can political monetary cycles be avoided?

*Correspondence author. E-mail: [email protected]

Journal of Monetary Economics 42 (1998) 525—545

Can political monetary cycles be avoided?

Ali al-Nowaihi!, Paul Levine",*! University of Leicester, UK

" CEPR and Department of Economics, University of Surrey, Guildford, Surrey GU2 5XH, UK

Received 12 February 1997; received in revised form 17 September 1997; accepted 31 October 1997

Abstract

This paper shows that political monetary cycles can be avoided in a monetary regimewith Walsh-type contracts. Such contracts were originally proposed to eliminate theinflationary bias of discretionary monetary policy. This requires some commitmentmechanism to enforce the contract and prevent its renegotiation, but here we rule thisout. Instead, in the context of a monetary regime with an instrument-independent centralbank and an inflation target (the goal) set by the government, Walsh contracts servea different purpose: namely, they provide an efficient signalling device that eliminates thepolitical monetary cycle, results in the election of competent governments and increasessocial welfare. ( 1998 Elsevier Science B.V. All rights reserved.

JEL classification: C72; E61

Keywords: Credibility; Central bank contract; Reputation; Renegotiation

1. Introduction

This paper addresses an important question which arises out of the rationalpolitical business cycle literature: can political monetary cycles (PMC), in whichpolicymakers engage in a pre-election monetary expansion, be avoided? Ina number of recent papers (Rogoff and Sibert, 1988; Rogoff, 1990; Persson andTabellini, 1990) a surprising pessimistic view is put forward that it may not bedesirable to even attempt to curtail the cycle because it provides an importantsignalling device that conveys information to the electorate regarding the

0304-3932/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved.PII S 0 3 0 4 - 3 9 3 2 ( 9 8 ) 0 0 0 3 2 - 4

1The Rogoff delegation game has been extensively studied in the literature. See, for example,Currie et al. (1996), Herrendorf and Lockwood (1997), Svensson (1997) for some recent contribu-tions).

incumbent government’s competence. According to this view it could well bethat suppressing the cycle would be counterproductive, resulting in the morefrequent election of incompetent governments, or the resort to more costlyforms of signalling.

But are there less costly forms of signalling? We argue that this indeed is thecase. The signalling device we propose is a Walsh-type contract (Walsh, 1995)between the government and the central bank (CB). This forms part of a mone-tary regime which consists of the following essential elements:

1. an instrument-independent (but goal-dependent) CB.2. an inflation target set by the government which is credible in a precise sense

to be spelt out. The CB pursues the target using the usual range of monetaryinstruments at its disposal.

3. The CB is accountable to the government for its performance in a way that istransparent to the public. This is achieved through a public contract betweenthe Government and CB that specifies the inflation target and the incentivemechanism to ensure that the CB pursues that target.

These three aspects of the regime merit some preliminary comments before weproceed with the substance of the paper. Instrument or operational indepen-dence implies that the CB is free to choose the best means of achieving anexternally chosen goal. Goal independence means that the CB is free to choosethe goal itself (see Debelle and Fischer (1994) for further discussion of thisdistinction). The absence of goal-independence distinguishes our regime fromthe form of delegation first proposed by Rogoff (1985) in which the ‘type’ ofbanker — measured by its relative averseness to inflation compared with thedeviation of output from some target — is first chosen by the government butthereafter the CB sets its own inflation target.1

Inflation targeting has been adopted in a number of countries in recent years.Table 1 provides a summary of these arrangements. In some of these countries(notably Finland and Sweden) there is no explicit form of accountability andinflation targeting consists of unilateral announcements by the CB to makemonetary policy more transparent. It is also of interest to note that the degree ofindependence — as measured by an index that awards a high mark for bothinstrument and goal independence — varies considerably among these countries.Inflation targeting is also being seriously considered by the European MonetaryInstitute as the appropriate monetary regime for the European Central Bank(European Monetary Institute, 1997).

526 A. Al-Nowaihi, P. Levine / Journal of Monetary Economics 42 (1998) 525–545

Table 1Countries with inflation targets

Country Date of Inflation target % Central bankintroduction (initial inflation) independence!

Australia 1993 2—3 (1.8) 9Canada 1991 1—3 (6.2) 11Finland 1993 2 by 1995 (2.6) 5Israel 1991 8—11 by 1995 (18) naNew Zealand 1990 0—2 (7.0) 3Spain 1995 below 3 by 1997 (4.4) 5Sweden 1993 2$1 by 1995 5UK" 1992 2.5 or less (4.2) 6

!Using the Grilli et al. (1991) measure of economic and political independence. The higher the score,the greater the independence."These figures correspond to arrangements under the previous Conservative government.Sources: King (1996) and Eijffinger and de Haan (1996).

2 al-Nowaihi and Levine (1996) pose the problem in terms of the non-renegotiation-proofness ofthe Walsh contract.

In the absence of some device that enables the government to precommit, theonly credible inflation target is the well-known discretionary inflation rate. Thisleaves no incentive for the government to spring an inflation surprise byannouncing a new target after public expectations and nominal contracts basedon these expectations have been formed. However, inflation is even higher in themonetary political business cycle model set out in Section 2 where there are noannounced inflation targets and CBs are not goal-independent. Then politicalconsiderations result in inflation being above the discretionary rate: bothcompetent and incompetent governments have incentives to raise inflation, theformer to reveal its type and the latter to conceal it.

