14 Balance of Payments Crises in a Cash-in-Advance Economy
- Jacob Frenkel, and Morris Goldstein
- Published Date:
- April 1996
This paper studies an experiment in which the Central Bank sets the rate of devaluation at a level consistent with other fiscal constraints and reverts to a targets-consistent rate of devaluation when the reserves constraint is binding. The results confirm previous findings: as soon as the inconsistent policy is announced, absorption increases, the current account deficit widens, and the real exchange rate appreciates. Once the crisis occurs the system returns to a steady state with a higher real exchange rate. During the transition, the current account deficit is wider and the exchange rate appreciates more, the more ambitious the (inconsistent) stabilization program is.
For many countries that are chronically afflicted with relatively high rates of inflation, anti-inflationary policies seem to have much in common with weight-reducing diets: they work for a while, sometimes even dramatically so, but only a minority of patients are able to maintain a lower weight in the long run. The standard conjecture here is that the lack of success must be due to the failure to uproot some of the fundamental causes of inflation or obesity, as the case may be. It is, therefore, interesting to understand the dynamics of these systems when some, but not all, the conditions for success are present.
A very neat example of this type of analysis is provided by the balance-of-payments-crises literature (e.g., Krugman (1979), Flood and Garber (1984), Obstfeld (1984a and b)). The basic scenario is one of a “small” open, economy subject to perfect capital mobility; a “crisis” develops, for example, because the monetary authority sets the rate of devaluation at a level that, given the path of domestic credit, would call for a permanent drainage of reserves from the Central Bank. Assuming that the Central Bank has an upper bound on the funds that it can borrow internationally, it follows quite trivially that the exchange rate regime will have to be modified in the future.1
Much less trivial, however, are the dynamics of the crisis itself. With perfect foresight, examples can be developed where the announcement of an inconsistent stabilization policy (in the above sense of not being sustainable in the long run) displays, in the short run, all the signs of success. For instance, in the case of a reduction in the rate of devaluation, the rate of inflation initially falls and the balance of payments dramatically improves; the regime ends, however, with a speculative attack, when all the “good” signs are suddenly reversed (see Connolly and Taylor 1984). What is remarkable about this type of result is that to the casual observer it looks as if the crisis has taken most people by surprise (given its sudden occurrence), while the fact of the matter is that the crisis is the equilibrium outcome of a model in which all the events are fully anticipated. Although there are still no formal extensions of this literature to incorporate “politicians” into the picture, these remarks suggest how tempting it might be for a politician—especially one who knows that his tenure will be over in the not too distant future—to resort to anti-inflationary policies of this sort, since (a) no “tough” decision has to be taken in the short run, (b) the policy immediately appears to be “successful,” and (c) if well calibrated, the “bomb” will explode in the hands of his successor.2
Typically this literature has concentrated on the balance of payments, leaving aside equally important aspects such as the current account and the real exchange rate. These aspects are particularly relevant for understanding the recent monetary experiences of Argentina and Mexico where the exchange-rate crises (with symptoms similar to the ones emphasized by the above-mentioned literature) came at the end of a protracted period of “low” real exchange rates and “high” current account deficits (see Blanco and Garber 1983 and Calvo 1986a).
Interestingly, accounting for the above-mentioned aspects of the phenomenon is not a trivial matter. If one works in terms of an extension of Calvo and Rodriguez (1977), for example, and assumes that the government gives back the inflation tax in the form of lump-sum taxes, then one can show that an exchange-rate crisis can occur without current account deficits or surpluses, and without any change in the real exchange rate. The reason for this is simple: aggregate demands in a model like that are assumed to be functions of real private wealth and relative prices; so, if the experiment does not change private wealth, the relative price of tradables with respect to nontradables (i.e., the real exchange rate) that equilibrates the home-goods market remains the same. Thus, our point is shown by noticing that during a balance of payments crisis the main action has to do with a reshuffling of assets between the private and the public sector (“capital flight”) that, if fully anticipated, does not change private sector wealth.3 Therefore, we are faced with a clear instance where, rather than continuing the search for ad hoc models that yield the desired results, our understanding might be better served by examining a simple monetary model with solid microeconomic foundations. This is the task that will be undertaken in the present paper.
