/*  fs2000 as a stoch model model    
Taylor rule determines ffr rate and ior rate is set equal */

var m ${m}$ (long_name='Money Stock')
    P ${P}$ (long_name='Price Level')
    c ${c}$ (long_name='Consumption')
    ER ${ER}$
     W ${W}$ (long_name='Nominal Wage')
     Rf ${R}$ (long_name='Nominal Rental Rate of Capital')
     k ${k}$ (long_name='Capital') 
     d ${d}$ (long_name='Deposits')
     n ${n}$ (long_name='Hours worked')
     l ${l}$ (long_name='Loans')
     gy_obs ${\Delta y^{obs}}$ (long_name='Observed growth rate of output')
     gp_obs ${\Delta m^{obs}}$ (long_name='Observed growth rate of prices')
     y ${y}$ (long_name='Output')
     dA ${\Delta A}$ (long_name='Labor Augm. Techn. Growth Rate')
     Pi ${\pi}$ (long_name='Inflation Rate')
     gap $\Delta$ (long_name='GDP gap')
%     ffr ${ffr}$ (long_name='Federal Funds Rate');
      Rh ${Rh}$ (long_name='Interest rate on deposits')
      er ${ior rate}$ (long_name='ffr and ior Rate');
 varexo e_a ${\varepsilon_a}$ (long_name='Technology shock')
        e_m ${\varepsilon_m}$ (long_name='Observed money growth rate');
          

parameters alp ${\alpha}$ (long_name='capital share')
           bet ${\beta}$ (long_name='discount factor')
           gam ${\gamma}$ (long_name='Average technology growth')
           mst ${\bar m}$ (long_name='Average money stock')
           rho ${\rho}$ (long_name='Autocorrelation money process')
           psi ${\psi}$ (long_name='Leisure weight in utility')
           del ${\delta}$ (long_name='depreciation')
     e g h Yf etta Rho phi_pi phi_y pi_star;  

alp = 0.33;
bet = 0.99;
gam = 0.003;
mst = 1.011;
rho = 0.7;
psi = 0.787;
del = 0.02;
e = 1;
g = .0001;
h = .3;
Yf = 0.608187;  % potential output
etta = .99;  % eta is fixed at .01
Rho = 0.8;
phi_pi=.5;  // 1.5;
phi_y=.5;   // 1.5;
pi_star=0.005;

% options_.TeX=1;
model;
dA = exp(gam+e_a);
log(m) = (1-rho)*log(mst) + rho*log(m(-1)) + e_m;
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*k^(alp-1)*n(+1)^(1-alp)+(1-del))/(c(+2)*P(+2)*m(+1))=0;
W = (l/n);
-(psi/(1-psi))*(c*P/(1-n))+ (l/n) = 0;
Rf = P*(1-alp)*k(-1)^alp*n^(-alp)/(W*etta);   % denominator is (W(1-eta))
1/(c*P)-bet*P*(1-alp)*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
c+k = k(-1)^alp*n^(1-alp)+(1-del)*k(-1);
P*c + ER = m;             % money equilibrium
d = l + ER;               % bank's balance sheet
ER = g + h*er;            % demand for ERs by banks
Rf*etta = Rh;           %  wedge between loan rate and ior rate is etta
y = k(-1)^alp*n^(1-alp);
gy_obs = dA*y/y(-1);
 gp_obs =(P/P(-1))*m(-1);  % /dA;  % doesn't like this
Pi = P/P(-1);           % inflation rate
gap = ((Yf-y)/y);

// Taylor Rule
// interest =Rho*interest(-1)+(1-Rho)*steady_state(interest)+phi_pi*(Pi-pi_star); % +(1-Rho)*phi_y*(y/y(-1)-1);
er =Rho*Rh(-1)+(1-Rho)*(er-1)+phi_pi*(Pi-pi_star)+(1-Rho)*phi_y*(y/y(-1)-1);
// er = Pi +.5*gap;        % .5*(Pi-1.02) + .5*gap + 1.02 -1;  // Walsh  

end;

initval;
er = 1.0098;
k = 6;
m = mst;
P = 2.25;
c = 0.45;
ER = .01;
W = 4.5;
Rf = 1.02;
d = 0.85;
n = .19;
l = 0.86;
y = 0.6;
Pi = 1;
gap = 0;
end;

steady;

check;


shocks;
var e_a; stderr 0.014;
var e_m; stderr 0.005;
end;


% simul(periods=2000);
%stoch_simul(order=1,irf=20,graph_format=eps,periods=1000);  
// use w 2016
% stoch_simul(order=1,irf=20,graph_format=eps,periods=1000,contemporaneous_correlation,conditional_variance_decomposition=[1,3]); %2016

%write_latex_original_model;
%write_latex_static_model;
%write_latex_parameter_table;
%write_latex_dynamic_model;
%write_latex_definitions;
%collect_LaTeX_Files(M_);



estimated_params;
alp, beta_pdf, 0.356, 0.02;
bet, beta_pdf, 0.993, 0.002;
gam, normal_pdf, 0.0085, 0.003;
mst, normal_pdf, 1.0002, 0.007;
rho, beta_pdf, 0.129, 0.223;
psi, beta_pdf, 0.65, 0.05;
del, beta_pdf, 0.01, 0.005;
stderr e_a, inv_gamma_pdf, 0.035449, inf;
stderr e_m, inv_gamma_pdf, 0.008862, inf;
end;
varobs gp_obs gy_obs;