The third element — the public Walsh-type contract setting out the target andthe incentive mechanism — is crucial. In Walsh (1995) the incentive mechanismlinks an income transfer to the CB or its executive, to the performance of theeconomy. Alternative mechanism can provide the same incentive — for exampleprovision for dismissal of the Governor (see Walsh, 1993). The Walsh contractwas originally devised to be optimal in the sense that it eliminated the inflation-ary bias of discretionary monetary policy without removing its stabilizationrole. This role for the contract has been criticised in the literature, notably byMcCallum (1995), who describes the arrangement as merely relocating thetime-inconsistency problem to that of enforcing the contract.2

This paper highlights another way in which the contract can serve a usefulpurpose. A contract between the government and a CB which can be observed

A. Al-Nowaihi, P. Levine / Journal of Monetary Economics 42 (1998) 525–545 527

3The new arrangement in the UK with the Labour Party administration incorporates elements1 and 2. There is an implied accountability of the Governor and his monetary committee for itsachievement but the mechanism is less direct and explicit compared with the New Zealand case. Forexample there is no explicit penalty for missing the target and incentive compatibility relies onpolitical embarrassment and civil servants’ commitment to public duty.

by the public will make the relationship between the two policymakers explicitand transparent. This we show provides an efficient signalling mechanism thatconveys information about the government’s type to the electorate. In particularwe will show that a competent government always signs a public contract withan inflationary target equal to the discretionary rate. Then whatever incompe-tent governments do they reveal their type and fail to get elected.

Among existing CBs, the arrangement closest to our proposal is the PolicyTarget Agreement in New Zealand.3 The Reserve Bank Act of 1989, which tookeffect in February 1990, specifies that inflation targets should be determinedby the Government, but may be revised by agreement between the FinanceMinister and the Governor. Any such revisions must be made public. The Act isexplicit in assigning responsibility for achieving the targets; in particular it is theGovernor’s duty ‘to ensure that the CB carries out the functions imposed on itby this Act’ and failure to achieve the target can lead to the removal of theGovernor. There is also provision for flexibility in the face of unexpected shocks.Events that would justify deviations from the 0—2% target range are aggregatesupply shocks spelt out as terms-of-trade price shocks from external sources,changes in indirect tax rates, a natural disaster or major fall in livestocknumbers owing to disease and price-level changes resulting from governmentlevies. Thus in effect the inflation target amounts to a monetary rule whichcombines low average inflation with a stabilization function.

Section 2 sets out a PMC model in which either competent incumbentadministrations attempt to signal their competence by a pre-election monetaryexpansion (the separating equilibrium), or incompetent administrations concealtheir incompetence by the same means (the pooling equilibrium). This sectionclosely follows the treatment of Persson and Tabellini (1990), °5.2). Section 3establishes our main result that there is a more efficient signalling device andSection 4 provides some concluding remarks.

2. The political monetary cycle as a signalling device

2.1. The setup

The setup is a two-period signalling model. There are two types of policy-maker, one ‘competent’ and the other ‘incompetent’ in the sense explainedbelow. Nature chooses the incompetent type with probability p3(0,1). The type


4Throughout the paper, E( ) ) refers to expectations formed at the beginning of the game.

of policymaker is known to itself, but not initially by the public. However, theprobability p is public knowledge. A competent policymaker will achieve a high-er natural rate of output. Thus we can write the natural rate as y*#XM when thecompetent type is in power and as y*#X for the incompetent type, whereXM 'X (output is expressed in logarithm form). The expected natural rate is theny*#pX#(1!p)XM . For convenience we redefine output y

tin deviation form

about this expected natural rate; define xN "XM !(pX#(1!p)XM )"p(XM !X)in deviation form about the expected value pX#(1!p)XM and similarly definex"X!(pX#(1!p)XM )"(1!p)(X!XM ). Then we can write a modifiedLucas supply curve at time t as

yt"n

t!n%

t#x

t, (1)

where nt

and n%t

denote inflation and beginning-of-contract expectations ofinflation, x

t"xN '0 if the competent type is in office and x

t"x(0 if the

incompetent type is in power and E(xt)"pxN #(1!p)xN "0.4

The electorate are assumed to have the same preferences over output andinflation given by the two-period social welfare function

¼"

2+t/1

dt~1wt"

2+t/1

dt~1[ayt!1

2n2t], a'0, (2)

where wtis the single-period social welfare.

Both policymakers are drawn from the same electorate and therefore have thesame preferences over output and inflation. However both types derive the sameextra utility v'0 from being in office. Corresponding to Eq. (2) we then havethe following two-period utility function for each policymaker:

º"

2+t/1

dt~1ut"

2+t/1

dt~1[ayt!1

2n2t#v

t], a'0, (3)

where vt"v'0 if the policymaker is in office, and v

t"0 otherwise. In order for

the incompetent type with xt"x to actually stand for office we need to assume

that v is sufficiently large to ensure that the incompetent type prefers to be inoffice than in opposition, i.e.

v'a(xN !x). (4)

The model is completed by assuming that wage-setters’ aim is to correctlyforecast inflation implied by a single-period utility function z

t"!(n

t!n%

t)2.

