# Determining a modified currency board's two-period exchange rate strategy.

AbstractIs it preferable for a modified currency board (MCB) to disguise its true characteristics and preferences and renege later? This paper analyzes a model in which a MCB determines its first-period exchange rate strategy to maximize a two-period welfare function. The inflation rate anchored by a classical currency board (CCB) is always a benchmark to the MCB in its first period decision. If the benchmark inflation rate is either sufficiently low or sufficiently high, the MCB chooses the optimal exchange rate in both periods without playing a credibility game over time. However, if the benchmark is at a moderate level, a strategy of overtly deceiving the public by pretending to be a CCB is shown to be superior to a strategy of concealing through policy randomization. (JEL E42, F32, F41)

Introduction

The orthodox or classical currency board (CCB) represents a stringent policy rule characterized by a 100% foreign reserve backing of the monetary base and the full convertibility between the domestic currency and the anchor (reserve) currency at a fixed official exchange rate. The CCB establishes and maintains its credibility and, thus, eliminates the public's inflationary expectations by precluding itself from discounting domestic assets (see Hanke et al. [1993] and Balino and Enoch [1997] for overviews of the currency-board theories and practices). Nevertheless, the currency board systems in today's world are more or less differently structured from its pure type. While they share some fundamental common features, such as about 100% convertibility undertaking between the domestic currency and the reserve currency (or assets payable in the reserve currency), there are indeed many variations in respect of actual arrangements; in particular, the domestic circumstances have been important in shaping each of the systems now in practice.

Although the practice of CCB, as a transparent and binding rule, relinquishes the monetary authority's ability to determine the money supply and the exchange rate and, therefore, avoids, or at least mitigates, the possibility of dynamic inconsistence, it is difficult after all to consider all the contingencies into the preset policy rules; hence, the policy credibility needed to control inflation could be in conflict with the policy flexibility in dealing with various economic shocks. Especially, the loss of monetary policy autonomy whether to finance a budget deficit, rescue banks, or boost aggregate demand is exactly the price a currency board economy pays for putting inflation under control [Obstfeld and Taylor, 1998; Ghosh et al. 1998; Rodrik, 2000]. The inherent tradeoff between credibility and flexibility has yielded the practice of modified currency board (MCB). Under the MCB, the main advantage for a limited extent of exchange rate flexibility and monetary liquidity is to avoid the structural rigidity (price and wage rigidity, for example) that a pure currency board faces in combating large current account deficits, capital flight, and domestic unemployment, though their drawbacks are adverse impacts on the credibility of the currency board. Indeed, it is often a country-specific issue how far a currency board should go toward relaxing its discretionary power over exchange rates and domestic credit.

In spite of the existing practices of MCB, it is unfortunate that very few studies in the existing literature have attempted to explore formally variants of the CCB. Wu [2005] models a MCB that has two confined discretions: a moderate degree of flexibility in the domestic credit and a moderate degree of flexibility in exchange-rate variations, and shows that the two policy instruments optimally maintain a substitution relationship. It is also shown and tested with the data of Argentina and Hong Kong that the survival of such a MCB depends both on the nature of economic shocks and on the MCB's preference for credibility vs. growth. The question that is not answered in Wu [2005], however, is a dynamic one, concerning whether it is preferable for the MCB to invest in its low-inflation credibility over time at the expense of real benefits from output and employment and when and how the MCB considers to deviate from the path of a CCB.

Attempting to tackle these issues, the present paper is mainly motivated by the following two considerations. First, theoretically, time inconsistency can arise from discretionary policy [Kydland and Prescott, 1977; Barro and Gordon, 1983; Backus and Driffill, 1985; Barro, 1986] or a rule that allows constrained discretion (see Bernanke and Mishkin [1997] on inflation targeting) or even a rule that does not formally allow discretion even if it in fact exists [Enoch and Gulde, 1997]. Although the currency board as a rule-bound regime is not supposed to be flexible by its nature, it is not, after all, completely immune from the problem of time inconsistency since moral hazard remains with policymakers at times, even if any flexibility in this context is substantially confined and repressed. As a currency board arrangement is not just a legal matter but also an operational matter, stringent restrictiveness by ensuring strong discipline on the system could jeopardize its credibility while seemingly strengthening it.

