Dynare forums

Hello,

I'm doing my first steps with Dynare at the moement. At the moment, I basically try to reproduce the result, that Gali gets in his Introductions book to NKM. Sofar it seems very nice. And after some starting problems I am very happy that dynare makes so much work for me.

I'm trying to perform a positive technological shock that is defined as

with persistence parameter at 0.0 and 0.8.

The problem:

When using persistence 0.8 i get:


When I use persistence 0.0:



Gali tells us (in 4.1.2 The Effects of a Technology Shock):

Hence, and as long as < 1; a positive technology shock leads to a per-
sistent decline in both inflation and the output gap.

So why do I not get persistent declines in case = 0.0? I get just a one period peak

My mod file looks like this:

Code: Select all

//------------------------------------------
//                Preambel
//------------------------------------------
var pi y Y rn i m_r a;

varexo a_init;

parameters beta epsilon theta sigma rho psi alpha phi_pi phi_y eta   PSI_yan THETA lambda kappa   rho_a LAMBDA_a;
    beta = 0.99;
    epsilon = 0.3;
    theta = 2/3;
    sigma = 1;
    rho = 0;
    psi = 1;
    alpha = 0;
    phi_pi = 1.5;
    phi_y = 0.5/4;
    eta = 4;

    PSI_yan = (1+psi) / ( sigma*(1-alpha)+psi+alpha );
    THETA = (1-alpha)/(1-alpha+alpha*epsilon);
    lambda = (1-theta)*(1-beta*theta)*THETA/theta;
    kappa = lambda * (sigma + (psi+alpha)/(1-alpha));

    rho_a = 0.0;
    LAMBDA_a = 1  /  ( (1-beta*rho_a)*(sigma*(1-rho_a)+phi_y)+kappa*(phi_pi-rho_a) );

//------------------------------------------
//                 Model
//------------------------------------------

model(linear);
   

// Taylor-Rule
    i = rho + phi_pi*pi  +  phi_y*y;
// IS-Equation
    y = y(+1) - 1/sigma * (i - pi(+1) - rn);
    rn = rho + sigma*PSI_yan*  (a(+1)-a);
    Y = a * PSI_yan * ( 1 - sigma*(1-rho_a)*(1-beta*rho_a)*LAMBDA_a );
// Phillips-Kurve
    pi = beta*pi(+1) + kappa*y;
// Money Demand
    m_r = y - eta*i;

// Autoregressive Error
    a = rho_a*a(-1) + a_init;
end;



//------------------------------------------
//               Steady State
//------------------------------------------


check;

//------------------------------------------
//                 Shocks
//------------------------------------------

shocks;
var a_init = 0.25;
end;


//------------------------------------------
//               Computation
//------------------------------------------

stoch_simul(periods=1000);



//------------------------------------------
//                  Plots
//------------------------------------------

figure(1); clf;
subplot(4,2,1); plot(pi_a_init); title('inflation');
subplot(4,2,2); plot(y_a_init); title('output gab');
subplot(4,2,3); plot(i_a_init); title('nominal interest rate');
subplot(4,2,4); plot(Y_a_init); title('output');
subplot(4,2,5); plot(i_a_init(1:39)-[ pi_a_init(2:40)]); title('real interest rate');
subplot(4,2,6); plot(m_r_a_init); title('real money');

subplot(4,2,8); plot(m_r_a_init- [0;m_r_a_init(1:39)]); title('real money growth');

Thank you very much ahead,
MegaMatze

Your model is right -- with rho_a = 0, the effects of shocks only last one period. Strictly speaking, the line in Gali's book should read "...as long as 0<rho_a<1, ...".

PS

Thanks!