DSGE Estimation - Financial Accelerator

Estimation
1

Hi,

I was trying to replicate the DSGE estimation of The financial accelerator in an estimated New Keynesian model. This paper applies the Bernanke-Gertler-Gilchrist financial accelerator model to Canadian data.

I followed Johannes Pfeifer’s guide, and firstly did the stochastic simulation by directly using the paper’s empirical results as parameters and initial values. My simulation successfully gave the IRFs.

However, when I tried to estimate the parameters, I used

estimated_params_init(use_calibration); end;

Dynare continuously told me that “POSTERIOR KERNEL OPTIMIZATION PROBLEM!”. At this point, I was confused because my stochastic simulation is okay, and my initial values for estimation directly come from the calibration. I thought it should be all right, but not. If possible, can anyone have a look at my file “bgg.mod” and give me some hints? The block for estimation starts with line 150. Thanks.
bgg.mod (3.8 KB)

2

The data file is missing.

3

Thanks for your reply, Professor. Below is my data file.
est_data.mat (8.2 KB)

4

Please take a look at Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf . You are performing a fundamental mistake by parameters depend on estimated parameters and not using either model local variables or a steady_state_model-block. It also seems that you are matching zero mean model variables to non-zero mean data.

5

Hi Professor,

Thanks for your reply. I checked my previous codes and your guide, and found two mistakes. Specifically, the steady state values (ss) for my endogenous variables should not be used in the initval; end; block. The reason is that my model’s equations are log-linearized. So, y,c,etc. are the conventional hat notation, that is the percentage deviation from the ss. Therefore, I specified their initial values as 0, that is the equilibrium.

Second, because of my model’s equations, I need to specify the relationship between my endogenous variables and the data. For instance, y_obs = y*yss + yss; However, after this modification, Dynare still told me “POSTERIOR KERNEL OPTIMIZATION PROBLEM!”. At this point, I’m unclear about the meaning of your comment “You are performing a fundamental mistake by parameters depend on estimated parameters and not using either model local variables or a steady_state_model-block.”?

If possible, can you have a look at my attached new file and give me some hints? Thank you.
bgg.mod (4.0 KB)

6 
xi_ss = (theta - 1)/theta;
R_ss = pi_ss/beta;

f_ss = (S*R_ss)/pi_ss;
z_ss = f_ss - 1 + delta;

lambdac = 1/(1 + b_ss*(pi_ss/(pi_ss - beta))^(gamma - 1));
lambdam = lambdac * b_ss * (pi_ss/(pi_ss - beta))^(gamma);

ky_ratio = (alpha*xi_ss)/z_ss;
cy_ratio = 1 - delta*ky_ratio;

whlambda = ((1 - alpha)*lambdac*xi_ss) / cy_ratio;

hss = whlambda/(eta+whlambda);
Ass = 1;

yss = Ass*hss*(ky_ratio)^(alpha/(1-alpha));
iss = delta*ky_ratio*yss;

css = yss - iss;
mss = css*b_ss*(pi_ss/(pi_ss-beta))^gamma;

are all dependent objects. Thus, it should be

%% Endogenous variables
var y, c, m, i, h, k, n, w, z, R, f, q, lambda, xi, pi_v, mu, e, b, A, x,
    y_obs, i_obs, m_obs, pi_v_obs, R_obs;

%% Shocks
varexo eps_R, eps_e, eps_b, eps_A, eps_x;

%% parameters
parameters beta, eta, theta, delta, b_ss, pi_ss, nu, S, psi, chi, alpha,
gamma, phi, rho_pi, rho_y, rho_mu, sigma_R, rho_A, sigma_A, rho_b,
sigma_b, rho_e, sigmae, rho_x, sigma_x
;

%% parameters' values
beta=0.9928;
eta=1.315;
theta=6;
delta=0.025;
b_ss=0.062;
pi_ss=1.0079;
nu=0.9728;
S=1.0075;

psi=0.0420;
chi=0.5882;
alpha=0.3384;
gamma=0.0598;
phi=0.7418;
rho_pi=1.4059;
rho_y=0.2947;
rho_mu=0.6532;
sigma_R=0.0058;
rho_A=0.7625;
sigma_A=0.0096;
rho_b=0.7206;
sigma_b=0.0103;
rho_e=0.6156;
sigmae=0.0073;
rho_x=0.6562;
sigma_x=0.0331;


%% model
model;
#xi_ss = (theta - 1)/theta;
#R_ss = pi_ss/beta;

#f_ss = (S*R_ss)/pi_ss;
#z_ss = f_ss - 1 + delta;

#lambdac = 1/(1 + b_ss*(pi_ss/(pi_ss - beta))^(gamma - 1));
#lambdam = lambdac * b_ss * (pi_ss/(pi_ss - beta))^(gamma);

