Convertibility Risk: The Precautionary Demand for Foreign Currency in a Crisis
  • 1 0000000404811396 Monetary Fund

Contributor Notes

This paper presents theoretical work linking money demand to the perceptions of households about the risk that domestic currency may become inconvertible or that it may be devalued. An empirical investigation of the size of this effect is carried out using both cross section data and then monthly data for Korea to estimate an augmented demand for money equation. It is found that the fear of inconvertibility arising from the 1997 Korean currency crisis may have caused broad money demand to fall by 4-5 percentage points, equivalent to the loss of reserves of $6-72 billion (or about 30 percent of reserves as measured at end-November 1997).


This paper presents theoretical work linking money demand to the perceptions of households about the risk that domestic currency may become inconvertible or that it may be devalued. An empirical investigation of the size of this effect is carried out using both cross section data and then monthly data for Korea to estimate an augmented demand for money equation. It is found that the fear of inconvertibility arising from the 1997 Korean currency crisis may have caused broad money demand to fall by 4-5 percentage points, equivalent to the loss of reserves of $6-72 billion (or about 30 percent of reserves as measured at end-November 1997).

I. Introduction

Understanding the forces driving currency crises is a key task for the international community, especially in the aftermath of several such episodes affecting emerging markets in the second half of the 1990s. To identify countries with vulnerabilities to crises, several well established indicators are being used, such as a large current account deficit, sustained loss of competitiveness, and low external reserves. Work on Early Warning Systems (EWS) has produced econometric evidence underscoring the usefulness of such indicators in predicting foreign exchange crises (see Berg et al, 2000).

Despite these advances, however, the specific channels through which currency crises are propagated remain less well understood, weakening policymakers’ ability to design appropriate preventive policies. One challenge is how to decide which set of vulnerability indicators is the most relevant for a particular country, and the work on EWS, although useful, is based much more on statistical concepts than on a well understood theoretical framework. Hence, even ex post, it is often difficult to assign a quantitative weight on the importance of various factors in explaining the incidence and severity of a crisis.

The theory of currency substitution can provide an organizing framework in the search for early warning indicators and effective policy responses to currency crises. At an abstract level, currency substitution can be expected to intensify when the quality of the currency in the future comes into question. The quality of the currency, in turn, may be compromised either because of increased devaluation risk or because future access to foreign currency for transactions or other purposes is put into question even if the official parity is maintained (inconvertibility risk). Either way, the public’s portfolio will shift in favor of foreign currencies if it comes to question the continued commitment of the monetary authorities to sustain the value of the domestic currency in terms of its purchasing power over domestic and foreign goods. In particular, domestic residents will respond to a heightened risk of interference with normal market access or devaluation by self-insuring through the buildup of foreign currency hoards. Such precautionary demand for foreign currency will manifest itself in a simultaneous drop in the demand for domestic money and shrinkage of the central bank’s reserve assets.

In this paper, we illustrate the impact of increased currency risk on the precautionary demand for foreign currency and the effectiveness of monetary policy, including an interest rate defense and devaluation, using a simple two-period optimizing model of currency substitution. We find that as long as the demand for foreign goods underlying the demand for foreign currency satisfies an Inada condition, an interest rate defense is not very helpful as a response to inconvertibility risk. When market access to foreign exchange is unquestioned, on the other hand, the portfolio shift generated by heightened devaluation risk can be much more effectively dealt with by an interest rate defense.

This basic lesson is worth elaboration. First, in the face of increased currency pressures the authorities may face incentives to limit the quantities of foreign exchange they make available in the foreign exchange market. But nonmarket measures to “conserve” their reserves are likely to be counterproductive. Anything the authorities may do to impair the actual purchasing power of the currency, for example by infringing the ability of domestic residents to freely convcrt local into foreign currency, will enhance the fears of domestic residents. Perversely, effective rationing may hasten the very flight from domestic currency the monetary authorities seek to avoid. One might describe impaired convertibility as a “limping” currency standard. See, for example, Aliber (1973) and McKinnon (1974) where the impaired gold-dollar link is named the “limping” dollar standard. In these circumstances, it is preferable for the authorities to attack the direct causes of the problem by restoring full convertibility, albeit at a depreciated exchange rate.

More importantly, the focus on inconvertibility risk for current transactions requires explanation. Even though the convertibility of currencies under attack for current payments has not been an issue in a formal sense in recent crises, anecdotal evidence suggests that de facto suspensions did occur in some crisis countries. When fixed parities came to be doubted, the monetary authorities in more than one country responded by limiting market participants’ ability to obtain foreign currency rather than by letting their currency float. In Korea, in the height of the crisis in December 1997, for instance, trading sessions in the exchange market were extremely short. The market would open at 10 am every morning, immediately drop 5 percent (the allowable band), and close in about 10 minutes, leaving many unsatisfied dollar buyers. Likewise, in Russia in 1998, where convertibility was generally maintained in the days before the August 17, 1998 devaluation, some banks resorted to freezing dollar withdrawals and closed exchange points (Oxford Analytica, 1998). After the attempt at controlled devaluation failed, foreign exchange trading was brought to a halt on August 26 when the Central Bank of Russia (CBR) terminated the fixing of the exchange rate in the Moscow International Currency Exchange (M1CEX) auctions.1 The foreign exchange market reopened on September 3 after the CBR had abolished the exchange rate band the previous day and let the exchange rate float.2 The situation in Ukraine in the fall of 1998 was broadly similar3 Similarly, in Argentina on December 1, 2001, in response to a surge in the demand for U.S. dollars, the authorities limited domestic residents’ access to dollars through the imposition of banking and exchange controls designed to protect currency convertibility, interfering with normal business activity.4 Despite these steps, the crisis did not abate.

