You should always fully calibrate your model to see whether it runs. See Remark 2 (Using stoch_simul before Estimation) in Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf. Whenever you want to run command like steady, check, or stoch_simul before estimation, the parameters need to be set. If you only want to run estimation without any other commands before it, you do not need to set the parameters. Dynare will then use the prior mean by default. As you saw in your model, nothing guarantees that the prior mean is a feasible parameter set. In your case, the BK conditions were not satisfied. In contrast, if you already ran stoch_simul with a sensible parameterization and it worked, you now know that this is a problem with the parameters, not with the model setup itself. That is why we recommend calibrating the model and then trying the calibration as a starting value.
With the
estimated_params_init;
bet, 0.253;
rho, 0.90253;
end;
block, you tell Dynare to use the given values for the specified parameters as starting values. For all others, it uses the prior mean (the default). If you use
estimated_params_init(use_calibration);
bet, 0.253;
rho, 0.90253;
end;
Dynare will use the calibrated parameter values instead of the prior mean for all parameters not explicitly specified in the block.
Regarding updating: all estimated parameters will be updated during mode-finding/estimation.
The last problem is that for Bayesian estimation, one requires being at a mode. That does not seem to be the case as you are getting a non-positive definite Hessian. Thus, have a look at the mode_check plots. They often give you an indication of what is wrong. Most of the time, there still a mismatch between data and the model. See Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.