// Model: NK_IR04 = modified version by Renate
 
// Further references:
// Ireland, Peter N. "Money's Role In The Monetary Business Cycle," 
// "Journal of Money, Credit and Banking, 2004, v36(6,Dec), 969-983.
 
 
// endogenous variables
// ====================
var y   ${y}$           (long_name='Output')
    m   ${m}$           (long_name='Households Real Balances')
    pi  ${pi}$          (long_name='Gross Inflation Rate')
    r   ${r}$           (long_name='Gross Nominal Interest Rate')
    mu  ${mu}$          (long_name='Percentage Deviation of Money Growth')
    a   ${a}$           (long_name='log Preference Shock a')
    e   ${e}$           (long_name='log Preference Shock e on money demand')
    z   ${z}$           (long_name='log Aggregate Productivity Shock')
;
 
// exogenous varibales
// ====================
varexo eps_a ${\varepsilona_}$ (long_name='Preference Shock a (IS Shock)') 
       eps_e ${\varepsilone_}$ (long_name='Preference Shock e (Money Demand Shock)')
       eps_z ${\varepsilonz_}$ (long_name='Aggregate Productivity Shock')
       eps_r ${\varepsilonr_}$ (long_name='Policy Shock')
;
 
// Parameters
// ==================
parameters  
    omega1  ${\omega1}$      (log_name='depends inversely on HH risk aversion')
    omega2  ${\omega2}$      (log_name='measure importance of real balances in IS and Phillips curve')
    psi     ${\psi}$         (log_name='labor disutility parameter')
    gamma1  ${\gamma1}$      (log_name='Income Elasticity of Money Demand')
    gamma2  ${\gamma2}$      (log_name='Semi-Elasticity of Money Demand')
    gamma3  ${\gamma3}$      (log_name='____')
    rhor    ${\rho_r}$       (log_name='persistence Gross Nominal Interest Rate')
    rhoy    ${\rho_y}$       (log_name='persistence Output')
    rhopi   ${\rho_pi}$      (log_name='persistence Gross Inflation Rate')
    rhomu   ${\rho_mu}$      (log_name='persistence Households Real Balances')
    rhoa    ${\rho_a}$       (log_name='persistence Preference Shock')
    rhoe    ${\rho_e}$       (log_name='persistence Preference Shock on money demand') 
    rhoz    ${\rho_z}$       (log_name='persistence Productivity Shock')
    sigmaa  ${\sigma_a}$     (log_name='normal distributed standard diviation of preference shock a') 
    sigmae  ${\sigma_e}$     (log_name='normal distributed standard diviation of preference shock e on money demand') 
    sigmaz  ${\sigma_z}$     (log_name='normal distributed standard diviation of productivity shock z') 
    sigmar  ${\sigma_r}$     (log_name='normal distributed standard diviation of policy shock r') 
    lny     ${\log(y)}$      (log_name='log Output')
    lnm     ${\log(m)}$      (log_name='log Households Real Balances')
    lnpi    ${\log(pi)}$     (log_name='log Gross Inflation Rate')
    lnr     ${\log(r)}$      (log_name='log Gross Nominal Interest Rate')  
    y_ss    ${\bar Y}$       (log_name='Output in Steady State')
    m_ss    ${\bar M}$       (log_name='Households Real Balances in Steady State')
    pi_ss   ${\bar PI}$      (log_name='Gross Inflation Rate in Steady State')
    r_ss    ${\bar R}$       (log_name='Gross Nominal Interest Rate in Steady State')
;
 
 
 
