If the policymaker's wrists were already bound by exchange target duct tape, what would be the effects of an additional pair of handcuffs from inflation targets and yet another loop of rope from central bank independence? One could argue that the effect would be nil, because the exchange rate commitment already credibly limited the central banker's discretion. One could instead argue that that the effect would still be greater credibility, albeit with diminishing returns, because inflationary government officials are escape artists and the more restraints the better … Theory gives no single answer to this empirical question.Footnote 1
Economic theory and empirical evidence show that high inflation cannot deliver employment and economic growth. In fact, not only is inflation a way for the government to cheat small savers and the poor, but bringing down inflation from high levels is also likely to cause a deep recession. Altogether, the recent consensus stresses the importance of maintaining stable prices and avoiding inflationary spikes. The overall economic policy of a country, however, is sometimes inconsistent with the goal of low inflation. The literature identifies independent central banks and fixed exchange rates as the main institutional mechanisms that governments use to gain anti-inflationary credibility. Both institutions are argued to increase credibility and help maintain price stability because both restrain the use of monetary policy by governments. In this article I explore how governments design the set of institutional constraints they place on themselves when it comes to inflation and monetary policy. To this end, I develop a model describing when and why policymakers would choose independent central banks and fixed exchange rates together, alone, or not at all, given that the two institutions lack perfect credibility and policymakers are partisan.
In terms of framework, this article draws on recent research suggesting that the choice of the exchange-rate regime and the degree of independence of the central bank are correlated processes as opposed to unconnected decisions.Footnote 2 The argument is that if both institutions work similarly to insure stable prices and the focus is on inflation fighting, there is a need to explain why countries adopt different mixes of institutions. In this light, it is puzzling that a notable 26 percent of countries after the collapse of the Bretton Woods system of fixed exchange rates choose both an independent bank and fixed exchange rates, whereas the rest of the countries choose only one institution or none.Footnote 3 In a more specific example, all postcommunist countries struggled with high inflation and lack of credibility during the transition to market economy. Yet, these countries adopted diverse mixes of anti-inflationary institutions with very different timing as well: the Czech Republic in 1993 chose both a fixed exchange rate and an independent central bank. Similarly, Bulgaria in 1997 adopted a currency board and granted more independence to its central bank. However, Moldova in 1995 chose only a very independent central bank, while in the early 1990s, Romania had neither fixed rates nor an independent bank. The examples above show that governments engage in “comparative shopping” when it comes to delegation of monetary policy, and that, potentially, there is both complementarity and substitution between fixed rates and independent central banks. To try to explain the diversity of monetary institutions in the post–Bretton Woods period, in this article the government has at its disposal a larger set of actions than in much of the previous literature:Footnote 4 it can choose fixed or flexible exchange rates and a dependent or independent central bank.
In addition, I explicitly consider the benefits and costs of the two monetary institutions and extend the analysis by allowing the government to choose more realistic institutions than previous studies. Focusing on stable prices, the benefit of adopting fixed exchange rates or an independent central bank is increased credibility in monetary policy. The major cost of delegation is common to both fixed rates and independent central banks: the government is restricted in the use of monetary policy to react to domestic economy slowdowns. Yet fixed rates and independent central banks also have particular disadvantages. Central bank procedures and performance lack transparency when compared to fixed rates.Footnote 5 Visible fixed rates, on the other hand, run the risk of severe misalignment and currency devaluations.Footnote 6 These shortcomings diminish the ability of each individual institution to deliver increased credibility, thus making it worthwhile for governments to doubly tie their hands in monetary policy.
The question of what type of constraints countries place on themselves in monetary policy has remained salient as the answers have changed over time due to the liberalization of global capital transactions and a growing recognition of the importance of transparency for achieving stable prices. In the last two decades, delegation to an independent central bank has been on the rise, most notably in developing countries,Footnote 7 but also in Western Europe, in the context of the Economic and Monetary Union, and Japan in 1998. Independent central banks have been argued to reduce inflation because central bankers tend to take a longer view of the policy process and are, on average, more conservative about price stability than elected politicians.Footnote 8 However, while there have been efforts to improve central bank transparency (publication of macroeconomic projections, direct inflation targeting), central bank procedures and performance remain more vague when compared to fixed rates, and are harder to monitor in the short run.Footnote 9 Fixed exchange rates, on the other hand, work by tying domestic economic policy to that of a low inflation country, thus ‘importing’ the lower foreign inflation.Footnote 10 The advantage of fixed exchange rates is that both the fix and the subsequent adjustments are visible and relatively easier to monitor. On the down side, in a world of mobile capital, fixed exchange rates can be and are devalued and generate political costs for governments when a currency devaluation occurs. In the post–Bretton Woods period, most countries that had a de jure fixed exchange rate regime adjusted it at some point, remaining within the fix or moving to flexible exchange rates.Footnote 11 In the terminology of Reinhart and Rogoff, the reality is that many de jure fixed rate arrangements become de facto floating rates, due to devaluations.Footnote 12 Also, while fixed exchange rates remain the choice of a monetary institution in the majority of developing countries, in the past two decades the risk of a costly adjustment has reduced countries' appetite for formally fixing their currency.Footnote 13
In terms of results, this article is able to replicate key findings from the literature on inflation and monetary institutions and, more importantly, it has novel hypotheses as well. The first set of new findings pertains to the issue of institutional complementarity. In this article, institutions overlap with respect to the goal they need to achieve (low inflation) but each institution can only achieve its goal imperfectly. The model shows that governments operating in such a monetary policy institutional environment end up with a mix of institutions that keep inflation in check. In particular, a complementary relationship and a mix of monetary institutions is likely when the political costs of fixed exchange rate adjustments are low and delegation to an independent central bank is relatively transparent. The second set of results identifies specific conditions that make the two monetary institutions complements or substitutes. For example, when monetary institutions are not trusted, right-wing governments start behaving the way one would expect the left to behave in normal times. That is, in bad times for macroeconomic stability, the right is more likely to adopt an independent central bank either alone or in combination with a fixed exchange rate. In hyperinflation episodes or in countries democratizing after an authoritarian regime, the model predicts that the right will be more likely to adopt a monetary institution that is conservative but whose independence is not entirely clear to the public.
The Fall 2002 issue of International Organization aimed to explain the evolution of monetary institutions in the post–Bretton Woods period by analyzing independent central banks and fixed exchange rates together. The present article builds on this research in that it explicitly considers a correlated institutional choice by the government and allows the two institutions to have different degrees of transparency. In addition, this article's main contribution is threefold: first, by letting fixed exchange rates be an imperfect commitment instrument, it takes into account real world features that figure prominently in the current thinking about exchange rate regime classification. Also, by allowing the government the choice of two imperfect policy instruments, it gives a motivation to governments to choose a mix of institutions. Second, the literature on the political economy of monetary institutions has had mixed results on the relevance of partisanship.Footnote 14 Contributing to this literature, this article suggests that the effect of partisanship on the adoption of monetary institutions is likely to be conditional on economic and political circumstances influencing the credibility of institutions. Finally, the article generates new testable hypotheses and suggests ways to operationalize the parameters of the model.
