Silviase/jgov_v1.4_full_ann huggingface dataset:
It results in an asymmetric demand from Mexicans to hold dollars as a store of value, a demand that is not reciprocated by Americans holding pesos as a hedge against the devaluation of the dollar! $ ^{4} $ This can lead to a systematic change in exchange rate parities. Girton and Roper (1981), for example, emphasized that currency substitution can magnify small swings in expected money growth differentials into large changes in exchange rates. Kareken and Wallace (1981) also showed that the free-market international economy generates the multiplicity of equilibrium exchange rates which highlight the potential instabilities caused by currency substitution. Our specific focus is the substitution of the hard currency for the soft and the ensuing systematic devaluation of the latter. Capital flight constitutes a form of this currency substitution. A complete flight from a currency, in the form of dollarization, represents the extreme case where any or all of the three functions of a currency - unit of account, means of exchange, and, in particular, store of value – are discharged in a foreign currency (Calvo and Végh, 1996).

We extend the “fundamentals model” (or the “first-generation model”) of currency crisis by incorporating the endogenous currency substitution effects explicitly. Recently, several papers have tried to extend this “first-generation model” by introducing an endogenous risk premium or an endogenous regime-switching of economic policy (Flood and Marion, 2000; Cavallari and Corsetti, 2000). By focusing on an optimal dynamic response of domestic agents our model is distinguished within this genre of recent literature by its generality. We show that the more pronounced the currency substitution is in a country the earlier and the stronger is the tendency for the local currency to devalue. This tendency holds whether the origins of currency substitution lie in a risk premium or simply in a "taste" for ratcheting up liquid asset holdings to a harder currency. The intuition behind our theory is straightforward. With strong currency substitution the demand for the domestic currency, relative to the foreign (hard) currency, declines. Given the stream of domestic money-supply growth, a decline in domestic money demand will
increase the equilibrium domestic price level. This increased domestic price level will lead to devaluation through arbitrage among tradable goods - or simply according to purchasing power parity. A novel feature of this paper is to show empirically that, controlling for the fundamentals, the reputation-asymmetry via-a-vis the reserve currencies triggers systematic devaluations of the soft currencies of emerging economies and developing countries. $ ^{5} $

The paper is organized as follows. Section 2 sets the main thrust of this paper in the context of the literature. Section 3 extends the fundamentals model of the currency crisis by incorporating the currency substitution effect. The empirical model and results are presented in Section 4. Section 5 presents the policy implications of the currency substitution hypothesis of devaluation, emphasizing specifically the departures from the conventional treatment of financial crises. It turns out, for example, that the simple extension of incorporating in the extant models currency substitution becomes germane for modeling "speculative attacks" on a currency and for designing the "new architecture" of the international financial system. The concluding Section 6 follows.

### 2. The Predecessors

This paper builds on two strands of the literature. Krugman (1979) first developed a model of the balance of payment crisis due to speculative attacks on the fixed-exchange-rate regime. Flood and Garber (1984) presented the linear version of Krugman's model. This crop of the “first generation” models fingers the deteriorating “fundamentals” of an economy as the trigger to the currency crisis (Eichengreen, Rose, and Wyplosz, 1994).

It seems that this literature implicitly assumes that the important role of money is as a medium of exchange, since the model introduces the arbitrage equation of tradable goods prices or the purchasing power parity equation. The idea of money as the medium of exchange was expanded in two alternative directions that formalized the micro-foundation of the money demand function: the cash-in-advance
model (Clower, 1967; Lucas and Stokey, 1987) and the transaction model (Baumol, 1952; Tobin, 1956). In either model, money is held for transaction purposes. However, money also serves a store of value, and enters as such the utility function. Sidrauski (1967) first formulated the Ramsey optimal growth model with both consumption and real money balances in the utility function subject to an intertemporal budget constraint with money.

