Krzysztof Makarski Dollarization as a signaling device

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Bank i Kredyt 45(1), 2014, 17–36

Dollarization as a signaling device

Krzysztof Makarski*

Submitted: 24 November 2012. Accepted: 8 August 2013.

Abstract

The objective of this paper is to point out that dollarization may be used as a signaling device. To this end, we introduce into a standard monetary policy model two types of governments: good and bad. Information is asymmetric, the government type is uncertain and the policy of the bad government is suboptimal. This uncertainty does not allow the good government to achieve the first best outcome even though it conducts optimal policy. Since, the bad government would never dollarize, the good government by dollarizing reduces uncertainty about the type of government and achieves the first best allocation. Here, unlike in models emphasizing the time inconsistency motive for dollarization, it does not change the actual policy. Thus, dollarization plays the role of a signaling device rather than a commitment device.

Keywords: dollarization, monetary policy, signaling JEL: E42, F40, E32, E44, E52

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1. Introduction

There are many countries, for example in Latin America, that have a long history of high inflation rates. In a number of these countries, governments conducted policies, that were not necessarily optimal for the societies they governed. As a result, in these countries, the public does not trust its government. Furthermore, many countries do not have long stable tradition of independent central bank. In some countries, even guaranteeing independence of the central bank in the constitution, does not ensure public belief in the low inflation policy. As the result of this heritage, a government that wants to implement optimal policy has low credibility. In such cases, establishing reputation is costly both in terms of welfare and GDP hence, dollarization may lead to savings on the costs of gaining credibility. We want to study this problem from the point of view of such a government, and see how dollarization can solve the problem of the lack of trust.

The standard argument for dollarization is that it brings credibility since it is a commitment device. We propose a new mechanism for building reputation through dollarization. We argue that dollarization may bring credibility since it provides the way to signal the intentions of the government. Therefore, we build a model with two types of the government: good and bad.1_{The good government} wants to conduct optimal policy, and the bad government wants to use inflationary taxation in order to increase government expenditure above the socially optimal level.2_{The knowledge of the type of} the government is private, the public knows only the probability distribution over the government types. The uncertainty about the government type distorts the equilibrium allocation away from optimal, therefore the good government cannot achieve optimal outcome, even if it conducts optimal policy. In the model there is a separating equilibrium: the good government dollarizes and the bad government does not dollarize. Hence, dollarization by eliminating the uncertainty about the government types, has real effects. Furthermore, in our model dollarization does not change the actual policy, as it would be the case if dollarization were a commitment device. Thus, in our model dollarization plays the role of a signaling device rather than a commitment device. It allows the good government to signal its type.

The model is a standard cash-credit goods model. We also assume that the government’s budget is balanced in each period to avoid any complications with time inconsistency (coming from the fact that government may want to default on its debt). The only source of uncertainty in the model is the type of government.

The key force that drives the result is the fact that expected inflation is costly even if at the end the actual inflation is low. We assume that people decide how much labor to supply before they know monetary policy therefore, they base their decision on expectations. Dollarization brings down inflation expectations, so it improves welfare. In this view dollarization brings instantaneous reputation at no cost. The results are not driven by time inconsistency, since the only reason why the good government cannot achieve an optimal allocation is the fact that people are unsure whether they deal with the good or the bad government. Dollarization allows the good government to separate itself from the bad government.

There is an extensive literature on the pros and cons of dollarization (see Berg 2000). The two most important arguments in favor of dollarization are that it allows to import credibility which results in

1_{The idea of having two types of government is taken from Phelan (2006).}

2_{Click (1998) documents that seigniorage accounted for a large share of government income in many Latin American}

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Dollarization as a signaling device

