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This work studies the class of new Keynesian models.
We are looking at stability properties and
conducting a bifurcation analysis. Bifurcation
analysis is often overlooked while examining the
properties of the model. Bifurcation is a
qualitative change in the nature of a solution that
occurs due to change of the parameter value. For
example stable system can become unstable. The
parameter space of most dynamic models is stratified
into subsets, each of which supports a different
kind of dynamic solution. Since we do not know the
parameters with certainty,knowledge of the location
of the bifurcation boundaries is of fundamental
importance. Without it there is no way to know
whether the confidence region about the parameters
point estimates might be crossed by such a boundary,
thereby stratifying the confidence region itself and
damaging inferences about dynamics.Central results
in this work are the theorems on the existence and
location of Hopf bifurcation boundaries.We also
solve numerically for the location and properties of
the Period Doubling bifurcation boundaries and their
dependency upon policy-rule parameters.
We are looking at stability properties and
conducting a bifurcation analysis. Bifurcation
analysis is often overlooked while examining the
properties of the model. Bifurcation is a
qualitative change in the nature of a solution that
occurs due to change of the parameter value. For
example stable system can become unstable. The
parameter space of most dynamic models is stratified
into subsets, each of which supports a different
kind of dynamic solution. Since we do not know the
parameters with certainty,knowledge of the location
of the bifurcation boundaries is of fundamental
importance. Without it there is no way to know
whether the confidence region about the parameters
point estimates might be crossed by such a boundary,
thereby stratifying the confidence region itself and
damaging inferences about dynamics.Central results
in this work are the theorems on the existence and
location of Hopf bifurcation boundaries.We also
solve numerically for the location and properties of
the Period Doubling bifurcation boundaries and their
dependency upon policy-rule parameters.