Silviase/jgov_v1.4_full_ann huggingface dataset:
speculative attacks are not profitable without currency substitution, a currency substitution due to an expected devaluation can cause the immediate collapse of a fixed exchange rate regime. Hence, the expectation of devaluation can become a self-fulfilling prophecy. Note that this story does not depend on the usual assumption of the second generation model of currency crisis where the existence of speculative bubbles itself generates multiple-equilibria and a self-fulfilling expectation of speculative attacks (Obstfeld, 1996). Rather, in our model, the expectations of devaluation of optimizing domestic residents evitable.

Moreover, as is often pointed theoretically and empirically, there is a habit-formation of currency substitution (Uribe, 1997). The self-fulfilling expectation of devaluation is likely to have hysteresis on currency substitution. This mechanism creates the possibility of self-validating devaluation spirals. An expected devaluation generates currency substitution of agents [equation (5b)]. Currency substitution, in turn, leads to a further expected devaluation [equation (16)]. Soft currencies depreciate systematically because of the currency substitution effect and crises occur more frequently. This is a formal representation of the Y-Proposition elaborated by Yotopoulos (1996, 1997).

### 4. Empirical Implementation

The previous sections have generalized the treatment of currency crises by introducing currency substitution as a trigger for devaluation while controlling for the fundamentals of an economy. We can examine this process intuitively by constructing an imperfect proxy of the currency substitution variable, $ \alpha_{t} $ , and observing its behavior over time and especially during a crisis. Lacking data on foreign currency deposits, we define the proxy as the ratio of time, savings, and foreign-currency deposits in the deposit money banks to a broader measure of money, M2, which also includes time, savings, and foreign currency deposits. $ ^{12} $ Monthly data of these variables from January 1991 to September 2000 are extracted from International Financial Statistics of the International Monetary Fund. This measure of currency
substitution can be regarded as the upper-bound of $ \alpha_{t} $ since the data commingle in the numerator foreign currency deposits with other time and savings deposits.

Figure 2 represents the above ratio-proxy estimate of monthly currency substitution for Indonesia, Korea, Malaysia, and Thailand. Over the period from January 1991 to September 2000, there was no trend except a slight upward trend in Indonesia until July 1997 when there was a renounced increase in the proxy variable. Casual observation suggests a synchronicity between the increase in the proxy variable and the currency devaluations of 1997 and 1998. This is consistent with our theoretical framework: switching behavior from domestic to foreign currency ratchets up to devaluation. In Korea particularly, gradual currency substitution preceded the massive devaluation of November 1997.

Actually, in our model currency substitution is no longer an issue of fundamentals. As long as currency used for asset-holding purposes is a positional good and a free currency market provides for currency switching at negligible transaction costs, it pays for agents to ratchet up by substituting the reserve/ hard currency for the soft. Agents' expectations for devaluation generate self-fulfilling outcomes. Expectations thus become important determinants of devaluation.

### 4.1 The Empirical Model

The formal cross-country empirical implementation of the model rests on Equation (16) above which represents a modified version of Krugman's collapse of the fixed exchange rate regime, with $ e_{T} $ indicating the cross-over point from fixed to flexible exchange rate, denoting devaluation. The modifications consist of introducing currency substitution that impacts on the timing of the collapse of the exchange rate regime (Figure 1) and of releasing the strong assumption of perfect international capital mobility. We therefore rewrite Equation (16) to represent a hypothetical exchange rate under PPP and UIP:

$$ e_{t}=b_{H t}+\log\upmu+\alpha_{t}+\upeta\lambda+\upbeta_{,} $$

where $ \beta $ is a parameter which represents the degree of capital mobility.
In estimating Equation (16a) the following four components need be distinguished: First, recall that the first two terms of the RHS are equal to nominal money holdings, $ m_{1t} $ , that determine $ e_{t} $ when foreign exchange is used for transactions purposes. In other words, these two terms represent the fundamental PPP components of exchange rate due to trade in goods (and services), combined with the money market equilibrium condition. This part reflects the role of money as the medium of exchange, i.e., for transaction purposes. Figure 3-a represents the implicit mechanism that determines the PPP exchange rate by clearing the market for tradables, $ PPP_{Tt} $ .

Second, the third and fourth terms of Equation (16) modify the PPP-determination of the exchange rate to reflect the impact of other endogenous components. The latter term reflects the impact of the domestic money supply, while the third term represents the additional splice on the demand for foreign exchange that serves for asset-holding purposes. Figure 3-b shows the “equilibrium” exchange rate that accounts also for currency substitution, $ \alpha $ .