Despite such informal evidence, establishing the empirical relevance of inconvertibility risk—as opposed to devaluation risk or the risk of capital controls—is not straightforward. Our econometric approach is twofold. First, we estimate a simple demand for money equation in which we include variables that capture actual or expected inconvertibility. This cross section demand for money function takes the form of a velocity equation, augmented to include a dummy variable reflecting the presence or absence of current account convertibility, measuring the long-run negative effect of inconvertibility on the demand for money. Second, we modify a conventional time series money demand equation for Korea by including variables linked to the probability that domestic currency becomes inconvertible. Such variables are helpful in explaining money demand, and especially the large drop around the time when the foreign exchange crisis afflicted Korea (toward the end of 1997). We also conduct a counterfactual simulation to measure the impact of these “crisis” variables on money demand. These results are then contrasted with empirical findings on the effects of inconvertibility from a cross-sectional data based approach. Finally, conclusions are drawn regarding the quantitative importance of inconvertibility in crises, as well as more tentative conclusions on how to design policies to minimize external vulnerability given the findings in this paper.

II. A Model of Currency Inconvertibility

A. The Model

Consider a small open economy that lasts for two periods, t and t+1. A large number of representative agents consume two nonstorable goods at t+1, an internationally tradable domestic good x and an imported good y. The utility function u(xt+1,yt+1) exhibits positive and diminishing marginal utilities and satisfies the Inada conditions for both goods. Each agent is endowed with W units of good x in period l. Households are subject to a cash-in-advance constraint: purchases of domestic goods at t+1 must be made using domestic currency while purchases of imported goods must be made with foreign currency. Home currency is available in the date-t home-country currency market at unit price 1/pt in terms of goods, that is determined by domestic market conditions. Real domestic balances ht/pt yield a gross return R>1 in real terms. Agents may also access the foreign exchange market at date t to purchase foreign currency balances f at an exchange rate that is pegged to unity. If currency convertibility is maintained, households can buy or sell accumulated currency balances at t+1 before they purchase goods. If convertibility is suspended, on the other hand, households must rely on accumulated foreign currency balances to buy imported goods at t+1. Accumulating foreign currency assets, which pay a gross return of unity in foreign currency terms, is beneficial because of the risk that the convertibility of the domestic currency will be suspended at t+1. We let αt+1 ∈ [0,1] denote the probability that households will be unable to convert their holdings of domestic currency into foreign currency in period t+1. This could arise, for instance, if the monetary authority runs short of foreign exchange and rations its availability rather than allowing its price to rise to clear the market.

The decision problem facing a household entering period t is to maximize


subject to the following constraints: At date t,


At date t+1, with probability 1-αt+1,


At date t+1, with probability αt+1,


We let mtht/pt denote real domestic currency balances, πt ≡(pt+1pt)/pt home-country inflation, and Rt ≡ (1 + it)/(1 +πt) the gross return of domestic currency, where it is the net nominal net rate of interest on domestic asset holdings. The quantity bt+1 is the planned purchases (sales if negative) of foreign currency in the spot foreign exchange market in period t+1 if convertibility is maintained.

Using the budget constraints, utility can be written in terms of the asset demands as follows.


As a preliminary exercise, consider the situation in which the risk of inconvertibility is zero, αt+1 = 0. In this case, the problem is simply to maximize u [(Wft)Rtbt+1,ft +bt+1 ]. If Rt > 1 and the agent cannot borrow foreign-currency assets at t, the agent will select ft = 0, mt = W and bt+1 solves max u[WRtbt+1,bt+1].5 Stated differently, if the domestic real interest rate is positive, precautionary demand for foreign currency will be zero and foreign currency balances needed for imports will be met from the spot foreign exchange market.

An example illustrates the currency demand schedules obtained in this framework. Suppose utility is logarithmic, u(x, y) = γ ln(x)+(1−γ)ln(y) and there is no convertibility risk. Then demand schedules for domestic and foreign goods are x = γ [f + R(Wf)] and y =(1−γ)[f + R(W−f)]. Utility is U(f) = γ log(γ) + (1 − γ) log(1 − γ) + log [f + R(Wf)], implying that U′(f) = (1 − R) [f + R(Wf)]-1 < 0 if R > 1. Abstracting from short sales, if αt+1 = 0 we have a corner solution, f=0, and a plan for spot demand for foreign currency at t+1 of bt+1 = (1 − γ )RtW. At the other extreme, if inconvertibility is deemed inevitable, domestic households must plan to pay for their imports exclusively by building up precautionary balances of foreign currency, i.e., bt-1 =0 and ft maximizes u[(Wft)Rt, ft]. From the Inada conditions, the solution for ft is interior and satisfies the usual intertemporal condition u2u1[(Wft)Rt,ft]=Rt which, in the case of logarithmic utility, gives ft =(1 −γ)W.

More generally, if α is positive but less than unity, ft will be positive because of the Inada condition on good y, which requires that ∂u/∂y→∞ as y → 0. The first order conditions for an interior optimum are:


The first condition simply reflects equality of the marginal rate of substitution of goods x and y to their relative price in the convertibility state:


The second condition, equation (6), reflects the household’s weighing of risk and return from holding safe but barren foreign currency and productive but risky domestic currency balances. Substituting (7) into (6) and simplifying yields an implicit precautionary demand schedule for foreign currency:


Total differentiation with respect to αt+1 and using the notation u1 = u(x1, y1), etc., yields


since the denominator is negative. Thus an increased risk of currency inconvertibility leads to increased precautionary holdings of foreign currency assets at the expense of domestic money.

