%DEEP_PARAMETERS.M
%Deep Structural parameters of the model in ``Optimal Inflation Stabilization in a Medium-Scale Macroeconomic Model'' by S. Schmitt-Grohe and Martin Uribe (2005)
%(c) Stephanie Schmitt-Grohe and Martin Uribe, October 2005 .

function [BETTA, THETA, DELTA, NU,  ETATIL, ETA, ALFA, ALFATIL, B, KAPA, CHI, CHITIL, PSSI, PHI1, PHI2, PHI3, PHI4, GAMA1, GAMA2,  RHOMUZ, RHOMUUPSILON, RHOG, STD_EPSMUZ, STD_EPSMUUPSILON, STD_EPSG, G, MUI, MUZ, MUUPSILON ] = deep_parameters;

U = 1; %SS capital utilization

GAMA2_O_GAMA1 =  1.46; %cost of capital utilization

PAISTAR = 1.042^(1/4); %Inflation target


%Exogenous processes, all from ACEL and CE 
RHOMUZ = 0.89; %Serial correlation of neutral tech. shock growth, 

STD_EPSMUZ = 0.0007; %Std. dev.  of innovation to neutral tech. shock

RHOMUUPSILON = 0.20; %Serial correlation of neutral tech. shock growth, 

STD_EPSMUUPSILON = 0.0031; %Std. dev.  of innovation to neutral tech. shock

% gOVE PROCESS FROM Christiano and Eichenbaum 1992
RHOG = 0.9;%0.96; %Serial correlation of gov't consumption (Christiano and Eichenbaum 1992).   
SG = 0.17; %Share of gov't expenditures in gdp (own estimate)
STD_EPSG = 0.008;%0.020; %Std. Dev. of  innovation to gov't consumption  (Christiano and Eichenbaum 1992). 


%Calibration of Money demand block
SMH = 0.44; %Share of household money in total money (own estimate). 
SM = 0.1695*4; %M1/GDP. Sample: 1959:1-2004:3. Source: GDP NIPA and M1 FRB. Produced with m1_gdp.m  
EPS_MH_R = -0.81; %annualized inerest rate semielasticity of money demand (ACEL)


H = 0.5; %Steady State labor supply 

PHI3 = 1; %reciprocal of intertemporal elasticity of substitution

BETTA =  1.03^(-1/4); %Discount factor;

THETA = 0.36;%Capital share; I use a much smaller capital share to avoid the problem of getting an investment share of over 1/3 of GDP.

DELTA = 0.025; 

ETATIL = 21; %Labor elasticity of subst (ACEL)

ETA = 6; %goods elasticity of substitution (ACEL)

ALFA = 0.8; %Degree of price stickiness (CEE)

ALFATIL = 0.69; %degree of wage stickiness (ACEL)

B = 0.69; %degree of habit formation (ACEL)

KAPA = 2.79; %Capital adjustment cost (ACEL)

CHI = 0; %Degree of price ndexation (Cogley and Sbordone, LOWW)

CHITIL = 1; %Degree of wage indexation (ACEL)

MUZ = 1.00213; %steady state growth rate of neutral technological growth, ACEL%The report 1.00013, but to square with their text it should be 1.0045/1.0042^(THeTA/(1-THETA))

MUUPSILON = 1.0042; %ACEL

MUZSTAR = MUZ * MUUPSILON^(THETA/(1-THETA));

MUI = MUUPSILON * MUZSTAR; 

MULAMBDA = 1/ MUZSTAR;% THIS IS ONLY TRUE IF PHI3=1, ELSE USE  MUZSTAR^((1-PHI3)*(1-PHI4)-1);

PAI = PAISTAR; %Inflation

QQ = 1; %Tobin's q

SK = THETA; %capital share

R = PAI / BETTA / MULAMBDA; %Nominal interest rate

PTIL = ((1-ALFA * PAI^((ETA-1)*(1-CHI))) / (1-ALFA)) ^ (1/(1-ETA)); %relative price of optimizing firms

