var y yf yi c cf ci R pi_f pi_i pi lf li mcf mci wf wi rk k p p_f p_i tao_c tao_l tao_k kg af ai i g gi b tr epsilon_g epsilon_gi epsilon_tc epsilon_tk epsilon_tl epsilon_R epsilon_tr ; //c - total consumption // cf - consumption of formal sector // ci-consumption of informal sector // p -aggregate price // p_f - price of formal goods // p_i- price of informal goods //lf- labour supply to formal sector // li- labour supply to informal sector // R- nominal rate of interest // mcf-marginal cost of formal sector firm // mci-margianl cost of informal sector firms // pi aggregate inflaion // pi_f- inflaion in formal sector // pi_i-inflation in informal sector // tao_c - tax rate on consumption // tao_k - tax rate on capital // tao_l - income tax rate on tax on formal labour. // kg - public capital // k - private capital // y - aggregate output // yf - formal sector output // yi - informal sector output // af - productivity of formal sectors firm // af - productivity of informal sectors firm // rk - rent of the capital // wf - wages of formal laboour // wi - wages of informal labour // i - investment // gi - government investment // g - government consumption // tr - governemtn transfers // b - bonds // epsilon_g // epsilon_gi // epsilon_tc // epsilon_tk // epsilon_tl // epsilon_R varexo phi_R phi_af phi_ai phi_g phi_gi phi_tc phi_tk phi_tl phi_tr; parameters beta h nu alfa_f alpha_g Theta gamma delta delta_g sigma_c sigma_l sigma_w epsilon_i epsilon_f epsilon_w gamma_f gamma_i gamma_w rkK_bar R_bar b_bar wflf_bar rk_bar cf_bar if_bar gf_bar gif_bar tr_bar tao_cbar tao_kbar tao_lbar psi_bg psi_yg psi_bgi psi_ygi psi_btr psi_ytr psi_btc psi_ytc psi_btk psi_ytk psi_btl psi_ytl rho rho_y rho_pi rho_g rho_af rho_ai rho_gi rho_tc rho_tk rho_tl rho_tr ci_bar kappa std_phi_af std_phi_ai std_phi_g std_phi_gi std_phi_tl std_phi_tk std_phi_tr std_phi_tc std_phi_R; sigma_c = 0.84; // - the elasticity of intertemporal substitution of consumption (adnan 2008) beta = 0.990; // discount factor (ahmed 2012) h = 0.36; // -habbit forfmation (haider and khan 2008) nu = 0.70; // elasticity of substitution between formal and informal goods (ahmed 2012) gamma = 0.65; // the share of formal sector consumtpion in total consumption (ahmed 2012) and (khan and khan 2011) sigma_l = 1.5; // - inverse labour elasticity (ahmed 2012) delta = 0.025; // depreciation of private capital (ahmed 2012) alpha_g = 0.010; // output elasticity of public capital delta_g = 0.025; // depreciation of public capital Theta = 0.5; // fraction of the public captial available to informal sector. //alfa_f = 0.45; // capital chare in the formal production (Bukhari and khan 2008) alfa_f = 0.30; // capital chare in the informal production gamma_f = 0.65; // - degree of indexation of formal firm ( Choudhary (2011) haider and khan 2008 Castro (2011)) gamma_i = 