Would it be possible with Dynare to reproduce papers such as “The 1990s in Japan: A Lost Decade” by Hayashi and Prescott or “The Japanese Saving Rate Between 1960 and 2000: Productivity, Policy Changes, and Demographics” by Chen et al.?

Okay, thank you very much. It is just, that I don’t see how to confront the model with real data. Of course one could extend the program by hand-coding the relevant Matlab routines, but that is not what I am looking for. I admit I have not read all documentation, and generally should have researched the subject more, before I should ask this question.
I can paraphrase my question: is it possible, within the Dynare framework and without any further technicalities, to simulate models with real data, such as done in the said papers.

it is possible to estimate any DSGE model ( OLG or IFRA) models with this toolbox with real world data. however the fit of many of these models is not upto scratch since DSGE models, are essentially economic and not statistical models. we can estimate them as they have a statistical state space representation , and the likelihood can be evaluated and maximised as in a regression model. one needs to adjust the model, to fit the persistence of the data, so that the estimates makes some sense. one measure of the fit of the model would be the size of the std errs of the shock. the thing to be careful is that the model variables should correspond one-to-one with the data transformation for the observables.