Determinacy in 2nd Aproximation

[bigbigben]

I am just curious about how to set up the criterion for indeterminacy in a 2nd order approximation. I know we can look at the number of controls and number of explosive engenvalues, but how to do it in a 2nd order system. For example, If we have

c(t+1)=a11*c(t)+a12*k(t)+b11*c(t)^2+b12*k(t)^2
k(t+1)=a21*c(t)+a22*k(t)+b21*c(t)^2+b22*k(t)^2

How many controls do we have and how many eigenvalues do we have?

[StephaneAdjemian]

Blanchard and Kahn conditions are conditions for local determinacy. They are defined from the first order approximation of the model.

Best,
Stéphane.

I am just curious about how to set up the criterion for indeterminacy in a 2nd order approximation. I know we can look at the number of controls and number of explosive engenvalues, but how to do it in a 2nd order system. For example, If we have

c(t+1)=a11*c(t)+a12*k(t)+b11*c(t)^2+b12*k(t)^2
k(t+1)=a21*c(t)+a22*k(t)+b21*c(t)^2+b22*k(t)^2

How many controls do we have and how many eigenvalues do we have?