%FIGURE2.M
function figure2 
%This program produces part of figure 2 of the paper ``Deep Habits,'' by Morten Ravn, Stephanie Schmitt-Grohe, and Martin Uribe (Review of Econmic Studies)
%Note: In the paper figure 2 has 2 lines, one for the case of good-specific
%subsitence points and one for the case of deep habits. The latter is
%reproduced from figure 1. The program figure2.m  produces only the impulse response corresponding to the case of good-specific subsistence points. 
%
%Calls: gx_hx.m, anal_deriv.m, num_eval.m, and ir.m
% 
%(c) Stephanie Schmitt-Grohe and Martin Uribe
%
%Date December 23, 2003

%SHOCKS
%shock=1 preference
%shock=2 government
%shock=3 technology
for shock=1:3

%Compute analytical derivatives of equilibrium conditions
[fx,fxp,fy,fyp,f] = sp;


%Numerical evaluation

%Assign values to parameters and steady-state variables
[THETA,GBAR,SIGMA,CHI,GAMA,BETTA,DELTA,ALFA,ETA,CSTAR,IVVSTAR,GSTAR,RHOZ,RHOG,RHOV,w,h,c,u,k,ivv,markup,a,g,v,output,wp,hp,cp,up,kp,ivvp,markupp,ap,gp,vp,outputp,W,H,C,U,K,IVV,MARKUP,A,G,V,OUTPUT,PHI,EHW,SC,SG,SI,THETA_C,THETA_G,THETA_I]=sp_ss(0.275,0.275,0);

approx = 1; %Order of approximation desired

%Compute numerical derivatives of f
num_eval

%Obtain first-order accurate approximation to the policy functions
[gx,hx] = gx_hx(nfy,nfx,nfyp,nfxp); 

%Set time horizon for the impulse responses
T=21;

%Compute impulse responses
IR = ir(gx,hx,[0 (shock==1)*(C-CSTAR) (shock==2)*1 (shock==3)*1],T);
Ir(:,:,shock) = IR;

t=(0:size(IR,1)-1)';

c = squeeze(Ir(:,5,:));
h = squeeze(Ir(:,4,:));
w = squeeze(Ir(:,3,:));
ivv = squeeze(Ir(:,6,:)); 
u= squeeze(Ir(:,7,:));
output = squeeze(Ir(:,2,:));
markup = squeeze(Ir(:,1,:));
g = squeeze(Ir(:,10,:));
a = squeeze(Ir(:,11,:));

subplot(3,4,1+(shock-1)*4)
plot(t,markup(:,shock),'-')
title('Markup')

subplot(3,4,2+(shock-1)*4)
plot(t,output(:,shock))
title('Output')

subplot(3,4,3+(shock-1)*4)
plot(t,w(:,shock))
title('Wage')

subplot(3,4,4+(shock-1)*4)
plot(t,c(:,shock))
title('Consumption')

end
shg


%SP.M
function [fx,fxp,fy,fyp,f] = sp
%This program computes a log-linear approximation to the  function f for an
%economy with good-specific subsistence points. The model is described in
%section 4.1 of  ``Deep Habits'' by M. Ravn, S. Schmitt-Grohe, and M.
%Uribe, Review of Economic Studies, 2005. 
%
%Calls: anal_deriv.m 
%
%(c) Stephanie Schmitt-Grohe and Martin Uribe
%
%Date December 23, 2003

%Define parameters
syms SIGMA CHI GAMA BETTA DELTA ALFA ETA RHOZ RHOG RHOV GBAR PHI CSTAR IVVSTAR GSTAR  

%Define variables 

syms c cp h hp w wp u up k kp ivv ivvp markup markupp a ap g gp output outputp v vp 

%Give functional form for  production, and utility functions

%Utility function
util = ((c-CSTAR-log(v))^(1-SIGMA) -1) / (1-SIGMA) + GAMA * ((1-h)^(1-CHI)-1) / (1-CHI);
utilp = ((cp-CSTAR-log(vp))^(1-SIGMA) -1) / (1-SIGMA) + GAMA * ((1-hp)^(1-CHI)-1) / (1-CHI);

pf = a*k^(ALFA)*h^(1-ALFA);
pfp = ap * kp^(ALFA)*hp^(1-ALFA);

%Write equations (ei, i=1:n)

%Labor supply
e1 = w + diff(util,'h') / diff(util,'c');

%Euler equation
e2 = -diff(util,'c') + BETTA *  diff(utilp,'cp') * (1-DELTA+up);

%Resource constraint
e3 = -(pf - PHI) + c + ivv + g;

%Evoluiton of capital
e4 = -kp + (1-DELTA) * k + ivv - IVVSTAR;

%Markup
e5 = -markup + diff(pf,'h') / w;

%nu
e6 = (1-ETA) * output  + ETA * (CSTAR+GSTAR+IVVSTAR) + ETA / markup * (output-CSTAR-GSTAR-IVVSTAR);


%MRT = w/u
e7 = -w / u + diff(pf,'h') / diff(pf,'k');

%Technology shock
e8 = log(ap) - RHOZ * log(a);

%Government Purchases shock
e9 = log(gp/GBAR) - RHOG * log(g/GBAR);