Inflation, Central Banks, and Exchange Rates
The traditional monetary policy model goes back to Barro and Gordon's seminal 1983 article.Footnote 15 In such a model, executives make inflation announcements, private actors make decisions based on their inflationary expectations, and policymakers act again, trying to cheat by introducing surprise inflation after private actors have made decisions about the quantity of money they will hold. The effect of this cheating, if it comes as a surprise, is to increase output and employment. A rational public, however, anticipates government's moves and does not believe the initial inflation announcements. The result is higher inflation than optimally desired by the government without the benefit of increased employment and output.
Rational expectations and the incentives to cheat underlined above combine to create a time-inconsistency problem. Policymakers facing such a problem find it difficult to make credible commitments by themselves. In this context, Rogoff, Giavazzi and Pagano, Alesina and Grilli, and Milesi-Ferretti show the advantages of delegating monetary policy by fixing the exchange rate or by allowing the central bank to be independent.Footnote 16 The two mechanisms restrain opportunistic politicians and achieve the same goal of low inflation, albeit in different ways. Granting independence to the central bank works because central bankers, generally, come from business, financial, or academic circles, tend to take a longer view of the policy process, and are, on average, more conservative about price stability than elected politicians or the median voter. Fixed exchange rates work by tying domestic economic policy to that of a less inflation-prone country, thus ‘importing’ the lower foreign inflation.
For open economies, the major cost of delegation is common to both fixed rates and independent central banks: the government is restricted in its use of monetary policy to smooth large negative shocks to the domestic economy. In a recession, for example, policymakers lack flexibility in using monetary policy to stimulate output and employment.Footnote 17 Lohmann addresses the loss of flexibility due to delegation and designs an optimal delegation rule that allows flexible policy response to unforeseen large shocks to the economy.Footnote 18 Her model allows the government the choice of the degree of central bank conservatism as well as the cost at which it could override the central banker in setting inflation. In equilibrium, the government never overrides the central banker, as the central banker accommodates the government when large negative shocks occur.
The more recent literature addresses additional political economy issues relevant to monetary policy delegation. Moser studies the cost of withdrawing the independence granted to the central banker.Footnote 19 He analyzes the interaction between a conservative central banker and two legislative bodies with veto power over legislation to amend the independence of the central banker. He shows that a nominally independent bank can freely choose monetary policy only if the two legislative bodies have heterogeneous preferences. Keefer and Stasavage show empirically that the presence of multiple political veto players is crucial to the effectiveness of independent central banks in reducing inflation.Footnote 20 They also find that fixed exchange rates have a greater anti-inflationary impact when it is hard for the public to ascertain the sources of the inflationary process, emphasizing the transparency qualities of fixed rates. Further, Broz argues that central bank independence and fixed rates are alternative monetary commitments that vary in transparency and that the transparency of political systems is a substitute for the transparency of monetary commitment devices.Footnote 21 He finds empirical evidence that dictatorial regimes are more likely to use fixed exchange rates. Copelovitch and Singer also find that inflation is significantly higher in countries where central banks have regulatory responsibilities, although this effect is conditional on the choice of exchange rate regime and the relative size of the banking sector.Footnote 22
Closer to this article in terms of methodology, Canavan and Tommasi investigate the incentives created by incomplete information about a government's type in a game where the choice is over the transparency of a single policy instrument.Footnote 23 Transparency of commitment institutions is a central concern in this article, yet the structure of the model is more similar to that of Clark.Footnote 24 Clark explores the policymaker's choice of two commitment institutions—the exchange rate regime and the status of the central bank—in a one period game of complete information.Footnote 25 The value added in Clark's model is that he takes seriously the potential for both institutional substitution (fixed rates and independent central banks) and policy substitution (fiscal and monetary policy). In doing so, however, he chooses to model a perfectly predictable economy. The problem with assuming no unanticipated shocks to output is that delegation of monetary policy ceases to be costly if one allows players to be strategic and use rational expectations. Clark's model takes inflation expectations as exogenously determined, while admitting that endogenizing beliefs is desirable.Footnote 26 With endogenous rational expectations on the part of markets, the policymaker that does not delegate monetary policy faces the time inconsistency problem and ends up in a situation with high inflation and no output growth. If the economy is considered perfectly predictable the traditional problem of delegation—credibility versus flexibility—disappears as policymakers do not need flexibility to react to future unanticipated downturns in the business cycle. The immediate solution to the game, then, is that the policymaker always prefers to delegate monetary policy under a contract specifying appropriate action for all contingencies. Such a result is problematic because, in practice, monetary policy delegation is a hotly debated domestic policy choice and delegation is not ubiquitous. The analysis in this article departs in several ways from that of Clark: the model allows inflation expectations to be determined endogenously, and allows the economy to suffer shocks unanticipated by either markets or the policymaker. Most importantly, I let both fixed exchange rates and independent central banks be imperfect commitment institutions.
Central Banks and Exchange Rates—Imperfect Institutions
To date, there is limited systematic research investigating the complementarity between fixed rates and an independent central bank, as well as the conditions that make the two institutions complements or substitutes.Footnote 27 In particular, the theoretical literature on time-inconsistent monetary policy has overlooked the fact that central banks and fixed rates have specific disadvantages. The two commitment institutions are flawed in different ways. In the short term, central bank procedures and performance lack transparency and clarity when compared to fixed rates, and therefore central bank actions are more difficult to monitor.Footnote 28 Many times, central banks do not publish their intermediary targets for achieving price stability, or it is hard for markets to understand central bank targets or public statements, as well as the relationship between inflation and intermediary targets, such as the growth rates of money.
More recently, however, central banks in a number of countries have adopted a monetary rule that directly targets the rate of inflation.Footnote 29 Such a rule specifies the numerical inflation target as well as the time frame for it to be achieved. Undoubtedly, inflation targets are improving the transparency of central bank objectives. Still, it is the case that central banks have only imperfect control over inflation and targeting has a medium-term horizon, as inflation reacts with considerable time lags to changes in interest rates and is also influenced by factors beyond the control of monetary policy.Footnote 30 This means that in the short run, it is still difficult for the public to identify the reasons behind an increase in inflation. It is also difficult to assess whether, after a spike, inflation will be falling within the time frame specified in the law for the inflation target to be achieved. For these reasons, fixed rates are easier to monitor even than an independent central bank with an inflation target.Footnote 31 For example, following the recent spike in oil and food prices in 2007–2008, most inflation targeting central banks failed to achieve their targets. Also, the estimated time frame for a return to price stability was anywhere from a couple of months to a year or longer.Footnote 32 Moreover, the literature identifies various preconditions for successful inflation targeting, one of which is to have an independent and accountable central bank.Footnote 33 Such preconditions appear all the more important in times with large price shocks, such as the 2007–2008 increases in commodity prices. In such circumstances, the independence and reputation of the central bank can anchor inflation expectations and prevent broad-based wage indexation, despite temporary deviations from inflation targets.
