Abstract
During the past decade or so economists have emphasized the critical role that interest rate policies play in the development process. The growing literature on financial “reforms” and financial “liberalization” in developing countries has dealt with a variety of issues, such as the relation between financial intermediation and economic growth, the sensitivity of the volume of savings to changes in real interest rates, and the relation between investment and interest rates. Generally speaking, the empirical evidence indicates that there is indeed a positive association between the degree of development of the financial sector, including in particular freer interest rates, and economic performance in developing countries.1 This finding has undoubtedly prompted the authorities in a number of such countries to pursue policies to remove controls on interest rates and to allow market forces to play a relatively greater role in the determination of interest rates.
During the past decade or so economists have emphasized the critical role that interest rate policies play in the development process. The growing literature on financial “reforms” and financial “liberalization” in developing countries has dealt with a variety of issues, such as the relation between financial intermediation and economic growth, the sensitivity of the volume of savings to changes in real interest rates, and the relation between investment and interest rates. Generally speaking, the empirical evidence indicates that there is indeed a positive association between the degree of development of the financial sector, including in particular freer interest rates, and economic performance in developing countries.1 This finding has undoubtedly prompted the authorities in a number of such countries to pursue policies to remove controls on interest rates and to allow market forces to play a relatively greater role in the determination of interest rates.
Now that the process of financial liberalization is well under way, however, economists and policymakers are faced with a different set of issues relating to interest rates in developing countries. The focus has begun to shift away from investigating the effects of freeing interest rates to examining how interest rates are in fact determined once the domestic financial market has been liberalized. The interest in this particular issue has been heightened by two factors. The first is the recent experiences of the countries of the Southern Cone of Latin America—Argentina, Chile, and Uruguay—where domestic interest rates rose to extraordinarily high levels following the implementation of financial reform policies.2 The second is the evidence that has accumulated suggesting that the high and volatile world interest rates in recent years were at least partially transmitted into developing countries. Both these factors have been a cause of concern to policymakers and have generated some fundamental questions about the behavior of interest rates in developing countries—in particular, about what should be expected when controls on interest rates are eliminated. At present, however, there are few studies dealing with this general issue, and even fewer specifically examining the respective influences of foreign factors and domestic monetary conditions as they affect interest rates in developing countries.3
It is obvious that the process of determination of interest rates will be significantly different under alternative degrees of openness of the capital account of the balance of payments. For example, in the case of a fully open capital account some form of interest arbitrage will hold, with domestic interest rates depending on world interest rates, expected devaluation, and perhaps some risk factors. In contrast, in countries with a completely closed economy (closed capital and current accounts) open economy factors will obviously play no role, and the nominal interest rate will be determined by conditions prevailing in the domestic money market and by expected inflation. Most developing countries, however, do not fall in either of these two extreme categories, so that interest rates will in general depend on domestic money market conditions, as well as on the expected rate of devaluation and world interest rates.4 From a policy perspective it is important to determine the way in which these different factors actually affect interest rates. For example, how expected devaluations or changes in domestic monetary conditions or both affect interest rates in developing countries is crucial for assessing the significance of one of the possible mechanisms through which stabilization policies will affect aggregate demand. Stabilization programs typically involve both exchange rate adjustments and tighter credit and monetary policies. If these policies generate an increase in the domestic (real) interest rate, there will be an additional channel (usually not considered in formal studies about stabilization programs in developing countries) through which aggregate demand will be affected.5
In this paper a framework is proposed for empirically analyzing the determination of nominal interest rates in developing countries. Even though the model is quite general and of relevance for any small country, the discussion is carried out with those developing countries in mind that have liberalized their domestic financial sectors in the sense that controls on interest rates have been removed. The model, which is described in Section I, combines features of models for both closed and open economies, and it is shown that the relative importance of the domestic monetary conditions and the open economy factors will depend essentially on the openness of the capital account. An interesting property of the model is that the approximate degree of openness of the financial sector in a particular country can be estimated from the data. In Section II of the paper the usefulness of this framework for analyzing interest rate behavior is illustrated using data for Colombia and Singapore. The results obtained indicate that, as expected, in Singapore only open economy factors appear to matter; in Colombia, however, both domestic monetary disequilibria and open economy conditions have influenced nominal interest rates during the past 15 years. Section III describes some areas in which the analysis could be extended—including, for example, studying the behavior of real interest rates, the determination of interest rates under changing degrees of openness, the modeling of the effects of expected exchange rate changes, and, finally, introducing the possibility of currency substitution. The concluding section summarizes the main points and results of the analysis.
I. Theoretical Models of Interest Rate Determination
In this section three basic models for analyzing interest rate behavior in developing economies are briefly presented. The first is a simple model that assumes that the country in question is completely closed to the rest of the world. Under these circumstances it is assumed that the nominal interest rate depends on the real interest rate and on expected inflation. The second model considers the other extreme, in which the capital account is completely open. In this case domestic interest rates are closely linked to world interest rates through interest arbitrage. Finally, a more general model that allows both foreign and domestic factors to affect the behavior of the nominal interest rate, and thus contains the other two models as special cases, is presented and discussed.
Interest Rates in a Closed Economy
Following the standard Fisher approach, we can specify the nominal interest rate as equal to6
where
| i | = | the nominal rate of interest |
| rr | = | the real (ex ante) rate of interest |
| πe | = | the expected rate of inflation. |
| i | = | the nominal rate of interest |
| rr | = | the real (ex ante) rate of interest |
| πe | = | the expected rate of inflation. |
The real interest rate in turn can be specified as
where ρ is a constant and represents the long-run equilibrium real interest rate. The variable EMS represents the excess supply of money, λ is a parameter (λ > 0), and ω, is a random error term. According to equation (2), the real rate of interest deviates from its long-run value p if there is monetary disequilibrium; and excess demand (supply) for (of) real money balances will yield a temporarily higher (lower) real interest rate. This relation has been called the “liquidity effect” in the literature (Mundell (1963)). In the long run, however, the money market would be in equilibrium, and the variable EMS would play no role in the behavior of rrt.7 Introducing this liquidity effect into the model, contrary to most recent empirical studies of interest rate behavior, allows the real rate of interest to be variable in the short run.8 As such, even though the Fisher equation (1) is assumed to hold continuously, the possibility of slow adjustment of the real interest rate (given by λ) implicitly allows for the possibility of delayed response of the nominal interest rate to monetary changes.