Third, if there is effective capital control and foreign exchange allocation is limited, then the last term in Equation (16a) $ \beta > 0 $ (Figure 3-c). In this case the “equilibrium” exchange rate is overridden at a level higher than in Figure 3-b. $ ^{13} $ The resulting foreign exchange rate is the black market exchange rate, BM, which is higher than the equilibrium nominal exchange rate under perfect capital mobility in Figure 3-c:

$$ B M_{_{t}}=\ln P P P_{_{T t}}+\alpha_{_{t}}+\beta, $$

where $ PPP_{Tt} $ is the fundamental PPP part and $ \beta $ represents the degree of capital control.

Finally, the official nominal exchange rate (NER) is often managed by the government, especially in soft-currency countries. There is a certain degree of discretion in setting the NER, and in any event it
is lower than the BM which is regarded as the logarithm of the black market exchange rate that reflects the existence of currency substitution by the domestic residents and foreign exchange market interventions of the governments.

We can now subtract NER from both sides of (16b) in order to have the empirical model that yields currency substitution, or else an operational index of the softness of the currency, $ \alpha_{it} $ , as a residual:

$$ BM_{it}\text{·}\mathbf{\Lambda}\mathbf{h}NER_{it}=\ln PPP_{Tit}-\ln NER_{it}+\beta D_{it}+\alpha_{it}, $$

where D is a dummy for the extent of capital control that is in effect.

For estimation purposes, let BP denote the black market premium relative to the nominal exchange rate. Then, by applying a first-order Taylor expansion to equation (18), we have

$$ BP_{it}=\ln DNER_{it}+\beta D_{it}+\alpha_{it}, $$

where $ \ln DNER_{it}=1\ln PPP_{Tit}-\ln NER_{it} $ . If data sets are available, the currency softness index, $ \alpha_{it} $ , can be derived as the residual of this empirical model, by regressing black market premium, $ BP_{it} $ , on the NER distortion index, $ \ln PPP_{Tit}-\ln NER_{it} $ , and the capital control indicator variable, $ D_{it} $ , which takes value of one if there are any foreign exchange controls and zero otherwise.

Equation (19) calls for imposing coefficient restrictions. We thus estimate Equation (19) with coefficient restriction on the NER distortion index, $ \ln DNER $ , by using OLS with the Huber-White robust standard error. Finally, we obtain the currency softness index, $ \alpha_{i} $ , as the estimated residuals of Equation (19) with the coefficient restriction. $ ^{14} $

### 4.2 The Data Set
In order to estimate the regression equation (19), we need three variables: the exchange-rate black-market premium, BP; the nominal exchange rate, NER; the NER distortion index, 1n DNER; and qualitative information about foreign capital control.

First, the data for the black market premium on the foreign exchange rate are widely available from different sources. We utilized a comprehensive annual cross-country panel data set of black market premium, which is compiled by Adrian Wood (1999). This data set covers 42 countries over a period of ten years (Table A2).

Second, consistent annual panel information on exchange rate restrictions is reported in Ernst & Whinney (various years) $ ^{15} $ . The data denote restrictions on equity capital; debt capital; interest; dividends and branch profits; and royalties, technical service fees, etc. Based on this information we construct a binary variable of foreign capital control (Table A2).

Obtaining the appropriate NER distortion index that the theory requires is more difficult. The empirical version of the NER distortion index that is broadly used for gauging a currency's tendency to appreciate or depreciate is supposed to measure the deviation of the nominal exchange rate (NER) from the ideal world where PPP holds and the prices of tradables tend to converge internationally (McKinnon, 1979). The empirical application of the index, however, whether it relies on the differential rate of inflation or other shortcut methods, reflects the prices of both tradables and nontradables. Measuring the deviation of the NER, which is formed exclusively in the world of tradables, by using a (PPP-deflated) general price index introduces a distortion that makes the resulting index of questionable value. This shortcoming is remedied by utilizing the unique set of data on the prices of tradables alone that Yotopoulos (1996) has developed.

Yotopoulos' point of departure is the PPP exchange rate that is constructed from the price-parity (micro-ICP) data of the Penn World Tables (Summers and Heston, 1991). The familiar expression that gives purchasing power parity, PPP, for country I as the geometric average of the k GDP-exhaustive commodity categories, is
$$ PPP_{I}=\prod_{i=1}^{k}\left(\frac{P_{i}^{I}}{P_{i}^{W}}\right)^{Q_{i}^{I}\bigg/\sum_{i=1}^{k}Q_{i}^{I}} $$

where $ P_{i}^{I} $ and $ P_{i}^{W} $ are the prices of i homogeneous commodity for country I and for the numeraire country (world), and Q are the quantity weights.

