voting and learning in a model of monetary policymaking*

VOTING AND LEARNING IN A MODEL OF MONETARY POLICYMAKING*

MARK CROSBY

University of New South Wales

I. INTRODUCTION

One of the features of the performance of developed economies in the 1970s and 1980s was the persistence of inflation. Yet this inflation was quite different from one economy to the next. West Germany and Japan have had consistently lower inflation than other G-7 economies, and Italy has had high inflation over most of this period. Few economies have made the transition from a high inflation economy to a low inflation one, or vice versa. Why has this been the case? The usual answer is that monetary and fiscal policies have differed in these economies, leading to different inflation rates. But what explains the existence of different policies? If the long run Phillips curve is vertical then why have we not seen institutions developing which lead to the same low level of inflation in all western economies? In this paper a game theoretic model of public and private sector behaviour is used to explain inflation persistence, and it is argued that the important role of voting has been overlooked in the determination of an economy's mean inflation rate.

In the monetary policy game literature, the question addressed is the following. If the long-run Phillips curve is vertical, why do we not observe low (possibly zero) inflation, given that inflation is disliked by both the private sector and policymakers? The short answer to this question is that in an economy where monetary authorities have some discretion over the rate of money growth, there is an incentive for the monetary authority to surprise the private sector by providing higher inflation than the private sector expects. Such unanticipated inflation would cause output and employment to increase, as the economy moves along an upward sloping short run aggregate supply curve. The private sector knows however that these incentives exist, and in a rational expectations equilibrium, expects the policymaker to provide non-zero inflation. In equilibrium we see positive inflation and the level of output at its natural level.

This stylised model has been extended in many directions. Most obviously, the simple game above is repeated period after period, allowing more complicated equilibria than the one above. In a repeated game a policymaker can build a reputation for being a low inflation policymaker by consistently achieving low inflation, and the private sector may be able to choose among strategies which force the policymaker to choose low inflation. In an uncertain world, a

* I would like to thank, without implicating, Michael Devereux, Gregor Smith, James Bergin, Huw Lloyd- Ellis, and an anonymous referee for helpful comments.

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multiplicity of these reputational equilibria can exist. This paper examines how voters choose among different policymakers, based on their differing reputations for providing low inflation. In most western economies voters have a choice among many policymakers, who differ in their incentives to provide low inflation. A model is developed in which the voter’s decision problem is examined, and the implications of these decisions for inflation is found.

The problem that a voter faces is to try to choose the policymaker who will deliver the lowest inflation, among a set of policymakers who will generate different average rates of inflation. The observation that inflation is low does not, however, ensure that we have elected an anti- inflationary policymaker. Inflation is generated according to some stochastic process, and low inflation could occur because of the low realisation of an inflation shock. Voters have to combine the historical record of a policymaker’s inflation performance with their subjective beliefs about a policymaker’s type in order to evaluate whether a policymaker is tough or weak on inflation.

Voters have different beliefs about the mean inflation that each policymaker will deliver, but hold these beliefs with differing degrees of certainty. Some policymakers are known to be tough on inflation, for example, while others are only thought to be tough. The voter has to trade off different inflation performances against these differences in the degree of subjective uncertainty in choosing a policymaker. Baye’s Rule is used to update beliefs after each inflation observation is made. Hence the voter’s beliefs about policymakers will only be changing for the policymaker who was in power for the last period. The decision problem is analagous to a ‘bandit problem’, where a gambler has to choose which machine to play among a set of poker machines (or ‘one- armed bandits’) which are presumed to differ in the average payout that they make. The bandit approach allows us to formalise and solve the median voter’s decision problem.

The solution to this problem is not what we may expect. Even if this game is played infinitely often, it will not neccessarily be true that voters will eventually choose the policymaker who will provide the lowest inflation. Hence it is possible that two countries could both have the same set of policymakers, in terms of the spectrum of average inflation rates that the set of policymakers could provide, and yet have very different average rates of inflation. For example if a party existed in Italy which was very tough on inflation, there is no guarantee that voters would elect this government and realise lower average inflation.