WTIL_O_W = ((1-ALFATIL * (MUZSTAR*PAI)^((CHITIL-1)*(1-ETATIL))) / (1-ALFATIL)) ^ (1/(1-ETATIL)); 

MUTIL = (ETATIL / (ETATIL-1)) * ((1-ALFATIL * BETTA * MUZSTAR * MULAMBDA * (MUZSTAR*PAI)^((1-CHITIL)*(ETATIL-1))) / (1 - ALFATIL * BETTA * MUZSTAR * MULAMBDA * (MUZSTAR*PAI)^((1-CHITIL)*ETATIL))) * (1/WTIL_O_W); % inverse of wage markup

S = ((1-ALFA) * PTIL^(-ETA)) / (1-ALFA*PAI^((1-CHI) * ETA)); %distortion between output and total production

STIL = (1-ALFATIL) * WTIL_O_W^(-ETATIL) / (1-ALFATIL * (PAI*MUZSTAR)^((1-CHITIL)*ETATIL));%distortion between hours supplied and hours used as factor input

HD = H / STIL; %steady state labor input

MC = PTIL * (ETA -1 ) * (1- ALFA * BETTA * MULAMBDA * MUZSTAR * PAI^(ETA*(1-CHI))) / (ETA * (1-ALFA*BETTA * MULAMBDA * MUZSTAR * PAI^((CHI-1)*(1-ETA)))); % marginal cost of producing a unit of final good

SI = (MUI - (1-DELTA) ) * SK / (MUUPSILON/BETTA/MULAMBDA -1 + DELTA);

RK = MUUPSILON/BETTA/MULAMBDA -1 + DELTA; %rental rate of capital

K = (RK/MC/THETA)^(1/(THETA-1))*HD * MUI; %aggregate capital factor input

IV = (1 - (1-DELTA)/MUI) * K; %investment

NU = SM * (1-SMH) / (1-SK - SM * (1-SMH) *(1- 1/R)); %Working capital constraint

W = MC * (1-THETA) * (K/MUI/HD)^THETA / (1 + NU*(1-1/R));%average real wage rate

WTIL = WTIL_O_W * W; %Wage charged by optimizing unions

PSSI = (K/MUI)^THETA * HD^(1-THETA) - S * (RK*K/MUI + W*HD * (1 + NU * (1-1/R))); %FIXED Cost

OUTPUT = ((K/MUI)^THETA * HD^(1-THETA) - PSSI) / S; %aggregate demand  

PHI2=-1/8*(8*EPS_MH_R*R^2-8*EPS_MH_R*R+1)/EPS_MH_R/R^2; %Paramter of transactions cost technology

VTILDE = sqrt(PHI2+1-1/R); %auxiliary variable, V=VTILDE/ sqrt(PHI1)

SC = 1 - SI - SG; %Consumption share in gdp (this includes the transactions cost

PHI1 = VTILDE^2 / (SC/SMH/SM +2* VTILDE* sqrt(PHI2) - VTILDE^2-PHI2)^2; %Paramter of transactions cost technology

V = sqrt(PHI2/PHI1 + 1/PHI1 * (R-1)/R); %Consumption-based money velocity

ELL = PHI1 * V + PHI2/V - 2 * sqrt(PHI1*PHI2); %Transactions consts

C = (OUTPUT*(1-SG)-IV) / (1+ELL);%Steady state consumption, one should subtract a(u)k, but this is zero

G = SG * OUTPUT; %Government spending

PHI4 = ((1-B*BETTA*MULAMBDA) * (1-H) / C / (1-B/MUZSTAR)) / (((1-B*BETTA*MULAMBDA) * (1-H) / C / (1-B/MUZSTAR))+MUTIL/W*(1+2*PHI1*V-2*(PHI1*PHI2)^(1/2))); 

GAMA1 = RK;

GAMA2 = GAMA2_O_GAMA1 * GAMA1;