Different aggregations of Equation (20) can lead to alternative price indexes, such as the national price level of consumption or of government expenditure. For the Yotopoulos application the normalized index of the prices of tradables is constructed as:

$$ P P P_{I}^{T}=\prod_{i=N+1}^{T}\left(\frac{P_{i}^{I}}{P_{i}^{W}}\right)^{Q_{i}^{I}\bigg/\sum_{i=N+1}^{T}Q_{i}^{I}} $$

where $ i = N + 1, \ldots, T $ is defined for commodities that are tradable in country I, (and symmetrically for $ i = 1, \ldots, N $ for the nontradables). The PPP indexes in equation (21) are expressed in local currency per US (numeraire country) dollar.

It still remains to be determined how to delineate the two subsets of commodities, $ i = 1, \ldots, N $ and $ i = N + I, \ldots, T $ . Tradability is certainly related to tradedness. It could therefore be defined based on the empirical-positivist rule of whether a good enters (international) trade or not. One could then define two mutually exclusive categories of traded and nontraded goods. This heuristic approach, however, fails to address some important issues. Is any participation in international trade sufficient to make a good tradable? If so few nontradable goods would probably remain. Empirically Yotopoulos (1996:112) addresses the issue by adopting the standard definition of openness in an economy (the ratio of imports and exports to GDP) and designating as tradable any commodity group that has exports plus imports valued at more than 20 percent of the total share of that commodity's expenditure in GDP. By distinguishing a large number of commodity groups and by weighting both prices and the participation of each individual commodity into tradability by actual expenditure weights, the arbitrariness of the criterion has been blunted.

Implementation of the definition of the real exchange rate (RER) relies on the micro-PPP data of
the ICP (Kravis, Heston, and Summers, 1982; Penn World Tables). For the "basic classification" prices and nominal and real per capita expenditures (expressed in domestic currency per U.S. dollar) are available for 152 GDP-exhausting commodities for the "benchmark" countries and years. They were used in a flexible aggregation form to derive prices of tradables and nontradables. The data for the definition of tradability come from the United Nations Yearbook of International Trade Statistics which provides in 5-digit SITC classification for each country the value of exports (f.o.b.) and imports (c.i.f.) in U.S. dollars. The 5-digit classification was re-aggregated to achieve concordance with the ICP data. Appendix Table A1 presents the value of the index for prices of tradables for the benchmark countries that were included in at least one of the phases II, III, IV, and V of the ICP for 1970, 1975, 1980, and 1985, respectively.

Let a variable NER represent a country’s nominal exchange rate (NER) expressed in local currency/US dollar. A country i’s tradable goods price at time t is represented by $ PPP_{it}^{T} $ . Let $ PPP^{T} $ denote the PPP level of tradable goods, as in equation (21). Then, as we have discussed already, we can define a NER distortion index, DNER, as follows:

$$ D N E R_{_{i t}}\equiv\frac{P P P_{_{i t}}^{^{T}}}{N E R_{_{i t}}}, $$

where T is a superscript for tradables. The ratio of tradable prices in the parentheses represents an implicit long-run equilibrium purchasing power parity of tradable prices. Therefore, $ DNER_{it} $ represents the nominal exchange rate distortion, which is defined as the deviation of NER from the PPP for tradable goods, i.e., the long-run equilibrium exchange rate. We can then formulate formally:

Proposition 2 (NER Misalignment): If $ DNER_{it}>1 $ or $ \ln DNER_{it}>0 $ , then the NER is overvalued relative to the purchasing power parity level; and if $ DNER_{it}<1 $ or $ \ln DNER_{it}<0 $ , then it is undervalued. If there are no time-specific and country-specific distortions, then absolute PPP holds among tradables.

Proof: From Equation (22), if $ DNER_{it} > 1 \Leftrightarrow NER_{it} < PPP_{it}^{T} $ , NER is overvalued, and if $ DNER_{it} < 1 \Leftrightarrow NER_{it} > PPP_{it}^{T} $ , NER is undervalued. Moreover, if $ DNER_{it} = 1 \Leftrightarrow NER_{it} = PPP_{it}^{T} $ . Q.E.D.
Therefore, we can simply estimate this NER distortion index from Equation (22) by taking the ratio of the relative price level of tradables to the NER, i.e.,

$$ \ln DNER_{it}=\ln\left(\frac{PPP_{it}^{T}}{NER_{it}}\right). $$

Note that the index takes the value of zero if there is no NER distortion. In order to quantify this measure of distortion, we take advantage of Yotopoulos' (1996) estimates of $ PPP^{T}/\varepsilon $ that rely on the price parities (micro-ICP) data set. The resulting estimates of NER distortions are also presented in Appendix Table A1.

