# RBC with Government Sector

I attempt to add a government to the RBC model. The government levies distortionary taxes and issues non-state-contingent bonds. Dynare tells me that There are 3 eigenvalue(s) larger than 1 in modulus for 2 forward-looking variable(s). The rank condition ISN’T verified! I think that the problem lies in the bond interest rate, but I want someone to help me explain the reason. Thank you!

// Endogenous variables:
var C K Y B R W r z g;

// Exogenous variable:
varexo epis_z,epis_g;

// Parameters declaration and calibration
parameters alfa betta delta rho_z rho_g sigmma_z sigmma_g gbar tau_a tau_n;
alfa=0.34;
betta=0.98;
delta=0.025;
rho_z=0.95;
rho_g=0.87;
sigmma_z=0.007;
sigmma_g=0.04;
gbar=0.28;
tau_a=0.2;
tau_n=0.3;

// Equilibrium conditions
model;
log(z)=rho_z * log(z(-1))+epis_z;
log(g/gbar)=rho_g * log(g(-1)/gbar)+epis_g;
tau_nW+tau_arK(-1)+B=B(-1)R(-1)+g;
1/C=betta
((1-tau_a)r(+1)+1-delta)/C(+1);
1/C=betta
R/C(+1);
W=(1-alfa)Y;
r=alfa
Y/K(-1);
Y = z
K(-1)^alfa;
C+K+g=Y+(1-delta)*K(-1);
end;

initval;
z = 1;
g = gbar;
R=1/(betta);
r = 1/((1-tau_a)betta)+delta-1;
K=(r/alfa)^(1/(1-alfa));
Y = z
K^alfa;
C = Y-g-delta*K;
end;

// Check the Blanchard-Kahn conditions
check;

// Declare a positive technological shock in period 1
shocks;
var epis_z;
stderr sigmma_z;
var epis_g;
stderr sigmma_g;
end;

stoch_simul;

That can’t work. All the tax revenue and the spending are exogenous. There is nothing that assures that debt is not explosive, i.e. the government’s intertemporal budget constraint is not satisfied. In Leeper’s terms, at least one policy must be active, but in your case, there is only passive policy. You would need e.g. some feedback of debt to taxes or debt.

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