From the technical perspective, in order to examine whether putting money in the utility function is appropriate, we can ask whether it is possible to rewrite the maximization problem of an agent with transaction costs of money holdings. Feenstra (1986) showed that maximization subject to a Baumol-Tobin transaction technology can be approximately rewritten as maximization with money in the utility function. Moreover, the simple cash-in-advance model of money can be written as a maximization problem by ignoring the cash-in-advance constraint but introducing money in the utility function (Blanchard and Fischer, 1989: 192). Also Obstfeld and Rogoff (1996: 530-532) showed that the money-in-utility-function formula can be viewed as a derived utility function that includes real balances because agents economize on time spent in transacting. Therefore, the-money-in-utility-function formula can be regarded as a general formulation of the micro-foundations of the money demand function.

The novelty in our model lies in fusing and expanding both strands of this literature into a micro-fundamentals model in which optimizing agents engage in currency substitution thus setting-off endogenously serial devaluations that can culminate in a currency crisis. In the process, we expand Krugman's model by introducing money not only as a medium of exchange but also in its role as an asset. Moreover, the utility function in our model contains both domestic and foreign currency, with possibilities of substituting one for the other, especially for asset-holding purposes. Flood and Marion (2000) and Cavallari and Corsetti (2000) extended the first-generation model of currency crises by incorporating an endogenous risk premium and by introducing an endogenous policy, respectively. Our contribution lies in constructing and testing a general model that extends the first-generation model by introducing endogenous currency substitution by optimizing agents.

### 3. The Fundamentals Model of Balance-of-Payments Crisis under Currency Substitution

If a country with a soft currency fixed its exchange rate initially, an expansionary fiscal and/or
monetary policy will render the fixed exchange rate regime untenable, sooner or later. In this section, we will construct a simple model of currency crisis that is triggered by currency substitution. The model portrays a situation where speculation-led crises can occur in a completely rational environment under the basic principles of efficient asset-price arbitrage.

In what follows we first derive the optimal condition of currency substitution in a dynamic model of optimizing agents. Then we extend the Obstfeld and Rogoff (1996) log-linear version of Krugman's (1979) model by introducing currency substitution effects while controlling for the fundamentals.

### 3.1 The Micro-fundamentals of Currency Substitution

Our focus is to model the role of money as an asset and a store of value. However in the real world, money as a store of value is dominated by several assets. To account for this we construct a dynamic optimization model of currency substitution, applying the basic setup of Obstfeld and Rogoff (1996: 551-553). By definition, a domestic representative agent's total money for asset-holding purposes, M, is composed of domestic currency, $ M_{1} $ and foreign currency, $ M_{F} $ :

$$ M_{t}=M_{1t}+\varepsilon M_{F t} $$

where $ \varepsilon $ is the nominal exchange rate. Then the optimal allocation of money-holding (of two different currencies in our case) can be solved as a dynamic optimization problem of a household with money-in-the-utility-function in a model with log-linear utility components of real balance.

Assuming a small open economy, a representative household maximizes the following lifetime utility:

$$ U_{_{t}}=\sum_{s=t}^{\infty}\mathsf{\rho}^{s-t}\left\{\theta u(C_{_{s}})+(1-\theta)\left[\gamma\log\left(\frac{M_{_{1s}}}{P_{_{s}}}\right)+(1-\gamma)\log\left(\frac{\varepsilon M_{_{Fs}}}{P_{_{s}}}\right)\right]\right\}, $$

where $ u(C) $ represents instantaneous utility from consumption and $ \rho $ is a discount factor. The parameters $ \theta $ and $ \gamma $ are utility parameters and $ P_{t} $ represents the price level. The household can accumulate foreign bonds and two kinds of monetary assets. The optimal consumption and money
demand are determined by maximizing (1) subject to the following intertemporal budget constraint:

$$ (B_{_{t+1}}-B_{_{t}})+\frac{(M_{_{1t}}-M_{_{1t}})}{P_{_{t}}}+\frac{\varepsilon_{_{t}}(M_{_{Ft}}-M_{_{Ft-1}})}{P_{_{t}}}=rB_{_{t}}+Y_{_{t}}-C_{_{t}}-T_{_{t}}, $$

where B is the stock of foreign bonds or assets. Y and T represent the exogenously given income and lump-sum tax, respectively. Note that the left-hand side of the budget constraint represents three different devices to accumulate assets, i.e., bonds, real domestic money and real foreign money, all converted in the local currency, and by definition equal to the real surplus during the period t on the right-hand side. In order to derive a tractable analytical solution, we assume that there is no consumption-titling effect, i.e., $ (1 + r)\rho = 1 $ . Then we obtain the following first-order conditions with regard to C, $ M_{1} $ , and $ M_{F} $ , respectively (see Appendix A):

$$ u^{\prime}(C_{_{t}})=u^{\prime}(C_{_{t+1}}), $$

$$ \frac{(1-\theta)\gamma}{M_{_{1t}}}+\frac{\mathsf{\rho}\theta u^{\prime}(C_{_{t+1}})}{P_{_{t+1}}}-\frac{\theta u^{\prime}(C_{_{t}})}{P_{_{t}}}=0, $$

$$ \frac{(1-\theta)(1-\gamma)}{M_{_{Ft}}}+\frac{\mathsf{\rho}\theta u^{\prime}(C_{_{t+1}})\boldsymbol{\varepsilon}_{_{t+1}}}{P_{_{t+1}}}-\frac{\theta u^{\prime}(C_{_{t}})\boldsymbol{\varepsilon}_{_{t}}}{P_{_{t}}}=0. $$

For the purpose of deriving the optimal allocation condition of two different currencies in a regime of currency substitution, let us define the foreign-currency-preference variable, $ \alpha $ , as follows:

$$ \begin{aligned}&M_{1t}=\left(1-\boldsymbol{\alpha}_{t}\right)M_{t}\\ &\quad\varepsilon M_{Ft}=\boldsymbol{\alpha}_{t}M_{t}.\\ \end{aligned} $$

This foreign-currency preference, $ \alpha $ , is the key variable since its value, as it rises from 0 to 1, activates progressively greater currency substitution. If $ \alpha = 0 $ , there is no currency substitution effect and a consumer holds only the domestic currency as an asset. The condition $ \alpha = 0 $ is also satisfied in the case of non-convertibility of the domestic currency and strict capital control. In either case, foreign money-holding is forced to zero. On the other hand, the case of $ \alpha = 1 $ indicates that domestic residents hold
monetary assets exclusively in the form of foreign currency. This is the case of complete dollarization. Hence, the variable $ \alpha $ reflects the degree of softness of a currency, defined as the proclivity for currency substitution for asset-holding purposes. The value of $ \alpha $ then represents an inverse transformation of Gresham's law since, as it ranges from 0 to 1, it is the good (hard) currency that progressively drives out the bad.

Denote that $ \varepsilon_{t+1}/\varepsilon_{t}=1+z_{t+1} $ , where $ z_{t+1} $ is (future) devaluation rate. Then, combining equations (2), (3a), and (3b) yields (see Appendix B):

$$ \boldsymbol{\alpha}_{t}=\frac{(1-\gamma)i_{t+1}}{i_{t+1}-\gamma z_{t+1}}, $$

where $ i_{t+1} $ is the nominal interest rate, which is defined by the following expression: $ i_{t+1} = (1+r)(P_{t+1}/P_t) $ .

