Liviatan, Nissan, Pablo E. Rodriguez, Discussion Papers. Ramirez-Rojas, Alberto Giovannini, Saurman, David S, Ross, Myron H, Frenkel, Jacob A, Cuddington, John T. Dallas S. Hafer, Ghosh, Sukesh K. Brittain, Bruce, Poloz, Stephen S. Allan W. Mackinnon, Miles, Marc A, Boyer, Russell S. Melvin, Michael, Benedict J. Kim, Kyung-Soo, Franco Spinelli, Marquez, Jaime, Case ," Economics Letters , Elsevier, vol.
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See our disclaimer. A second limitation of existing studies results from the fact that the degree of currency substitution is usually estimated without explicitly accounting for the existence of foreign currency holdings. This occurs in part because of the notorious difficulties involved in estimating comprehensively the existing stocks of such assets. A number of countries have.
Although such data are not comprehensive, they provide information that could prove quite useful in studies of currency substitution. The purpose of this paper is to formulate and estimate a dynamic, forward-looking model of currency substitution, using data on deposits held abroad for a group of ten developing countries—Bangladesh, Brazil, Ecuador, Indonesia, Malaysia, Mexico, Morocco, Nigeria, Pakistan and the Philippines.
The model, which incorporates the assumption of rational expectations, is developed in two steps. The desired composition of currency holdings is first derived from an optimizing model of household behavior. The multi-period costs-of-adjustment framework results in an empirical specification that incorporates both backward- and forward-looking components. One of the particularly appealing features of the empirical implementation of the model is that it does not require information on the domestic interest rate. In previous studies, the lack of a suitable domestic interest rate series has inhibited the estimation of currency substitution models relying on relative rates of return between domestic and foreign currencies that are based on interest rates.
The approach taken here circumvents this particular problem, utilizing instead data on the foreign interest rate and the premium on the domestic currency in the parallel exchange market. The model is estimated using quarterly data for a group of ten developing countries by an errors-in-variables procedure. For comparison purposes, an alternative model based on a conventional, partial adjustment formulation is also estimated. The alternative models are then compared on the basis of tests on properties of residuals, forecasting capabilities, and by a statistical technique for comparing non-nested models.
The remainder of the paper is divided into four sections.
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The next section describes the behavior of foreign currency deposits held abroad by developing-country residents over the past decade. Section III presents the theoretical framework. Section IV outlines the estimation procedure, presents the empirical results, and compares the statistical properties of the model with those of the conventional currency-substitution model.
Finally, the concluding section Section V provides an overall assessment of the analysis. Since the early s, the International Monetary Fund has been collecting and publishing data on foreign currency deposits held abroad by residents of a large number of developing countries. These figures, while large in absolute terms, are even more striking when expressed as a proportion of foreign exchange reserves and trade flows. For developing countries as a whole, foreign currency deposits held abroad were over percent of the official foreign exchange reserves; for Latin America they were nearly four times the level of official reserves.
The proportions for Africa percent and the Middle East percent are also sizable. The corresponding figures for Asia 41 percent and Europe 54 percent appear quite modest by comparison to the other regional groupings. As a proportion of exports and imports, for all developing countries foreign currency deposits held abroad amounted to about 42 percent.
Again, the picture for Latin America is quite dramatic, where such deposits were percent of exports and percent of imports. The corresponding ratios for the other three regional groupings are much smaller, but by no means insignificant. For example, in the case of Africa the reserves-to-import ratio averaged only about 15 percent, while the ratio of foreign currency deposits to imports was over 30 percent.
The growth of foreign currency deposits held abroad has also been very rapid in the s Figure 1. For Latin America, the annual average growth rate was over 70 percent, while that for African countries was around 60 percent. The ratios of foreign currency deposits to foreign exchange reserves has remained relatively stable Panel 2 of Figure 1 , except for Latin America, where the phenomenon seems to stem to a large extent from the acceleration of capital flight during the s. Notwithstanding the fact that foreign currency deposits held abroad by residents are large by most standards, and growing over time, it is worth noting that the data do not capture the full extent of foreign currency holdings.
