%-------------------------------------------------- % % WELCOME, TO DYNARE % This version includes the nx static equation. No further calibration. Domestic stochastic shock removed for simplicity. %-------------------------------------------------- %-------------------------------------------------- % % Variables % %-------------------------------------------------- var c cH // home economy consumption for entrepreneurs (c) and HH (cH) c_for cH_for // foreign economy consumption for entrepreneurs (c_for) and HH (cH_for) h h_for // home economy entrep real estate (h) and foreign economy entrep real estate (h_for) k k_for // home economy entrep capital stock (k) and foreign economy entrep capital stock (k_for) y y_for //home economy output (y) and foreign economy output (y_for) b //HH borrowing between home and foreign HHs bH_dom bH_for //domestic entrpreneurs borrowing from home economy (dom) and from foreign economy (for) bF_dom bF_for //foreign entrepreneurs borrowing from home economy (dom and from foreign economy (for) R //Real interest rate alpha alpha_for //share of domestic real estate collateral for home firm (alpha) and foreign firm (alpha_for) sigma sigma_for //share of domestic capital collateral for home firm (sigma) and foreign firm (sigma_for) q q_for //value of real estate in home economy (q) and foreign economy (q_for) i i_for //investment inhome economy (i) and foreign economy (i_for) A A_for; //technology shocks in home economy (A) and foreign economy (A_f) //nx; // nx_f //Net exports - check this out still! varexo epsilon_f //foreign technology shock epsilon; //home technology shock parameters mu nu beta eta gamma delta psi m_h m_f z_h z_f omega omega_hat j alpha_ss alpha_for_ss sigma_ss sigma_for_ss k_ss k_for_ss q_ss q_for_ss h_ss h_for_ss R_ss bH_dom_ss bH_for_ss bF_dom_ss bF_for_ss b_ss cH_ss cH_for_ss c_ss c_for_ss i_ss i_for_ss y_ss y_for_ss; //nx_ss; %-------------------------------------------------- % % Calibration % %-------------------------------------------------- mu = 0.25; //Capital share for output nu = 0.1; //Asset share of output (i.e. Real Estate) beta = 0.99; //Household discount factor eta = 21; //Labor elasticity factor for HH gamma = 0.98; //Firms discount factor delta = 0.03; //depreciation rate m_h = 0.9; //LTV ratio:domestic borrowing on assets m_f = 0.8; //LTV ratio:foreign borrowing on assets psi = 0.001; // portfolio adjustment cost parameter for HH z_h = 0.9; //LTV ratio:domestic borrowing on capital z_f = 0.8; //LTV ratio:foreign borrowing on capital j = 0.1; //asset weight in HH utility function omega = 0.9; //coefficient for technology process - found paper stating move between 0.65 - 0.85 past decade cite: technology persistence and monetary policy 2012 omega_hat = 0.009; //coefficient for technology spillover alpha_ss = 0.75; //share of real estate borrowing from home economy (steady state) alpha_for_ss = 0.75; sigma_ss = 0.75; //share of capital borrowing from home economy (steady state) sigma_for_ss = 0.75; k_ss = 6; //capital share of output in SS k_for_ss = 6; i_ss = 0.18; //steady state investment: just replace depreciated capital i.e. keep capital stock constant i_for_ss = 0.18; q_ss = 16; //value of real estate in SS q_for_ss = 16; h_ss = 0.5; //quantity of real estate in SS h_for_ss = 0.5; R_ss = 1.01; //Interest rate in SS (1/beta) bH_dom_ss = 2.5; //SS share of domestic borrowing in output bF_dom_ss = 0.8; bH_for_ss = 2.5; //SS share of foreign borrowing in output bF_for_ss = 0.8; cH_ss = 0.78; //HHs consumption share of output in SS cH_for_ss = 0.78; c_ss = 0.04; //Entreps consumption share of output in SS c_for_ss = 0.04; b_ss = 0.0001; //Between HHs borrowing in SS *check this cos not sure about value y_ss = 1; //SS output y_for_ss = 1; //nx_ss = 0; %-------------------------------------------------- % % The model % %-------------------------------------------------- //write_latex_dynamic_model; model(linear); %-----------DOMESTIC