%FIGURE1.M
function figure1 
%This program produces figure 1 of the paper ``Deep Habits,'' by Morten Ravn, Stephanie Schmitt-Grohe, and Martin Uribe (Review of Econmic Studies)
%
%Calls: gx_hx.m, and ir.m
% 
%(c) Stephanie Schmitt-Grohe and Martin Uribe
%
%Date December 23, 2003

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

%Theta = [theta_s theta_d; theta_g]
%where theta_s=superficial habit parameter; theta_d=deep habit parameter; and theta_g=government deephabit parameter

%The matrix Theta: row 1: deep habits; row 2: superficial habits; row 3: no habits.
Theta=0.86*[1 1 1; 1 0 0;0 0 0 ];

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

for iter=1:size(Theta,1)
theta_s = Theta(iter,1);
theta_d=Theta(iter,2);
theta_g=Theta(iter,3);


%Numerical evaluation

%Assign values to parameters and steady-state variables

[RHO, THETA_S,THETA_D,THETA_G,GBAR,SIGMA,CHI,GAMA,BETTA,DELTA,ALFA,ETA,RHOZ,RHOG,RHOV,RHOVV,nu,nug,w,h,c,s,u,k,ivv,markup,a,g,v,vv,stockg,output,xx,nup,nugp,wp,hp,cp,sp,up,kp,ivvp,markupp,ap,gp,vp,vvp,stockgp,outputp,xxp,NU,NUG,W,H,C,S,U,K,IVV,MARKUP,A,G,V,VV,STOCKG,OUTPUT,XX,PHI,EHW]=dh_ss(theta_s,theta_d,theta_g);

approx = 1; %Order of approximation desired

%Compute numerical derivatives of f
num_eval

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

%Time horizon for impulse responses
T=21;

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

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


c = squeeze(Ir(:,5,:,:));
h = squeeze(Ir(:,4,:,:));
w    = squeeze(Ir(:,3,:,:));
ivv = squeeze(Ir(:,6,:,:)); 
output = squeeze(Ir(:,2,:,:));
markup = squeeze(Ir(:,1,:,:));
nu = squeeze(Ir(:,8,:,:));
nug = squeeze(Ir(:,9,:,:));
s = squeeze(Ir(:,12,:,:));
g = squeeze(Ir(:,16,:,:));
a = squeeze(Ir(:,17,:,:));

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

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

subplot(3,4,3+(shock-1)*4)
plot(t,w(:,1,shock),'-',t,w(:,2,shock),'--',t,w(:,3,shock),':')
title('Wage')
%ylabel('% dev. from ss')


subplot(3,4,4+(shock-1)*4)
plot(t,c(:,1,shock),'-',t,c(:,2,shock),'--',t,c(:,3,shock),':')
title('Consumption')
%ylabel('% dev. from ss')


end
shg

%DH.M
function [fx,fxp,fy,fyp,f] = dh
%This program computes a log-linear approximation to the  function f for an economy with catching up with the Joneses good by good. The model is described in ``Deep Habits,'' by M. Ravn, S. Schmitt-Grohe, and M. Uribe (RES). 
%The function f defines  the DSGE model (a p denotes next-period variables) : 
%  E_t f(yp,y,xp,x) =0. 
%
%Inputs: theta_s theta_d theta_g (the degree of superficial, deep, and government habit)
%
%Output: analytical first derivative of f
%
%Calls: anal_deriv.m 
%
%(c) Stephanie Schmitt-Grohe and Martin Uribe
%
%Date December 23, 2003

%Define parameters
syms RHO THETA_S THETA_D THETA_G SIGMA CHI GAMA BETTA DELTA ALFA ETA RHOZ RHOG RHOV RHOVV GBAR PHI  

%Define variables 

syms xx xxp s sp c cp h hp w wp u up k kp ivv ivvp nu nup nug nugp markup markupp a ap g gp stockg stockgp output outputp v vp vv vvp

%Give functional form for  production, and utility functions

%Utility function
util = ((xx-log(vv))^(1-SIGMA) -1) / (1-SIGMA) + GAMA * ((1-h)^(1-CHI)-1) / (1-CHI);
utilp = ((xxp-log(vvp))^(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)

e1 = -xx + c-THETA_S * s; %Habit-adjusted consumption

%Labor supply
e2 = w + diff(util,'h') / diff(util,'xx');

%Euler equation
e3 = -v^(1-SIGMA) * diff(util,'xx') + BETTA * vp^(1-SIGMA) * diff(utilp,'xxp') * (1-DELTA+up);

%Resource constraint
e4 = -(pf - PHI) + c + ivv + g;

%Evoluiton of capital
e5 = -kp + (1-DELTA) * k + ivv;

%Markup
e6 = -markup + diff(pf,'h') / w;

%nu
e7 = - (c+g+ivv) / ETA + nu * (c - THETA_D * s) + nug * (g - THETA_G * stockg) + ivv * (1-1/markup);