This result can be illustrated with a CES utility function with elasticity of substitution between home and foreign goods θ = 0.8, R = 1.2, W = 10, and the share of home goods in the utility function γ = 0.7. As the risk of inconvertibility rises, the share of assets held in foreign currency rises from near zero to almost 30 percent (Figure 1).

Figure 1.
Figure 1.

Inconvertibility Risk: Share of Assets Held in Foreign Currency

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

Note that the volume of transactions in the spot market, b, declines and the precautionary demand for foreign currency, f, rises as the crisis probability increases. This suggests that changes in the volume of transactions in the spot market could contain useful information for the probability of crisis—an insight derived from the model which may be useful in designing early warning systems. Note, in addition, that the precautionary demand for foreign currency rises sharply with the probability of crisis. While this result holds for a general utility function, it can be illustrated nicely in the case of logarithmic preferences. If u(x, y) = ln(x) + δ ln(y), where δ > 0 is the weight of imported goods, asset demands are:


where the solution f <1 is the smaller root of the quadratic in equation (11). The precautionary demand for foreign currency rises sharply with the probability of crisis. At a 5 percent real interest rate, agents facing a five percent crisis probability put 25 percent of their wealth in precautionary foreign currency balances. If the crisis probability rises to about 50 percent, the share of foreign currency in the household’s portfolio rises to 40 percent. While these particular numbers refer to the Cobb-Douglas case, the main result—that the share of foreign currency assets rises steeply as the probability of crisis rises above zero—is robust so long as an Inada condition applies on the consumption of imported goods. This condition is clearly realistic in most developing country contexts. The example also illustrates that the precautionary demand for foreign currency is higher the larger is the weight of imports in preferences. Hence, the vulnerability due to inconvertibility risk is greater the more dependent on imports an economy is. Finally, the example illustrates that the opportunity cost of holding foreign currency depends on the real domestic interest rate. We now turn to examine this issue in detail.

B. An Interest Rate Defense

A central bank’s main weapon during a currency crisis is to raise its short-term policy interest rate, which raises demand for domestic assets and tends to avert or at least delay the crisis. The feasibility and optimality of raising interest rates to counter a currency crisis is the subject of a growing literature. Krugman (1979) assumed that the central bank is passive. Flood and Jeanne (2000) analyzed an interest rate defense in the Krugman-Flood-Garber model and concluded that its is never effective. In their model, an interest rate defense worsens the fiscal situation and helps bring about the crisis forward. Drazen (1999) and Végh and Lahiri (2000) argue that the relationship between the exchange rate and the interest rate is nonlinear. In Drazen’s model, in which higher interest rates have signaling effects, higher interest rates may indicate either that the authorities are more or less able to defend a peg depending on speculators’ information sets. Vègh and Lahiri focus on the output and budgetary costs of an interest rate defense in a shopping-time model in which non-cash, interest-bearing financial assets are part of money demand. They find that raising interest rates beyond a certain point raises public debt service or lowers output and could bring forward the crisis.

In our model, an interest rate defense of the domestic currency could be effective in offsetting the increase in precautionary demand for foreign currency associated with an increase in the probability of a crisis. Unfortunately, however, this strategy is most effective when the probability of crisis is low, which is when it is least needed. For example, when the probability of a crisis is 5 percent, a tripling of real interest rates from 10 to 30 percent is sufficient to halve f from 16 to 8 percent of income. At high crisis probabilities, on the other hand, even very large increases in real interest rates cannot fully offset the resulting increase in the precautionary demand for foreign currency. If a rises to 50 percent, for example, hiking interest rates to 1000 percent succeeds in lowering f from nearly 40 percent to only 30 percent of income. Things are nearly impossible for the monetary authority if the convertibility crisis is viewed as nearly inevitable. In such cases, even massive increases in real interest rates would be incapable of reversing the currency shift and would likely involve large economic and budgetary costs. Again, while the specific numbers depend on the particular utility function, the general result— the ineffectiveness of an interest rate defense to stem flight from the domestic currency when inconvertibility risk is high—is due to the Inada condition on imported goods. This result is therefore robust to the specification of the utility function.

The main message of this analysis is that it is absolutely crucial for the monetary authorities to deal with the root causes of currency flight by allaying the fears feeding domestic residents’ precautionary demand for foreign currency. Convertibility could be promoted by abandoning the currency peg at once (as discussed in Section III), in which case the required depreciation of the currency would be dictated by the elasticity of supply of foreign currency with respect to the price. However, if the central bank is not willing to allow the exchange rate to fluctuate enough to elicit the needed supply (or dampen the demand sufficiently) then the remaining options are for the central bank to (a) initiate adjustment via some combination of interest rates, expenditure restriction, or devaluation; possibly in conjunction with an IMF-supported program of financial stabilization that provides the government a financing package from the IMF and other official creditors.

Figure 2.
Figure 2.

Interest Rate Defense: The Share of Assets Held in Foreign Currency *

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

*Cobb-Douglas preferences u(x, y) = ln(x) + δ ln(y), δ = 0.7, R varies from 1.05 to 10.

III. Devaluation Risk

In this section we consider devaluation as an alternative to imposing inconvertibility. While in principle devaluation risk could exist in parallel (and be positively or negatively correlated) with convertibility risk, it is of some interest to compare the impact on the demand for domestic assets of a devaluation as an alternative to declaring the currency inconvertible. We show that while devaluation risk also generates a precautionary demand for currency, the strength of the asset substitution it induces is weaker and can be more easily countered via an interest rate defense. Moreover, the extent of devaluation can be traded off with the magnitude of the interest rate defense.

