A. Complete Information Model

Let us consider a continuum of speculators in an economy characterized by a state of fundamentals θ that can take values over the real line ℜ, with θ = +∞ corresponding to a situation of “sound fundamentals”. We assume that public authorities (“the government”) are pegging the exchange rate and that speculators decide whether to attack it. If a speculator attacks and the government abandons the peg, the speculator obtains D − t, with D > t > 0; when the attack is not successful, the speculator looses the transaction cost t. If speculators refrain from attacking, they get 0. The government’s utility from defending the currency is increasing in the fundamental θ, and decreasing in the share of speculators that attack the currency, denoted by l. Specifically, we assume that the government gets θ − l, when he maintains the peg and zero when he abandons it.

We consider a very simple two-stage game with complete information. In the first stage, speculators observe θ and simultaneously decide whether to attack the currency. In the second stage, the government–who knows θ–observes the share of speculators attacking the currency and decides whether to maintain the peg.

This game can be solved backward, by finding the government’s optimal strategy, which is simply the function:⁵

Given ψ, the solution of the reduced-form game of speculators provides the tripartition of the space of fundamentals that characterizes second generation models of currency crises. Specifically, if the fundamental θ lies in:⁶

• (−∞, 0] $\Rightarrow$ there is a unique equilibrium: all agents attack the currency and the government devalues.

• (0,1] $\Rightarrow$ there are multiple equilibria: agents can either attack the currency (and force a devaluation) or refrain from attacking (and allow the peg to be maintained);

• (1, +∞) $\Rightarrow$ there is a unique equilibrium: all agents refrain from attacking and the government maintains the peg.

Hence, outside the interval (0, 1], maintaining the currency peg is solely a function of the fundamental θ. By contrast, when θ falls in (0, 1] the outcome depends on which (self-fulfilling) equilibrium speculators coordinate. If speculators expect the currency peg to fail, they attack the currency and force the government to devalue. If they expect the peg to hold, they do not attack the currency and allow the government to maintain the peg. This feature of the game is shared also by the incomplete information model that we present in the following Section, at least for some speculators’ beliefs.

B. Incomplete Public Information

Let us assume that speculators do not know the fundamental θ, but only have expectations about it, in the form of a normal probability distribution with mean y and variance 1/α (with α > 0)–denoted by Θ. Note that the complete information model can be obtained as a special case, for α = +∞. Since Θ is common knowledge to all speculators, this probability distribution represents the public information available to them. Thus, we will refer to α as the “precision of public information”.

In this paper, we do not use the term public information as a synonym of official information (i.e., information provided by the authorities of a country or by other national or international bodies) but as the opposite of private information. Public information consists of signals on the level of fundamentals which are common (publicly observable) to all agents, whereas private information differs from one agent to the other. In this framework, an increase in the variance of the distribution of public information does not necessarily reflect noisier official information but it could be due to greater uncertainty–common to all agents–about the economic outlook.⁷ Virtually any event which is publicly observable and affects economic fundamentals–including a currency crisis elsewhere or rumors of political troubles–could be classified under that label. The crisis in Thailand, for example, may have made the growth outlook of other Asian countries equally more uncertain for all agents. At the same time, uncertainty about the policies that each country would have followed in the midst of the crisis may well have contributed to the overall uncertainty. In this paper, we do not distinguish between these two sources of uncertainty, which would both affect the precision of public information. An implication of this approach is that, differently from Morris and Shin (2000), we do not perform any welfare analysis on the provision of public information.

As the government knows θ and observes l, his optimal strategy is the same function ψ of the complete information model. Therefore, if θ falls in (−∞, 0] the government devalues the currency, whilst if θ falls in (1, +∞) the government maintains the peg. When θ belongs to (0, 1], speculators’ expectations will determine the outcome of the game.

Given ψ we can focus on the reduced-form game of speculators. We need to calculate the expected payoff of a speculator who attacks the currency, when all other speculators also attack–denoted by u(a_i, a_−i)−, and the expected payoff of a speculator who attacks the currency when all other speculators do not attack–denoted by u(a_i, d_−i). Analytically these expected payoffs are given by:

where η is the probability density function of Θ. The following proposition specifies the equilibria of the reduced-form game of speculators:

Proposition 1 The (“attack”) strategy profile in which all agents attack the currency is an equilibrium iff u(a_i, a_−i) ≥ 0. The (“don’t-attack”) strategy profile in which all agents refrain from attacking is an equilibrium if u(a_i, d_−i) ≤ 0.