The game-theoretic monetary policy literature provides no adequate explanation for differences in mean inflation rates in different economies, especially given that elections should allow the private sector to eventually choose low inflation governments. This paper resolves this problem by resorting to a voting model of inflation determination, while maintaining the game-theoretic aspects of private and public sector behaviour. An essential aspect of the model is the uncertainty of the private sector about both the type of government that it faces, and the actions that governments take at each point in time.

Existing models of voting in monetary policy games (some of these will be discussed in the next section) focus on the political business cycle aspects of elections, or on one-shot interactions between policymakers and the private sector. In this paper the actions of voters are explicitly modelled, and the relationship between policymaker’s actions and electoral outcomes is examined, in a dynamic model where private agents learn slowly about the types of policymakers that they face. It is found that a realistic voting model can explain differences in trend inflation rates both across countries and over different time periods.

VOTING AND LEARNING IN A MODEL OF MONETARY POLICYMAKING 19

Models of monetary policy games usually allow uncertainty to enter in one of two ways. In the first, the private sector is uncertain of which of a number of possible types of government (often two) is in power. The usual example is that there are two types of government, with known and distinct preferences, but that the private sector is uncertain of which of the two is in power. In these models there exist a number of possible equilibria, including reputational equilibria and signalling equilibria. 1

Another type of uncertainty occurs when agents are unaware of the actions of policymakers, due to the stochastic nature of inflation. In these circumstances private agents may be unable to infer what action a policymaker has taken, even after the rate of inflation has been observed. Canzoneri (1985) considers a model in which inflation is stochastic due to shocks to money demand, and the private sector is able to observe only actual inflation, rather than the level of inflation that the policymaker intended. It is shown that an equilibrium exists in which the policymaker behaves in the way that the private sector expects, and the rate of inflation is determined jointly by the policymaker’s action and the stochastic shock. The equilibrium requires that the policymaker be ‘punished’ when inflation is above some limiting level, even though in equilibrium the government never behaves in a manner that the private agent does not expect (i.e. it never cheats in equilibrium). Cukierman and Meltzer (1986) and Alesina and Cukierman (1990) also examine models where outcomes are ambiguous.

In Section III a model is presented which utilises uncertainty about policymaker’s type, and ambiguity of outcomes in a model where the private sector must choose among policymakers in an election. Since government actions affect private sector welfare, individuals will elect the government which they zhink will take the action which will give them the most welfare. Governments take into account agents’ voting rules when choosing their expected inflation outcomes. It is shown, however, that private sector voting may still result in the election of a party which does not minimise the private sector’s loss function. In addition, voters may elect such a party permanently. This can occur despite the fact that the government uses operating rules which agents expect them to employ. There is thus no ambiguity in policymaker’s procedures, only imperfection as to outcomes. It is also shown how outcomes are related to the beliefs of voters about both a government’s type, and to the kinds of shocks that affect inflation.

The voting model is formulated as a median voter problem, in which the voter is faced with the choice at the end of each period of re-electing the incumbent, or electing an alternative party. This decision problem is analogous to a bandit problem, in which a gambler chooses to play a single one-armed bandit amongst many, on the basis of beliefs about payoffs, and on the histories of payouts for each machine. The solution to such a problem can involve persistent errors, in the sense that governments can be elected despite being more inflationary than (some) opposition parties. Solutions also stress the role of information and uncertainty, as well as private and public preferences and learning. The solution also shows that even if countries faced identical choices among policymakers, the combination of median voter’s beliefs and country specific shocks can lead citizens to elect different governments in the long run. Hence we can have different trend inflation rates occurring despite the availability of identical institutions and policymakers in all economies. Voting behaviour will not lead us to elect the ‘best’ (least inflationary) government available, as we might expect.

I Examples of these types of models can be found in Backus and Driffill (1985a. 1985b), Barro (1986), Barro and Gordon (1983), Vickers (1986) and Cukierman and Meltzer (1986).


In the following section some of the literature mentioned above will be outlined in sufficient detail to motivate the models presented in this paper. In Section 111 the bandit problem will be introduced and applied to a model of private sector uncertainty about the government’s inflationary preferences. The final section offers comments and conclusions.

