//Tests Occbin estimation with IVF and PKF with 1 constraints

// this file implements the model in:
// Atkinson, T., A. W. Richter, and N. A. Throckmorton (2019).
// The zero lower bound andestimation accuracy.Journal of Monetary Economics
// original codes provided by Alexander Richter
// adapted for dynare implementation
// adapted to avoid stochastic singularity at the ZLB
// ------------------------- Settings -----------------------------------------//

@#ifndef small_model
    @#define small_model = 0
@#endif


// ----------------- Defintions -----------------------------------------//
var
    c          //1  Consumption
    n          //2  Labor
    y          //5  Output
    yf         //6  Final goods
    yg         //11 Output growth gap
    w          //12 Real wage rate
    wf         //13 Flexible real wage
    pigap      //15 Inflation rate -> pi(t)/pibar = pigap
    inom       //16 Nominal interest rate
    inomnot    //17 Notional interest rate
    mc         //19 Real marginal cost
    lam        //20 Inverse marginal utility of wealth
    g          //21 Growth shock
    s          //22 Risk premium shock
    mp         //23 Monetary policy shock
    pi         //24 Observed inflation
    @#if !(small_model)
        x          //3  Investment
        k          //4  Capital
        u          //7  Utilization cost
        ups        //8  Utilization choice
        wg         //9  Real wage growth gap
        xg         //10 Investment growth
        rk         //14 Real rental rate
        q          //18 Tobins q
    @#endif
    ;

varexo
    epsg       // Productivity growth shock
    epsi       // Notional interest rate shock
    epss       // Risk premium shock
    ;
parameters
    // Calibrated Parameters
    beta        // Discount factor
    chi         // Labor disutility scale
    thetap      // Elasticity of subs. between intermediate goods
    thetaw      // Elasticity of subs. between labor types
    nbar        // Steady state labor
    eta         // Inverse frish elasticity of labor supply
    delta       // Depreciation
    alpha       // Capital share
    gbar        // Mean growth rate
    pibar       // Inflation target
    inombar     // Steady gross nom interest rate
    inomlb      // Effective lower bound on gross nominal interest rate
    sbar        // Average risk premium
    // Parameters for DGP and Estimated parameters
    varphip     // Rotemberg price adjustment cost
    varphiw     // Rotemberg wage adjustment cost
    h          	// Habit persistence
    rhos        // Persistence
    rhoi    	// Persistence
    sigz        // Standard deviation technology
    sigs        // Standard deviation risk premia
    sigi        // Standard deviation mon pol
    phipi       // Inflation responsiveness
    phiy        // Output responsiveness
    nu          // Investment adjustment cost
    sigups      // Utilization
    ;


// ---------------- Calibration -----------------------------------------//

beta     = 0.9949;    // Discount factor
thetap   = 6;         // Elasticity of subs. between intermediate goods
thetaw   = 6;         // Elasticity of subs. between labor types
nbar     = 1/3;       // Steady state labor
eta      = 1/3;       // Inverse frish elasticity of labor supply
delta    = 0.025;     // Depreciation
alpha    = 0.35;      // Capital share
gbar     = 1.0034;    // Mean growth rate
pibar    = 1.0053;    // Inflation target
sbar     = 1.0058;    // Average risk premium
rkbar    = 1/beta;
varphiw  = 100;       // Rotemberg wage adjustment cost
nu       = 4;         // Investment adjustment cost
sigups   = 5;         // Utilization
varphip  = 100;       // Rotemberg price adjustment cost
h        = 0.80;      // Habit persistence
rhos     = 0.80;      // Persistence
rhoi     = 0.80; 	  // Persistence
sigz     = 0.005;     // Standard deviation
sigs     = 0.005;     // Standard deviation
sigi     = 0.002;      // Standard deviation
phipi    = 2.0;       // Inflation responsiveness
phiy     = 0.5;       // Output responsiveness
inomlb   = 1 ;         // Inom LB

// ---------------- Model -----------------------------------------------//
model;

@#if !(small_model)
    [name = 'HH FOC utilization (1)']
    rk = steady_state(rk)*exp(sigups*(ups-1));

