increase in utility from more expenditure on public goods today is exactly offset by a reduction in utility tomorrow. To determine accumulate how in period 1, much debt a right-wing is willing to dictator it suffices again to see how (c + l g, ) and (c 2 + g2 ) vary with d. The right-wing dictator minimizes public expenditures and thus dp sets T = t2 = Total consumption in periods 1 and 2, respectively, ; t — . for an individual of type a^ then becomes : 12 °<R d + d 1 Ea p P tt 22 c2 + g2 a- ^ = — .Ea d ( - 1 I d — s ) + d 1 Ea p -^ (3-8) (1 + P) pj k H + Differentiating (3-7) and (3-8) with respect to d{c x + gj) ! - =-l i 3d Since > o^^ dictator Ect 6(c 2 o^n, ( 1+p ; strictly prefers g2 ) Ea 1+p (3-9) y conclusion that obtain the : o^n ( x dd Ea.) assumption we by + one obtains d, a right-wing issue any public debt in period not to 1 . This result is all the more striking in that taxes are not distortionary in our model. The intuition with the with one behind this result is straightforward. The consumers incomes above the average bear most of the taxation cost of servicing period 2. debt in incomes below dollar of In fact, it is easy to verify that those consumers pay less than one dollar in taxes for any the average debt-repayment they receive. Therefore, indirectly serves right-wing administrations strictly does the not, however, between role of explain why debt-accumulation and a redistributive tax. This explains why prefer not no debt debt. This accumulation. The latter result is because superior instrument of income redistribution and to accumulate left-wing administrations are indifferent obtained taxes debt accumulation expenditure public goods are a (weakly) on ; so that the role of debt in redistributing income becomes irrelevant. IV. DYNAMIC POLITICAL EQUILIBRIUM WITH NO DEFAULT If elected, expenditure on a right-wing the public administration good by setting . will the choose period-2 to minimize tax rate 13 t, = max<0; t2 = 1 — This was established in the previous section. Note that the policy . objective in period of 2 of each type of administration is the same regard] ess what fiscal policy was implemented in period Ea < 1 . What affects the policy in period 2 is only the location of the political party in power objective (a, opposite and set do the administration will left-wing A f. < aH ). Voters know the policy objectives of each party and rationally foresee what fiscal policy each party will implement. We assume that voters always vote and that they vote for the party implementing the fiscal policy which is which in individual best in their interest' voters with right-wing group can define an income-group, denoted by a, such that all We : . the derivation of the political equilibrium considerably simplifies period 2 Our model has a useful feature ] income this government and is uniquely indifferent are between the policies of the the left-wing government. This income those of all voters determined, and with incomes a less than a vote for the left-wing candidate, and those with incomes a above a vote for the right-wing candidate. income shown given that government representing that a between of voting behavior. In section III, it was perfect predictor is a words, our model has the feature that In other minimizing or the income maximizing expenditure group Ea is indifferent public good for any on the first-period fiscal policy. It follows that in our model a there is right-wing majority if a left-wing majority a when > Ea the median Our income a discussion so Ea, = < Ea far and and a not only characterizes the second-period political equilibrium, but also establishes our first important result Proposition 1 : : When governments debt, then strategic past cannot default and effect. In current on outstanding domestic budget other words, deficits public debt used to influence the outcome of future elections. have no cannot be in Proposition policy and fiscal d e 1 [O.Ea.p] constrain the median with Thus, . from the follows the policies each candidates' period 2 fact that voter's preferences remain the same for any default, no public debt can only be used to administrations as in Alesina-Tabellini of future [1987] and Persson-Svensson [1989]- The remaining part of this section will be the analysis of optimal first-period fiscal policy when the devoted to incumbent party knows that it will be replaced in period 2. We determine to what extent the party in place in period of its opponent in period We knows wants to constrain the policies 2. where a left-wing administration in period the case 1 that it will be followed by a right-wing administration in period 2. Such a situation there was a may arise, for instance, if after the period-1 elections shift in the income distribution (or a change in tastes) such in the new elections in period 2 there is a right-wing majority (that that is, begin with 1 f(a) choose is its fiscal clientele, am such that policy, ?, anticipating log(c : H (r 1 ;d;g 1 policy + g2 e t + gj = r l Bx + d + c 2+ g 2 = aL - — Ea ) (l * ;p) = aL (l-Tj) + ) s(a L ;l/p) that policy it is the left-wing : We have : ) - (4.1) ;p) aL (l - dp — (1+P)/P g, t, 3(c 2 ) easy to verify that government sets s(a L - s(a L ;p).p 3(c,+ Again, right-wing the ) a L (l- Tl d y ( by : r Ea where s(a followed (3log(c 2 gl the utility of its to maximize ) + + 1 subject to the left-wing administration will Then, . the administration in period 2 max T i: d 'Si Ea) > > = 1. More and + g2 ) > 0, so interesting is the debt 15 tt L 1 1 5 (c,+ g,) Ea'p 1 1 - :'i.2: i ad + (i i +p p)/p Ecu and 3(c,+ g-J 5l Since a, < assumption) Ea (by utility is increasing in Proposition 2 C».3) Ea 1+3 3d both period have that we , 1 and period 2 We thus obtain our second noteworthy result d. : A left-wing government followed by a right-wing government : will run deficits budget in order to "constrain" the right-wing government. In fact the left-wing government will choose to accumulate the maximum sustainable expenditure utility goods . The intuition behind Proposition 2 is the left-wing government can increase 1. This increases the period-1 incomes below the average income. Perhaps period in consumers with from the that it also increases their utility in period 2. This most of fact that the tax burden of servicing the debt on the wealthy consumers with incomes above the average. For any one dollar of consumer debt neither repayment with income debt transfer It public of all follows Thus on surprising is falls d = Ea.