As I wrote above: this equation is definitely wrong as presented in the model. Hence, it’s unclear what the authors actually did.
I replaced the multiplication and division operators of equation 19 with the addition and subtraction operators respectively, and the following appears:
Starting Dynare (version 5.5).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Substitution of exo lags: added 1 auxiliary variables and equations.
Found 53 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 2).
Processing outputs ...
done
Preprocessing completed.
Residuals of the static equations:
Equation number 1 : -36.3523 : Consumption euler eq.(1)
Equation number 2 : -0.048647 : Investment euler eq.(2)
Equation number 3 : -1.0372 : Capital arbitrage eq.(3)
Equation number 4 : -0.0049369 : Capital stock evolves eq.(4)
Equation number 5 : 0.39916 : Output produced using capital and labor services eq.(5)
Equation number 6 : -49.4859 : Cost minimization yields the demand for labor eq.(6)
Equation number 7 : 0.4217 : Firms entrepeneurs net worth evolves eq.(7)
Equation number 8 : 0 : Firms entrepeneurs net worth equals your consumption eq.(8)
Equation number 9 : 212.7314 : Hybrid price setting eq.(9)
Equation number 10 : 27.2498 : Hybrid wage setting eq.(10)
Equation number 11 : 0.025745 : Credit spread eq.(11)
Equation number 12 : -50.8805 : Notional interest rate eq.(12)
Equation number 13 : 0 : Nominal interest rate eq.(13)
Equation number 14 : 0 : Monetary base eq.(14)
Equation number 15 : -0.28529 : Broad monetary supply.(15)
Equation number 16 : 0.63529 : Export demand eq.(16)
Equation number 17 : 1.4999 : Import demand eq.(17)
Equation number 18 : 163.795 : Expected movement in the real exchange rate eq.(18)
Equation number 19 : -0.9834 : Evolution of foreign bonds eq.(19)
Equation number 20 : 1.4364 : Aggregate resource constraint eq.(20)
Equation number 21 : 0.502 : Government spending shock eq.(21)
Equation number 22 : 0 : Investment specific shock eq.(22)
Equation number 23 : 0 : Productivity shock eq.(23)
Equation number 24 : 0 : Wage mark up shock eq.(24)
Equation number 25 : 0.00435 : Credit spread shock eq.(25)
Equation number 26 : -0.29735 : M1 shock eq.(26)
Equation number 27 : -0.16 : Import demand shock eq.(27)
Equation number 28 : 0 : Foreign real interest rate shock eq.(28)
Equation number 29 : 0 : Preference shock eq.(29)
Equation number 30 : 0 : Taylor rule shock eq.(30)
Equation number 31 : -0.315 : Price mark up shock eq.(31)
Equation number 32 : 0 : Labour supply shock eq.(32)
Equation number 33 : -0.015 : Net worth shock eq.(33)
Equation number 34 : -0.155 : Export demand shock eq.(34)
Equation number 35 : 0 : Foreign consumption shock eq.(35)
Equation number 36 : 0 : Foreign inflation shock eq.(36)
Equation number 37 : -0.4 : Observation equation output
Equation number 38 : -0.4 : Observation equation consumption
Equation number 39 : -0.4 : Observation equation investment
Equation number 40 : -0.4 : Observation equation real wage
Equation number 41 : -0.4 : Observation equation net worth
Equation number 42 : -0.4 : Observation equation monetary base
Equation number 43 : -0.4 : Observation equation monetary supply
Equation number 44 : -0.4 : Observation equation exports
Equation number 45 : -0.4 : Observation equation imports
Equation number 46 : 0.0258 : Observation equation foreign bonds
Equation number 47 : -1.26 : Observation equation inflation
Equation number 48 : 163.1623 : Observation equation interest rate
Equation number 49 : 0 : Observation equation hours worked
Equation number 50 : 0.0174 : Observation equation credit spread
Equation number 51 : 0.8416 : Observation equation cost of credit
Equation number 52 : 0.0068 : Observation equation real exchange rate
Warning: Matrix is singular to working precision.