### 4.3 Estimation Results of the Currency Softness Index

The summary statistics of the empirical estimation are presented in Table 1. The values of the black market premium and of the Yotopoulos exchange rate distortion index indicate that, on the average, the countries in the sample had exchange rates that were relatively high by the standards of Figure 3-c, meaning that the components of $ \alpha $ and $ \beta $ had come into play. The indication from both sets of variables is the same, despite the fact that the variables are different and so are their origins. The statistic on the currency softness index is the resulting residual of the estimating equation. Its value indicates that the sample of countries, on the average, had soft currencies. This is consistent with the other statistics described in the table.

As we can see, the exchange control has a positive and significant coefficient. This is consistent with the theoretical prediction that foreign capital controls will increase a country’s foreign exchange black market premium (Figure 3-c). Another finding is that the dummy for 1985 has a positive and significant coefficient. This year-specific positive effect probably represents the impact of the significant appreciation of US dollar in the early 1980s and the resultant systematic depreciation of other countries’ currency toward the US dollar.

The immediate objective of Equation (19) is the derivation of the currency softness index, the
values of which are summarized in Table A2. This statistic, besides revealing important country- and time-specific information could also be used for investigating causality in various episodes of currency crisis. Unfortunately the data set and the episodes of currency crises are not rich enough to rigorously investigate causality hypotheses. However, we can still examine empirically the relevance of the currency softness index to financial crises by other methods. In order to characterize empirically the currency softness, we employ two different approaches.

First, the relationship between the softness measure and the currency distortion index is represented in Figure 4. The Figure clearly indicates a negative relationship between the constructed currency softness index and the degree of NER overvaluation. The fact that soft currencies are more likely to be undervalued (i.e., too many pesos to the dollar) is consistent with the theoretical expectation of the model. The operational difference between a hard and soft currency is that the exchange rate for the latter reflects not only the demand and supply of foreign exchange for transaction (balance-of-payments) purposes, but includes also an additional splice of “precautionary” demand for foreign exchange to be held as an asset. To the extent that hard-currency-country residents do not need to hedge their domestic-money-asset holdings by accumulating soft currency, the latter is bound to devalue. This asymmetry in demand for the “other” currency for asset-holding purposes is rooted in asymmetric reputation between the reserve/hard and the soft currency in free currency markets. It is precisely this asymmetry that characterizes serial devaluations and financial crises as predominantly soft-currency phenomena. The tendency then for soft currencies to have “high” nominal exchange rates in Equation (22) drives the DNER values below 1 (and to negative territory) thus indicating a perennially undervalued domestic currency. This is consistent with the finding of Yotopoulos (1996: Chapter 6) in the original study of exchange rate parity relying on micro-PPP data. Also, we can easily see that capital control is negatively related with the currency substitution/softness indicator, $ \alpha $ , which is fully consistent with our theoretical framework in Section 2.1. Controls imposed on domestic agents engaging in capital flight, on the other hand, tend to moderate the degree of the currency substitution, and therefore of the undervaluation of the soft currency.

The second empirical finding relates to the negative relationship between the currency softness index and
per capita real GDP as is verified in Figure 5. $ ^{16} $ To examine this relationship statistically, we regressed the estimated currency softness index on the per capita GDP. We also included the year dummy variables in order to control for a potential bias due to year-specific systematic effects. The estimation results are presented in Table 3. The coefficient of per capita GDP is negative and highly significant. This result confirms that there is a systematic relationship between the credibility of a currency and the level of economic development. This argument is consistent with the story that a less-developed country is more likely to be subjected to systematic devaluations due to its reputation-challenged currency. In fact, there might be a circular causation between a currency's softness and a country's low level of economic development. Unconstrained by controls, residents in a poor economy prefer holding the dollar because the domestic currency lacks in its credibility. A poor country, in turn, finds it difficult to establish its currency's reputation because of the low level of economic development. This two-way causality could conceivable turn into a poverty trap for a country at a low stage of economic development.

The obverse side of this finding holds that the best way for a soft currency to acquire reputation and therefore to act with impunity like a hard currency, e.g., by removing all controls, is for development to succeed. In other words, liberalizing the currency market as a policy (dis)intervention for promoting development amounts to putting the cart in front of the horse. A currency cannot become hard by behaving like a hard currency, i.e., by trading freely in the world’s exchange markets. There is an appropriate sequence in the process of economic liberalization. Freeing the foreign exchange market comes towards the end of this process when the main business of development has been done (Yotopoulos, 1996: Chapter 11).

### 5. Speculative Attacks and Policy Implications

The first-generation models of financial crises have focused on balance-of-payments disequilibria and the collapse of the fundamentals of an economy. Our model, on the other hand, predicts that even under a prudent fiscal policy and with pristine economic fundamentals, strong currency substitution