(3 : By accumulating public debt, simple. more public debt the right-wing the government in period 2, a less than the average is taxed less than one dollar. accumulation from by with wealthy no to default the poor. amounts to an indirect income The only income group that is hurt nor favored by debt accumulation is the average-income group. follows that, from the perspective of a left-wing party, being replaced by a right-wing party debt-accumulation is favorable in both periods.' lj) We is close this section with the case where a right-wing administration followed by a left-wing administration. We know that the left-wing 16 will choose t 2 = administration administration chooses maxlog(Cj+ gj plog(c 2 + ) = ?, + 1 and g 2 (Tjjdjg^ g2 Ea = - to solve Cj + t, g, . ) Ea+d+a^ 1-Tj ( Again will g, TjEa+d+a,, (1-Tj i + PL straightforward to minimize taxes in period ) 3(c x + g! 1+ id 3(c 2 - (Ea ci.'t: d/p)' + p/p (t, 1 =0). the right-wing administration If we differentiate (Cj+ g ) and t : 1/3 (1+P)/P g2 ) 1 1 1+ + (4.6) 3d This ) - check that with respect to d, we obtain (4.5) d/p] (Ecu- Ea-d/p+ = it is (c 2 + g 2 - ) ) 1+3/p 1 c? + so that the right-wing : TjEa+d+a,, (1-Tj s. t. dp, 3 1/P (l + 3)/3 P implies that a right-wing administration followed by a left-wing administration is indifferent between any level of debt d [ 0, € L Proposition 3 right-wing A : administration administration does not gain followed by Eal — 3 a left-wing by constraining the future administration's policy choices through the accumulation of debt. This result is Persson-Svensson when a [1989] right-wing administration. in sharp contrast to the conclusions obtained by, say ; and also to those obtained in the present model administration The reason is followed by another right-wing why the right-wing incumbent is indifferent is because debt plays no indirect redistributive role when all income is taxed away in period increase 2. As a result, any increase in debt today resulting in an in period-1 utility is exactly offset by a decrease in utility in 17 1 period V. since the equilibrium interest rates is p 1, — = DYNAMIC POLITICAL EQUILIBRIUM WITH COSTLESS DEFAULT have already pointed out in section III that with no distortionary We taxes, a social period 2. planner is indifferent between default and no default in first important Our left-wing this section result of that is both the government and the right-wing government strictly prefer default period 2, in . even though non-distortionary taxes are . We go on to show, that this conclusion crucially depends on the assumption that the however, private and rate of transformation between the than or) equal As soon as the rate of transformation in different from one, it to one. longer generally is no true that the public good is (less both types of government strictly prefer default. Consider (a L < Ea) first default the decision of a left-wing administration inheriting a total debt of d. We know that such an administration maximizes expenditure on public goods by setting t, = 1. If it defaults, total expenditure on public goods is given by Ea, and every consumer in the economy utility gets expenditure period-2 > Ea it If default, not does total then on the public good is Ea-d/p and a consumer with income a gets utility administration Ea logEa. (l6) - d/p d > of log[Ea prefers + to - d/p + s (a; 1/p) default . 1/p] if . and Thus a only left-wing if s(a L 1/p) 1/p or ; . s(a L ;l/p). (5.1) We know from the credit-market equilibrium that d = Jjs(a,l/p)f(a)da = Es(a,l/p) = s(Ea,l/p). (5.2) : 18 last equality The function s(a,l/p) in for all d € ; t Since a. follows from the linearity of the savings (5-2) a. Ea, < Ea.p). Thus we obtain (0, Proposition in to default prefers is verified (5-1) : administration (such A left-wing : it follows that that a L positive level on any < Ea) strictly of outstanding public debt. refusing By administration repay to can increase the outstanding debt, the left-wing even further its expenditure on public goods. Since savings are an increasing function of income, default becomes another form taxation. The of redistributive interests those of agents who left-wing government represents the benefit from this redistribution and therefore favors default. This is alltogether not very surprising. We were, however, astonished at first to get the next result about the incentives to default right-wing administration. of a minimize We know that the latter wants to expenditure on the public good and therefore sets t 2 = ( d max<0, In that case, an individual with income a gets a d * s(a,l/p) period-2 utility right-wing of log a 1 If the pEaJ government defaults, period-2 utility becomes simply logo^ Thus a if not default. it does right-wing government defaults if and only if (where a^ In 0^ > a,, > 1 + pEa s(aR .l/p).l/p, : (5.3J Ea) words, if the costs of increased taxation required to finance debt repayments outweigh the the average, then out that the benefits to the right-wing government prefers to default. It turns always greater than the benefits for any positive costs are level of inherited debt those individuals with incomes above : 19 Proposition 5 administration such that aR A right-wing : > Eg: default on any positive level of outstanding debt. Proof : Condition (5-3) is equivalent to Or where > j£ sto^il/p) : d + aR (1-Tj ) Ea.Tj + - aR pEaJ sCOpil/p) (1 + P)/P «R 1 .Ea p + 1 (l+p)/p but, a_ Ea — Ea > s(a R .l/p) > (1+p) since a R (l+p) pEa > pointed out We + <=* 0^ aR > Ea. earlier that if there is no default, then the agents with incomes above the average pay more in taxes to finance debt repayment than the value of their bond holdings. the government to default. The implications of Propositions prefer are far-reaching. aL financed = am = Ea distortionary equilibrium = . default If through a^ ) . The is that is costless, (except debt This is reason no one all why the there will agree in cannot not 4 and 5 exist a government expenditures degenerate the more does there political-equilibrium where rational-expectations are It is then obvious that they should striking case where that taxes are not be positive public debt in to lending to the government in 20 period consequence these of default anticipate they if 1 propositions in that is period 2. Another obvious public debt plays neither strategic role nor a constraining role when default is costless ex-post.' leave it To Propositions 4 5 if the rate of transformation between the private good and the public good is 1 X (X + and 5 are n o longer generally valid. The main transformation preferring modification is ' are not robust to small changes in the parameters of model. Specifically, the 1 however, would be misleading. It turns out that at that, and a given by 0) > X + 1, into the model when the rate of that the subset of income groups is maximization expenditure then Propositions H () introduced 1 instead of (respectively, expenditure minimization) on public goods no longer coincides with the subset of income groups who maximized prefer default on public groups who when period-2 tax rates are As a result, (respectively, minimized). middle-income debt strictly prefer there exists a range of no default. We demonstrate this last point rigorously below and investigate the implications of this result for the dynamic political equilibrium. When good the rate is less other things between the of transformation private and the public than one, supplying the public good becomes less attractive, being equal. As a result, one should expect fewer income groups to prefer expenditure maximization on public goods than before. This is indeed the group result we obtain here a is elected in period 2, : If a government representing income it will set the tax rate t 2 to solve : 1 21 max log(c 2 + subject to g2 ) c, : a(l-T 2 s(a;p) .p ) (5-'D T 2 Ea-dp g? 1+A that there is no default on public debt) (assuming . Notice that any dollar 1 more units of through taxes and spent on the public good yields raised 1+A the public good. From the first-order conditions we obtain that T2 = t2 While = if 1 max a< Ea 5-5) Ea iO if a > l7\ previous sections all income groups below the average income in the preferred strictly maximum expenditure on public goods, now only those Ea income groups below prefer expenditure maximization. 1+A If the public good is more expensive to produce one should also expect that fewer income groups prefer default in order to increase expenditure on the public good, and consequently that fewer possible administrations would choose to default in period 2. The next result shows that this intuition is indeed correct that the first-period tax rate has been set equal to zero' 1 ^ 1 , an elected government located at a assesses a default decision Suppose only if first that t2 Ea-dp ~ = : Ea - 1+a — 1+A - + -. s(a.p) .p 1. ! Assuming consider how : In that case default is attractive if and 22 or s(a.p) > (5-6) 1+A d N/here and s(a,p) : a + PPl U+A — = Ea-dp ^ - 1+A ) (5-7) (1+P)p p is the (correctly anticipated) equilibrium interest rate in period 2 when t, = 1 and the elected government does not default We can then establish the following lemma Lemma 1 3 : d, Proof : € : a e(0,Ba) such that if t 2 is to be chosen equal to groups a income a : prefer (a,l) and First, € a(0) then all prefer default whereas all income groups default no Furthermore . a is decreasing in Ea. equilibrium the government = (0,a) 1, interest rate p , when the period-2 is expected both to set t 2 = 1 and to avoid default, defined by is : Es(a.p) s(Ea,p) = = d, where s(a,p) is defined in (5-7) for all a We then have, s(a,p) = d + = d • : (s(a,p) - s(Ea,p)) (a-Ea)p + 1+P Hence (5-6) can be rewritten as (a-Ea)p d > 1+A d + 1+p Which in turn is equivalent to (l+p)Ad a < a(d) = Ea (1+A)p We immediately verify that d. : : : a(0) = Ea and that a is decreasing in a 23 words In is greater than one and if t 2 goods (20) Furthermore, government chooses t, = 1 Consider government debt . > — Ea or t, = a chooses t 2 that a (left-wing) = 1 — Ea = the default decision when the minimizes expenditure on the public good whether the government honors depending on Then an agent earning income a strictly prefers the government + " T s(a,p) : P- S Ea] pp > a 2 dp ad : implies and defaults on Ea government located between a and 1+A = assess in period ( or far so and a = agents to default if and only if tt a whereas ; how next in place debts) its the range of middle incomes which 1, and no default. when t 2 (i.e., analysis our located between outstanding its = default increases with the amount of outstanding debt, prefer no strictly d. when the rate of transformation between public and private : ( a -P)« d \ a + U+A - a 1 - { ) — dp^ ( EaJ = (5.10) (l+(3)p (s(a,p) is derived assuming that the government will not default). We can then prove the following lemma which is similar to Lemma Lemma 2 If : t 2 is minimized by the period-2 government, then all to be groups a income Ea < above Ea prefer default Proof : We begin by period-2 prefer no default all income groups and deriving the equilibrium interest rate, p* government is = , . expected to interest rate is given by the equation Es(a,p") s(Ea,p*) 1. = d. set g 2 = : , when the the equilibrium : (5-H) 24 where s(a,p) is defined in (5. 