// Set parameter values
// ====================
omega1 = 0.0548;    % depends inversely on HH's risk aversion (response of aggregate demand to changes in real interest rate)
omega2 = -0.0199;   % non-zero => measures the importance of real balances on inflation & output
gamma1 = 1.4337;    % income elasticity of money demand    
gamma2 = 7.7532;    % interest semi-elasticity of money demand 
gamma3 = 0.8553;    % 
psi = 0.0002;       % inverse relation to cost-of-price adjustemnt 
rhoy = 0.0288;      % not persistens 
rhopi = 0.7589;     % High rhopi and rhomu inidcates taht the Feederal Reserve policy has responded to changes in both inflation and money growth
rhomu = 0.8126;     % deviation of money growth from it's ss level
lny = 8.8221;       % log output (detrented)
lnm = 9.6860;       % log real balance (detrented)
lnpi = 0.0099;      % log inflation (detrented)
lnr = 0.185;        % log inflation (detrented)
rhoa = 0.9426;      % since the values of rhoa, rhoe and rhoz are prettey 
rhoe = 0.9482;      % high, this indicates that the shocks are quite persistent 
rhoz = 0.9308;      % to the IS curve, the money demand and the Phillips curve
sigmaa = 0.1518;    % normal distributed standard deviation sigmaa of preference shock at
sigmae = 0.9482;    % normal distributed standard deviation sigmae of preferece shock et on money demand
sigmaz = 0.9308;    % normal distributed standard deviation sigmaz of productivity shock zt
sigmar = 0.0062;    % dormal distributed standard deviation sigmar of policy shock rt 
y_ss = 7148.8015;   % output ss
m_ss = 16954.6939;  % money demand ss
pi_ss = 1.0101;     % gross inflation rate ss
r_ss = 1.0188;      % gross nominal interest rate ss
 
rhor = 0.5481;
 
 
// Declaration of the model
// ========================
model(linear);
 
// Model Code consistend with the Paper "Money's Role in the Monetary Business Cycle" Peter N. Ireland (2001):
// ===========================================================================================================
 
[name='exogenous Preference process a']
a = rhoa*a(-1) + eps_a;
 
[name='exogenous Preference process e on money demand']
e = (1-rhoe)*e + rhoe*e(-1) + eps_e;
 
[name='Aggregate Productivity process z']
z = (1-rhoz)*z + rhoz*z(-1) + eps_z;
 
[name='Forward Looking IS curve']    // parameter of interest is omega2
y = y(+1) - omega1*(r - pi(+1)) + omega2*((m - e) - (m(+1) - e(+1))) + omega1*(a - a(+1));
 
[name='Money Demand']
m = gamma1*y - gamma2*r + gamma3*e;
 
[name='Forward Looking Phillips Curve']
pi = (pi_ss/r_ss)*pi(+1) + psi*((1/omega1)*y - (omega2/omega1)*(m-e)-z);
 
[name='Monetary Policy Rule']
r = rhoy*y + rhopi*pi + rhomu*mu + eps_r;  //modified interest rate rule
 
[name='Percentage Deviation of Money Growth']
mu = m - m(-1) + pi;
 
end;
 
// Solving the model
// =================
 
// Tempoary shocks => set shock variance
// ===============
shocks;
var eps_a = sigmaa^2;
var eps_e = sigmae^2;
var eps_z = sigmaz^2;
end;
 
 
// Check Starting Values for the Steady State
// =========================================
 
resid;
 
 
// Compute steady state values
// ===========================
 
steady;
 
 
// Blanchard-Kahn condition: compute Eigenvalues and check for stability
// =====================================================================
 
check;
 
// Solve the model
// ===============
 
//VAR dosn't work
//stoch_simul(periods=500,irf=0); 
//datatomfile('datarabanal_hybrid',[]); 
 
 
stoch_simul(irf=40, order=1, hp_filter=1600, nograph) y m pi r mu a e z;
 
 
 
// Create a graph
// ==============
for i=1:200 
    set_dynare_seed(i);
    stoch_simul(periods=200, noprint, nograph);
    y_sim(:,i)  = y;
    pi_sim(:,i) = pi;
end;
 
// plot a graph - dosn't work
// ========================
rhomu_params = 0:0.05:1;
 
for i=1:length(rhomu_params)
    rhomu = rhomu_params(i);
    stoch_simul(noprint, nograph);
    m_eps_a_mat(:,i) = m_eps_a;
end;
 
>> surf(rhomu_eps_a_mat(1:5,:)); xlabel(‘\mu’); ylabel(‘t’); zlabel(‘\m’);