We assume that there exists a “representative” infinitely lived family that derives utility from consumption. The family can accumulate assets in the form of noninterest-bearing domestic money, or in the form of an international bond. Money is demanded for cash-in-advance reasons (Clower 1967, Lucas 1980, Stockman 1981, Feenstra 1985), and the minimum necessary holdings of real monetary balances are assumed to be a fixed proportion of intended consumption. Section II describes this economy under the assumption that there exists only one fully tradable commodity. The basic results of the paper are presented in section III, and extended to the case of tradable and nontradable goods in section IV.
The central experiment studied in the paper is one in which the Central Bank sets the rate of devaluation at a level inconsistent with the other fiscal constraints, and reverts to a targets-consistent rate of devaluation when the reserves constraint is binding. The main results can be summarized as follows:
(a) The anatomy of the balance-of-payments crisis confirms previous findings;
(b) As soon as the inconsistent (in the above sense) policy is announced, the level of absorption takes an upward jump, generating a current-account deficit and an appreciation of the real exchange rate. Once the crisis occurs, the system returns to steady state with a permanently higher real exchange rate;
(c) Finally, a relatively more novel qualitative result, during the transition, the current-account deficit is larger and the appreciation of the real exchange rate greater, the “more ambitious” is the (inconsistent) stabilization program (i.e., the lower is the rate of devaluation before the crisis occurs).
II. The Basic Model: Preliminary Results
We assume that the domestic economy is composed of a single price-taking, Sidrauski-type family, whose utility function at time t, Ut, is represented as follows:
where c stands for consumption, and r is the (constant and positive) subjective rate of discount. We assume that u(·) is twice differentiable, that it is strictly concave, and that it exhibits a positive derivative for all c > 0.
Output is homogeneous (i.e., we assume a one-good world); there are no barriers to international trade; international capital mobility is perfect; and the country is “small” in all international markets. For convenience, we further assume that the international rate of interest is equal to r.
In order to motivate a demand for money, we shall assume, as in the money-in-advance literature, that the level of real monetary balances, m, must satisfy4
meaning that in order to make the c units of consumption effective, the family must hold a stock of monetary balances not smaller than ac.
We assume that money and bonds are the only forms of holding wealth; thus, real wealth at time t, at, is given by
where b is the family’s bond holdings. Furthermore, a evolves according to the following relationship:5
where y is a constant flow of output produced by the family per unit of time (the equivalent to the gross domestic product), g is real lump-sum government transfers, and ε is the rate of domestic inflation. If we further assume that the international price level (i.e., the price of output in terms of foreign currency) is constant over time, our previous assumptions permit us to identify ε with the rate of devaluation. Alternatively, taking (3) into account, we can express (4) as follows:
Integrating (4’), and imposing the condition that ate-rt → 0 as t → ∞, we note that under perfect foresight the following overall budget constraint must hold:
This is the familiar condition that the present value of future expenditure (i.e., consumption, c, plus the opportunity cost of holding money, r + ε) should be equal to the all-inclusive measure of wealth (i.e., a plus the present discounted value of net future receipts, y + g)6.
At time t the family chooses the paths of c and m in order to maximize (1) subject to (2) and (5), given at. Assuming the existence of an interior solution for c (this assumption will be maintained in what follows7), this yields the following first-order condition:
where λ is the associated (time-invariant) Lagrange multiplier. In (6) we implicitly assume that money is not held in excess of the minimum requirement given by (2). This will, in fact, be an implication of an optimal individual plan if money is return-dominated by the bond, that is, if r + ε > 0. Thus, (6) is the correct expression for our experiments, given that we will assume that the above inequality (that is, r + ε > 0) holds at all times. Notice that (6) is just the familiar first-order condition, “marginal utility equals price times the marginal utility of wealth”; in our application, the “price” of consumption equals its direct cost (1) plus the opportunity cost of money held against that unit of consumption (a(r + ε)); the latter term plays a key role in our analysis (for related examples, see Obstfeld 1985 and Calvo (1986b)).
We shall assume that the government is committed to maintaining a constant positive level of real lump-sum transfers,8g, and to following a given path of the rate of devaluation, ε. At each point in time, the government stands ready to exchange domestic for foreign money at the predetermined exchange rate (more on this in section III).