Second, practically, time inconsistency has existed in the real-world currency boards, many of which have departed from the 'orthodox' model one way or another to adapt to the changing economic environment. Take three examples: Argentina, Hong Kong, and Bulgaria. Argentina's currency board can serve as a lender of last resort by issuing money to a level beyond what can be supported by its foreign reserves (Zarazaga [1995], p. 16). The convertibility law actually allowed a less than 100% backing of the monetary base by reserve assets. In particular, the adverse impact of the Mexican peso devaluation in the mid-1990s led the Argentina monetary authority to take several measures, including reduction of the reserve requirement and flexibility in the discount-window policies [Caprio et al. 1999; Silva, 1997]. For Hong Kong, in addition to some measures influencing money and credit such as the discount window lending and modest sterilization operation [Corden, 2002], the monetary authority in Hong Kong only temporarily triggers a convertibility undertaking against the domestic currency sold in the foreign exchange market, and "this is done at an undisclosed exchange rate determined by the Currency Board from time to time but not at the fixed exchange rate of HK$7.80 to US$1. This results in the market exchange rate deviating significantly from the fixed rate, possibly creating doubts on the robustness of the system" (Hong Kong Monetary Authority HKMA [1998], p. 38). Finally, the case of Bulgaria also supports flexibility at the margin in its currency board arrangement. As stated in Gulde [1999], p. 14, "In view of the macroeconomic and structural challenges, it was well recognized that the currency board plan could not gain credibility from the legal change alone. Instead, a set of measures and provisions to address the most likely 'stress-factors' needed to be at hand. Such 'stabilizers' were included both in law itself, as well as into the stabilization program, of which the currency board was the integral part." Under the Bulgarian currency board arrangement, there is more foreign exchange than is needed to cover the monetary liabilities ('excess coverage'), which can be used to make collateralized loans to commercial banks in the case of an acute liquidity crisis.

This paper uses a two-period model in which the MCB needs to determine its best first period strategy in order to balance its welfares goals of inflation control and output expansion over a two-period horizon. It is shown that the inflation rate anchored by a CCB is always a benchmark for the MCB's decision in the first period. If the benchmark inflation rate is either sufficiently low or sufficiently high, the strategy to build up its low-inflation credibility for reneging later becomes neither necessary nor effective. Therefore, the MCB simply chooses the exchange rate to maximize its welfare both at the present and in the future. If the benchmark inflation rate is at a moderate level, however, a MCB tends to deceive the public at the present by sticking with the rule, as if it were a CCB, before reneging in the future to grab real benefits. Such an overtly deceiving strategy is shown to be superior to the strategy whereby the MCB conceals its preference through policy randomization.

The remainder of this paper is organized as follows. The next section introduces the basic elements of the model and their setup, followed by a section that analyzes the MCB's three possible exchange rate strategies in the first period. Then the paper compares the welfare values of various exchange rate strategies and determines the MCB's first-period policy preference with respect to the benchmark inflation rate and other parameters. The final section briefly concludes.

The Setup of Model

Consider a two-period currency board model in which the monetary authority has an option in each period either to stick with the policy rule of a CCB or to deviate from it. Since a deviation from the classical rule of game may damage its reputation and credibility and, consequently, face a less favorable menu of output-inflation choices, the currency board has incentive not to modify the rule until doing so is necessary and it is really ready for the change. The key feature of the model is that the public knows neither the currency board's preferences between the classical regime and the modified specie nor when the currency board may deviate from the classical regime. Under the circumstances, the public can learn about the currency board's characteristics only by observing its behavior in the first period and forming their expectations of inflation accordingly.

