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Dear all,

The attached file contains codes for identification analysis I did on the simple model of An and Schorfheide (2007, Econometric Reviews: Bayesian Analysis of DSGE Models). The log file (estimate_M1D1.log) is also attached, which shows that all the parameters in the Taylor rules are collinear with respect to other parameters. When I do monte carlo analysis, the same problem arises. Does this problem mean that the Taylor rule coefficients are not identified? Could anyone please provide some deeper insights into the problem? Thanks a lot!!!

Testing prior mean
Evaluating simulated moment uncertainty ... please wait
Doing 100 replicas of length 300 periods.
Simulated moment uncertainty ... done!

WARNING !!!
The rank of H (model) is deficient!

eps_R is collinear w.r.t. all other params!
psi1 is collinear w.r.t. all other params!
psi2 is collinear w.r.t. all other params!
rho_R is collinear w.r.t. all other params!

WARNING !!!
The rank of J (moments) is deficient!

eps_R is collinear w.r.t. all other params!
psi1 is collinear w.r.t. all other params!
psi2 is collinear w.r.t. all other params!
rho_R is collinear w.r.t. all other params!

Take a look at the appendix to Iskrev (2010): Local identification in DSGE models at http://www-personal.umich.edu/~niskrev/. It says

rank deficiency of H means that the necessary rank condition for identification fails. Dynare shows that this is due to the exact linear dependence among
the columns of H associated with the Taylor rule parameters psi1, psi2, rhor and the standard deviation of the policy shock stdr. In other words these 4
parameters cannot be identified together but if any one of them was known the remaining would be identifiable.

See also Section "7.2 The An and Schorfheide (2007) model" of Mutschler (2014): Identification of DSGE Models - the Effect of Higher-Order Approximation and Pruning:

Thank you so much, Dear Johannes! These references are very helpful!