The only net asset available to the government for the purpose of wealth accumulation is the bond (there exists foreign exchange but it is return dominated by the bond); we denote the government’s bond holdings by k. At points in time where m is smooth, the rate of accumulation of k is given by
since, by hypothesis, the only way available for the private sector to increase, say, its holdings of domestic money instantaneously is to sell foreign bonds.
In line with the balance-of-payments-crises literature (e.g., Krugman 1979; Flood and Garber 1984; Obstfeld 1984a and b) we will assume that there is a lower bound on k, which, for the sake of definiteness, is assumed to be zero;9 thus,
Denoting the total holdings of bonds in the economy by f, we have
and, by (3), (4), (7), and (9), we get
which simply says that the net accumulation of assets by the economy as a whole is equal to the current-account balance, as should be the case in any well-defined open-economy model.
We are going to be particularly interested in perfect-foresight situations where ε is a constant over certain intervals of time. Clearly, by (6), ε is a constant over each one of those intervals (but not necessarily the same constant in any two disjointed intervals.) Thus, by (2) and (7a), and recalling that we have ensured that (2) holds with equality, in any interval of time where ε is a constant, we have
This formula will come in handy for calculating the timing of crises.
We close this section by studying the case where ε is constant over the interval [T,∞] under the assumption that T is the “present,” so that we do not have to bother about the “transition” until T, a subject that will be the focus of the next section. Since c and ε are constant forever, we can integrate (5) to yield
That is, expenditure (consumption, c, plus the inflation tax, εm = εac) equals disposable income. This implies, of course, that
Hence, by (11) and (13), given g, kT, and aT, there exists a unique value of ε such that k remains constant at its initial level (kT in the present notation). If ε is assumed to be less than this critical level, then k < ω for some ω < 0; thus, by (8), the assumed rate of devaluation would be sustainable only over a finite interval. This is going to be a useful result for the ensuing analysis.
III. Balance of Payments Crises
For the sake of definiteness we will assume that up to time zero (the “present”), the economy has been traveling along a perfect-foresight steady-state path with a constant rate of devaluation
To give an alternative description of the above situation one could say that initially the rate of devaluation is set at a level which is “unsustainable” in the long run; when reserves are depleted, the authorities withdraw from the foreign exchange market and let the exchange rate float freely without changing real transfers.”10 Under this interpretation, it is quite natural to call the events at time T “a crisis.”
By the concluding remarks of the previous section, we know that given k0 and a0, there exists a unique value of ε (
We will denote the rate of devaluation after T by ε∞. By our discussion in the previous section, we know that consumption is a constant on [0, T], and on [T,∞]. We will denote consumption in the former interval by x, and in the latter by z. Since, by hypothesis, ε∞ is chosen so that k =
i.e., after T the inflation tax must equal government transfers. Hence, by (6) and (14),
Consequently, if we further assume that the right-hand side of (15) decreases with z, (15) implies a positive relationship between x and z (depicted as curve AA in Figure 1).11 In the Appendix we will show that, as in Figure 1, the curve AA lies below the 45° line at x = y + rf0.
Figure 1.Determination of Equilibrium x and z
We now study the behavior of k; if the crisis occurs at T, then it should be the case that kT = 0. However, there are two values of kT that concern us; the value “right before” the crisis, denoted by
On the other hand, integrating (11) over the interval [0,T], we get
where ∆k0, is the initial (stock) accumulation of reserves following the announcement of the reduction in the rate of devaluation to ε0. Clearly, since the economy started at a steady state, we have, recalling that (2) is binding,
Integrating (10) over the interval [0, T], we get
Furthermore, since beginning at time T the economy locks itself into a steady state where kt = 0, it follows that, for t > T consumption, z, must equal gross national product or, in other words,
Hence, by (19) and (20),
In order to satisfy (16), it is necessary that
Hence, by (17), (18), and (22)
Combining (21) and (23), we get
The above relationship is depicted as curve BB in Figure 1. It is immediate to show that BB is downward sloping for x ≥ y + rf0; one can in fact show that the slope is negative on the entire relevant range12 (see the Appendix). Thus, curve BB together with curve AA determines the unique equilibrium levels of x and z. This information and (23) can in turn be used to determine T. It is clear from Figure 1 that at equilibrium (denoted by asterisks on the respective variables), we have x* > y + rf0 > z*.