Being always u(a_i, a_−i) ≥ u(a_i, d_−i), the “attack,” the “don’t-attack,” or both strategy profiles are equilibria of this game. Let us rewrite the two expected payoffs as:

where Φ is the cumulative distribution function of a standard normal distribution. By rearranging those expressions, we obtain a necessary and sufficient condition for the attack and the don’t attack strategy profiles being both equilibria of this game; namely:

Therefore, this incomplete information model may have multiple equilibria or a unique equilibrium depending on whether condition (2) is or is not fulfilled.⁸ We can now examine the effects of y and α on both the attack and the don’t attack strategy profiles, irrespectively of the number of equilibria. These effects are summarized by the following proposition (see Appendix A.1):

Proposition 2 (i) Both u(a_i, a_−i) and u(a_i, d_−i) are decreasing in y. (ii) u(a_i, a_−i) is decreasing (increasing) in α if y > 1 (y < 1). (iii) u(a_i, d_−i) is decreasing (increasing) in α if y > 0 (y < 0).

An increase in y, by reducing u(a_i, a_−i) and u(a_i, d_−i), shrinks the range of parameter values for which the attack strategy profile is an equilibrium and enlarges the range of parameter values for which the don’t-attack strategy profile is an equilibrium. In other words, an improvement in the expected fundamental always makes it less likely that the attack strategy profile is an equilibrium and more likely that the don’t attack strategy profile is an equilibrium.

Proposition 2 also states that the effect of the precision of the public signal, α, depends on the expected fundamental y. Specifically, if α increases and expected fundamentals are sufficiently good (bad), it becomes less (more) likely that the attack strategy profile is an equilibrium and more (less) likely that the don’t attack strategy profile is an equilibrium. In order to understand this dependence of the effect of α on the mean y, recall that an increase in α makes speculators more confident that the fundamental θ is in a neighborhood of y. Therefore, when y is sufficiently good, the increase in α makes all speculators more confident that the peg will hold, dampening their willingness to attack. Conversely, when y is sufficiently bad, more precise public signals strengthen speculators’ belief that the exchange rate will depreciate, driving them to attack the currency peg.⁹

In the next section, we examine a more general game in which speculators also hold private information, under a condition which grants that a unique equilibrium exists. Despite the differences in the number of equilibria and in the information structure, we find that public information has the same effects of the incomplete information game considered in this section.

C. Incomplete Public and Private Information

Suppose that each speculator i has expectations about θ given by the probability distribution Θ and receives a private signal x_i drawn from the following normal distribution

with β > 0, X_i and X_j independent given θ for each i ≠ j. Note that by setting β = 0 we get back to the public information model, while the complete information model obtains with either α = +∞ or β = +∞ (or both).

Private information in economic models may arise from a variety of sources. In general, a noisy private signal may represent discrepancies in how public information is interpreted by different speculators (on this point, see Morris and Shin, 1998). Heterogeneity in speculators’ information sets may also be produced by costs of information acquisition. On exchange rate markets, international banks may gather valuable private information from monitoring the activity of their customers.

If private information is sufficiently precise with respect to public information, this model entails a unique equilibrium. As first shown by Carlsson and van Damme (1993), this result is driven by the lack of common knowledge induced by the presence of private information. The mechanism leading to a unique equilibrium can be explained using the infection argument, as in Morris et al. (1995). Suppose that a speculator is known to take a certain action at some (private) information set. This knowledge might imply a unique best response by the other speculators at some of their information sets where the first information set is thought possible. This, in turn, may imply that the original speculator responds to that knowledge choosing that same action at a larger information set, and so on. In the currency crisis game, if private information is sufficiently precise, this chain of reasoning results in a unique action profile, eliciting a unique equilibrium.¹⁰

A sufficient condition for this mechanism to select a unique equilibrium is:

The intuition for this condition is straightforward. If private signals were not sufficiently informative with respect to the public signal, speculators would regard them as unreliable and continue to ground their decisions mostly on public information, restoring a high degree of common knowledge. Under condition (3), the following proposition holds (see Appendix A.2):

Proposition 3 (Morris and Shin, 1999; Metz, 2001) If $\beta >\frac{{\alpha }^2}{2\pi }$, there exists a unique equilibrium, consisting of a unique value of the private signal x^* (such that each speculator receiving a signal lower than x^* attacks the currency peg) and a unique level of the fundamentals θ^* (such that the government abandons the peg when fundamentals are lower than θ^*).