A feature of this setup is that a member of the public behaves differentlyas a wage-setter and as a voter. This can be justified by the following con-siderations. Suppose that we interpret the model as one with involuntary


5Note that our setup is slightly simpler than that in Persson and Tabellini (1990). There the typesof government and opposition are random variables and if a government is re-elected, then its typein period 2 is positively, but not perfectly, correlated with its type in period 1. Crucially, however, theinformation assumptions are the same and both setups give qualitatively similar results.

unemployment. Then the collective action needed to increase employment andoutput would be difficult to coordinate and enforce. On the other hand unilat-eral action would impose significant costs on an individual, but would have aninsignificant effect on aggregate output. It follows that when the private sectorbargains over nominal wages they take aggregate output and inflation as givenand this is implied by the choice of utility function.

The situation facing an individual in her role as a voter is quite different. It istrue that collectively they can vote an incompetent government out of office, butindividually they only have a very small effect on the political and henceeconomic outcome. However, the crucial difference now is that the cost of votingfor a competent government is exactly the same as that for an incompetentgovernment. The rational voter, if she votes, will therefore take into accounteven the negligible effect of her vote on aggregate output and vote for thecompetent government. Of course the cost of participating in the election,although small, is not negligible. Political economy models such as ours cannotexplain why individuals participate in elections (in the absence of legal require-ments as in some countries). One must assume that citizens enjoy participatingin public events. What we can say is that the different behaviour of individuals asvoters (if they do participate) and wage-setters can be rationalised.

Now consider the timing of decisions. A central feature of political businesscycle models of the type represented here is the information assumption regard-ing the policy instrument in the period before the election. In our model themonetary instrument is taken to be the inflation rate which we assume is onlyobserved after the election. The expansionary effect of inflation on employmentand output is observed before the election. These information assumptions areconsistent with a world in which employment and output adjusts before prices.Neo-Keynesian models of imperfect competition with menu costs would pro-vide micro-foundations for such a world (see, for example, Romer, 1996).Different setups which capture the same basic idea are possible. For instance inRogoff (1990) an incompetent government has the incentive to divert govern-ment expenditure from less visible public investment to more visible publicconsumption.5

We now set out formally the sequencing of events in the game between thepolicymaker, the wage-setters and the voters. Throughout this section monetarypolicy is conducted by the government in contrast with Section 3 which intro-duces an instrument-independent monetary authority.


Period 11.1. Nature chooses the type of government in office; x

1"x with probability

p and x1"x6 with probability 1!p. The government knows its own type but

this is not revealed to the public. The public however know p which we assumeinitially satisfies p41

2. The opposition party is of the alternative type. These

types remain fixed for the duration of the two-period game. The public adoptsthe prior p

1"p.

1.2. The public forms its inflation expectation n%1

for the period and wage-setters sign wage contracts based on this expectation. Contracts last for oneperiod.

1.3. The government chooses n1.

1.4. The public observes output y1

but not inflation n1.

1.5. Having observed y1

the public updates its belief about the type ofgovernment from p

1"p to p

2.

1.6. An election is held in which the electorate elects the incumbent or votesfor the opposition.

Events 1.1 to 1.3 occur at the beginning of the period and remaining eventsoccur towards the end of the period. If p

2"1

2the electorate gives the incumbent

the benefit of the doubt. Period 2 is similar except that there is no electiontowards the end and the types of political parties are as chosen in period one.Specifically we have:

Period 22.1. The type of government is the winner of the election at stage 1.6.2.2. The public forms its inflation expectation n%

2for the period and signs

wage contracts.2.3. The government chooses n

2.

Note that it does not matter what observational assumptions are made aboutn1, y

2and n

2as long as n

1is observed after the election and n

2is chosen after

n%2

is formed.

2.2. The equilibria

First consider period 2. As in the standard Barro—Gordon type of game, forany n%

2the government’s best response is the discretionary inflation rate n

2"a.

Hence the public forms the expectation n%2"a. The inflation, output and

single-period social welfare outcomes are summarised as

¸emma 1: ¹he period 2 outcome

(i) In period 2 both types of government adopt the discretionary policy:n2"n%

2"a.


6We follow the definitions of Fudenberg and Tirole, 1991a, Fudenberg and Tirole, 1991b.7Recall the normalization px#(1!p)xN "0, i.e., p(xN !x)]"xN in Eq. (1).

(ii) If the competent type is in office then y2"xN , w

2"axN !1

2a2.

(iii) If the incompetent type is in office then y2"x, w

2"ax!1

2a2.

(iv) The expected outcome is E(y2)"0; E(w

2)"!1

2a2.

The following propositions (and that in Section 3) describe perfect Bayesianequilibria (PBE), the appropriate equilibrium concept for our dynamic game ofimperfect information.6 In the proofs provided in the Appendix we establish theconditions for a PBE: ie, we show that at each information set the strategy ofeach player is a best response to the strategies of the other players, given beliefs,and that beliefs are updated using Bayes’ rule given strategies. We also show thatthe ‘intuitive criterion’ of Cho and Kreps (1987) is not violated.

Proposition 1: ¹he pooling equilibrium(i) Assume that

v'a(xN !x)#1

2d(xN !x)2. (5)

Then the game has an intuitive pooling PBE described by the following strat-egies (S1) to (S3) in period 1 and (S4) in period 2:

(S1) The public sets n%1"a#p(xN !x)"a#xN .7

(S2a) The competent administration sets n1"a.

(S2b) The incompetent administration sets n1"a#xN !x.

(S3) If y150, then the electorate (a) set p

2"p and (b) re-elect the incumbent.