The solution for the nominal interest rate in a closed economy, therefore, is
To estimate equation (3), however, some assumptions have to be made regarding the unobserved variables, πe and EMS. The expected rate of inflation can be specified in a variety of ways. One is to use the traditional adaptive expectations model, in which the expected rate of inflation is assumed to be a (geometrically) distributed lag function of past rates of inflation. An empirical generalization of this approach is to assume an auto-regressive process for the rate of inflation and to use the predicted values as representing the expected rate of inflation.9 Other possible methods include the use of survey data (for example, the Livingston series on inflationary expectations) or of models that allow for the influence of additional economic variables (other than only past rates of inflation) in the formation of expectations.10 Of course, it can also be assumed that actual and expected rates of inflation are the same—an assumption that would imply a strict form of rational expectations (that is, perfect foresight). There is no compelling theoretical reason for preferring one method over any other, and the choice is ultimately an empirical one.
The excess supply of money is defined as
where m is the actual stock, and md the desired equilibrium stock, of real money balances.11 In an economy that has completed the financial reform process, we would expect substitution to take place between both money and goods, as well as between money and financial assets, so that the demand for money would be a function of two opportunity-cost variables (the expected rate of inflation and the rate of interest) along with a scale variable (real income).12 The equilibrium demand for money can therefore be written as
It should be noted that long-run demand for money is assumed to be a function of the equilibrium nominal interest rate, defined as the equilibrium real interest rate (ρ) plus the expected rate of inflation (πe), rather than of the current nominal interest rate.
The model can be closed by assuming that the stock of real money balances adjusts according to
where Δ is a first-difference operator, Δlog mt = log mt - log mt-1 and β is the coefficient of adjustment, 0 ≤ β ≤ 1. If the nominal stock of money is exogenous, then equation (6) really describes an adjustment mechanism for domestic prices. In essence, equation (6) introduces a process by which the nominal interest rate returns eventually to its equilibrium level.
The workings of the model given by equations (3), (4), and (6) can be conveniently described within the framework of Figure 1. In the figure the initial equilibrium is point A, where the long-run demand for real money balances is equal to the supply (EMS = 0), the nominal interest rate is at its equilibrium level (ρ + πe), and the actual stock of real money balances is equal to m0. Suppose now that there is an increase in the supply of money from
Interest Rate Determination in a Closed Economy
Citation: IMF Staff Papers 1985, 003; 10.5089/9781451972863.024.A001
Interest Rate Determination in a Closed Economy
Citation: IMF Staff Papers 1985, 003; 10.5089/9781451972863.024.A001
Interest Rate Determination in a Closed Economy
Citation: IMF Staff Papers 1985, 003; 10.5089/9781451972863.024.A001
Equation (6) can be simplified to
combining equations (4) and (6a), we obtain
Using equations (1), (5), and (7), we can derive the reduced-form equation for the nominal interest rate:
where the composite parameters are
| γ0 | = | ρ + λ(1 − β)(α0 − α2ρ) |
| γ1 | = | λ(1 − β)α1 |
| γ2 | = | λ(1 − β) |
| γ3 | = | [1 − λ(1 − β)(α2 + α3)]. |
| γ0 | = | ρ + λ(1 − β)(α0 − α2ρ) |
| γ1 | = | λ(1 − β)α1 |
| γ2 | = | λ(1 − β) |
| γ3 | = | [1 − λ(1 − β)(α2 + α3)]. |
Once πe is replaced by some appropriate measured variable, equation (9) can be directly estimated. In the estimation it would be expected that γ1 > 0 and that γ2 < 0; the sign of γ3 would be negative or positive depending on whether λ(1 − β)(α2 + α3) is greater or less than unity.
Interest Rates in a Fully Open Economy
If the economy is completely open to the rest of the world, and there are no impediments to capital flows, domestic and foreign interest rates will be closely linked. In particular, in a world with no transaction costs and risk-neutral agents the following uncovered interest arbitrage relation will hold:
where
The analysis of interest rate behavior in open economies usually has amounted to investigating the extent to which equation (9), or some variant of it, holds. One way of doing this is by adding transaction costs and defining a band within which the interest-parity differential can vary, without violating the arbitrage condition. Another way of testing equation (9) is through analysis of the time-series properties of the interest-parity differential. If these time series are not serially correlated—that is, if they are white noise—it is usually concluded that the domestic interest rate depends only on open economy factors. 14 Frenkel and Levich (1975, 1977), for example, have analyzed the extent to which the covered arbitrage condition, which replaces ėt by the forward premium in equation (9), held for industrialized countries during the period after adoption of floating rates in 1973. They showed that, once transaction costs are allowed into the analysis, this arbitrage condition has worked well for these countries. Using a similar methodology, Lizondo (1983), however, found evidence of large and persistent deviations in Mexico during 1979-80. Cumby and Obstfeld (1981) adopted the second of the two approaches and analyzed the time-series properties of the uncovered interest arbitrage differential using weekly data for six industrialized countries; they found that in five of the six cases these series exhibited strong serial correlation. They interpret these results as providing evidence that there exists a (time-varying) foreign exchange premium for most currencies (see Levich (1985) for a review of other studies of related isues). The tests performed by Blejer (1982) using monthly data for Argentina for June 1977 through August 1981, however, could not disprove the hypothesis that for Argentina during this period the uncovered interest rate differential was white noise.15 Broadly speaking, the evidence appears fairly mixed on the interest-parity condition in open economies.
Of course there exists the possibility that, because of frictions arising from transactions costs, information lags, and the like, domestic interest rates respond with delay to any changes in the foreign rate of interest or in exchange rate expectations. This type of lagged response can be modeled straightforwardly in a partial adjustment framework as follows:
where θ is the adjustment parameter, 0 ≤ θ ≤ 1. If the financial market adjusts rapidly, this parameter θ will tend toward unity. Conversely, a small value of θ would imply slow adjustment of the domestic interest rate.16 The solution of equation (10) in terms of the domestic interest rate is
The General Case
The preceding discussion has examined interest rate determination in the two polar cases related to the degree of openness of the economy. If, however, the economy under consideration is one that has some controls on capital movements, as most developing countries do, it is possible to visualize that both open and closed economy factors will affect the behavior of domestic interest rates at least in the short run. A straightforward way of constructing a model for such an economy is to combine the closed economy and open economy extremes. In particular, it can be assumed that the equation for the nominal interest rate can be specified as a weighted average, or linear combination, of the open and closed economy expressions discussed above. Denoting the weights by Ψ and (1 - Ψ) and combining equations (1) and (9) allows the following model for the nominal interest rate to be specified:
where the parameter Ψ can be interpreted as an index measuring the degree of financial openness of the country. If Ψ = 1, the economy is fully open, and equation (12) collapses into the interest arbitrage condition (9). If Ψ = 0, however, the capital account is closed, and equation (12) becomes equal to the Fisher closed economy equation (1). In the intermediate case of a semiopen (semiclosed) economy, the parameter Ψ will lie between zero and unity; the closer it is to unity, the more open the economy will be. In a sense, estimating Ψ from the data makes it possible to determine the degree of openness of the financial sector in a particular country. This estimated degree of openness will provide some information on the actual degree of integration of the domestic capital market with the world financial market. 17 To the extent that official capital and exchange controls are not fully effective, the empirically estimated “economic” degree of openness can be significantly higher than the “legal” degree of openness given by the system of capital controls in the country.
