//AUTHOR:JUSTAS DAINAUSKAS, UNIVERSITY OF YORK, DEPARTMENT OF ECONOMICS AND RELATED STUDIES //TITLE OF THE PAPER: Why Do High-Interest Rate Currencies Revalue? Bayesian DSGE Approach //Typed and annotated by Justas Dainauskas, February 2017 //Dynare 4.3.3 // //------------------------------------------------------------------------------------------------- // DECLARATION OF ENDOGENOUS VARIABLES //------------------------------------------------------------------------------------------------- var // @#define countries = [ "US", "UK" ] @#define nth_co = "US" @#define nth_co = "UK" @#for co in countries y_@{co} //(1,27) aggregate output c_@{co} //(2,28) aggregate consumption nx_@{co} //(3,29) trade balance uc_@{co} //(4,30) marginal utility of consumption ul_@{co} //(5,31) marginal disutility of labour um_@{co} //(6,32) marginal utility of real money balances PHI_V_@{co} //(7,33) auxiliary preference variable l_@{co} //(8,34) labour supply w_@{co} //(9,35) real wage OMEGA_@{co} //(10,36) stock of bonds d_@{co} //(11,37) firm profit divident PI_@{co} //(12,38) cpi inflation PIp_@{co} //(13,39) ppi inflation (pcp) R_@{co} //(14,40) nominal interest rate r_@{co} //(15,41) real interest rate mc_@{co} //(16,42) real marginal costs PHI_1_@{co} //(17,43) auxiliary price setting variable 1 PHI_2_@{co} //(18,44) auxiliary price setting variable 2 DELTA_pi_@{co} //(19,45) menu costs dDELTA_pi_@{co} //(20,46) slope of the menu costs XIp_@{co} //(21,47) relative pcp prices XIl_@{co} //(22,48) relative lcp prices m_@{co} //(23,49) real money balances PSI_@{co} //(24,50) stochastic preference element LAMBDA_@{co} //(25,51) stochastic taylor rule element a_@{co} //(26,52) stochastic total factor productivity @#endfor DELTA_m //(53) transaction costs dDELTA_m //(54) slope of transaction costs m //(55) currency portfolio e //(56) currency pricing error s //(57) forward discount/premium q //(58) real exchange rate q_dot //(59) gross change in the real exchange rate ; // // //------------------------------------------------------------------------------------------------- // DECLARATION OF IDIOSYNCRATIC SHOCKS //------------------------------------------------------------------------------------------------- varexo // // @#for co in countries u_psi_@{co} //(1,2) preference shock u_lambda_@{co} //(3,4) transitory monetary policy shock u_a_@{co} //(5,6) total factor productivity shock @#endfor ; // // //------------------------------------------------------------------------------------------------- // DECLARATION OF PARAMETERS //------------------------------------------------------------------------------------------------- parameters l_ss //(1) hours of labour in the steady state q_ss //(2) steady state of the real exchange rate PI_ss //(3) steady state gross rate of inflation nu_pi //(4) policy responsiveness to inflation nu_y //(5) policy responsiveness to output gap rho_r //(6) persistence of policy rate tau //(7) transportation costs // beta //(8) time-invariant discount factor varepsilon //(9) elasticity of substitution between varieties within an economy gamma //(10) average GBP price of the USD omega //(11) curvature of utility function varphi //(12) elasticity of labour chi //(13) strength of consumption habits eta //(14) elasticity of substitution between varieties of different origins phi_m //(15) curvature of transaction costs // @#for co in countries phi_pi_@{co} //(16,17) curvature of menu costs pi_@{co} //(18,19) size of countries population relative to the rest of the world mu_@{co} //(20,21) local share of imported goods from abroad rho_psi_@{co} //(22,23) persistence of preference shocks rho_a_@{co} //(24,25) persistence of tfp shocks sigma_psi_@{co} //(26,27) standard error of preference shocks sigma_lambda_@{co} //(28,29) standard error of monetary policy shocks sigma_a_@{co} //(30,31) standard error of tfp shocks @#endfor ; // // //------------------------------------------------------------------------------------------------- // CALIBRATION OF PARAMETERS //------------------------------------------------------------------------------------------------- // l_ss = 0.3000; q_ss = 0.6100; PI_ss = 1.0050; nu_pi = 1.5000; nu_y = 0.5000; rho_r = 0.7500; tau = 0.1000; // beta = 0.9950; varepsilon = 6.0000; gamma = 0.100; omega = 1.5000; varphi = 3.0000; chi = 0.5000; eta = 1.5000; phi_m = 200.000; // phi_pi_US = 20.000; phi_pi_UK = 20.000; pi_US = 0.8300; pi_UK = 0.1700; mu_US = 0.1000; mu_UK = 0.2400; rho_psi_US = 0.7500; rho_psi_UK = 0.7500; rho_a_US = 0.6500; rho_a_UK = 0.6500; sigma_psi_US = 0.0050; sigma_psi_UK = 0.0050; sigma_lambda_US = 0.0050; sigma_lambda_UK = 0.0050; sigma_a_US = 0.0050; sigma_a_UK = 0.0050; // //------------------------------------------------------------------------------------------------- // NON-LINEAR MODEL EQUATIONS //------------------------------------------------------------------------------------------------- model; ///////////////////////// //model-local variables// ///////////////////////// #Delta_1=1/(1-mu_UK); %(--) #Delta_2=mu_UK*((q_ss/(1-tau))^(1-eta)); %(--) #Delta_3=1-mu_US*Delta_1*((q_ss*(1-tau))^(eta-1)); %(--) #Delta_4=1-mu_US*(1+Delta_1*Delta_2*((q_ss*(1-tau))^(eta-1))); %(--) #XIp_ss_US=(Delta_3/Delta_4)^(1/(1-eta)); %(--) #XIp_ss_UK=(Delta_1*(1-Delta_2*(XIp_ss_US^(1-eta))))^(1/(1-eta)); %(--) #XIl_ss_UK=XIp_ss_UK/(q_ss*(1-tau)); %(--) #XIl_ss_US=(q_ss/(1-tau))*XIp_ss_US; %(--) @#for co in