The setup is as described in the inconvertibility case. The value of the domestic currency in terms of U.S. dollars at the planning stage is still fixed at unity: et, = 1; domestic agents expect the currency peg to be maintained with some probability: et+1 = 1 with probability l-αt+1, and 0 < et+1 < 1 with probability αt+1. Agents are competitive in the spot market for foreign exchange, so they can buy or sell unlimited amounts of domestic for foreign currency. They are also able to borrow unlimited amounts at the prevailing interest rate, subject only to their wealth constraint. Households maximize (1) subject to (2) and

The setup is as described in the inconvertibility case. The value of the domestic currency in terms of U.S. dollars at the planning stage is still fixed at unity: et, = 1; domestic agents expect the currency peg to be maintained with some probability: et+1 = 1 with probability l-αt+1, and 0 < et+1 < 1 with probability αt+1. Agents are competitive in the spot market for foreign exchange, so they can buy or sell unlimited amounts of domestic for foreign currency. They are also able to borrow unlimited amounts at the prevailing interest rate, subject only to their wealth constraint. Households maximize (1) subject to (2) and


This problem can again be solved in two steps. We begin by deriving household decision rules (the b’s), taking as given the first-stage choices (f and m). Then the first stage decision rules are derived taking into consideration agents’ second-stage best responses. In the second stage agents treat mt, ft and et+1i as given and select bt+1i to maximize


The solution bt+1i=bt+1i(ft,et+1i) satisfies


In the first stage, agents choose mt, and ft to maximize expected utility taking into account their choices of bt+1i. Expected utility as a function of ft is:


In this problem f is the safe asset that earns a gross dollar return of 1 and m is the risky asset earning a dollar return R > 1 with probability 1 −α and R · e with probability α. An interior solution exists if foreign currency is not dominated in rate of return: if e · R were greater than or equal to 1, agents would face incentives to borrow arbitrarily large amounts of foreign currency during the planning period, invest the proceeds in domestic assets and enjoy arbitrarily large expected utility: eRt ≥I ⇒ ft = −∞, mt = + ∞. On the other hand, demand for domestic assets would vanish if the expected return of m were equal to the return of the safe asset: (1−α)Rt +αeRt=1 ⇒ mt = 0. Moreover, Rt < (1 − α+ αe)−1 implies mt < 0 and ft > W. In this last case, agents would sell their entire endowment plus borrowed funds in the foreign exchange market and hoard the foreign exchange proceeds. In light of these considerations, an interior solution in which eRt < 1 is characterized by


Using the FONC for the second-stage problem to simplify this expression leads to the following tangency condition, which can be used to derive the precautionary demand for f:


From equation (20) it is evident that the demand for f will depend on the difference between the expected returns on foreign and domestic currency assets:


IV. A CRRA Economy

A. Currency Demands

Analytical solutions to the portfolio problem are possible for the CRRA class of preferences. Let u(x,y)=x1σ1σ+δy1σ1σ, σ ≠ 1; and u(x, y) = log(x) + δ log(y), σ = 1. If σ > 0, these preferences feature risk aversion and lead to smooth asset demands that correspond to the ones described in Sargent (1987), Chapter 8. Consumer demands in state i = 1, 2 are


These schedules are positive in the f-interval f0ff1, where f0eR1eRW, f1RR1W. Assuming f0ff1, Expected Utility is a strictly concave function of f if and only if σ > 0. In this case the unique maximum f* is given by


where the parameter ρ > 0 is defined by


The value of ρ depends on the preference parameter σ and the extent of devaluation e. ρ=1 if σ =1, while ρ > 1 if σ > 1 and e < 1.

As can be seen from (23), f depends on the difference (actually the ratio of) the expected returns on foreign and domestic currency assets α(e−1R) + (1−α)(1 − R).

In the log case σ = ρ = 1, and (34) reduces to f*WR[αR11αe1R].

B. Comparative Statics

Comparative static exercises were conducted by varying the parameters (α, e, R, σ): Figure 3 draws a family of demand schedules for foreign currency, one for each value of σ, as function of the probability of crisis α. The calculations assume a 40 percent devaluation (e=0.6) and a 20 percent domestic real interest rate (R= 1.2).

Figure 3.
Figure 3.

Devaluation Risk: Share of Assets Held In Foreign Currency

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

Several properties of the/fschedules stand out: (1) As in the inconvertibility case, the share of foreign currency in the optimal portfolio rises with the probability of devaluation. (2) However, unlike the inconvertibility case, where f > 0 for all values of α, in the devaluation case f <0 for “low” values of the crisis probability. (3) Higher values of σ reduce the amount of foreign currency desired at each value of a such that f is positive (in our example the threshold value of α is about 35 percent); on the other hand, for values of α below the threshold, increasing σ raises the amount of foreign currency desired; (4) The f-schedules become flatter as σ increases and then rise rapidly to approach f1 as the probability of crisis approaches unity; (5) An increase in the magnitude of the devaluation (a lower value of e) raises f at each probability and interest rate combination.

C. An Interest Rate Defense

Demand for foreign currency in the presence of devaluation risk is positive if domestic real interest rates are “low”. As in the logarithmic case, f is positive only if the domestic real interest rate is below a threshold that depends on the parameters (e,α,σ). For the currency demand (23) generated by CRRA preferences, f* is positive if and only if


Equation (25) illustrates an important difference between inconvertibility and devaluation risk. It will be recalled from Section II that the currency substitution due to inconvertibility risk cannot be successfully countered with interest rate hikes when the crisis probability is high. The situation is quite different for an interest rate defense when currency substitution is due to devaluation risk. Here an interest rate defense can be quite successful. All that is required to extinguish demand for foreign currency is to raise domestic real interest rates to the threshold given in (25). This threshold depends on the characteristics of the crisis and of preferences (e,α,σ) in predictable ways. Worsening crisis conditions require a higher interest rate (at each value of σ) to dampen currency flight. In Figure 4 the threshold interest rate is plotted against the crisis probabilityα for various values of (these calculations also assume e=0.6). It is also clear that, given α, higher values of σ raise the threshold interest rate.