%Firm's FOC w.r.t. s
e8 = - (1-nu - 1/markup ) / (RHO-1) + BETTA * diff(utilp,'xxp') / diff(util,'xx') * (vp/v)^(1-SIGMA) * (THETA_D * nup + RHO * (1-nup-1/markupp) / (RHO-1));


%Firm's FOC w.r.t. stockg
e9 = - (1-nug - 1/markup ) / (RHO-1) + BETTA * diff(utilp,'xxp') / diff(util,'xx') * (vp/v)^(1-SIGMA) * (THETA_G * nugp + RHO * (1-nugp-1/markupp) / (RHO-1));

%MRT = w/u
e10 = -w / u + diff(pf,'h') / diff(pf,'k');

%Evolution of habit stock
e11 = - sp + RHO * s + (1-RHO) * c;
%Evolution of gov't habit stock
e12 = -stockgp + RHO * stockg + (1-RHO) * g;

%Technology shock
e13 = log(ap) - RHOZ * log(a);

%Government Purchases shock
e14 = log(gp/GBAR) - RHOG * log(g/GBAR);

%Evolution of preference shock
e15 = - log(vp) + RHOV * log(v);


e16 = - log(vvp) + RHOVV * log(vv);

%Definition of output
e17 = -output + pf - PHI;


%Create function f
f = [e1;e2;e3;e4;e5;e6;e7;e8;e9;e10;e11;e12;e13;e14;e15;e16;e17];


% 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 = [stockg s k v vv g a];

xp = [stockgp sp kp vp vvp gp ap];

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

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


%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);


%DH_SS.M
function [RHO, THETA_S,THETA_D,THETA_G,GBAR,SIGMA,CHI,GAMA,BETTA,DELTA,ALFA,ETA,RHOZ,RHOG,RHOV,RHOVV,nu,nug,w,h,c,s,u,k,ivv,markup,a,g,v,vv,stockg,output,xx,nup,nugp,wp,hp,cp,sp,up,kp,ivvp,markupp,ap,gp,vp,vvp,stockgp,outputp,xxp,NU,NUG,W,H,C,S,U,K,IVV,MARKUP,A,G,V,VV,STOCKG,OUTPUT,XX,PHI,EHW]=dh_ss(theta_s,theta_d,theta_g);
%This program produces the deep structural parameters and computes the steady state of the additive external deep habit model described in  ``Deep Habits.'' by Morten Ravn, Stephanie Schmitt-Grohe, and Martin Uribe (RES).
%(c) Stephanie Schmitt-Grohe and Martin Uribe, December 23, 2003

%Calibrated parameters

THETA_S=theta_s;%superficial habit parameter 

THETA_D = theta_d;%deep habit parameter

THETA_G = theta_g; %govt deep habit parameter

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

RHOVV = 0.9; %Persistence of additive preference shock

RHO = 0.85; %1-RHO is the weight on current consumption in the evolution of the stock of habit. S_t = RHO s_{t-1} + (1-RHO) C_{t}. Taken from the econometric estimates presented in ``Deep Habits.''

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

BETTA = 1/R; %Subjective discount factor

SI = 1-SC-SG; %INVESTMENT SHARE

m = SC * ((1-BETTA * RHO) * (1-THETA_D) / (BETTA * THETA_D * (RHO-1) +1 - BETTA * RHO)) + SG * ((1-BETTA * RHO) * (1-THETA_G) / (BETTA * THETA_G * (RHO-1) +1 - BETTA * RHO)) + SI;
 
MARKUP = 1/ (1-1/ETA/ m); %Markup

ALFA = 1 - SH; %capital elasticity of output

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

DELTA = SI  * (1/BETTA-1)/ (SK-SI);

NU = (1-1/MARKUP)/ ((BETTA * THETA_D * (RHO-1) + 1 - BETTA * RHO)/ (1-BETTA*RHO));

NUG = (1-1/MARKUP)/ ((BETTA * THETA_G * (RHO-1) + 1 - BETTA * RHO)/ (1-BETTA*RHO)); %Lagrange multiplier on aggregate demand faced by monopolist i


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

K = (SI/DELTA/MARKUP)^(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; %Investment

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

C = SC * OUTPUT; %consumption

S = C; %Stock of habit

XX = C - THETA_S * S; %Habit-adjusted consumption


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

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

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


VV =0; %Steady-State value of additive preference shock

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


G = SG * OUTPUT; %Government consumption

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

STOCKG = G;

%Log values
nu=log(NU);
nug=log(NUG);
w=log(W);
h=log(H);
c=log(C);
s=log(S);
u=log(U);
k=log(K);
ivv=log(IVV);
markup=log(MARKUP);
a=log(A);
g = log(G);
stockg=g;
output = log(OUTPUT);
xx = log(XX);
v=log(V);
vv=VV;
%Future values of logged variables
nup=log(NU);
nugp=log(NUG);
wp=log(W);
hp=log(H);
cp=log(C);
sp=log(S);
up=log(U);
kp=log(K);
ivvp=log(IVV);
markupp=log(MARKUP);
ap=log(A);
gp = log(G);
stockgp=g;
outputp = log(OUTPUT);
xxp = log(XX);
vp=log(V);
vvp=VV;