10). ad s(a,p Now, let g(a) = Ea g(Ea) = 0. From (5-11). we have ) : Furthermore g is linear in a and therefore monotonic in a. Next, we can show that the function g is increasing in a. (Ejdc) have we Indeed, fact that when a (1+X)d which g(D = + < This follows from the . inequality (5-10) becomes equivalent to 1, dA > and g > : d.Ea, automatically is > g(l) Ea since true < 1 ; this establishes : ; Ea when a = inequality (5-10) becomes equivalent to , 1+A 3p*(l+p)d > pp*(l+p)d + : p.(p*p-l), which is violated since Ea(l+A) PP hence g Ea(l+A)-dA " (Ea) < and Lemma 2 is proved. Lemma 2 then implies that a moderate-right-wing government located Ea between and Ea chooses both no default and minimum taxation in period 2 1+A dp') hand a government located betwen Ea and on the other Ea chooses to default and sets t 2 = i.e. t,2 The = ; following distribution function figures 1 0. representing summarize our the results period 2 and the default decision when Tj = : support of the income about optimal tax rates in 25 t, 1/default = t, = dp* 1/no default t, a(d) -^—/no default = r = 2 O/default 1+A Ea Figure 2A : a(d) < 1+A Ty 1/default = t2 Ea = dp — —/no oc< a default r? O/default = ) Ea 1+A Ea Figure 2B As we shall : a(d) > T7\ now see, the presence of the middle-class of incomes ae[a,Ea] can create a situation where it is in the interest of a moderate right wing- party in power to excessively accumulate public debt in order to raise the likelihood (somewhat of being reelected . arbitrarily) defined Recall that a left or right-wing party was to be a party representing primarily the interests of the income groups respectively below the average and above the average. Casual empiricism suggests that this is not always an unreasonable approximation. party as one favourable In same the that puts to large moderate- right- wing spirit more weight public party as we shall define a moderate-left-wing expenditure one that income groups but remains on middle public on puts more goods and a weight on middle income groups but prefers fiscal restraint. In terms of our model, a moderate-left party defends the interests of income groups a ( e EcO a, moderate-right party represents the interests of those groups a and fEa € a ^ ;Ea . 26 The next two propositions establish that under certain conditions a moderate right-wing party in power in period (i) modify successfully the voting may 1 behavior : of the median voter by accumulating debt and thus ensure its reelection, (ii) be better off by following that strategy of debt accumulation. Consider the situation where a Then with zero outstanding 6 debt 1+A there is a majority in favor of a left-wing candidate (a < a in period 2, standing Ea < . right-wing incumbent against a a^ (Ea ^ , Eot I . We show in the first proposition that for a large enough outstanding debt, a new majority arises favouring this "moderate" right-wing incumbent. Proposition c 6 Ea When am : is close enough to & there exists a level of , 1+A outstanding debt d such that all a € [am ,l] strictly prefer the right-wing candidate over the left-wing challenger. Proof Ea : In what follows, we suppose that am Let d (a) (b) < be a level of debt such that > — 1+A with am close to Ea . 1+A : Ea ad) < 1+A d.p* < Ea (where p* is defined in Lemma 2). (This debt d condition says ! is feasible that it to repay the amount of ) Condition (b) is equivalent to : — p.Ea d < (5-12) 1+p. 1+A Whereas condition (a) is equivalent to p.Ea d > : — l+P Note that these two inequalities (5-13) (5-12) and (5-13) are consistent they define a non-empty set of debt levels d. ; ) 27 Using that a(d) is continuously decreasing in d, we can the fact p.Ea always choose d sufficiently close to - — - in order to have 1-3 Ea aL < a(d) < (5-1*0 1+A [see Figure 3 below] a, \ a 4— ^4- Ea a(d) 1+7 Figure Ea (=a(0)) 1 3 For such a level of debt the left-wing candidate a L will default in period elected if 2 analysis that ; this furthermore left-wing we know from the foregoing candidate will set : Ea t 2* = 1 and g d . hand the right-wing candidate o^ will not default on the other On —— 1+A = this oustanding debt, d, if elected, since we have assumed o^ furthermore T2 = we know a right-wing that such < Ea candidate will set ; : dp' Ea Clearly, : S, 0. = median voter am were located below a(d) if the automatically vote for am and a L would choose t 2 the left-wing candidate aL , he would since both and default in that case. However, if Ea am is sufficiently close to the level of debt d can always be 1+A chosen such that = 1 , : 28 a, a(d) < a < (by continuity of a w.r.t. d) of d such For choice a default elected a(d)) < (oc t, = : the 1 and the left-wing candidate will default on d if However, . government. most preferred period-2 policy becomes median-voter's no incumbent the by right-wing candidate will minimize and the ; { taxes t 2 h> B > voter must compare the losses involved in electing the median So, either of the is elected he gets dp *l p H + Ea • . if : Ea : ; 1+A the left-wing candidate is if the right-wing candidate : ( s la *\ Km'*p ] , to show is easy (It candidates two the median voter gets elected, a - J that the right-wing incumbent is given by Tj =0. Given left-wing party will indeed always default) earner (and therefore incumbent if and only if a dp f,1 - 'l Ea = , X +A . t. by the this choice of t. , a Thus the median income voter) votes for the right-wing : — Ea i Let am the median , p s(a ,p*) + choice of first period > (5.15) then (5-15) is equivalent to dam < Ea s(am .p*) (5-16) But from the proof of Lemma 2 we know that (5-l6) is satisfied when Ea Ea a = By continuity, the same inequality will hold for am < 1+A 1+A . - 29 Ea but sufficiently close to debt accumulating By moderate the challenger look left-wing . 