If we assume slow adjustment to interest parity and thus use equation (11) instead of equation (9), the appropriate form for the general case becomes
In this case full interest parity would require the condition Ψ = θ = 1; when Ψ = 0, the Fisher closed economy condition would emerge. It should be noted that there will be some relation between the index of financial openness, Ψ and the speed of adjustment, θ. For example, if the domestic financial market is fully integrated with the international capital markets, it is also likely that domestic interest rates would adjust quite rapidly.
Assuming that the excess money supply term is given by equation (4) and that the demand for real money function is provided by equation (5),18 we obtain from equation (13) the following expression for the nominal interest rate: 19
where the reduced-form parameters δi are
| δ0 | = | (1 − ψ)[ρ + λ(1 − β)(α0 − α2ρ)] |
| δ1 | = | ψθ |
| δ2 | = | (1 − ψ)λ(1 − β)α1 |
| δ3 | = | -(1 − ψ)λ(1 − β) |
| δ4 | = | (1 − ψ)[1 − γ(1 − β)(α2 + α3)] |
| δ5 | = | ψ(1 − θ), |
| δ0 | = | (1 − ψ)[ρ + λ(1 − β)(α0 − α2ρ)] |
| δ1 | = | ψθ |
| δ2 | = | (1 − ψ)λ(1 − β)α1 |
| δ3 | = | -(1 − ψ)λ(1 − β) |
| δ4 | = | (1 − ψ)[1 − γ(1 − β)(α2 + α3)] |
| δ5 | = | ψ(1 − θ), |
and є is a random error term. If we assume that the income elasticity of the demand for money is unity, then the model can be further simplified. In this case δ2 = -δ3, and real income and lagged real money balances can be combined into one composite variable—that is, [log yt - log mt-1].
Equation (14) is quite general because it not only incorporates open economy and closed economy features but also permits the possibility of slow adjustment on both the foreign and domestic sides. 20 One can see that, in the case of a completely open economy with instantaneous adjustment of the domestic interest rate (that is, ψ = θ = 1), δ1 becomes equal to unity, and δ0 = δ2 = δ3 = δ4 = δ5 = 0. According to equation (14), the nominal interest rate will then be equal, in both the long and short run, to
The preceding discussion has assumed that agents are risk neutral. As mentioned, if agents are risk averse, equation (14) should be modified to take this fact into account. The simplest way of doing so is to replace the expected rate of devaluation ėt by the forward premium. From a practical viewpoint, however, this substitution poses difficulties because there are few developing countries that have forward markets for their currencies. An alternative way to deal with the problem of risk aversion is to introduce a risk premium explicitly into the analysis, and to make some assumptions about its statistical properties. For example, it can be assumed that the risk premium is equal to a constant plus a random term. In this case the constant part of the premium will be added to the constant in equation (14), and the random component becomes a part of the error term. In principle it would be possible to incorporate any number of alternative assumptions about the behavior of the risk premium into the empirical analysis.
II. Empirical Tests of the Model
To assess the ability of the general model to describe the process of interest rate determination in developing countries, it was estimated using quarterly data for Colombia and Singapore. Because these two countries are quite different, both in the development of their domestic financial markets and in the extent of controls over capital flows, they should provide a fair test of the basic model. Since both countries vary in their openness, it would have been preferable to round out the picture by also including in the analysis an example of a closed economy. For obvious reasons this was not possible.21
Since 1967 Colombia has followed a growth strategy based on export promotion. During the past 15 years a crawling peg exchange rate system has been in effect, and, at least in a segment of the capital market, interest rates have been allowed to fluctuate freely (Diaz-Alejandro (1976), Wiesner (1978), and Montes and Candelo (1982)). Over this period the domestic capital market was slowly liberalized, but some restrictions to capital movements were maintained. For example, there were restrictions on the minimum maturity of loans obtained from abroad (usually five years); the movement of capital in and out of the country required formal approval from a number of government agencies, including the Exchange Office, the Ministry of Finance, and the National Planning Department; and there was a 95 percent advance payment deposit on all capital outflows.22 Although there was some capital mobility, the existence of such legal restrictions make it best, for practical purposes, to characterize Colombia as a semi-open economy rather than a fully open one. In terms of our model, therefore, we would expect to obtain a positive value for the openness parameter ψ and a value for θ of less than unity.
In contrast, the Singapore economy can be regarded as highly open, with virtually no restrictions on trade and capital flows (see Blejer and Khan (1983)). For example, imports are mostly unrestricted, with a very small number subject to tariffs, and all payments can be made freely. As far as the capital account is concerned, the last elements of exchange controls were eliminated in June 1978, and there are no hindrances to the movement of capital.23 After being pegged to the pound sterling, the Singapore dollar floated from June 1973 through late 1975. From then on the currency has been pegged to a trade-weighted basket of the currencies of Singapore’s major trading partners. The floating of the Singapore dollar led to a rapid development of the foreign exchange market, and, although the volume of transactions is not as large as in the world’s major financial centers, the Singapore market has over the years become among the largest in developing countries. An active forward market, covering transactions of various maturities, has also developed, with quotations being given on a daily basis by participating banks. In general, the progressive freeing of financial transactions, the exchange rate policy, and direct encouragement by the government through its financial development program have combined to make Singapore an important financial center with close links to other major financial markets. These institutional factors would suggest that for Singapore the openness parameter ψ would be close to unity, and that domestic interest rates would respond rapidly to foreign developments (θ ≃ 1).