Otherwise if y1(0 the electorate (a) set p

2"1 and (b) elect the opposition.

(S4) The game continues as described by Lemma 1.

(ii) All intuitive pooling PBE generate the same (unique) outcome describedas follows: inflation outcomes and expectations are as in (S1) to (S4). Outputin period 1 is given by y

1"0 for both types but welfare is w

1"!1

2a2

if the competent government in office and w1"!1

2(a#xN !x)2 for the in-

competent type. The expected social welfare in period 1 is given byE(w

1)"!1

2[p(a#xN !x)2#(1!p)a2] and the incumbent wins the election.

In period 2 the outcome is as described by Lemma 1 and over the two periodsthe social welfare is

E(¼)"E(w1#dw

2)"!1

2[p(a#xN !x)2#(1#d!p)a2]. (6)

Proposition 2. ¹he separating equilibrium(i) Assume that assumption (5) holds. Then the game has an intuitive separat-

ing PBE described by the following strategies (S1) to (S3) in period 1 and (S4) in


period 2:(S1) The public sets n%

1"a#(1!p)[h!(xN !x )] where h"

J2d[v!a(xN !x )]'xN !x from assumption (5). Hence n%1'a.

(S2a) The competent administration sets n1"a#h!(xN !x )'n%

1.

(S2b) The incompetent administration sets n1"a(n%

1.

(S3) If y15a#x!n%

1#h, then the electorate (a) set p

2"0 and (b) re-elect

the incumbent. Otherwise the electorate (a) set p2"1 and (b) elect the opposi-

tion.(S4) The game continues as described by Lemma 1.

(ii) All intuitive PBE generate the same (unique) outcome described as fol-lows: inflation outcomes and expectations are as in (S1) to (S4). Output in period1 is given by y

1"ph'xN '0 (the first inequality following from S2a and (1)) if

the competent type is in office with welfare w1"aph!1

2[a#h!(xN !x)]2. If

the incompetent government is in office, then y1"!(1!p)h(x(0 (from

S2b and (1)) and w1"!1

2a2!a(1!p)h. The expected social welfare in period

1 is given by E(w1)"!1

2pa2!1

2(1!p)[a#h!(xN !x)]2. The competent type

wins the election. In period 2 the outcome is as described by Lemma 1 and overthe two periods the social welfare is

E(¼)"E(w1#dw

2)"daxN !1

2a2(p#d)!1

2(1!p)[a#h!(x!xN )]2.

(7)

To summarise, both pooling and separating equilibria exist. In a poolingequilibrium the incompetent administration conceals its type by engaging ina pre-election monetary expansion. The outcome is the election of the incum-bent if we assume that p41

2. In the separating equilibrium the competent

government reveals its type to the electorate by the same means that itsincompetent rival would conceal its type — a monetary expansion. The outcomenow is the election of the competent type.

3. Efficient signalling

In this section we turn to ways of avoiding the PMC. The most obviousinstitutional arrangement would be the establishment of a genuinely goal andinstrument-independent CB in which the government has no influence on theconduct of monetary policy. Then for the CB v

5"0 in Eq. (3) and the outcome is

the discretionary inflation rate in both periods. The type of government isrevealed to the electorate and the competent government elected. If, in addition,a Rogoff-conservative banker (Rogoff, 1985) is elected who cares only aboutinflation (i.e. a"0 in Eq. (3) for the CB), then the discretionary inflation rate is


zero and both the inflationary bias and the distortionary effect of the PMC isavoided.

The fundamental problem with this solution is that it assumes that somecommitment mechanism is in place that prevents government intervention inthe conduct of monetary policy when it is rational to do so. Constitutionalguarantees of political and economic independence in the form of appropriateappointment procedures, a requirement of price stability etc, which will earna high mark for the various measures of central bank independence discussedearlier, may not be sufficient. Indeed there is considerable evidence that govern-ments influence monetary policy even in countries where central banks enjoya substantial degree of legal independence (see, for example the discussion inCukierman (1992) (Chapter 17) and the introduction in Persson and Tabellini(1994)). As one might expect political authorities appear to respond to the legalindependence of the CB by finding more subtle ways of influencing monetarypolicy. For example in the US where, on the basis of various indices, the CBscores highly on the degree of legal and political independence, the precisechannels of influence have been extensively documented by Havrilesky (1991,1993).

It is clearly of interest to explore mechanisms for avoiding the PMC whichdoes not assume a commitment device is in place and which accepts thatincumbent administrations can exert pressure on monetary authorities. The keyto the solution we propose is to make the relationship between government andCB explicit and visible. The means by which this objective can be achieved isthrough a Walsh-type contract in which the government makes the implementa-tion of its chosen monetary policy by the CB incentive-compatible by anappropriate incentive mechanism such as an income transfer linked to theperformance of the economy or provision for dismissal of the governor.

The Walsh contract was originally proposed as a device to eliminate theinflationary bias of discretionary monetary policy whilst allowing the CB toengage in stabilization policy in response to random shocks to the economy.Again its success at achieving this depends on some commitment mechanism: inthis case the mechanism must enforce the contract and prevent its renegotiation.Legal constraints (implicitly assumed by Walsh) would achieve this; but thiswould require the courts to uphold a contract even when both government andCB deem its renegotiation to be in both their own interests. Alternative mecha-nisms for supporting a Walsh contract equilibrium have been examined in therecent literature: for example a private sector trigger strategy equilibrium inHerrendorf (1995) and a reputational equilibrium in al-Nowaihi and Levine(1996). But here we assume none of these devices are in place. This enables us tofocus clearly on two other ways in which the Walsh contract serves a usefulpurpose.