11. RELATED LITERATURE

The first presentation of monetary policymaking as a strategic game between policymakers and the private sector was by Barro and Gordon (1983a, 1983b). The model of Barro and Gordon is centred around a payoff function for the policymaker, and an upward sloping short run aggregate supply curve such as:

where p , is the rate of inflation in time t and p ; is the private sector’s expectation of the rate of inflation, y, is the level of output and is the natural rate of output, p * and y * are the policymaker’s desired values of inflation and output,fand g are general functional forms and a is a constant.

The first term in the policymaker’s payoff (or loss) function reflects the costs associated with deviations of inflation from some optimal level. The second term reflects the policymaker’s preference for some target level of output (or employment). It is usually assumed that existing labour market institutions (such as the existence of trade unions, or distortionary taxation) cause an upward bias to the natural rate of unemployment. The policymaker regards as too low, and attempts to increase output above this level.

In order to find optimal strategies for the players in the game, j g, p * , and y * need to be specified. Throughout this paper it has been assumed that f is quadratic, g is linear, and that policymakers’ preferred inflation rates are always zero. A different optimal inflation rate could have been used without affecting any of the results. Finally it is assumed that y * equals which, together with the linearity of g, implies that the policymakers’ loss is decreasing in output. Using these assumptions, and substituting (2) into (l), we are left with

where a and b are preference parameters.

Policymakers are assumed to choose p r to minimise (3). Private sector behaviour is described as their choice of p : . Agents are assumed to be atomistic, and have knowledge of the policymaker’s equation (3). Using this information, they use rational expectations to forecast the rate of inflation so as to minimise inflation forecast errors.

In a one-shot game, the policymaker minimises (3), treating p ; as fixed, resulting in the level of inflationi = b/a. If rational agents know the policymaker’s objective function thenp” = b/u (where hats represent equilibrium values). There is inflation, but this inflation is perfectly

1995 VOTING AND LEARNING IN A MODEL OF MONETARY POLICYMAKING 21

anticipated. The cost to the government of this inflation is bV2a. If the policymaker were able to commit to zero inflation it could achieve zero costs. The problem with such a commitment is that it is not an equilibrium. Once the policymaker has made an agreement to provide zero inflation, the policymaker has an incentive to break this agreement by inflating and gaining the benefits of surprise inflation. Note that we can renormalise (3) so that the level of inflation is uniquely described by b, the policymaker’s relative preference for inflation control over output expansion.

This very simple model explains why we might not have zero inflation, despite the fact that zero inflation is optimal, and is a policymaker’s preferred inflation rate. In this model there is full certainty, and the players in the game face each other only once. Relaxing these assumptions will clearly have implications for the equilibrium outcomes of the model.

Backus and Driffill (1985b) and Barro (1986) extend the above framework to allow for uncertainty over the preferences of the incumbent policymaker. Many governments claim to be tougher on inflation than their predecessors, but how do individuals in the private sector know if these claims are true? These authors examine the case where there are two different types of policymaker, differing in their degree of aversion to inflation.

Barro assumes that the preferences of the different policymakers are still as in (3), but that b differs according to type. If the private sector knows which policymaker is in power then there is no incentive for deceit, and inflation will be simply b,la, where i represents the policymakers type. If, however, the private sector is uncertain as to the type of the policymaker in power, there exist a number of reputational and signalling equilibria, with associated paths for inflation and the money supply (see also Vickers, 1986). Signalling equilibria differ from reputational equilibria in the assumptions made about b. In reputational models it is assumed that for strong governments b, equals zero. Since these governments care only about inflation they will always seek to set inflation equal to zero, regardless of private sector expectations. Vickers shows that if this assumption is relaxed to allow for different non-zero bs for each government then equilibria can exist in which the government signals its type to the private sector, thus limiting the recessionary impact of reputation building.

In the models above there are two policymakers, but these policymakers are chosen exogenously. What happens if the private sector chooses the policymaker through voting? Papers that allow for the election of different policymakers, generating a political business cycle similar to that of Nordhaus (1973, include Ellis and Thoma (1991), and Persson and Tabellini (1990). In these papers the incumbent is re-elected with some exogenous probability, independent of the actions taken by the incumbent when in power.