1+A incumbent makes the right-wing the eyes of moderate voters. The latter bad in the government care about preserving the real value of their savings (i.e., not defaulting) problem for maximizing expenditure on hand one outstanding the this candidate left-wing the that he cannot commit to both and not defaulting on the public is public goods When it comes to choosing between no default but fiscal restraint on debt. the like large expenditures on public goods. The they also ; increased and spending on public goods, but default on the other, a lower-middle class voter may well prefer debt on former alternative . An incumbent moderate-right-wing party can foresee and thus use public debt to enhance its likelihood of reelection. The question remains, whether in the interest of a right-wing party to it is follow that strategy. The next proposition establishes this. Proposition 7 When am : Ea is sufficiently close to J. right-wing incumbent's interest amount of debt (d Proof : If the incumbent sets d 0) > - 0, —A it will be in the to accumulate a positive in order to ensure its reelection. the left-wing challenger wins the next election so that the right-wing party's total utility is given by —Ea— log a^+ plog Now let d 1+A > be minimum the amount of debt necessary for the candidate to reverse the outcome of the elections. With right-wing 5 that 1 and Thus, level of public debt he gets ftp 1 - + - + a,,- : 1+A " s(a,.d,p ., ) in period ' p.s (a H d p* J in period 2. (p*is given by (5.11)). , , the difference in first-period total consumption (measuring 30 the costs of debt accumulation) s a n. 5 ( is given by : d -p") " J7 A' Ea closer a m The is to from the follows in period the loss zero, , (This directly the lower d needs to be. 1+A proof of Proposition 1 6) . Now as d converges to total consumption from issuing debt d becomes negligible. (When d — p* 0, > — = p" (d) 1/(3 therefore and s^.d.p*) given by (5-10) converges to zero). But the gain in period-2 consumption is bounded away from zero as d f M — the gain in period-2 consumption given by 0, » dp'l 1 P lo7j « / • + " : - s K' d -P .\ J " ^ — E" Y7X converges to o^ - > 0. This establishes the proposition. VI. CONCLUSION To . sum up, even though that, strategic we established in this section what have ? We have shown forward-looking, debt can play an important agents are the political game between a left-wing and a right-wing role in party. The particular illustration of the strategic role of debt considered here was about a right-wing party (21) accumulating excessively large amounts of debt so as to change the preferences of the median voter in its favour by financially creating a situation irresponsible in where the eyes the of a left-wing party appears majority of voters holding a substantial fraction of their savings in government bonds. The monetizing in fact voters become more concerned about the government the debt, when they hold a sustantial fraction of their savings government experience that bonds, (at least seems rather plausible. In light of historical in the 20th century) it seems equally plausible that 31 administrations may left-wing outstanding than right-wing administrations. The next step in public debt logically from following argument, the be more inclined to erode the real value of observations these two - namely, that a right-wing administration may deliberately increase the government's to create indebtedness as ensure to a problem of potential monetization of the debt so reelection its - somehow seems less plausible. Perhaps governments are not as cynical as we make them appear in this model else, Or the outcome of elections. For more conservatively. vote mechanism is might be reason bond-holdings has often been argued that a instance, it administrations partly by right-wing pursued superior instruments available to manipulate voters to become home-owners on even shareholders is inducing more policy the may have they ? Exactly how similar to because home-owners tend to this work is not clear but perhaps highlighted in this paper the one ? A third that governments may not know exactly the distribution of in the economy. They may then not be able to predict exactly the preferences of voters concerning default. A fourth reason, (perhaps the most important of all) is that a government accumulating large deficits may itself appear financially irresponsible and thus be voted out of office for incompetent management (recent events, however, do not seem to corroborate this explanation) any event, In we do model developed here whole reasoning Other in propositions is summarized about behind these policy) not wish to argue that the main interest of the government action propositions is 6 and 7- Rather the (and specifically about fiscal as instructive as the conclusions. interesting aspects of the model relate to how empirically plausible predictions about fiscal policy of one or the other party emerge from simple assumptions about which income group's interests each party seeks to promote. Moreover a interest may exist between the middle-income groups and the extremes (very low and very general lesson from this section is that conflicts of high income groups). In this respect our model has similar 32 properties as one the [1988]. These conflicts of Cuikerman-Meltzer arise whenever general and are quite interest in the public good is not a good. We expect that even if there is the private perfect substitute for perfect substitution between public and private goods, such a conflict may if the income-tax schedule is sufficiently progressive, exist higher bear most income groups result, a may conflict of the costs of servicing the debt. As concerning arise for then the the a default decision between middle-income earners and the other income groups. Many aspects relating to model of course need much further development. A systematic treatment this of uncertainty is system : equilibrium political how parties number of choose parties equilibrium