19

lower inflation, and can increase trade by eliminating the exchange rate risk and the transaction costs associated with the currency exchange, for example see Alesina and Barro (2002). Similarly, Cooper and Kempf (2001) argue that dollarization may solve the time inconsistency problem, and Mendoza (2001) analyzes how dollarization can be beneficial by eliminating the distortions created by the exchange rate uncertainty and by weakening the informational and institutional frictions in the credit market. The main argument against dollarization is that it strips countries off the monetary independence. For example, Cooley and Quadrini (2001) analyze the effect of dollarization in the case of Mexico. They assume that the Mexican government conducts optimal policy and that the US policy is not optimal for Mexico. As the result in their model dollarization leads to non optimal policy, and does not improve the Mexican welfare. There are many more arguments for dollarization than presented above. To name just a few, Calvo (2001) argues that dollarization solves the “fear of floating” problem, and Arellano and Heathcote (2010) show that dollarization may broaden the access to financial markets. They show, that since dollarization increases the value of maintaining access to international financial markets, it makes it costlier for governments to default, thereby increasing the amount of debt that can be supported in equilibrium.

The crucial contribution of this paper to the literature is to point out that dollarization may improve credibility of government by signaling its intentions. We show that in the presence of uncertainty regarding the goals of government dollarization provides means to signal those goals. Hence, our work shows the mechanism of credibility building through dollarization that to the best of our knowledge has been absent from the debate. We want to stress that our argument complements the existing literature instead of rivaling it.

The structure of this paper is as follows. In Section 2 we show how governments behave in our framework. In Section 3 we present the model. In Section 4 we show the results. Section 5 concludes the paper.

2. Preliminaries

Our paper extends and modifies the Lucas and Stokey (1983) economy. First, we introduce the uncertainty about the type of government, second we allow each government to dollarize or not. Furthermore, following Svensson (1985) and Albanesi, Chari and Christiano (2003), we require households to use money accumulated in the previous period to purchase cash good in the current period. We use a version of a cash-credit good model with households, producers and government. Households buy consumption, supply labor and trade assets. Government collects taxes, issues money and finances the stream of government expenditure.

In this section we take a closer look at the behavior of government in a world with no uncertainty about the type of government and no possibility of dollarization. We examine the behavior of both types of government when agents know exactly the type of government they face. In the next section we introduce a fully specified model with the uncertainty about the type of government and the choice of whether to dollarize or not.

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policy should satisfy the Friedman rule. Usually, we say that the monetary policy satisfies the Friedman rule if the nominal interest is zero. In our model there is no nominal interest rate, but the analog of the zero nominal interest rate is _{μ = β, where β denotes the discount factor of households. We define} this monetary policy as satisfying the Friedman rule.

2.1. Households

There is measure one of households, households take government’s policy, _{π, as given. Each household} starts each period with nominal assets _a. In the beginning of each period in the assets market, the households trade money, _m, and one-period bonds, _b. Each bond costs _q and pays one unit of nominal value in the next period. The asset market constraint has the following form:

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is a large enough finite number. Next the households split into two parties. One party goes to the goods market and buys cash goods, _c₁, with money, credit goods, _c₂_{, with credit, and next period assets,}_a'. The other party goes to the labor market and supplies labor, _{l. Since cash goods can only be bought with money each household} faces the cash-in-advance constraint

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1 2 } , { 0 1 ) ( Pr , 1 ) ( Pr , ] , 1 [ ) ( Pr ), ( Pr = ) ( Pr G if G if G if G G 0 = ) ( Pr G ) ( ), ( 2 1 G c G c } , {GL GH G ( )G q G) ( Pr θ θ ξ ξ β β π π ; a π π π π π π a π π π π β _β π π π π π θ ) (1; Vθ π θ uθ uθ = ) , , , (c1 c2 G l b b uθ θ μ +2 β μ + + 2 β β μ + + + + + + + + + + + + + + – 2 β β β β ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ρ ρ ξ 1+ + + + ξ (1 ξ ξ (1 ξ 1+ξ ξ ξ 3+ + + 3+ ξ ξ 1+ ξ 1+ + + + + + + ξ ξ ξ ξ ξ ξ 3+_ξ ξ ξ θ 3+ξ ξ ξ ξ ξ ) (1 log logG+ –l – – – – – – – – – – – – – – ξ ) (1; Vθ π β β β β β β β ∞ β μ μ μ μ μ μ μ π θ μ μ β ∈ μ μ μ θ γ γ γ γ γ ζ γ ρ , ,d θ θ θ θ θ θ θ θ θ ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε → ε θ θ θ θ θ θ θ θ θ θ θ θ ρ ρ ρ ρ ρ ∈ ∈ ∈ ∈ ∈ ∈ ≤ ≤ ≥ (2) where P denotes the price level.