Unlike the CCB, the MCB has such a strong desire for greater output that it can sometimes attempt to make it by deviating from the rule for the CCB. To a MCB, more output is preferred to less output with constant marginal welfare so that output enters the MCB's periodical social welfare function linearly. Since increases in real economic activity are related to unanticipated monetary expansions, output expansions are related with surprise inflation, [[pi].sub.t] - [[pi].sub.t.sup.e] (for the related formulation, see DeLong [2002], for example). Inflation per se is assumed to generate increasing marginal welfare-loss and, therefore, enter the welfare function quadratically. Hence, the MCB's periodical objective involves a social welfare function of inflation (or the negative of net cost of inflation), which is given by

[[omega].sub.t] = -[a/2]([[pi].sub.t])[.sup.2] + b([[pi].sub.t] - [[pi].sub.t.sup.e]), t = 1, 2 (1)

where the cost parameter a (a > 0) measures the sensitivity of net welfare cost to inflation, the benefit parameter b (b > 0) reflects the marginal benefit of an unexpected inflation in increasing the net welfare, and t is period index (for the two-period quadratic welfare function, see Barro and Gordon [1983] for the early work, and Batiz and Sy [2000] for its use in the context of currency board modeling). The first term in (1) is cost of inflation, which rises at an increasing rate with the rate of inflation itself, whereas the second term reflects the output benefit that linearly rises with the unexpected inflation.

The rate of inflation is determined in a two-sector framework of tradable goods and nontradable goods. Suppose that the domestic and foreign aggregate output price indexes, P and P*, are geometric weighted averages of their respective traded and nontraded prices, that is, [P.sub.T] and [P.sub.N] for the domestic economy, and [P*.sub.T] and [P*.sub.N] for the foreign economy. The weighting for traded prices, [sigma], is an exogenously determined structural parameter and simply assumed to be the same for the two economies. Let E represent the domestic exchange rate (units of domestic currency per unit of the reserve currency). Then, after taking logarithm on P and P*, we have the following expressions for the domestic and foreign price levels:

P = [sigma][p.sub.T] + (1 - [sigma])[p.sub.N] (2)

e + P* = [sigma](e + [p*.sub.T]) + (1 - [sigma])(e + [p*.sub.N]) (3)

where the small-case symbols denote the logarithms of the same variables originally expressed as large-case symbols, and in particular [bar.p] [equivalent to] log P and [bar.p*] [equivalent to] log P*.

The production processes for both the tradables and nontradables in any economy are assumed to use labor only, and the production technology in each sector is linear in labor inputs. Denoting marginal productivities of labor in the production of two goods by [a.sub.T] and [a.sub.N], respectively ([a*.sub.T] and [a*.sub.N] are their counterparts for the foreign economy). It is also assumed that the purchasing power parity holds for tradable goods so that e + [P*.sub.T] = [p.sub.T]. In this setting, the wage level in a unified economy-wide labor market is linked to the prices of tradable goods and marginal productivity in the production of tradables. Under these assumptions, it follows that in both economies, the nontradable price is a multiple of the tradable price with the multiple being the relative productivity of labor in the two sectors, and in logarithm the domestic and foreign nontradable prices can be expressed as

[p.sub.N] = [p.sub.T] + log [a.sub.T] - log [a.sub.N] (4)

e + [p*.sub.N] = [p.sub.T] + log [a*.sub.T] - log [a*.sub.N] (5)