To summarize, we have found that if the economy begins at a situation where there is no accumulation or decumulation of bonds by the government, and the monetary authority decides to lower the rate of devaluation, a crisis will develop in finite time. Furthermore, and more central for our analysis, before the crisis occurs, the country will run a current account deficit, i.e., during the period [0,T] absorption will rise above the original level. After the crisis, the system locks itself into another steady state with a permanently higher rate of devaluation, and a permanently lower level of absorption.
What happens as ε0 is further reduced? This is an interesting question because it is a way of asking what happens as the monetary authorities become “more ambitious” in their attempt to lower the rate of inflation in the short run (without, of course, attacking any of the fundamental causes of inflation). Figure 2 depicts the shift of the AA and BB curves as ε0 is reduced. Clearly, this leads to an increase in x (absorption during the transition). Consequently, we have found that a more ambitious short-term stabilization program will lead to a bigger current account deficit. As seen from (23), however, we do not seem to be able to ascertain whether the crisis will happen sooner as ε0 is lowered. The reason for this is that the timing of the crisis depends on the ability to collect the inflation tax, which is proportional to ε0x, and not just to x.13
Figure 2.Effect of a Smaller ε0
IV. The Real Exchange Rate
In this section we will show that the previous analysis can readily be extended to account for the existence of tradable and nontradable goods. The presentation will be sketchy, leaving out finer points that could be easily derived by the interested reader.
For the sake of simplicity, we will assume that domestic consumption, c, is produced with tradable consumption, cT, according to the following production function:
where h(·) is assumed to be strictly concave and nonnegative for all cT ≥ 0. (Notice that the analysis of the previous section can be thought of as being conducted under the assumption that h(·) ≡ 1.)
Denoting by p the relative price of domestic (or home) consumption with respect to tradable consumption (i.e., the relative price of c with respect to cT), we get in competitive equilibrium that p = 1/h′. Thus, recalling (25),
Consequently, we get the perfectly natural implication that the relative price of home goods with respect to tradable goods (the inverse of what is sometimes called the “real exchange rate”), is an increasing function of the level of home consumption, c.
The natural extension of (2) is
Thus, (14) becomes, recalling (26),
(Note that we have implicitly assumed that government transfers are denominated in terms of tradables.) Therefore, the first-order condition (6) becomes
Hence, relationship (15) that defines curve AA in Figure 1 takes now the following form:
Consequently, recalling (27), the assumption we made in section III that u’(z)/(1 + αr + g/z) declines with z is, again, sufficient to ensure that curve AA is upward sloping.14
The derivation leading to curve BB is slightly more involved. Following the steps of previous section, we have, instead of (17),
and, instead of (18)
Finally, instead of (21), we have
and, instead of the first equality in (22),
By (32), (33), and (35), we get
[cf. (23)]. Using (36) in (34), we obtain an expression in x and z that corresponds to (24), and can be shown to give rise to a downward-sloping BB curve.
Consequently, the above findings together with (26) and (27) allow us to conclude that if we start from a noncrisis steady state with constant official reserves over time, and the rate of devaluation is lowered as described in the previous section, a crisis will eventually develop. The real exchange rate will exhibit an immediate appreciation, and will remain at the appreciated level until the moment that the crisis actually occurs. At the time of the crisis, there is a sudden permanent depreciation of the real exchange rate that drives p to a level below that prevailing prior to the stabilization experiment.15
We first show that the curve AA in Figure 1 must lie below the 45° line at x = y + rf0. At x = y + rf0 = z (note the last postulated equality) we have
The first inequality is a hypothesis of the crisis scenario, in turn,
Hence, since we assume that u’(Z)/(1 + αr + g/z) is a decreasing function of z, it follows that at x = y + rf0, the value of z that solves for (15) must be such that z < x = y + rf0. Q.E.D.
The inequality in (A3) follows from the first inequality in (A1), recalling that in (A1) x = y + rf0. Q.E.D.
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