Two papers that explicitly relate voter’s decision rules to policymaker actions are Alesina and Grilli (1992), and Milesi-Ferretti (1993). Alesina and Grilli examine the choice of voters in different electorates between entering a monetary agreement with other countries, or staying with an independent central bank. When should voters in Europe choose to join the ERM, and when should they stick with the present independent central banking arrangements? It is shown that voters who live in countries with high average inflation have more incentive to join the ERh4, as the lower inflation that results will outweigh the cost of a loss in ability to offset real shocks.

Milesi-Ferretti asks the related question of what regime a policymaker should choose, when it knows that its electoral success will depend at least in part on this choice. If a policymaker has a


choice between fixed and flexible exchange rates, when should it choose to fix the exchange rate? This choice will be based not only on the benefit to the party in power of the different regime, but also on the benefit to opposition parties. If opposition parties are known to reap large benefits from fixed exchange rates, then an incumbent seeking re-election may choose not to fix the exchange rate, despite this policy being the incumbent’s own preferred policy. This may explain the reluctance of the Conservative party in the UK to join the ERh4. This paper is related to the idea in Persson and Svensson (1989) that governments less prone to public spending may choose to leave a large public debt to constrain the spending of a less spendthrift successor.

Milesi-Ferretti allows for policymakers to be chosen endogenously, but assumes that the policymaker’s preferences are known to the private sector. The following Section of this paper allows for endogenous choice of policymaker, as well as uncertainty about the characteristics that describe each policymaker. It is shown that such a modification can significantly alter inflation paths in our model economy and, in particular, inflation need not converge to the preferred inflation rate of the least inflationary policymaker.

111. VOTING AND THE BANDIT GOVERNMENT

a) The bandit problem In order to introduce voting into a model of policymaker’s inflationary behaviour we must give

the private sector an incentive to vote. In the models above the function E ( p , - p : ) * is used as the private sector’s objective function, representing the fact that agents are assumed to forecast inflation optimally - i.e. using rational expectations. As far as these policy games are concerned this is the only aspect of private sector behaviour which is important. Agents can have preferences over inflation and any other variable, but it will turn out that preferences over economy wide variables will not affect the equilibrium because agents are assumed to be atomistic. In a voting model however, it is important to include inflation in the private sector’s preferences, since the median voter knows that in voting she is choosing an inflation rate. In the following it is assumed that the objective function of the median voter remains fixed over time, so that we can use her preferences as representative of private sector preferences (using the median voter theorem, we know that the preferences of the median voter solely determine outcomes).

When voters care about the level of inflation, an agent’s electoral problem will be akin to so called ‘Bandit’ problems encountered in probability theory. Bandit problems are so named because the models were originally formulated in order to solve the problem of which one armed bandit to play amongst k available machines, and when to switch to another machine. It is assumed that each machine pays out some stochastic amount with fixed mean, but that this mean differs according to machine and is unknown to players. Players know the distribution from which the means are drawn, and make inferences about these after observing the payouts from different machines. An optimal strategy will have players using prior beliefs and Baye’s rule to update beliefs about each machine, after observing a payout. The decision as to when to switch to another machine will depend on the extent of knowledge about each machine, and expected mean payouts from each machine.

The original application of the bandit model in economics is due to Rothschild (1974). Rothschild considers the problem of an infinitely lived seller attempting to correctly price a good,


but limited to the prices PL and Pw One customer arrives each period, initially unaware of the sellers price, and purchases one item with probability n (P) . The seller is a risk neutral expected profit maximiser who discounts future profits at rate 6 cc 1 . The seller thus seeks to maximise n(P) (P- C) each period, where Cis the cost of the good.

The solution to this problem is straightforward if the ns are known, but suppose instead that the seller does not know either n, = H(P,) or n2 = n(P,). Instead, our Bayesian seller has a prior belief density g ( q , a,) > 0 that the probability pair (q, n2) E (0,l) x (0,l) is realised. Sellers must evaluate not only the anticipated profit from charging a particular price, but also the value of incremental information about the ns that is gained by charging such a price. Rothschild’s main proposition is that, when 0 < n, , IT, < 1, a seller following an optimal strategy will with positive probability select one price infinitely often, and the other price only a finite number of times. Optimal behaviour can forever lead to charging the least profitable price! This model will be adapted to the problem of voting for a political party in the presence of uncertainty about some of the parties’ preferences, as in Backus and Driffill(1985a, 1985b) and Barro (1986).