To obtain a more accurate measure one would need to add foreign currency deposits in domestic banks, as well as foreign currency notes in the hands of the public. Few developing countries allow foreign currency deposits in the domestic banking system—although the number is rising—and data on foreign currency notes in circulation is virtually impossible to obtain. All in all, the published data on foreign currency deposits abroad probably represent a lower bound of the amount of foreign money balances held by residents of developing countries. Foreign currency deposits may be held abroad for a variety of reasons: for financing legal and illegal imports and other expenditures abroad, for protection of financial wealth, for speculation, and for capital flight.
In general, the actual level of foreign currency deposits abroad, relative to domestic deposits, should depend on their respective risk-adjusted rates of return. This relationship forms the basis of the formal portfolio diversification model developed in the next section.
This section develops a dynamic model of currency holdings with forward-looking rational expectations in a developing-country context. The model is developed in two steps. In the second step, actual currency holdings are determined in a multi-period costs of adjustment framework. The hypothetical world of this model consists of a small open developing economy with no commercial banks and a dual exchange rate regime.
The dual exchange market consists of an official market for foreign exchange, in which the official parity is pegged, which coexists with a legal or quasi-legal parallel market for foreign exchange. The rest of commercial transactions and all capital transactions are settled in the parallel market at the free exchange rate s t , which is determined by market forces. The price of the good is set on world markets. In each period, producers surrender a given proportion of their foreign exchange earnings at the official exchange rate, and repatriate the remaining proceeds via the parallel market.
There is no domestic expenditure on the domestically produced good; thus, total output is exported and total consumption is imported. Domestic agents consume two goods, both of them produced abroad. The second good is assumed to be prohibited by law, and thus can only be smuggled in and traded illegally in the economy. Residents are assumed to hold four types of assets: domestic money, foreign money, bonds denominated in domestic currency, and bonds denominated in foreign currency. Domestic and foreign money are imperfectly substitutable, non-interest-bearing assets. There is a single representative agent who maximizes a discounted sum of future instantaneous utilities.
Equation 2 defines nominal wealth as the sum of holdings of domestic and foreign currency, and holdings of domestic and foreign bonds. The last term in equation 3 represents valuation effects on the stock of foreign currency and foreign bonds. Equation 4 indicates that total real expenditure on both goods cannot exceed the flow of liquidity services produced by the use of domestic and foreign currencies.
It implies that an expected future depreciation of the domestic currency in the parallel market for foreign exchange would cause domestic residents to shift out of domestic money into foreign money, and vice versa. By substituting the interest parity condition 7 b in equation 7 a , the domestic interest rate can be eliminated—a procedure that will prove particularly useful at the estimation stage, because of the lack of suitable data on market-determined rates in developing countries.
Formally, therefore, the representative agent undertakes a two-stage decision process. It is given by:. Equation 10 shows that the currency ratio depends on a backward-looking component, q t -1 , and forward-looking variables—a geometrically-declining weighted sum of the opportunity-cost variable. This section first describes the estimation procedure and then discusses the results obtained from estimation of equation As noted in Section II , one needs to recognize several shortcomings and limitations in the data.
Data on all three components are extremely difficult to obtain for any country. Moreover, even when it is possible to isolate, say, foreign currency deposits in the domestic financial system, it is not always possible to identify whether the deposits are held by foreigners or by domestic residents. The quantitative importance of this component is extremely difficult to estimate—especially in a country where parallel currency markets are important. Such a procedure does not take into account foreign currency deposits held in domestic banks and domestic nonbank foreign money balances.
Accordingly, this measure will underestimate the magnitude of currency substitution if residents hold significant foreign currency deposits in domestic banks and if a significant portion of financial transactions in foreign currency takes place outside the formal banking system. To estimate equation 10 , multi-step ahead predictions for the determinants of the currency ratio must be derived. Several alternative procedures can be used for modeling the expectational terms appearing in the model. In the first case, the unknown future expectations entering the equation to be estimated are replaced by generated or predicted values derived from a forecasting equation for the driving process.
In principle, estimation of the model in a restricted form would require the use of nonlinear least squares. Instead, the model is here estimated in an unrestricted form and the parameter constraints imposed by the rational expectations assumption are tested for three different values of 7 0. Using the econometric procedure described above, the model described by equation 10 was estimated for ten developing countries: Bangladesh, Brazil, Ecuador, Indonesia, Malaysia, Mexico, Morocco, Nigeria, Pakistan and the Philippines.