emerges Alesina-Tabellini of necessary. More a democratic needs to their ? ? location If there Finally, and Persson-Svensson be said and about the political what determines the are more than two parties what this paper along with those of have highlighted some of the costs two-party system. An interesting and important project is to investigate and formalize what the benefits of such a system are. 33 REFERENCES Alesina, Alberto [1988] Public High (ed.). of Large Public Debts", in Spaventa, "The End Debt Experience the : in Italy, New York L. : Cambridge University Press. Alesina, Alberto and Guido Tabellini [1987a] "A Political Theory of Fiscal "NBER Working Paper No. Debt in a Democracy, and Government Deficits 2308, July. Alesina, Alberto and Tabellini Guido [1987b] "External Debt, Capital Flights and Political Risk", Mimeo, Harvard University. Alesina, Alberto and Guido Tabellini [1988] "Voting on the Budget Deficit", MIT CEPR Discussion Paper No. 269. Cuikerman, Debt Alex and Allan Meltzer [I988] "A Political Theory of Government and Deficits in a Neo-Ricardian Framework", Mimeo, Carnegie-Mellon University. Persson, Would Torsten Run and a Svensson Lars Deficit : [1989] "Why a Stubborn Conservative Policy with Time-Inconsistent Preferences", Quaterly Journal of Economics 65, 325 - 3^6. 3^ FOOTNOTES 1. 2. In our model even a proportional income tax has redistributive effects. Our for any utility function satisfying the be obtained results can following properties : - private and public consumption are substitutes - the marginal rate of substitution between the private and the public good is increasing with consumption of the private good d ( dU/dcA dcj { d\J/d Si 0. < A utility conflict with function about fiscal average prefer above average prefer conflict large properties these fiscal restraint expenditure and agents public default on model regarding in our on gives rise to the basic where agents with income our model policy in : with income below goods. Similarly, the public debt would arise with any utility function with the properties above. Moreover our social planner that the Section separability one also obtains Ricardian super indeterminacy (provided of result about course (See assumes intertemporal if one III for a only cares about Pareto-efficiency) derivation of the result of Ricardian super indeterminacy) 3. of the utility function, we only consider such public Given the form goods as public education, health care, social security, etc. ; these can be viewed quite naturally as substitutes for private consumption. 4. Introducing distortionary taxation would not alter our main results about the roles of debt. Interesting additional effects probably arise if taxes political equilibrium and the committment and strategic 35 are distoritionary on . For instance, off between equity and efficiency. We shall known trade the well the political equilibrium may depend pursue these additional aspects in future research. 5- In our model we have normalized the set of taxable incomes to be [0,1]. Equivalently tax schedule income uniform tax have taken we could , rate function to be composed of t [0,1] e an to a and a redefined the consumers' utility : that introducing imposing [a,l+a], with an to be exemption equal a tax and , u(c) Note this set upper tax-exemption. a savings functions : lower bound By doing = t Log(c-a) bound on on 1 < so, we taxable incomes the avoid an tax amounts to rate when there is no unpleasant feature of our that agents may have positive savings even namely, if all their income is taxed away (See Footnote (11)). 6. Agents can save by holding three different assets which provides zero interest rate p Holding ; interest ; they can : they can hold cash buy government bonds with or they can lend to other agents who wish to borrow. cash is always dominated by either lending to other agents or buying government bonds. We that assume that private assumptions, there is agents default never the interest competitive capital market and a perfectly their on debts. Given these rate on private loans must always be equal to the interest rate on government bonds (when the government does not default on its debt) 7- An interesting implications extension for fiscal of our policy of model would having more shall investigate this in future research. be to analyse the than two parties. We 36 8. We that parties in power break their campaign pledges if thus assume is in their interest and that there is no reputational loss from this doing Electoral so. have programs Judging campaigns then commitment no recent from are pure "cheap talk". Electoral value campaigns, and this nobody not does is fooled by them. seem to be a very unrealistic assumption. 9. A full-blown analysis of the political game with uncertainty is beyond scope of the introduction with, We shall of uncertainty. issues arise with the just mention two to begin : uncertainty about future income may result in uncertainty about outcome the Several interesting this paper. of elections. future This may bring about default in equilibrium so that government bonds become a risky asset. Agents then problem ex-ante a portfolio-choice face decision. governments choose their debt policy in the Secondly, when first-period instead of a simple savings have to make difficult compromises because of they also uncertainty of the electoral outcome. Thirdly, interesting issues the arise concerning default when the government is uncertain about the distribution of bond-holdings in the economy. 10. In other all respects, democratically-elected above the law the dictator is identical to a government. In particular, our dictator is not and behaves so as to respect all constitutional rules imposed on him. 11. An extremely useful linearity solve with respect for s(a,p,T t ;g t property of s(a,p;T t ;g t the ) to a. equilibrium This allows ) for our purposes is the us for instance to easily interest-rate. While the shape of simplifies our analysis considerably, none of our results seem to depend directly on its specific form. This is reassuring since linearity is probably not a robus property. 