“Threshold Models with Multiple Threshold Variables and their Applications” by Isabel Kit-Ming YAN
Isabel Kit-Ming YAN
City University of Hong Kong
Terence Tai-Leung CHONG
The Chinese University of Hong Kong
Conventional threshold models contain only one threshold variable. Such models are of limited economic application. This paper provides the theoretical foundation for threshold models with multiple threshold variables. The new model is much more complicated than a model with a single threshold variable as several novel problems arise with an additional threshold variable. First, models with multiple threshold variables cannot be converted into change-point models in the manner of Tsay (1998) and Hansen (1999). Second, asymptotic joint distribution of the threshold estimators may be ill-behaved should the threshold variables be dependent. Third, having more threshold variables introduces the curse of dimensionality to the estimation. In this paper, we establish the consistency of the threshold estimators. In particular, under certain conditions, we obtain the asymptotic joint distribution of threshold estimators and suggest a quick algorithm to estimate the threshold values. Tests for the number of threshold variables and their critical values are also developed. Asymptotic critical values of the LR type test for multiple threshold variables are computed. Simulations that support our asymptotic result are given. The model is applied to the study of currency crises. The major contribution of the empirical application is that it is the first study to provide clear estimates of the joint critical threshold values of multiple crisis indicators, which can be used by governments as guidelines in the regulation of short-term external borrowings and interest rate differentials.