Figure 4.
Figure 4.

Threshold Interest Rate

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

To summarize, in the face of inconvertibility risk demand for foreign currency assets remains positive regardless of the level of real domestic interest rates. This is due to the presence of the Inada condition on good y: agents would suffer large utility losses if they found themselves in the inconvertibility state with no precautionary foreign currency balances and no access to the spot foreign exchange market. Under devaluation risk, on the other hand, an interest rate defense is much more potent, hi the latter case access to the foreign exchange market is not an issue and, in light of assured access to the market a t+1, agents’ calculations are driven entirely by rate-of-return considerations.

D. Interest Rate Defense and the Magnitude of Devaluation

Shifts in the public’s perceptions of the features of the expected devaluation are all-important in deciding how large a hike in interest rates is required to defend the currency. There is clearly a tradeoff between e and R¯: a larger devaluation requires a higher threshold interest rate to contain pressure on the domestic currency (expression (25) and Figure 5). Assuming a 50 percent crisis probability, expectation of a 30 percent devaluation requires interest rates between 21 and 27 percent to induce domestic asset holders not to switch into dollars. If the expected devaluation is 60 percent, interest rates between 71 percent and 124 percent are required to keep asset substitution at bay. If an 80 percent devaluation is expected, real interest rates of between 185 and 380 percent would be needed.

Figure 5.
Figure 5.

The Tradeoff Between Interest Rate Defense and Devaluation

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

V. Cross Section Demand for Money6

In order to estimate the effect of permanent lack of convertibility on the demand for money, a dummy variable reflecting restrictions on current account foreign exchange transactions was calculated from the IMF’s Annual Report on Exchange Arrangements & Exchange Restrictions for 135 countries. The velocity of broad money (M2) was then calculated from International Financial Statistics, as the logarithm of the ratio of nominal GDP to M2, averaged over the five-year period 1991-1995. In addition, consumer price inflation was averaged over the same five- year period. To account for the effect of increasing development on the demand for money, per capita GDP in US dollars was averaged over the same five year period. The following regression equation was specified in log terms, where Vi is velocity in country i, πi is inflation, yi is per capita GDP, and Di is the dummy for lack of convertibility.


The results of estimating this equation are as follows, with standard errors below the coefficients.


According to these results, permanent loss of convertibility in the form of restrictions on current account payments is associated with a 10.3% increase in the velocity of broad money. This equation provides a simple description of the effect of inconvertibility on the quality of money and the demand for money.

VI. Time Series Demand for Money

A. Estimation Strategy

The estimation strategy is to extend the usual equation for money demand to encompass variables that are linked to the likelihood of crisis. The modern approach to the estimation of money demand functions is to use cointegration methods, which take into account the stationarity properties of the variables and which separate out the long-run from the short-run effects. This strategy has the important additional advantage that the effect of crises is most likely to be quantitatively important over the short-run, since a country (at least, a country like Korea, which has enjoyed relatively good macroeconomic performance over the past 30 years) will generally not be in a crisis or close to a crisis. Hence, the estimation strategy needs to focus separately over the short-run if it is to have any chance to separate out the impact of the crisis on money demand.

Equation (28) below focuses on the long-run relationship, as it estimates the link between the levels of money demand and the levels of the explanatory variables. In this setup, the coefficients give the estimated long-run impact of a change in the explanatory variables on money demand. Equation (29) focuses on the short-run relationship, as it estimates the link between the changes of money demand and the changes of the explanatory variables. In this setup, the coefficients give the estimated short-run impact. The link between the short-run and the long-run is captured by the inclusion of the “cointegration” variable in the short-run equation, which allows for a feedback between a disequilibrium today on short-run money demand.

The starting point of the empirical investigation is to select the candidate explanatory variables and to subject them to stationarity tests. The variable to be explained is real money demand, and the potential explanatory variables comprise real output, interest rates and inflation (these variables are standard), plus the exchange rate and reserves (the new variables that are thought to be linked to the probability that domestic currency will become inconvertible).7 8 Standard augmented Dickey-Fuller (ADF) tests are performed, confirming that the variables are non-stationary, and that they are integrated of order one (their differences are stationary).9 Hence, a cointegration framework is the statistically appropriate way to estimate the money demand equation. The Annex presents more detail on the variable definitions and on the stationarity tests.

Given the focus of the study on the short-run, a two-step estimation procedure is selected, although the longest possible sample is included in the estimation (monthly data starting in February 1970 and ending in September 2000). The two-step Engle-Granger estimation procedure is followed here, as it allows us to focus on the short-run, and because of its simplicity, allowing for instance for an easy implementation of an instrumental variables estimation technique.10 One important complication that needs to be dealt with is the possible endogeneity of exchange rates (they would in general be affcctcd by money demand) and the link of reserves to money through the central bank balance sheet identity (the sum of reserves and net domestic assets equals money). To ameliorate the impact of endogeneity on the estimated coefficients, an instrumental variables estimation technique was used (2SLS), using as instruments for the exchange rate and for reserves lagged exchange rate and lagged reserves.11

B. Econometric Results

After some experimentation, the following long-run and short-run specifications were respectively selected:


where in addition to symbols already defined, yi denotes real output, it the interest rate, et the (average period) exchange rate in won per dollar, RtMt reserves divided by imports, u, the estimated residuals from the long-run equation, ∆ the difference operator, and seasonals a set of monthly seasonal dummies (not shown here to conserve space). In terms of statistical significance, all variables except inflation and the exchange rate are found to be statistically significant at the 5 percent level in the long-run equation, and all variables except interest rates are found to be statistically significant at the 5 percent level in the short-run equation.