Equation (14) and its equilibrium variant excluding the lagged interest rate term were estimated by ordinary least-squares methods for the two countries using quarterly data. For Colombia the data were for the period running from the third quarter of 1968 through the fourth quarter of 1982, whereas for Singapore the data cover the period from the third quarter of 1976 through the last quarter of 1983 (see the Appendix for data sources and definitions). In the estimation equations for Colombia, the expected rate of devaluation between periods t and t + 1, ėt, was replaced by the actual rate of depreciation in period t. This assumption implies that, during the period under consideration, the rate of devaluation in Colombia can be represented approximately as a random walk process with zero drift (Edwards (1985a)). Because forward rates are available for the Singapore dollar, we used the forward premium to proxy the expected exchange rate change. Thus it is implicitly assumed in the analysis that the exchange rate risk premium is captured in the constant and error terms. 24 For both countries the expected rate of inflation was calculated by fitting an autoregressive process (with seven lags) to the actual rate of inflation, then using the predicted values to represent
Results of General Interest Rate Model
Adjusted for expected exchange rate change.
From the third quarter through the fourth quarter of the years indicated.
Results of General Interest Rate Model
| Country and Period | Constant (δ0) | Foreign Interest Rate1 (δ1) | Real Income - Lagged Real Money Balances (δ2 = δ3) | Expected Inflation (δ4) | Lagged Interest Rate (δ5) | R2 | DW | H | |
|---|---|---|---|---|---|---|---|---|---|
| Colombia | -0.189 | 0.353 | 0.303 | 0.256 | 0.484 | 0.820 | — | -1.29 | |
| (1968-82)2 | (3.08) | (1.98) | (3.03) | (2.00) | (3.89) | ||||
| -0.326 | 0.786 | 0.517 | 0.422 | — | 0.768 | 1.41 | — | ||
| (5.78) | (4.99) | (5.49) | (3.11) | ||||||
| Singapore | -0.200 | 0.922 | 0.052 | 0.026 | 0.001 | 0.991 | — | 0.39 | |
| (1976-83)2 | (0.20) | (23.68) | (0.24) | (1.40) | (0.02) | ||||
| -0.203 | 0.923 | 0.053 | 0.026 | — | 0.991 | 1.83 | — | ||
| (0.21) | (39.62) | (0.25) | (1.42) | ||||||
Adjusted for expected exchange rate change.
From the third quarter through the fourth quarter of the years indicated.
Results of General Interest Rate Model
| Country and Period | Constant (δ0) | Foreign Interest Rate1 (δ1) | Real Income - Lagged Real Money Balances (δ2 = δ3) | Expected Inflation (δ4) | Lagged Interest Rate (δ5) | R2 | DW | H | |
|---|---|---|---|---|---|---|---|---|---|
| Colombia | -0.189 | 0.353 | 0.303 | 0.256 | 0.484 | 0.820 | — | -1.29 | |
| (1968-82)2 | (3.08) | (1.98) | (3.03) | (2.00) | (3.89) | ||||
| -0.326 | 0.786 | 0.517 | 0.422 | — | 0.768 | 1.41 | — | ||
| (5.78) | (4.99) | (5.49) | (3.11) | ||||||
| Singapore | -0.200 | 0.922 | 0.052 | 0.026 | 0.001 | 0.991 | — | 0.39 | |
| (1976-83)2 | (0.20) | (23.68) | (0.24) | (1.40) | (0.02) | ||||
| -0.203 | 0.923 | 0.053 | 0.026 | — | 0.991 | 1.83 | — | ||
| (0.21) | (39.62) | (0.25) | (1.42) | ||||||
Adjusted for expected exchange rate change.
From the third quarter through the fourth quarter of the years indicated.
Taking the case of Colombia first, we can see from Table 1 that the results are quite satisfactory. All the coefficients have the correct signs and are significant at the conventional levels. 27 In particular, the significance of the coefficients of
We further calculated the values of what we regard as the key structural parameters: the openness parameter (ψ) and the adjustment parameter for the interest rate (θ). The value of ψ turns out to be 0.84 (with a t-value of 5.94), which is quite high and indicates that the Colombian financial sector has, in practice, been more integrated with the rest of the world than one would have believed from the nature and extent of capital controls during this period. According to this estimated value of ψ, an increase in the foreign interest rate of 10 percentage points, for example, would be translated into an increase of the domestic interest rate of over 8 percentage points in the long run. Because the coefficient of adjustment (θ) is equal to 0.422 (with a t-value of 2.5), however, the average (or mean-time) lag in adjustment of the nominal interest rate to a change in either the foreign interest rate or the exchange rate would be between three and four quarters.
The results for Singapore are quite different from those for Colombia, with foreign factors clearly playing the dominant role in the determination of the domestic interest rate. The coefficient of the foreign interest rate and expected exchange rate change, 8i, is not significantly different from unity at the 5 percent level. The remaining coefficients in the equation have the expected signs but are all statistically insignificant. This result implies that for all intents and purposes the openness parameter ψ is unity, which is a result one would have expected in the case of Singapore. Domestic monetary developments have no direct effect on the interest rate, although it is possible that they still could have indirect influence through their effect on the forward premium. This particular channel, however, has not been considered here (see Section III). Moreover, because the value of θ is unity, implying that the adjustment of the domestic interest rate is instantaneous and that interest parity is maintained continuously, it is clearly a matter of indifference which of the two specifications for Singapore is considered. Both the equations—that is, with and without the lagged interest rate term—appear equally well specified.
The results reported above were obtained by using the excess supply of real money balances as the appropriate formulation for the monetary disequilibrium term. As mentioned earlier, there are other ways in which a monetary disequilibrium could affect nominal interest rates. For example, it has recently been argued (in Makin (1982), for example) that nominal monetary surprises can have a temporary effect on nominal interest rates. To investigate this proposition, equation (14) was re-estimated by replacing [log mt - log
III. Limitations and Extensions
The model presented here has its limitations and can obviously be expanded in several directions. In this section we briefly discuss four possible extensions: (1) analysis of the determinants of real interest rates in developing countries; (2) analysis of interest rate behavior during the process of liberalization of the capital account of the balance of payments; (3) explicit modeling of the expected rate of devaluation in the context of interest rate behavior in open developing countries; and (4) consideration of the effects of currency substitution. This list is by no means exhaustive; specifically, it does not incorporate various econometric issues that could arise in estimating a model of interest rate determination. Such issues would include, among others, simultaneity, specification of the underlying dynamics, and the proper treatment of the error structure. Here we focus on what we see as the principal theoretical extensions.
