What is endogenous state variable in this simple model?

[leolee]

Dear DGSE experts,

The following model is famous simple 3 equation forward-looking NK model with forward-looking Taylor rule. I know the following model is easily solved using Dynare.

Code: Select all

model(linear);
   //CB model
      # kappa = (1-theta)*(1-theta*beta)/theta;
      
      y   = y(+1) - (1/sigma)*(R - pi(+1)) + g;
      pi     = beta*pi(+1) + kappa*y + z;
      R      = rhoR*R(-1) + (1-rhoR)*(phipi*pi(+1)+phiy*y) + em;

      // process of preference/cost shocks   
      g       = rhog*g(-1) + eg;
      z       = rhoz*z(-1) + ez;
end;

However, when I tried to solve this using Uhlig's toolkit, I couldn't figure out what is endogenous state variable in this model, which was necessary to construct matrices for Uhlig toolkit.

I know that capital is the endogenous state variable in RBC model, but there is no capital in this NK model. There are 3 endogenous variables (y, pi, R) in this model, and they don't seem to be state variables.

Is there anyone who kindly help me to figure it out?

Thank you in advance.

Regards,

Leo

Please someone help me to understand this..

[jpfeifer]

The 3 equation NK model has no endogenous states. But depending on how you set up the code, it can be necessary to define the lags of endogenous variables as endogenous states, i.e. R(-1), g(-1), z(-1)

[leolee]

Thank you!

The 3 equation NK model has no endogenous states. But depending on how you set up the code, it can be necessary to define the lags of endogenous variables as endogenous states, i.e. R(-1), g(-1), z(-1)