Identification and Estimation in an Incoherent Model of Contagion∗

This paper deals with the issues of identification and estimation in a bivariate simultaneous equations system with endogenous dummy variables and continuous observable dependent variables. The model is an extension of threshold models to a simultaneous equations framework. Depending on the sign of relevant parameters, for a range of values of the exogenous variables the relationship between the errors and the dependent variables no longer is a function: either it does not exist; or, if it does, it is just a mapping. The model therefore belongs to the class of incoherent econometric specifications: the joint density of the dependent variables (conditional upon the exogenous variables) no longer integrates to unity. Because of the nonlinear nature of the system, identification of the model is achieved without imposing any restriction on the parameters space. Due to the coherency issue, construction of the likelihood function requires rescaling the conditional joint density of the dependent variables. The resulting Full Information Maximum Likelihood (FIML) estimator is compared to a GIVE estimator, and by Monte Carlo analysis it is shown to be likely to provide better performance. From an economic point of view, the model can be applied to assess the presence of contagion in financial markets: in this sense, a relevant application to equity returns is provided; the obtained results cannot rule out the presence of contagion effects between the markets we consider. JEL classification: C10, C13, C15, C32, G10, G15