By comparison, fixed exchange rates are clear and visible rules for the behavior of the currency and the public can recognize quickly a devaluation of the fixed rate. In the short term, markets can monitor easily whether a commitment has been broken. For example, Eichengreen and colleagues compare fixed exchange rates and inflation targets with respect to their visibility: “even when countries have accomplished a successful transition to a more flexible exchange rate, there is a tendency for the easily monitored exchange rate to become the focal point of private sector expectations, to the detriment of the less visible and more medium term inflation target.”Footnote 34
Yet, fixed rates are not a perfect commitment mechanism either. First, they present the risk of serious misalignment and are prone to being abandoned: “aside from a few minor tourist economies, oil sheikdoms and heavily dependent principalities, only a very small number of fixed exchange rates have survived the past years intact.”Footnote 35 Compared to fixed rates, reversals in central bank independence are rare. In the last decades, countries have generally moved toward granting their central banks more legal independence. For example, in Eastern Europe and the former Soviet Union after the fall of communism, there are only two cases of countries changing central bank legislation in the direction of less independence: Belarus in June 2001 and the Czech Republic in April 2002. In Latin America and the Caribbean, most central banks were granted substantial independence in the 1990s.Footnote 36 Still, opposition to independent central banks has gained some ground in recent years and countries passed new legislation undermining autonomy. For example, the Colombian Constitutional Court decided in 1999 to cap mortgage interest rates. Also, amidst a severe currency crisis and economic recession, Argentina changed the central bank charter to allow central bank financing of the fiscal deficit in 2002.Footnote 37 Second, policymakers face important political costs in the event of a devaluation or a collapse of the fixed exchange rate regime. Cooper shows that in the aftermath of devaluations, nearly 30 percent of governments fell within twelve months, as opposed to 14 percent in a contemporaneous control group.Footnote 38 Frankel goes on and expands Cooper's sample to 103 developing countries over the period 1971–2003.Footnote 39 He finds that the chief executive lost office 22.8 percent of the time in the six months following a currency crash, as opposed to 11.6 percent of the time otherwise.
In sum, independent central banks and fixed rates have specific disadvantages while bearing the same major cost of a constrained monetary policy. This article, then, assumes fixed rates that can be devalued and central banks whose independence cannot be clearly ascertained, and goes on to describe the conditions under which partisan policymakers choose institutions that help them improve monetary policy credibility. The possible institutional outcomes in this game are: flexible exchange rates and a dependent central bank; flexible exchange rates and an independent central bank; fixed rates and a dependent central bank; fixed rates and an independent central bank.Footnote 40 In the following sections I set up the model, translate the imperfect institutions discussed here into modeling assumptions, derive the conditions that make independent central banks complements or substitutes and discus policy implications.
Model Setup
There are two actors in the model, the government and the wage setters. The government has a quadratic loss function with a trade-off between inflation and deviation of output growth from target. Wage setters are rational and their utility depends only on the real wage. Production takes place according to an expectation-augmented Philips curve.
The preferences of the government are described by the quadratic loss function:
The loss function reflects the fact that there are distributional consequences to the choice of inflation rates. Capital owners who see the value of their holdings diminish with inflation prefer low inflation. To be sure, no one in the economy likes high inflation. However, labor is more vulnerable to economic recessions associated with tough anti-inflationary policies and is more willing to tolerate some inflation if that helps employment. Therefore, there are two types of government that differ with respect to the trade-off between inflation and output: the right (R), representing capital holders and the left (L), representing labor. By assumption, the right cares less than the left than about a drop in production below some target level ky*, so a R < a L. πt is the contemporaneous inflation, y t is the output produced in the economy, and y* is the market clearing level of output. k is greater than one because in the presence of distortions (income and labor taxation, unemployment compensation, minimum wage) y* is smaller than the socially optimal level of output ky*.Footnote 41 Because the market clearing level of output is too low and given the production equation (2), the government has incentives to increase inflation above expectations in order to raise output.
The specification of the loss function in equation (1) does not reflect the political cost, c, incurred by the government in situations when the fixed exchange rate commitment is abandoned.Footnote 42 The political costs of fixed rates are introduced later on, as omitting them simplifies computations and does not affect the establishment of the first set of results that show the complementarity between fixed rates and independent central banks.Footnote 43
Output in the economy takes place according to an expectations-enhanced Phillips curve:
where πte represents the expected rate of inflation. All variables are expressed in natural logarithms. In this economy, output y t grows above y* if inflation is above expected inflation, or if the shock to the economy ε is positive. As k is greater than one, the policymaker will have incentives to inflate the economy. The shock to the domestic country's output (ε) reflects the policymaker's dilemma in choosing between flexibility and credibility. By choosing to delegate monetary policy, the executive forfeits not only the option to behave opportunistically and inflate the economy after wages have been locked in, but also the liberty to react to negative output shocks.
The workers in this model aim to anticipate inflation and care about maintaining a constant level of the real wage:
The Game with Imperfect Monetary Institutions
The analysis in this section shows (1) how the imperfect institutions described previously translate into modeling assumptions, (2) the sequence of moves for the game with such imperfect institutions, (3) the solution concept for the game, and (4) derives the expected loss for the government for each terminal node of the game.
In the real world, one observes mixes of institutions. Bernhard and colleagues describe the monetary regimes after 1973 and show that about 26 percent of the sample has had an independent central bank and also sustained a pegged exchange rate regime for long periods of time.Footnote 45 It is quite clear then, that in many instances monetary institutions coexist. Consequently, in this article the government has a choice of two policy instruments: a fixed exchange rate regime and an independent central bank. Giving the executive the simultaneous choice of institutions is not enough, however, to be able to describe separate solutions for the adoption of individual institutions, a mix, or no institutions. With rational expectations and perfect commitment instruments, the government's set of two choices is superfluous. By construction, fixed rates and independent central banks are substitutes. The choice of either represents a commitment to low inflation rates.Footnote 46 With the more realistic assumption that institutions lack perfect credibility, the model is able to describe separate solutions for the adoption of individual institutions, a mix, or no institutions.
