Rational Voters, Elections, and Central Banks: Do Representative Democracies Need Nonrepresentative...

Economic Note

Rational Voters, Elections, and Central Banks:Do Representative Democracies NeedNonrepresentative Institutions?

Francesco Lippi, Bank of Italy and CEPROtto H. Swank, Erasmus University Rotterdam/TRACE

We show that the welfare-improving property of an independent central bank dependson how voters respond to the time consistency problem. Voters’ responsiveness to economicproblems may provide some flexibility to revise the policy delegation arrangement of thecentral bank. This may improve social welfare. Preliminary evidence on voters’ behaviorin the U.S. is presented, which indicates that voters seem to respond to economic problemsin a proper way, taking time-consistency problems into account when making their votedecisions. 1999 Society for Policy Modeling. Published by Elsevier Science Inc.

1. INTRODUCTION

In this paper we examine the case for an independent conservative centralbank in the presence of rational voters. The model presented in the next sectionis based on Barro and Gordon (1983), who developed a positive theory ofinflation that emphasizes the credibility aspects of monetary policy. In thatcontext, as shown by Rogoff (1985), the policy maker may increase his welfareby delegating monetary policy to a conservative banker. The basic argument isthat an independent central bank, ruled by an inflation averse banker, reducesthe incentive to create inflation surprises aimed at eroding the real value ofoutstanding government debt or at reducing real wages. This argument is madeby showing that the political decision maker increases his utility by carrying over

Address correspondence to Francesco Lippi, Servizio Studi, Banca d’Italia, Via Nazionale,91, 00184 Roma, Italy.

This paper was written while the first author was a PhD student at Erasmus University.We would like to thank Alex Cukierman for useful comments on an earlier draft of

this paper. Remaining errors are of course our own. The views presented in the paperare not necessarily endorsed by the Bank of Italy.

Received February 1997; final draft accepted September 1997.

Journal of Policy Modeling 21(4):515–525 (1999) 1999 Society for Policy Modeling 0161-8938/99/$–see front matterPublished by Elsevier Science Inc. PII S0161-8938(97)00157-9

516 F. Lippi and O. H. Swank

monetary policy to a conservative banker who dislikes inflation more than hedoes himself. Moreover, the optimal degree of inflation aversion of the appointedcentral banker depends on some structural features of the economy, namely theseriousness of the time-consistency problem and the magnitude of the shocksthat hit the economy. These findings seem to support the claim that monetarypolicy should be delegated to an independent banker who is more inflationaverse than the policy maker. However, this conclusion should not be draw toosoon. One should also consider how voters respond to the time consistencyproblem.

In Section 3, we examine how voters’ behavior may relate to the time-consis-tency problem. We argue that if voters take expected inflation as given, theyvote for the party whose preferences are closest to their own preferences. Inthis setting, the policy maker’s preferences coincide with the median voter’spreferences. Alternatively, if voters take the time consistency problem intoaccount when making their vote decisions, the winning candidate is more conser-vative than the median voter. It appears that the bigger is the time consistencyproblem (e.g., a higher natural rate of unemployment, or smaller shocks hittingthe economy) the more consecutive is the elected policy maker.

These findings suggest two considerations. First, they weaken the argumentin favor of an independent conservative central bank because if voters arerational the socially efficient delegation to an inflation averse policy makermay occur through the elections. Voters’ rationality reduces the need for anindependent central bank. Second, it appears that some degree of flexibility forthe revision of monetary policy goals is desirable, given the relationship betweenthe optimal degree of conservatism of monetary policy and the structural featuresof the economy. Voters’ responsiveness to economic problems may provide (atleast part of) the required flexibility to revise the policy delegation arrangementof the central bank. This may improve social welfare.

Some preliminary evidence on voters’ behavior in the U.S. does not contradictthis conjecture. In Section 4, we present simple estimates indicating that voters’support for US presidents varies with these structural features of the economyeven when partisan factors are accounted for. Republican presidents, usuallyregarded as more conservative than Democratic presidents, gain popularity whenthe seriousness of time consistency problems rises. This suggests that voters takethe time-consistency problem into account when making their vote decision.

