Comments Welcome Probabilities, Probits and the Timing of Currency Crises Susan M. Collins GeorgetownUniversity The Brookings Institution and NBER* Draft: March 2003 Abstract A growing empirical literature studies determinants of the probability of a currency crisis, often searching for a combination of indicators to provide an early warning system (EWS). The existing work frequently relies on discrete choice specifications, such as probits, that do not incorporate the time dimension of the occurrence of currency crises and that are not derived from an underlying behavioral model. These ad hoc specifications are defined over a fixed horizon (such as 24 months) and provide no consistent way of estimating crisis probabilities over other horizons (such as 3, 12 or 36 months). This paper shows how a probit can be interpreted in terms of restrictions on a simple threshold model of the timing of a currency crisis, that is based on recent theoretical models of crises. Using data for 25 emerging markets, the threshold specification is shown to fit better than either a probit specification, or the exponential waiting time distribution implied by a poisson model of crises. In addition, the threshold model can be used to generate estimates of the probability of a crisis occurring over any future time horizon, as a function of current indicators. _________________________ * Much of the work for this paper was done while I was visiting the IMF. I would like to thank Andrew Berg, Robert Flood, Olivier Jeanne, Kenneth Kletzer, Sam Oularis and Catherine Patillo for helpful discussions and suggestions. I am also grateful to Andrew Berg and Catherine Pattillo for providing their data, and to Haiyan Shi for research assistance. Views expressed do not necessarily represent those of any of the institutions listed.- 1 - 1. Introduction In the aftermath of several severe currency crises affecting countries around the globe, there has been an explosion of empirical studies of crises. This work has focused on a variety of interesting and important issues, including the following. How should crises be defined? Are crises predictable? What explanatory variables should be included in the empirical analysis? Can an early warning system (EWS) be designed that would signal the increased likelihood of a crisis? But although some papers also address the appropriate econometric specification for modeling the probability of a crisis, the most frequent estimation approach has been some form of probit (or logit). The simplest versions define the dependent variable as one or zero depending on whether the event (a currency crisis) does or does not occur within a particular time period. In other words, many studies use a specification designed to study the probability of a “discrete choice” so as to study the probable occurrence of a discrete event within a given time period. While this approach may provide useful descriptive information, it has a number of shortcomings. In particular, it is not clear how to interpret a discrete choice framework in the context of an event that unfolds over time. This framework is not based on a behavioral model of what causes a crisis. It does not provide a consistent means of studying the probability of a crisis at different time horizons – the timing of the crisis. And estimation typically ignores information about when crises actually occurred. This paper has three main tasks. First, building on Collins (1992) it uses a threshold model of currency crises to develop an econometrically tractable model of the timing of a crisis. This threshold model is consistent with many first generation models of currency crises as well as some specifications of second generation models. The paper then shows that a probit specification can be interpreted in terms of restrictions on the crisis probability implied by the threshold model. Second, a simple version of the threshold model is tested against a probit specification, using data for 25 emerging market economies during the period 1985-98. The threshold model is also tested against another alternative -- a poisson model of crises. Finally the paper estimates the full version of the threshold model and discusses the results. In particular, the estimates are used to construct the- 2 - implied evolution of the probability of a crisis over different time horizons, and implications for selected countries are discussed. It is important to note at the outset a number of things that this paper does not attempt to do. It breaks no new ground in terms of how currency crises should be defined, nor does it introduce additional explanatory variables. Instead, data from previous, well known work by Berg and Pattillo (1999a,b) are used for the estimations so that the threshold specification can be tested against an existing probit analysis. Also, and unlike much of the EWS literature, this work is not intended to provide an alternative approach to forecasting currency crises. Indeed, non-parametric and other methods may well out-perform more structural model based equations. No effort is made to examine the forecasting ability of the threshold model, either in or out of sample. The empirical literature on currency crises is large and growing rapidly.1 It can be divided loosely into four groups, discussed briefly below. (Some of the studies listed employ more than one methodology). One set of studies uses the signals -- or indicators -- approach, developed by Kaminsky, Lizondo and Reinhart (1998). The approach has been extended by Kaminsky and Reinhart (1999), Kaminsky (1999) and Edison (2000) among others. Borensztein et. al. (2000) describes the IMF usage of this approach as one of its EWS models. These studies define a crisis indicator equal to one if a crisis occurs and zero otherwise. They next construct zero/one indicator variables for a set of explanatory variables. The indicators can then be used to forecast crises. The second, and most numerous, set of studies uses limited dependent variable techniques (probit or logit) to relate the probability of a crisis to a set of explanatory variables. Early studies of exchange regime collapse using probit include Eichengreen, Rose and Wyplosz (1996), who study 20 industrial countries, and Frankel and Rose (1996) who study 105 developing countries. Klein and Marion (1997) use a logit specification to study exchange