The MCB uses two policy instruments to achieve its welfare goals; one instrument is to inject domestic credit to the monetary base so that the degree of monetary-base backing by official foreign reserves ([gamma]) is greater than one, (1) and the other is to fine-tune the exchange rate to allow a non-zero degree of the exchange rate deviation ([theta]) from the par level vis-a-vis the reserve currency. When the domestic aggregate demand falls, a depreciation can help the economy to move resources from the nontradable sector to the tradable sector by raising [P.sub.T]. In this paper, it is also assumed that advance in productivity is a function of investment, which in turn depends directly on the degree of availability of loanable funds or credit expansion, [gamma]. Although foreign productivity growth is an exogenous variable to the domestic economy, the domestic economy's (i.e., the currency-board economy's) productivity growth is expressed as an explicit function of [gamma]. Determined by aggregate market forces, the equilibrium output also increases with unexpected depreciation (a variant of unexpected inflation) and domestic credit expansion. Although the money supply ([M.sup.S]) is mainly determined by the foreign reserves held with the currency board at the officially fixed exchange rate, in a setting of MCB, the rate of depreciation and credit expansion can both influence the supply of money, which is eventually balanced with money demand.

Now, substituting Equations (4) and (5) into Equations (2) and (3), then subtracting Equation (2) from Equation (3), and differentiating the resulting equation with respect to time produces

[theta] + [pi]* - [pi] = (1 - [sigma])[[dot.a.sub.N]([gamma]) - [dot.a.sub.T]([gamma]) + ([dot.a*.sub.T] - [dot.a*.sub.N])] (6)

where [pi]* and [pi] are the foreign and domestic inflation rates respectively, and the symbol [dot.a] represents the growth rate of productivity. Rewriting Equation (6) produces the domestic inflation rate that the currency board authority faces in the two-sector economy

[pi]([theta]) = [theta] + [pi]* - (1 - [sigma]){[dot.a.sub.N][[gamma]] - [dot.a.sub.T][[gamma]] + ([dot.a*.sub.T] - [dot.a*.sub.N])}, (7)

where [theta] is nonzero if the currency board is a MCB type but equals zero if it is a CCB type. Based on Equation (7), the credit expansion and the rate of exchange rate depreciation, among other things, determine the inflation rate.

The MCB's Three Possible First-Period Strategies

What are possible strategies and the resulting welfare outcomes for a MCB that cares for both credibility and output expansions? How does the currency board's menu of output-inflation options interact with the public's inflation expectation in this two-period game? This section addresses these issues by analyzing a currency board's sequential decision problem in a two-period model.

A backward induction approach is used for analysis in this section. In the second period, a MCB will surely, by its nature, set credit and exchange rate variation in order to maximize its social welfare objective. (2) Formally, the MCB's problem in the second period is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

For a given [[pi].sub.2.sup.e], the first-order condition boils down to the following optimal depreciation rate:

[^.[theta]] = [b/a] + (1 - [sigma])[[dot.a.sub.N]([gamma]) - [dot.a.sub.T]([gamma]) + [dot.a*.sub.T] - [dot.a*.sub.N]] - [pi]* (9)

According to Equation (9), [gamma] is an endogenous variable because once the currency board selects the optimal depreciation rate, credit expansion is no longer a free decision variable. In other words, Equation (9) determines a MCB's policy-reaction function involving the two-decision variables; in particular, if [theta] = 0, [gamma] is a constant and can, thus, be standardized at one, which is the case of CCB.

Since the people's expectation of future inflation completely hinges upon their information of the MCB's conveyance of its behavior in the first period, the MCB's policy stance in the first period holds the key for the credibility game and welfare outcome in the two periods as a whole. As illustrated earlier, the MCB in the second period will take an optimal exchange rate in any case to maximize its welfare objective, the welfare outcome for the two-period model, therefore, totally hinges upon the way the MCB communicates with the public in the first period. We analyze three possible first-period scenarios: the MCB that is single-minded in pursuit of output expansion, even at the expense of its credibility (a reckless MCB); the MCB that complies with what it is supposed to be as a CCB (an overtly deceiving MCB); and the MCB that makes it uncertain whether it will deviate from the rules for CCB or not (a concealing MCB).

