# Government debt issue in an RBC model

**URL:** <https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749>\
**Category:** Stochastic simulations\
**Created:** [22 August 2021 00:29 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749 "2021-08-22T00:29:57Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![Ezek](https://forum.dynare.org/letter_avatar_proxy/v4/letter/e/71c47a/32.png) [@Ezek](https://forum.dynare.org/u/Ezek)\
**Post date:** [22 August 2021 00:29 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/1 "2021-08-22T00:29:57Z")

</div>

Hi,  
I attach below the dynare code of an RBC model with government and fiscal policy shocks.  
There’s an error on the number of forward looking variables and I can’t really find which one. tax rates are exogenous (become endo. with shocks) and government investment, spending and transfers are all proportions of output. it works when I move some variables one period forward (with results that make sense) but the timing become weird.  
Here’s the code:

```auto
% Endogenous variables 
var C L K KG I IG G B Y A iB T R W BtY TRA Tw Tc Tr g ig tra sTc sTw sTr sG sIG sTRA;

% Exogenous variables (Shocks)
varexo eA eTc eTw eTr eG eIG eTRA;

% Parameters 
parameters Phi Sigma Beta Alpha1 Alpha2 Alpha3 Rho Delta DeltaG RhoTRA RhoG RhoIG RhoTc RhoTw RhoTr;

% Parameter values
Beta = 0.985;
Sigma = 2;
Phi = 1.5;
Delta = 0.025;
DeltaG = 0.025;
Alpha1 = 0.4;
Alpha2 = 0.6;
Alpha3 = 0.05;
Rho = 0.9;
RhoTc = 0.0;
RhoTr = 0.0;
RhoTw = 0.0;
RhoG = 0.0;
RhoIG = 0.0;
RhoTRA = 0.0;

% The Steady State
Tcss = 0.2;
Twss = 0.1;
Trss = 0.35;
igss = 0.2/3;
gss = 0.8/9;
trass = 0.4/9;
Rss = ((1/Beta)-1+Delta)/(1-Trss);
iBss = (1/Beta);
m1 = (((((1-Twss)/(1+Tcss))^(1/Sigma))*((Alpha2)^(-Phi/Sigma)))/(1-Delta*(Alpha1/Rss)-igss-gss))^(-Sigma/(Sigma+Phi));
m2 = (((DeltaG/igss)^Alpha3)*((1/Alpha2)^Alpha2)*((Rss/Alpha1)^Alpha1))^(1/Alpha3);
m3 = 1/(((Phi+1)/(Phi+Sigma))-(Alpha2/Alpha3));
Wss = (m1*m2)^m3;
Yss = m2*(Wss^(Alpha2/Alpha3));
Kss = Alpha1*Yss/Rss;
Lss = Alpha2*Yss/Wss;
Iss = Delta*Kss;
Gss = gss*Yss;
IGss = igss*Yss;
TRAss = trass*Yss;
KGss = IGss/DeltaG;
Css = Yss-Iss-IGss-Gss;
Tss = Tcss*Css+Twss*Wss*Lss+Trss*Rss*Kss;
Bss = (Tss-Gss-IGss)*(1/(1-Beta));
BtYss = Bss/Yss;

% The (Nonlinear) Model
model;
(C^Sigma)*(L^Phi) = ((1-Tw)/(1+Tc))*W;
(C(+1)/C)^Sigma = Beta*(1-Delta+(1-Tr)*R(+1));
1-Delta+(1-Tr)*R(+1) = iB;
I = K-(1-Delta)*K(-1);

Y = A*(K(-1)^Alpha1)*(L^Alpha2)*(KG(-1)^Alpha3);
K(-1) = Alpha1*(Y/R);
L = Alpha2*(Y/W);

G+IG+TRA+B(-1) = T+B/iB;
IG = KG-(1-DeltaG)*KG(-1);
T = Tc*C+Tw*W*L+Tr*R*K(-1);
IG = ig*Y;
G = g*Y;
TRA = tra*Y;
BtY = B/Y;

ig = (0.2/3)*sIG;
g = (0.8/9)*sG;
tra = (0.4/9)*sTRA;
Tc = 0.2*sTc;
Tw = 0.1*sTw;
Tr = 0.35*sTr;

Y = C+I+IG+G;

A = exp(eA)*(A(-1))^Rho;
sTc = exp(eTc)*(sTc(-1))^RhoTc;
sTr = exp(eTr)*(sTr(-1))^RhoTr;
sTw = exp(eTw)*(sTw(-1))^RhoTw;
sG = exp(eG)*(sG(-1))^RhoG;
sIG = exp(eIG)*(sIG(-1))^RhoIG;
sTRA = exp(eTRA)*(sTRA(-1))^RhoTRA;
end;

% Initial guess values for the definitive steady state
initval;
A = 1;
C = Css;
Y = Yss;
K = Kss;
KG = KGss;
L = Lss;
W = Wss;
R = Rss;
I = Iss;
B = Bss;
iB = iBss;
T = Tss;
BtY = BtYss;

G = Gss;
IG = IGss;
TRA = TRAss;
Tc = Tcss;
Tw = Twss;
Tr = Trss;

sG = 1;
sIG = 1;
sTRA = 1;
sTc = 1;
sTr = 1;
sTw = 1;
end;

% Finding the steady state and checking for stability
steady;
check;options_.noprint=1;

% AR(1) processes with exogenous shocks (All shocks but TFP's set to zero)
shocks;
var eA; stderr 0.01;
var eTc; stderr 0.0;
var eTr; stderr 0.0;
var eTw; stderr 0.0;
var eG; stderr 0.0;
var eIG; stderr 0.0;
var eTRA; stderr 0.0;
end;

%Simulation and Impulse-response 
stoch_simul(irf=50,periods=500,qz_zero_threshold=1e-20);