b) The voting model At this point it is helpful to define some notation. Denote the discount factor as D, = (p,, p,+],

pl+*....). A strategy, z, assigns to the empty history the integer indicating the choice of party to be made in the initial periods election, and z ( p J indicates the policymaker that is chosen in the second period (it is assumed that elections take place at the end of each period), after an inflation rate of p , has been observed in period one. Thus a strategy defines the choice of government given an inflation history. It is assumed that the preferences of each policymaker can be represented by the single period loss function

Z; = p: /2-bi(pl - p e ) i = 1,2 ... (4)

where bi is drawn from some distribution which is common knowledge, but is known only to party i. The idea here is that the private sector has some idea about the characteristics of a given party, but it does not have full information.’ The size of bi tells us about the strength of a party’s desire to increase output. The smaller is this parameter, the lesser is a policymaker’s desire to raise output above it’s natural level.

Each policymaker minimises

T n’,=Cp S Z l

s=1

where T is the horizon (which can be infinite). At time t this problem results in government i attempting to achieve pi = bi, and equilibrium expectations are p : = E,bi. We will assume that the government is restricted to choosing this b as its policy variable, hence policymakers behave as if they do not care about their appointment, but only represent the interests of their constituents.3 Private agents minimise the loss function

2 Another paper in this spirit is Cukierman and Meltzer (1986).

3 Crosby (1993) extends this model to allow the policymaker to choose different bs, and signal their type to the private sector.

24 AUSTRALIAN ECONOMIC PAPERS NNE

where E, represents the expectations operator, and p; are inflationary expectations at time t. Note that the solution to this problem still involves private agents attempting to minimise inflation forecast errors.

It is also assumed that there is a shock to money demand so that actual inflation is

pr = bi + E, E - N(0, 02) (7)

It is further assumed that agents know which policymaker, i , is in power but that agents have to infer bi from actual inflation outcomes. For simplicity we will restrict the horizon to two periods, and assume that there are only two possible parties.4

Our rational, Bayesian agents have beliefs represented by the following

Party2 b 2 = A

(note that we are assuming that party 2’s preferences are known with certainty).s Thus the private sector’s beliefs are that the preference type of Party 1 is drawn from a normal distribution having mean pl and variance p* (where we assume that E and p are independently distributed). The one period private sector loss function when each party is in power becomes

The uncertainty about the preferences of party 1 is costly to agents, and this cost is represented by the term in p2 above.6 If agents can costlessly elect either party then party 1 will be elected if

4 The two period case is easily extended to the n-period case, since the discount sequence, and the posterior distribution confronting the voter at the beginning of each period characterise the bandit that the decision maker faces at this time. This fact can be used to show that a strategy, T, can be defined in either of two ways. In the usual definition z specifies an action for agents for each possible history. An alternative definition is based on the observation that each inflation outcome will result in a new bandit. Hence T specifies an arm to be played for each set of initial beliefs. For a further discussion see Banks and Sundaram (1991, p.5) or Berry and Fristedt (1985, pp.18-22).

5 This assumption is made for reasons of analytical convenience and can be altered without affecting the results. The assumption can perhaps be justified by assuming that at time 1 Party 2 has been around forever and has preferences which are known. At this time a new party forms, whose preferences are not known. It can be seen from the following that the results depend on beliefs about relative means, and the extent of uncertainty about the two types. A discussion of two-armed bandits where both arms are unknown can be found in Berry and Fristedt (1985) or Banks and Sundaram (1992).

6 The second term in J( 1) becomes

“ / E @ - p 3 2 = y E ( b + € - p , ) 2 = YE ( b - p,)2 + YE (€)*

= y(p2 + 0 2 ) .

1995 VOTING AND LEARNING IN A MODEL OF MONETARY POLICYMAIUNG 25

If this condition does not hold then party 2 will be elected. This says that the private sector may not elect what it thinks is the least inflationary party, if it is uncertain about the preferences of this party. This uncertainty is costly, and is traded off against the benefits of choosing the party whose preferences are known, but is thought to deliver higher mean inflation.

