Add lagged information set in VAR based expectations.
parent
87b1d5bdf6
commit
fe63082c42
GPG Key ID:
295C1FE89E17EB3C
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@ -84,6 +84,18 @@ if discountfactor>1
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error('The discount cannot be greater than one.')
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end
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% Set timeshift
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if isfield(varexpectationmodel, 'time_shift')
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timeshift = varexpectationmodel.time_shift;
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else
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timeshift = 0;
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end
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% Throw an error if timeshift is positive
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if timeshift>0
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error('Option time_shift of the var_expectation command cannot be positive.')
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end
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% Set variables_id in VAR model
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m = length(varexpectationmodel.expr.vars);
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variables_id_in_var = NaN(m,1);
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@ -148,11 +160,17 @@ if length(horizon)==1
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elseif horizon>1
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parameters = alpha*mpower(discountfactor*CompanionMatrix, varexpectationmodel.horizon);
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end
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if timeshift<0
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parameters = parameters*mpower(CompanionMatrix, -timeshift);
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end
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else
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% Compute the reduced form parameters of the discounted sum of forecasts between t+horizon(1) and
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% t+horizon(2). Not that horzizon(2) need not be finite.
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if horizon(1)==0 && isinf(horizon(2))
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parameters = alpha/(eye(n)-discountfactor*CompanionMatrix);
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if timeshift<0
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parameters = parameters*mpower(CompanionMatrix, -timeshift);
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end
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elseif horizon(1)>0 && isinf(horizon(2))
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% Define the discounted companion matrix
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DiscountedCompanionMatrix = discountfactor*CompanionMatrix;
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@ -162,8 +180,14 @@ else
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tmp1 = tmp1 + mpower(DiscountedCompanionMatrix, h);
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end
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tmp1 = alpha*tmp1;
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if timeshift<0
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tmp1 = tmp1*mpower(CompanionMatrix, -timeshift);
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end
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% Second compute the parameters implied by the discounted sum from h=0 to h=Inf
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tmp2 = alpha/(eye(n)-DiscountedCompanionMatrix);
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if timeshift<0
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tmp2 = tmp2*mpower(CompanionMatrix, -timeshift);
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end
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% Finally
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parameters = tmp2-tmp1;
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elseif isfinite(horizon(2))
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@ -174,6 +198,9 @@ else
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tmp = tmp + mpower(DiscountedCompanionMatrix, h);
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end
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parameters = alpha*tmp;
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if timeshift<0
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parameters = parameters*mpower(CompanionMatrix, -timeshift);
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end
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end
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end
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@ -1,4 +1,4 @@
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function print_equations(variable_name, withexpansion)
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function str = print_equations(variable_name, withexpansion)
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% Prints equations where the variable appears in.
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%
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@ -84,6 +84,9 @@ for it = 1:length(M_.mapping.(variable_name).eqidx)
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withexpansion = false;
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end
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end
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if nargout
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str = sprintf('%s = %s;\n', model{M_.mapping.(variable_name).eqidx(it)}.lhs, rhs);
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end
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fprintf('%s = %s;\n', model{M_.mapping.(variable_name).eqidx(it)}.lhs, rhs);
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end
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@ -74,6 +74,10 @@ end
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id = 0;
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if isequal(expectationmodelkind, 'var')
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timeindices = (0:(maxlag-1))+abs(expectationmodel.time_shift);
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end
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for i=1:maxlag
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for j=1:length(auxmodel.list_of_variables_in_companion_var)
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id = id+1;
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@ -114,8 +118,8 @@ for i=1:maxlag
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end
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switch expectationmodelkind
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case 'var'
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if i>1
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variable = sprintf('%s(-%d)', variable, i-1);
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if timeindices(i)
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variable = sprintf('%s(-%d)', variable, timeindices(i));
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end
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case 'pac'
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variable = sprintf('%s(-%d)', variable, i);
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@ -440,12 +440,19 @@ MODFILES = \
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ECB_MODFILES = \
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var-expectations/1/example1.mod \
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var-expectations/1-with-time-shift-a/example1.mod \
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var-expectations/2/example1.mod \
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var-expectations/2-with-time-shift/example1.mod \
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var-expectations/3/example1.mod \
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var-expectations/3-with-time-shift/example1.mod \
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var-expectations/4/example1.mod \
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var-expectations/4-with-time-shift/example1.mod \
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var-expectations/5/example1.mod \
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var-expectations/5-with-time-shift/example1.mod \
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var-expectations/6/example1.mod \
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var-expectations/6/substitution.mod \
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var-expectations/6-with-time-shift/example1.mod \
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var-expectations/6-with-time-shift/substitution.mod \