It is easy to verify that θ^* ∈ [0, 1]. As a consequence of the unique equilibrium result, the maintenance of the currency peg solely depends on the actual fundamental θ. However, speculators’ expectations still matter, as they determine the equilibrium trigger points θ^* and x^*. Note also that the existence of a unique equilibrium does not eliminate all the “inefficiencies” of the model: when θ^* ∈ (0,1) we can still have currency crises (for 0 < θ < θ^*) that could have been avoided with a different information structure and speculators coordinating on a good equilibrium.

The presence of a unique equilibrium allows for rigorous comparative statics. Instead of calculating the effects on the range of parameters for which two strategy profiles are equilibria of the game (see Section II.B), within this model we can simply analyze the effect of y, α, and β on the unique equilibrium. Specifically, by assuming that condition (3) holds–so that the existence of unique values for θ^* and x^* is granted–we can study the effects of the parameters y, α, and β on θ^* and x^*. In addition, we can calculate the effects of the parameters on the probability that speculator i attacks, Pr(X_i ≤ x^* | θ), which also represents the share of speculators attacking the currency and, therefore, has an empirical counterpart in indices of exchange rate pressure. Given the assumptions on Θ and X_i | θ, we find that the share of speculators attacking the currency varies continuously with the parameter values. Indeed, this is a distinguishing feature of models with private information that is not shared by complete information models or models with only public information which are, instead, characterized by equilibria in which either all speculators attack or nobody attacks.¹¹

Expectation effects on the share of attackers

We can finally derive the effects of the parameters on the share of speculators attacking the currency. This share is given by Pr(X_i ≤ x^* | θ), which is equal to ${\Phi }\left[\sqrt{\beta }(x^{*}-\theta )\right]$, and which depends on the actual fundamental θ and on the parameters y, α and β. By differentiating ${\Phi }[\sqrt{\beta }(x^{*}-\theta )]$, it is easy to obtain the following results:

Proposition 6 Assume that $\beta >\frac{{\alpha }^2}{2\pi }$; then the probability Pr(X_i ≤ x^* | θ) is: (i) decreasing in θ; (ii) decreasing in y; (iii) decreasing (increasing) in α if y > s₁ (y < s₁). (iv) decreasing (increasing) in β if $\frac{(x^{*}-\theta )}{2\sqrt{\beta }}+\sqrt{\beta }\frac{{\mathit{\text{dx}}}^{*}}{d\beta }<0(\frac{(x^{*}-\theta )}{2\sqrt{\beta }}+\sqrt{\beta }\frac{{\mathit{\text{dx}}}^{*}}{d\beta }>0)$.

As expected, an improvement in θ and/or in y reduces the share of speculators attacking the currency. Similarly, the effect of the precision of public information is in line with previous results, since it only depends on the expected fundamental y: when y is sufficiently good (bad), an increase in α makes the share of speculators to decrease (increase). However, unlike the prediction of Propositions 4 and 5, the effect of the precision of private information is not necessarily opposite to that of public information. In order to understand this new result, we need to consider that β not only affects the equilibrium trigger point x^* (and, thus, it indirectly influences the share of speculators attacking the currency), but it also directly affects the probability Pr(X_i ≤ x^* | θ), since it determines the dispersion of the messages x_i around the actual fundamental θ.

Consider the following example. Assume that y is good (y > s₃), so that an increase in β makes x^* to increase $\left(\frac{{\mathit{\text{dx}}}^{*}}{d\beta }>0\right)$, making speculators more aggressive. One could expect that the share of speculators attacking the currency increases as well. Notwithstanding, if the actual fundamental θ is sufficiently good (θ > x^*), the increase in β reduces the dispersion of the distribution around the good fundamental and, therefore, a larger number of speculators receives good signals. When this second effect is sufficiently strong, it offsets the indirect effect of β on x^* and the resulting share of attackers decreases. Figure 3 provides an illustration the effect of an increase in β for a good value of y. When β raises, the resulting increase in x^* (indirect effect) tends to increase the share of attackers for each value of θ (dotted line). However, as a consequence of the direct effect, the slope of the curve changes, so that the share of attackers only increases for low values of θ, while it decreases for large values of θ.

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Effects of an Increase in β for y “Good”

Citation: IMF Working Papers 2002, 003; 10.5089/9781451841916.001.A001

Note: the thick line is the share of attackers (as a function of θ) for α = β = t = 1, D = 2, and y = 0.6 (y is “good” since x^* ⋍ 0.268). The thin line is the share of attackers for β increased to 4 (x^* raises to 0.444). The dotted line singles out the indirect effect of β as it shows the share of attackers with the new x^* = 0.444 and the old β = 1.