0.70; // - degree of indexation of informal firm ( Choudhary (2011) haider and khan 2008 Castro (2011)) epsilon_f = 0.64; // - fraction of formal firm which can't reoptimize price each period ( Choudhary (2011) haider and khan 2008 Castro (2011)) epsilon_i = 0.21; // - fraction of informal firm which can't reoptimize price each period ( Choudhary (2011) haider and khan 2008 Castro (2011)) gamma_w = 0.2639; // - degree of wage indexation of formal labour kappa=0.6; epsilon_w = 0.56; //wage stickness parameter. sigma_w = 0.05; // wage markup ci_bar=0.75; // Fiscal instruments response to debt psi_bg = 0.1562; psi_bgi = 0.2007; psi_btr=0.0776; psi_btc = 0.0998; psi_btk = 0.1765; psi_btl = 0.0552; // fiscal instruments response to GDP psi_yg = 0.2457; psi_ygi = 0.9173; psi_ytr=0.2941; psi_ytc = 0.1552; psi_ytl = 0.0847; psi_ytk = 0.6287; // monetary policy rho = 0.63; rho_y = 0.60; rho_pi = 1.21; // AR (1) coefficients rho_af = 0.9432 ; rho_ai = 0.9432; rho_g = 0.9246; rho_tr=0.8760; rho_gi= 0.3110; rho_tc= 0.7521; rho_tk= 0.7863; rho_tl= 0.7746; // standard deviations of shocks std_phi_af = 0.0074; std_phi_ai = 0.0074; std_phi_g = 0.05; std_phi_tr = 0.0583; std_phi_gi = 0.5; std_phi_tl = 0.0493; std_phi_tk = 0.1149; std_phi_tc = 0.0796; std_phi_R = 0.0069; tao_cbar = 0.20; // - steady state value of consumption tax rate tao_kbar = 0.29; // - steady state value of captial tax rate tao_lbar = 0.29; // - steady state value of labour tax rate //cf_bar = 0.75; // Cf/yf //if_bar = 0.12; // I/yf gf_bar = 0.20; // G/yf gif_bar = 0.02; // Gi/yf b_bar = 2.4; // b/yf R_bar=1/beta; // nominal interest rate rkK_bar=alfa_f; // capital income/GDP wflf_bar=1-alfa_f; // labour income/GD rk_bar=(1/(1-tao_kbar))*(1/(beta-(1-delta))); // rental rate if_bar=delta*rkK_bar/rk_bar; // Investment/GDP ratio cf_bar=1-gf_bar-if_bar-gif_bar; // consumption/GDP ratio tr_bar=tao_cbar*cf_bar+tao_lbar*wflf_bar+tao_kbar*rkK_bar-gf_bar-gif_bar-R_bar*b_bar+b_bar; // transfers/GDP ratio = tr/yf model(linear); //1. Consumption Euler equation. c=((h/(1+h))*c(-1))+((1/(1+h))*c(+1))-((1-h)/((1+h)*sigma_c))*(R) +((1-h)/((1+h)*sigma_c))*pi(+1) -((1-h)/((1+h)*sigma_c))*(tao_cbar/(1+tao_cbar))*(tao_c-tao_c(+1)); // 2. consumption of formal goods cf=(-nu)*(p_f-p)+c; // 3. consumption of informal goods ci=(-nu)*(p_i-p)+c; // 4 interest rate R=pi(+1)+(((1-tao_kbar)*rk_bar)/(1-delta+(1-tao_kbar)*rk_bar))*rk(+1) -(((tao_kbar)*rk_bar)/(1-delta+(1-tao_kbar)*rk_bar))*tao_k(+1); // 5. wage equation of fromal sector wf=(beta/(1+beta))*wf(+1)+(1/(1+beta))*wf(-1)+(beta/(1+beta))*pi(+1) -((1+beta*gamma_w)/(1+beta))*pi+(gamma_w/(1+beta))*pi(-1) -((((1-epsilon_w)*(1-beta*epsilon_w))/((1+((1+sigma_w)/(sigma_w))*sigma_l)*epsilon_w)) *(1/(1+beta)))*(wf-sigma_l*lf-(sigma_c/(1-h))*(c-h*c(-1))-(tao_lbar/(1-tao_lbar)) *tao_l-(tao_cbar/(1+tao_cbar))*tao_c); // 6 private capital