Data are quarterly and seasonally unadjusted for the period to Table 2 presents unrestricted estimates for the parameters of equation The coefficient of determination is relatively low only for Malaysia, indicating that the regression accounts for a sizable fraction of the variance of the currency ratio for the other countries.
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With the exception of Mexico, there is no evidence of departure from normality of the residuals, as shown by the Jarque-bera JQ test statistic, and evidence of autoregressive conditional heteroscedasticity seems to appear only for Bangladesh. The predictive Chow test, which examines the ex ante forecasting capability of the model over the period indicates parameter instability only for Morocco, and only at a 5 percent significance level.
Interestingly enough, Brazil and Mexico are countries that have experienced considerable macroeconomic instability over the estimation period, a phenomenon which has often been viewed as conducive to a high degree of substitution between domestic and foreign currencies. Second, they also indicate that in no cases are the restrictions rejected at a 5 percent significance level, while they are rejected for only one country Malaysia at a 10 percent significance level.
Unit root tests and cointegration tests between the currency ratio, q, and the opportunity cost ratio, z, were also conducted. The results, given in Appendix II , show identical orders of integration for these variables in the majority of cases. Following Cuthbertson and Taylor , it can be shown that estimation of the forward-looking model developed here is tantamount to estimation of an error-correction representation. Thus similar estimates of the long-run parameters should be observed from cointegration analysis by the Granger Representation Theorem Engle and Granger, A conceptually similar formulation has been used in the context of analytical work on dual exchange markets by Lizondo and Kharas and Pinto Although the adjusted coefficient of determination seems significantly higher in several cases Mexico, Nigeria, Pakistan, and the Philippines than what obtains for the forward-looking estimates reported in Table 2 ; other test statistics are more favorable to the latter formulation.
In Table 4 , the Lagrange Multiplier test statistic indicates the presence of autocorrelated residuals in five countries Ecuador, Indonesia, Mexico, Nigeria and Pakistan , and there is evidence of departure from normality of the error term in four cases Brazil, Morocco, Nigeria and Pakistan. Heteroscedasticity also seems to be present in the estimation results for Morocco and Nigeria. The predictive Chow test indicates parameter instability for Brazil, Ecuador Indonesia, Mexico, Morocco, Nigeria, and to a lesser extent the Philippines.
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Finally, coefficients on the lagged endogenous variable are substantially higher than those estimated with the forward-looking model for several countries—a result that indicates an implausibly slow speed of adjustment and implausible long-run elasticities. A more formal comparison between the forward-looking optimizing model 10 and the conventional formulation 11 can be implemented by using the non-nested PE procedure of MacKinnon et al.
The significant statistical effect of the difference between the predictions of the forward-looking and conventional models in the prediction error of the conventional model suggests in all but one case Malaysia that the forward-looking model can help improve the forecasts produced by the conventional model see the first column of Table 5. By contrast, as indicated in the second column of Table 5 , prediction errors from the conventional model help to improve the predictive capacity of the forward-looking model in only four cases Mexico, Morocco, Nigeria, and the Philippines —a result that does not hold at the 1 percent significance level for two of the countries Mexico and Nigeria.
The general implication of the above results is that both direct regression diagnostic tests and indirect non-nested tests statistical evidence suggest that the forward-looking model performs better than a conventional partial adjustment model for most countries in the sample. Given that the forward-looking model is rigorously derived from an optimizing framework, that it embodies theoretical restrictions on its parameters, and that it provides an adequate representation of the data, it can be viewed as a plausible alternative to the more conventional partial adjustment model.
The purpose of this paper has been to derive and test a currency substitution model in which portfolio decisions depend upon forward-looking variables. The long-run, or equilibrium, currency ratio is derived from an optimizing model in which agents can hold domestic and foreign currencies, as well as domestic and foreign bonds.
The actual currency ratio is derived in a framework that is based on a multi-period cost of adjustment scheme, involving rational forward-looking expectations. Empirical implementation of the model for ten developing countries has proven encouraging.
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The forward-looking model had statistically significant coefficients as implied by the theory, and the forecasting ability of the model appeared satisfactory.