The first role of the contract whose existence and content is made public is tosolve the principal-agent problem in that it provides an incentive mechanism to


8 In another paper that links the political economy and contracting literature, Fratianni et al(1997) do consider the stabilization problem and also allow for the CB to be motivated by theprospect of reappointment. However the main point of our paper — that Walsh contracts may servea useful role even when they fail as a commitment device — is not considered.

induce a legally independent CB to choose the government’s preferred monetarypolicy when it may have different objectives and/or private information onmatters relevant to the conduct of this policy. The second role which is empha-sised in this paper is to provide an important signalling device that conveysinformation about the government’s type to the private sector and the elec-torate. We consider these two aspects in turn.

3.1. The incentive mechanism: Enforcing the inflation target

Suppose that the government (the principal) signs a contract with the CB (theagent) to implement the government’s chosen monetary policy. In the setup ofWalsh (1995) there are stochastic supply and velocity of circulation shocks.Supply shocks are observed with a forecast error that depends on the forecastingeffort expended by the CB and the latter has private information regarding itsforecast, the effort expended, its forecasting efficiency and the monetary instru-ment, the money supply. Despite this extreme asymmetry of information, thegovernment can design a state-contingent transfer that results in the CB imple-menting the government’s chosen stabilization rule without an inflation bias.

This paper focuses on the political business cycle and abstracts from thestabilization problem.8 In our setup the CB possesses no private informationand ‘sets inflation’ (i.e. pursues inflation targets) in the familiar way. The aspectof the principal-agent relationship considered here is the possibility that the CBand government have different objectives. In particular suppose that the welfarefunction for the CB takes the form

ºCBt

"a(aCByt!1

2n2t)#¹

t"f (y

t, n

t)#¹

t, a'0, (8)

say, where ¹tis a monetary transfer from the government to the CB, aCB(a

reflecting the more conservative character of bankers and the parameter a con-verts the utility of the CB associated with a particular output and inflationoutcome into monetary units so that it can be added to the monetary transfer ¹

t.

Suppose that the government chooses an inflation rate nt"nL

twhich it would

implement if it had responsibility for monetary policy. Can the incentive-compatibility problem be solved by means of a monetary transfer; i.e., can ¹

tbe

designed so that legally independent CB pursues a discretionary monetarypolicy n

t"nL

t? It is straightforward to show that if the CB’s utility function can


9Haldane (1996) expresses similar ideas on this subject.

be revealed to the government, then by setting the transfer

¹t"F#¹

t(y

t, n

t, nL

t)"F#b[ay

t!1

2(n

t!nL

t)2!an

t]!f (y

t, n

t), (9)

where b'0 and F is a fixed transfer sufficiently high to satisfy the participationconstraint, this simple Walsh contract will result in the CB implementing thegovernment’s chosen inflation target n

t"nL as a discretionary policy.

There is one further aspect regarding inflation targets which we have up tonow ignored. We have assumed that the CB has perfect control over inflation.This thereby abstracts from a potentially serious problem with regard to theimplementation of the inflation target by the CB. The first point to note is thatthere is no monitoring problem for the public: all they need to do is monitor theexistence or otherwise of a Walsh contract. Regarding implementation Svensson(1996) has considered this issue in some detail.9 He employs a simple ad hocforecasting model in which the actual instrument of the CB — the short-terminterest rate — affects output with a one-year lag which in turn affects inflationwith a further two-year lag. Thus the monetary instrument controls its targetwith a two-year lag. This is perfectly consistent with our setup if wage contractslast at least one year. It is straightforward to show that the interest rate in thecurrent period is set by the CB such that its 2-year ahead forecast of inflationequals the assigned inflation target. Exogenous random disturbances in the tworelationships linking the interest rate to output and output to inflation meansthat control over inflation is not perfect, but this does not alter the effectivenessof the Walsh contract as a device for rendering the inflation target incentive-compatible, or as a signalling device. Actual inflation will of course depend onthe actual realisation of the disturbances so that if the incentive mechanismconsists of an income transfer then the latter will also be stochastic and so may,on occasions, fall through no fault of the CB. Some may see this as a potentialproblem for the contract approach.

3.2. Walsh contracts as a signalling device

In both our setup and in cases of extreme informational asymmetries a Walshcontract will provide an incentive device that results in the CB adopting thegovernment’s desired monetary policy. We now show that its role as a signal cansolve the PMC problem as well. Faced with a legally independent CB thegovernment has the following decisions to make: it must decide its desiredmonetary stance nL

tin period t, whether to formalise its relationship with the CB


in the form of a Walsh contract or use some alternative means of influencingmonetary policy, whether to publicise the nature of the contract if it exists andfinally whether to renegotiate a contract signed at some earlier time.

In our two-period model the optimal solution is to sign a two-period Walshcontract, before inflationary expectations are formed in period 1, that imple-ments zero inflation in both periods i.e., nL

1"nL

2"0. As we have discussed

previously the possibility of renegotiation after inflationary expectations areformed rules out this possibility. We therefore assume that the governmentchoice of the inflation target and whether to sign the Walsh contract both takeplace after the formation of inflationary expectations.