If there are two periods then private agents minimise

Private agents must therefore choose a strategy specifying their second period action (who they elect) as a function of the inflation that they observe this period. In order to find an optimal strategy, it is easy in this example to consider all possible strategies beginning with electing each party in period 1.7 Denote the worth of a strategy, z, by

Consider first the strategies which begin with party 2 in power in period 1, i.e z(@) = 2. If party 1 is not elected in period 1, the private sector has no new information about this party, and so El(pl) = E2(p l ) = pl. An optimal strategy in period 2 must therefore be

1 i f p , < i l - r p 2 +:,={ 2 otherwise

where p,' is inflation in period i when party j is in power. Given the inflation in period 1 when party 2 was in power, elect party 1 (whose preferences are not known) only if expected inflation is less than that expected if party 2 were elected by enough to compensate for the uncertainty about party 1's preferences. Let V represent the minimum. Then the worth of strategies which begin by electing party 2 is

Now consider strategies which begin with the election of party 1 at stage 1 . The mean of the posterior distribution, given that the prior is as specified above, and the innovation is normally distributed with mean zero and variance 02, is given by

(see DeGroot, 1970, p.248). Thus an optimal strategy in period 2 is

I if (p2p1 + a2p,)/(a2 + p 2 ) 5 a - rpz

- 2 otherwise

7 For general details on bandit problems see Berry and Fristedt (1985).


Hence the worth of strategies which begin with party 1 is

We can combine (9) and (12) to find the optimal strategy, which satisfies

We can use Theorem 5.5.1 of Berry and Fristedt (1985) to show that the strategy z = (2,l) is not an optimal strategy. This theorem states that for 'regular' discount sequences (which include the geometric discounting case) it can never be optimal to switch from a known arm (party) to an unknown one. The reasons for playing an unknown arm are twofold: firstly to gain information about the characteristics of the arm, and second, to gain instantaneous payoff. In the two period game that we are examining information gained in period 2 is of no use. Therefore the only reason for playing arm 1 at stage 2 is to gain immediate payoff. For this to be optimal it must have greater expected payoff than arm 2, but if this is true it must also be true that arm 1 was optimal at stage 1 (it is assumed that the information set does not change between periods, so that expectations cannot change). Thus any strategy which switches from a known to an unknown arm, such as Z= (2,1), cannot be an optimal strategy.

Eliminating the strategy Z = (2,l) yields

Optimal strategies depend on the sign of


Taking expectations in (15) involves finding the probability that the random variable p1 is less than the constant (a -p2 ) / [02 (pz + u z ) ] - ( p 2 / u 2 ) p , .

Evaluating (15) yields (16), where y = p-'(pl + "/p2 - A)p-2 J'( o2 + p 2 ) , the transform

(DeGroot, 1970, p.247), and @ and @ are the standard normal density and distribution functions, respectively. The function 'I-' is positive, continuous, and strictly decreasing. There is therefore a unique yo such that "(yo) = yo; numerically y o = 0.276. If y > 0.276 then z = (2,2) is optimal, i.e. the party whose preferences are known should be elected in both periods. If y I 0.276 then an optimal strategy is T(@) = 1, and

1 if p, I (a - ap2)/[uz(p2 +.')I - (p2 /o2)pI

T ( p l ) = 2 otherwise ! (This can be derived from (1 l).) So it is optimal to select party 1 initially if

and it is optimal to stay with party 1 in period 2 if the posterior mean of pl is less than ( A - p2).

This result accords with our intuition that the probability of electing party 1 initially is increasing in p (since the information that we obtain about party 1 is more valuable the greater is the discount factor) and increasing in 2, the rate of inflation that is expected if party 2 is elected.

The effects of uncertainty, reflected in p2 and 02, are more complicated than is usually the case in bandit problems. This is because the degree of uncertainty enters voters' payoff functions. The

term p - 2 , , / m decreases to zero as p -+ w. If p entered (18) only through these terms then

party 1 would be optimal for sufficiently large p for any fixed pl and A . Thus if prior beliefs are sufficiently diffuse (large p ) then any expected loss will be tolerated initially in return for the possibility of large gain in the second period vote. For fixed p, the amount of this expected loss reflects the value of information. Offsetting this is the term in (p, + p2 - 1) in (18), which reflects the difference in expected payoffs from electing party 1 as opposed to party 2. Increases in o make it less likely that (18) will hold. This accords with our intuition that a more noisy inflation signal makes observing an inflation outcome less valuable, reducing the informational value of any observation.

