Economic assignment need use matlab

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help me finish this assignment use matlab ..

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USEMMP - Simulation exercise Part 1 A. Please open MatLab, copy the code below and run it. You now run the behavioural macromodel of chapter one of De Grauwe’s book. B. Run it a couple of times. C. Interpret the results, particularly: a. Highlight a period where chartists take over and explain what happens to output. b. Comment on the frequency with which spells occur in which chartists take over. c. Comment on the autocorrelations in output and inflation and on the Kurtosis you find and relate it to the empirical results mentioned in the book. D. Set rho to 1 eliminating the capacity to forget. Run the model a couple of times again and interpret the results again. Explain why the capacity to forget is necessary to generate behavioural cycles. E. Set the capacity to forget to its initial value. Now play with the willingness to learn. Set it very high and very low and interpret the results again. Part 2 You can do this exercise in MatLab building using parts of the code provided in part 1, but it can just as well be done in an environment in which you are more familiar, like Excel or Stata. The choice is yours; I do not care what software you use to solve this exercise. A. Start form the macromodel in equation 1.1-1.3 of De Grauwe and the coefficient values in appendix 1. Please plot the evolution of inflation, output and the nominal interest rate over time if there is a positive shock of size one to output at time 0 (i.e. 𝜖0 = 1 and 𝜖𝑡 = 0 if 𝑡 ≠ 0). Assume expectations are fundamentalist forever. B. Explain the economics of what you see. Hint: use the model in equation 1.22 𝑍𝑡 = 𝐴−1 [𝐵 𝐸̃𝑡 𝑍𝑡+1 + 𝐶𝑍𝑡−1 + 𝑏𝑟𝑡−1 + 𝜈𝑡 ] with for the expectations equation 1.14 and equation 1.4 and for the interest rate equation 1.3. 𝑏 0 Also: please note that there is a typo in the DeGrauwe book. Matrix B equals ( 1 ). You can −𝑎2 𝑎1 see this is a typo by deriving equation 1.22 from equations 1.1 to 1.3. C. Now assume expectations for both inflation and output are given forever by 𝐸̃𝑡 𝑦𝑡+1 = 𝑦𝑡−1 − 𝑦𝑡−2 and 𝐸̃𝑡 𝜋𝑡+1 = 𝜋𝑡−1 − 𝜋𝑡−2 Again plot the evolution and explain the economics. D. Now assume expectations for both inflation and output are given forever by 𝐸̃𝑡 𝑦𝑡+1 = 0.5𝑦𝑡−1 and 𝐸̃𝑡 𝜋𝑡+1 = 0.5𝜋𝑡−1 Again plot the evolution and explain the economics. E. Now assume expectations for both inflation and output are given by 𝐸̃𝑡 𝑦𝑡+1 = 0.5𝑦𝑡−1 and 𝐸̃𝑡 𝜋𝑡+1 = 0.5𝜋𝑡−1 For period 0 to 4 and are fundamentalist from period 5 onwards. Again plot the evolution and explain the economics of what you see. F. What does it mean when a model is stationary? And are models C-E stationary? % Appendix 2 of De Grauwe Lectures on behavioural macroeconomics % Adjustments by Jasper Lukkezen 11-3-2017. % Parameters of the mode % Appendix 2 of De Grauwe Lectures on behavioural macroeconomics % Adjustments by Jasper Lukkezen 11-3-2017. % Parameters of the model % expectation formation mm=1; % switching parameter gamma in Brock Hommes /// == willingness to learn rho=.5; % rho in mean squares errors /// == capacity to forget rhoBH=0.0; % rho in forecast rule selection pstar=0; % the central bank's inflation target eprational=0; % if all agents have rational forecast of inflation this parameter is 1 epextrapol=0; % if all agents use inflation extrapolation this parameter is 1 epfs=pstar; % forecast inflation targeters alfap=0.5; % percentage of extrapolators in inflation in the first period alfay=0.5; % percentage of extrapolators in output in the first period % length of the simulation T=20000; % length of simulation TI=300; % plot length xlimits=[1 TI]; % limits of x-axis ylimits=[0 1]; % limit of y-axis % parameters of the macro model (1.21) a1=0.5; % coefficent of expected output in output equation a2=-0.2; % a is the interest eleasticity of output demand b1=0.5; % b1 is coefficent of expected inflation in inflation equation b2=0.05; % b2 is coefficient of outout in inflation equation c1=1.5; % c1 