Identification and Estimation in an Incoherent Model of Contagion

This paper deals with the issues of identification and estimation in the canonical model of contagion advanced in Pesaran and Pick (2007). The model is a two-equation nonlinear simultaneous equations system with endogenous dummy variables; it also represents an extension of univariate threshold autoregressive (TAR) models to a simultaneous equations framework. For a range of economic fundamentals, the model produces multiple (i.e. two) equilibria, and the choice of the equilibrium is modelled as being driven by a Bernoulli process; further, the presence of multiple equilibria leads to an incoherent econometric specification. The coherency issue is then reflected in the analytical expression for the likelihood function derived in the paper. It is proved that neither identification nor Full Information Maximum Likelihood (FIML) estimation of the model require knowledge of the Bernoulli process driving the solution choice in the multiple equilibria region. Monte Carlo experiments show that the FIML estimator performs better than the GIVE estimators proposed in Pesaran and Pick (2007). Finally, an empirical illustration based on stock market returns is provided.