Appeared the exogenous variables in the procedure Solving for Steady State Analytically

Steady state
1

To my knowledge, the variables belong to the varexo type shouldn’t attend the computation of the Steady State of the dsge model, but I met the exogenous variables when I debug the model.the question is that it affects Solving for Steady State.
how can i cope with…

var
      hA_Cap vA_Cap;
varexo
      SigmaA_Cap;
parameters
      …;
model;
       #OGS=…；


  [name = 'ln(hA_Cap) '] 	    
  ln(hA_Cap) = ln(SigmaA_Cap^2) - OGS; 

  [name = 'vA_Cap'] 
  ln(vA_Cap)    = rhoA*ln(vA_Cap(-1)) + hA_Cap;


end;

steady_state_model;
      hA_Cap = exp(- OGS);
      vA_Cap    =  exp(hA_Cap/(1-rhoA));
      …
end

debug: the SigmaA_Cap^2 appeared, it is the ‘x(3)^2’ in the “static_resid.m”, residual(15) != 0

lhs = log(y(22));
rhs = log(x(3)^2)-(params(123)\*(-((-2.302585092994045)\*params(127)))-(-((-2.302585092994045)*params(127)))*(1-params(123)));
residual(15) = lhs - rhs;
2

In typical steady state computations, exogenous variables are zero. How is

ln(SigmaA_Cap^2)=ln(0)

supposed to work?

3

It doesn’t return an error information, but report in the part of the Residuals of the static equations:

Equation number 14 : inf : ln(hA_Cap)
Equation number 15 : inf : ln(hC_Cap)
Equation number 16 : inf : ln(hB_Cap)
Equation number 17 : inf : ln(hH_Cap)
Equation number 18 : inf : ln(hS_Cap)

here,

rhs = log(x(3)^2)-(params(123)\*(-((-2.302585092994045)\*params(127)))-(-((-2.302585092994045)*params(127)))*(1-params(123)));

is a compiling expression of the equation

ln(hA_Cap) = ln(SigmaA_Cap^2) - OGS

so I doubted the SigmaA_Cap attended the compution of the …

4

As I wrote above, your setup results in taking the logarithm of 0, which is -\infty. Thus, your setup will not work.

5

I understood , but To my knowledge, the exogenous variables shouldn’t appear in the procedure of computation of the Steady State. because in practice , sometimes we have to use such expression ‘ln(sigma^2) ‘

6

No, the steady state is always conditional on the value of the exogenous variables. For stochastic simulations the exogenous variables are assumed to have steady state 0. For perfect foresight simulations, you can provide a different value and compute the steady state conditional on that value.

7

I get it, thanks a lot, professor