    [name = 'Utilization definition (3)']
    u = steady_state(rk)*(exp(sigups*(ups-1))-1)/sigups;

    [name = 'Firm FOC capital (4)']
    rk = mc*alpha*g*yf/(ups*k(-1));

    [name = 'HH FOC capital (17)']
    q = beta*(lam/lam(+1))*(rk(+1)*ups(+1)-u(+1)+(1-delta)*q(+1))/g(+1);

    [name = 'HH FOC investment (18)']
    1 = q*(1-nu*(xg-1)^2/2-nu*(xg-1)*xg)+beta*nu*gbar*q(+1)*(lam/lam(+1))*xg(+1)^2*(xg(+1)-1)/g(+1);

    [name = 'Wage Phillips Curve (20)']
    varphiw*(wg-1)*wg = ((1-thetaw)*w+thetaw*wf)*n/yf + beta*varphiw*(lam/lam(+1))*(wg(+1)-1)*wg(+1)*(yf(+1)/yf)   ;

    [name = 'Real wage growth gap (6)']
    wg = pigap*g*w/(gbar*w(-1));

    [name = 'Law of motion for capital (15)']
    k = (1-delta)*(k(-1)/g)+x*(1-nu*(xg-1)^2/2);

    [name = 'Investment growth gap (14)']
    xg = g*x/(gbar*x(-1));
@#endif


@#if small_model
    [name = 'Production function (2)']
    yf = n;

    [name = 'Firm FOC labor (5)']
    w = mc*yf/n;

    [name = 'Output definition (7)']
    y = (1-varphip*(pigap-1)^2/2)*yf;

    [name = 'ARC (13)']
    c = y;

    [name = 'Household labpur supply equals flex wage']
    w = wf;
@#else
    [name = 'Production function (2)']
    yf = (ups*k(-1)/g)^alpha*n^(1-alpha);

    [name = 'Firm FOC labor (5)']
    w = (1-alpha)*mc*yf/n;

    [name = 'Output definition (7)']
    y = (1-varphip*(pigap-1)^2/2-varphiw*(wg-1)^2/2)*yf - u*k(-1)/g;

    [name = 'ARC (13)']
    x = y-c;
@#endif

[name = 'Output growth gap (8)']
yg = g*y/(gbar*y(-1));

[name = 'Notional Interest Rate (9)']
inomnot = inomnot(-1)^rhoi*(inombar*pigap^phipi*yg^phiy)^(1-rhoi);

[name = 'Nominal Interest Rate (10)', bind='zlb']
inom = inomlb*exp(mp);
[name = 'Nominal Interest Rate (10)', relax='zlb']
inom = inomnot*exp(mp);

[name = 'Inverse MUC (11)']
lam = c-h*c(-1)/g;

[name = 'Flexible real wage definition (12)']
wf = chi*n^eta*lam;

[name = 'HH FOC bond (16)']
1 = beta*(lam/lam(+1))*s*inom/(g(+1)*pibar*pigap(+1));

[name = 'Price Phillips Curve (19)']
varphip*(pigap-1)*pigap = 1-thetap+thetap*mc+beta*varphip*(lam/lam(+1))*(pigap(+1)-1)*pigap(+1)*(yf(+1)/yf);

[name = 'Stochastic productivity growth (21)']
g = gbar+ sigz*epsg;

[name = 'Risk premium shock (22)']
s = (1-rhos)*sbar + rhos*s(-1)+sigs*epss     ;

[name = 'Notional interest rate shock (23)']
mp = sigi*epsi;

[name = 'Observed inflation (24)']
pi = pigap*pibar;

end;

occbin_constraints;
name 'zlb'; bind inomnot <=  inomlb; relax inomnot > inomlb;
end;