A Reckless Modified Currency Board

The monetary authority for a reckless MCB does not want to disguise its true characteristics so that it will choose the optimal depreciation rate even in the first period, as specified in Equation (9). Thus, [[pi].sub.1] will be equal to [[pi].sub.2], and both are equal to b/a. In this case, the public learns that it is facing a reckless MCB, and, therefore, expects the inflation in the second period to be b/a. Using Equation (1), we can then express the value of the reckless MCB's objective function as

[[OMEGA].sub.R] = [[omega].sub.1] + [beta][[omega].sub.2] = (1 - [beta])[[b.sup.2]/[2a]] - b[[pi].sub.1.sup.e] (10)

An Overtly Deceiving Modified Currency Board

The MCB now hopes to invest in its credibility in the first period by convincing the public that it behaves like a CCB. But in the second period, after the public have acted on the basis of their expectations, the MCB is tempted to renege on the CCB rules so as to grab greater gains from real economic performance. The game player in this typical dynamic-inconsistence problem, unlike a reckless MCB, needs to disguise its second-period preference by pretending to be a CCB in the first period. Hence, by setting [theta] = 0 (and thus [gamma] = 1) in Equation (7), it chooses the following benchmark inflation rate characteristic of a CCB:

[[pi].sub.1] = [pi](0) = [pi]* - (1 - [sigma]){[dot.a.sub.N][1] - [dot.a.sub.T][1] + [dot.a*.sub.T] - [dot.a*.sub.N]} (11)

The strategy can mislead the public into a belief that it is facing a CCB, and accordingly, the public bases its expectation of future inflation on [[pi].sub.1] above, i.e., [[pi].sub.2.sup.e] = [[pi].sub.1]. Hence, after substitution and rearrangement, the overtly deceiving MCB's strategy implies the following value of social welfare objective function:

[[OMEGA].sub.OD] = [[omega].sub.1] + [beta][[omega].sub.2] = {-[a/2][[pi](0)][.sup.2] + b[[pi](0) - [[pi].sub.1.sup.e]]} + [beta]{-[a/2](b/a)[.sup.2] + b[[b/a] - [pi](0)]} (12)

A Concealing Modified Currency Board

A concealing MCB conveys only uncertainty about its characteristics by randomizing between the policy stance of a CCB and that of a reckless MCB. Let p represent the public's prior subjective probability that the currency board is a modified specie and q represent the probability that the MCB chooses [theta] = 0 in the first period. When the public observes [theta] = 0 in the first period, it can use the Bayesian formula to estimate the posterior probability of MCB as {qp/[qp + (1 - p)]}. (3) Hence, the public's expectation of the second-period inflation is a weighted average of a MCB's inflation choice and a CCB's inflation choice, with the weight being the posterior probability of MCB and that of CCB respectively:

[[pi].sub.2.sup.e] = ([qp]/[qp + (1 - p)])[b/a] + ([1 - p]/[qp + (1 - p)])[pi](0) (13)

It then follows that the concealing MCB's social welfare objective is

[[OMEGA].sub.C] = [[omega].sub.1] + [beta][[omega].sub.2] = {-[a/2][[pi](0)][.sup.2] + b[[pi](0) - [[pi].sub.1.sup.e]]} + [beta][[b.sup.2]/a]{[1/2] - [[qp]/[qp + (1 - p)]] - [[b(1 - p)]/[qp + (1 - p)]][pi](0)} (14)

Determining the MCB's Preferences

Would it be preferable for a MCB to disguise its true preference in some way until the second period commences? If so, how would it like to do it? This section analyzes the MCB's preference with respect to its three possible first-period scenarios.