```

Thank you.

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<div class="post-metadata">

**Author:** ![alchi49](https://forum.dynare.org/letter_avatar_proxy/v4/letter/a/c37758/32.png) [@alchi49](https://forum.dynare.org/u/alchi49)\
**Post date:** [23 August 2021 06:50 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/2 "2021-08-23T06:50:01Z")

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Hi,  
You must specify tax rules or spending rules so that they react to deviations in the debt to GDP ratio avoiding exploding debt. I tried and your model works perfectly.

Best

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<div class="post-metadata">

**Author:** ![Ezek](https://forum.dynare.org/letter_avatar_proxy/v4/letter/e/71c47a/32.png) [@Ezek](https://forum.dynare.org/u/Ezek)\
**Post date:** [23 August 2021 07:17 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/3 "2021-08-23T07:17:34Z")

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Thank you so much for your enlightening answer.  
If your ran it with a particular modification would you please provide me with it here (including parameter values of the rule)? I’d really appreciate.  
Thanks again.

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<div class="post-metadata">

**Author:** ![alchi49](https://forum.dynare.org/letter_avatar_proxy/v4/letter/a/c37758/32.png) [@alchi49](https://forum.dynare.org/u/alchi49)\
**Post date:** [23 August 2021 07:29 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/4 "2021-08-23T07:29:24Z")

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I have simply modified the consumption tax but you can play around with the other fiscal instruments.  
[test.mod](https://forum.dynare.org/uploads/short-url/tfkHZPAVZA9Po54jsu2JJHPXtFw.mod) (2.9 KB)

best

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<div class="post-metadata">

**Author:** ![Ezek](https://forum.dynare.org/letter_avatar_proxy/v4/letter/e/71c47a/32.png) [@Ezek](https://forum.dynare.org/u/Ezek)\
**Post date:** [23 August 2021 14:22 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/5 "2021-08-23T14:22:59Z")

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Thank you so much Dear alchi49,  
the model is now working perfectly!  
Thanks again !!

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<div class="post-metadata">

**Author:** ![Zerayehu](https://forum.dynare.org/letter_avatar_proxy/v4/letter/z/3d9bf3/32.png) [@Zerayehu](https://forum.dynare.org/u/Zerayehu)\
**Post date:** [16 September 2021 17:03 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/6 "2021-09-16T17:03:09Z")

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Dear Ezek,  
Thank you for sharing knowledge. Would you please share me the model equations via [email:zerayehu2005@gmail.com](mailto:email:zerayehu2005@gmail.com)

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<div class="post-metadata">

**Author:** ![Ezek](https://forum.dynare.org/letter_avatar_proxy/v4/letter/e/71c47a/32.png) [@Ezek](https://forum.dynare.org/u/Ezek)\
**Post date:** [16 September 2021 18:43 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/7 "2021-09-16T18:43:44Z")

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Hello Zerayehu,  
You can just download the above version posted by alchi49 since that one works well.  
I suggest that you change the file name after downloading (from test.mod to mymodel.mod for ex. before running).  
Let me know if there’s any issue.

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<div class="post-metadata">

**Author:** ![Zerayehu](https://forum.dynare.org/letter_avatar_proxy/v4/letter/z/3d9bf3/32.png) [@Zerayehu](https://forum.dynare.org/u/Zerayehu)\
**Post date:** [16 September 2021 19:47 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/8 "2021-09-16T19:47:10Z")

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Thank for this. I go through it. But, to understand the code and symbols, I need to have mathematical model equations if you do not mind it. Kindly

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<div class="post-metadata">

**Author:** ![RodrigoFranco](https://forum.dynare.org/letter_avatar_proxy/v4/letter/r/c0e974/32.png) [@RodrigoFranco](https://forum.dynare.org/u/RodrigoFranco)\
**Post date:** [21 August 2024 12:59 UTC](https://forum.dynare.org/t/government-debt-issue-in-an-rbc-model/18749/9 "2024-08-21T12:59:23Z")

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@Zerayehu @Ezek Would you share your model here as well or if you got it from a paper, the link or name of the paper.

Than you!