119 lines
3.6 KiB
Modula-2
119 lines
3.6 KiB
Modula-2
var y pi i;
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varexo e_y e_pi e_i;
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parameters a1 a2 a3 b1 b2 b3 c1 c2 c3;
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a1 = .2;
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a2 = .8;
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a3 = .05;
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b1 = .3;
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b2 = .7;
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b3 = .1;
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c1 = 0.9;
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c2 = 1.5;
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c3 = 0.5;
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model(bytecode);
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y = a1*y(-1) + a2*y(1) - a3*(i-pi(1)) + e_y ;
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pi = b1*pi(-1) + b2*pi(1) + b3*y + e_pi ;
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i = c1*i(-1) + c2*pi(1) + c3*y + e_i ;
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end;
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steady;
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check;
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shocks;
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var e_y = 0.002;
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var e_pi = 0.004;
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var e_i = 0.001;
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end;
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// Set the periods where some of the endogenous variables will be constrained.
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subsample = 2Y:100Y;
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// Load all the data generated by simulate.mod
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SimulatedData = dseries('truedata.mat');
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// Set the constrained paths for the endogenous variables.
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constrainedpaths = SimulatedData{'i'}(subsample);
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/* REMARKS
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**
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** In this example we constrain only the nominal interest rate from 2Y to 100Y to match the same variable as given by simulated.mod.
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** When we invert the model, we search the sequence of innovations e_i that leads to these realizations of the nominal interest rate. If
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** the model is the same, the sequence of innovations returned by the inversion routine has to match the true sequence of shocks (used
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** in simulated.mod and available for reference in SimulatedData dseries object). In this example, we invert the model with a slightly
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** different model by removing the max operator in the Taylor rule. Because of this difference, the innovations returned by the inversion
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** routine are not equal to the true innovations.
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**
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*/
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// Set the instruments (innovations used to control the nominal interest rate).
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exodata = SimulatedData{'e_y', 'e_pi', 'e_i'}.data;
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exodata(2:100,3) = NaN;
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exogenousvariables = dseries(exodata, 1Y, {'e_y';'e_pi';'e_i'});
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/* REMARK
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**
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** We need as many instruments as contrained endogenous variables. In this case we control the nominal interest rate path with the shock
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** in the Taylor rule. The other shocks have non NaN values (we use the values generated by simulation.mod). These shocks are considered as observed
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** exogenous variables.
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**
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*/
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// Invert the model by calling the model_inversion routine.
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[endogenousvariables, exogenousvariables] = model_inversion(constrainedpaths, exogenousvariables, SimulatedData, M_, options_, oo_);
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// Check the path for the nominal interest rate
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if max(abs(endogenousvariables.i(subsample).data-SimulatedData.i(subsample).data))>1e-6
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error('Constrained on endogenous variable paths are not all satisfied!')
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end
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// Save the simulations on disk.
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endogenousvariables.save('endogenousvariables', 'mat');
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exogenousvariables.save('exogenousvariables', 'mat');
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// Plot the differences on e_y (shock in the Euler equation)
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figure(1)
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plot(exogenousvariables.e_y-SimulatedData.e_y) % Not zero because of the misspecification related to the ZLB
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title('e_y')
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// Plot the differences on e_pi (shock in the Phillips curve)
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figure(2)
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plot(exogenousvariables.e_pi-SimulatedData.e_pi) % Not zero because of the misspecification related to the ZLB
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title('e_pi')
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// Plot the differences on e_ik (shock in the Taylor rule)
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figure(3)
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plot(exogenousvariables.e_i-SimulatedData.e_i) % Not zero because of the misspecification related to the ZLB
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title('e_i')
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hold on
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id = find(endogenousvariables.i.data==-.05);
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plot(id, zeros(1,length(id)), 'or')
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hold off
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figure(4)
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plot(endogenousvariables.i,'-k','linewidth',2)
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hold on
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plot(SimulatedData.i(1Y:100Y),'--r','linewidth',2)
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hold off
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title('Nominal interest rate')
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figure(5)
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plot(endogenousvariables.y,'-k','linewidth',2)
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hold on
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plot(SimulatedData.y(1Y:100Y),'--r','linewidth',2)
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hold off
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title('Output gap')
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figure(6)
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plot(endogenousvariables.pi,'-k','linewidth',2)
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hold on
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plot(SimulatedData.pi(1Y:100Y),'--r','linewidth',2)
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hold off
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title('Inflation gap')
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