Hi,
I am asking a very general question. Given an RBC model, the assumption is quite usual, technology follows the AR(1) process. However, the professor asks us to plot IRFs for both one-time shock and persistent shock(AR prcoess).I am confused about it, since i use stoch_simul(irf=50,order =1) it automatically gives me the IRFs.
My question is:
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Is this automatically generated IRFs by “stoch_simul(order=1, irf=50)” one-time or persistent?
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Since i think the definition of IRFs is supposed there is an impulse at a certain period, it means that it is one_time shock right? But how about persistent shock(professor said AR(1))?
Thanks in advance.
%----------------------------------------------------------------
% Endogenous variables
%----------------------------------------------------------------
var k, y, c, n, r, a, i;
%----------------------------------------------------------------
% Exogenous variables - shocks
%----------------------------------------------------------------
varexo eps;
%----------------------------------------------------------------
% Parametrization
%----------------------------------------------------------------
parameters beta, rho, delta, alpha, A, sigma, kbar, ybar, cbar, nbar, rbar;
beta = 0.99;
rho = 0.95;
delta = 0.025;
alpha = 0.33;
A = 1.75;
sigma = 0.0032;
% Calculating steady state values
nbar = (1 + (A/(1-alpha)) * (1 - betadeltaalpha/(1-beta*(1-delta))))^(-1);
kbar = nbar*(alpha/(1/beta - 1 + delta))^(1/(1-alpha));
ybar = kbar^alpha * nbar^(1-theta);
cbar = ybar - deltakbar;
rbar = alpha(kbar/nbar)^(alpha-1);
%----------------------------------------------------------------
% Model equations
%----------------------------------------------------------------
model;
//1. Euler equation
c = c(+1) - betarbarr(+1);
//2. Consumption-leisure trade-off
y - c = n/(1-nbar);
//3. Budget constraint
cbarc = ybary + kbar*((1-delta)*k(-1) - k);
//4. Production function
y = a + alpha*k(-1) + (1-alpha)*n;
//5. Return on capital
r = y - k(-1);
//6. Law of motion for productivity
a = rho*a(-1) + eps;
//7. Investment (auxiliary variable)
i = (k - (1-delta)*k(-1))/delta;
end;
%----------------------------------------------------------------
% define shock variances
%---------------------------------------------------------------
shocks;
var eps = sigma^2;
end;
%----------------------------------------------------------------
% steady states: all 0 due to linear model
%----------------------------------------------------------------
steady;
check;
%----------------------------------------------------------------
% generate IRFs
%----------------------------------------------------------------
stoch_simul(order = 1, irf=40) a i k y c n ;