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In general, the net effect of an increase in β on the share of speculators depends on the relative strength of these two effects. When the direct effect prevails, the effect of the precision of private information is analogous to that of public information. Note, also, that the direct effect tends to prevail either when θ and y are both sufficiently good or when they are both sufficiently bad. Conversely, the effect of the precision of private information tends to be opposite to that of public information when the indirect effect dominates, which occurs when either θ is good and y is bad or when θ is bad and y is good.

A. The Data

To verify whether expected fundamentals and their dispersion affect the fraction of speculators attacking the currency, we build an index of exchange rate pressure.¹⁵ In recent years, several empirical studies developed indicators of exchange rate pressure aimed at identifying currency crisis periods and trying to predict them. In this paper, we follow a similar methodology but we do not transform the index of exchange rate pressure into a discrete zero-one variable separating tranquil from crisis periods as this previous literature does.¹⁶ The reason is that, in practice, some speculators attack a currency while others do not, consistently with the prediction of a private information model in which the number of speculators attacking a currency varies continuously with fundamentals and the distribution of beliefs about them.

Our index of exchange rate pressure IND3 is the sum of normalized values of three indicators of exchange rate pressure:¹⁷ i) the percentage depreciation of the domestic currency against the U.S. dollar over the previous month; ii) the fall in international reserves over the previous month as a percentage of the 12-month moving average of imports; and iii) the three-month interest rate less the annualized percentage change in consumer prices over the previous six months. To check the robustness of our results, we also compute an index IND2, which sums only normalized values of i) and ii),¹⁸ and an index BIS, which is the continuous version of an index recently developed by the Bank for International Settlements for monitoring purposes.¹⁹ Figure 4 shows the time-series behavior of these three indices.

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Indices of Exchange Rate Pressure

(1995:01–2001:05)

Citation: IMF Working Papers 2002, 003; 10.5089/9781451841916.001.A001

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Every month, Consensus Economics collects forecasts of a series of macro variables for the current and the following year. Following Brooks et al. (2001), to reproduce a constant forecast horizon of one year, we compute a weighted average of current and following year forecasts with weights equal respectively to 11/12 and 1/12 in January, 10/12 and 2/12 in February, and so on until 0/12 and 12/12 in December.²⁰ To reduce the effect of possible outliers on the results, we use the median (instead of the mean) of Consensus Economics’ forecasts at each date and the mean absolute median difference as a measure of dispersion. We limit our analysis to the forecasts of GDP growth. Consensus Economics’ forecasts for other variables–like CPI inflation, current account balance, trade balance, and exports–are available, but the number of forecasts is generally smaller than for GDP growth making mean and dispersion measures less reliable. Moreover, in preliminary estimates, these other variables tended not to perform as well as GDP growth and, when measures of the mean and variance of expected GDP growth were included in the regression, hardly any other Consensus Economics’ forecast variable was significant.

The real exchange rate index is computed by JP Morgan and is generally available with one-month lag. We found it to perform somewhat better than the nominal exchange rate. Preliminary estimates showed that actual values of GDP growth and other variables used in previous studies–such as international reserves, the ratio of M2 to international reserves, and the ratio of BIS external short-term debt to international reserves–had little effect on exchange rate pressures once we included the mean and variance of expected GDP growth in the estimated regression.

B. Benchmark Regression

Our benchmark regression is the following estimated version of equation (11):

where IND3_j,t is our index of exchange rate pressure for country j (Thailand, Korea, Indonesia, Malaysia, Singapore, Hong Kong) at time t. First, we estimated this system as a set of seemingly unrelated regressions (SUR) with country-specific coefficients and a country-specific AR(1) term to correct for serial correlation. We chose the SUR estimation method to allow for the likely correlation of the errors across countries during the Asian crisis. Second, we performed a Wald test of equality of parameters across countries, which showed that the coefficients ${\widehat{\gamma }}_1\text{and}{\widehat{\gamma }}_2$ could be constrained to be the same across countries (the null hypothesis of equality was accepted with a p-value of 0.745). Table 1 shows the results of this restricted estimation of (12). We use the restrictions accepted by the data to simplify the presentation and to conduct robustness tests involving recursive estimation (see below) on a specification with a limited number of parameters. The restriction is by no means necessary to obtain statistically significant coefficients. In the unrestricted estimates, all ${\widehat{\gamma }}_{1,j}(j=1,\mathrm{..},6)$ were negative and statistically significant at the 5 percent confidence level and all ${\widehat{\gamma }}_{2,j}(j=1,\mathrm{..},6)$ were positive and statistically significant at the 1 percent confidence level.

Table 1.

Exchange Rate Pressure (IND3 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.

Table 1.

