close all // ***************************************************************************** // Graduate Institute for Policy Study (GRIPS)_Japan_2017 // ---------------------------------------------------------------------------- // Macroeconomic Policy Game in the Multi-Sector Open Economy with Shifting Trend Inflation // Le Thanh Ha // ***************************************************************************** // all model variables are expressed in deviations from steady state // NOt use:eps_q @#define Nash =1 @#define Cooperation =0 % define string for saving different policies @#if Nash == 1 case_title='The Nash Equilibrium'; short_title='Nash'; @#else @#if Cooperation ==1 case_title='The Cooperating Equilibrium'; short_title='Cooperation'; @#endif @#endif // Declaration of variables //------------------------------------- var //Output y y_n y_t y_nf y_ni //Productivity a_t a_nf //Labor supply and wages n n_i n_f n_nf n_t w w_f w_i //Consumption c c_t c_tf c_th c_n c_nf c_ni // Calvo Price Setting pstar_th no_th de_th s_th pstar_nf no_nf de_nf s_nf //pibar //Prices and inflation p p_t p_tf p_th p_n p_nf p_ni pi pi_d pi_t pi_th pi_tf pi_n pi_nf pi_ni r //Open Economy e s q c_star p_star y_star_t dif1 dif2 //L_nash1 L_nash2 ; varexo eps_at eps_r eps_an eps_cstar eps_pstar; // Declaration of parameters //------------------------------------- parameters lambda omega h sigma phi nu eta mu alpha beta gamma chi rho_at rho_an sigma_at sigma_an kappa tau //rho_e sigma_ner rho_r psi_y psi_pi psi_q sigma_r rho_cstar rho_pstar rho_rstar sigma_cstar sigma_pstar sigma_rstar //Steady state shares iota //Calvo Parameters theta_t theta_n chi_t chi_n miu_t miu_n eps kappa_t kappa_n //rho_pibar sigma_pibar rgm ; rgm=1.02^0.25; beta = 0.973; // Rate of time preference (subjective discount factor) lambda = 0.3; // Share of non-tradables in aggregate consumption/output omega = 0.67; // Share of informal sector in non-tradables consumption/output 0.25 alpha = 0.88; // Share of imports consumption in the consumption of tradables kappa = 0.18; // Fraction of households providing labor to formal firms 0.75 chi = 0.50; // Share of tradable labor in formal labor market iota = 0.78; // Steady state share of exports in tradable output rho_cstar = 0.9063; // World consumption persistence rho_pstar = 0.6745; // World inflation persistence rho_rstar = 0.8818; // World interest rate persistence // Setting initial values of estimated parameters using prior mean //---------------------------------------------------------------- h = 0.85; // Habit persistence parameter sigma = 3; // Inverse of the elasticity of substitution between consumption and labor nu = 0.4; // Elasticity of subsitution between tradable and non-tradable goods consumption eta = 0.7; // Elasticity of substitution between domestic tradable and imported goods mu = 0.7; // Elasticity of substitution between non-tradable formal and informal goods consumption gamma = 1; // Elasticity of substitution between goods produced in different foreign countries phi = 1.5; // Inverse labor elasticity tau = 2; // Inverse elasticity of substitution between non-tradable formal and informal labor rho_at = 0.75; // Productivity persistence for domestic tradable firms rho_an = 0.75; // Productivity persistence for formal non-tradable firms sigma_at = 0.1; // Productivity shock for domestic tradable firms sigma_an = 0.1; // Productivity shock for formal non-tradable firms // Calvo Parameters theta_t = 0.5; // Calvo parameter for tradables firms (probability of keeping prices unchanged) theta_n = 0.5; // Calvo parameter for non-tradables firms (probability of keeping prices unchanged) chi_t = 0.0; // Price Indexation for tradable firms miu_t = 1.0; // Weight on lagged inflation for tradable firms chi_n = 0.0; // Price Indexation for nontradable firms miu_n = 