%DEEP_PARAMETERS.M
%Deep Structural parameters of the model in ``Stabilization Policy for the United States,'' by S. Schmitt-Grohe and Martin Uribe 
function [BETTA, THETA, DELTA, NU,  ETATIL, ETA, ALFA, ALFATIL, B, KAPA, CHI, CHITIL, PSSI, PHI1, PHI2, PHI3, PHI4, GAMA1, GAMA2,  RHOZ, RHOG, RHON, STD_EPSZ, STD_EPSG, STD_EPSN, Z, G, N, sig] = deep_parameters;
%This program produces the deep structural parameters and steady-state values of endogenous variables of a standard rbc model augmented to allow for price and wage  stickiness and monetary and fiscal policy  
%(c) Stephanie Schmitt-Grohe and Martin Uribe, December 17, 2004. 


U = 1; %SS capital utilization

GAMA2_O_GAMA1 = 2.02; %cost of capital utilization

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

TAUH = 0.285; %labor income tax (Mendoza, Razin, Tesar, JME, 1994)

TAUK = 0.407; %capital income tax (Mendoza, Razin, Tesar, JME, 1994)

%The following 2 parameters are set so as to match the standard volatility of HP-filtered quarterly US output, 1.6 percent, and its serial correlation, 0.84. Produced with CALIBRATE_TECHNOLOGY_SHOCK.TEX 
RHOZ = 0.24; %Serial correlation of tech. shock,   

STD_EPSZ = 0.07; %Std. dev.  of innovation to tech. shock (King and Rebelo, Handbook of Macro, p. 953)

RHOG = 0.87; %Serial correlation of gov't consumption (Christiano and Eichenbaum, AER Eq. (10) and table 1 

STD_EPSG = 0.016; %Std. Dev. of  innovation to gov't consumption (Christiano and Eichenbaum, AER Eq. (10) and table 1

RHON = 0.78; %Partial elasticity of of gov't transfers  w.r.t. its own lag (own estimate). 

STD_EPSN = 0.022; %Std. Dev. of  innovation to gov't transfers (own estimate)

SMH = 0.44; %Share of household money in total money

H=.195; %Steady State labor supply greater than those actually used at firm level

PHI3 = 1; %reciprocal of intertemporal elasticity of substitution

BETTA = 1.04^(-1/4); %Discount factor;

THETA = 0.25;%0.36; %Capital share (CEE)

SI = 0.1275; %Gross Private Domestic Investment-to-GDP ratio 1947:Q1 to 2004:Q3 NIPA table 116 lines 1 and 6. Matlab program iv_gdp.m 

SM=0.1695*4; %M1/GDP. Sample: 1959:1-2004:3. Source: GDP NIPA and M1 FRB. Produced with m1_gdp.m  

ETATIL = 21; %Labor elasticity of subst

ETA = 6; %goods elasticity of substitution

ALFA = 0.6; %Degree of price stickiness

ALFATIL = 0.64; %degree of wage stickiness

B = 0.65; %degree of habit formation

KAPA = 2.48; %Capital adjustment cost

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

CHITIL = 1; %Degree of wage indexation

SG = 0.17; %Share of gov't expenditures in gdp (Christiano and Eichenbaum, AER

SN = 0.078;%Share of gov't transfers in gdp 1985-2004 (own estimate)

sig = 1;%%parameter scaling the standard deviation of exogenous shocks

EPS_MH_R = -0.81; %annualized inerest rate semielasticity of money demand

PAI = PAISTAR; %Inflation

Z = 1; %SS productivity factor

QQ = 1; %Tobin's q

SK = THETA; %capital share

R = PAI / BETTA; %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 * PAI^((CHITIL-1)*(1-ETATIL))) / (1-ALFATIL)) ^ (1/(1-ETATIL)); 

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

RK = DELTA * SK / SI; %rental rate of capital

NU = SM * (1-SMH) / (1-SK - SM * (1-SMH) *(1- 1/R));

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

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

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^((1-CHITIL)*ETATIL));%distortion between hours supplied and hours used as factor input


HD = H / STIL; %steady state labor input

HTIL = WTIL_O_W^(-ETATIL) * HD; %hours supplied by those who can reset the wage this period      


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

IV = DELTA * K; %investment

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

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

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

OUTPUT = (K^THETA * HD^(1-THETA) - PSSI) / S; %aggregate demand = c + g +i 


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

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

N = SN * OUTPUT; %GOVERNMENT TRANSFERS


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

LA = MUTIL * PHI4 / (1-H) / W / (1-TAUH); %steady state marginal utility of income

GAMA1 = RK;

GAMA2 = GAMA2_O_GAMA1 * GAMA1;