%FINANCIAL_FRICTION_RUN.M computes unconditional moments implied by the financial-
%friction model in the paper  ``Real Business Cycles 
%in Emerging Countries?'' by Javier Garcia-Cicco, Roberto Pancrazi, and Martin Uribe (AER, 
%forthcoming). The estimated parameters 
%are assigned values corresponding to the median of their estimated posterior distribution.  This 
%distribution was estimated using Bayesian methods and annual Argentine data on  output 
%growth, consumption growth, investment growth, and the trade-balance-to-output ratio  from 1900 to 
%2005. The other parameters of the model are calibrated. Their values are contained  in the 
%program financial_friction_ss.m,  which also computes the steady state of the model and 
%evaluates the first derivatives of the equilibrium conditions . The dynamic system and 
%its derivatives are computed analytically  in the program financial_friction.m. 
%
%The auxiliary programs gx_hx.m, num_eval_print2f.m, and mom.m are taken from the package for computing first- and second-order 
%accurate dynamics of DSGE models produced by Stephanie Schmitt-Grohe and Martin Uribe and 
%available online at www.columbia.edu/~mu2166/2nd_order.htm
%
%(c) Martin Uribe, September 2009. 

%Mean of posterior distribution of estimated parameters

 b =[
   1.009890776104921
   0.010561526060797
   0.323027844166870
   0.033055089525252
   0.864571930755821
   0.539099453618175
   0.850328786147732
   0.018834174505537
   0.205034667802314
   0.057195449717680
   0.906802888826967
   4.810804146604144
   2.867166241970346
   0.000114861607534
   0.000130460798135
   0.001436553959841
   0.000109652068259];


%Order of approximation
approx = 1;


[nfx, nfy, nfxp, nfyp, nvarshock, nETASHOCK] = financial_friction_ss(b);

%Policy Functions
[gx,hx, deterflag] = gx_hx(nfy,nfx,nfyp,nfxp); 


%MOMENTS


%Compute Variance/covariance matrix of controls (var_y) and states (var_x)
[var_y,var_x] = mom(gx,hx,nvarshock,0);

clc

%SECOND MOMENTS OF of gY, gC, gI, and TB/Y
disp('From left to right, the figures correspond to output growth, consumption growth, investment growth and the trade-balance-to-output ratio')

disp('Standard Deviations')
STDEV = ((diag(var_y(1:4,1:4)).^(1/2))*100)'


disp('Correlations with Output Growth')
CGY = (var_y(1:4,1) ./ (diag(var_y(1:4,1:4)).^(1/2)) /var_y(1,1)^(1/2))'


%First-order autocovariance
[var_y1,var_x1] = mom(gx,hx,nvarshock,1);

disp('First-Order Autocorrelations')
autocorre1 =  diag(var_y1)./ diag(var_y);
FOAC = autocorre1(1:4)'


%Second-order autocovariance
[var_y2,var_x2] = mom(gx,hx,nvarshock,2);

disp('Second-Order Autocorrelations')
autocorre2 = diag(var_y2)./ diag(var_y);
SOAC = autocorre2(1:4)'

%Third-order autocovariance
[var_y3,var_x3] = mom(gx,hx,nvarshock,3);

disp('Third-Order Autocorrelations')
autocorre3 = diag(var_y3)./ diag(var_y);
TOAC = autocorre3(1:4)'

%Fourth-order autocovariance
[var_y4,var_x4] = mom(gx,hx,nvarshock,4);

disp('Fourth-Order Autocorrelations')
autocorre4 = diag(var_y4)./ diag(var_y);
FFOAC = (autocorre4(1:4))'


disp('Correlations with  the Trade-Balance-to-GDP Ratio')
CTBY = (var_y(1:4,4) ./ (diag(var_y(1:4,1:4)).^(1/2)) /var_y(4,4)^(1/2))'