Subtracting Equation (10) from Equation (12) produces

[[OMEGA].sub.OD] - [[OMEGA].sub.R] = -[a/2][[pi].sup.2](0) + b(1 - [beta])[pi](0) + ([beta] - [1/2])[[b.sup.2]/a] (15)

where [pi](0), as specified in Equation (7), is the inflation rate when the type of monetary authority is classical rather than modified. Assuming [beta] < 1/2, (4) [[OMEGA].sub.OD] - [[OMEGA].sub.R] is then positive if and only if (b/a)(1 - 2[beta]) < [pi](0) < (b/a). Similarly, subtracting Equation (14) from Equation (12) yields

[[OMEGA].sub.OD] - [[OMEGA].sub.C] = b[beta][[b/a][[qp]/[qp + (1 - p)]] - [[qp]/[qp + (1 - p)]][pi](0)] (16)

It is clear that [[OMEGA].sub.OD] - [[OMEGA].sub.C] is positive if and only if [pi](0) < [b/a]. Finally, comparing Equation (10) with Equation (14) results in the following expression:

[[OMEGA].sub.C] - [[OMEGA].sub.R] = -[a/2][[pi].sup.2](0) + b[[qp + (1 - p)(1 - [beta])]/[qp + (1 - p)]][pi](0) + [[b.sup.2]/a][[beta](1 - [[qp]/[qp + (1 - p)]]) - [1/2]], (17)

which is positive if and only if [b/a][1 - 2[beta][[(1 - p)]/[qp + (1 - p)]]] < [pi](0) < [b/a].

The currency board's preference can be ranked continuously over its first-period strategies, i.e., [[OMEGA].sub.OD], [[OMEGA].sub.R], and [[OMEGA].sub.C], in a domain of the benchmark inflation rate, [pi](0). The domain is divided into several intervals in which the values of [[OMEGA].sub.OD], [[OMEGA].sub.R], and [[OMEGA].sub.C] can be meaningfully compared (see Appendix 1). Figure 1 summarizes the result graphically. As depicted in Figure 1, if [pi](0) is less than [b/a](1 - 2[beta]) or greater than [b/a], the welfare value of a reckless MCB strategy exceeds the welfare values of the other two strategies. Only when [pi](0) lies in the interval bounded by the above two end values does the welfare value of an overtly deceiving MCB strategy dominate. The outer frontier (the thick line) depicts the upper envelope of the currency board's three welfare-value functions, indicating the maximum utility level and the associated strategy at any given value of [pi](0).

At a low benchmark inflation rate, the public naturally does not have high inflationary expectations, and, thus, the MCB can get desired output expansion easily without much investment in its credibility or reputation. In this case, the MCB clearly has no incentives to adopt an overtly deceiving strategy or a concealing strategy, as it would otherwise have to forgo real benefits of output expansion in the first period; instead, it will waste no time to set its exchange-rate strategy straightly to maximize the social welfare value. On the other hand, at a high benchmark inflation rate, there is not much room of maneuver for the MCB to invest in its credibility at the expense of real economic activities since the bar for the rate of inflation has already been set at a rather high level. Under the circumstances, to a MCB that cares for output expansion as well as inflation, the best strategy is again to behave as an unconditional optimizer rather than a constrained optimizer (constrained by its credibility consideration) in selecting its exchange rate strategy. Consequently, the only circumstance under which the MCB needs to weigh seriously its credibility in checking inflation against its desired output expansion occurs in a range of moderate benchmark inflation. Indeed, in this case, it gets not only more attractive but also more effective for the MCB to disguise its true type either completely or partially in the first period.

As depicted in Figure 1, the upper envelope (the thick line) is formed by only the portions of [[OMEGA].sub.R] and [[OMEGA].sub.OD]; that is, at any value of the benchmark inflation rate, the model in this paper does not support a concealing strategy of randomizing between a CCB policy stance and a reckless MCB policy stance. Since the forward-looking public is able to make rational expectations of the future inflation and then guide their present behavior accordingly, randomizing between the two opposite policy stances boils down to an opportunistic approach on a basis of generated uncertainty, which will confuse the public and, thus, lead to an inferior welfare outcome. No matter whether the MCB plays by an open discretion (a reckless MCB) or by manipulating the classical rule per se (an overtly deceiving MCB), the MCB is at least not generating uncertainty through its policy.