%Evolution of preference shock
e10 = - log(vp) + RHOV * log(v);

%Definition of output
e11 = -output + pf - PHI;


%Create function f
f = [e1;e2;e3;e4;e5;e6;e7;e8;e9;e10;e11];

% Define the vector of controls in period t, y, and t+1, yp, and the vector of states in period t, x, and t+1, xp

x = [k v g a];

xp = [kp vp gp ap];

y = [markup output w h c ivv u ];

yp = [markupp outputp wp hp cp ivvp up];


%Make f a function of the logarithm of the state and control vector
f = subs(f, [x,y,xp,yp], exp([x,y,xp,yp]));


approx = 1; %Order of approximation desired
%Compute analytical derivatives of f
[fx,fxp,fy,fyp]=anal_deriv(f,x,y,xp,yp,approx);


%SP_SS.M
function [THETA,GBAR,SIGMA,CHI,GAMA,BETTA,DELTA,ALFA,ETA,CSTAR,IVVSTAR,GSTAR,RHOZ,RHOG,RHOV,w,h,c,u,k,ivv,markup,a,g,v,output,wp,hp,cp,up,kp,ivvp,markupp,ap,gp,vp,outputp,W,H,C,U,K,IVV,MARKUP,A,G,V,OUTPUT,PHI,EHW,SC,SG,SI,THETA_C,THETA_G,THETA_I]=sp_ss(theta_c,theta_g,theta_i);
%This program produces the deep structural parameters and computes the steady state of the good-specific subsistence point model described in section 4.1 of  ``Deep Habits.'' by Morten Ravn, Stephanie Schmitt-Grohe, and Martin Uribe 
%(c) Stephanie Schmitt-Grohe and Martin Uribe, December 23, 2003

%Calibrated parameters

THETA_C=theta_c;%ratio of subsistence-consumption-to-consumption 
THETA_G=theta_g;%ratio of subsistence-gov'tconsumption-to-gov'tconsumption 
THETA_I=theta_i;%ratio of subsistence-investment-to-investment 

SIGMA = 2; %intertemporal elasticity of substitution

EHW = 1.3; %Frisch elasticity of labor suppy

H = 0.2; %hours (Prescott, 1986)

ETA = 5.3;%Long-run Price elasticity of demand for a particular variety. Taken from the econometric estimates shown in the paper ``Deep Habits''

R = 1.04^(1/4); %Gross quarterly real interest rate (Rotemberg & Woodford, JPE, 1991)

SH = 0.75;%Labor share (Rotemberg & Woodford, JPE, 1991)

SG = 0.12; % Steady State Share of Government Purchases (Rotemberg & Woodford, JPE, 1991)

RHOZ = 0.9; %Persistence of technology shock z_t

RHOG = 0.9; %Persistence of Government purchases shock

RHOV = 0.9; %Persistence of preference shock

SC = 0.7; %Consumption share (Rotemberg & Woodford, JPE, 1991)
 
%Implied parameters

BETTA = 1/R; %Subjective discount factor

SI = 1-SC-SG; %INVESTMENT SHARE

THETA = SC * THETA_C + SG * THETA_G + SI * THETA_I; %Average ratio of subsistence absorption to absorption 

MARKUP = 1 / (1-1/ETA/ (1-THETA)); %Markup

ALFA = 1 - SH; %capital elasticity of output

SK = SH * ALFA/(1-ALFA); %share of capital

ans = SI  / SH * (1-ALFA) / ALFA  * (1-THETA_I);
DELTA =  ans*(1/BETTA-1)/(1-ans); %Depreciation rate

U = 1/BETTA-1+DELTA; %rental rate of capital

K = (SI/DELTA/MARKUP*(1-THETA_I))^(1/(1-ALFA))*H; %Steady state capital stock

OUTPUT = K^ALFA * H^(1-ALFA) / MARKUP; %output

W = U * (1-ALFA)/ALFA *K/H; %Wage rate

IVV = DELTA * K / (1-THETA_I); %Investment

PHI = K^ALFA * H^(1-ALFA) - OUTPUT; %Fixed cost

C = SC * OUTPUT; %consumption

CHI = (1-H)/H / EHW;

GAMA = W * (1-H)^CHI / (C*(1-THETA_C))^SIGMA; 

V = 1; %Steady-State value of preference shock

A = 1; %steady-state value of technology shock

G = SG * OUTPUT; %Government consumption

GBAR=G; %Unconditional mean of gov't consumption

%Subsistence levels of consumption, gov't spending, and investment
CSTAR = THETA_C*C;
IVVSTAR = THETA_I*IVV;
GSTAR = THETA_G*G;

%Log values
w=log(W);
h=log(H);
c=log(C);
u=log(U);
k=log(K);
ivv=log(IVV);
markup=log(MARKUP);
a=log(A);
g = log(G);
output = log(OUTPUT);
v=log(V);
%Future values of logged variables
wp=log(W);
hp=log(H);
cp=log(C);
up=log(U);
kp=log(K);
ivvp=log(IVV);
markupp=log(MARKUP);
ap=log(A);
gp = log(G);
outputp = log(OUTPUT);
vp=log(V);