> In evaluate_steady_state (line 305)
In steady_ (line 55)
In steady (line 80)
In prueba.driver (line 891)
In dynare (line 281)
Residuals of the static equations:
Equation number 1 : NaN : Consumption euler eq.(1)
Equation number 2 : NaN : Investment euler eq.(2)
Equation number 3 : NaN : Capital arbitrage eq.(3)
Equation number 4 : NaN : Capital stock evolves eq.(4)
Equation number 5 : NaN : Output produced using capital and labor services eq.(5)
Equation number 6 : NaN : Cost minimization yields the demand for labor eq.(6)
Equation number 7 : NaN : Firms entrepeneurs net worth evolves eq.(7)
Equation number 8 : NaN : Firms entrepeneurs net worth equals your consumption eq.(8)
Equation number 9 : NaN : Hybrid price setting eq.(9)
Equation number 10 : NaN : Hybrid wage setting eq.(10)
Equation number 11 : NaN : Credit spread eq.(11)
Equation number 12 : NaN : Notional interest rate eq.(12)
Equation number 13 : NaN : Nominal interest rate eq.(13)
Equation number 14 : 0 : Monetary base eq.(14)
Equation number 15 : NaN : Broad monetary supply.(15)
Equation number 16 : NaN : Export demand eq.(16)
Equation number 17 : NaN : Import demand eq.(17)
Equation number 18 : NaN : Expected movement in the real exchange rate eq.(18)
Equation number 19 : NaN : Evolution of foreign bonds eq.(19)
Equation number 20 : NaN : Aggregate resource constraint eq.(20)
Equation number 21 : 0 : Government spending shock eq.(21)
Equation number 22 : 0 : Investment specific shock eq.(22)
Equation number 23 : 0 : Productivity shock eq.(23)
Equation number 24 : 0 : Wage mark up shock eq.(24)
Equation number 25 : NaN : Credit spread shock eq.(25)
Equation number 26 : NaN : M1 shock eq.(26)
Equation number 27 : NaN : Import demand shock eq.(27)
Equation number 28 : 0 : Foreign real interest rate shock eq.(28)
Equation number 29 : 0 : Preference shock eq.(29)
Equation number 30 : 0 : Taylor rule shock eq.(30)
Equation number 31 : NaN : Price mark up shock eq.(31)
Equation number 32 : 0 : Labour supply shock eq.(32)
Equation number 33 : NaN : Net worth shock eq.(33)
Equation number 34 : NaN : Export demand shock eq.(34)
Equation number 35 : 0 : Foreign consumption shock eq.(35)
Equation number 36 : 0 : Foreign inflation shock eq.(36)
Equation number 37 : NaN : Observation equation output
Equation number 38 : NaN : Observation equation consumption
Equation number 39 : NaN : Observation equation investment
Equation number 40 : NaN : Observation equation real wage
Equation number 41 : NaN : Observation equation net worth
Equation number 42 : 0 : Observation equation monetary base
Equation number 43 : 0 : Observation equation monetary supply
Equation number 44 : NaN : Observation equation exports
Equation number 45 : NaN : Observation equation imports
Equation number 46 : NaN : Observation equation foreign bonds
Equation number 47 : NaN : Observation equation inflation
Equation number 48 : NaN : Observation equation interest rate
Equation number 49 : NaN : Observation equation hours worked
Equation number 50 : NaN : Observation equation credit spread
Equation number 51 : NaN : Observation equation cost of credit
Equation number 52 : NaN : Observation equation real exchange rate
Error using print_info (line 32)
The steady state has NaNs or Inf.
Error in steady (line 102)
print_info(info,options_.noprint, options_);
Error in prueba.driver (line 891)
steady;
Error in dynare (line 281)
evalin('base',[fname '.driver']);
prueba.mod (21.1 KB)
However, I am not convinced that the modification affects the model.
Your model is still incorrectly linearized. E.g.
pk = (1-delt)/(1-delt)+crk*pk(+1)+(crk/(1-delt+crk))*rk(+1)-cy(-1);
has a constant term (1-delt)/(1-delt)=1. If your model is properly linearized, pretty much all variables must have steady state 0 (with the exception of your observables).