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I have a question on the feasibility of estimating the Gertler-Kiyotaki(2013)'s bank run model. Some features which might impose difficulty in the numerical implementation of the model are(I try to keep it as concise as I could! ):

1. There are two different regimes: in regime 1 (when the negative shock is not large enough), there wouldn't be bank run and it's a traditional DSGE world with financial intermediation; in regime 2 (when the negative shock is severe enough), there would be possibly be bank run where all banks would be liquidated. The region in which bank run can occur (regime 2) is endogenous, determined by fundamental.

2. Once the economy falls into region 2, there would multiple equilibria with sell-fulfuling prophecy: bank run can possibly but not necessarily occur based on non-fundamental factor.

2. The model is calibrated so that there would no bank-run in the non-stochastic steady state; HOWEVER, when the economy falls in region 2 and bank run occurs, the financial interemediaries would be absent in the economy, implying that the economy would not go back to its original steady state, and neither would the economy move back to regime 1.

To me, all the above considerations add many complexities to the canonical DSGE model. Is it possible to do some modification and take it to the data with implementing the Bayesian estimation?

Thanks very much!

I am not familiar with the particular model, but this seems impossible to do with standard Bayesian techniques. What you describe sounds like a regime-switching model. The way Dynare solves stochastic models for estimation with MCMC methods it assumes a recursive and stationary/time-invariant problem. In your case, the problem seems not time invariant, because there is an absorbing state.