Discontinuities in Indirect Estimation: an Application to EAR Models

Among the simulation-based methods, indirect estimation techniques like Indirect Inference (IndInf) and Efficient Method of Moments (EMM) provide a simple solution to many computational problems associatcd with intractable Likelihood functions. Optimisation of the objective function can be critical in presence of not-continuous response variables Iike, for instance, binary choice or discrcte choice models, limited dependent variables, switching regime models. In particular, gradient-based optimisation algorithms can face difficulties when the not continuous respones involve discontinuities in the objective function. A simple computational tool is suggested to "empirically" solve the problem. The case study is EMM applied to the autoregressive model with exponential marginal distribution (EAR). The proposed solution is also compared with the performance of the Conditional Least Squares estimation, suitable for this autoregressive model, by a set of Monte Carlo experiments.