Consider the decision problem facing the competent government. It is clearlyin the interests of such a government to distinguish itself from its incompetentrival by signing a Walsh contract and publicising the inflation target nL

1. The

rational electorate can work this out and so an incompetent government willreveal its type by either not having a Walsh contract or having one but notpublicising its contents. But in doing either of these things the incompetentgovernment will also reveal its type and fail to get elected. The same applies ifthe incompetent government chooses to adopt a public Walsh contract. At leastif it chooses a Walsh contract it gets the CB to implement its chosen inflationrate; but it will be indifferent as to whether to publicise the contents. Theannounced Walsh contract between the competent government and the CB isthen an efficient signal to ensure the election of the competent type. Incompetentgovernments are revealed by either the absence of a public contract or by lowoutput, the latter happening in equilibrium. There is no need for any furthersignalling device; for both types of government the CB will pursue the dis-cretionary inflation rate, eliminate the PMC and increase social welfare.

We can formalise this argument with a game-theoretic treatment similar tothat in Section 2. In particular consider the following sequencing of events forperiod 1. Period 2 is as before.

1.1. Nature chooses the type of government in office; x1"x with probability

p and x1"xN with probability 1!p. The government knows its own type but

this is not revealed to the public. The opposition party is of the alternative type.These types remain fixed for the duration of the two-period game. The publicadopts the prior p

1"p.

1.2. The public forms its inflation expectation ne1

for the period and signswage contracts based on this expectation. Contracts last for one period.

1.3. The government chooses n1. It chooses either to pursue this openly

through a Walsh contract specifying the inflation target nL1"n

1to the CB and

public alike, or it influences monetary policy covertly through other meanswhich includes the possibility of a covert Walsh contract.

1.4. The public observes output y1

and either the inflation target nL1

or thefailure of the government to implement a Walsh contract.


1.5. Using the observations of 1.4, the public updates its belief about the typeof government from p

1"p to p

2.

1.6. An election is held in which the public either elects the incumbent or theopposition.

Proposition 3(i) The game has an intuitive separating PBE described by the following

strategies (S1) to (S3) in period 1 and (S4) in period 2:(S1) The public sets ne

1"a.

(S2a) The competent type (if in office) signs a public Walsh contract specify-ing an inflation target nL

1"a.

(S2b) The incompetent government signs a Walsh contract. If it is public itspecifies the same inflation target nL

1"a.

(S3) If the Walsh contract is public and y15nL

1!n%

1#xN , then the electorate

(a) set p2"0 and (b) re-elect the incumbent. Otherwise, if the Walsh contract is

not public or y1(nL

1!n%

1#xN , the electorate (a) set p

2"1 and (b) elect the

opposition.(S4) The game continues as described by Lemma 1.

(ii) All PBE generate the same (unique) outcome described as follows: infla-tion outcomes and expectations are n

1"n%

1"nL

1"a. Output in period 1 is

given by y1"xN if the competent type is in office with welfare given by

w1"axN !1

2a2. If the incompetent government is in office, then y

1"x and

w1"ax!1

2a2. The expected social welfare in period 1 is given by

E(w1)"!1

2a2. The competent type wins the election. In period 2 the outcome

is as described by Lemma 1 and over the two periods the social welfare is

E(¼)"E(w1#dw

2)"daxN !1

2(1#d)a2, (10)

Proposition 4The availability of Walsh contracts eliminates the PMC and increases social

welfare.

4. Conclusions

Rogoff and Sibert (1988), Rogoff (1990) and Persson and Tabellini (1990) haveset out rational political business cycle models where economic fluctuationsresult from the government’s attempts to signal its competence to the electorate.Some empirical support for these genre of models is to be found in Alesina andRoubini (1990). In their overview of this literature Persson and Tabellini (1994,page 4) we read: “It is not clear, however how to get rid of this distortion. Thereason is that the electoral cycle conveys information to the voters. Trying tosuppress it, therefore may be counterproductive: the voters would choose an


incompetent government too often, or alternatively the incumbent could beforced to signal his type in costlier ways”. A similar viewpoint is expressed inRogoff (1990) (p. 21).

In contrast to these views, this paper has shown how the political monetarycycle can be avoided if Walsh-type contracts between the incumbent administra-tion and the CB are available to governments. Walsh (1995) originally proposedsuch contracts for the purpose of eliminating the inflationary bias of discretion-ary monetary policy whilst retaining its stabilization role. For this to work somemechanism is required to make Walsh contracts renegotiation-proof: forexample legal or institutional arrangements (implicitly assumed in Walsh(1995)), trigger strategies on behalf of the public (Herrendorf, 1995) or reputa-tional effects (al-Nowaihi and Levine, 1996). In the model presented in this paperwe assume none of these devices exist. Walsh contracts therefore do noteliminate the inflationary bias. Rather they serve the different purpose ofproviding an efficient signalling device to the electorate that eliminates thepolitical monetary cycle, results in the election of competent governments andincreases social welfare. Of course, if Walsh contracts could also eliminate theinflationary bias, this would further increase welfare.

Acknowledgements

The paper was produced as part of a Phare-Ace financed research programmeon Central Banking in Transition Economies no. P95-2038-R. The authors aregrateful to an anonymous referee and an editor of the Journal of MonetaryEconomics for constructive comments on an earlier version of this paper. Theusual disclaimer applies.