Exchange Rate Pressure (IND3 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−10.645 ***	−1.654	−17.254 ***	−13.830 ***	−18.052 ***	6.885 **
	(3.234)	(1.347)	(3.521)	(2.318)	(6.509)	(3.439)
γ1	−0.520 ***
	(0.085)
γ2	0.592 ***
	(0.066)
${\underset{¯}{\gamma }}_{{j}}$	1.360	1.151	0.495	0.160	3.468 ***	−0.710
	(0.971)	(0.946)	(1.312)	(1.249)	(1.310)	(1.439)
γ3,j	0.142 ***	0.047 ***	0.238 ***	0.165 ***	0.184 ***	−0.046 *
	(0.035)	(0.015)	(0.042)	(0.022)	(0.058)	(0.027)
ρj	0.340 ***	0.283 **	0.503 ***	0.345 ***	0.203 **	0.294 ***
	(0.088)	(0.125)	(0.090)	(0.082)	(0.085)	(0.092)
R2	0.330	0.647	0.518	0.475	0.227	0.389
DW	1.626	1.971	1.538	1.806	1.695	2.276
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.

View Table

Table 1.

Exchange Rate Pressure (IND3 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−10.645 ***	−1.654	−17.254 ***	−13.830 ***	−18.052 ***	6.885 **
	(3.234)	(1.347)	(3.521)	(2.318)	(6.509)	(3.439)
γ1	−0.520 ***
	(0.085)
γ2	0.592 ***
	(0.066)
${\underset{¯}{\gamma }}_{{j}}$	1.360	1.151	0.495	0.160	3.468 ***	−0.710
	(0.971)	(0.946)	(1.312)	(1.249)	(1.310)	(1.439)
γ3,j	0.142 ***	0.047 ***	0.238 ***	0.165 ***	0.184 ***	−0.046 *
	(0.035)	(0.015)	(0.042)	(0.022)	(0.058)	(0.027)
ρj	0.340 ***	0.283 **	0.503 ***	0.345 ***	0.203 **	0.294 ***
	(0.088)	(0.125)	(0.090)	(0.082)	(0.085)	(0.092)
R2	0.330	0.647	0.518	0.475	0.227	0.389
DW	1.626	1.971	1.538	1.806	1.695	2.276
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.

The results shown in Table 1 confirm that higher expected GDP growth reduces exchange rate pressures. More interestingly, these estimates indicate that uncertainty about GDP growth has an additional independent effect, which depends on the level of expected GDP growth as our theoretical models predict. A higher dispersion of GDP growth forecasts tends to increase exchange rate pressures when expected GDP growth is above the estimated country-specific threshold and to reduce them when expected GDP growth is below the threshold. The threshold is statistically different from zero only for Singapore. These results are consistent with changes in the precision of public information being the main factor behind the time-series variation of the dispersion of the forecasts or, if it is the precision of private signals that has changed, with the direct effect of precision changes on the distribution of the signals dominating the indirect effect on the trigger point x^* (see Proposition 6).

C. Sensitivity Analysis

This section presents a series of robustness tests of our benchmark specification (12) confirming our main result that uncertainty about fundamentals plays a role in currency crises and that such role depends on the expected level of fundamentals.

Tables 2 and 3 present estimates of the specification (12) with two alternative measures of exchange rate pressure as dependent variable (IND2 and BIS). The coefficient measuring the effect of uncertainty $({\widehat{\gamma }}_2)$ remains positive and strongly significant. Also the coefficient measuring the effect of expected fundamentals $({\widehat{\gamma }}_1)$ remains negative and statistically significant.

Table 2.

Exchange Rate Pressure (IND2 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

Table 2.

Exchange Rate Pressure (IND2 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−6.720 ***	−1.193	−11.187 ***	−4.630 ***	−8.223	6.385 **
	(2.569)	(1.528)	(2.865)	(1.775)	(5.484)	(2.719)
γ1	−0.203 **
	(0.081)
γ2	0.333 ***
	(0.067)
${\underset{¯}{\gamma }}_{{j}}$	0.954	−1.582	−0.592	0.933	4.719 **	0.328
	(1.447)	(1.699)	(2.204)	(1.857)	(2.140)	(2.162)
γ3,j	0.083 ***	0.018	0.144 ***	0.056 ***	0.084 *	−0.048 **
	(0.029)	(0.017)	(0.034)	(0.017)	(0.049)	(0.022)
ρj	0.173 **	0.308 **	0.304 ***	0.138	0.089	0.135
	(0.088)	(0.126)	(0.098)	(0.087)	(0.086)	(0.090)
R2	0.233	0.281	0.440	0.221	0.087	0.121
DW	1.590	1.912	1.500	1.706	1.593	2.252
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

View Table

Table 2.

