I am using Dynare to estimate a DSGE model (MLE). I choose the default searching algorithm by Sims by setting mode_compute=4. The trouble is that some times I got log-likelihood is positive. What does that mean? The possibility is higher than one?

It’s OK, because likelihood is density. It’s not probabylity for continius distribution function. It could be ilustrated by comaring of normal density(at point of mean) with standart deviation equal to 10^-2.