Real Interest Rates in Developing Countries
Some recent studies (for example, Cumby and Mishkin (1984)) have empirically analyzed the behavior of real interest rates in industrialized countries, placing special emphasis on whether these rates have tended to equalize across countries. Even if there are no exchange controls, the capital account is fully open, and the nominal arbitrage condition holds, from a theoretical perspective real interest rates can still differ among countries. For example, an expectation of a real depreciation would cause a country to have a higher real interest rate than the rest of the world. 28
The framework discussed in this paper can be easily extended to analyze the process of determination of (ex post and ex ante) real interest rates. Because the ex post real interest rate is defined as the nominal rate minus the actual rate of inflation, a simple way of analyzing this issue is to add an explicit inflation equation to the model.29 The resultant two-equation model could then be used to determine simultaneously the nominal interest rates and the rate of inflation, and the ex post real interest rates can then be directly obtained from these two equations.30 Furthermore, if the inflation equation is used to determine the expected rate of inflation, then one can calculate the ex ante real rate of interest.
To keep within the spirit of the model outlined here, the inflation equation specified should be general enough to allow both closed and open economy factors to play a role. In the extreme case of a fully open economy, domestic monetary conditions will have no direct effect, and the inflation rate will depend solely on foreign inflation and the (actual) rate of devaluation. If, in addition, it is assumed that the expected real exchange rate will remain constant, the model will predict the equality of domestic and foreign real interest rates. If the economy is completely closed, however, the domestic rate of inflation and the nominal and real interest rates will have no relation to their world counterparts.
Interest Rates and Liberalization
One of the limitations of the model presented in this paper is that it assumes a constant degree of openness of the financial sector in the country under study. But several developing countries have recently gone through liberalization processes characterized by, among other things, the relaxation or removal of existing capital controls. To the extent that these liberalization processes yield a higher degree of integration of domestic and world capital markets, the assumption of a constant ψ is clearly inappropriate. 31
There are several possible ways to proceed if the degree of openness is changing over time. The simplest way to model this variation would be to make the openness parameter a linear function of time:
where ψ0 is the constant part of the openness parameter and t is a time trend. We would expect that ψ1 > 0. If the level and intensity of capital controls vary smoothly and gradually over the period of study, then equation (15) would be a reasonable approximation. One could use equation (15) to substitute for ψ in the interest rate equation and then directly estimate the resultant reduced form. This simple form would obviously break down if the changes in capital controls were abrupt or erratic, and it would be necessary to consider other methods to capture the liberalization process formally.
Ideally, of course, one would wish to have some type of index that directly measured the degree of legal capital controls. It would then be possible to specify openness as a function of this index (C):
In the estimation process several alternative functional forms can be assumed. 32 The main problem with this formulation, however, is obtaining data for the capital controls index C. One possible way would be to construct a subjective measure from actual information on the system of capital controls in the country in question. Another approach would be to use some type of proxy measuring the severity of capital controls, such as the black market exchange premium. 33
Expected Devaluation and Interest Rate Determination
No mention has yet been made of the way in which the expected rate of devaluation or the forward premium is determined. For purposes of the present exercise, these were assumed to be exogenous. This is quite a restrictive assumption, and a more realistic analysis would have to recognize that the expected exchange rate change is likely to be affected by movements in domestic interest rates and by domestic monetary conditions in general. But recognizing this issue and actually doing something about it are quite different matters, since in practice endogenizing the expected rate of devaluation or the forward premium has in most cases proved to be exceedingly difficult.
The way to proceed would depend on the exchange rate system operative in the country in question. If the country has a floating exchange rate, standard contemporary theories of exchange rate behavior can perhaps be used. Even so, the task would not be easy because these models have not been particularly successful in predicting exchange rate movements (Levich (1985) has surveyed such models for the major industrial countries). Under fixed rates the problem becomes even more complicated because the probability of an exchange rate crisis would then have to be modeled explicitly. Some initial attempts have been made in this direction, but the modeling of exchange rate crises is still in its infancy (see Blanco and Garber (1983) for one such attempt for Mexico). By and large it seems that the present state of the art of exchange rate modeling would preclude paying anything more than lip service to this particular issue.
Effects of Currency Substitution
In combining the closed economy version of the interest rate model with the open economy formulation, the basic money demand function was left unchanged. Recall that this function allows for substitution to take place between money and domestic financial assets and goods. This substitutability is the appropriate specification for a closed economy, but it does prove to be somewhat restrictive when the possibility of substitution between domestic and foreign money, defined in general as currency substitution, is admitted. In other words, one now has another asset in the system—that is, foreign money, for which the rate of return also has to be taken into account. Thus, in combining the two models one has to recognize that the money demand function in an open economy could be different from that function for a closed economy.
The importance of the phenomenon of currency substitution has been documented in several studies (for example, Ortiz (1983) and Ramirez-Rojas (1985)). In contrast to earlier opinion, which held that currency substitution was relevant only in countries with developed financial and capital markets, these writers have recently shown that currency substitution takes place frequently in developing countries as well. Furthermore, it has been found to occur in countries that differ considerably in the degree of financial development and integration with the rest of the world and in the types of exchange rate regimes and practices. Currency substitution clearly is a factor that should be explicitly taken into account in any realistic analysis.
How one would proceed to model the effects of currency substitution is not, however, all that clear. The general consensus is that the principal determinant of currency substitution is the expected change in the exchange rate, although (as pointed out in the preceding subsection) there is considerable controversy about how it should be measured. Other things being equal, an expected depreciation of the domestic currency, for whatever reason, would cause residents to switch from domestic money into foreign money, and vice versa. Once the difficult problems associated with the choice of an appropriate empirical proxy for exchange rate expectations have been surmounted, however, the rest of the analysis becomes relatively straightforward. The (domestic) money demand function (5) in an open economy could be re-specified as:
The last term in this modified equation would then capture the effects of currency substitution.
This type of formulation would not be applicable in the extreme cases of interest rate determination in completely closed and completely open economies. In a closed economy the variable ė would obviously not enter; in a fully open economy domestic monetary disequilibrium (and thus the demand for money), with or without currency substitution, does not matter. Equation (5a) would certainly be relevant in the intermediate case, which of course does correspond to the actual case in most developing countries.
IV. Conclusions
As more developing countries proceed to liberalize their domestic financial systems and to remove restrictions on capital flows, the issue of interest rate determination becomes increasingly important. In particular, how interest rates can be expected to behave in the changed environment and how they will respond to foreign influences and domestic policies are questions that policymakers in developing countries must consider. Only when interest rate behavior is well understood will it be possible to predict confidently the effects of interest rate changes on key macroeconomic variables such as saving, investment, the balance of payments, and economic growth. To affect these variables is presumably the real purpose for which the liberalization policies were originally designed.