As shown earlier, the assumption that exchange rate commitments are fixed forever is not realistic. Countries sometimes are forced to give up fixed rates in the midst of speculative attacks, or governments simply renounce fixed rates after accomplishing the desired low inflation levels.Footnote 47 Suppose that the government announces a fixed rate regime and fixes the exchange rate at the beginning of the period. The public observes the fixed rate yet it does not believe the commitment will last forever, that is, the public expects that monetary policy may not be consistent with maintaining a fixed exchange rate and that an adjustment of the fix will come sooner or later.Footnote 48 The exchange rates are fixed but adjustable. In the game, I model the situation by introducing an exogenous probability, q ∈ (0,1), that the announced fixed exchange rate regime collapses at the end of the period, after workers have set inflation expectations, and that inflation will be determined by the government under the flexible exchange rate regime.
Further, I assume that the status of the central bank is not clearly ascertainable to the public making decisions about their wage level. Central banks tend to be less transparent than fixed rates with respect to their goals. Also, in the short run, transgressions against the independence of the central bank or missing inflation targets are more difficult to detect by the public. Therefore, I assume that when the government chooses and announces an independent central bank, there is an exogenous probability, p, that the announcement is not believed (p ∈ (0,1)). The public, on the other hand, takes the executive's choice to have a dependent central bank at face value: if the government chooses and announces that it will have a dependent bank, it is believed. In countries with a history of inflation and successive failed attempts at stabilization, the public has good reason to doubt the rhetoric of the government in economic policy, and for p to be positive. With learning, and as the central bank establishes its own reputation for inflation toughness, p may slowly go down to zero. Also, a more transparent inflation-targeting central bank that achieves its target will also help lower the probability, p. By comparison, however, the probability, q, remains essentially stochastic, reflecting the fact that while there are economic and political fundamentals that influence its relative size, q will be greater than zero due to the possibility of multiple equilibria in balance of payments crises or sudden reversal of market sentiment and heard behavior.Footnote 49
The play of the game is as follows:
1. The government chooses the mix of institutions: flexible exchange rate and a dependent central bank (terminal node 1); flexible exchange rate and an independent central bank (terminal node 2); fixed exchange rate and a dependent central bank (terminal node 3); fixed exchange rate and an independent central bank (terminal node 4).
2. Workers set inflation expectations πe; if the government has made the central bank independent, workers are not entirely sure whether to believe the government or not; when setting expectations, workers also anticipate that there is a chance that fixed rates do not survive.
3. The government observes the realization of the output shock, ε.
4. The fixed exchange rate collapses or maintains.
5. The government sets inflation if the fix has collapsed and if it chose flexible rates or a dependent central bank in the beginning of the period; the central bank sets inflation to zero if it was granted independence; inflation is zero if the fixed rate has survived.
The model is a sequential game of complete information solved by backward induction and the solution to the game is the subgame perfect Nash equilibrium.Footnote 50 In the game, the government chooses the institutional mix and the rate of inflation that minimizes its loss function, given the parameters a i, k, σ2, q, and p. The public wants to anticipate inflation correctly and sets inflation expectations according to the institutional setup selected by the government. To be able to discuss the institutional choice of the government, for each terminal node I compute below the expected loss function of the government E(L), that is, the loss function of the government at the beginning of the game when it looks down the path of play and anticipates how the game will unfold given its institutional choices. The government chooses the optimal institutional mix by comparing the expected loss function for each arrangement.
Terminal Node 1: Flexible Exchange Rate and a Dependent Central Bank
The government is assumed to be unable to commit to a specific inflation rate when the central bank is dependent or the exchange rate is flexible. Wage setters are aware of the government's problem and would not believe inflation promises. With no commitment, expected loss to the government is (see Appendix for derivation):Footnote 51
Terminal Node 2: Flexible Exchange Rate and an Independent Central Bank
When the government chooses a flexible exchange rate and an independent central bank, if wage setters believe that the central bank is truly independent, by assumption, they expect zero inflation. Yet, central bank independence is not perfectly visible: With some positive probability, p, wage setters do not believe the government and expect inflation to be the same as under a dependent central bank. In the beginning of the game, when it decides to delegate monetary policy to an independent central bank, the government knows that the public expects a rate of inflation higher than zero: πgove = (1 − p)π1−pe + pπpe, where π1−pe is the public's expected inflation if it believes that, in fact, the central bank is independent, and πpe denotes the expectation of nonbelievers. π1−pe = 0 and πpe equals a iH as in the case when the executives chooses a flexible exchange rate and a dependent central bank. Therefore, πe = pa iH.
Throughout this article, the central bank is a nonstrategic player: the bank's actions are determined by the government's choices. Specifically, if the government chooses an independent central bank, the central bank adopts a zero inflation rate (π = 0 if CBI = 1(p)). The behavior of the central bank is consistent with a situation in which the bank tries to establish its reputation and incurs an initial welfare loss by not matching high inflation expectations. Initially, the bank deflates the economy and the government that chooses an independent bank loses utility from low output growth. The expected loss to the government from choosing an imperfectly credible central bank and a flexible exchange rate is determined by plugging equation (2), πe = pa iH and π = 0 in equation (1) and equals:
Terminal Node 3: Fixed Exchange Rate and a Dependent Central Bank
When the government chooses a fixed but adjustable exchange rate and a dependent central bank, wage setters expect that, with probability, q, the fixed rate will collapse, in which case the inflation rate will be the same as under no commitment. With probability (1 − q), wage setters expect that fixed rates will maintain and inflation is zero. Public inflation expectations are then: πe = (1 − q)E(πFix) + qE(πCBI=0Flex). If fixed rates collapse and the central bank is dependent, the government gets to choose the optimal rate of inflation: πi = (a i /(1 + a i(1 − q)))H − (a i /(1 + a i))ε (proof similar with terminal node 1 in the Appendix).
The assumption is that the government is in good faith when it announces a fixed rate regime. At the beginning of the game, not even the government knows for sure whether its commitment will survive.Footnote 52 In this case, the expected loss for the government in the beginning of the game is a convex combination of the expected loss when the fix survives and when it collapses, given expectations πe: E(L CBI=0Fix(q)) = (1 − q)E(L Fix) + qE(L CBI=0Flex).
Terminal Node 4: Fixed Exchange Rate and an Independent Central Bank
When the government has selected a fixed rate and an independent central bank, inflation is chosen by the central bank and is zero (π = 0). If wage setters believe that in fact the central bank has been given independence, expected inflation is also zero (π1−pe = 0). However, if wage setters believe the central bank is dependent, the public's inflation expectation is a linear combination between the expected inflation under a fix and expected inflation under a float: πpe = (1 − q)E(πFix) + qE(πFlex) = (qa i /(1 + a i(1 − q)))H.