1. We can easily show that $ \partial\alpha_t/\partial z_{t+1} > 0 $ , indicating that exchange rate devaluation will induce currency substitution under the assumption of sticky prices. What happens when the prices adjust instantaneously? To see this, we assume that the purchasing power parity (PPP) condition holds given instantaneous and complete price adjustments. In this case, we have $ P_t = \varepsilon_t P^* $ , where $ P^* $ is the foreign price level which is assumed to be constant to avoid unnecessary complications. $ ^{6} $ Then equation (5) becomes:

$$ \boldsymbol{\alpha}_{t}=\frac{(1-\gamma)[r+(1+z_{t+1})]}{r+(1+r-\gamma)z_{t+1}} $$

As shown in Appendix B, the following property is satisfied:

$$ \frac{\partial\alpha_{_{t}}}{\partial z_{_{t+1}}}=\frac{(1-\gamma)r\gamma}{\left[r+(1+r-\gamma)z_{_{t+1}}\right]^{2}}>0 $$
This comparative statics result indicates that currency substitution is induced by (future) devaluation. Facing depreciation of the foreign exchange rate, households optimally switch their holdings of domestic currency to foreign currency, in order to maximize their intertemporal utility. This result holds in general, regardless of the speed of price adjustment. It is summarized by the following proposition:

Proposition 1 (Devaluation-induced Currency Substitution): Regardless of the adjustment speed of goods prices, a (future) devaluation induces currency substitution unambiguously.

Proof: See Appendix C.

Also, from equations (5), (5a) and (5b), it is straightforward to show that $ \partial\alpha_{t}/\partial\gamma<0 $ and $ \partial(\partial\alpha_{t}/\partial z_{t+1})/\partial\gamma<0 $ , indicating that strong utility preference towards the domestic currency decreases the effects of currency substitution by lowering its level and muffling the response toward devaluations. Alternatively, a particular utility preference toward foreign currency induces strong currency substitution as a behavioral consequence. These results are intuitively straightforward. Basically, equation (5b) captures the substitution effect of the money demand function: a decrease in the relative price of domestic currency induces substitution of the foreign currency for the domestic.

### 3.2 The Monetary Model of Currency Crisis

Now, utilizing the definition of total real balance of a representative household given by (4a) and (4b), we can rewrite the household’s objective function (1) as follows:

$$ U_{_{t}}=\sum_{s=t}^{\infty}\mathsf{\rho}^{^{s-t}}\left\{\theta u(C_{_{s}})+(1-\theta)\Bigg[\log\frac{M_{_{t}}}{P_{_{t}}}+\gamma\log\alpha_{_{t}}+(1-\gamma)\log(1-\alpha_{_{t}})\Bigg]\right\}, $$

In order to obtain a tractable formulation, examine the case of a symmetric preference between domestic real money balance and foreign real money balance in local currency., i.e., $ \gamma=(1-\gamma) $ . Then with an

constant.
approximated objective function, we can rewrite the household optimization problem as follows: $ ^{7} $

$$ \mathrm{M a x}\setminus U_{_{t}}=\sum_{s=t}^{\infty}\mathsf{\rho}^{s-t}\left\{\Theta u(C_{_{s}})+(1-\Theta)\left[\log\frac{M_{_{t}}}{P_{_{t}}}-\frac{1}{2}\right]\right\}, $$

$$ \mathrm{s.t.}B_{_{t+1}}+\frac{M_{_{t}}}{P_{_{t}}}=(1+r)B_{_{t}}+\frac{M_{_{t-1}}}{P_{_{t}}}+Y_{_{t}}-C_{_{t}}. $$

From the first order condition of this modified formulation, we have the conventional money demand function: $ ^{8} $

$$ \frac{M_{_{t}}}{P_{_{t}}}=\left(\frac{1-\theta}{\theta}\right)\left(\frac{1+i_{_{t+1}}}{i_{_{t+1}}}\right)\left[u^{\prime}(C_{_{t}})\right]^{-1}, $$

Combining Equations (4a) and (6), we have the following domestic money demand function:

$$ \frac{M_{1t}}{P_{t}}=(1-\alpha_{_{t}})\Biggl(\frac{1-\theta}{\theta}\Biggl(\frac{1+i_{_{t+1}}}{i_{_{t+1}}}\Biggr)\bigl[u^{\prime}(C_{t})\bigr]^{-1} $$