37 There are several other noteworthy features about the government runs no deficits so that d when below average with income agents s = (a.p.T ,g 0, ) . First, one observes that borrow from the capital market and those with incomes above average lend at the equilibrium interest rate p = 1/(3 if and only if , functions and high-income when the government the supply of Otherwise, . That is, are reversed. save > t2 t, if t, the borrowing and lending then low income agents t2 < These predictions agents borrow. are modified runs deficits only to the extent that the higher more all government-bonds, the income-groups tend to save. a slightly Second, agents may have of our awkward feature savings positive even savings function is that =1. They if Tj save, even though all their income is taxed away. This is possible since we allow for negative consumption. unpleasant feature normalization. litterally. A tax (5) model our of rate such =1 as t, tax income. have argued that this we simply is result the of a should not be interpreted upper bounds governments have In practice, can effectively they In footnote This upper-bound on how much is normalized to equal one in our model. 12. Since individual utility functions are strictly concave and identical, the utilitarian welfare consumption is implemented by setting equal function is the to t } that the utilitarian of debt d e t2 maximized when all individuals' average = 1. This outcome can be income. For Tj = t2 = 1, it can be shown social planner is indifferent between any level [O.Ea.p]. 13. Since t 2 is chosen in period 14 We thus rule out voting behavior driven by ideological considerations. This should 2, savings must be treated as a constant. is clearly a very strong assumption. point out However, in our defense, we that it has been widely observed that income is the 38 best predictor of voting behavior. 15- that Recall government since government left-wing a does not followed by another left-wing accumulate debt to redistribute income, need to more efficiently redistributed through high taxes in income is both periods. Debt is used only because the right-wing government sets low tax rates in period 2. 16. We assume here that the government defaults on its outstanding nominal debt by running real value of an infinitely-high government debt of other value inflation inflation, so is totally that not only the eroded but also the real nominal assets. In practice, implicit default through (monetization of the debt) seems more common that explicit default. This is why default we have focussed on this form of default. In addition, through inflation is more costly than explicit default to the extent that it also wipes out the real value of other nominal assets. If establih we that a government incentives has to default via inflation even though this hurts its own constituency by eroding their private savings then a fortiori these incentives are present if the government defaults explicitly and thus does not affect the real value of its constituency's savings. In footnote (17) In particular we we briefly analyse the effects of explicit default. consider whether a government prefers explicit default over monetization if given a choice. 17- The difference between the former case latter their over choice explicit default only government case government and monetization is that in bonds become worthless while in the bonds as well as all other nominal assets see value being eroded. Creditors therefore prefer explicit default monetization and debtors have between monetization the reverse preferences. Given a or explicit default a government is all 39 more tempted to default explicitly on the outstanding public debt the of monetizing (instead who are agents the debt) borrowers. Thus, default differ explicit represents the if it out how the incentives for to find from the interest of incentives of monetization in our we must determine who are the borrowers and who are the lenders model in the internal capital market. The identity of and lenders is most easily identified the borrowers when there is no outstanding government debt (d function is given by ) = immediately place when that = if 1/3 his Then the savings (1+P")/P intertemporal transfers then only take The reason is that an individual agent only wishes . perform intertemporal to p ^ t2 Tj . T 2 )(Ea-a) (t 1 - 1 notes 0) : s(a,l/p;T ;t 2 One = consumption her or the equilibrium interest-rate transfers at different in both periods. is Consumption smoothing is the motive for intertemporal transfers an ! Now, individual agent's consumption in both periods differs only if the tax-rates in both periods differ. Given that optimal tax-rates in both periods in are either equal to zero (when a right-wing administration is one (when place) or the left-wing only two cases to consider Tj - t2 = 1 (ii) Tj - t2 = -1 (i) (i) this In incomes a below Ea borrow. When t > average get government's period 2 Consumption a , there are : agents case, party is in power) higher with = 1 incomes a and t 2 = consumption in 0, < Ea save and those with the agents with incomes period 1, because of the policy of maximum redistribution in that period, (where a policy smoothing then of than in minimum redistribution is selected) dictates that they save. The opposite is 40 true for agents with income above average, which is why they borrow, is entirely symmetric to This case (ii) here low-income agents ; in anticipation of a more redistributive policy in the future borrow, exactly opposite for the and (i) wealthy save. reasons the (Note that these rather intuitive results depend critically on our assumptions of expectations on rational tax-treatment of savings savings