رژیم نرخ ارز، بانکداری و بخش غیر قابل تجارت

This paper presents a small-open-economy, two-good version of the Diamond and Dybvig model with cash constraints to analyze the implications on banking of different exchange rate regimes and monetary policies. I show that fixed exchange rates with a Central Bank providing liquidity in local currency imply Pareto efficiency, with conditions for a run equilibrium stronger than in the literature. In a flexible exchange rate regime, multiple equilibria may not be eliminated. In particular, for very a expansive monetary policy there exists an equilibrium where a fraction of patient consumers purchases dollars in the interim period, which constitutes a partial currency run. A dollarized banking system without international short-run credit may also implement the efficient allocation under certain conditions.

As part of the recent debate in Emerging Market countries, the relationship between the performance of the banking sector and the choice of exchange rate regime was one of the most important dimensions of that discussion. Those in favor of flexible exchange rates point out that the combination of a nominal peg and the absence of a lender of last resort may trigger a bank run due to banks illiquidity. In turn, those who defend fixed exchange rates emphasize how loose monetary policy may prevent the development of a financial system due to lack of credibility. This debate is far from being closed at this point. Some of the answers to the discussion sketched above may depend on the real effects of monetary factors. Those effects, in turn, depend on the transaction arrangements that are present in the economy. An important part of the theoretical macroeconomics literature (starting from Lucas, 1980) emphasizes this point by focusing on the transactions role of money assuming the use of cash to purchase commodities and services. This issue is even more crucial in cases where each non-tradeable and tradeable goods represent an important share of the country's GDP, as observed in most open economies.1 In such a case the way in which transactions are organized and the role that money plays in such transactions may have a key impact on the (equilibrium) allocations. This paper intends to capture these facts by building a model in the spirit of the traditional Diamond and Dybvig (1983) framework combining two important new features. In this economy agents are ex-ante identical but in the second period they are all subject to preference shocks, some will consume early and some in a later period. One novelty of this model is the introduction of a non-tradeable good in addition to a tradeable good. The second novelty is the assumption of cash-in-advance constraints that force agents to purchase each commodity with local currency (pesos). Thus, this model proposes a treatment of money as an explicit means of transaction, a well-known alternative to the money-in-the-utility function assumption.2 As stated above, the inclusion of two goods forces to carefully specify the transaction arrangement. In his traditional paper, Lucas (1982) assumed a two-country model where each agent needed country i's currency to purchase country i's (tradeable) good. That assumption may be called separation of currencies for purchasing commodities. This paper proposes a different market segmentation. I assume that agents must use pesos to purchase both commodities, but that there are two perfectly separate market sessions, one for each good. Thus, when the market for one good is open for trade, the other is closed and vice versa. I call this a (time) separation of market sessions. One reason for this assumption is that this is an only-three-period model with some agents consuming earlier than others. Given that these agents will have no (ex-post) incentives to bring cash between consecutive periods, this transactions arrangement allows for the use of local currency for transactions without any need of an intertemporal accumulation of money. On the other hand this assumption also allows implementation of the first-best allocation even with cash constraints, a feature that cannot be obtained in the traditional infinite-horizon, cash-in-advance models. This paper studies how different nominal exchange rate regimes and monetary policy induces Pareto-optimality and financial fragility of equilibrium allocations. The first case considered is the fixed exchange rate regime, where a Central Bank may temporarily issue non-convertible pesos to allow depositors buying non-tradeable goods. In this model the Central Bank needs to provide liquidity in pesos only within a period, not between periods. This liquidity in local currency is used in the exchange of non-tradeable goods. There is no other role for the Central Bank in this regime. Under fixed exchange rates two results are obtained. First, under this regime the banking system implements the optimal allocation as an equilibrium. Second, a run equilibrium exists under conditions that are stronger than in the literature. In particular, international illiquidity may not be a sufficient condition to generate such a run equilibrium due to self fulfilling expectations. Actually, the banking system may face a different set of illiquidity conditions depending now on the size of the Central Bank policy, a feature that is new in the literature. This paper is the first attempt of combining the two assumptions featured above. In the last 10 years, and especially after the recent financial crisis in Asia and other Emerging Market countries, the literature on banking theory starting from Diamond–Dybvig (1983) was extended to capture open-economy features. Some important contributions on these lines are Goldfajn and Valdés (1997), Allen and Gale (2000b) and Chang and Velasco, 2000c, Chang and Velasco, 2000d and Chang and Velasco, 2001. A common feature of these models is the assumption of a unique tradeable consumption good. This assumption does not fit in all actual open economies, some of which present an important non-tradeable component in their GDP. Moreover, most of these open-economy extensions of the Diamond–Dybvig model assume real, non-monetary economies.3 There are two exceptions concerning these two assumptions. First, Chang and Velasco (2000a) assume a non-tradeable good production technology that is actually adopted in this paper as well. However, the authors do not include fiat currency in their model, while assuming risk-neutral preferences instead of the original risk-aversion assumption in Diamond and Dybvig. On the other hand, Chang and Velasco (2000b) assume a unique tradeable good and money-in-the-utility function to derive a demand for real balances in local currency. In that framework they show that under a so-called flexible exchange rate regime the banking system implements the first-best allocation as the unique equilibrium, ruling out the possibility of currency runs. However, the authors implicitly recognize that this and the other results in that paper may not be robust to changes in the modelling of the precise relationships among depositors, private banks and the Central Bank. This paper, in turn, proves that, under the same flexible exchange rate regime, this model does not generate necessarily a unique equilibrium. If the monetary policy in period 1 is sufficiently expansive, there is an equilibrium where patient consumers are indifferent between purchasing dollars in either period 1 or 2, and so a fraction of those patient depositors decide to buy dollars in period 1 instead of period 2. This may be understood as a partial currency run.4 It is remarkable that this multiple-equilibrium result holds even without assuming any sequential service constraint at either commercial banks or the Central Bank. This assumption was stressed by many authors (starting from Wallace, 1988) as the key to generate illiquidity in the model and to make self-fulfilling bank-runs possible in equilibrium. I also consider a dollarized banking system within this framework. In this case, even without international intra-period credit, implementation of the optimal allocation is possible under certain conditions. However, this allocation is subject to runs given international illiquidity at the optimal allocation, contrary to the case where the Central Bank provides liquidity in pesos. The rest of the paper is organized as follows. Section 2 presents the environment common to all the sections in the paper and shows the characterization of the optimal allocation. Section 3 discusses the implementation through a banking system with peso-denominated deposits within a fixed exchange rate regime with a Central Bank providing short-run liquidity, as well as the existence of a run equilibrium. Section 4 presents a flexible nominal exchange rate policy and the possibility of runs. Section 5 develops a dollarized banking system, discusses its optimality and multiple equilibria. Section 6 shows concluding remarks and extensions.