Given p and q, in the beginning of the game the government anticipates a rate of inflation that is a linear combination between the inflation expected by the public if it believes the government has delegated monetary policy to an independent central banker, and the inflation expected by the public if it believes no delegation took place: πgove = (1 − p)π1−pe + pπpe = (pqa i /(1 + a i(1 − q)))H.
Government expected loss is then given by the following expression:
![\begin{equation}
E(L^{Fix(q)}_{CBI=1(p)}) = a_{i}\sigma^{2} +
H^{2}a_{i}\left[1+\frac{p q a_{i}}{1 + a_{i}(1-q)}\right]^{2}.
\end{equation}](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151007081401668-0001:S0020818310000111jra_eqn007.gif?pub-status=live){kind=small}
The Choice of Imperfectly Credible Institutions
The ultimate goal of the model is to describe the decision process of the government over its two institutional choices and to define the specific circumstances when independent central banks and fixed exchange rates are complements or substitutes. This section compares the expected loss function of the government for the different institutional solutions and describes the main results of the model based on the loss function comparisons.
The finding in proposition (1) below shows formally the complementarity between fixed rates and an independent central bank. To derive the result, I compare the government's expected loss for the institutional mix with the other three outcomes:
• Two institutions are preferred to no commitment at all when the following holds: E(L CBI=1(p)Fix(q)) ≤ E(L CBI=0Flex). This is equivalent to σ2 ≤ H 2α(p,q,a i).Footnote 53
• Two institutions are preferred to just fixing the exchange rate when E(L CBI=1(p)Fix(q)) ≤ E(L CBI=0Fix(q)). This is equivalent to σ2 ≤ H 2β(p,q,a i).
• Without the additional political cost, c, for fixed rate adjustments, the government always prefers two institutions relative to just an imperfectly credible central bank. That is, E(L CBI=1(p)Fix(q)) ≤ E(L CBI=1(p)Flex), for all parameter values p,q,a i.
Proposition (2) below further characterizes the solution space of the game. To fully describe the institutional solution space, I compare the government's expected loss for the other possible outcomes—fixed but adjustable rates, imperfectly credible central bank, and no institutions at all:
• Fixed but adjustable rates are preferred to no commitment at all when E(L CBI=0Fix(q)) ≤ E(L CBI=0Flex). This is equivalent to σ2 ≤ H 2η(q,a i).
• An independent central bank is preferred to no commitment institutions at all when E(L CBI=1(p)Flex) ≤ E(L CBI=0Flex). This is equivalent to σ2 ≤ H 2x(p,a i).
• An imperfectly credible independent central bank is preferred to a fixed but flexible exchange rate when E(L CBI=1(p)Flex) ≤ E(L CBI=0Fix(q)). This is equivalent to σ2 ≤ H 2y(p,q,a i).
Proposition 1. A mix of two commitment institutions is the subgame perfect equilibrium to the game when σ2 ≤ H 2β(p,q,a i) and β > 0. (Proof is in the Appendix.)
Proposition 1 establishes the conditions under which the government treats fixed exchange rates and independent central banks as complementary solutions to its credibility problem. The existence of the equilibrium and the effect of parameters on β are discussed using the graphical representation in Figure 1. Figure 1 fully describes the solution space of the institutional game as a function of H 2 and σ2, both of which represent important structural features of the economy and institutions of particular countries. H 2 reflects the wedge between the actual output and its socially optimal level (H = (k − 1)y*). Countries have a larger or smaller H 2 as they differ in their tax policies, unemployment benefits, and minimum wage provisions. The term H 2 is relevant as time inconsistency in monetary policy arises because the government can use unanticipated inflation to push output toward its socially optimal level. Thus, higher levels of H 2 reflect more temptation on the side of the government to inflate the economy. The variance of the shock to the economy, σ2, is relevant because the cost of monetary policy delegation is reflected in the loss of flexibility to address large negative shocks to the economy. A large variance of the shocks facing a country implies high costs of delegation of monetary policy. The two lines in Figure 1 represent conditions (E(L CBI=1(p)Fix(q)) ≤ E(L CBI=0Fix(q))) and (E(L CBI=0Fix(q)) ≤ E(L CBI=0Flex)) holding with equality. The two lines in the graph separate the solution space of the game. β and η are the slopes of the lines labeled (1) and (2), respectively. As β and η are functions of the parameters a i, p, and q, the two lines can be steeper or flatter, changing the government's choice of institutions for any given pair H 2 and σ2.
FIGURE 1. Imperfect institutions: The choice of an institutional mix (β ≤ η)
The mix of two commitment institutions exists as an equilibrium to the game as long as β > 0. The parameter, β, is larger than zero for 0 < p < .48 and for all values of a i and q. This means that for a low probability that the public does not recognize the independence of the central bank, a mix of institutions is an equilibrium choice to the game. In graphic terms, the mixed solution is represented by all the points below line (1): σ2 = H 2β. This means that for high levels of the credibility problem (high H 2) and low expected shocks to output (low σ2) an institutional mix is the preferred solution to time inconsistency. However, as the variance of the shocks to the economy increases, there are fewer incentives for policymakers to doubly tie their hands with both fixed rates and an independent central bank.
The behavior of the slope, β, as a function of parameters is complex. As can be expected, for a higher probability, p, it becomes less likely that an independent bank would be adopted in addition to having a fixed exchange rate. The effect of government ideology on β depends on the levels of p and q. At low levels of public distrust of central bank independence, more leftist executives will prefer to adopt an institutional mix. However, as p approaches .48, the dynamics change: right-wing governments are more likely to adopt a mixed institutional structure as opposed to just fixing the exchange rate. Moreover, as q goes up, the change in dynamics occurs at lower levels of p and a i.Footnote 54 Comparative statics suggest that when banks lack credibility, right-wing governments are more likely to adopt independent central banks in addition to fixed exchange rates. Also, when the fixed rate does not lower inflation expectations enough (q is large), the right starts being more likely to adopt the independent central bank at ever lower levels of p.Footnote 55
Proposition 2. A fixed exchange rate that the public knows can be devalued is the subgame perfect equilibrium to the game when H 2β(p,q,a i) ≤ σ2 ≤ H 2η(p,q,a i). No delegation is the subgame perfect equilibrium when σ2 ≥ H 2η(p,q,a i). An imperfectly credible independent central bank is never a single institutional solution to the game without the additional political cost, c, for fixed rate adjustments. (Proof is in the Appendix.)