The estimated equations perform reasonably well when examined against standard benchmarks, which is striking considering that no allowance was made for possible breaks in the relationship and that different components of money are not modeled separately.12 The long-run equation has an R¯2 close to 0.99, and the short-run equation has an R¯2 of 0.45, with a D.W. statistic of 2.05. Perhaps more impressive is the ability of the estimated equation to produce forecasts of real money that track actual real money even during December 1997, the month when the crisis hit in earnest (see Figure 6). Finally, the “cointegration” residual ut is found using the ADF test to be stationary, which further validates the use of the cointegration framework.13

Figure 6.
Figure 6.

Actual and Fitted Money Demand Equation Money Demand Equation

(in changes; logarithmic scale)

Citation: IMF Working Papers 2001, 210; 10.5089/9781451874808.001.A001

The estimated coefficients are in accord with theoretical expectations, including for the new theoretical framework that incorporates the effect of inconvertibility. Over the long-run, the demand for real money is driven positively by real output and negatively by nominal interest rates, while inflation turns out to be insignificant. Since the inconvertibility framework does not provide clear predictions over the long-run relationship between risk variables (here, proxied by exchange rate and reserves) and real money, we do not attempt to interpret their coefficients in the long-run equation.

Over the short run, real money demand adjusts sluggishly toward its long-run equilibrium. The coefficient on the ut−1 term in equation (8) shows that money demand adjusts by 1.8 percent per month in response to a disequilibrium (about 24 percent of the disequilibrium disappears over the course of one year, and 50 percent after 23 months). From the point of view of this paper, the key implication is that one can focus mainly on the short-run impact multipliers from the exchange rate and reserve variables onto money demand (which is very helpful for the counterfactual simulations), as any long-run disequilibrium effects would be negligibly small at the one-month frequency.

The main finding is that the “crisis” variables have the predicted impact on real money demand. As the short-run equation shows, a depreciation of the exchange rate and a loss of reserves both act to depress the demand for money, and the result is statistically significant. The next section examines the quantitative significance of this effect more closely, and provides a comparison with an alternative estimate based on the cross-sectional approach in the previous section.

C. A Counterfactual Simulation

Armed with the estimated money demand equations, it is possible to produce an ex post estimate of the impact of the crisis. The money stock fell by about 3 percent in December 1997 and a further 2.5 percent in January 1998. The model predicted a fall of 2.0 and 2.6 percent respectively, a good prediction for what was an unusual period. One implication is that the model did not explain about 1 percentage point of the decline in money demand (this could have happened for various reasons, including the possibility that the proxy variables used to capture the risk of inconvertibility were less than perfectly correlated with the information set available to households at that time). Nevertheless, the key question is how much of what the model explains is due to the “crisis” variables.

A counterfactual simulation reveals that the “crisis” variables (exchange rates and interest rates) helped explain an important part of the reduction in money demand during December 1997. As already mentioned, the key question is how much of the model-predicted fall in demand can be explained by the “crisis” variables. This calculation can be done by (counterfactually) setting the change in the exchange rate and in reserves to zero during December 1997, and recomputing the model forecasts. The difference between these new, conditional, forecasts and the earlier forecasts is the model’s estimated impact of the crisis variables onto money demand. It is found that the model counterfactually forecasts that the demand for money would actually have increased (which is reasonable, as this would have been expected in line with the usual seasonal pattern) by 2.0 percent, a difference of 4.0 percentage points versus the model’s unconditional forecast (and 5.0 percentage points versus the growth in the actual money stock during December 1997).

Using real money at end-November 1997 as a base, the counterfactual simulation implies that the inconvertibility channel from the crisis to the demand for money translated into a loss of reserves of between $6-7.5 billion.14 The calculation is performed by using the end-of-period November 1997 exchange rate (1,163.8 won per dollar) to calculate broad money in dollars ($150 billion). Then, one applies the estimated effect (4-5 percent) of the crisis variables on money demand to this number. To put the estimated impact on reserves in perspective, it represented almost 30 percent of foreign exchange reserves (excluding gold) measured as of end-November 1997 ($24.4 billion).

One important problem discovered after the initial impact of the crisis is that reserves were mismeasured, with truly useable reserves being much lower than those reported publicly at that time. This has two distinct sets of implications for the analysis in this paper. One is whether the mismeasurement would influence the estimated coefficients, and the other is in assessing the importance of the inconvertibility effect on money demand. As to the former, it is in all likelihood not an important problem, because people would be reacting to the data that they had available at the time of the crisis. It therefore makes sense to use data that is closest to what would have been observable at the time. As to the latter implication, however, it is important to have an understanding of the true extent of the deterioration in reserves.

Given that useable reserves, excluding the emergency Fund assistance, declined to practically zero at end-1997, it is concluded that the impact of the possible loss of convertibility on reserves was a significant, but not the most important factor. Estimating the decline in reserves in the last few months of 1997 to be approximately $24 billion, of which 30 percent was due to the inconvertibility effect on money demand, it is concluded that 70 percent of the loss of reserves was due to other factors. Without performing a detailed analysis of those other factors, it is not possible to conclude with precision how important these other factors might be. This could be a topic of future research endeavoring to isolate further the other channels by which crises influence reserves. However, it is known that much of the outflow from Korea during the crisis was linked to the inability to roll over short term debt, as creditors became unwilling to refinance their exposure. Tentatively, therefore, one can conclude that the short-term debt vulnerability indicator may have been of more significance than the inconvertibility channel.