[FIGURE 1 OMITTED]

Finally, the first-period strategy which the currency board will choose also depends upon the parameters that set boundaries for different ranges of the benchmark inflation rate. When the parameters change, the currency board's preference could accordingly change at the margin. For example, the discount factor [beta] determines the length of benchmark-inflation intervals in which the MCB prefers one strategy to another. With a larger [beta], the public is more farsighted and, thus, places more weight on the future period. Therefore, the MCB tends to downplay the reckless strategy and invest more on its credibility of inflation checking instead. As a result, playing a card of an overtly deceiving strategy becomes more preferable than following a straight reckless MCB strategy, which is shown in Figure 1 as a lengthier benchmark-inflation interval in which [[OMEGA].sub.OD] dominates [[OMEGA].sub.R] at the lower end of the benchmark inflation. In addition, although a larger posterior probability ([1 - p]/[qp + (1 - p)]) that the currency board is a CCB can cause the public to revise its inflation expectation downwardly and, thus, increase the attractiveness of a concealing strategy relative to a reckless strategy, the concealing strategy remains inferior to the overtly deceiving strategy anyway, as depicted in Figure 1.

Recall that the benchmark inflation rate, as specified in (11), is a function of the foreign inflation rate ([pi]*), weighting of traded prices ([sigma]), the rates of productivity growth rates in the domestic tradable sector and the nontradeable sector ([dot.a.sub.T] and [dot.a.sub.N]), as well as their counterparts in the foreign sectors ([dot.a*.sub.T] and [dot.a*.sub.N]). Although changes in these parameters cannot change the boundaries for different ranges of the benchmark inflation rate, they can certainly cause marginal changes in the currency board's preference with respect to its three strategies. Even if these variables are totally exogenous, their impact on the benchmark inflation rate is noticeable. In contrast, the inflation cost and benefit parameters (a and b) can only uniformly shift the established MCB preference across all the strategies by proportionately changing all the boundaries for different ranges of the benchmark inflation rate, but they cannot distinctively have marginal impact on its preference for any individual strategy in the first period.

Conclusions

This paper analyzes a two-period model in which the modified currency board (MCB) needs to determine its first-period exchange rate strategy to maximize its welfare function in a two-period horizon. To the MCB, the inflation rate anchored by a classical currency board (CCB) is always a benchmark in any case; it is mainly determined by productivity growth and foreign inflation rate. As the benchmark inflation rate is either sufficiently low or sufficiently high, the MCB has no incentive to play a credibility game, i.e., the game to disguise its true preference first and then renege later, in order to take advantage from output benefit over time; instead, the strategy of a reckless MCB is always a dominant strategy. Nevertheless, at a moderate benchmark inflation rate, the MCB favors an overtly deceiving strategy and, thus, plays a card of CCB in the first period to build up its credibility and lower the public's inflation expectations. In contrast, the concealing MCB strategy of randomizing between policy stances of a CCB and a reckless MCB is shown to be inferior to the other two strategies.

Additionally, the currency board's preference in respect of the three possible strategies is marginally sensitive to changes in its discount factor, the public's posterior probability for the type of the currency board, productivity growth, foreign inflation rate, and the weight of the tradeable sector. In contrast, the inflation cost and benefit parameters cannot distinctively have marginal impact on the MCB preference for any individual first-period strategy, except for uniformly changing all the boundaries for different ranges of the benchmark inflation rate.