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var-expectations/7/example1.mod \
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var-expectations/7/substitution.mod \
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var-expectations/8/example1.mod \
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@ -588,7 +595,8 @@ XFAIL_MODFILES = ramst_xfail.mod \
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estimation/tune_mh_jscale/fs2000_1_xfail.mod \
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estimation/tune_mh_jscale/fs2000_2_xfail.mod \
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estimation/no_init_estimation_check_first_obs/fs2000_init_check_XFAIL.mod \
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estimation/no_init_estimation_check_first_obs/fs2000_init_check_XFAIL2.mod
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estimation/no_init_estimation_check_first_obs/fs2000_init_check_XFAIL2.mod \
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var-expectations/1-with-time-shift-b/example1.mod
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MFILES = histval_initval_file/ramst_initval_file_data.m
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@ -821,6 +829,8 @@ kalman/likelihood_from_dynare/fs2000ns_corr_ME_missing.o.trs: kalman/likelihood_
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var-expectations/6/substitution.m.trs: var-expectations/6/example1.m.trs
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var-expectations/6/substitution.o.trs: var-expectations/6/example1.o.trs
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var-expectations/6-with-time-shift/substitution.m.trs: var-expectations/6-with-time-shift/example1.m.trs
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var-expectations/6-with-time-shift/substitution.o.trs: var-expectations/6-with-time-shift/example1.o.trs
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var-expectations/7/substitution.m.trs: var-expectations/7/example1.m.trs
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var-expectations/7/substitution.o.trs: var-expectations/7/example1.o.trs
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var-expectations/8/substitution.m.trs: var-expectations/8/example1.m.trs
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@ -839,6 +849,9 @@ lmmcp/sw_newton.o.trs: lmmcp/sw_lmmcp.o.trs
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var-expectations/4/example1.m.trs: var-expectations/3/example1.m.trs
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var-expectations/4/example1.o.trs: var-expectations/3/example1.o.trs
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var-expectations/4-with-time-shift/example1.m.trs: var-expectations/3-with-time-shift/example1.m.trs
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var-expectations/4-with-time-shift/example1.o.trs: var-expectations/3-with-time-shift/example1.o.trs
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trend-component-and-var-models/tcm7.m.trs: trend-component-and-var-models/tcm6.m.trs
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trend-component-and-var-models/tcm7.o.trs: trend-component-and-var-models/tcm6.o.trs
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trend-component-and-var-models/tcm8.m.trs: trend-component-and-var-models/tcm6.m.trs
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@ -0,0 +1,64 @@
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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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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** var_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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** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
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** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
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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 = x, auxiliary_model_name = toto, horizon = 1, time_shift=-1, discount = beta) ;
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model;
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[ name = 'X' ]
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x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
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[ name = 'Z' ]
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z = f*z(-1) + e_z;
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[ name = 'Y' ]
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y = d*y(-2) + e*z(-1) + e_y;
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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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if ~isfield(M_.var_expectation.varexp, 'time_shift') || ~isequal(M_.var_expectation.varexp.time_shift, -1)
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error('Preprocessor does not honour time_shift option as expected.')
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end
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@ -0,0 +1,66 @@
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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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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** var_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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** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
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** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
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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 = x, auxiliary_model_name = toto, horizon = 1, time_shift=1, discount = beta) ;
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model;
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[ name = 'X' ]
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x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
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[ name = 'Z' ]
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z = f*z(-1) + e_z;
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[ name = 'Y' ]
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y = d*y(-2) + e*z(-1) + e_y;
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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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try
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var_expectation.update('varexp');
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if isfield(M_.var_expectation.varexp, 'time_shift')
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error('Preprocessor should not allow positive values for time_shift option.')
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end
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catch
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end
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@ -0,0 +1,86 @@
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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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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** var_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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** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
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** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
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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 = x, auxiliary_model_name = toto, time_shift=-2, horizon = 2, discount = beta) ;
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model;
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[ name = 'X' ]
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x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
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[ name = 'Z' ]
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z = f*z(-1) + e_z;
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[ name = 'Y' ]
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y = d*y(-2) + e*z(-1) + e_y;
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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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// Print equations where the variable appears in
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fprintf('x is in: \n')
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print_equations('x')
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fprintf('\n')
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fprintf('y is in: \n')
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str = print_equations('y', true);
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fprintf('\n')
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if ~isfield(M_.var_expectation.varexp, 'time_shift') || ~isequal(M_.var_expectation.varexp.time_shift, -2)
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error('Preprocessor does not honour time_shift option as expected.')