% estimation(order=1,datafile=fsdat_simul, nobs=192, loglinear, mh_replic=2000, mh_nblocks=2, mh_jscale=0.8);
estimation(order=1,datafile=fsdat_simul, nobs=192, loglinear, mh_replic=2000, mh_nblocks=2, mh_jscale=0.8,diffuse_filter,conf_sig=.95, bayesian_irf);

/*
// Figures
 tt=0:2001;

    figure('Name','ior, R and Rf');
    subplot(1,1,1);
    plot([0:49], oo_.exo_simul(1:50,1),'k','LineWidth',1.5);
    hold on;
    plot([51:1999], oo_.exo_simul(52:2000,1),'--k','LineWidth',1.5);
    hold on; plot([0:49], oo_.endo_simul(6,1:50),':r');  // both interest rates together
    hold on; plot([51:1999], oo_.endo_simul(6,52:2000),'-.b');//both interest rates together   
    title('IOR, deposit, and loan interet rates');
    axis([0 100 1.005 1.035]);
    xlabel('time')
    ylabel('percent %,\xi')
    legend('ior & R before change', 'ior & R after change','Rf before change','Rf after change','Location','southeast')

// figure 2    
figure('Name','banks balance sheet');
    subplot(3,1,1); 
    plot(tt, oo_.endo_simul(4,:));
    title('ER');
    xlabel('1')
    ylabel('ER(ior)')
    axis([0 200 0.3 .31]);

    subplot(3,1,2);
    plot(tt, oo_.endo_simul(10,:));
    title('loans to firms');
    xlabel('2');
    ylabel('l');
    axis([0 200 0.57 .62]);

    subplot(3,1,3);
    plot(tt, oo_.endo_simul(8,:));
    title('deposits');
    ylabel('d');
    xlabel('3');
    axis([0 200 .89 .91]);


// figure 3
figure('Name','labor equation');
    subplot(3,1,1);
    plot(tt, oo_.endo_simul(10,:));
    title('loans to firms');
    xlabel('1');
    ylabel('loans');
    axis([0 200 0.582 .6]);

    subplot(3,1,2);
    plot(tt, oo_.endo_simul(12,:));
    title('Labor'); % from new Labor 
    xlabel('2');
    ylabel('\zeta');
    axis([0 200 .184 .186]);

    subplot(3,1,3);
    plot(tt, oo_.endo_simul(5,:));
    title('wages');
    xlabel('3');
    ylabel('\omega');
    axis([0 200 3.158 3.24]);

// figure 4
figure('Name','Money equilibrium');
    subplot(2,2,1);
    plot(tt, oo_.endo_simul(1,:),'--b');
    title('Money Supply');
    axis([0 2000 .5 2]);
    xlabel('1')
    ylabel('M(m*,m(-1),\rho)')

    subplot(2,2,2); 
    plot(tt, oo_.endo_simul(4,:));
    title('ER');
    xlabel('2')
    ylabel('ER(ior)')
    axis([0 200 0.3 .31]);

    subplot(2,2,3);
    plot(tt, oo_.endo_simul(2,:),'c');
    title('Price Level');
    axis([0 400 1.483 1.5]);
    xlabel('3')
    ylabel('P(k,m,c,\delta)')
   
    subplot(2,2,4);
    plot(tt, oo_.endo_simul(3,:),'g');
    title('Consumption');
    xlabel('4')
    ylabel('C')
    axis([0 200 0.47 .47555]);

//figure 5
figure('Name','GDP');
    subplot(3,1,1);
    plot(tt, oo_.endo_simul(11,:));
    title('output');
    xlabel('1');
    ylabel('Y');
    axis([0 200 .58 .63]);

    subplot(3,1,2);
    plot(tt, oo_.endo_simul(3,:),'g');
    title('Consumption');
    xlabel('2')
    ylabel('C')
    axis([0 200 0.47 .48]);

    subplot(3,1,3);
    plot(tt, oo_.endo_simul(7,:));
    title('capital');
    xlabel('3');
    ylabel('K');
    axis([0 200 6.6 6.8]);

    // fig 6
    figure('Name','inflation');
    subplot(3,1,1);
    plot(tt, oo_.endo_simul(13,:));
    title('inflation');
    xlabel('1');
    ylabel('\pi');
    axis([0 200 .99 1.01]);

    subplot(3,1,2);
    plot(tt, oo_.endo_simul(14,:));
    title('GDP gap');
    xlabel('3');
    ylabel('percent \Delta');
    axis([0 200 -0.5 .1]);

    subplot(3,1,3);
    plot(tt, oo_.endo_simul(15,:));
    title('FFR - taylor rule');
    xlabel('2');
    ylabel('FFR');
    axis([0 200 -0.9 1.3]);
*/
/*  //fig. 5
    figure('Name','Labor equations');
    subplot(2,2,1);
    plot(tt, oo_.endo_simul(9,:));
    title('original labor');
    xlabel('1');
    ylabel('l');
    axis([0 200 .1 .25]);

    subplot(2,2,2);
    plot(tt, oo_.endo_simul(12,:));
    title('new Labor Equation');
    xlabel('2');
    ylabel('L');
    axis([0 200 0.16 .22]);

    subplot(2,2,3);
    plot(tt, oo_.endo_simul(5,:));
    title('wages');
    xlabel('3');
    ylabel('\omega');
    axis([0 200 2 4]);

    subplot(2,2,4);
    plot(tt, oo_.endo_simul(10,:));
    title('Loans to firms');
    xlabel('4');
    ylabel('\lambda');
    axis([0 200 0.25 .8]);   */