Appendix A. Proof of propositions

¸emmaResults (i) to (iii) are the standard results for the discretionary inflation rates.

Welfare outcomes follow from (3). Result (iv) follows because E(y2)"p%

2x

#(1!p%2)xN "0 and E(p

2)"p.

The proofs of propositions 1 and 2 are very similar. Proposition 2 is slightlymore difficult to prove and we therefore proceed straight to this proof. Fulldetails of all proofs are available from the authors on request.

Proposition 2The first period of the game consists three stages. In the first stage the public

forms its expectation of inflation n%1. The second and third stages together form


a signalling game with the government as sender and the electorate as receiver.In the second stage the government chooses inflation n

1thus sending a message

y1

to the electorate. In the third stage the electorate observe y1, but not n

1,

updates its belief about the type of government in office to p2, and decides

whether to re-elect the incumbent or elect to opposition. The second period ofthe game is then described by the lemma.

Proof of part (i)An intuitive PBE must satisfy the following:

(1) ¹he electorate’s strategy S3b is optimal given its beliefs as described by S3a.This follows from fact that p

2"1 (p

2"0) implies that the electorate believes the

government to be incompetent (competent) and from the electorate’s wish toelect a competent government.

(2) ¹he electorate’s beliefs as described by S3 a are updated using Bayes’ law giventhe equilibrium strategy of the government as described by S2. Suppose that thegovernment is playing its equilibrium strategy as given by S2, Then from (1) theequilibrium outputs for a competent and incompetent government are given by

yN1"a#x!n%

1#h (A.1)

and

y1"a#x!n%

1, (A.2)

respectively. If the electorate observe the higher output then they know that thegovernment is competent. A trivial application of Bayes’ law then sees themsetting p

2"0 and re-electing the incumbent party, in agreement with S3a.

Similarly if the lower output is observed they will set p2"1 and elect the

opposition, again in agreement with S3a.

(3) ¹he strategies (S2a) and (S2b) of the two types of government are optimal giventhe strategy of the electorate as described by S3. First consider the competenttype of government whose equilibrium output is given by (A.1). Hence by S3b itwill be re-elected with equilibrium payoff

ºM *"a[a#x!n%1#h]!1

2[a!(xN !x)#h]2#d[axN !1

2a2]#v#dv,

(A.3)

using the lemma and (A.1). From (1) an inflation rate higher than equilibriuminflation as given by S2a will produce an output higher than the equilibriumoutput given by Eq. (A.1). But re-election is ensured without this extra output


and, moreover, since Lº/Ln1(0 for n

1'a, the payoff to the government will

be lower. Hence the competent type has no incentive to adopt an inflation ratehigher than that specified by (S2a). A lower inflation rate on the other hand willresult in output being lower than (A.1) and hence the government will lose theelection (by S3b). In this case the best policy is then to adopt n

1"a which gives

the deviation payoff

ºM $"a(a#xN !n%1)!1

2a2#d(ax!1

2a2)#v, (A.4)

using the lemma and (A.1). Now condition (5) becomes relevant. A straightfor-ward calculation using this condition gives ºM d(ºM * which completes the proofof proposition (3) for the competent type.

Now consider the incompetent type. Its equilibrium output is given by (A.2).Hence by S2b it loses the election. From this, Eq. (3), the lemma and Eq. (A.2)we have the equilibrium payoff

º*"a(a#x!n%1)!1

2a2#d(axN !1

2a2)#v. (A.5)

On the other hand if the incompetent type adopts the inflation rate

n$1"a#h (A.6)

then from (1) output will be

y$1"a#x!n%

1#h (A.7)

and by S3b the incompetent type will win the election. From (3), the lemma andEq. (A.7) its deviation payoff will be

º$1"a(a#x!n%

1#h)!1

2(a#h)2#d(ax!1

2a2)#v(1#d). (A.8)

Any inflation rate above (A.6) will result in output being above (A.7) and hencere-election, by S3b. However the payoff would be below Eq. (A.8) becauseLº/Ln

1(0 for n

1'a. Any inflation below Eq. (A.6) would result in output

below Eq. (A.7). The election would be lost by S3b and the payoff would bebelow Eq. (A.5) unless n

1"a. Hence we only need to compare Eqs. (A.5) and

(A.8). It is straightforward to show that º$"º*. Hence the incompetentgovernment has no incentive to depart from its equilibrium strategy whichcompletes the proof of (3).

(4) ¹he public forecasts inflation optimally given the strategy of the government asdescribed by S2. This follows from (S1) and (S2) and the fact that the publicknows p.

(5) ¹he ‘intuitive criterion’ of Cho and Kreps is not violated. One unsatisfactoryaspect of a PBE is that it may allow one player to believe that another playerwould take an equilibrium-dominated move at an information set off the


equilibrium path. If this does not happen, the PBE is said to satisfy the ‘intuitivecriterion’ of Cho and Kreps (1987). We now show that the equilibrium satisfiesthe ‘intuitive criterion’.