In terms of the external vulnerability indicators, the analysis in this paper implies that Korean reserves are now at levels that are adequate to cover plausible shocks to money demand. Assuming that the shock from the 1997 crisis to money demand was at the high end (representing a kind of natural “stress test”), reserves should cover at least 5 percent of broad money. In fact, the reserve level of $96 billion at end-2000 covers 11 percent. This should be contrasted with the inadequate level at end-1997, when useable reserves, inclusive of the emergency support from the Fund, were at 2.2 percent of broad money.

The alternative approach using cross-sectional data finds a larger impact on money demand and reserves from a potential lack of convertibility. The main finding in the preceding section was that long run money demand was 15.6 percent lower for countries with permanently inconvertible currencies. This effect is between 3.1-3.9 times larger than what was estimated using the Korean-specific time series money demand function. The finding in the cross section analysis would have meant that reserves would have fallen to zero (or to below zero) on the strength of the inconvertibility channel alone.

It seems unlikely that the higher estimate for the impact on reserves is applicable in the majority of the cases. Given the method of estimation, it seems that only full and permanent inconvertibility would result in a reduction in money demand of the full 15.6 percent (so that amount can be viewed, in general, as an overestimate). More likely, households ascribe some probability to the possibility of inconvertibility that is less than 100 percent. Even given the severity of the crisis in Korea, it is not plausible that households came to expect full (not to mention permanent) inconvertibility. Under these circumstances, the estimate that money demand fell by between 4-5 percentage points seems a more reasonable one.

VII. Concluding Remarks

This paper presented a theoretical and empirical analysis of the impact of anticipated and actual inconvertibility on domestic money demand and reserves. Using a simple model featuring multiple currencies we showed that the prospect of inconvertibility gives rise to a precautionary motive for foreign exchange. Whereas in normal times the domestic currency is freely convertible at a fixed exchange rate, the threat of loss of convertibility raises demand for foreign currency assets at the expense of the demand for domestic money. Naturally, an increase in the probability that the currency will become inconvertible—as would occur during a crisis—leads to a decline in demand for domestic real currency balances. The central bank could respond by raising domestic interest rates, which would raise domestic money demand through a direct substitution effect. However, an interest rate defense of the currency is offset by budgetary and other economic costs. Instead, convertibility could be maintained by abandoning the currency peg and floating the currency, in which case the required depreciation of the currency would be dictated by market forces. Alternatively, if a fixed exchange rate regime is to be maintained, then the only options left arc initiating adjustment via some combination of devaluation, supported by interest rate increases and expenditure restriction, possibly in conjunction with an IMF-supported program.

In the empirical part of the paper, we use time series cointegration techniques to estimate the impact of the prospect of inconvertibility on money demand during several recent currency crises on Korea. Our preliminary estimates of the effect of the foreign crisis on money demand and reserves for Korea show that the impact of inconvertibility is significant. The loss of reserves attributed to inconvertibility was of the order of $7 billion, or about one-third the reserves available at the time. This effect is separate from the reserve loss attributed to the non- rolling over of short term capital driven by the over-leveraging of Korean corporations.

This study offers some insights for policies designed to contain external vulnerability and particularly for reserves. Some of the conclusions, however, are tentative pending further research.

  • At times of crisis, money demand will generally fall as households perceive the risk of domestic currency becoming inconvertible as rising. This intuitive theoretical prediction is born out by the empirical analysis carried out for the case of Korea in this paper.

  • The negative impact of a crisis on money demand, and the attendant negative spillovers to international reserve holdings, can be significant but, for countries whose problems are perceived to be temporary, and that have a reasonable amount of initial reserves, manageable. Korea’s current reserves, when compared with broad money, would more than cover a shock to money demand equivalent to that sustained during the 1997 crisis.

  • From the usual indicators of external vulnerability, the analysis in this paper finds that the reserves-to-broad money ratio is an important indicator. At least for the case of Korea, one can tentatively say that the reserves-to-short term debt (measured by residual maturity) variable may have been quantitatively more important. Further theoretical and empirical work needs to be done, however, to conclusively rank the importance of alternative indicators of vulnerability.

VIII. Data Annex

The data used are all collected from the Fund’s International Financial Statistics (IFS) database, and are monthly series for the period February 1970 to September 2000.

The key definitions used include:

  • Real broad money is the end-of-period sum of money and quasi money (minus foreign currency deposits) deflated by the CPI index, seasonally unadjusted.

  • Real output is the industrial production index, seasonally adjusted.

  • The interest rate is the monthly yield on deposits longer than 1 year.

  • Reserves is end-of-period foreign exchange reserves excluding gold measured in dollars, divided by imports also measured in dollars.

  • The exchange rate is the monthly average market rate, measured in won per US dollar. For converting money stocks to dollars the end-of-period rate is used instead.

To extend the sample back to 1970, it was necessary to use the aforementioned interest rate (some alternative series started much later). This entailed some loss of information as there were periods over which that rate did not change (there were periods over which it apparently was changed only infrequently). There was no definition of quasi money in the IFS database that was seasonally adjusted, and there was no definition of industrial production that was seasonally unadjusted. To account for this discrepancy, the short-run regression equation includes seasonal dummies.

The tests of variable stationarity yielded the following results:

Table 1.

ADF Tests

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Performed assuming 12 lags and including a constant and no trend, and assuming that the constant equals zero under the null hypothesis.

