Tech Shock in standart NKM

Dynare contributions and examples
1

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
http://www.texify.com/img/\normalsize\!a%20%3D%20\rho_a%20\cdot%20a_{t-1}%20%2B%20\nu_t.gif
with persistence parameter http://www.texify.com/img/\normalsize\!\rho_a.gif 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):

[quote]Hence, and as long as http://www.texify.com/img/\normalsize\!\rho_a.gif < 1; a positive technology shock leads to a per-
sistent decline in both inflation and the output gap.[/quote]

So why do I not get persistent declines in case http://www.texify.com/img/\normalsize\!\rho_a.gif = 0.0? I get just a one period peak :frowning:

My mod file looks like this:

[code]//------------------------------------------
// 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_pipi + phi_yy;
// IS-Equation
y = y(+1) - 1/sigma * (i - pi(+1) - rn);
rn = rho + sigmaPSI_yan (a(+1)-a);
Y = a * PSI_yan * ( 1 - sigma*(1-rho_a)(1-betarho_a)LAMBDA_a );
// Phillips-Kurve
pi = betapi(+1) + kappay;
// Money Demand
m_r = y - etai;

// 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’);[/code]

Thank you very much ahead,
MegaMatze
NKM_basic_techshock_zinsregel.mod (2.3 KB)

2

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

3

Thanks!