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end
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str = strrep(str, 'foo = .5*foo(-1)', '');
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str = strrep(str, '+ var_expectation_model_varexp_x_0*x(-2)', '');
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str = strrep(str, '+ var_expectation_model_varexp_y_0*y(-2)', '');
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str = strrep(str, '+ var_expectation_model_varexp_z_0*z(-2)', '');
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str = strrep(str, '+ var_expectation_model_varexp_x_1*x(-3)', '');
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str = strrep(str, '+ var_expectation_model_varexp_y_1*y(-3)', '');
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str = strrep(str, '+ var_expectation_model_varexp_z_1*z(-3)', '');
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str = strrep(str, ';', '');
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if ~isempty(strtrim(str))
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error('Printed equation is wrong.')
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end
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@ -0,0 +1,72 @@
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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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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** var_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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** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
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** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
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**
|
||||
** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
|
||||
** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
|
||||
** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
|
||||
** 0:Inf, then VAR_EXPECTATION_MODEL computes:
|
||||
**
|
||||
** ∑ βʰ Eₜ[yₜ₊ₕ]
|
||||
**
|
||||
** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
|
||||
*/
|
||||
|
||||
var_expectation_model(model_name = varexp, expression = x, auxiliary_model_name = toto, time_shift=-1, horizon = 0:Inf, discount = beta) ;
|
||||
|
||||
|
||||
model;
|
||||
[ name = 'X' ]
|
||||
x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
|
||||
[ name = 'Z' ]
|
||||
z = f*z(-1) + e_z;
|
||||
[ name = 'Y' ]
|
||||
y = d*y(-2) + e*z(-1) + e_y;
|
||||
|
||||
foo = .5*foo(-1) + var_expectation(varexp);
|
||||
end;
|
||||
|
||||
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
|
||||
var_expectation.initialize('varexp')
|
||||
|
||||
// Update VAR_EXPECTATION reduced form parameters
|
||||
var_expectation.update('varexp');
|
||||
|
||||
/*
|
||||
** REMARK The VAR model is such that x depends on past values of x
|
||||
** (xₜ₋₁ and xₜ₋₂) and on zₜ₋₂. Consequently the reduced
|
||||
** form parameters associated to yₜ₋₁, yₜ₋₂ have to be zero.
|
||||
*/
|
||||
|
||||
weights = M_.params(M_.var_expectation.varexp.param_indices);
|
||||
|
||||
if weights(2) || ~weights(3) || weights(5) || ~weights(1) || ~weights(4) || ~weights(6)
|
||||
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
||||
end
|
||||
|
||||
save('weights.mat','weights');
|
||||
|
|
@ -68,4 +68,4 @@ if weights(2) || ~weights(3) || weights(5) || ~weights(1) || ~weights(4) || ~wei
|
|||
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
||||
end
|
||||
|
||||
save('weights.mat','weights');
|
||||
save('weights.mat','weights');
|
||||
|
|
|
|||
|
|
@ -0,0 +1,78 @@
|
|||
// --+ options: stochastic,json=compute +--
|
||||
|
||||
var foo z x y;
|
||||
varexo e_x e_y e_z;
|
||||
parameters a b c d e f beta ;
|
||||
|
||||
a = .9;
|
||||
b = -.2;
|
||||
c = .3;
|
||||
f = .8;
|
||||
d = .5;
|
||||
e = .4;
|
||||
|
||||
beta = 1/(1+.02);
|
||||
|
||||
// Define a VAR model from a subset of equations in the model block.