In this paper we have derived a theoretically consistent model that we believe can serve as a starting point for analyzing the process of interest rate determination in those developing countries that have undertaken policies of financial reform. Although the model has a fairly simple structure, it is nevertheless able to incorporate the principal determinants of interest rates, such as foreign interest rates, expected changes in exchange rates, and domestic monetary developments. One of the interesting characteristics of the model is that it is sufficiently general to be applicable to a variety of developing countries that differ widely in their financial openness. Indeed, through the model it is possible to determine empirically, from data for the individual country, the degree of financial openness (defined as both the extent to which domestic interest rates are linked to foreign interest rates and the speed with which domestic rates respond to changes in world rates). This measure of “economic” openness may differ quite significantly from the “official” or “legal” degree of openness implied by the prevailing system of capital controls.
For illustrative purposes the model was applied to two countries—Colombia and Singapore—that, because they are at quite different stages of financial development, provided a useful first test of the general nature of the model. Colombia still maintains restrictions on capital movements, and only part of the financial sector can be characterized as free; Singapore, in contrast, is a highly open economy with a dynamic and sophisticated financial market that has close links with the world’s major financial centers. The estimates from the model confirmed our prior assumptions: we found that both foreign and domestic factors were important in interest rate determination in Colombia, but that only foreign factors appeared to matter in Singapore. Our results also indicated that Colombia is more open than suggested by the actual system of capital controls. In conclusion, although one should obviously be careful in generalizing from the results for only two countries, we nonetheless feel that this model has considerable potential and can serve as a useful starting point for studying the behavior of interest rates in developing countries.
APPENDIX: Data Sources and Definitions
This Appendix briefly gives the major sources of the country data and defines the principal variables used in the model.
Colombia (1968-82)
The basic sources for the data were Montes and Candelo (1982); Dirección Nacional de Planeación (DNP); Dirección Administrativa Nacional de Estadística (DANE), Boletín Mensual de Estadística (Bogotá), various issues; and International Financial Statistics (IFS), International Monetary Fund (Washington), various issues.
The definitions of the variables and specific sources are as follows:
| ė | Percentage change in the official buying rate for export receipts and capital inflows (Montes and Candelo (1982), and DNP) |
| i | Domestic interest rate: for 1968-69, the average rate on mortgage bills, for 1970-82, the effective annual yield on three-month certificados de abono tributario, or tax certificates (Montes and Candelo (1982) and DNP) |
| i* | Three-month U.S. Treasury bill rate (IFS) |
| M | Narrow (Ml) money balances: for 1968-80, data are from Montes and Candelo (1982); for 1981-82, from DNP |
| P | Consumer price index (DANE, Boletín Mensual de Estadística); π is defined as the percentage change in this index |
| y | Quarterly real gross domestic product (GDP; Montes and Candelo (1982)); updated through 1982. |
| ė | Percentage change in the official buying rate for export receipts and capital inflows (Montes and Candelo (1982), and DNP) |
| i | Domestic interest rate: for 1968-69, the average rate on mortgage bills, for 1970-82, the effective annual yield on three-month certificados de abono tributario, or tax certificates (Montes and Candelo (1982) and DNP) |
| i* | Three-month U.S. Treasury bill rate (IFS) |
| M | Narrow (Ml) money balances: for 1968-80, data are from Montes and Candelo (1982); for 1981-82, from DNP |
| P | Consumer price index (DANE, Boletín Mensual de Estadística); π is defined as the percentage change in this index |
| y | Quarterly real gross domestic product (GDP; Montes and Candelo (1982)); updated through 1982. |
Singapore (1976-83)
The sources of the data are IFS and the Monetary Authority of Singapore (MAS), Monthly Bulletin (Singapore), various issues.
The definitions and specific sources are as follows:
| ė | Three-month forward premium (MAS) |
| i | Three-month interbank rate (MAS) |
| i* | Three-month Eurodollar rate (IFS) |
| M | Narrow (Ml) money balances (IFS) |
| P | Consumer price index (IFS); the variable π is defined as the percentage change in this index |
| y | Quarterly real GDP; the annual series were obtained from IFS and interpolated to a quarterly basis using an index of manufacturing production, also from IFS. |
| ė | Three-month forward premium (MAS) |
| i | Three-month interbank rate (MAS) |
| i* | Three-month Eurodollar rate (IFS) |
| M | Narrow (Ml) money balances (IFS) |
| P | Consumer price index (IFS); the variable π is defined as the percentage change in this index |
| y | Quarterly real GDP; the annual series were obtained from IFS and interpolated to a quarterly basis using an index of manufacturing production, also from IFS. |
REFERENCES
Blanco, Herminio, and Peter M. Garber, “Recurrent Devaluation and Speculative Attacks on the Mexican Peso” (unpublished; Rochester, New York: University of Rochester, December 1983).
Blejer, Mario I., “Interest Rate Differentials and Exchange Risk: Recent Argentine Experience,” Staff Papers, International Monetary Fund (Washington), Vol. 29 (June 1982), pp. 270–80.
Blejer, Mario I., and Mohsin S. Khan, “The Foreign Exchange Market in a Highly Open Developing Economy: The Case of Singapore,” Journal of Development Economics (Amsterdam), Vol. 12 (February-April 1983), pp. 237–49.
Blejer, Mario I., and José Gil Diaz, “On the Determination of the Real Interest Rate in a Small Open Economy: Domestic Versus External Factors” (unpublished; Washington: International Monetary Fund, 1985).
Cumby, Robert E., and Maurice Obstfeld, “A Note on Exchange-Rate Expectations and Nominal Interest Differentials: A Test of the Fisher Hypothesis,” Journal of Finance (New York), Vol. 36 (June 1981), pp. 697–703.
Cumby, Robert E., and Frederic S. Mishkin, “The International Linkage of Real Interest Rates: The European-U.S. Connection” (unpublished; New York: New York University, 1984).
Darby, Michael R., “The Financial and Tax Effects of Monetary Policy on Interest Rates,” Economic Inquiry (Long Beach, California), Vol. 13 (June 1975), pp. 266–76.
Diaz-Alejandro, Carlos F., Colombia (New York: Columbia University Press for the National Bureau of Economic Research, 1976).