ECONOMY----------------------------------% alpha = ((1 - alpha_ss)/(alpha_ss))*(q(+1) + h); //1.15 sigma = ((1 - sigma_ss)/(sigma_ss))*k; //log linearized derivation of choice of sigma i_ss*i = k_ss*k + delta*k_ss*k(-1); //capital accumulation equation cH_ss*cH + bH_dom_ss*bH_dom + bH_for_ss*bH_for + b_ss*b = R_ss*(bH_dom_ss + bH_for_ss + b_ss)*R(-1) + R_ss*b(-1) + R_ss*bH_dom_ss*bH_dom(-1) + R_ss*bH_for_ss*bH_for(-1) + (1-nu-mu)*y + q_ss*h_ss*(h - h(-1)) - R_ss*bH_dom_ss*psi*b(-1) + R_ss*bH_for_ss*psi*b(-1); //5.1 (mu + nu)*y + bH_dom_ss*bH_dom + bH_for_ss*bH_for = R_ss*(bH_dom_ss + bH_for_ss)*R(-1) + R_ss*bH_dom_ss*bH_dom(-1) + R_ss*bH_for_ss*bH_for(-1) + q_ss*h_ss*(h - h(-1)) + c_ss*c + k_ss*(k - (1-delta)*k(-1)) - R_ss*bH_dom_ss*psi*b(-1) - R_ss*bH_for_ss*psi*b(-1); //5.2 cH(+1) = cH + R - psi*b; //5.3 q = beta*q(+1) + (((1-beta)*h_ss)/(1-h_ss))*h + cH - beta*cH(+1); //6.4 (1 - ((1-nu-mu)/eta))*y = A + nu*h(-1) + mu*k(-1) - ((1-nu-mu)/eta)*cH; //6.5 R + bH_dom - psi*b = (1/alpha_ss)*((m_h*q_ss*h_ss)/(m_h*q_ss*h_ss + z_h*k_ss))*(q(+1) + h) + (1/sigma_ss)*((z_h*k_ss)/(m_h*q_ss*h_ss + z_h*k_ss))*k; //5.6 R + bH_for - psi*b = 0; //5.7 q - (gamma + m_h*(beta - gamma))*q(+1) = (1 - beta*m_h)*(c - c(+1)) + (1 - gamma + m_h*(beta - gamma))*(y(+1) - h) - m_h*beta*R + m_h*beta*psi*b; //5.8 0 = (1 - beta*z_h)*(c - c(+1)) + (1 - gamma*(1-delta) - z_h*(beta-gamma))*(y(+1) - k) - beta*z_h*R + beta*z_h*psi*b; //5.9 %-----------FOREIGN ECONOMY----------------------------------% alpha_for = ((1 - alpha_for_ss)/(alpha_for_ss))*(q_for(+1) + h_for); //log linearization of domestic real estate collateral choice for foreign economy sigma_for = ((1 - sigma_for_ss)/(sigma_for_ss))*(k_for); //log linearization of domestic capital collateral choice for foreign economy i_for_ss*i_for = k_for_ss*k_for + delta*k_for_ss*k_for(-1); //capital accumulation equation cH_for_ss*cH_for + bF_dom_ss*bF_dom + bF_for_ss*bF_for - b_ss*b = R_ss*(bF_dom_ss + bF_for_ss - b_ss)*R(-1) - R_ss*b(-1) + R_ss*bF_dom_ss*bF_dom(-1) + R_ss*bF_for_ss*bF_for(-1) + (1-nu-mu)*y_for + q_for_ss*h_for_ss*(h_for - h_for(-1)) + R_ss*bF_dom_ss*psi*b(-1) - R_ss*bF_for_ss*psi*b(-1); //5.10 (mu + nu)*y_for + bF_dom_ss*bF_dom + bF_for_ss*bF_for = R_ss*(bF_dom_ss + bF_for_ss)*R(-1) + R_ss*bF_dom_ss*bF_dom(-1) + R_ss*bF_for_ss*bF_for(-1) + q_for_ss*h_for_ss*(h_for - h_for(-1)) + c_for_ss*c_for + k_for_ss*(k_for - (1-delta)*k_for(-1)) + R_ss*bF_dom_ss*psi*b(-1) + R_ss*bF_for_ss*psi*b(-1); //5.11 cH_for(+1) = cH_for + R + psi*b; //5.12 q_for = beta*q_for(+1) + (((1-beta)*h_for_ss)/(1-h_for_ss))*h_for + cH_for - beta*cH_for(+1); //6.13 (1 - ((1-nu-mu)/eta))*y_for = A_for + nu*h_for(-1) + mu*k_for(-1) - ((1-nu-mu)/eta)*cH_for; //6.14 R + bF_dom + psi*b = (1/alpha_for_ss)*((m_h*q_for_ss*h_for_ss)/(m_h*q_for_ss*h_for_ss + z_h*k_for_ss))*(q_for(+1) + h_for) + (1/sigma_for_ss)*((z_h*k_for_ss)/(m_h*q_for_ss*h_for_ss + z_h*k_for_ss))*k_for; //5.15 R + bF_for + psi*b = 0; //5.16 q_for - (gamma + m_h*(beta - gamma))*q_for(+1) = (1 -beta*m_h)*(c_for - c_for(+1)) + (1 - gamma + m_h*(beta - gamma))*(y_for(+1) - h_for) - m_h*beta*R - m_h*beta*psi*b; //5.17 0 = (1 - beta*z_h)*(c_for - c_for(+1)) + (1 - gamma*(1 - delta) - z_h*(beta - gamma))*(y_for(+1) - k_for) - beta*z_h*R - beta*z_h*psi*b; //5.18 %-----------SHOCK(S)-----------------------------% A = (omega*A(-1)) + (omega_hat*A_for(-1)) + epsilon; A_for = (omega*A_for(-1)) + (omega_hat*A(-1)) + epsilon_f; end; %-------------------------------------------------- % % Checks % %-------------------------------------------------- steady; check; %-------------------------------------------------- % % Shocks % %-------------------------------------------------- shocks; var epsilon; stderr (0.852); var epsilon_f; stderr (0.852); //changed shock intensity from 0.9 to 0.6 corr epsilon, epsilon_f = 0.187; end; %-------------------------------------------------- % % Simulation % %-------------------------------------------------- stoch_simul(irf=60);