Substituting from (1) and using the lemma, we can express the government’spayoff (3) as the following function of y

1and n%

1

ºM (y1, n%

1)"ay

1!1

2(y

1#n%

1!x

1)2#d(ax

2!1

2a2)#v

1#dv

2. (A.9)

The payoff to the competent type if it is in office for both periods can be found byputting x

1"x

2"xN and v

1"v

2"v in Eq. (A.9) to get:

ºM (y1, n%

1)"ay

1!1

2(y

1#n%

1!xN )2#d(axN !1

2a2)#(1#d)v. (A.10)

Similarly, the payoff to the incompetent type if it is in office for both periods isgiven by

º(y1, n%

1)"ay

1!1

2(y

1#n%

1!x)2#d(ax!1

2a2)#(1#d)v. (A.11)

From Eqs. (A.3) and (A.10)

ºM *(n%1)'(",(,)ºM (y

1, n%

1)

according to

[y1!(a#x!n%

1#h)#2(h!(xN !x)][y

1!(a#x!n%

1#h)]

'(",(,)0. (A.12)

and from Eqs. (A.5) and (A.11)

º*(n%1)'(",(,)º(y

1, n%

1)

according to

[y1!(a#x!n%

1#h)#2h][y

1!(a#x!n%

1#h)]'(",(,)0.

(A.13)

Let y1

be equilibrium dominated for one type of government. From Eqs. (5),(A.12) and (A.13) we can show that this can only happen when y

1is equilibrium

dominated for the competent type, but not the incompetent type; i.e. whenºM *(n%

1)'ºM (y

1, n%

1) but º*(n%

1)4º(y

1, n%

1). Furthermore, the latter two inequal-

ities can only hold if y1(a#x!n%

1#h. But then, by S3a, the electorate set

p2"1 ruling out a belief in equilibrium dominated moves off the equilibrium

path. This establishes the intuitive criterion and completes part (i) of the proof.

Proof of part (ii)A simple calculation shows that the strategies S1—S3 generate the outcomes

described in (ii). The following reasoning shows that any intuitive separatingPBE must generate this outcome. Any separating PBE must result in: (a) theelectorate voting for the competent type; (b) the incompetent type selecting the


optimal inflation rate n1"a; (c) the beliefs and behaviour of the electorate being

such that the competent type is forced to separate. Also the intuitive criterionrequires that the electorate force the competent type to separate at a minimumwelfare loss. Then by arguments similar to (3) above we can show that theoptimal strategy for the competent type is n

1"a#h!(xN !x).

Although the model has infinitely many intuitive separating PBE (dependingon how we define out-of-equilibrium beliefs) they all generate the uniqueoutcome in (ii).

Proposition 3The proof of part (i) of proposition 3 follows the same structure as proposi-

tion 2.

(1) ¹he electorate’s strategy S3b is optimal given its beliefs as described byS3a. As before this follows from fact that p

2"1 (p

2"0) implies that the

electorate believes the government to be incompetent (competent) and from theelectorate’s wish to elect a competent government.

(2) ¹he electorate’s beliefs as described by S3a are updated using Bayes’ law giventhe equilibrium strategy of the government as described by S2. Suppose that theincompetent type signs a public Walsh contract. Then the only two possibleoutput levels are yN

1"nL

1!n%

1#xN and y

1"nL

1!n%

1#x(yN

1. If the electorate

observe the higher output then they know the competent type is in office andBayes’ law gives p

2"0. If they observe the lower output or the incompetent

government fails to publicise the contract then they know that the incompetentgovernment is in office and Bayes’ law gives p

2"1.

(3) ¹o show that the strategies (S2a) and (S2b) of the two types of government areoptimal given the strategy of the electorate as described by S3. The incompetenttype can either sign a public contract or a secret contract. In both cases she losesthe election. Therefore she will choose the optimal inflation rate target nL

1"a.

By the same token the competent type wins the election whatever inflation rateshe chooses. Therefore she also chooses the optimal inflation rate target.

(4) ¹he public forecasts inflation optimally given the strategy of the government asdescribed by S2. Since the inflation target is enforced by the incentive mecha-nism (9), n

1"nL

1"a"n%

1and the public forecasts optimally. This completes

the proof that the strategies S1—S3 form a PBE.

(5) ¹he ‘intuitive criterion’ of Cho and Kreps is not violated. Let n1Oa be off the

equilibrium path. Since the competent type always wins the election n1Oa must

be equilibrium dominated for this type. For the incompetent type suppose thatn1

is not equilibrium dominated; i.e. n1

is sufficiently close to a so that winning


the election would not compensate for the suboptimality of n1. Then

y1"n

1!n%

1#x"nL

1!n%

1#x(nL

1!n%

1#xN and hence by S3a the elec-

torate set p2"1 as required by the intuitive criterion.

Proof of part (ii)A simple calculation shows that strategies S1—S3 generate the outcome stated.

We now show that any PBE must generate this outcome. Since the public eitherobserves the target nL

1, n%

1and y

1, or the failure to announce the target the type of

government becomes public knowledge before the election. Hence any PBEmust be separating and must also result in the election of the competent type.Hence each type can do no better than select the optimal inflation rate n

1"a.

Hence in any PBE n%1"a. These considerations are sufficient to determine the

stated outcome in (ii) uniquely.However the equilibrium is not unique. For example, we could replace S3

with: (S3@) If the Walsh contract is public and y1'nL

1!n%

1#x, then the

electorate (a) set p2"0 and (b) re-elect the incumbent. Otherwise the electorate

(a) set p2"1 and (b) elect the opposition.

Then S1, S2, S3@ and S4 would define an alternative PBE leading to the sameoutcome.

Proposition 4This is confirmed by comparing the welfare outcomes (6) and (10) and some

simple calculations.

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