Diaz-Alejandro, Carlos F., “Southern-Cone Stabilization Plans,” in Economic Stabilization in Developing Countries, ed. by William R. Cline and Sidney Weintraub (Washington: Brookings Institution, 1981), pp. 119–41.
Dornbusch, Rudiger (1982a), “PPP Exchange-Rate Rules and Macroeconomic Stability,” Journal of Political Economy (Chicago), Vol. 90 (February), pp. 158–65.
Dornbusch, Rudiger (1982b), “Stabilization Policies in Developing Countries: What Have We Learned?” World Development (Oxford, England), Vol. 10 (September), pp. 701–08.
Edwards, Sebastian (1985a), “Money, the Rate of Devaluation, and Interest Rates in a Semi-Open Economy: Colombia, 1968-1982,” Journal of Money, Credit and Banking (Columbus, Ohio), Vol. 17 (February), pp. 59–68.
Edwards, Sebastian (1985b), “Stabilization with Liberalization: An Evaluation of Ten Years of Chile’s Experiment with Free-Market Policies, 1973-1983,” Economic Development and Cultural Change (Chicago), Vol. 32 (January), pp. 223–54.
Fama, Eugene F., “Short-Term Interest Rates as Predictors of Inflation,” American Economic Review (Nashville, Tennessee), Vol. 65 (June 1975), pp. 269–82.
Frenkel, Jacob A., and Richard M. Levich, “Covered Interest Arbitrage: Un-exploited Profits?” Journal of Political Economy (Chicago), Vol. 83 (April 1975), pp. 325–38.
Frenkel, Jacob A., and Richard M. Levich, “Transactions Costs and Interest Arbitrage: Tranquil Versus Turbulent Periods,” Journal of Political Economy (Chicago), Vol. 85 (December 1977), pp. 1209–26.
Fry, Maxwell J., “Models of Financially Repressed Developing Economies” World Development (Oxford, England), Vol. 10 (September 1982), pp. 731–50.
Hanson, James A., and Jaime de Melo, “External Shocks, Financial Reforms, and Stabilization Attempts in Uruguay: 1974-1983,” World Development (Oxford, England), Vol. 13 (forthcoming, August 1985).
Harberger, Arnold C., “The Chilean Economy in the 1970s: Crisis, Stabilization, Liberalization, Reform,” in Economic Policy in a World of Change, ed. by Karl Brunner and Allan M. Meltzer, Carnegie-Rochester Conference Series on Public Policy, Vol. 17 (Amsterdam: North-Holland, 1982; New York: Elsevier, 1982), pp. 115–52.
International Monetary Fund, Annual Report on Exchange Arrangements and Exchange Restrictions, 1984 (Washington, 1984).
Khan, Mohsin S., “The Dynamics of Money Demand and Monetary Policy in Singapore,” in Monetary Authority of Singapore, Papers on Monetary Economics (Singapore: Singapore University Press for the MAS, 1981), pp. 46–76.
Lanyi, Anthony, and Rüşdü Saracoglu, “The Importance of Interest Rates in Developing Economies,” Finance & Development (Washington), Vol. 20 (June 1983), pp. 20–23.
Levich, Richard M., “Empirical Studies of Exchange Rates: Price Behavior, Rate Determination and Market Efficiency,” in Handbook of International Economics, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985; New York: Elsevier, 1985), pp. 979–1040.
Lizondo, José Saul, “Interest Differential and Covered Arbitrage,” in Financial Policies and the World Capital Market: The Problems of Latin American Countries, ed. by Pedro Aspe Armella, Rudiger Dornbusch, and Maurice Obstfeld (Chicago: University of Chicago Press, 1983), pp. 221–40.
McKinnon, Ronald I., Money and Capital in Economic Development (Washington: Brookings Institution, 1973).
Makin, John H., “Effects of Inflation Control Programs on Expected Real Interest Rates,” Staff Papers, International Monetary Fund (Washington), Vol. 29 (June 1982), pp. 204–32.
Mathieson, Donald J., “Inflation, Interest Rates, and the Balance of Payments During a Financial Reform: The Case of Argentina,” World Development (Oxford, England), Vol. 10 (September 1982), pp. 813–28.
Mathieson, Donald J., “Estimating Models of Financial Market Behavior During Periods of Extensive Structural Reform: The Experience of Chile,” Staff Papers, International Monetary Fund (Washington), Vol. 30 (June 1983), pp. 350–93.
Melvin, Michael, “The Vanishing Liquidity Effect of Money on Interest Rates: Analysis and Implications for Policy,” Economic Inquiry (Long Beach, California), Vol. 21 (April 1983), pp. 188–202.
Montes, Gabriel, and Ricardo Candelo, “El enfoque monetario de la balanza de pagos: El caso de Colombia, 1968-1980,” Revista de Planeación y Desarrollo (Bogotá), Vol. 14 (May-August 1982), pp. 11–40.
Mundell, Robert A., “Inflation and Real Interest,” Journal of Political Economy (Chicago), Vol. 71 (June 1963), pp. 280–83.
Ortiz, Guillermo, “Currency Substitution in Mexico: The Dollarization Problem,” Journal of Money, Credit and Banking (Columbus, Ohio), Vol. 15 (May 1983), pp. 174–85.
Ramirez-Rojas, C. Luis, “Currency Substitution in Argentina, Mexico, and Uruguay” (unpublished; Washington: International Monetary Fund, 1985).
Sjaastad, Larry A., “Failure of Economic Liberalism in the Cone of Latin America,” World Economy (Oxford, England), Vol. 6 (March 1983), pp. 5–26.
Tanzi, Vito, “Inflation, Indexation and Interest Income Taxation,” Quarterly Review, Banca Nazionale del Lavoro (Rome), No. 116 (March 1976), pp. 64–76.
Tanzi, Vito, “Inflationary Expectations, Economic Activity, Taxes, and Interest Rates,” American Economic Review (Nashville, Tennessee), Vol. 70 (March 1980), pp. 12–21.
Townsend, Robert M., “Financial Structure and Economic Activity,” American Economic Review (Nashville, Tennessee), Vol. 73 (December 1983), pp. 895–911.
van Wijnbergen, Sweder, “Interest Rate Management in LDCs,” Journal of Monetary Economics (Amsterdam), Vol. 12 (September 1983), pp. 433–52.
Wiesner, Eduardo, “Devaluación y mecanismo de ajuste en Colombia,” in Política económica externa Colombiana, ed. by Eduardo Wiesner (Bogotá: Asociación Bancaria de Colombia, 1978).