|
||||
var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
|
||||
|
||||
/* Define a VAR_EXPECTATION_MODEL
|
||||
** ------------------------------
|
||||
**
|
||||
** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
|
||||
** var_model_name: the name of the VAR model used for the expectations (mandatory).
|
||||
** variable: the name of the variable to be forecasted (mandatory).
|
||||
** horizon: the horizon forecast (mandatory).
|
||||
** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
|
||||
** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
|
||||
** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
|
||||
**
|
||||
** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
|
||||
** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
|
||||
** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
|
||||
** 0:Inf, then VAR_EXPECTATION_MODEL computes:
|
||||
**
|
||||
** ∑ βʰ Eₜ[yₜ₊ₕ]
|
||||
**
|
||||
** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
|
||||
*/
|
||||
|
||||
var_expectation_model(model_name = varexp, expression = x, auxiliary_model_name = toto, time_shift=-1, horizon = 0:500, discount = beta) ;
|
||||
|
||||
|
||||
model;
|
||||
[ name = 'X' ]
|
||||
x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
|
||||
[ name = 'Z' ]
|
||||
z = f*z(-1) + e_z;
|
||||
[ name = 'Y' ]
|
||||
y = d*y(-2) + e*z(-1) + e_y;
|
||||
|
||||
foo = .5*foo(-1) + var_expectation(varexp);
|
||||
end;
|
||||
|
||||
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
|
||||
var_expectation.initialize('varexp')
|
||||
|
||||
// Update VAR_EXPECTATION reduced form parameters
|
||||
var_expectation.update('varexp');
|
||||
|
||||
/*
|
||||
** REMARK The VAR model is such that x depends on past values of x
|
||||
** (xₜ₋₁ and xₜ₋₂) and on zₜ₋₂. Consequently the reduced
|
||||
** form parameters associated to yₜ₋₁, yₜ₋₂ have to be zero.
|
||||
*/
|
||||
|
||||
weights = M_.params(M_.var_expectation.varexp.param_indices);
|
||||
|
||||
if weights(2) || ~weights(3) || weights(5) || ~weights(1) || ~weights(4) || ~weights(6)
|
||||
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
||||
end
|
||||
|
||||
WEIGHTS = load('../3-with-time-shift/weights.mat');
|
||||
|
||||
if max(abs(weights-WEIGHTS.weights))>1e-12
|
||||
error('Inconsistent results in var-expectations/3-with-time-shift and var-expectations/4-with-time-shift.')
|
||||
end
|
||||
|
||||
delete('../3-with-time-shift/weights.mat')
|
||||
|
|
@ -0,0 +1,69 @@
|
|||
// --+ options: stochastic,json=compute +--
|
||||
|
||||
var foo z x y;
|
||||
varexo e_x e_y e_z;
|
||||
parameters a b c d e f beta ;
|
||||
|
||||
a = .9;
|
||||
b = -.2;
|
||||
c = .3;
|
||||
f = .8;
|
||||
d = .5;
|
||||
e = .4;
|
||||
|
||||
beta = 1/(1+.02);
|
||||
|
||||
// Define a VAR model from a subset of equations in the model block.
|
||||
var_model(model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
|
||||
|
||||
/* Define a VAR_EXPECTATION_MODEL
|
||||
** ------------------------------
|
||||
**
|
||||
** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
|
||||
** var_model_name: the name of the VAR model used for the expectations (mandatory).
|
||||
** variable: the name of the variable to be forecasted (mandatory).
|
||||
** horizon: the horizon forecast (mandatory).
|
||||
** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
|
||||
** time_shift: shifts the information set to the past, must be a non positive scalar. By default, expectations
|
||||
** about `variable` in period `t+horizon` are formed in period t (time_shift=0)
|
||||
**
|
||||
** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
|
||||
** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
|
||||
** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
|
||||
** 0:Inf, then VAR_EXPECTATION_MODEL computes:
|
||||
**
|
||||
** ∑ βʰ Eₜ[yₜ₊ₕ]
|
||||
**
|
||||
** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
|
||||
*/
|
||||
|
||||
var_expectation_model(model_name = varexp, expression = x, auxiliary_model_name = toto, time_shift=-2, horizon = 15:50, discount = beta) ;
|
||||
|
||||
model;
|
||||
[ name = 'X' ]
|
||||
x = a*x(-1) + b*x(-2) + c*z(-2) + e_x;
|
||||
[ name = 'Z' ]
|
||||
z = f*z(-1) + e_z;
|
||||
[ name = 'Y' ]
|
||||
y = d*y(-2) + e*z(-1) + e_y;
|
||||
|
||||
foo = .5*foo(-1) + var_expectation(varexp);
|
||||
end;
|
||||
|
||||
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
|
||||
var_expectation.initialize('varexp')
|
||||
|
||||
// Update VAR_EXPECTATION reduced form parameters
|
||||
var_expectation.update('varexp');