Note: The 5 percent critical value for the ADF test is −2.88 (James Hamilton Time Series Econometrics, 1994, Table B.6, case 2).

One notable result, often found also in other country cases, is that inflation is integrated of order one (hence, the difference of inflation is stationary). This implies that the CPI is integrated of order two. This explains why in the long run equation it is inflation that is used (to keep the orders of integration commensurate between the left-hand and the right-hand sides of the equation) and why it is that in the short-run equation it is the difference in inflation that is used.

IX. Annex: Optimal Currency Portfolio With Devaluation Risk

This Annex derives the optimal foreign-currency portfolio in the presence of devaluation risk for the CRRA class of preferences. Consumer demands in state i = 1,2 are


These schedules are positive in the f-interval f0ff1, where f0eR1eRW, f1RR1W.

Assuming f0ff1, indirect utility in state i, Ui, is proportional to real wealth in that state raised to the power 1 − σ:


Expected utility and its first and second derivatives may be written as function of f as follows:




EU”(f) < 0 if and only if σ > 0. In this case there is a unique maximum f* given by


Rearranging terms and simplifying yields the following:


Define the parameter ρ > 0 by


The value of ρ depends on the preference parameter σ and the exchange rate in the devaluation state e. ρ = 1 if σ = 1, while ρ > 1 if σ > 1 and e < 1. From equations (32)-(33), the optimal portfolio is


As can be seen from (34), f depends on the difference (actually the ratio) of the expected returns on foreign and domestic currency assets α(e−1−R)+(1−α)(1−R).

In the log case σ = ρ = 1, and (34) reduces to f*WR[αR11αe1R].


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University of North Carolina and International Monetary Fund, International Monetary Fund. We are indebted for useful comments to Tim Lane, Ydahlia Metzgen, Tony Richards, Christian Mulder, Roberto Perrelli, Steve Russell, and to participants at seminars at the IMF Institute, Federal Reserve Board, and Bank of Indonesia.


To relieve exchange market pressures, on August 17, 1998, the Russian government widened the exchange rate band from 5.3-7.1 to 6.0-9.5 rubles per U.S. dollar.


Subsequently the CBR introduced wide-ranging administrative measures to suppress demand for foreign exchange, even for current account purposes. Surrender requirements on exporters were raised, advanced import deposit requirements were introduced, and the ruble accounts of nonresident banks with domestic banks were not convertible freely into foreign exchange.


On Russia, see IMF Country Report 99/100, paragraph 98 (September 1999). On Ukraine, see IMF Country Report 99/42 (May 1999), paragraph 89. Both are available on the Internet at


“Argentina’s Move,” Financial Times. December 3, 2001.


If households had access to the international capital market at a gross interest rate of unity, they would have incentives to borrow foreign currency and invest domestically.


This empirical work was ably performed by Sergiy Peredriy.


One issue which is not entirely clear from theoretical framework is the monetary aggregate that would be appropriate to use in the empirical tests. Clearly, the fear of inconvertibility could in principle spill over to longer-maturity components of money, if they were liquid enough, which would argue for using a broad monetary aggregate. We ran our regressions both on narrow and broad definitions of money. While both definitions were influenced by the “crisis” variables, the residuals for narrow money were larger, presumably because that equation was not able to account satisfactorily for shifts between components of money. As these shifts are not the main objective of this paper, the analysis is focused on broad money (the sum of money and quasi money, as defined in the IFS database, excluding foreign currency deposits—series BBAA2113, obtained from the Bank of Korea web site, The national (Bank of Korea) definition of broad money is consistent with the IFS definition.


Another qualification concerns the interpretation of inconvertibility. If the exchange rate is allowed to float, movements in the exchange rate capture return (akin to the interest rate) rather than inconvertibility considerations. The two versions of the theoretical model earlier presented capture these two different possibilities. The empirical equations here do not distinguish cleanly between the two complementary motivations.


Noting that the fact that inflation is found to be integrated of order one (a result also sometimes found for other countries) implies that the CPI price index is integrated of order two. To keep the estimated equations balanced in terms of the order of integration between the left- hand and the right-hand sides implies that we use inflation in the long-run equation, and the change in inflation in the short-run equation.


It remains for future work to implement more sophisticated estimation methods, such as the method due to Johanssen. This would allow us to investigate the presence of multiple cointegrating relationships, which is a real possibility given the endogeneity of exchange rates and reserves (which the paper uses as indicators of inconvertibility risk). Another challenge for future work is empirically distinguishing between inconvertibility risk and depreciation risk.


This solution has its costs, mainly that one uses proxies that by necessity are not as informative as the actual variables themselves. To see how significant this loss of information is, the regressions were run both with and without the use of instruments. In the event, the regression coefficients for the exchange rate and reserves were fairly close between the two sets of regressions, and the main results from the counterfactual simulation were not significantly affected (although, as expected, the t-statistics are generally lower for the 2SLS estimates). For concrctcncss, the results reported in the paper focus on the 2SLS estimated long-run equation and the OLS estimated short-run equation.


E.g., the macroeconomic model used by the Bank of Korea has several different equations separately explaining various components of broad money (Yang Woo Kim et al (1998).


The ADF statistic (using the same assumptions as described in the Annex for the other variables) is−3.1, with a critical value for a test at a 5 percent significance level of −2.88.


The effect could be somewhat larger if the value of real money then were translated into today’s money (between end-November 1997 and the end of the sample period in September 2000 the CPI index rose by about 10 percent).

Convertibility Risk: The Precautionary Demand for Foreign Currency in a Crisis
Author: Mr. Alex Mourmouras, Mr. Stabley W. Black, and Mr. Charalambos Christofides