Commit eab165d3 authored by MichelJuillard's avatar MichelJuillard
Browse files

added in manual a section on how to use steady_state_model block with

initval and endval for deterministic models. Added test cases for
deterministic models.
parent 31f6831b
......@@ -2569,6 +2569,15 @@ function returning several arguments:
Dynare will automatically generate a steady state file using the
information provided in this block.
@customhead{Steady state file for deterministic models}
@code{steady_state_model} block works also with deterministic
models. An @code{initval} block and, when necessary, an @code{endval}
block, is used to set the value of the exogenous variables. Each
@code{initval} or @code{endval} block must be followed by @code{steady}
to execute the function created by @code{steady_state_model} and set the
initial, respectively terminal, steady state.
@examplehead
@example
......
......@@ -125,7 +125,13 @@ MODFILES = \
second_order/ds1.mod \
second_order/ds2.mod \
ep/rbc.mod \
ep/linear.mod
ep/linear.mod \
deterministic_simulations/deterministic_model_purely_forward.mod \
deterministic_simulations/rbc_det1.mod \
deterministic_simulations/rbc_det2.mod \
deterministic_simulations/rbc_det3.mod \
deterministic_simulations/rbc_det4.mod \
deterministic_simulations/rbc_det5.mod
EXTRA_DIST = \
$(MODFILES) \
......
var y i pi rbar ;
varexo r tauw taus taua gn;
parameters khia khiw khis phipi phiy taubs taubw tauba w sigma psi kappa alpha mu beta teta;
teta = 12.7721;
sigma = 1.1599;
beta = 0.9970;
alpha = 0.7747;
mu = 0.9030;
taubs = 0.05;
taubw = 0.02;
tauba = 0;
w = 1.5692;
phipi = 1.5;
phiy = 0.5/4;
khia = (1-beta)/(1-tauba);
khiw = 1/(1-taubw);
khis = 1/(1+taubs);
psi = 1/(sigma + w);
kappa = (1-alpha)*(1-alpha*beta)*(sigma+w)/(alpha*(1+w*teta));
model(linear);
y = y(+1)-sigma*(i-pi(+1)-r)+(gn-gn(+1))+(sigma)^-1*khis*(taus(+1)-taus)+sigma*khia*taua;
pi=kappa*y+kappa*psi*(khiw*tauw+khis*taus-sigma*gn)+beta*pi(+1);
i=max(0,r+phipi*pi+phiy*y);
rbar = -((kappa*phipi+(1-beta*mu)*phiy)*sigma^-1*khia*taus)/((1-mu+sigma^-1*phiy)*(1-beta*mu)+kappa*sigma^-1*(phipi-mu))
- (((1-mu)*kappa*psi*phipi+sigma^-1*mu*kappa*psi*phiy)*khiw*tauw)/((1-mu+sigma^-1*phiy)*(1-beta*mu)+kappa*sigma*(phipi-mu))
-(kappa*sigma*(1-mu)*(sigma^-1-psi)*phipi+((1-mu)*(1-beta*mu)-kappa*psi*mu)*phiy)*(gn-sigma^-1*khis*taus)/((1-mu-sigma^-1*phiy)*(1-beta*mu)+kappa*sigma^-1*(phipi-mu));
end;
initval;
y=0;
i=-log(beta);
pi=0;
rbar = 0;
end;
steady;
check;
shocks;
var r;
periods 1:9;
values -0.0104;
end;
simul(periods=2100);
var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model(block,bytecode,cutoff=0);
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
efficiency = EfficiencyInnovation/(1-rho);
Efficiency = effstar*exp(efficiency);
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
end;
steady;
ik = varlist_indices('Capital',M_.endo_names);
CapitalSS = oo_.steady_state(ik);
histval;
Capital(0) = CapitalSS/2;
end;
simul(periods=300);
rplot Consumption;
rplot Capital;
\ No newline at end of file
var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model(block,bytecode,cutoff=0);
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/effstar)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
Efficiency=effstar;
efficiency=0;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
LagrangeMultiplier=0;
end;
//steady;
shocks;
var EfficiencyInnovation;
periods 1;