2. THE MODEL

In this section we examine a stochastic rational-expectations model of stabili-zation policy based on Rogoff (1985). We closely follow previous work onmonetary policy games (Barro and Gordon 1983) and assume that policy maker’spreferences are represented by the following loss function:

L 5 p2 1 b · u2, (1)

where p and u denote the inflation of the unemployment rate, respectively.Policy maker’s losses increase as inflation and unemployment deviate from their

RATIONAL VOTERS, ELECTIONS, AND CENTRAL BANK 517

ideal targets, normalized to zero in Equation 1. The parameter b indicates thecosts the policy maker attaches to unemployment (u) relative to inflation (p).Each type of policy maker is fully characterized by his degree of inflation aversion(1/b). We suppose that the policy maker is elected. Under the usual assumptions,it can be shown that in such a setting the median voter is decisive. However, aswe will show later, this does not necessarily imply that b coincides with thepreference weight of the median voter.

The simple economic structure of this model is described by the followingequation:

u 5 un 1 u(pe 2 p) 1 e, (2)

where un and pe denote the natural unemployment rate (subscript n) and inflationexpectations (superscript e). Equation 2 is an expectations-augmented Phillipscurve that can be derived from a model of a monopolistic trade union wherewages are contracted in nominal terms and are not fully indexed to inflation(Fischer, 1977; Schaling, 1994). In this setting, unanticipated inflation decreasesunemployment by cutting real wage costs and thus making it optimal for thefirms to employ more labor.1 In the absence of policy surprises, unemploymentis determined by its natural level,2 un, and by the realization of an i.i.d. randomshock, e, with zero mean and standard deviation equal to: se. This random shockmay be interpreted as a proxy for productivity shocks or transitory changes inthe intertemporal consumption preferences. It is assumed that at the time whenwages are contracted private agents cannot observe the shock e. Because of thisassumption monetary policy turns out to have a well-defined role for stabilizationpolicy.

Throughout this paper we do not allow the policy maker to enter into abinding commitment. Hence, the policy maker minimizes Equation 1 with respectto p, subject to Equation 2, given pe.3 This yields the policy maker’s reactionfunction:

p 5b · u(un 1 u · pe 1 e)

1 1 b · u2. (3)

In equilibrium p 5 pe holds, so that inflation expectations are given by:

pe 5 b · u · un. (4)

Equation 4 reveals the well-known Barro-Gordon determinants of the struc-tural inflation: the gap between the natural and desired unemployment (un), theslope of the Phillips curve (u), and the weight attached by the policy maker to

1 Cukierman (1992, ch.3) analyses the microfoundations of this mechanism in details.2 For an analysis of the determinants of the natural rate of unemployment that is consis-

tent with this model see, for instance, Schaling (1994), who studies the behavior of amonopolistic trade union bargaining over real wage and the employment level.

3 For simplicity, the policy maker is assumed to control inflation directly so as to minimizelosses associated with unemployment and inflation.


the real target (b). Substituting Equation 4 into Equation 3 yields the equilibriumpolicy of the policy maker:

p 5 b · u · un 1b · u

1 1 b · u2· e. (5)

Equation 5 shows that the policy effectiveness is limited to the neutralizationof the unemployment shock over which the policy maker has an informationadvantage (e). It is important to observe that less inflation averse policy makers(higher b) and larger gaps between natural and desired unemployment (un)increase the structural component of policy: buun. This happens because privateagents anticipate that larger values of un and b increase the policy maker’stemptation to generate surprise inflation and, therefore, incorporate this informa-tion into their inflation expectations. Hence, the structural component of policygives rise to an inflationary bias (excessive inflation), which raises equilibriuminflation but has no real effects on the unemployment.

This is why the policy maker may decrease his loss by delegating monetarypolicy to a conservative banker4 whose preference weight bi is lower than b, sothat he implements Equation 5 with bi. To see this, substitute Equation 5 withb 5 bi into Equation 1, and take the first-order condition with respect to bi tominimize expected losses as perceived by the policy maker before the game isplayed (see footnote 4). After some simplifications this yields:

bi · u2n[1 1 bi · u2]3 1 s2

e · [bi 2 b] 5 0, (6)

where bi is the optimal preference weight of the banker from the policy maker’spoint of view. Equation 6 shows Rogoff’s (1985) results that if the naturalrate of unemployment is larger than zero, the policy maker benefits from aconservative monetary policy (bi , b). Furthermore Equation 6 shows that theoptimal bi depends on the natural unemployment rate and of the amount ofshocks (se) that hit the economy. Applying the implicit function theorem toEquation 6, it is easy to see that:

]bi

]un

, 0 and]bi

]s2e

. 0, (7)

from which it follows that the optimal type of central banker depends on thestructural features of the economy. A higher unemployment gap (the differencebetween desired and natural unemployment) increases the policy maker’s temp-tation to generate inflation surprises (Equation 3), and hence, requires a moreconservative central banker (lower bi) to counter the inflationary effects of

4 As usual, we imagine that the delegation takes place before inflation expectations areformed and that the banker is independent, i.e., that it cannot be removed from the officeonce expectations have been formed (see Lohmann, 1992).


discretionary policy. On the contrary, a higher level of supply shocks (se) in-creases the policy maker’s costs that follow from a distorted stabilization policy.5

Hence, if the level of shocks that hit economy increases, the optimal centralbanker’s type becomes less conservative (higher bi).