APPENDIX

The following table summarizes the MCB's preference in respect of three possible welfare outcome derived from its three distinctive strategies, respectively (Table 1).</p> <pre> TABLE 1 Comparing MCB's Value Functions Range for [pi](0) Results of Comparison [pi](0) [less than or equal to] Since [[OMEGA].sub.OD] [b/a](1 - 2[beta]) [greater than or equal to]

[[OMEGA].sub.C],

[[OMEGA].sub.OD]

[less than or equal to]

[[OMEGA].sub.R], and

[[OMEGA].sub.C]

[less than or equal to]

[[OMEGA].sub.R], therefore,

it follows that

[[OMEGA].sub.R] [greater than or equal to] [[OMEGA].sub.OD]

[greater than or equal to]

[[OMEGA].sub.C]. [b/a](1 - 2[beta]) Since [[OMEGA].sub.OD] [less than or equal to] [pi](0) [greater than or equal to] [less than or equal to] [b/a] [[OMEGA].sub.C], [1 - 2[beta][[1 - p]/[qp + (1 - p)]]] [[OMEGA].sub.OD]

[greater than or equal to]

[[OMEGA].sub.R], and

[[OMEGA].sub.C]

[less than or equal to]

[[OMEGA].sub.R], therefore,

it follows that

[[OMEGA].sub.OD] [greater than or equal to] [[OMEGA].sub.R]

[greater than or equal to]

[[OMEGA].sub.C]. [b/a][1 - Since [[OMEGA].sub.OD] 2[beta][[1 - p]/[qp + (1 - p)]]] [greater than or equal to] [less than or equal to] [pi](0) [[OMEGA].sub.C], [less than or equal to] [b/a] [[OMEGA].sub.OD]

[greater than or equal to]

[[OMEGA].sub.R], and

[[OMEGA].sub.C]

[greater than or equal to]

[[OMEGA].sub.R], therefore,

it follows that

[[OMEGA].sub.OD] [greater than or equal to] [[OMEGA].sub.C]

[greater than or equal to]

[[OMEGA].sub.R]. [pi](0) [greater than or equal to] Since [[OMEGA].sub.OD] [b/a]

[less than or equal to]

[[OMEGA].sub.C],

[[OMEGA].sub.OD]

[less than or equal to]

[[OMEGA].sub.R], and

[[OMEGA].sub.C]

[less than or equal to]

[[OMEGA].sub.R], therefore,

it follows that

[[OMEGA].sub.R] [greater than or equal to] [[OMEGA].sub.C]

[greater than or equal to]

[[OMEGA].sub.OD]. </pre> <p>Footnotes

(1) Because a CCB is not supposed to inject domestic credit without foreign reserve backing, the degree of monetary-base backing ([gamma]) is identically equal to one in the case of CCB. With a MCB, however, credit expansion based on factors other than increases in foreign reserves, though confined, raises the value of [gamma].

(2) Here, the concept of a terminal period and the associated decision problem make sense, not only because any currency board is not immortal, but also because the issue of tradeoff between output performance and credibility is relevant at any specific point of time to a MCB.

(3) Given [theta] = 0, Bayes' formula gives the probability as

Prob(MCB|[theta] = 0) = Prob(MCB [intersection] [theta] = 0)/Prob([theta] = 0) = Prob([theta] = 0|MCB)Prob(MCB)/[Prob([theta] = 0|MCB)Prob(MCB) + Prob([theta] = 0|CCB)Prob(CCB)] = qp/[qp + (1 - p)]

(4) With [beta] > 1/2, one of the roots in Equation (14) would be negative so that it has to be discarded; this way, there would be a loss of some meaningful values for [pi](0).

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YING WU*

*Salisbury University--U.S.A. The author would like to thank an anonymous referee for the helpful comments made on an earlier version of the paper. He would also like to thank the participants on his session at the 58th International Atlantic Economic Conference, Chicago, October 8, 2004, and the participants of a research seminar at Salisbury University in November 2004.

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Author: | Wu, Ying |
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Publication: | International Advances in Economic Research |

Geographic Code: | 1USA |

Date: | Nov 1, 2005 |

Words: | 6065 |

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