// ---------------- Steady state -----------------------------------------//
steady_state_model;
mp = 0;
xg = 1;
s = sbar;
n = nbar;
ups =1;
u =0;
q =1;
g = gbar;
yg = 1;
pigap = 1;
wg =1;
pi = pigap*pibar;
// FOC bond
inom = gbar*pibar/(beta*s);
inomnot = inom;
inombar = inom;
// Firm pricing
mc = (thetap-1)/thetap;
// FOC capital
rk = gbar/beta+delta-1;
// Marginal cost definition
@#if small_model
alpha = 0;
thetaw=1;
@#endif
w = (mc*(1-alpha)^(1-alpha)*alpha^alpha/rk^alpha)^(1/(1-alpha));
@#if small_model
wf = w;
@#else
wf = (thetaw-1)*w/thetaw;
@#endif
// Consolidated FOC firm
k = w*n*gbar*alpha/(rk*(1-alpha));
// Law of motion for capital
x = (1-(1-delta)/gbar)*k;
// Production function
yf = (k/gbar)^alpha*n^(1-alpha);
// Real GDP
y = yf;
// Aggregate resouce constraint
c = y-x;
// FOC labor
lam = (1-h/gbar)*c;
chi = wf/(n^eta*lam);

end;

// ---------------- Checks -----------------------------------------//
steady;
check;

// ---------------- Simulation -----------------------------------------//
shocks;
var epsi   =  1;
var epss   =  1;
var epsg   =  1;
end;

steady;
check;

// ---------------- Estimation -----------------------------------------//

varobs yg inom pi;

// -----------------Occbin ----------------------------------------------//
options_.occbin.smoother.debug=1;
occbin_setup(likelihood_piecewise_kalman_filter);
options_.nobs=110;
calib_smoother(datafile=dataobsfile,first_obs=1,smoothed_state_uncertainty,smoother_redux);
oo_PKF=oo_;

occbin_setup(likelihood_inversion_filter,smoother_inversion_filter);
calib_smoother(datafile=dataobsfile,first_obs=1,smoothed_state_uncertainty,smoother_redux);

figure
subplot(3,1,1)
plot(1:options_.nobs,oo_.SmoothedShocks.epsg,'b-',1:options_.nobs,oo_PKF.SmoothedShocks.epsg)
subplot(3,1,2)
plot(1:options_.nobs,oo_.SmoothedShocks.epsi,'b-',1:options_.nobs,oo_PKF.SmoothedShocks.epsi)
subplot(3,1,3)
plot(1:options_.nobs,oo_.SmoothedShocks.epss,'b-',1:options_.nobs,oo_PKF.SmoothedShocks.epss)
figure
plot(1:options_.nobs,oo_.SmoothedVariables.inom,'b-',1:options_.nobs,oo_PKF.SmoothedVariables.inom)

burnin=40;
if max(abs(oo_.SmoothedShocks.epsg(burnin+1:end)-oo_PKF.SmoothedShocks.epsg(burnin+1:end)))>0.1 || ...
    max(abs(oo_.SmoothedShocks.epsi(burnin+1:end)-oo_PKF.SmoothedShocks.epsi(burnin+1:end)))>0.1 || ...
    max(abs(oo_.SmoothedShocks.epss(burnin+1:end)-oo_PKF.SmoothedShocks.epss(burnin+1:end)))>0.1
    error('Smoothed shocks differ too much')
end

if max(abs(oo_.SmoothedVariables.inom(burnin+1:end)-oo_PKF.SmoothedVariables.inom(burnin+1:end)))>0.001 || ...
    max(abs(oo_.SmoothedVariables.yg(burnin+1:end)-oo_PKF.SmoothedVariables.yg(burnin+1:end)))>0.001 || ...
    max(abs(oo_.SmoothedVariables.pi(burnin+1:end)-oo_PKF.SmoothedVariables.pi(burnin+1:end)))>0.001
    error('Smoothed observables differ too much')
end

temp_data=load('dataobsfile.mat');
if max(abs(temp_data.inom(options_.first_obs+burnin:options_.first_obs+options_.nobs-1)-oo_PKF.SmoothedVariables.inom(burnin+1:end)))>0.0001 || ...
    max(abs(temp_data.yg(options_.first_obs+burnin:options_.first_obs+options_.nobs-1)-oo_PKF.SmoothedVariables.yg(burnin+1:end)))>0.0001 || ...
    max(abs(temp_data.pi(options_.first_obs+burnin:options_.first_obs+options_.nobs-1)-oo_PKF.SmoothedVariables.pi(burnin+1:end)))>0.0001
    error('Smoothed observables differ too much')
end