For (18) to hold requires pl I A - p 2 + yopp-2 (02 + pz)-O.5. For given 2 and p,, whether or not this will hold depends on the size of x p, u and p. The size of ytells us how much agents care about inflation forecast errors. The larger is this term the less likely is party 1 to get elected. This


is because it has been assumed that agents know one party’s type, but not the other’s. This implies that expected forecast errors are larger for party 1. The more agents care about these forecast errors, the less likely is party 1 to get elected.

It is possible that party 1 can be elected despite having a higher expected mean than the opposition, as long as yis less than p-4y0p(02+ p2)-0.5. This is more likely to be true the smaller is p, and the smaller is o. p is entering these results in two ways. The first is through the fact that a large p implies that a lot of information will be acquired through observing an inflation outcome. What is important here is the size of p relative to 0. The larger is p relative to 0, the more the posterior will be concentrated relative to the prior, implying that a lot of information has been gleaned from an observation; i.e. if the private sector is uncertain about a policymaker’s type, but knows that the noisy component of inflation is small, an inflation observation will convey a lot of information about a policmaker’s type. However p also affects forecast errors, and this will make a voter less likely to elect an unknown party. The term in yop( l + p2)-0.5

reflects the value of information, while ” / p 2 reflects the cost of larger forecast errors relative to the known party. A final point to note is that a proportional increase in both p and o will both reduce the probability that the unknown party will be elected initially, and reduce the probability that they will be elected in period 2. A more uncertain environment implies a less concentrated posterior distribution and reduces the benefits of electing the unknown party.

In this example we have seen that it is possible that a government may be elected in both periods even though an alternative party may be preferable to voters from the perspective of maximising the welfare of the private sector. This occurs if beliefs or the stochastic shock result in the election of the party with lower expected welfare for the private sector. Thus we can get stuck with an inflationary government. More interesting is the possibility that agents can vote the incumbent out of office despite them being less inflationary than the opposition. Hence in this stochastic environment voters prefer operating rules which are less ambiguous (lower 02),

because such rules give us more information about a policymaker’s type. Policymakers on the other hand, may prefer more ambiguous operating procedures (larger 02), if they are more inflationary than opposition parties, and y is small. This finding is consistent with Alesina and Cukierman (1990), who found that policymakers who can choose the variance of the noise coming between actions and outcomes will not always choose the action having the lowest variance.


IV. CONCLUSIONS

In this paper the implications of endogenising voters choice among rival political parties, differing in their inflationary preferences has been examined. Voters learn about the preferences of a government by observing its past inflation, and use beliefs as the basis for optimal voting rules. It was shown that these rules may not lead to the election of the least inflationary party, if there exists uncertainty. In reality voters may find it difficult to find the least inflationary government. This suggests that we may want to force policymakers to act less ambiguously by, for example, constitutionally binding the actions of central banks or fiscal policymakers. The combination of noisy outcomes and uncertainty about policymakers’ preferences can lead to upward biases in inflation in some countries.

Possible extensions to the model include allowing policymakers to be motivated by electoral considerations, as well as by the purely ideological considerations that govern policymakers’ actions in this paper. This would allow policymakers to take actions different to their ideologically preferred positions in order to try to win elections. Experiments in Crosby (1994) suggest that the conclusions to his paper are robust to such extensions. Another suggestion which is currently being explored is to allow policymakers’ preferences to change over time, and allowing the two policymakers’ preferences to be correlated (in an environment where there is some uncertainty about the type of both policymakers). In this environment the private sector learns about the preferences of both policymakers when an inflation outcome is observed. It is not expected that such a modification to the model would alter the conclusions above, since more rather than less uncertainty is added to the model.

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Alesina, A. and Tabellini, G. (1992), ‘Positive and Normative Theories of Public Debt and Inflation in Historical Perspective’, European Economic Review, vol. 36.

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voting and learning in a model of monetary policymaking*

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