This paper has developed a small-open-economy version of the Diamond and Dybvig (1983) model with two commodities and cash-in-advance constraints, to analyze the interaction between banks, exchange rate regimes and monetary policy. This model generates the following results (all of which are clearly different from the literature). In a banking system with deposits in local currency, fixed exchange rates with a Central Bank issuing non-convertible pesos for transactions in the non-tradeable good market, conditions for self-fulfilling currency runs are more demanding than in the literature. Those conditions essentially depend on preferences, features of the first-best allocation, the liquidation policy of the non-tradeable good technology and the monetary policy in the interim period. The second important result is that, given a sufficiently expansive monetary policy, a flexible exchange rate regime does not eliminate multiple equilibria (although still eliminating bank failures) provided that the productivity of the non-tradeable sector is large enough. This regime generates a new type of inefficient equilibrium, one where banks do not fail but where impatient consumers bear the cost of the very expansive monetary policy. Finally, a dollarized banking system with no international short run credit implements the optimal allocation under certain conditions. This framework can be extended to consider other questions that are relevant. Specially important seems to consider solvency shocks to banks's investment and crisis due to fundamentals, as analyzed by Allen and Gale, 1998 and Allen and Gale, 2000b. They show that flexible exchange rates may imply better risk-sharing than nominal pegs. It seems relevant to extend such a one-good model to a framework considering one non-tradeable commodity and fiat currency as a mean-of-exchange, like in this paper, to evaluate the robustness of that result to these modifications. Also, this framework has also a natural two-country extension. This is interesting to study the interaction between international banks, monetary and exchange rate policies and the possibility of contagion, as studied in the real version of the Diamond and Dybvig framework in Allen and Gale (2000a). Perhaps one of the most fundamental limitations of this model is the assumption of ad hoc cash-in-advance constraints. The model takes this assumption as given to address issues on the relationship between banks and monetary and exchange rate policies. Although not completely satisfactory, the cash-in-advance approach adds at least a more explicit role for money, which was absent in the banking literature available up-to-date. However, in this economy money cannot be considered as essential, at least in the sense of Wallace (2000). The ad hoc assumption is specially problematic if we want to study, for example, the interaction between currency substitution and monetary and exchange rate policies and banking stability. This calls for endogeneizing the use of money for transactions, as studied by the growing search literature starting from Kiyotaki and Wright (1989). However, this implies a modeling a Diamond–Dybvig banking system with infinitely-lived households, which to my knowledge was not fully addressed in a satisfactory manner. This last extension seems much more complicated to construct.