Exchange Rate Pressure (IND2 Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−6.720 ***	−1.193	−11.187 ***	−4.630 ***	−8.223	6.385 **
	(2.569)	(1.528)	(2.865)	(1.775)	(5.484)	(2.719)
γ1	−0.203 **
	(0.081)
γ2	0.333 ***
	(0.067)
${\underset{¯}{\gamma }}_{{j}}$	0.954	−1.582	−0.592	0.933	4.719 **	0.328
	(1.447)	(1.699)	(2.204)	(1.857)	(2.140)	(2.162)
γ3,j	0.083 ***	0.018	0.144 ***	0.056 ***	0.084 *	−0.048 **
	(0.029)	(0.017)	(0.034)	(0.017)	(0.049)	(0.022)
ρj	0.173 **	0.308 **	0.304 ***	0.138	0.089	0.135
	(0.088)	(0.126)	(0.098)	(0.087)	(0.086)	(0.090)
R2	0.233	0.281	0.440	0.221	0.087	0.121
DW	1.590	1.912	1.500	1.706	1.593	2.252
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

Table 3.

Exchange Rate Pressure (BIS Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

Table 3.

Exchange Rate Pressure (BIS Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−30.862 ***	−7.491 ***	−26.437 ***	−23.790 ***	−26.928 ***	19.706 ***
	(7.044)	(2.184)	(4.356)	(3.528)	(7.693)	(7.097)
γ1	−0.641 ***
	(0.130)
γ2	0.623 ***
	(0.094)
${\underset{¯}{\gamma }}_{{j}}$	1.511	−0.702	0.505	−1.660	5.530 ***	2.820
	(1.254)	(1.080)	(1.076)	(1.746)	(1.532)	(2.018)
γ3,j	0.374 ***	0.117 ***	0.361 ***	0.269 ***	0.275 ***	−0.136 **
	(0.076)	(0.026)	(0.054)	(0.034)	(0.069)	(0.056)
ρ1,j	0.568 ***	0.443 ***	1.076 ***	0.330 ***	0.514 ***	0.510 ***
	(0.096)	(0.102)	(0.083)	(0.081)	(0.075)	(0.088)
ρ2,j	−0.123 *	0.148 *	−0.452 ***	0.037	−0.255 ***	0.170 **
	(0.072)	(0.081)	(0.069)	(0.074)	(0.071)	(0.078)
R2	0.258	0.452	0.599	0.323	0.297	0.353
DW	1.815	2.170	1.853	1.894	1.959	2.245
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

View Table

Table 3.

Exchange Rate Pressure (BIS Index) Estimates

(SUR estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−30.862 ***	−7.491 ***	−26.437 ***	−23.790 ***	−26.928 ***	19.706 ***
	(7.044)	(2.184)	(4.356)	(3.528)	(7.693)	(7.097)
γ1	−0.641 ***
	(0.130)
γ2	0.623 ***
	(0.094)
${\underset{¯}{\gamma }}_{{j}}$	1.511	−0.702	0.505	−1.660	5.530 ***	2.820
	(1.254)	(1.080)	(1.076)	(1.746)	(1.532)	(2.018)
γ3,j	0.374 ***	0.117 ***	0.361 ***	0.269 ***	0.275 ***	−0.136 **
	(0.076)	(0.026)	(0.054)	(0.034)	(0.069)	(0.056)
ρ1,j	0.568 ***	0.443 ***	1.076 ***	0.330 ***	0.514 ***	0.510 ***
	(0.096)	(0.102)	(0.083)	(0.081)	(0.075)	(0.088)
ρ2,j	−0.123 *	0.148 *	−0.452 ***	0.037	−0.255 ***	0.170 **
	(0.072)	(0.081)	(0.069)	(0.074)	(0.071)	(0.078)
R2	0.258	0.452	0.599	0.323	0.297	0.353
DW	1.815	2.170	1.853	1.894	1.959	2.245
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁ and γ₂ are restricted to be the same across countries.

Table 4 reports the results of estimating a restricted version of our benchmark regression (12) only on the precrisis sample 1995:01-1997:07. Because of the dramatic reduction in the number of observations, we now restrict also $\underset{¯}{\widehat{\gamma }},{\widehat{\gamma }}_3,\text{and}{\widehat{\rho }}_j$ to be the same across countries, allowing only the intercepts ${\widehat{\gamma }}_{0,j}$ in each equation to be country-specific. This is equivalent to estimating a panel model with fixed effects. The effect of uncertainty is positive and statistically significant also in this precrisis sample. The negative effect of higher expected fundamentals on exchange rate pressures is also confirmed. These results hold with all measures of exchange rate pressure.