Proposition 2, together with Proposition 1, fully characterize the solution space of the game. With respect to the existence of the equilibria, both no delegation and the adjustable peg are more prevalent solutions, as they exist for all a i,p, q ∈ (0,1), whereas the mixed institutional solution exists only when β > 0, i.e. when the probability, p, is not too large. Comparative statics show that the slope, η, increases in the partisanship parameter, a i, and decreases in the probability, q. That is, left-wing governments are more likely to choose a fixed but adjustable exchange rate regime, yet, fixed rates lose their appeal when the public believes there is a large probability that they will be adjusted. Proposition 2 also shows that an independent central bank is never a single institutional solution to the simple game in which fixed rate devaluations are assumed to be costless for politicians. The explanation for this is that for the government, adopting an independent central bank that is not completely believed by the public generates a cost that increases with p. The cost to the government is in terms of lost output due to inflation expectations that are higher than the zero inflation rate pursued by the independent banker. A costless fixed rate, even if markets know it can be devalued, lowers the cost of an independent bank that sets inflation at zero when the public believes that inflation will be positive.
So far the analysis has left out the political costs of fixed exchange rates because of simpler computations that do not affect establishing the first set of results showing the complementarity between fixed rates and independent central banks. However, the assumption that politicians face penalties when they abandon or devalue fixed exchange rates is well documented. As described below, making the model more realistic by adding political costs maintains the existence results from proposition (1) and only restrains the parameter space for which an institutional mix of institutions is the equilibrium solution (Figure 1 versus Figure 2). Also, the more realistic analysis offers additional empirical implications.
FIGURE 2. Imperfect institutions and costly devaluation: c < c*
Previous work has shown that politicians are punished for mistakes in exchange rate policy. Cooper finds that devaluation of fixed exchange rates entails significant political costs for governments in developing countries. Building on Cooper, Frankel discovers that when one month prior to a devaluation, government members had given assurances that there would be no devaluation, and a devaluation did subsequently occur, the probability that the chief executive would lose his or her job within twelve months was .67.Footnote 56 Where there was no evidence of such assurances, the frequency of job loss was only .39, despite the devaluation. Clarke, Ho, and Stewart also find that in the aftermath of the 1992 devaluation of the British Pound, government approval ratings in Great Britain dropped by 18 to 19 percent.Footnote 57 Furthermore, Blomberg, Frieden, and Stein show that, due to political costs, governments postpone the exit from a pegged exchange rate until after elections.Footnote 58
In the model, accounting for the costly devaluation of fixed rates, the loss function from equation (1) becomes a mix of social welfare and political survival motivations: L ti(πt,y t) = (πt)2 + a i(y t − ky*)2 + ϕc, where ϕ = 1 if the peg does not survive and ϕ = 0 if the peg maintains. That is, politicians incur the cost, c, if the fixed exchange rate does not maintain.
Proposition 3. With costly devaluation of fixed rates, an imperfectly credible central bank is a subgame perfect equilibrium to the game when the cost, c, is larger than c*, σ2 ≤ H 2y(p,q,a i), σ2 ≤ H 2x(p,a i), and x > 0. (Proof is in the Appendix.)
Figures 2 and 3 show graphically the solution space when fixed exchange rate adjustment is costly. When the cost, c, is low, c < c* (Figure 2), policymakers still prefer a mix of two institutions to an independent central bank alone. The executive chooses to supplement an institution that pays an up-front and certain cost (the independent central bank) with an institution that entails the delayed and probabilistic cost, c (the fixed rate). However, with adjustment costs, it becomes less likely that the policymaker chooses fixed exchange rates either alone or in combination with an independent central bank.
FIGURE 3. Imperfect institutions and costly devaluation: c > c*
Figure 3 shows the solution space of the game when the cost of a fixed rate devaluation is large: c > c*. When c is large, a peg that can be devalued stops being an institutional arrangement that makes an imperfectly credible independent bank more attractive. That is, a mixed institutional solution is not an equilibrium anymore. An independent central bank alone is the equilibrium solution when x > 0, which holds for small values of the probability, p (p < .5). The comparative statics of x with respect to the ideology of the policymaker, a i, are similar to the comparative statics of the parameter, β: in an environment where delegation of monetary policy to an independent central banker has large chances of being believed by the public (p ≤ .36), left-wing policymakers will be more likely to adopt an independent central bank. However, circumstances marked by deep distrust in the inflation policy of the government (.37 ≤ p ≤ .5) induce a reversed dynamic. That is, right-wing, conservative politicians will be more prone than the left to delegate monetary policy to an independent central banker.
Discussion and Policy Implications
The model has several implications that are in line with previous work. For example, in countries that are expected to face large negative shocks to the domestic economy, politicians do not limit their discretion to use monetary policy in recessionary periods. Another implication similar to the existing literature is that, in general, the government with the worst inflation-fighting credentials will be more likely to adopt institutions that restrain inflation. That is, left-wing governments that are known to cater to labor are more prone to tie their hands in monetary policy.
More importantly, however, this article generates new hypotheses characterizing the conditions that make monetary institutions complements or substitutes. In general terms, the model shows that if institutions do not suffer from similar weaknesses and are able to only partly fulfill their role, then one observes some institutional proliferation. In particular, one can expect to see an independent central bank coupled with fixed exchange rates when the political costs of fixed exchange rate adjustments are low and delegation to an independent central bank is relatively transparent. Previous research suggests that the cost, c, of a fixed rate adjustment is likely to vary along several dimensions, including (1) the degree of accountability of political regimes, (2) the clarity of responsibility for policy actions of elected politicians, and (3) the rules for electoral competition.
In the case of exchange rate policy, surprise changes in the exchange rate regime generate a range of negative outcomes from loss of purchasing power to larger debt if debt is denominated in foreign currency, bankruptcies, and unemployment.Footnote 59 In accountable political systems, the presence of free media and disputed elections allows domestic political audiences to vote according to the state of the economy and punish governments reneging on commitments, especially when breaking promises has negative economic consequences.Footnote 60 Autocratic regimes, on the other hand, survive with the support of a small number of domestic actors.Footnote 61 Such regimes need not be concerned about the aggregate costs of exchange rate crises because they survive by using rents targeted at a restricted selectorate. In such autocratic regimes, then, the costs of fixed exchange rate realignments are low. However, autocracies are also characterized by limited transparency of central bank independence.Footnote 62 In the model, low political costs of fixed rate realignments and a relatively transparent independent central bank are both necessary conditions for a mix of institutions to exist. One empirical implication is that autocracies would prefer a fixed exchange rate due to the low political costs of adjustment. This result is consistent with findings in Broz and suggests that his causal mechanism (relative transparency of fixed rates) is augmented by the costliness of fixed rate adjustments.Footnote 63 Another empirical implication is that autocracies will prefer a mix of monetary institutions only if their general lack of transparency is mitigated by specific circumstances. Such mitigating conditions include the presence of a strong financial sector with a preference for low inflation,Footnote 64 a central bank that publishes macroeconomic forecasts,Footnote 65 or the presence of external monitoring by foreign investors or international organizations, such as the International Monetary Fund. Also, in the presence of mitigating conditions, the model suggests that autocracies would prefer a mix of institutions to an independent central bank alone.
