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RBCmodel.mod
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RBCmodel.mod
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%/////////////////////////////////////////////////////////////
%//// Model: RBC model with habit formation and variable labor ////
%//// Author: Willi Mutschler ////
%//// Email: willi@mutschler.eu ////
%//// Version: August 26, 2016 ////
%/////////////////////////////////////////////////////////////
%----------------------------------------------------------------
% 0. Specify options: User Settings (For other settings and defaults see updateOptions.m
%----------------------------------------------------------------
% Order of approximation
@#define orderApp = 3
% Which distribution in state space system: 0:for Gaussian, 1:for Student_t
@#define distrib = 0
@#if distrib == 1
opt.distrib = 'Student_t';
@#endif
opt.numSim = 250; % Number of observations of simulated data
opt.burnin = 0; % Initial burnin periods, will be discarded from simulation
opt.autoLagsIdx = [1] % Which autocovariances to include
opt.HOSThirdOrder = 0; % Use third-order statistics, 0: do not include or 1: include
opt.HOSFourthOrder = 0; % User fourth-order statistics, 0: do not include or 1: include
opt.seed_nr = 10;
opt.transpar = 0;
%----------------------------------------------------------------
% 1. Declare variables and parameters
%----------------------------------------------------------------
var k c a iv y la n rk w;
predetermined_variables k;
varexo u_a;
varobs c iv n;
parameters DELTA BETTA B ETAl ETAc THETA ALFA RHOA STDA;
@#if distrib == 1
parameters df_studt; % Please always use df_studt for degrees of freedom
@# endif
%----------------------------------------------------------------
% 2. Calibrate parameter values for simulated series (i.e. true values
%----------------------------------------------------------------
@#if distrib == 1
df_studt = 13;
@# endif
DELTA = 0.025;
BETTA = 0.984;
B = 0.5;
ETAl = 1;
ETAc = 2;
THETA = 3.48;
ALFA = 0.667;
RHOA = 0.979;
STDA = 0.0072;
%----------------------------------------------------------------
% 3. Declare model equations
%----------------------------------------------------------------
model;
% FOC for consumption
0 = -exp(la) +(exp(c)-B*exp(c(-1)))^(-ETAc) - BETTA*B*(exp(c(+1))-B*exp(c))^(-ETAc);
% Household's FOC for labor
0 = -THETA*(1-exp(n))^-ETAl + exp(la)*exp(w);
% FOC for capital
0 = -exp(la) + BETTA*exp(la(+1))*(exp(rk(+1)) + (1-DELTA));
% Firm's FOC for capital
0 = -exp(a)*(1-ALFA)*exp(k)^(-ALFA)*exp(n)^(ALFA) + exp(rk);
% Firm's FOC for labor
0 = -exp(a)*ALFA*exp(k)^(1-ALFA)*exp(n)^(ALFA-1) + exp(w);
% National income identity
0 = -exp(c) - exp(iv) + exp(y);
% Production function
0 = -exp(y) + exp(a)*exp(k)^(1-ALFA)*exp(n)^(ALFA);
% Law of motion for capital
0 = -exp(k(+1)) + (1-DELTA)*exp(k) + exp(iv);
% Law of motion for technology
0 = -log(exp(a)) + RHOA*log(exp(a(-1))) + STDA*u_a;
end;
%----------------------------------------------------------------
% 4. Specify variance of shock processes depending on distribution
%----------------------------------------------------------------
shocks;
@#if distrib == 1
% Student-t distribution
var u_a = df_studt/(df_studt-2);
@#else
% Gaussian distribution
var u_a = 1;
@#endif
end;
%----------------------------------------------------------------
% 5. Specify steady-state (either steady_state_model or initval)
%----------------------------------------------------------------
% steady_state_model;
% errorMes = 0;
% A = 1; % The value of technology
% RK = 1/BETTA - (1-DELTA); % The rental rate of capital
% K_O_N = (RK/(A*(1-ALFA)))^(-1/ALFA); % Capital divided by labor
% % if K_O_N <= 0
% % errorMes = 1;
% % end
% W = A*ALFA*(K_O_N)^(1-ALFA); % The wage level
% IV_O_N = DELTA*K_O_N; % Investment over labor
% Y_O_N = A*K_O_N^(1-ALFA); % Output over labor
% C_O_N = Y_O_N - IV_O_N; % Consumption over labor
% % if C_O_N <= 0
% % errorMes = 1;
% % end
% %if ETAc == 1 && ETAl == 1
% N = (1-BETTA*B)*(C_O_N*(1-B))^-1*W/THETA/(1+(1-BETTA*B)*(C_O_N*(1-B))^-1*W/THETA);
% %else
% % % No closed-form solution and we therefore use a fixed-point algorithm
% % if errorMes == 0
% % options = optimset('Display','off','TolX',1e-12,'TolFun',1e-12);
% % N0 = 1/3;
% % [N,~,exitflag] = fsolve(@findN,N0,options);
% % if exitflag <= 0
% % errorMes = 1;
% % end
% % else
% % N = NaN;
% % end
% % end
% C = C_O_N*N;
% Y = Y_O_N*N;
% IV = IV_O_N*N;
% K = K_O_N*N;
% LA = (C-B*C)^(-ETAc)-BETTA*B*(C-B*C)^(-ETAc);
% k = log(K);
% c = log(C);
% a = log(A);
% iv = log(IV);
% y = log(Y);
% la = log(LA);
% n = log(N);
% rk = log(RK);
% w = log(W);
% end;
%----------------------------------------------------------------
% 6. Specify parameters for GMM estimation
% Syntax: parameter, initial value, lower bound, upper bound, unifrom_pdf,,,,,tr
% Note that uniform_pdf has no meaning, we simply abuse Dynare's syntax to enable
% parameter transformations (if selected as an option: opt.transpar = 1, default is opt.transpar = 0)
% tr is parameter transformation type
% 0: no transformation needed
% 1: [a,b] -> [-1,1] -> [-inf,inf] by z/sqrt(1-z^2)
% 2: [0,inf] -> [-inf,inf] by b + ln(z-a);
% with a: lower bound and b: upper bound:
%----------------------------------------------------------------
estimated_params;
%parameter, initial value, lower bound, upper bound, unifrom_pdf,,,,, tr
DELTA, 0.025, 0, 1, uniform_pdf,,,,, 1;
BETTA, 0.984, 0, 1, uniform_pdf,,,,, 1;
B, 0.5, 0, 1, uniform_pdf,,,,, 1;
%ETAl, 1, 0, 10, uniform_pdf,,,,, 1;
ETAc, 2, 0, 10, uniform_pdf,,,,, 1;
ALFA, 0.667, 0, 1, uniform_pdf,,,,, 1;
RHOA, 0.979, 0, 1, uniform_pdf,,,,, 1;
STDA, 0.0072, 0, 1, uniform_pdf,,,,, 1;
%THETA, 3.48, 0, 10, uniform_pdf,,,,, 1;
end;
%----------------------------------------------------------------
% 7. Computations
%----------------------------------------------------------------
steady; check;
stoch_simul(order=@{orderApp},pruning,noprint,nomoments,irf=0);
[resultsGMM,paramsGMM] = RunGMM(opt);