When running th estimation command for a medium-size DSGE model, I get the message “Numerical noise in the likelihood”. What kind of problem is that (from a numerical point of view), and it is an indication that there is some type of problem in the model I am using ?

I guess this is displayed with mode_compute = 5. In that optimizer, some numerical checks are performed when computing the gradient. In particular we try to tune the perturbation of each parameter (say dx(i)) such that the change in the log-likelihood (df) is in the order of 1.e-5. Typically df versus dx(i) is monotonic, so it is quite easy to tune dx(i), up to reasonable numerical precision. When this is not possible, usually the estimation is near to some unit root or prior boundary, then the precision for df is relaxed to higher values (1.e-4 1.e-3 and so on) and the warning is displayed.

This warning may appear in some iterations, then if the optimizer manages to escape the bad region, it disappear, otherwise, in most cases, your optimization will end-up in some boundary.