In the most recent version of Dynare, I haven’t come across instances of a non-positive definite Hessian after the first stage search for the mode, whereas this has occurred in earlier versions.
Is this because of a programming change?
Was this problem in previous versions due to rounding errors in large models, and if so, is there an option to increase the size of the increment to the parameter values so as to avoid these errors?
Finally, given that most of the algorithms used for the mode are algorithms that have been around in various forms for the past 40 years, it seems likely that they have correctly converged, and therefore that 2nd order conditions are satisfied, even though the calculation of the Hessian may suggest otherwise. Given that many of these search algorithms use approximations to the Hessian, is it not possible to substitute the last Hessian approximation from the algorithm if the numerical value is not +ve definite? Then one could go straight to the MCMC stage without the program stopping.