1.0; // Weight on lagged inflation for nontradable firms eps = 10; // Shock Parameteres psi_pi = 1.5; // Taylor inflation psi_y = 0.125; // Taylor output psi_q = 1.5; // Taylor exchange rate //r_dq = 1.5; //r_dy = 0.125; // Taylor output growth //r_dpi = 1.5; // Taylor inflation growth rho_r = 0.95; // Taylor interest rate sigma_r = 0.01; // Monetary policy shock //rho_pibar = 0.995; // Persistence Inflation AR(1) sigma_cstar = 0.01; // World consumption shock sigma_pstar = 0.01; // World inflation shock sigma_rstar = 0.01; // World interest rate shock sigma_q = 0.01; // Nominal exchange rate shock sigma_tot = 0.01; // Term of trade shock //sigma_pibar = 0.01; // Persistence Inflation shock kappa_t = (1-beta*theta_t)*(1-theta_t)/theta_t; kappa_n = (1-beta*theta_n)*(1-theta_n)/theta_n; // Declaration of the log-linearized model //----------------------------------------- model(linear); y = (1 - lambda)*y_t + lambda*y_n ; // 1. Aggregate output y_n = (1 - omega)*y_nf + omega*y_ni ; // 2. Non-tradable output c = w-p ; // 3. Aggregate consumption c(-1) = c+pi-r(-1) ; // 4. Euler equation c_t = c + p - p_t ; // 5. Tradables consumption c_tf = (-p_tf + p_t) + c_t ; // 6. Foreign tradables consumption c_th = (-p_th + p_t) + c_t ; // 7. Domestic tradables consumption c_n = (-p_n + p) + c ; // 8. Non-tradables consumption c_nf = (-p_nf + p_n) + c_n ; // 9. Formal non-tradables consumption c_ni = (-p_ni + p_n) + c_n ; // 10. Informal non-tradables consumption p = (1 - lambda)*p_t + lambda*p_n ; // 11. CPI Inflation pi_d = (1 - lambda)*pi_th + lambda*pi_n ; // 12. Domestic inflation p_t = (1 - alpha)*p_th + alpha*p_tf ; // 13. Tradables inflation p_n = (1 - omega)*p_nf + omega*p_ni ; // 14. Non-tradables inflation p_tf = e + p_star ; // 15. Foreign tradables inflation (From law of one price when LOP=1 p = p(-1) + pi ; // 16. CPI price level p_t = p_t(-1) + pi_t ; // 17. Tradables price level //p_th = p_th(-1)+pi_th ; // 18. Domestic tradables price level p=p_th+alpha*s; p_tf = p_tf(-1) + pi_tf ; // 19. Foreign tradables price level p_n = p_n(-1) + pi_n ; // 20. Non-tradables price level p_nf = p_nf(-1) + pi_nf ; // 21. Formal non-tradables price level p_ni = p_ni(-1) + pi_ni ; // 22. Informal non-tradables price level n = n_f + n_i ; // 23. Aggregate supply of labor n_f = (1/tau)*(w_f - w) + n ; // 24. Supply of formal labor n_i = (1/tau)*(w_i - w) + n ; // 25. Supply of informal labor // Foreign Sector q = (1-alpha)*s - lambda*(p_t-p_n) ; // 26. The relationship bw Real exchange rate and term of trade //Production Sector //Traded Firm y_t = a_t + n_t -s_th; // 27. Domestic tradable output pstar_th = no_th - de_th; //29 no_th = (1-theta_t*beta*rgm^((1-chi_t)*eps))*w_f + (beta*theta_t*rgm^((1-chi_t)*eps))*(eps*pi_th(+1)-eps*chi_t*miu_t*pi_th+no_th(+1)); //30 de_th = (beta*theta_t*rgm^((1-chi_t)*(eps-1)))*((eps-1)*pi_th(+1)+chi_t*miu_t*(1-eps)*pi_th+de_th(+1)); //31 pstar_th = ((theta_t*rgm^((1-chi_t)*(eps-1)))/(1-theta_t*rgm^((1-chi_t)*(eps-1))))*(pi_th-chi_t*miu_t*pi_th(-1)); //32 s_th = (-eps*(1-theta_t*rgm^((1-chi_t)*eps)))*pstar_th+(theta_t*rgm^((1-chi_t)*eps))*(eps*pi_th+s_th(-1)-chi_t*miu_t*eps*pi_th(-1)); //33 // Non-traded Formal Firm y_nf = a_nf + n_nf - s_nf ; // 34. Formal non-tradable output pstar_nf = no_nf - de_nf; //36 no_nf = (1-theta_n*beta*rgm^((1-chi_n)*eps))*w_f + (beta*theta_n*rgm^((1-chi_n)*eps))*(eps*pi_nf(+1)-eps*chi_n*miu_n*pi_nf+no_nf(+1)); //37 de_nf = (beta*theta_n*rgm^((1-chi_n)*(eps-1)))*((eps-1)*pi_nf(+1)+chi_n*miu_n*(1-eps)*pi_nf+de_nf(+1)); //38 pstar_nf = ((theta_n*rgm^((1-chi_n)*(eps-1)))/(1-theta_n*rgm^((1-chi_n)*(eps-1))))*(pi_nf-chi_n*miu_n*pi_nf(-1)); //39 s_nf = (-eps*(1-theta_n*rgm^((1-chi_n)*eps)))*pstar_nf+(theta_n*rgm^((1-chi_n)*eps))*(eps*pi_nf+s_nf(-1)-chi_n*miu_n*eps*pi_nf(-1)); //40 // Non-traded informal Firm y_ni = n_i ; // 41. Informal non-tradable