countries #w_ss_@{co}=XIp_ss_@{co}*((varepsilon-1)/varepsilon); %(--) #psi_@{co}=(w_ss_@{co}*(1-chi*beta))/(varphi*l_ss^(varphi-1)); %(--) #R_bar_@{co}=PI_ss/beta; %(--) #y_bar_@{co}=l_ss; %(--) #b_@{co}=(XIp_ss_@{co}-1)*l_ss; %(--) //goods market clearing (1-DELTA_pi_@{co})*y_@{co}=c_@{co}+nx_@{co}; %(1,2) //household optimisation c_@{co}+R_@{co}*m_@{co}+(OMEGA_@{co}(+1)/r_@{co})=OMEGA_@{co}+w_@{co}*l_@{co}+d_@{co}; %(3,4) R_@{co}=r_@{co}*PI_@{co}(+1); %(5,6) PSI_@{co}*uc_@{co}=beta*r_@{co}*PSI_@{co}(+1)*uc_@{co}(+1); %(7,8) R_@{co}=um_@{co}/uc_@{co}; %(9,10) w_@{co}=-ul_@{co}/uc_@{co}; %(11,12) uc_@{co}=PHI_V_@{co}-chi*beta*PHI_V_@{co}(+1)*(PSI_@{co}(+1)/PSI_@{co}); %(13,14) ul_@{co}=-psi_@{co}*varphi*PHI_V_@{co}*(l_@{co}^(varphi-1)); %(15,16) um_@{co}=gamma*PHI_V_@{co}*(m_@{co}^(gamma-1)); %(17,18) PHI_V_@{co}=(c_@{co}-chi*c_@{co}(-1)-psi_@{co}*(l_@{co}^varphi)+(m_@{co}^gamma))^(-omega); %(19,20) //production technology y_@{co}=a_@{co}*l_@{co}; %(21,22) mc_@{co}=w_@{co}/a_@{co}; %(23,24) //price setting PI_@{co}=(XIp_@{co}(-1)/XIp_@{co})*PIp_@{co}; %(25,26) DELTA_pi_@{co}=(phi_pi_@{co}/2)*(((PIp_@{co}/PI_ss)-1)^2); %(27,28) dDELTA_pi_@{co}=phi_pi_@{co}*((PIp_@{co}/PI_ss)-1); %(29,30) d_@{co}=((1-DELTA_pi_@{co})*XIp_@{co}-mc_@{co})*y_@{co}-b_@{co}; %(31,32) XIp_@{co}=PHI_1_@{co}/PHI_2_@{co}; %(33,34) PHI_1_@{co}=(varepsilon/(varepsilon-1))*mc_@{co}; %(35,36) PHI_2_@{co}=1-DELTA_pi_@{co}+(dDELTA_pi_@{co}/(varepsilon-1))*PIp_@{co}/PI_ss -(y_@{co}(+1)/y_@{co})*(dDELTA_pi_@{co}(+1)/(varepsilon-1))*(PIp_@{co}(+1)/(R_@{co}*PI_ss)); %(37,38) //monetary policy R_@{co}/R_bar_@{co}=((R_@{co}(-1)/R_bar_@{co})^(rho_r))*((LAMBDA_@{co}*((PI_@{co}/PI_ss)^nu_pi)*((y_@{co}/y_bar_@{co})^nu_y))^(1-rho_r));%(39,40) //stochastic shocks log(PSI_@{co})=rho_psi_@{co}*log(PSI_@{co}(-1))+sigma_psi_@{co}*u_psi_@{co}; %(41,42) log(a_@{co})=rho_a_@{co}*log(a_@{co}(-1))+sigma_a_@{co}*u_a_@{co}; %(43,44) LAMBDA_@{co}=exp(sigma_lambda_@{co}*u_lambda_@{co}); %(45,46) @#endfor //currency trade m=m_UK+q(-1)*m_US; %(47) DELTA_m=(phi_m/2)*(((m/m(-1))-1)^2); %(48) dDELTA_m=phi_m*((m/m(-1))-1); %(49) q_dot=s*e; %(50) q_dot=q_ss/q; %(51) (1-DELTA_m-dDELTA_m*(m/m(-1)))*(e-1)+beta*dDELTA_m(+1)*((m(+1)/m)^2)*(e(+1)-1)=0; %(52) s=r_UK/r_US; %(53) //terms of trade (1-tau)*XIl_US=q*XIp_US; %(54) XIp_UK=(1-tau)*q*XIl_UK; %(55) 1=(1-mu_UK)*(XIp_UK^(1-eta))+mu_UK*(XIl_US^(1-eta)); %(56) 1=(1-mu_US)*(XIp_US^(1-eta))+mu_US*(XIl_UK^(1-eta)); %(57) //trade balance nx_US=mu_US*(XIl_US^(-eta))*y_UK-mu_UK*(XIl_UK^(-eta))*y_US; %(58) nx_UK=-nx_US; %(59) end; // //------------------------------------------------------------------------------------------------- // NON-LINEAR MODEL EQUATIONS //------------------------------------------------------------------------------------------------- // steady_state_model; r_US=1/beta; %(1) r_UK=1/beta; %(2) PI_US=PI_ss; %(3) PI_UK=PI_ss; %(4) PIp_US=PI_ss; %(5) PIp_UK=PI_ss; %(6) R_US=r_US*PI_US; %(7) R_UK=r_UK*PI_UK; %(8) s=1; %(9) e=1; %(10) q_dot=1; %(11) q=q_ss; %(12) DELTA_m=0; %(13) dDELTA_m=0; %(14) a_US=1; %(15) a_UK=1; %(16) PSI_US=1; %(17) PSI_UK=1; %(18) LAMBDA_US=1; %(19) LAMBDA_UK=1; %(20) DELTA_pi_US=0; %(21) DELTA_pi_UK=0; %(22) dDELTA_pi_US=0; %(23) dDELTA_pi_UK=0; %(24) delta_1=1/(1-mu_UK); %(--) delta_2=mu_UK*((q_ss/(1-tau))^(1-eta)); %(--) delta_3=1-mu_US*delta_1*((q_ss*(1-tau))^(eta-1)); %(--) delta_4=1-mu_US*(1+delta_1*delta_2*((q_ss*(1-tau))^(eta-1))); %(--) XIp_US=(delta_3/delta_4)^(1/(1-eta)); %(25) XIp_UK=(delta_1*(1-delta_2*(XIp_US^(1-eta))))^(1/(1-eta)); %(26) XIl_UK=XIp_UK/(q_ss*(1-tau)); %(27) XIl_US=(q_ss/(1-tau))*XIp_US; %(28) mc_US=XIp_US*((varepsilon-1)/varepsilon); %(29) mc_UK=XIp_UK*((varepsilon-1)/varepsilon); %(30) PHI_1_US=(varepsilon/(varepsilon-1))*mc_US; %(31) PHI_1_UK=(varepsilon/(varepsilon-1))*mc_UK; %(32) PHI_2_US=1; %(33) PHI_2_UK=1; %(34) w_US=mc_US; %(35) w_UK=mc_UK; %(36) l_US=l_ss; %(37) l_UK=l_ss; %(38) y_US=l_US; %(39) y_UK=l_UK; %(40) nx_US=mu_US*(XIl_US^(-eta))*y_UK-mu_UK*(XIl_UK^(-eta))*y_US; %(41) nx_UK=-nx_US; %(42) c_US=y_US-nx_US; %(43) c_UK=y_UK-nx_UK; %(44) psi_ss_US=(w_US*(1-chi*beta))/(varphi*(l_US^(varphi-1))); %(--) psi_ss_UK=(w_UK*(1-chi*beta))/(varphi*(l_UK^(varphi-1))); %(--) m_US=(gamma/(R_US*(1-chi*beta)))^(1/(1-gamma)); %(45) m_UK=(gamma/(R_UK*(1-chi*beta)))^(1/(1-gamma)); %(46) m=m_UK+q_ss*m_US; %(47) PHI_V_US=(c_US*(1-chi)-psi_ss_US*(l_US^varphi)+(m_US^gamma))^(-omega); %(48) PHI_V_UK=(c_UK*(1-chi)-psi_ss_UK*(l_UK^varphi)+(m_UK^gamma))^(-omega); %(49) ul_US=-psi_ss_US*varphi*PHI_V_US*(l_US^(varphi-1)); %(50) ul_UK=-psi_ss_UK*varphi*PHI_V_UK*(l_UK^(varphi-1)); %(51) uc_US=PHI_V_US*(1-chi*beta); %(52) uc_UK=PHI_V_UK*(1-chi*beta); %(53) um_US=gamma*PHI_V_US*(m_US^(gamma-1)); %(54) um_UK=gamma*PHI_V_UK*(m_UK^(gamma-1)); %(55) d_US=y_US-w_US*l_US; %(56) d_UK=y_UK-w_UK*l_UK; %(57) OMEGA_US=((R_US*m_US-nx_US)/(1-beta)); %(58) OMEGA_UK=((R_UK*m_UK-nx_UK)/(1-beta)); %(59) end; steady; check; model_diagnostics; // //------------------------------------------------------------------------------------------------- // SPECIFICATION OF SHOCKS //------------------------------------------------------------------------------------------------- shocks; // // var u_psi_US; stderr 1; var u_lambda_US; stderr 1; var u_a_US; stderr 1; var u_psi_UK; stderr 1; var u_lambda_UK; stderr 1; var u_a_UK; stderr 1; // // end; // // stoch_simul(order=1,pruning,irf=12,irf_shocks=(u_lambda_UK),periods=10000,nograph);