is coefficient of inflation in Taylor equation c2=0.5; % c2 is coefficient of output in Taylor equation c3=0.5; % interest smoothing parameter in Taylor equation A=[1 -b2; -a2*c1 1-a2*c2]; B=[b1 0; -a2 a1]; C=[1-b1 0; 0 1-a1]; square = 0; % set to 1 if you want to use the other interest rate rule smooth=[0; a2*c3]; % smoothing parameter of lagged interest rate sigma1=0.5; sigma2=0.5; sigma3=0.5; % standard deviation shocks output % standard deviation shocks inflation % standard deviation shocks Taylor % the rho variables % move slower, i.e. rhoout=0.0; rhoinf=0.0; rhotayl=0.0; insert autoregressive components, which makes variables x(t) = rhox x(t-1) + other terms % rho in shocks output % rho in shocks inflation % rho in shocks Taylor % define empty time series (will be filled with the simulation results p=zeros(T,1); % inflation y=zeros(T,1); % output plagt=zeros(T,1); % lagged inflation ylagt=zeros(T,1); % lagged output r=zeros(T,1); % interest epf=zeros(T,1); % fundamental forecast inflation epc=zeros(T,1); % extrapolative forecast inflation ep=zeros(T,1); % combined forecast inflation eyfunt=zeros(T,1); % fundamental forecast output ey=zeros(T,1); % combined forecast output CRp=zeros(T,1); % forecast error extrapolators inflation FRp=zeros(T,1); % forecast error fundamentalists inflation alfapt=zeros(T,1); % percentage extrapolators in inflation CRy=zeros(T,1); % forecast error extrapolators output FRy=zeros(T,1); % forecast error fundamentalists output alfayt=zeros(T,1); % percentage extrapolators output anspiritsy=zeros(T,1); % animal spirits output anspiritsp=zeros(T,1); % animal spirits inflation epsilont=zeros(T,1); % shock in output etat=zeros(T,1); % shock in inflation ut=zeros(T,1); % shock in Taylor rule %%%%%%%%%%%%%%%%%% %Behavioral Model% %%%%%%%%%%%%%%%%%% for t=2:T %%% provide schocks epsilont(t)=rhoout*epsilont(t-1)+sigma1*randn; equation (demand shock) etat(t)=rhoinf*etat(t-1)+sigma2*randn; equation (supply shock) ut(t)=rhotayl*ut(t-1)+sigma3*randn; (interest rate shock) epsilon=epsilont(1); eta=etat(t); u=ut(t); shocks=[eta;a2*u+epsilon]; %shocks in output %shocks in inflation %shocks in Taylor rule %%% set expectations % for inflation epcs=p(t-1); % extrapolative forecast (1.14) if eprational==1; % if everyone is a fundamentalist epcs=pstar; end eps=alfap*epcs+(1-alfap)*epfs; % expectations are a combination of the extrapolative forecsst and the fundamental forecast (1.16) if epextrapol==1; % overwrite the previous result if all agents are extrapolators eps=p(t-1); end % for output eychar=y(t-1); % chartist expectations (1.5) eyfun=0+randn/2; % fundamentalist expectations (1.4) eyfunt(t)=eyfun; eys=alfay*eychar+(1-alfay)*eyfun; % combined expectations (1.6) % expectatins forecast=[eps; eys]; %%% evolution of the model % initial bookkeeping plag=p(t-1); ylag=y(t-1); rlag=r(t-1); lag=[plag;ylag]; % calculate inflation and output using the model D=B*forecast+C*lag+smooth*rlag+shocks; % (1.21) X= A^(-1)*D; % (1.22) p(t)=X(1,1); y(t)=X(2,1); r(t)=c1*p(t)+c2*y(t)+c3*r(t-1)+u; % (1.3) % different interest rate rule, used if square == 1 if square==1; r(t)=c1*(p(t))^2+c2*y(t)+c3*r(t-1)+u; end % final bookkeeping plagt(t)=p(t-1); ylagt(t)=y(t-1); %%% evolution of the expectations CRp(t)=rho*CRp(t-1)-(1-rho)*(epcs-p(t))^2; % forecast error of extrapolators for inflation (1.24) FRp(t)=rho*FRp(t-1)-(1-rho)*(epfs-p(t))^2; % forecast error of fundamentatists for inflation (1.23) CRy(t)=rho*CRy(t-1)-(1-rho)*(eychar-y(t))^2; % forecast error of extrapolators for output (1.24) FRy(t)=rho*FRy(t-1)-(1-rho)*(eyfun-y(t))^2; % forecast error of fundamentatists for output (1.23) alfap=rhoBH*alfapt(t-1)+(1rhoBH)*exp(mm*CRp(t))/(exp(mm*CRp(t))+exp(mm*FRp(t))); % percentage of extrapolators in inflation (1.19) alfay=rhoBH*alfayt(t-1)+(1rhoBH)*exp(mm*CRy(t))/(exp(mm*CRy(t))+exp(mm*FRy(t))); % percentage of extrapolators in output (1.19) alfapt(t)=alfap; % bookkeeping alfayt(t)=alfay; % bookkeeping if eychar>0; anspiritsy(t)=alfay; end if eychar0; anspiritsp(t)=alfap; end if eps
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