Table 4.

Exchange Rate Pressure Estimates on Pre-Crisis Sample

(fixed-effect panel estimates with SUR standard errors in parenthesis; sample: 1995:03–1997:07)¹

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The panel includes Thailand, Indonesia, Korea, Malaysia, Singapore, Hong Kong.

Table 4.

Exchange Rate Pressure Estimates on Pre-Crisis Sample

(fixed-effect panel estimates with SUR standard errors in parenthesis; sample: 1995:03–1997:07)¹

	IND3	IND2	BIS
γ1	−1.450 ***	−1.140 ***	−1.632 ***
	(0.328)	(0.227)	(0.427)
γ2	3.073 ***	2.198 ***	3.185 ***
	(0.862)	(0.642)	(1.098)
$\underset{¯}{\gamma }$	7.297 ***	7.572 ***	6.996 ***
	(0.267)	(0.344)	(0.244)
γ3	−0.008	−0.025	0.029
	(0.024)	(0.018)	(0.029)
ρ	0.375 ***	0.149 *	0.608 ***
	(0.066)	(0.077)	(0.065)
R2	0.384	0.094	0.392
DW	1.507	1.477	1.577
Observations	174	174	174

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The panel includes Thailand, Indonesia, Korea, Malaysia, Singapore, Hong Kong.

View Table

Table 4.

Exchange Rate Pressure Estimates on Pre-Crisis Sample

(fixed-effect panel estimates with SUR standard errors in parenthesis; sample: 1995:03–1997:07)¹

	IND3	IND2	BIS
γ1	−1.450 ***	−1.140 ***	−1.632 ***
	(0.328)	(0.227)	(0.427)
γ2	3.073 ***	2.198 ***	3.185 ***
	(0.862)	(0.642)	(1.098)
$\underset{¯}{\gamma }$	7.297 ***	7.572 ***	6.996 ***
	(0.267)	(0.344)	(0.244)
γ3	−0.008	−0.025	0.029
	(0.024)	(0.018)	(0.029)
ρ	0.375 ***	0.149 *	0.608 ***
	(0.066)	(0.077)	(0.065)
R2	0.384	0.094	0.392
DW	1.507	1.477	1.577
Observations	174	174	174

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The panel includes Thailand, Indonesia, Korea, Malaysia, Singapore, Hong Kong.

Table 4 shows that uncertainty affected exchange rate pressures prior to the breakdown of the exchange rate regime. This result implies that the breakdown of the exchange rate regime that most countries in our panel experienced during the second half of 1997 is not the sole determinant of the estimated effect of uncertainty on exchange rate pressures.²¹ This is consistent with the increase in uncertainty about GDP growth prior to the crisis in Thailand (from mid 1996), Korea (from end 1996), and, to a smaller extent, Malaysia (Figure 2). The increase of uncertainty in Hong Kong–which maintained a currency board for the entire period–also suggests that the breakdown of the exchange rate regime might not be the only cause of the uncertainty about fundamentals that we observe in the data.²²

More generally, the correction for serial correlation used in all regressions allows us to exclude that spurious correlation between exchange rate pressures and uncertainty about fundamentals might affect our results.²³ This problem would emerge if uncertainty about fundamentals were a function of exchange rate pressures and the time series of exchange rate pressure were serially correlated. In this case, the estimated coefficient on the lagged variance of GDP forecasts would mainly reflect the serial correlation of the exchange rate pressure series. By including a correction for serial correlation, we avoid this potential spurious regression problem (see Hamilton (1994), pp. 561-62). Results remained unchanged when we tried the alternative approach of introducing a lagged dependent variable.

Another robustness check regards the coefficients ${\widehat{\gamma }}_1\text{and}{\widehat{\gamma }}_2$. Proposition 6 implies that the predicted effect of expected fundamentals on exchange rate pressures is always negative but may vary over time together with the precision of public and private information. We allow for this possibility by estimating ${\widehat{\gamma }}_1$ recursively with state-space techniques. Figure 5 (top panel) shows that the estimated ${\widehat{\gamma }}_1$ varies within a relatively narrow range over the sample remaining always negative and strongly significant. Similarly, the effect of uncertainty on exchange rate pressures may change over time depending not only on the level of expected fundamentals (for which we control) but also on whether it is the precision of public or private information that changes and on the difference between actual fundamentals θ and the cutoff point x^*. In particular, there may be instances in which changes in the precision of private information may make the parameter ${\widehat{\gamma }}_2$ become negative. We check this possibility by estimating ${\widehat{\gamma }}_2$ recursively. Figure 5 (bottom panel) shows that the recursive estimate changes over time but remains always positive and significantly different from zero.²⁴

