APPENDIX I. Proof for proposition 2
APPENDIX II. Equilibrium of the public and private information game
APPENDIX III. Proof for propositions 4, and 5
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IMF Research Department and the Bank of Italy. The authors thank Nikila Tarashev for helpful comments and Bianca Bucci, Rosanna Gattodoro, Alessandra Liccardi, and Giovanna Poggi for valuable research assistance. The views expressed in the paper are those of the authors and do not necessarily reflect those of the IMF or the Bank of Italy.
The shaded area marks the period from July 1997 to the end of 1998, which includes the Asian crisis, the Russian crisis, and the near-collapse of the hedge fund Long Term Capital Management. The evolution over time of the mean and variance of other macro forecasts in the Consensus dataset is similar to that of GDP.
In Goldberg (1991), domestic credit growth follows a random walk process with errors distributed as a displaced exponential with zero mean; as long as the variance of the errors does not exceed an upper bound, greater uncertainty increases the probability of an attack. In counterfactual simulations, Goldberg (1994) finds, however, that a higher variance of domestic credit growth would have reduced the probability of an attack in Mexico between 1980 and 1986. In Grilli (1986), fundamentals follow an AR(1) process with normal errors; as long as fundamentals are “good,” the effect of the variance on the probability of an attack is positive, but with sufficiently “bad” fundamentals it may become negative.
In the unique-equilibrium model with both public and private information, comparative statics exercises predict the likelihood of a speculative attack. In the model with only public information, which may yield multiple equilibria, we refer to the likelihood of an attack more loosely to indicate–as it is common in the literature on speculative attacks–that the range of parameters in which an attack takes place has either widened or shrunk.
We assume–without altering the analysis–that the government chooses to abandon the peg when he is indifferent.
Hereafter we restrict our attention to pure strategies.
The sharp increase in the dispersion of GDP forecasts in the aftermath of currency crises documented in Figure 2 may reflect an increase in “model uncertainty” (i.e., an increase of the uncertainty about the “true” model of Asian economies), as defined by Routledge and Zin (2001). In the theoretical framework of our paper, an increase in model uncertainty may translate into a higher variance of public or private information depending on whether uncertainty increased in a similar or different way across agents.
Note that, given D, t, and y, changes in α (i.e. changes in speculators’ uncertainty about θ) may produce a shift from a model with multiple equilibria to a model with a unique equilibrium. Hence, one can find examples in which modifications in uncertainty trigger a speculative attack, even if the mean of speculators’ expectations y does not change. This feature of currency crisis games is further analyzed in Sbracia and Zaghini (2001).
Note also that for intermediate values of y (0 < y < 1), if α increases, there is a widening of the range of parameters in which both the attack and the don’t attack strategy profiles are equilibria of the game.
Using a somewhat different framework, Chan and Chiu (2001) show that if the complete information game does not include both regions characterized by a unique equilibrium, than private information may not select a unique equilibrium. In other words, for the unique-equilibrium result it is also crucial that there is a non-negative probability that θ belongs to (−∞, 0) and to (1, +∞). This condition is fulfilled when we assume normal distributions.
An exception is given by equilibria in mixed strategies that–in both complete and public information models–could give rise to shares of speculators attacking the currency that are neither zero nor one.
Heinemann and Illing (1999) obtain a different result on the effect of private information. In their model, an increase in the precision of private information, β, always decreases θ*, making speculative attacks less likely. However, Heinemann and Illing assume that θ is uniformly distributed over the unit interval. In terms of our model, this assumption would correspond to a fixed y, set equal to 1/2. Hence, their result is consistent with our model–which, for a fixed y, predicts that an increase in β always reduces θ*, provided that condition (5) is not fulfilled. It should also be noted that, when uncertainty is high, Heinemann’s and Illing’s model tends to favor the attack strategy profile because, in case of a successful attack, speculators’ payoffs are assumed to depend negatively on θ. This assumption means that, if the attack is successful and θ is low, speculators may obtain a large payoff, whereas they loose only the transaction cost t if their attack is not successful. As a result, in their model, an increase in uncertainty–making extreme values of θ more likely–tends to drive speculators on the attack strategy profile.
In Section II, we show that the variance of public information has similar effects in a model with only public information, independently on the number of equilibria. A proper test of a model with multiple equilibria would, however, require a different econometric approach that allows for jumps across multiple equilibria.
Girton and Roper’s (1977), Roper and Turaovsky (1980), and Weymark (1998) discuss the assumptions needed to justify different definitions of indices of exchange rate pressure in theoretical macro models.
An exception is Sachs et al. (1996) who use a weighted sum of the percent decrease in reserves and the percent depreciation of the exchange rate in a cross-country regression.
To normalize, we subtract from each indicator the country-specific mean and divide the result by the country-specific standard deviation.
Indices based only on exchange rate and reserve changes are the most common in the empirical work on early warning systems because of the lack of reliable data on interest rates for panel datasets with a large number of developing countries and a long time series dimension. This is the case of the early warning system used by the IMF (see Berg et al. (2000)).
The BIS index is based on four indicators of exchange rate pressure: i) the percentage depreciation of the domestic currency against the U.S. dollar over three months; ii) the percentage depreciation of the domestic currency against the U.S. dollar over one year; iii) the three-month interest rate less the annualized percentage change in consumer prices over the previous six months; and iv) the fall in international reserves over three months as a percentage of the 12-month moving average of imports. The BIS transforms the values taken over time by each indicator into scores which are then weighted to compute an index that can take 21 different values from −10 (maximum appreciating pressure) to +10 (maximum depreciating pressure). Annex B of Hawkins and Klau (2000) describes in detail the construction of this index. By contrast, we compute a continuous index by adding normalized values of each of the four indicators of exchange rate pressure.
Multicollinearity of current and following year forecasts prevents us from including both variables in the regression. We obtained, however, very similar estimates by including only the following year forecast or the following year forecast together with the difference between the following and current year forecasts. In this case, we seasonally adjusted the dispersion measures to account for the smaller dispersion of forecasts–documented by Loungani (2001)–at the end of the year than at the beginning of the year and after data releases.
Jeanne and Rose (2000) show, for example, that market expectations should be noisier under a floating exchange rate regime.
Some related evidence is the fact that the peak in uncertainty about GDP growth is at the time of the Russian crisis (between August and October 1998) whereas the peak of exchange rate depreciation is in January 1998 for Thailand, Korea, and Malaysia, in July 1998 for Indonesia, and in August 1998 for Singapore and Taiwan.
Note that this problem is distinct from the possible contemporaneous feedback effect of exchange rate pressures onto the mean and variance of fundamentals, which would cause a potential endogeneity problem that we address by lagging all regressors.
We also estimated separate recursive coefficients