宏觀研學會 - 【課程Slides】DSGE與Dynare/Stata編程導論－鑽石舞台

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今天下午，許文立老師受北京大學經濟學院李博老師邀請在《數量經濟學》課程做了一次Guest Lecture（因疫情改為線上）。許老師主要給北大經濟學院一、二年級博士生們介紹了DSGE分析框架，並舉了三個例子——貨幣RBC、隨機增長RBC和凱恩斯主義-內生增長模型，然後詳細講解了Dynare編程的語法結構和例子演示。

下面將課程的Slides分享給大家，其中還包括對應的Dynare與Stata代碼。

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上述RBC模型的Dynare代碼如下：

%ThisfilewaswrittenbyJohannesPfeifervar y c k A z R Pi;varexo eps_z;parameters beta delta alpha rhoz phi_pi Pibar;alpha = 0.33; // capital sharedelta = 0.025; //deprecation ratebeta = 0.99; //discount factorPibar = 1;phi_pi = 1.5;rhoz = 0.97; //TFP autocorr. from linearly detrended Solow residualmodel;#Rbar = 1/beta;1/c=beta*1/c(+1)*(alpha*A(+1)*k^(alpha-1)+(1-delta));1/c=beta*1/c(+1)*(R/Pi(+1));A*k(-1)^alpha=c+k-(1-delta)*k(-1);y=A*k(-1)^alpha;R/Rbar=(Pi/Pibar)^phi_pi;A=exp(z);z=rhoz*z(-1)+eps_z;end;steady_state_model;k=((1/beta-(1-delta))/alpha)^(1/(alpha-1));y=k^alpha;c=y-delta*k;R=1/beta;Pi=Pibar;A=1;z=0;end;shocks;var eps_z=0.0068^2; //estimated valueend;steady;check;stoch_simul(order=1,irf=20,periods=250);rplot y;

上述rbc模型的stata代碼如下（DSGE在stata中的應用參見【Stata 17更新】DSGE的貝葉斯估計、DSGE建模與編程(92):Stata複製Sims et al(2021 REStat):"四方程NK模型"）：

* 北大經濟學院《數量經濟學》Guest Lecture：DSGE與編程導論* 經典貨幣經濟RBC模型* stata代碼 * @許文立，2022-3-31* 加載數據use "/Users/xuwenli/Desktop/北京大學-DSGE與編程/example_code/usmacro2.dta",clear* 校準參數constraint 1 _b[alpha]=0.33 // 資本收入份額constraint 2 _b[delta]=0.025 constraint 3 _b[beta]=0.8constraint 4 _b[Pibar]=1constraint 5 _b[phi_pi]=1.5constraint 6 _b[rho]=0.9* 聲明模型dsgenl (1/c={beta}/F.c*({alpha}*F.A*(F.k)^({alpha}-1)+(1-{delta}))) /// (1/c={beta}/F.c*(r/F.p)) /// (A*k^{alpha}=c+F.k-(1-{delta}*k)) /// (y=A*k^{alpha}) /// (r*{beta}=(p/{Pibar})^{phi_pi}) /// (ln(F.A)={rho}*ln(A)) /// ,observed(p) unobserved(c y r) exostate(A) endostate(k) /// constraint(1/6)* 政策函數estat policy* 轉移函數estat transition* 脈衝響應irf set rbc_cme.irfirf create model1irf graph irf, impulse(A) response(y c k A) byopts(yrescale)

上述隨機增長RBC模型的dynare代碼如下：

% This file was written by Johannes Pfeifervar y_tilde c_tilde k_tilde z R_tilde Pi_tilde mu_tilde Y;varexo eps_z eps_x;parameters beta delta alpha rhoz phi_pi Pibar Lambda_x;alpha = 0.33; // capital sharedelta = 0.025; //deprecation ratebeta = 0.99; //discount factorPibar = 1;phi_pi = 1.5;rhoz = 0.97; //TFP autocorr. from linearly detrended Solow residualLambda_x= 0.0055; //2.2% output growth per yearmodel;#Rbar = exp(Lambda_x)/beta;1/exp(c_tilde)=beta/exp(mu_tilde(+1))*1/exp(c_tilde(+1))*(alpha*exp(z(+1))*(exp(k_tilde)/exp(mu_tilde(+1)))^(alpha-1)+(1-delta));1/exp(c_tilde)=beta/exp(mu_tilde(+1))*1/exp(c_tilde(+1))*(exp(R_tilde)/exp(Pi_tilde(+1)));exp(z)*(exp(k_tilde(-1))/exp(mu_tilde))^alpha=exp(c_tilde)+exp(k_tilde)-(1-delta)*exp(k_tilde(-1))/exp(mu_tilde);exp(y_tilde)=exp(z)*(exp(k_tilde(-1))/exp(mu_tilde))^alpha;exp(R_tilde)/Rbar=(exp(Pi_tilde)/Pibar)^phi_pi;z=rhoz*z(-1)+eps_z;mu_tilde=Lambda_x+eps_x;Y=y_tilde*exp(mu_tilde);end;steady_state_model;mu_tilde=Lambda_x;k_tilde=log(exp(mu_tilde)*((exp(mu_tilde)/beta-(1-delta))/alpha)^(1/(alpha-1)));y_tilde=log((exp(k_tilde)/exp(mu_tilde))^alpha);c_tilde=log(exp(y_tilde)-(1-(1-delta)/exp(mu_tilde))*exp(k_tilde));R_tilde=log(exp(mu_tilde)/beta);Pi_tilde=log(Pibar);z=0;Y=y_tilde*exp(mu_tilde);end;shocks;var eps_z=0.0068^2;var eps_x=0.005^2; //just some numberend;steady;check;stoch_simul(order=1,irf=20,periods=200);rplot Y;

%北大經濟學院《數量經濟學》Guest Lecture：DSGE與編程導論%新凱恩主義內生增長模型%dynare代碼%@許文立，2022-3-31var c g i l;varexo ei;parameters beta piss rho phi1 phi2 lss chi omega psi;beta=0.9;piss=1;rho=0.9;phi1=1.5;phi2=1;lss=1;chi=0.1;omega=0.1;psi=1;model;1+i=(piss/beta)*piss^phi1*(l/lss)^phi2+ei;c=g*c(1)*piss/(beta*(piss/beta)*piss^phi1*(l/lss)^phi2);g(1)=beta*(c/c(1))*(chi*omega*l(1)+1);psi*l=c+(g(1)-1)/chi;end;steady_state_model;i=piss/beta-1;l=lss;g=beta*(chi*omega*l+1);c=psi*l-(g-1)/chi;end;shocks;var ei=0.01^2;end;steady;check;model_diagnostics;stoch_simul;