Beyond the dichotomy between democracies and autocracies, political costs vary across democracies with the clarity of responsibility for economic policies and the type of electoral competition. Powell and Whitten suggest that when policy responsibility cannot be clearly attributed to the parties in the governing coalition, the executive may actually face low costs from breaking a commitment.Footnote 66 Also, political costs are low when governments can call elections before the mandatory end of their term, as well-timed elections which coincide with an expanding economy or an economy without a crisis improve the re-election prospects of incumbents.Footnote 67 The important empirical implication is that countries with multiparty coalition governments, a proportional representation electoral system, or endogenous election timing will be more likely to choose fixed exchange rates either alone or in combination with an independent central bank.Footnote 68
The comparative statics of parameter, β, generate further testable implications. In particular, the model predicts that right-wing and left-wing governments are bound to adopt an independent central bank coupled with a fixed exchange rate at different times. The policymakers more concerned with inflation, the right, will be more likely to choose an independent central bank in addition to a fixed rate in bad times for macroeconomic stability, that is, when there is a low probability that the public believes announcements made by politicians about monetary institutions. The reverse argument applies to the left: in good times, it is more likely that the left would doubly tie its hands. For empirical testing, either qualitative or quantitative, examples of bad times range from hyperinflationary episodes to swift transitions from authoritarian rule to democracy. In periods of regime transition, both q and p are arguably high due to a general and acute lack of credibility of all domestic institutions and politicians. In hyperinflation cases, on the other hand, it is specifically monetary institutions that lack credibility, and innovations such as a newly independent central bank or a fixed exchange rate are likely to be regarded with skepticism by the public.
Furthermore, the probabilities p and q can be gauged more directly. For example, Keefer and Stasavage identify specific economic circumstances that capture uncertainty about the policymaker's intended rate of inflation, which are reflected in low central bank credibility.Footnote 69 Accordingly, the probability, p, that the announced independence of the central bank will not be believed by the public is higher when there is (1) a high volatility in a country's money multiplier (the ratio of base money, M0, which is under the control of the central bank, to broad money, M2, which is not entirely under the control of the central bank); (2) a high volatility of the terms of trade; or (3) low quality in a country's economic data, in particular frequent mistakes in the consumer price statistics. Moreover, independent central banks that publish their macroeconomic forecastsFootnote 70 or come with specific targets such as inflation targets or monetary targets are more likely to believed by the public (lower p) because they come with specific institutional features that allow the public to verify target compliance over the medium term.Footnote 71
The probability, q, that a fixed exchange rate will be adjusted can be predicted from research that specifically studies the likelihood of devaluations. For example, Klein and Marion study the determinants of devaluations of fixed exchange rates in Latin American countries.Footnote 72 The predicted probabilities from their model (which can also be computed out of sample) directly reflect the parameter, q. Moreover, the probability, q, is likely to be influenced by the chances of speculative attacks on the currency, which are instances when markets lose confidence in the fixed rate and pressure the government to adjust or completely give up the fixed exchange rate regime.Footnote 73 Because speculative attacks increase the costs of maintaining the fixed rate (higher interest rates and spending of foreign reserves), a greater vulnerability of a country to a speculative attacks increases the probability, q.Footnote 74 Also, Reinhart and Rogoff suggest that countries with a large black market premium versus the official exchange rate face a larger probability, q, of an adjustment to the official rate.Footnote 75 Furthermore, the probability, q, is likely to be affected by the capital controls that a country has in place. In recent decades there has been a move toward the liberalization of capital transactions, which partly accounts for the moderation of countries' interest in the fixing of their currencies.Footnote 76 Nevertheless, there are still global discrepanciesFootnote 77 and countries with lower capital mobility will face a lower probability, q, of an exchange rate regime adjustment.
Conclusion
Institutions, along with policymaker and voter preferences, shape economic policy outcomes. Therefore, understanding outcomes involves understanding the factors that influence the choice of particular institutional structures. This article started out with a question: “If the policymaker's wrists were already bound by exchange target duct tape, what would be the effects of an additional pair of handcuffs from inflation targets and yet another loop of rope from central bank independence?”Footnote 78 This article offers an explanation as to why governments choose a mixture of institutions to reign in inflation. I show that when exchange rates are fixed but adjustable and central bank independence is not transparent, policymakers can choose both of these institutions. That is, institutional solutions will overlap if policymakers are not fully able to control inflation due to their particular imperfections. The model has specific, testable hypotheses for the existence and prevalence of the mixed institutional solution and, more generally, for the conditions that make fixed exchange rates and independent central banks complements or substitutes. This article also suggests ways to operationalize the parameters of the model for empirical testing, thus contributing to an understanding of the diversity of monetary institutions in the post–Bretton Woods period.
In addition, this article has implications for the partisan design of institutions, conditioning the effect of partisanship on the prevailing economic conditions. I find that in a situation where declarations about central bank independence are not entirely believed by the public (lack of bank transparency), it is the right-wing policymaker that is more likely to choose a central bank that is conservative but not credible. The right wing is also more likely to choose an independent central bank, in addition to a fixed exchange rate that markets do not trust, as such a fixed rate does not reduce inflation sufficiently. Hyperinflation episodes and periods of deep distrust of public institutions can be examined to get support for the hypotheses developed in the model. For example, the most recent Bulgarian hyperinflation was brought to a halt by the adoption of a fixed exchange rate under a currency board arrangement in July 1997. The policy was carried out by the right-wing government of Ivan Kostov, which came to power in elections held in April 1997. In Bulgaria, the currency board and a more independent central bank were adopted despite initial opposition from the right-wing Sofiyanski government that was arguing that the currency board arrangement imposed too much constraint on the government. Another similar example is Argentina in the beginning of the 1990s. The Argentine economy went through a series of severe recessions and hyperinflation episodes in the 1980s. In March 1991, the neo-liberal Economy Minister Domingo Cavallo pushed through the Convertibility Plan, establishing a currency board with an explicitly legislated, fixed exchange rate and a requirement that the central bank back two-thirds of monetary base with international reserves. Further, in 1992, the same center-right Argentine government granted substantial independence to the central bank. The stated purpose of the Convertibility Plan and the move to a more independent central bank was to improve policy credibility and to generate macroeconomic stability. In the case of Argentina, as expected from the model, the policy changes occurred under a liberal-leaning government in a period of clear lack of credibility of monetary policy institutions.