3. VOTER BEHAVIOR

In the previous section, we have demonstrated that the policy maker canreduce the time-consistency problem by delegating monetary policy to a conser-vative banker. Does this mean that monetary policy should actually be carriedover to a conservative banker? In this section, we argue that the answer to thisquestion depends on how voters deal with the time-consistency problem.

Rational voters vote for the party that minimizes their expected losses. Sup-pose that elections are held that revolve only around the issue of stabilizationpolicy. Then voters, like the policy maker, face the optimization problem:

min Ln 5 p2 1 bn · u2,

with respect to p and subject to Equation 2, where bv denotes voter v’s preferenceweight. If voters take inflation expectations as given, their optimization problemcorresponds to the optimization problem the policy maker faces given by Equa-tions 1 and 2. In this setting, each voter casts his ballot for the policy makerwhose preference weight is closest to his own preference weight (cf. Swank,1995). This implies that the policy maker whose preference weight coincideswith the median voter’s preference weight wins the elections. Note that in thiscase, the model implies that election outcomes only depend on agents’ prefer-ences and are not affected by the structural features of the economy such asthe natural unemployment rate or the magnitude of unemployment shocks.

Suppose now that voters do not take inflation expectations as given, or toput it differently, that they take the time-consistency problem into account whenmaking their vote decisions. Then the vote decision problem resembles thedelegation problem faced by a policy maker who determines the optimal prefer-ence weight of an independent central bank. The only difference here is thatwe consider a different level of delegation, that which occurs via the elections.In this setting, each voter casts his ballot for the party (i.e., policy maker’s type)whose preference weight is closest to the preferences of her most preferredcentral banker, as implied by Equation 6. Hence, the policy maker who winsthe elections is more conservative than the median voter. Note that in this casethat election outcomes vary with the natural level of unemployment and withthe magnitude of the unemployment shocks.

5 Because the preferences of the central banker (bi) are different from that of the policymaker, the central banker’s response to the shocks differs from the one of the policymaker. Obviously, this is costly for the policy maker, and these costs increase as thestabilization problem increases its importance compared to the credibility problem.


The above implies that if voters take the time-consistency problem into ac-count when casting their ballots the elected policy maker is already more conser-vative than the median voter. Hence, in this case, thanks to the delegationscheme created by the elections, discretionary equilibrium is equivalent to anautonomous central bank from the median voter’s point of view.

However, there remains a difference between the two regimes in the model.It is clear from Equations 6 and 7 that the optimal delegation arrangementdepends on some features of the economy (e.g., the relative importance of theinflationary bias versus the need for shocks stabilization). Thus, an exogenouschange of economic conditions (un, se) makes it optimal to change the monetarypolicy maker type. This implies that an optimal delegation arrangement shouldlink the central banker in office to the exogenous conditions faced by the econ-omy. For instance, in periods of large supply shocks, the central banker shouldbe one who is less concerned with controlling inflation relative to output stabiliza-tion. Although it may be difficult to write such a detailed monetary policyarrangement, relating monetary policy goals (bi in our model) to economicconditions, the flexibility required by this problem can be provided by rationalvoters. The economic benefits of democratic institutions are apparent here,because they allow the voters to change the policy maker’s type, at least periodi-cally. Therefore, if the delegation arrangement for the central bank cannot bemade contingent on exogenous economic conditions, and if voters take time-consistency problems into account, the setup of a “political” central bank maydominate the delegation of monetary policy to an autonomous central bank. Infact, under the former regime the median voter can adapt to the “new conditions,”while under the latter she cannot.6

In our model, whether an additional level of delegation (e.g., an autonomouscentral bank) is required to increase the median voter’s welfare depends onvoters’ behavior. Hence, this is an empirical issue. In the next section we, there-fore, investigate voters’ behavior in the US to search for information on whethervoters take account of the economic circumstances when delegating their politicalrepresentatives or whether they do not.