accumulation k=(1-delta)*k(-1)+delta*i; //7 public capital accumulation kg=(1-delta_g)*kg(-1)+delta_g*gi; // 8 formal firm production function yf=af+alfa_f*k(-1)+(1-alfa_f)*lf+alpha_g*kg(-1); //9 formal sector marginal cost mcf= (1-alfa_f)*wf+alfa_f*rk-af-alpha_g*kg(-1); // 10 capital labour ratio lf=rk+k(-1)-wf; // 11 Formal firm NKPC pi_f=(beta/(1+beta*gamma_f))*pi_f(+1)+(gamma_f/(1+beta*gamma_f))*pi_f(-1) +((((1-epsilon_f)*(1-beta*epsilon_f))/(epsilon_f))*(1/(1+beta*gamma_f))) *(mcf); // 12 wage equation of informa sector wi-p=sigma_l*li-(sigma_c/(1-h))*c+(sigma_c)*(h/(1-h))*c(-1)+(tao_cbar/(1+tao_cbar))*tao_c; //13 informal firm production function yi=ai+li+alpha_g*kg(-1); //14 informal sector marginal cost mci= wi-ai-alpha_g*kg(-1); //16 Inormal firm NKPC pi_i=(beta/(1+beta*gamma_i))*pi_i(+1)+(gamma_i/(1+beta*gamma_i))*pi_i(-1) +((((1-epsilon_i)*(1-beta*epsilon_i))/(epsilon_i))*(1/(1+beta*gamma_i))) *(mci); //17 CPI inflation pi=(gamma)*pi_f+(1-gamma)*pi_i; // 18 aggregate price level p=p(-1)+pi; // 19 formal sector price level p_f=p_f(-1)+pi_f; //20 informal sector price level p_i=p_i(-1)+pi_i; // 21 government budget constraint. gf_bar*g+gif_bar*gi+tr_bar*tr+b_bar*R_bar*(b(-1)+R(-1)-pi)=b_bar*b +tao_cbar*cf_bar*(c+tao_c)+tao_lbar*wflf_bar*(wf+lf+tao_l)+tao_kbar*rkK_bar*(rk+k(-1)+tao_k); //22 goverment consumption rule g=-psi_bg*b(-1)-psi_yg*yf+epsilon_g; // 23 government investment rule gi=-psi_bgi*b(-1)-psi_ygi*yf+epsilon_gi; tr=-psi_btr*b(-1)-psi_ytr*yf+epsilon_tr; // 24 consumption tax rule tao_c=psi_btc*b(-1)+psi_ytc*yf-epsilon_tc; // 25 capital tax rule tao_k=psi_btk*b(-1)+psi_ytk*yf-epsilon_tk; // 26 labour tax rule tao_l=psi_btl*b(-1)+psi_ytl*yf-epsilon_tl; // 27 government consumption shock epsilon_g=rho_g*epsilon_g(-1)+phi_g; // 28 government investment shock epsilon_gi=rho_gi*epsilon_gi(-1)+phi_gi; epsilon_tr=rho_tr*epsilon_tr(-1)+phi_tr; // 29 consumption tax shock epsilon_tc=rho_tc*epsilon_tc(-1)+phi_tc; // 30 capital tax shock epsilon_tk=rho_tk*epsilon_tk(-1)+phi_tk; // 31 labor tax shock epsilon_tl=rho_tl*epsilon_tl(-1)+phi_tl; // 32 monetary policy rule R=rho*R(-1)+(1-rho)*rho_y*(yf-yf(-1))+(1-rho)*rho_pi*pi+epsilon_R; // 33 monetary policy shock epsilon_R = phi_R; // 34 formal sector productivity shock af=rho_af*af(-1)+phi_af; // 35 informal sector productivity shock ai=rho_ai*ai(-1)+phi_ai; // 36 formal sector output yf=cf_bar*cf+if_bar*i+gf_bar*g+gif_bar*gi; // 37 informal sector output yi=ci; // 38 aggregate level of output y=(gamma)*yf+(1-gamma)*yi; end; steady; check; shocks; var phi_af; stderr std_phi_af; var phi_ai; stderr std_phi_ai; var phi_g; stderr std_phi_g; var phi_tr; stderr std_phi_tr; var phi_gi; stderr std_phi_gi; var phi_tl; stderr std_phi_tl; var phi_tk; stderr std_phi_tk; var phi_tc; stderr std_phi_tc; var phi_R; stderr std_phi_R; end; stoch_simul(order=1, irf=20);