Monetary Shock

[Daniel Bendel]

Hey folks,

i get very strange irf when i ran the following little monetary model. My problem is, when i look at the irf of U (the monetary shock) I would expect that when U rises R (the nominal interest rate) will also rise due to the standard taylor rule (R/Rss = (PI)^(jotaPI)*(Y/Yss)^(jotaY)*U;). But the opposite is the case. PLEASE WHERE IS THE MISTAKE?? Do I think wrong??


THE MODEL:

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var LAM R PI RK C W L Y A K MC B G U I RR TAX UTIL;
varexo eps_A eps_U eps_G;

parameters beta delta sigmaL omega alpha phiP Phi tau jotaR jotaPI jotaY rhoA rhoU rhoG sigmaA sigmaU sigmaG nu
TAXss Gss Yss Rss sc AUX Kss Lss Css Wss Iss RKss LAMss Ass Uss Bss t TAXBAR;


beta = 0.90;
delta = 0.025;
sigmaL = 5;
omega = 1;
alpha = 2/3;
phiP = 1.25;
Phi = 1.5;
tau = 5;
jotaR = 0;
jotaPI = 1.5;
jotaY = 0.125;
rhoA = 0.90;
rhoU = 0.90;
rhoG = 0.90;
sigmaA = 0.01;
sigmaU = 0.01;
sigmaG = 0.01;
nu = 0.8;
sc = 0.2;
t = 0.25;
AUX = ((1-alpha)*(1-1/Phi)/(1/beta - 1 + delta))^((1-alpha)/alpha);
Wss = AUX *alpha*(1-1/Phi);
Lss = ((1-sc-delta*AUX^(alpha/(1-alpha)))*sigmaL/(sigmaL-1)*omega*1/alpha*(1-1/Phi)^(-1))^(1/(-nu-1));
Kss = Lss*AUX^(1/(1-alpha));
Yss = Lss^(alpha)*Kss^(1-alpha);
Gss = sc*Yss;
Css = Yss - delta*Kss - Gss;
Rss = 1/beta;
TAXBAR = t;
Bss = (sc*Yss-TAXBAR)/(1-Rss+tau);
TAXss = TAXBAR + tau*Bss;
Iss = delta*Kss;
RKss = 1/beta - 1 + delta;
LAMss = 1/Css;
Ass = 1;
Uss = 1;

model;
UTIL = log(C) -omega/(1+nu)*L^(1+nu);
LAM = beta*LAM(+1)*R/PI(+1);
LAM = beta*LAM(+1)*(RK(+1) + (1-delta));
LAM = 1/C;
W = sigmaL/(sigmaL-1)*omega*L^(nu)*1/LAM;
Y = A*L^(alpha)*K(-1)^(1-alpha);
RK = (1-alpha)*MC*A*L^(alpha)*K(-1)^(-alpha);
W = alpha*MC*A*L^(alpha-1)*K(-1)^(1-alpha);
1 - phiP*(PI-1)*PI + beta*phiP*LAM(+1)/LAM*(PI(+1)-1)*Y(+1)/Y*PI(+1) - (1-MC)*Phi = 0;
B = R(-1)*B(-1)/PI + G - TAX;
TAX/TAXBAR =  (B/Bss)^tau;
R/Rss = (PI)^(jotaPI)*(Y/Yss)^(jotaY)*U;
K = (1-delta)*K(-1) + I; 
Y = C + I + G + phiP/2*(PI-1)^2*Y;
RR = R/PI(+1);
A = ((Ass)^(1-rhoA) )*( A(-1)^rhoA )*exp(eps_A);
U = ((Uss)^(1-rhoU) )*( U(-1)^rhoU )*exp(eps_U);
G = ((Gss)^(1-rhoG) )*( G(-1)^rhoG )*exp(eps_G);
end;


initval;
UTIL = log(Css) -omega/(1+nu)*Lss^(1+nu);
B = Bss;
PI = 1;
A = Ass;
U = Uss;
G = Gss;
MC = (Phi-1)/Phi;
TAX = TAXss;
R = Rss;
W = Wss;
L = Lss;
K = Kss;
Y = Yss;
C = Css;
LAM = LAMss;
RK = RKss;
I = Iss;
RR = Rss;
end;

steady;


shocks;
var eps_A = sigmaA;
var eps_U = sigmaU;
var eps_G = sigmaG;
end;

stoch_simul(periods=0,irf=20,order=1);




[jpfeifer]

See http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=4558

[Daniel Bendel]

so if i understand that right, it is no mistake, that my nominal interest rate drops. But how can that be: "For example, in the standard New Keynesian model the nominal interest rate can move in either direction after a contractionary monetary policy shock. The only thing that is guaranteed is that the real interest rate increases." ??

[jpfeifer]

All I am saying is that it could be a feature and not a bug. I did not check your model.

The mechanism is the following: Assume the initial monetary policy shock increases the nominal and thus the real interest rate. The central bank then reacts to lower output and inflation endogenously by lowering the nominal interest rate. If the response is strong enough, it overcompensates the initial increase due to the shock. The only thing you know is that the real interest rate increases, so that the shock is still contractionary, although the nominal interest rate goes down. This is one of the reasons why you cannot look at interest rates to determine whether monetary policy is expansionary.

[Daniel Bendel]

Okay! I think I understand you. Many thanks for our fast answer!!