4. SOME PRELIMINARY EVIDENCE

Numerous studies have examined the relationship between voter behaviorand macroeconomic outcomes. Two strands of research can be distinguished.The first is based on the assumption that voters reward the incumbent party forfavorable economic outcomes and punish it for unfavorable outcomes (for asurvey of this literature see, Paldam, 1994). In these studies, inflation and unem-ployment negatively affect the popularity of the party in office. The second

6 According to Alesina (1989, section 5.3) there are two main economic benefits ofdemocratic institutions. The first one is that they may promote efficiency in helping distin-guishing the competent policy makers from the incompetent ones. The second is that theycan serve the “purpose of signaling the (possibly evolving) social preferences [ . . . ].” Ourresult provides a formal treatment of this second point.


strand of the literature builds on the partisan theory (Alesina, 1987; Hibbs, 1977)The key idea behind the partisan theory is that different political parties havedifferent preferences over economic goals. For the United States, Democraticadministrations are assumed to assign a higher priority to reducing unemploy-ment, whereas Republican administrations are assumed to care more aboutreducing inflation. In terms of Equation 1, this implies that the policy weight b

is higher under Democratic administrations than under Republican administra-tions. Several studies report strong evidence in support of the partisan theoryfor the United States (for a survey of this literature see, Alesina and Rosenthal,1995). The partisan theory of voter behavior is based on the assumption thatvoters take into account that political parties have different preferences overeconomic goals when casting their ballots. The main prediction of this theoryis that voters choose the party that best fits the economic situation. The Demo-cratic party wins votes when the unemployment rate is rising, while the Republi-can party becomes more popular when inflation is rising (see, Swank 1993, 1995).

The model discussed in the previous section suggests that if voters take thetime consistency problem into account when casting their ballots, a rise in thenatural unemployment rate, or a decline in the variance of the output shocks,induces them to vote for a policy maker who is relatively inflation averse. It isevident that the voters can do so only if different political parties differ in theirpreferences and voters are aware of these differences. For this reason, thepartisan theory of voter behavior is a proper starting point for the examinationof the electoral effects of the natural rate of unemployment and the stochasticproperties of the supply shocks.

The empirical analysis below is based on the following equation:

log(popd/1 2 popd) 5 a1 · u 1 a2p 1 a3 · un

1 a4 · f(pener) 1 a · D 1 intercept, (8)

where popd denotes the approval rate of Democratic presidents and popr 5 12 popd is the approval rate of Republican presidents.7 Furthermore, pener is thegrowth rate of energy prices that we regard as an important determinant ofsupply shocks (see, Gordon, 1985) and D is a vector of political dummy variablesto account for the effects of major political events on presidential popularity.The first two terms of Equation 8 represent the usual effects of unemploymentand inflation in a partisan voter model, according to which a Democratic presidentbenefits from unemployment and suffers from inflation in terms of popularity.This leads us to expect that a1 and a2 have a positive and a negative sign,respectively. The third and fourth term of Equation 8 represent the effects of thenatural rate of unemployment and the variation of supply shocks on presidential

7 We use popularity instead of election outcomes to describe voters’ behavior. Thismeasure is less directly related to the theoretical model, but it allows us to increase thenumber of observations.


Table 1: Estimates of Popularity Functions for the United States, 1960–1992

Model excluding political variables Model including political variables

Intercept 6.816 (1.174) 6.594 (1.488)a1 0.062 (0.041) 0.127 (0.045)a2 20.481 (0.346) 25.284 (0.309)a3 20.115 (0.029) 20.119 (0.023)a4 0.160 (0.061) 0.106 (0.048)Water 0.553 (0.177)War 20.189 (0.076)Johnson 0.451 (0.138)Bush 20.743 (0.378)R2 0.855 0.937D.W. 1.639 2.026

Data are annual. Because the logit model is heteroscedastic the popularity functionsare estimated with weighted least squares. The figures in parentheses are standard errors.

popularity.8 As discussed in the previous section, if voters are aware of the time-consistency problem, the Democratic party is predicted to suffer from a rise inthe natural rate of unemployment and to benefit from uncertainty about supplyshocks.9 Thus, the expected signs of a3 and a4 are negative and positive, respec-tively. As a measure for the variance of the supply shocks, we have used thefollowing indicator:

f(pener) 5 o4i51[pener(t 2 i) 2 pa(t 2 i)],

with pa as a 4-year average of pener.