|
||||
|
||||
/*
|
||||
** REMARK The VAR model is such that x depends on past values of x
|
||||
** (xₜ₋₁ and xₜ₋₂) and on zₜ₋₂. Consequently the reduced
|
||||
** form parameters associated to yₜ₋₁, yₜ₋₂ have to be zero.
|
||||
*/
|
||||
|
||||
weights = M_.params(M_.var_expectation.varexp.param_indices);
|
||||
|
||||
if weights(2) || ~weights(3) || weights(5) || ~weights(1) || ~weights(4) || ~weights(6)
|
||||
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
||||
end
|
||||
|
|
@ -0,0 +1,109 @@
|
|||
// --+ options: stochastic,transform_unary_ops,json=compute +--
|
||||
|
||||
var foo x1 x2 x1bar x2bar;
|
||||
|
||||
varexo ex1 ex2 ex1bar ex2bar;
|
||||
|
||||
parameters a_x1_0 a_x1_0_ a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
|
||||
a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
|
||||
beta ;
|
||||
|
||||
a_x1_0 = -.9;
|
||||
a_x1_0_ = -.8;
|
||||
a_x1_1 = .4;
|
||||
a_x1_2 = .3;
|
||||
a_x1_x2_1 = .1;
|
||||
a_x1_x2_2 = .2;
|
||||
|
||||
|
||||
a_x2_0 = -.9;
|
||||
a_x2_1 = .2;
|
||||
a_x2_2 = -.1;
|
||||
a_x2_x1_1 = -.1;
|
||||
a_x2_x1_2 = .2;
|
||||
|
||||
beta = 1/(1+.02);
|
||||
|
||||
// Define a TREND_COMPONENT model from a subset of equations in the model block.
|
||||
trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']);
|
||||
|
||||
/* Define a VAR_EXPECTATION_MODEL
|
||||
** ------------------------------
|
||||
**
|
||||
** model_name: the name of the VAR_EXPECTATION_MODEL (mandatory).
|
||||
** auxiliary_model_name: the name of the VAR model used for the expectations (mandatory).
|
||||
** variable: the name of the variable to be forecasted (mandatory).
|
||||
** horizon: the horizon forecast (mandatory).
|
||||
** discount: the discount factor, which can be a value or a declared parameter (default is 1.0, no discounting).
|
||||
**
|
||||
**
|
||||
** The `horizon` parameter can be an integer in which case the (discounted) `horizon` step ahead forecast
|
||||
** is computed using the VAR model `var_model_name`. Alternatively, `horizon` can be a range. In this case
|
||||
** VAR_EXPECTATION_MODEL returns a discounted sum of expected values. If `horizon` is set equal to the range
|
||||
** 0:Inf, then VAR_EXPECTATION_MODEL computes:
|
||||
**
|
||||
** ∑ βʰ Eₜ[yₜ₊ₕ]
|
||||
**
|
||||
** where the sum is over h=0,…,∞ and the conditional expectations are computed with VAR model `var_model_name`.
|
||||
*/
|
||||
|
||||
var_expectation_model(model_name = varexp, expression = x1, auxiliary_model_name = toto, time_shift=-1, horizon = 15:50, discount = beta) ;
|
||||
|
||||
|
||||
model;
|
||||
|
||||
[name='eq:x1', data_type='nonstationary']
|
||||
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;
|
||||
|
||||
[name='eq:x2', data_type='nonstationary']
|
||||
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;
|
||||
|
||||
[name='eq:x1bar', data_type='nonstationary']
|
||||
x1bar = x1bar(-1) + ex1bar;
|
||||
|
||||
[name='eq:x2bar', data_type='nonstationary']
|
||||
x2bar = x2bar(-1) + ex2bar;
|
||||
|
||||
foo = .5*foo(-1) + var_expectation(varexp);
|
||||
end;
|
||||
|
||||
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
|
||||
var_expectation.initialize('varexp')
|
||||
|
||||
// Update VAR_EXPECTATION reduced form parameters
|
||||
var_expectation.update('varexp');
|
||||
|
||||
weights = M_.params(M_.var_expectation.varexp.param_indices);
|
||||
|
||||
if ~all(weights(1:6)) || ~all(weights(9:10)) || weights(7) || weights(8) || weights(11) || weights(12)
|
||||
error('Wrong reduced form parameter for VAR_EXPECTATION_MODEL')
|
||||
end
|
||||
|
||||
var_expectation.print('varexp');
|
||||
|
||||
shocks;
|
||||
var ex1 = .01;
|
||||
var ex2 = .01;
|
||||
var ex1bar = .02;
|
||||
var ex2bar = .02;
|
||||
end;
|
||||
|
||||
|
||||
verbatim;
|
||||
initialconditions =zeros(4,5);
|
||||
initialconditions(4,1) = .10; % foo(-1)
|
||||
initialconditions(4,2) = .20; % x1(-1)
|
||||
initialconditions(3,2) = .22; % x1(-2)
|
||||
initialconditions(2,2) = .24; % x1(-3)
|
||||
initialconditions(4,3) = .30; % x2(-1)
|
||||
initialconditions(3,3) = .32; % x2(-2)
|
||||
initialconditions(2,3) = .34; % x2(-3)
|
||||
initialconditions(4,4) = .25; % x1bar(-1)
|
||||
initialconditions(4,5) = .25; % x2bar(-1)
|
||||
initialconditions = ...