For the sake of expositional simplicity suppose for the time being that $ \alpha_{t} $ is exogenously given – an issue that we will revisit later in section 3.4. We thus set aside the endogenous structure of equation (5a). Now we draw on the first-generation models of Krugman (1979), as log-linearized by Obstfeld and Rogoff (1996), to model a small open economy with a foreign exchange rate that

complies with purchasing power parity (PPP) and uncovered interest parity (UIP). This model assumes perfect goods market adjustment and perfect capital mobility: $ ^{9} $
$$ p_{t}=e_{t}+p_{t}^{*} $$

$$ i_{t+1}=i_{t+1}^{*}+E_{t}e_{t+1}-e_{t}, $$

where e is the logarithm of the nominal exchange rate of this economy. The log of the price level, $ P_{t} $ , is denoted by p, and the interest rate is denoted by i. Then, log-linearizing Equation (6b), the money market equilibrium condition, becomes: $ ^{10} $

$$ m_{1t}-p_{t}=\log\left(1-\alpha_{t}\right)+\phi c_{t}-\eta i_{t+1}, $$

where m and c are the log of the money supply and the consumption, respectively. The parameters, $ \phi $ and $ \eta $ , are income elasticity and semi-interest elasticity of money demand, respectively.

Combining (7a), (7b), and (8), we have a dynamic equation of the exchange rate which satisfies PPP, UIP, and money market equilibrium:

$$ m_{1t}-\phi c_{t}-e_{t}+\eta\dot{i}_{t+1}*-p_{t}^{*}=\log(1-\alpha_{t})-\eta(E_{t}e_{t+1}-e_{t}), $$

Under the assumption of the small open economy, foreign variables are exogenously given. In order to simplify the argument, we assume that $ -\phi c_{t} + \eta i_{t+1}^{*} - p_{t}^{*} = 0 $ . Then we have a continuous version of the exchange rate dynamics under perfect foresight as follows:

$$ m_{t}-e_{t}\;=\;\log(1-\alpha_{t})-\upeta\dot{e}_{t} $$

### 3.3 The Role of the Central Bank

The balance sheet of the Central Bank is represented as
$$ B_{H}+\varepsilon A_{F}=M $$

where $ B_{H} $ represents the domestic government bond ownership of the Central Bank and $ A_{F} $ is its total foreign asset holdings, i.e., foreign bonds and reserve currency. The Central Bank’s monetary base is $ M_{1} = \mu MB $ , where $ \mu > 1 $ represents the money multiplier. Hence, Equation (10) gives

$$ M_{1}=\upmu(B_{H}+\upvarepsilon A_{F}). $$

### 3.4 The Collapse of the Fixed Exchange Rate Regime

From Equation (9a), we can see that a fixed exchange rate regime generates

$$ m_{1t}-\overline{e}=\log(1-\alpha_{t}). $$

Suppose that the Central Bank is required to finance an ever-increasing fiscal deficit by buying government bonds thus expanding its nominal holdings of domestic government debt, $ B_{H} $ . If the growth rate of domestic bond stock is constant at $ \lambda $ , we have

$$ \dot{B}_{H}=B_{H}\lambda. $$

Following Krugman (1979), we can calculate the shadow exchange rate under the flexible exchange rate assumption and no foreign reserves, i.e., $ A_{F} = 0 $ . In this situation, the Central Bank’s balance sheet equation (11) implies that

$$ m_{1t}=\log\upmu+b_{H t}, $$

where $ b_{H} $ indicates the log of the Central Bank’s bond holding. By combining Equations (13) and (14),
it becomes obvious that the money supply increases at the constant rate $ \lambda $ after the collapse of the fixed exchange rate regime, i.e., $ \dot{m}_{1t} = \lambda $ . Moreover, from Equation (9a), we can easily see that $ \dot{m}_{1t} = \dot{e}_t = \lambda $ along the balanced growth path. Therefore, inserting Equation (14) into Equation (9a), we obtain