The first column of Table 1 reports the estimation results of Equation 9 whenpolitical variables are excluded from the analysis. All estimates have the correctsign, though the estimates of a1 and a2 are only marginally significant. Theestimates of a3 and a4 suggest that Republican administrations benefit from arise in the natural rate of unemployment and a decline in the variability ofenergy prices. These findings are consistent with the view that voters take thetime consistency problem—faced by policy makers—into account when castingtheir ballots. Apart from economic effects on presidential popularity, majorpolitical events may affect presidential popularity. The second column of Table1 reports the estimation results of a popularity function that includes politicaldummy variables. First, a dummy variable Water is included for the Watergate

8 The values for the natural rate of unemployment are taken from Gordon (1993).9 The “seriousness” of the inflationary bias is given by the difference between the natural

rate of unemployment and the desired rate of unemployment. The latter is assumed tobe equal to zero in our model. If the desired rate of unemployment is different from zero,but constant over time and across parties, our assumption is not restrictive because itamounts to a distortion on the constant term (intercept) of the equation.


period. Second, a dummy variable war is included to account for the dissatisfac-tion of the electorate with the involvement of the United States in the Vietnamwar. Finally, we have experimented with dummy variables for each presidentto look for personality effects. These effects have been found for Johnson andBush, but not for other presidents. The estimates of the popularity functionincluding the political dummy variables are consistent with the partisan modelof voter behavior (a1 and a2 are statistically significant under this specification)and with the view that voters consider the time consistency problem the policymaker faces when casting their ballots. The estimates of a1 and a2 indicate thatvoters have more confidence in Democratic presidents as to reducing unemploy-ment and more confidence in Republican administrations as to fighting inflation.Moreover, a rise in the natural rate of unemployment increases the popularityof Republican presidents, while fluctuations of energy prices, which we associatewith the magnitude of supply shocks, tend to increase the popularity of Demo-cratic presidents.

5. CONCLUSIONS

Rogoff (1985) showed that credibility problems of monetary policy mightbe efficiently dealt with by means of an optimal delegation arrangement. Thetheoretical results are well known in the literature: in the presence of a time-consistency problem the principal improves his welfare if he credibly delegatespolicy to an agent who is more conservative (inflation averse) than himself.

Rogoff does not explicitly deal with the question of the institutional stage atwhich the delegation to the conservative agent is supposed to take place. Mostauthors who follow Rogoff assume that the delegation occurs between the policymaker (government) and the central banker. In this paper we analyze an alterna-tive level of delegation, that between voters and the policy maker that takesplace through the elections.

We propose a simple model where voting revolves around the issue of stabili-zation policy. In our model, if voters are rational and account for the time-consistency problem when casting their ballot, the elected policy maker will bemore conservative than the median voter. The theoretical implication of themodel is that rational voters’ behavior may help solving the credibility problemsof an economy by appointing a conservative policy maker, just like a policymaker may solve his time consistency problems appointing a conservative centralbanker.

Although the two solutions appear to be equivalent, rational voters mayendow the economic system with some useful policy flexibility. The reason isthat in principle the delegation arrangement for an independent central bankshould make the policy targets (i.e., the central banker’s type) contingent onthe fundamental economic conditions. In case the delegation arrangement cannotbe made contingent, monetary policy has a limited capacity to adjust to changingeconomic conditions. In this paper we show that voters’ awareness of economicproblems may provide the economic system with a certain degree of flexibility.


At least theoretically, it seems that voters’ rationality may improve economicwelfare.

In Section 4 of this paper we try to discover whether voters’ behavior in theUnited States appears to respond to the seriousness of the time-consistencyproblems of the economy, as implied by the theoretical model. The evidenceshows that the popularity of republican presidents increases if the natural rateof unemployment rises, indicating that voters respond to a more serious infla-tionary bias (larger natural unemployment rate) by supporting a policy makerwho is supposedly more inflation averse. Vice versa, the popularity of democraticpresidents increases if the relative importance of the time-consistency problemsdecrease (larger variance of supply shocks or lower natural unemployment rate).This indicates that American voters seem to be aware of the economic problemfaced by the policy maker, and that they respond to it in a proper way. Moreover,the results are consistent with rational partisan voters theories.

The results of this paper can be related to other studies that have analyzedthe relationship between voters’ behavior and monetary policy, such as Minford(1995) and Waller and Walsh (1996). In this respect, part of the value added ofthis paper is to corroborate the purely theoretical approach of the previousstudies with some empirical evidence on voters’ behavior.

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