109 lines
3.6 KiB
Modula-2
109 lines
3.6 KiB
Modula-2
// --+ options: stochastic,transform_unary_ops,json=compute +--
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var foo x1 x2 x1bar x2bar;
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varexo ex1 ex2 ex1bar ex2bar;
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parameters a_x1_0 a_x1_0_ a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
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a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
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beta ;
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a_x1_0 = -.9;
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a_x1_0_ = -.8;
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a_x1_1 = .4;
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a_x1_2 = .3;
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a_x1_x2_1 = .1;
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a_x1_x2_2 = .2;
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a_x2_0 = -.9;
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a_x2_1 = .2;
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a_x2_2 = -.1;
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a_x2_x1_1 = -.1;
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a_x2_x1_2 = .2;
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beta = 1/(1+.02);
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// Define a TREND_COMPONENT model from a subset of equations in the model block.
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trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']);
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/* Define a VAR_EXPECTATION_MODEL
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** ------------------------------
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**
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** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
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** auxiliary_model_name: the name of the VAR model used for the expectations (mandatory).
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** variable: the name of the variable to be forecasted (mandatory).
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** horizon: the horizon forecast (mandatory).
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** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
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**
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**
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** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
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** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
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** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
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** 0:Inf, then VAR_EXPECTATION_MODEL computes:
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**
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** ∑ βʰ Eₜ[yₜ₊ₕ]
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**
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** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
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*/
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var_expectation_model(model_name = varexp, expression = x1, auxiliary_model_name = toto, horizon = 15:50, discount = beta) ;
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model;
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[name='eq:x1', data_type='nonstationary']
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diff(x1) = a_x1_0*(x1(-1)-x1bar(-1))+a_x1_0_*(x2(-1)-x2bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;
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[name='eq:x2', data_type='nonstationary']
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diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;
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[name='eq:x1bar', data_type='nonstationary']
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x1bar = x1bar(-1) + ex1bar;
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[name='eq:x2bar', data_type='nonstationary']
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x2bar = x2bar(-1) + ex2bar;
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foo = .5*foo(-1) + var_expectation(varexp);
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end;
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// Initialize the VAR expectation model, will build the companion matrix of the VAR.
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var_expectation.initialize('varexp')
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// Update VAR_EXPECTATION reduced form parameters
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var_expectation.update('varexp');
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weights = M_.params(M_.var_expectation.varexp.param_indices);
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if ~all(weights(1:6)) || ~all(weights(9:10)) || weights(7) || weights(8) || weights(11) || weights(12)
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error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
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end
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var_expectation.print('varexp');
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shocks;
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var ex1 = .01;
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var ex2 = .01;
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var ex1bar = .02;
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var ex2bar = .02;
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end;
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verbatim;
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initialconditions =zeros(3,5);
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initialconditions(3,1) = .10; % foo(-1)
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initialconditions(3,2) = .20; % x1(-1)
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initialconditions(2,2) = .22; % x1(-2)
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initialconditions(1,2) = .24; % x1(-3)
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initialconditions(3,3) = .30; % x2(-1)
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initialconditions(2,3) = .32; % x2(-2)
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initialconditions(1,3) = .34; % x2(-3)
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initialconditions(3,4) = .25; % x1bar(-1)
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initialconditions(3,5) = .25; % x2bar(-1)
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initialconditions = ...
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dseries(initialconditions, dates('2000Q1'), {'foo', 'x1','x2', 'x1bar', 'x2bar'});
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set_dynare_seed('default');
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ts = simul_backward_model(initialconditions, 100);
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foo = ts.foo.data;
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save('example1.mat', 'foo');
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end; |