Zahler, Roberto, “Recent Southern Cone Liberalization Reforms and Stabilization Policies: The Chilean Case, 1974-1982,” Journal of Interamerican Studies and World Affairs (Beverly Hills, California), Vol. 25 (November 1983), pp. 509–62.
Professor Edwards was a consultant with the Research Department when this paper was written. He is currently with the University of California, Los Angeles, and with the National Bureau of Economic Research. He is a graduate of the Universidad Católica de Chile and of the University of Chicago.
Mr. Khan, Advisor in the Research Department, is a graduate of Columbia University and of the London School of Economics and Political Science.
See, for example, McKinnon (1973), Fry (1982), Lanyi and Saracoglu (1983), Mathieson (1983), and Townsend (1983); for a contrary view, see van Wijnbergen (1983).
This subject has been addressed by, among others, Diaz-Alejandro (1981), Edwards (1985b), Hanson and de Melo (1985), Harberger (1982), Sjaastad (1983), and Zahler (1983).
The only studies we are aware of that include both open economy and domestic monetary factors in the analysis of interest rates are Mathieson (1982, 1983), on Argentina and Chile respectively; Blejer and Gil Diaz (1985) and Hanson and de Melo (1985) on Uruguay; and Edwards (1985a) on Colombia.
Even if the capital account of the balance of payments is closed but there is some trade with the rest of the world, open economy factors can still indirectly affect domestic interest rates. For example, a terms of trade shock can produce changes in real income and prices that will affect the domestic demand for credit and, thus, equilibrium interest rates.
Until now most studies that have analyzed the effect of stabilization policies on output, prices, and the balance of payments in developing countries have not included the interest rate as a possible transmission mechanism. The main reason for this omission is that the experience with liberalized capital markets is still relatively recent. A theoretical discussion, however, of the effects of a stabilization program working through increases in real interest rates is contained in Dornbusch (1982b).
We are ignoring here, for example, the effects of taxation on the relation between expected inflation and the nominal interest rate. On this topic see Darby (1975), and Tanzi (1976).
Note that EMSt could also affect
Recent empirical studies on interest rate behavior in the United States include, among others, Fama (1975), Tanzi (1980), Makin (1982), and Melvin (1983).
In this formulation the weights of the lag distribution are not assumed to follow any specific pattern.
These would be the empirical representations of the rational expectations model in which economic agents are assumed to take into account all available information in forming their (conditional) expectations.
Note that equation (4) is only one of the alternative ways to specify excess money supply, or monetary disequilibrium. For example, it can be postulated that only money surprises will influence the real interest rate (Makin (1982)). In such a case EMS would have to be replaced by some proxy of unanticipated monetary changes in equation (2).
Of course, one could also introduce an “own” rate of return into the money demand formulation. This would certainly be advisable when dealing with broad definitions of money that include deposits paying positive rates of interest (see Mathieson (1982, 1983)). Because we work with narrow money (currency plus demand deposits) throughout, in our case this omission is obviously not serious, since demand deposits typically are non-interest-bearing.
Introducing the forward premium into the specification in place of the expected change in the exchange rate implies, of course, that the forward premium is a good approximation of the change in the future spot exchange rate.
From a methodological point of view, even if interest-parity arbitrage differentials are white noise it is still possible that other variables, besides the world interest rate and the expected rate of devaluation, will affect the domestic interest rate. For this reason a more appropriate procedure is to test directly whether other variables suggested by the theory have an effect on it.
In a more recent study of Uruguay, Blejer and Gil Diaz (1985) found that the risk premium was highly serially correlated.
During the period when the parity condition does not exactly hold there would obviously be unexploited profit opportunities. The attempts by transactors to take advantage of these opportunities would set in motion the very forces that would bring about equality between domestic and foreign interest rates (adjusted for expected exchange rate changes). How long this process takes is an empirical question and would have to be estimated from the data.
It is, of course, assumed here that the degree of openness (Ψ) is constant over time. The implications of relaxing this assumption, and the possible procedures for doing so, are considered in Section III.
Strictly speaking, in the shift from the closed economy to the open economy case the demand for money function should be generalized to allow for foreign interest rates, the expected change in the exchange rate, or both. A suggested procedure for doing so is presented in Section III (under “Effects of Currency Substitution”).
Note that when θ = 1 the lagged interest rate term would drop from the specification, so that the equilibrium model is only a restricted version of this formulation.
Note that an equation of the form of equation (14) can be derived from a portfolio model with imperfect substitutability between domestic and foreign assets.
First of all, there are few developing countries that can be viewed as completely closed; second, those that would qualify do not have developed financial systems with market-determined interest rates.
See International Monetary Fund (1984) for a detailed description of the nature and extent of capital controls in Colombia.
Even before 1978 there were no limits on residents’ investments in the Scheduled Territories (comprising the former Sterling Area). Because Hong Kong was included in the Scheduled Territories, residents could, in theory, transfer funds anywhere via the Hong Kong market, so that this restriction was not particularly effective.
Experiments with alternative approximations for the expected exchange rate, such as the fitted values from a distributed lag function of the actual exchange rate, yielded broadly similar results. This is to be expected because in Singapore the forward rate has been a reasonably good predictor of the future spot exchange rate. See Blejer and Khan (1983).
Using the actual rate of inflation (that is, the perfect foresight model) did not produce any significant differences in the results.
This assumption is consistent with independent empirical evidence on the demand for money relation for both countries—for example, Montes and Candelo (1982) for Colombia, and Khan (1981) for Singapore.
Recall that the sign of the reduced-form coefficient for expected inflation (δ4) was ambiguous; the result in Table 1 indicates that λ(1 - β)(α2 + α3) < 1.
On the relation between real exchange rates and real interest rates, see Dornbusch (1982a).
Note that the adjustment equation (6) in our model could be interpreted as an inflation equation, although we do not explicitly do so.
Blejer and Gil Diaz (1985) specify a two-equation model for the real interest rate and inflation. Their model, of course, can be used to determine the nominal interest rate as well.
Note also that ψ would depend on the interest rate chosen. For different interest rates one could easily have different values of ψ. We are indebted to Michael Mussa for this point.
In formulating such equations, one has to recognize that the endogenous variable (ψ) is bounded (0,1). For this constraint to be taken properly into account, the precise functional forms would be more complicated than the linear ones described here.
A problem with the black market premium is that it will tend to capture a variety of factors, including the effect of actual and expected capital controls.
