var y ${y}$ (long_name='output')
    y_nat ${y^{nat}}$ (long_name='natural output')
    y_gap ${\tilde y}$ (long_name='output gap')
    pi ${\pi}$ (long_name='inflation')
    c ${c}$ (long_name='consumption')
    lam ${\lambda}$ (long_name='Lagrange multiplier')
    n ${n}$ (long_name='hours worked')
    w ${w}$ (long_name='real wage')
    r ${r}$ (long_name='nominal interest rate')
    mc ${\tau}$ (long_name='Marginal cost')
    e ${e}$ (long_name='demand elasticty')
    x ${x}$ (long_name='Preference shock')
    a  ${a}$ (long_name='AR(1) technology shock process')
    nu  ${\nu}$ (long_name='monetary shock process')

    y_fd ${\varepsilon_e}$   (long_name='markup shock')
    w_fd ${\varepsilon_e}$   (long_name='markup shock')
    r_obs ${\varepsilon_e}$   (long_name='markup shock')
    pi_obs ${\varepsilon_e}$   (long_name='markup shock')
    ;     

varexo eps_a ${\varepsilon_a}$   (long_name='technology shock')
       eps_nu ${\varepsilon_\nu}$   (long_name='monetary policy shock')
       eps_x ${\varepsilon_x}$   (long_name='preference shock')
       eps_e ${\varepsilon_e}$   (long_name='markup shock')
       ;

parameters 
        alppha ${\alpha}$ (long_name='capital share')
    	betta ${\beta}$ (long_name='discount factor')
    	h ${h}$ (long_name='Parameter habit consumption')
        phi ${\phi}$ (long_name='unitary Frisch elasticity')
        chix ${\chi}$ (long_name='price indexation')
    	rho_pi ${\phi_{\pi}}$ (long_name='inflation feedback Taylor Rule')
    	rho_y ${\phi_{y}}$ (long_name='output feedback Taylor Rule')
        rho_r ${\phi_{y}}$ (long_name='degree of smoothing Taylor rule')
    	epsilon ${\epsilon}$ (long_name='steady state demand elasticity')
    	theta ${\theta}$ (long_name='Calvo parameter')  
    	rho_a ${\rho_{x}}$ (long_name='autocorrelation technology shock') 
    	rho_x ${\rho_{x}}$ (long_name='autocorrelation preference shock')
    	rho_nu ${\rho_{x}}$ (long_name='autocorrelation monetary shock')
    ;
%---------------------------------------------------------------
% Parametrization, p. 52
%---------------------------------------------------------------
alppha	= 0.3;
betta 	= 0.99;
h 		= 0.7;
phi 	= 1;
chix    = 0.6;
rho_pi 	= 1.5;
rho_y  	= 0.2;
rho_r  	= 0.8;
epsilon	= 6;
theta	= 0.6;
rho_a   = 0.8;
rho_x 	= 0.5;
rho_nu 	= 0.4;

%---------------------------------------------------------------
% First Order Conditions
%---------------------------------------------------------------
model(linear); 

//1. F.O.C. consumption for Households 
lam*(1-(h*betta)) = x-((c-(h*c(-1)))*(1/(1-h)))-(h*betta*x(+1))+((c(+1)-(h*c))*((h*betta)/(1-h)));
//2. F.O.C. leisure for Households
phi*n=lam+w;
//3. F.O.C. bonds for Households
0=lam(+1)-lam+r-pi(+1);
//4. Average marginal cost
mc=w+(y*(alppha/(1-alppha)))-(a*(1/(1-alppha)));
//5. First auxiliary variable
pi=((betta/(1+(betta*chix)))*pi(+1))+((chix/(1+(betta*chix)))*pi(-1))+((mc-(e*(1/(epsilon-1))))*(((1-theta*betta)*(1-theta)*(1-alppha))/((1+betta*chix)*(1-alppha+alppha*epsilon)*theta)));
//8. Natural output
alppha*y_nat=a-((1-alppha)*w)+(((1-alppha)/(epsilon-1))*e); 
//9. Taylor Rule
r=(r(-1)*rho_r)+((1-rho_r)*((rho_pi*pi)+(rho_y*y_gap)))+nu;
//10. Definition output gap
y_gap = y-y_nat;
//12. Equilibrium
y=c;
//13. Production function
y=(n*(1-alppha))+a;
//14. TFP shock
a=(rho_a*a(-1))+eps_a;
//15. Preference shock
x=(rho_x*x(-1))+eps_x;
//16. Markup shock
e=((1-epsilon)/epsilon)*eps_e;
//17. Monetary shock
nu=(rho_nu*nu(-1))+eps_nu;  

//// Observation equations 
//18. Output
y_fd = y;

//19. Wage
w_fd = w;

//20. Interes Rate
r_obs=r;
//21. Inflation
pi_obs=pi;

end;

varobs y_fd w_fd r_obs pi_obs;

estimated_params;
alppha, 0.3, 0, 1,beta_pdf, 0.3, 0.05;
h, 0.7, 0, 1,beta_pdf, 0.33, 0.15; 
phi, 1, , ,gamma_pdf, 1.17, 0.351;
chix, 0.6, 0, 1, beta_pdf, 0.61, 0.112; 
rho_pi, 1.5, 0, 10, normal_pdf, 1.5, 0.2; 
rho_y, 0.2, 0, 10, normal_pdf, 0.2, 0.1;
theta, 0.6, 0, 1, beta_pdf, 0.61, 0.112;
rho_a, 0.7, 0, 1, beta_pdf, 0.61, 0.112;
rho_x, 0.5, 0, 1, beta_pdf, 0.61, 0.112;
rho_nu, 0.4, 0, 1, beta_pdf, 0.61, 0.112;

stderr eps_a, inv_gamma_pdf, 0.1, 2;
stderr eps_nu, inv_gamma_pdf, 0.1, 2;
stderr eps_x, inv_gamma_pdf, 0.1, 2;
stderr eps_e, inv_gamma_pdf, 0.1, 2;
end;


estimated_params_init;
alppha, 0.3;
h, 0.7; 
phi, 1;
chix, 0.6; 
rho_pi, 1.5; 
rho_y, 0.2;
theta, 0.6;
rho_a, 0.7;
rho_x, 0.5;
rho_nu, 0.4;

stderr eps_a, 0.02;
stderr eps_nu, 0.04;
stderr eps_x, 0.02;
stderr eps_e, 0.2;
end;

identification;
estimation(datafile=observables_gali2_filt_119, selected_variables_only,mh_replic=0, mode_compute=0,mode_file=gali2_fd_mode,load_mh_file) y_fd w_fd y;
shock_decomposition (parameter_set=posterior_mean) y y_fd;
write_latex_dynamic_model;