Degrees of indeterminacy and Jocobian matrix

General DSGE Modeling Replication Attempts
1

Dear Professor Pfeifer,

My DSGE model input in dynare has the indeterminacy problem, which is solved by adding one sunspot shock to either of two variables. Adding sunspot shocks to other variables does not work. Does it mean the indeterminacy degree of my model is one, and only relates one of those two variables? I am wondering how to figure out what is the degree of indeterminacy exactly?

I thought this problem can be solved by asking the dynare codes to print the Jocobian matrix. In dynare manual, there is one command for it.

"Command: print_bytecode_dynamic_model ;
Prints the equations and the Jacobian matrix of the dynamic model stored in the bytecode binary format file. Can only be used in conjunction with the bytecode option of the model "

But I do not know how to change change the model codes in dynare into bytecode binary format.

To sum up, my question is how to figure out the exact degree and variables for indeterminacy. If it can be solved by printing Jocobian matrix, how to command to display Jocobian matrix in dynare? Such information will provide the reference and guidance for our strategy of sunspot shocks.

Many thanks for your instruction!

Best wishes,
Claire

2
  1. You would determine the degree of indeterminacy based on the Blanchard-Kahn conditions as provided by the output of check;. The discrepancy between the number of unstable eigenvalues and forward-looking variables is the degree.
  2. Sunspots are related to expectational errors and can be solved by associating such a forward-looking variable with a sunspot shock. You cannot simply put it anywhere.
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Dear Professor Pfeifer,

Your replies are very helpful! Many thanks for your instruction!

The output of check shows that “There are 6 eigenvalue(s) larger than 1 in modulus
for 7 forward-looking variable(s)”. It makes it clear that the degree of indeterminacy is 1. It solves the problem.

I still have another two questions relevant about indeterminacy:

(1) How to display the jumpers in dynare? I am wondering what variables are regarded as jumpers exactly by dynare computation.

MODEL SUMMARY

Number of variables: 36
Number of stochastic shocks: 3
Number of state variables: 7
Number of jumpers: 6
Number of static variables: 23

(2) I adding a sunspot shock to two looking-farward variables respectively, and both models solve the indeterminacy problem. Is there any selection criterion to decide which expectational error is better to move to the set of fundamental shocks in the model?

Many thanks for your help again!

Best wishes,
Claire

4
  1. See Perfect foresight model - What variables predetermined and forward looking? - #2 by jpfeifer
  2. Maybe have a look at the Bianchi/Nicolo paper: https://onlinelibrary.wiley.com/doi/full/10.3982/QE949