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Recursive Estimates of ${\widehat{\gamma }}_1\text{and}{\widehat{\gamma }}_2$

(1995:08–2001:05)

Citation: IMF Working Papers 2002, 003; 10.5089/9781451841916.001.A001

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The last robustness check regards the estimation of the thresholds separating “high” from “low” expected GDP growth. These are also likely to be time-varying reflecting changes in the parameters in s₁, s₂, and s₃, or, more simply, because investors might have revised estimates of potential growth rates as the crisis progressed. To address this potential concern, we estimate recursively the six parameters $\underset{¯}{{\widehat{\gamma }}_j}$ in (12). Figure 6 shows the recursive estimates of the $\underset{¯}{{\widehat{\gamma }}_j}$ parameters. In all countries except Hong Kong, the estimated thresholds tend to decline until end-1997 before rebounding and stabilizing below their precrisis level. Nevertheless, Table 5 shows that allowing for time-varying thresholds is of little consequence for the estimates ${\widehat{\gamma }}_1\text{and}{\widehat{\gamma }}_2$, with the latter remaining strongly significant and positive. Note that the overall estimated effect of ${\sigma }_{{\mathit{\text{GDP}}}_j,t-1}^e$ on exchange rate pressures (measured by ${\widehat{\gamma }}_2\cdot (f_{{\mathit{\text{GDP}}}_j,t-1}^e-{\underset{¯}{{\widehat{\gamma }}_j}}_{\mathit{\text{GDP}},t-1})$) may also vary as GDP forecasts $(f_{{\mathit{\text{GDP}}}_j,t-1}^e)$ and country-specific thresholds $({\underset{¯}{{\widehat{\gamma }}_j}}_{\mathit{\text{GDP}},t-1})$ change. Figure 7 shows that this estimated effect varies substantially over time but remains mostly positive with the main exception of Indonesia in 1998–99 and Singapore at end-1998.

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Recursive Estimates of the Threshold Separating High from Low Expected GDP Growth

(1996:07–2001:05)

Citation: IMF Working Papers 2002, 003; 10.5089/9781451841916.001.A001

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Table 5.

Exchange Rate Pressure (IND3 Index) Estimates with Recursive Threshold

(state-space estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.

Table 5.

Exchange Rate Pressure (IND3 Index) Estimates with Recursive Threshold

(state-space estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−9.609	−1.294	−12.448	−14.402 *	−18.941	7.397
	(8.147)	(1.604)	(8.576)	(8.020)	(12.549)	(6.090)
γ1	−0.290 *
	(0.159)
γ2	0.400 ***
	(0.085)
${\underset{¯}{\gamma }}_{{j}}$	estimated recursively (see Fig. 6)
γ3,j	0.113	0.034 *	0.168 *	0.153 **	0.178	−0.062
	(0.087)	(0.020)	(0.102)	(0.071)	(0.113)	(0.046)
ρj	0.385 **	0.250	0.487 *	0.418	0.285	0.154
	(0.159)	(0.182)	0.264	(0.273)	(0.209)	(0.207)
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.

View Table

Table 5.

Exchange Rate Pressure (IND3 Index) Estimates with Recursive Threshold

(state-space estimates; standard errors in parenthesis; sample: 1995:03–2001:05)¹

	Thailand	Indonesia	Korea	Malaysia	Singapore	Hong Kong
γ0,j	−9.609	−1.294	−12.448	−14.402 *	−18.941	7.397
	(8.147)	(1.604)	(8.576)	(8.020)	(12.549)	(6.090)
γ1	−0.290 *
	(0.159)
γ2	0.400 ***
	(0.085)
${\underset{¯}{\gamma }}_{{j}}$	estimated recursively (see Fig. 6)
γ3,j	0.113	0.034 *	0.168 *	0.153 **	0.178	−0.062
	(0.087)	(0.020)	(0.102)	(0.071)	(0.113)	(0.046)
ρj	0.385 **	0.250	0.487 *	0.418	0.285	0.154
	(0.159)	(0.182)	0.264	(0.273)	(0.209)	(0.207)
Observations	76	76	76	76	76	76

¹Data are monthly.

Three (***), two (**), and one (*) stars mark statistical significance respectively at one, five, and ten percent levels.

The coefficients γ₁, and γ₂ are restricted to be the same across countries.