output p_ni = w_i ; // 42. Informal non-tradables inflation // Monetary Authority r = rho_r*r(-1) + (1 - rho_r)*(psi_y*y + psi_pi*pi + psi_q*q) + eps_r ; // 43. Monetary policy under flexible exchange rate // Market Clearing Condition y_t = (1 - iota)*(s*(alpha+(1-lambda)*alpha)-p_t+(1-lambda)*p_th+lambda*p_n+c) + iota*((1-lambda)*alpha*s-lambda*(p_th-p_n) + q + c_star) ; // 44. Tradables market clearing condition y_nf = c_nf ; // 45. Formal non-tradables market clearing condition y_ni = c_ni ; // 46. Informal non-tradables market clearing condition dif1 = p_n - p_t; // 47. The evolution of price differential between the tradable and nontradable sector dif2 = p_ni - p_nf; // 48. The evolution of price differential between the formal and informal sector n_f =n_t + n_nf ; // 49. Formal labor market clearing condition //p=p_th+alpha*s; // Shocks // External Shocks c_star = rho_cstar*c_star(-1) + eps_cstar ; // 50. World consumption p_star = rho_pstar*p_star(-1) + eps_pstar ; // 51. World inflation // 52. World interest rate // Internal Shock a_t = rho_at*a_t(-1) + eps_at ; // 53. Domestic tradable firms productivity a_nf = rho_an*a_nf(-1) + eps_an ; // 54. Non-tradable formal firms productivity q=c-c_star; // 55 Uncovered interest parity condity with a risk premium shock (compute) s = y_t-y_star_t ; // 56. The evolution of term of trade c = (1-lambda)*(1-alpha)*y_t + alpha*(1-lambda)*y_star_t+lambda*y_n; // 57. //c_n = omega*y_ni+ (1-omega)*y_nf; // 58. //pibar = rho_pibar*pibar(-1)+eps_pibar; // 57 . The shifting trend inflation shock %compute loss function //L_nash1 = ((1-lambda)*(1-alpha))*(y_t^2+theta_t/kappa_t*pi_th^2)+lambda*(1-omega)*(y_nf^2+theta_n/kappa_n*pi_nf^2)+ lambda*omega*y_ni^2; //L_nash2 = ((1-lambda)*(1-alpha)*theta_t/kappa_t*pi_th^2+lambda*(1-omega)*theta_n/kappa_n*pi_nf^2)+(1-lambda)*c^2+(lambda*lambda)*(1-lambda)*dif1^2+lambda*c_n^2+lambda*omega*(1-omega)*dif2^2+(1-lambda)*alpha*(-alpha+1)*s^2; end; resid(1); steady(solve_algo=0); check; model_diagnostics; // Calibration of Shocks //------------------------------------- shocks; var eps_r = sigma_r^2; var eps_an = sigma_an^2; var eps_at = sigma_at^2; var eps_cstar = sigma_cstar^2; var eps_pstar = sigma_pstar^2; //var eps_rstar = sigma_rstar^2; //var eps_q = sigma_q^2; //var eps_tot = sigma_tot^2; // var eps_pibar = sigma_pibar^2; end; /* // Simulation of the model // ---------------------------------------- check; stoch_simul(order=1,periods=2100,irf=21) y c pi r q e; */ estimated_params; h, beta_pdf, 0.25, 0.1; sigma, normal_pdf, 3, 0.1; nu, normal_pdf, 0.4, 0.1; eta, normal_pdf, 0.7, 0.1; mu, normal_pdf, 0.7, 0.1; gamma, normal_pdf, 1, 0.1; phi, normal_pdf, 1.5, 0.1; tau, normal_pdf, 2, 0.5; theta_t,beta_pdf, 0.5, 0.1; // Calvo parameter for tradables firms (probability of keeping prices unchanged) theta_n,beta_pdf, 0.5, 0.1; // Calvo parameter for non-tradables firms (probability of keeping prices unchanged) chi_t,normal_pdf, 0.0, 0.1; // Price Indexation for tradable firms miu_t,normal_pdf, 1.0, 0.1; // Weight on lagged inflation for tradable firms chi_n,normal_pdf, 0.0, 0.1; // Price Indexation for nontradable firms miu_n,normal_pdf, 1.0, 0.1; // Weight on lagged inflation for nontradable firms eps ,normal_pdf, 10, 0.1; rho_at, beta_pdf, 0.75, 0.1; rho_an, beta_pdf, 0.75, 0.1; stderr eps_at, inv_gamma_pdf, 0.1, 2; stderr eps_an, inv_gamma_pdf, 0.1, 2; rho_r, beta_pdf, 0.95, 0.1; // stderr eps_r, inv_gamma_pdf, 0.1, 2; psi_y, gamma_pdf, 1.5, 0.5; psi_pi, gamma_pdf, 0.125, 0.5; psi_q, gamma_pdf, 1.5, 0.5; end; estimated_params_init(use_calibration); end; varobs y pi r q s; estimation(lik_init=2,plot_priors = 0,bayesian_irf,datafile=data,conf_sig =.95,prefilter = 1,filtered_vars,smoother,first_obs=6,mode_check,mode_compute=9,moments_varendo,mh_nblocks=5,mh_replic=1000,mh_jscale=0.5,mh_init_scale=1); identification;