The budget constraint in the goods market has the following form:

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1 2 } , { 0 1 ) ( Pr , 1 ) ( Pr , ] , 1 [ ) ( Pr ), ( Pr = ) ( Pr G if G if G if G G 0 = ) ( Pr G ) ( ), ( 2 1 G c G c } , {GL GH G ( )G q G) ( Pr θ θ ξ ξ β β π π ; a π π π π π π a π π π π β_β π π π π π θ ) (1; Vθ π θ uθ uθ = ) , , , (c1 c2 G l b b uθ θ μ +2 β μ + + 2 β β μ + + + + + + + + + + + + + + – 2 β β β β ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ρ ρ ξ 1+ + + + ξ (1 ξ ξ (1 ξ 1+ξ ξ ξ 3+ + + 3+ ξ ξ 1+ξ 1+ + + + + + + ξ ξ ξ ξ ξ ξ 3+ξ ξ ξ θ 3+ξ ξ ξ ξ ξ ) (1 log logG+ –l – – – – – – – – – – – – – – ξ ) (1; Vθ π β β β β β β β ∞ β μ μ μ μ μ μ μ π θ μ μ β ∈ μ μ μ θ γ γ γ γ γ ζ γ ρ , ,d θ θ θ θ θ θ θ θ θ ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε → ε θ θ θ θ θ θ θ θ θ θ θ θ ρ ρ ρ ρ ρ ∈ ∈ ∈ ∈ ∈ ∈ ≤ ≤ ≥ (3) where T denotes lump sum taxes.3

Denote aggregate values with capital letters, and individual values with small letters. We follow Albanesi, Chari and Christiano (2003) in normalizing all nominal variables by dividing each nominal variable (money, nominal assets, bonds, price and wage) in each period by the aggregate stock of nominal assets, so A= 1. Due to this normalization we have μ in the households budget constraint (3). The household have the following instantaneous utility function:

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1 2 } , { 0 1 ) ( Pr , 1 ) ( Pr , ] , 1 [ ) ( Pr ), ( Pr = ) ( Pr G if G if G if G G 0 = ) ( Pr G ) ( ), ( 2 1 G c G c } , {GL GH G ( )G q G) ( Pr θ θ ξ ξ β β π π ; a π π π π π π a π π π π β β π π π π π θ ) (1; Vθ _π θ uθ uθ = ) , , , (c1 c2 G l b b uθ θ μ +2 β μ + + 2 β β μ + + + + + + + + + + + + + + – 2 β β β β ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ρ ρ ξ 1+ + + + ξ (1 ξ ξ (1 ξ 1+ξ ξ ξ 3+ + + 3+ ξ ξ 1+ξ 1+ + + + + + + ξ ξ ξ ξ ξ ξ 3+ξ ξ ξ θ 3+ξ ξ ξ ξ ξ ) (1 log logG+ –l – – – – – – – – – – – – – – ξ ) (1; Vθ π β β β β β β β ∞ β μ μ μ μ μ μ μ π θ μ μ β ∈ μ μ μ θ γ γ γ γ γ ζ γ ρ , ,d θ θ θ θ θ θ θ θ θ ε ε ε ε ε ε ε ε ε ε ε ε ε ε → ε θ θ θ θ θ θ θ θ θ θ θ θ ρ ρ ρ ρ ρ ∈ ∈ ∈ ∈ ∈ ∈ ≤ ≤ ≥ (4)

3_{The assumption that taxes are lump sum instead of distortionary is not crucial here, since as Chari and Kehoe (1999)}

show − given relatively weak assumptions − optimal monetary policy should still follow the Friedman rule even if income taxes are distortionary.