In the past decades, the world economy has moved toward the liberalization of global capital transactions. This trend has also been accompanied by more independent central banks and the increased use of inflation targeting. Together, the two developments point to higher costs of fixing the exchange rate due to the risk of adjustment, and more transparent central banks due to the medium term inflation accountability afforded by targets. In this context, this article suggests that one is likely to see further moderation of countries' interest in formally fixing their exchange rates, consistent with the trend recently pointed out by the International Monetary Fund. This prediction comes with caveats, however. Most central banks in the developing world have a limited ability to implement the inflation-targeting framework and, in the meanwhile, a fixed exchange rate remains the more visible, transparent policy instrument. Specifically, central bankers in developing countries still need to improve their understanding of the transmission mechanism of domestic monetary policy and to develop reliable inflation forecasting models able to predict accurately future inflation, and hence, to support inflation target announcements. In addition, the very recent 2007–2008 experience with high and volatile oil and food prices shows the more general challenges faced by the inflation-targeting framework. In the face of imported inflation, most inflation-targeting countries have failed to achieve their targets. Given such developments, future work will have to determine more precisely the relationship between inflation targeting and central bank independence, and to what extent central bank independence is important in anchoring inflation expectations when inflation targets are missed. Finally, while the formal fixing of their exchanges is on a downward trend, developing countries are still likely to continue to use de facto fixed rates both due to the fear of floating, pointed out by Calvo and Reinhart, and because exchange rate stabilization has proven helpful in achieving inflation targets.Footnote 79
A more general implication of the article is that if institutions do not suffer from similar weaknesses and are able to only partly fulfill their role, then one will observe some degree of institutional proliferation. Beyond the choice of monetary commitment institutions, the results and modeling framework can contribute to the understanding of rational institutional design. As an illustration, the results could be relevant to the literature on international organizations where there has been renewed interest in the reasons behind the proliferation of international institutions.Footnote 80 The findings in this article suggest that, as long as existing general-purpose institutions covering multiple issues are fostering country interests only imperfectly and countries are not limited to devise additional arrangements that focus on specific areas, proliferation is a very likely outcome. Consistent with this framework, Drezner shows that powerful states engage in forum-shopping in the sphere of international regimes and, if need be, do not hesitate to create new fora.Footnote 81 After the Asian financial crisis of 1997, Drezner stresses the ability of the global economic powers to arbitrate between governance structures to advance their common preferences for new codes and standards. Thus, big countries used the International Monetary Fund and the World Bank. However, since such institutional structures worked imperfectly to advance their interests, the great powers also created new coordination venues, such as the Financial Stability Forum, and empowered pre-existing ones, such as the Bank for International Settlements.
Appendix
Terminal Node 1
With no commitment, the government observes the output shock and simply minimizes its loss function (1) subject to the output equation (2). The game lasts for only one period, so time subscripts are dropped. The optimal inflation rate is: πi = (a i /(1 + a i))(πe − ε + H), where H = (k − 1)y*. Workers make their decision before the output shock is observed but have rational expectations, so π = πe. Therefore, expected inflation equals 
(A1). The time consistent inflation rate is obtained by making πe in the previous equation equal to 
(A2). The expected loss to the government if it decides to choose flexible rates and a dependent central bank is computed by plugging equations (2), (A1), and (A2) in equation (1): E(L CBI=0Flex) = a i(1 + a i)H 2 + (a i /(1 + a i))σ2.
Expected loss comparisons
1. E(L CBI=1(p)Fix(q)) ≤ E(L CBI=0Flex). This is equivalent to: σ2 ≤ H 2α(p,q,a i), where α = [(1 + a i)/a i][((1 + a i)(1 + a i − a iq)2 − (1 + a i − a iq + a iqp)2)/(1 + a i − a iq)2].
2. E(L CBI=1(p)Fix(q)) ≤ E(L CBI=0Fix(q)). This is equivalent to: σ2 ≤ H 2β(p,q,a i), where β = [(1 + a i)/a iq][((1 + a i)(1 + a i − a iq) − (1 + a i − a iq + a iqp)2)/(1 + a i − a iq)2].
3. E(L CBI=0Fix(q)) ≤ E(L CBI=0Flex). This is equivalent to: σ2 ≤ H 2η, where η = (1 + a i)2/ (1 + a i − qa i).
4. E(L CBI=1(p)Flex) ≤ E(L CBI=0Flex). This is equivalent to: σ2 ≤ H 2x, where x = [(1 + a i)/a i][1 + a i − (1 + pa i)2].
5. E(L CBI=1(p)Flex) ≤ E(L CBI=0Fix(q)). This is equivalent to: σ2 ≤ H 2y, where y = [(1 + a i)/a iq][((1 + a i)/(1 + a i − a iq)) − (1 + a ip)2].
Proposition 1 Proof.
For an institutional mix to be a solution to the game, the expected loss from adopting a mix of institutions needs to be smaller than the expected loss from a fixed rate alone (σ2 ≤ H 2β(p,q,a i) and β > 0), and it should be the case that a mix generates a lower expected loss than no institutions at all (σ2 ≤ H 2α(p,q,a i) and α > 0). In the absence of costly devaluation of fixed rates, a mix of institutions is always preferred to an independent bank alone. Moreover, α ≥ β for all a i, p and q ∈ (0,1), so it is only needed that σ2 ≤ H 2β(p,q,a i) and β > 0.
Proposition 2 Proof.
The slope η is larger than β for all p, q, and a i. Therefore, as shown graphically in Figure 1, the adjustable peg is the equilibrium solution of the game for H 2β ≤ σ2 ≤ H 2η, or the points above line (1) and below line (2). No delegation is the equilibrium for all the points above line (2) σ2 = H 2η. Also, an imperfectly credible independent central bank would be an equilibrium solution to the government's time inconsistency problem if x > 0, y > 0 and β < 0. However, x < 0 for all parameter values (a i, p, and q) for which β < 0, and if β > 0 an institutional mix is always preferred to just having an independent central bank.
Proposition 3 Proof.
The cost c* makes the government just indifferent between choosing an independent bank alone or together with a fixed rate: E(L CBI=1(p)Flex) = E(L CBI=1(p)Fix(q)). c* is derived from the indifference condition and equals c* = (a i /q)H 2[(1 + pa i)2 − [1 + (a ipq/(1 + a i − a iq))]2]. For an independent central bank alone to be the solution to the game: c > c*. In addition, E(L CBI=1(p)Flex) ≤ E(L CBI=0Flex) and E(L CBI=1(p)Flex) ≤ E(L CBI=0Fix(q)) need to hold. That is, σ2 ≤ H 2x(p,a i) and σ2 ≤ H 2y(p,q,a i), or all the points in Figure 3 that are below both line (4) and line (5). The binding condition for existence is x > 0 and the solution space is illustrated in Figure 3.