#ky_ratio = (alpha*xi_ss)/z_ss;
#cy_ratio = 1 - delta*ky_ratio;

#whlambda = ((1 - alpha)*lambdac*xi_ss) / cy_ratio;

#hss = whlambda/(eta+whlambda);
#Ass = 1;

#yss = Ass*hss*(ky_ratio)^(alpha/(1-alpha));
#iss = delta*ky_ratio*yss;

#css = yss - iss;
#mss = css*b_ss*(pi_ss/(pi_ss-beta))^gamma;

((1-gamma)*lambdac - 1)*c = gamma*lambda + ((lambdam*(R_ss - 1))/R_ss)*
    (b + (gamma-1)*m) - gamma*e;

(gamma*R)/(R_ss - 1) = b + c - m;

(whlambda/(eta + whlambda))*h = (eta/(eta + whlambda))*(w + lambda);
% Replace the h in C.3 by B.11

y = alpha*k(-1) + (1-alpha)*h + (1-alpha)*A;

y = cy_ratio*c + (1 - cy_ratio)*i;
% iy_ratio = 1 - cy_ratio

w = y + xi - h;

z = y + xi - k(-1);

mu = m - m(-1) + pi_v;

R = rho_pi*pi_v + rho_mu*mu + rho_y*y + sigma_R*eps_R;

f = (z_ss*z)/f_ss + ((1-delta)/f_ss)*q - q(-1);

q = chi*(i - k(-1)) - x;

pi_v = beta*pi_v(+1) + ((1-beta*phi)*(1-phi)*xi)/phi;

lambda(+1) = lambda - R + pi_v(+1);

k = delta*i + delta*x + (1-delta)*k(-1);

f(+1) = R - pi_v(+1) + psi*(q + k - n);

n/(nu*f_ss) = 2*f - (R(-1) - pi_v) - psi*(k(-1) + q(-1)) + (psi + 1)*n(-1);
% CD page 9 Table 1 directly gives that kn_ratio is 2.

% Below is AR1 processes for the four endogenous shocks.
e = rho_e*e(-1) + sigmae*eps_e;

b = rho_b*b(-1) + sigma_b*eps_b;

A = rho_A*A(-1) + sigma_A*eps_A;

x = rho_x*x(-1) + sigma_x*eps_x;

y_obs = y*yss + yss; 

i_obs = i*iss + iss;
m_obs = m*mss +mss;

pi_v_obs = pi_v*pi_ss + pi_ss;
R_obs = R*R_ss + R_ss;

end;


%% initial values for endogenous variables
initval;

xi=0;
R=0;
f=0;
z=0;

h=0;
y=0;
A=0;

eps_R=0;
eps_e=0;
eps_b=0;
eps_A=0;
eps_x=0;

end;

%% find steady state (ss)
steady;

%% shocks
shocks;

var eps_R; stderr 1;
var eps_e; stderr 1;
var eps_b; stderr 1;
var eps_A; stderr 1;
var eps_x; stderr 1;

end;

%% stochastic simulation
stoch_simul(periods = 1000, irf=40,  order=1);


%% estimation
estimated_params;

% NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR1, PRIOR2, PRIOR3, PRIOR4, JSCALE
psi, , 0, 1;% inv_gamma_pdf, 0.04, 1;
chi, , 0, 1;% inv_gamma_pdf, 0.5, 1;
gamma, , 0, 1;% inv_gamma_pdf, 0.05, 1;
alpha, , 0, 1;% inv_gamma_pdf, 0.3, 1; % beta distribution is a suitable prior for proportions.
phi, , 0, 1;% inv_gamma_pdf, 0.5, 1;

rho_pi, , 0, 3;% inv_gamma_pdf, 1.2, 1;
rho_y, , 0, 1;% inv_gamma_pdf, 0.25, 1;
rho_mu, , 0, 1;% inv_gamma_pdf, 0.6, 1;
sigma_R, , 0, 1;% inv_gamma_pdf, 0.004, 1;
rho_A, , 0, 1;% inv_gamma_pdf, 0.7, 1;

sigma_A, , 0, 1;% inv_gamma_pdf, 0.007, 1;
rho_b, , 0, 1;% inv_gamma_pdf, 0.6, 1;
sigma_b, , 0, 1;% inv_gamma_pdf, 0.009, 1;
rho_e, , 0, 1;% inv_gamma_pdf, 0.5, 1;
sigmae, , 0, 1;% inv_gamma_pdf, 0.006, 1;

rho_x, , 0, 1;% inv_gamma_pdf, 0.6, 1;
sigma_x, , 0, 1;% inv_gamma_pdf, 0.025, 1;

end;

estimated_params_init(use_calibration);
end;

varobs y_obs, i_obs, m_obs, pi_v_obs, R_obs;

estimation(datafile=est_data,mode_compute=4);