$$ b_{H t}-e_{t}\;=\;-\;\log\upmu+\log(1-\upalpha_{t})\;-\upeta\lambda $$

Finally, we can derive the log of the shadow exchange rate, which is defined as the floating exchange rate that would prevail if the fixed exchange rate regime collapsed, as follows:

$$ e_{t}=b_{H t}+\log\upmu-\log(1-\alpha_{t})+\upeta\lambda. $$

We can see that $ \partial e_{t}/\partial\alpha > 0 $ . This indicates that the currency substitution effects due to agents' preference toward foreign currency will induce potential devaluation of the exchange rate over time. As a result, controlling for the fundamentals, the collapse of the fixed exchange rate would occur earlier. We can formally derive the time path to the collapse as follows. From Equation (12), we have

$$ b_{_{H t}}=b_{_{H0}}+\lambda t, $$

where $ b_{H_{0}} $ is the initial value of the Central Bank’s government bond holding. Combining Equations (16) and (17), together with $ e_{T} = \overline{e} $ , we can derive the time elapsed to the collapse of the fixed exchange rate regime as follows:

$$ T=\frac{\overline{{e}}-b_{_{H0}}-\log\upmu+\log(1-\upalpha_{_{t}})}{\lambda}-\upeta. $$

Hence, we can easily inspect that $ \partial T/\partial\alpha < 0 $ . Again, the softness of a currency is negatively related to
the timing of the currency crisis. As indicated in Figure 1, $ e_{T} $ is the cross-over point from fixed to flexible exchange rate, the onset of devaluation. The equation and figure denote that currency substitution, totally independently of the fundamentals and induced by a shift in the preference parameters, will lead to an early collapse of the stable exchange rate regime (Figure 1). $ ^{11} $ For example, such a change in the substitution parameter, $ \alpha $ , can be induced by a preference shift from domestic currency to foreign currency, i.e., a decrease in $ \gamma $ (equation 5a). It is important to note that even with a modest expansion in the level of government indebtedness, $ \lambda $ , a large currency substitution effect, $ \alpha $ , can accelerate the onset of the crisis. This is applicable to the recent Asian crises where the government account was in balance and otherwise the fundamentals were solid (Yotopoulos and Sawada, 1999).

The intuition behind this result should be straightforward. A high degree of currency substitution results in shrinking the demand for the domestic currency (Equation 6b). Given the flow of money supply, a decline in money demand will increase the equilibrium price level. According to the PPP, Equation (7a), this increased price level will lead to devaluation. Although the devaluation rate itself will be the growth rate of the money supply, it is the currency substitution that shifts the locus of the shadow exchange rate toward the devaluation.

So far, for the sake of tractability, we have assumed that the currency substitution variable, $ \alpha $ , is exogenously given. Yet, equation (5b) and Proposition 1 indicate that this variable is endogenously determined by a household's dynamic optimization behavior. The true equilibrium exchange rate behavior should take into account this endogeneity of the currency substitution variable. Although we have imposed the perfect foresight assumption of the model so far, the future devaluation rate, $ z_{t+1} $ , should be treated as an expected variable in reality. For convenience, we denote an expected devaluation rate as $ z_{t+1} $ . A correct interpretation of Proposition 1 is that the foreign-currency-preference variable will increase in response to an expected devaluation, i.e., make the collapse of the fixed exchange rate regime in $ \alpha_{t} = \alpha \left( z_{t+1}^{e} \right) $ with $ \partial \alpha_{t} / \partial z_{t+1}^{e} > 0 $ , because of endogeneity of the currency substitution variable, $ \alpha_{t} $ . Then once a country's currency behaves as a soft currency with an expected devaluation, the dynamic locus of the shadow exchange rate line, represented by Equation (16), will shift toward further devaluation (Figure 1). In this case, even if a country is initially at the point A', where the