is from hand and on our assumptions on the the one on the other. to the principle of no double We appeal not taxed. In our model interest revenue taxation to justify this assumption. Of course this principle is never systematically applied practice, in obvious for reasons. An interesting extension of our model, thus might be to allow taxation of interest income) consider Next, government have how increases level the savings change when the agent's individual an of oustanding government debt. We : - (Tj s(«.l/ P ;T i: f 2 — T 2 )(Ea-a)+d(l+l/p.) ^^ = ;d) ds(.) Thus , = 1 dd As the government compensate of for expected the borrowers level with d future increases in taxes. Thus the identity of private funds is independent of the and lenders of government varies everyone saves more so as to exactly increases d, the volume of borrowing and lending (Only debt. d extent that to the now t,2 £<1, > . In fact, the Ea.p/ higher is d the lower is the volume of funds exchanged in the internal \ capital markets). Since the identity of the borrowers and lenders does not change with difference it d is now straightforward to default in incentives to determine explicitly rather the than through monetization. Basically, a left-wing government following a right wing government (t 2 constituency is mainly where a = 1 right-wing ; Tj = 0) prefers composed of government monetization borrowers. In follows a since its the opposite case left-wing government 41 d (t = 1 = t, ; ) (case (i))- the case In Finally when arise. explicit = (Tj t2 = the issues does not 1) ( the right follows the right preferred to default is d = t, ; t, "I = monetization. Since, in this final that monetization we establish case, where a left-wing government is followed by administration left-wing another mainly of borrowers then composed constituency is since its again, prefers monetization government right-wing the , is better than no default, it follows that a fortiori explicit default is better than no default. 18. A interpreted in can be technological units of 1+A public to : ways. It may be a pure to produce one unit of public good one requires private good. Alternatively, it may represent a cost of funds (A then measures the efficiency-loss of allocating funds the strong public sector) assumption to . maintain this Whatever suppose and independent constant We cost several different intrepretation that of transformation is rate the one takes it is a of the level of production of public goods. assumption mainly to remain in the spirit of the model where everything is linear. Finally, note that propositions and 5 are false, only if A 4 A < 0, all types of government a £ [ > 0. When 0,1 ] prefer to default in period 2 . (See footnote (20) infra for details). 19. It is easy government. to show that Tj We restrict is optimal for a right-wing incumbent = attention to case the where t. = for expositional reasons. In fact a more general result can be established that holds for all Tj £[0,1]. 20. If A < matter 0, this set of (See footnote (20)). income-groups is which income-group's empty. All interests they default ex-post. This can be seen as follows Consider first the case where t, = 1 . seek to governments, no promote, favour : Then, condition (5-6) becomes : 42 = s(Ea,p) = d, since t = t = 1 > s(a,p) 2 1+A In other words, default is attractive, if and only if A < 0. Note that Ea Ea dp ( Next, when a > and t,2 £s0, 1 for all a < we can >, 2 1+A 1+A Ea/ \ lemma and conclude that all types a the following apply default > Ea wish to : — Ea ad Lemma Proof : : > s(a,p) a e[Ea,l] <=> begin by deriving the equilibrium interest rate, We government period-2 the is expected set to g2 p° = when , : the equilibrium interest rate is given by the equation fo s(a,p)f(a)da Es(a.p) = = s(Ea,p) = d or d+T 1 Ea + PP 1+A ^-t) Ea(l-T.l d(l+(3)p. Rearranging terms one obtains (l+A)Ea (5-10) p[Ea(l + A(l-T ))-dA] 1 Let a be the income group indifferent between default and no default, then — Ea ad . = . s(a,p ) or using (5-9) The ad — Ea d+T, Ea adp 1+A Ea { lemma now follows from the mono tonicity and linearity of the . ,1 + P)p = PP savings function w.r.t. a. + a(l-Tj) a - o ^3 that the proof works for any value T i e[0,l] and for any A. The ad simply says that any income group a satisfying > s(a,p) condition Ea property prefers default when g 2 = 0. To summarize, when Tj = 1 this Notice — A < and verify < £s0, &P\ > the incentives suffices a ( and t = t, a(d) = Ea > to default when t and t 2 = } Lemma which 1 default prefer - Ea prefer default. It remains to all types a apply (l+3)Ad to prefer default. Moreover, when government of types all = states (this 1 Here, . that it all lemma applies for all (1+A)(3 value of A) Note . A < for that who wish to set t, governments into wish to set t 2 21. = 1 when Thus, A < 0, all prefer default and all governments prefer default as well. = strategic use of debt-accumulation is not the exclusive attribute The of a(d) > Ea. have we right-wing possibility that amounts large administration. debt so as to ensure its reelection against a [implausible] situation corresponds to the opponent. Such right-wing for the symmetric allows model left-wing party accumulate excessively moderate a of Our following political configuration : a a, a„ -+- Ea a(d) 1+A (1) aR > Ea , so that the = right-wing Ea a(0) candidate defaults on the outstanding debt if reelected. (Ea \ am £ .Eoc so that without debt-accumulation the right-wing (2) , candidate is elected, and with debt-accumulation the median-voter w prefers no default on the outstanding debt. Ea Ea < but close to oc, so that by accumulating a sufficient (3) L 1+X 1+X amount of debt d, the left-wing party ends up being located above the , cut-off point Qf(d) ; this in turn provides the left-wing party will not default on d if reelected. 2385 OU guarantee that the Date Due SEP* 1 * MIT LIBRARIES DUPL 3 1 1060 D057fl1b7 1