I am trying to figure out if it is possible to use posteriors that are coming out of Bayesian estimation as priors for another Bayesian estimation exercise.

For instance if there are 2 rolling estimations, I would like to use the posteriors that are coming out from the 1st estimation as priors for the 2nd estimation. Is that doable in dynare?

If I understand correctly you want to split the sample in two parts and use the first part as a prior for the estimation on the second sub-sample. In this case I don’t think you need to do anything because it’s perfectly equivalent to estimate with the whole sample. Let Y be the sample and Y_0 and Y_1 be the two subsamples. Let theta be the vector of estimated parameters. The likelihood of the
model is:

p(Y|theta)

which, by virtue of the Bayes theorem, can be rewritten as:

p(Y_1|Y_0,theta)*p(Y_0|theta)

the second term can then be interpreted as a prior for the estimation with the second sub-sample. Obviously we can add a prior density for theta, but this does not change the way we can decompose the likelihood.

If I misunderstand your problem, you can use a posterior as a prior for a model by fitting the prior density on the posterior draws from the metropolis hastings. But there is nothing in Dynare to do this an you have to code it yourself…