|
||||
dseries(initialconditions, dates('2000Q1'), {'foo', 'x1','x2', 'x1bar', 'x2bar'});
|
||||
set_dynare_seed('default');
|
||||
ts = simul_backward_model(initialconditions, 100);
|
||||
foo = ts.foo.data;
|
||||
save('example1.mat', 'foo');
|
||||
end;
|
||||
|
|
@ -0,0 +1,76 @@
|
|||
// --+ options: stochastic,transform_unary_ops,json=compute +--
|
||||
|
||||
var foo x1 x2 x1bar x2bar;
|
||||
|
||||
varexo ex1 ex2 ex1bar ex2bar;
|
||||
|
||||
parameters a_x1_0 a_x1_0_ a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
|
||||
a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
|
||||
beta ;
|
||||
|
||||
a_x1_0 = -.9;
|
||||
a_x1_0_ = -.8;
|
||||
a_x1_1 = .4;
|
||||
a_x1_2 = .3;
|
||||
a_x1_x2_1 = .1;
|
||||
a_x1_x2_2 = .2;
|
||||
|
||||
|
||||
a_x2_0 = -.9;
|
||||
a_x2_1 = .2;
|
||||
a_x2_2 = -.1;
|
||||
a_x2_x1_1 = -.1;
|
||||
a_x2_x1_2 = .2;
|
||||
|
||||
@#include "example1/model/var-expectations/varexp-parameters.inc"
|
||||
|
||||
beta = 1/(1+.02);
|
||||
|
||||
model;
|
||||
|
||||
[name='eq:x1', data_type='nonstationary']
|
||||
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;
|
||||
|
||||
[name='eq:x2', data_type='nonstationary']
|
||||
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;
|
||||
|
||||
[name='eq:x1bar', data_type='nonstationary']
|
||||
x1bar = x1bar(-1) + ex1bar;
|
||||
|
||||
[name='eq:x2bar', data_type='nonstationary']
|
||||
x2bar = x2bar(-1) + ex2bar;
|
||||
|
||||
foo = .5*foo(-1) +
|
||||
@#include "example1/model/var-expectations/varexp-expression.inc"
|
||||
;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var ex1 = .01;
|
||||
var ex2 = .01;
|
||||
var ex1bar = .02;
|
||||
var ex2bar = .02;
|
||||
end;
|
||||
|
||||
|
||||
verbatim;
|
||||
initialconditions =zeros(4,5);
|
||||
initialconditions(4,1) = .10; % foo(-1)
|
||||
initialconditions(4,2) = .20; % x1(-1)
|
||||
initialconditions(3,2) = .22; % x1(-2)
|
||||
initialconditions(2,2) = .24; % x1(-3)
|
||||
initialconditions(4,3) = .30; % x2(-1)
|
||||
initialconditions(3,3) = .32; % x2(-2)
|
||||
initialconditions(2,3) = .34; % x2(-3)
|
||||
initialconditions(4,4) = .25; % x1bar(-1)
|
||||
initialconditions(4,5) = .25; % x2bar(-1)
|
||||
initialconditions = ...
|
||||
dseries(initialconditions, dates('2000Q1'), {'foo', 'x1','x2', 'x1bar', 'x2bar'});
|
||||
set_dynare_seed('default');
|
||||
ts = simul_backward_model(initialconditions, 100);
|
||||
ex = load('example1.mat');
|
||||
delete('example1.mat')
|
||||
if max(abs(ex.foo-ts.foo.data))>1e-12
|
||||
error('Simulations do not match!')
|
||||
end
|
||||
end;
|
||||
Loading…
Reference in New Issue