values -0.1;
end;
simul(periods=300);
rplot Consumption;
rplot Capital;
\ No newline at end of file
var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model(block,bytecode,cutoff=0);
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/effstar)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
Efficiency=effstar;
efficiency=0;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
LagrangeMultiplier=0;
end;
steady;
shocks;
var EfficiencyInnovation;
periods 4, 5, 6, 7, 8;
values 0.04, 0.05, 0.06, 0.07, 0.08;
end;
simul(periods=300);
rplot Consumption;
rplot Capital;
\ No newline at end of file
var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model(block,bytecode,cutoff=0);
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
efficiency = EfficiencyInnovation/(1-rho);
Efficiency = effstar*exp(efficiency);
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
end;
initval;
EfficiencyInnovation = 0;
end;
steady;
endval;
EfficiencyInnovation = (1-rho)*log(1.05);
end;
steady;
simul(periods=300);
rplot Consumption;
rplot Capital;
\ No newline at end of file
var Capital, Output, Labour, Consumption, Efficiency, efficiency, ExpectedTerm;
varexo EfficiencyInnovation;
parameters beta, theta, tau, alpha, psi, delta, rho, effstar, sigma2;
beta = 0.9900;
theta = 0.3570;
tau = 2.0000;
alpha = 0.4500;
psi = -0.1000;
delta = 0.0200;
rho = 0.8000;
effstar = 1.0000;
sigma2 = 0;
model(block,bytecode,cutoff=0);
// Eq. n°1:
efficiency = rho*efficiency(-1) + EfficiencyInnovation;
// Eq. n°2:
Efficiency = effstar*exp(efficiency);
// Eq. n°3:
Output = Efficiency*(alpha*(Capital(-1)^psi)+(1-alpha)*(Labour^psi))^(1/psi);
// Eq. n°4:
Capital = Output-Consumption + (1-delta)*Capital(-1);
// Eq. n°5:
((1-theta)/theta)*(Consumption/(1-Labour)) - (1-alpha)*(Output/Labour)^(1-psi);
// Eq. n°6:
(((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption = ExpectedTerm(1);
// Eq. n°7:
ExpectedTerm = beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)*(alpha*((Output/Capital(-1))^(1-psi))+(1-delta));
end;
steady_state_model;
efficiency = EfficiencyInnovation/(1-rho);
Efficiency = effstar*exp(efficiency);
Output_per_unit_of_Capital=((1/beta-1+delta)/alpha)^(1/(1-psi));
Consumption_per_unit_of_Capital=Output_per_unit_of_Capital-delta;
Labour_per_unit_of_Capital=(((Output_per_unit_of_Capital/Efficiency)^psi-alpha)/(1-alpha))^(1/psi);
Output_per_unit_of_Labour=Output_per_unit_of_Capital/Labour_per_unit_of_Capital;
Consumption_per_unit_of_Labour=Consumption_per_unit_of_Capital/Labour_per_unit_of_Capital;
% Compute steady state share of capital.
ShareOfCapital=alpha/(alpha+(1-alpha)*Labour_per_unit_of_Capital^psi);
% Compute steady state of the endogenous variables.
Labour=1/(1+Consumption_per_unit_of_Labour/((1-alpha)*theta/(1-theta)*Output_per_unit_of_Labour^(1-psi)));
Consumption=Consumption_per_unit_of_Labour*Labour;
Capital=Labour/Labour_per_unit_of_Capital;
Output=Output_per_unit_of_Capital*Capital;
ExpectedTerm=beta*((((Consumption^theta)*((1-Labour)^(1-theta)))^(1-tau))/Consumption)
*(alpha*((Output/Capital)^(1-psi))+1-delta);
end;
initval;
EfficiencyInnovation = 0;
end;
steady;
endval;
EfficiencyInnovation = (1-rho)*log(1.05);
end;
steady;
shocks;
var EfficiencyInnovation;
periods 1:5;
values 0;
end;
simul(periods=300);
rplot Consumption;
rplot Capital;
\ No newline at end of file
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