solve_model_for_online_filter.m 13.7 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
function [ys,trend_coeff,exit_flag,info,Model,DynareOptions,BayesInfo,DynareResults,ReducedForm] = solve_model_for_online_filter(observation_number,xparam1,DynareDataset,DynareOptions,Model,EstimatedParameters,BayesInfo,DynareResults)
% solve the dsge model for an particular parameters set.

%@info:
%! @deftypefn {Function File} {[@var{fval},@var{exit_flag},@var{ys},@var{trend_coeff},@var{info},@var{Model},@var{DynareOptions},@var{BayesInfo},@var{DynareResults}] =} non_linear_dsge_likelihood (@var{xparam1},@var{DynareDataset},@var{DynareOptions},@var{Model},@var{EstimatedParameters},@var{BayesInfo},@var{DynareResults})
%! @anchor{dsge_likelihood}
%! @sp 1
%! Evaluates the posterior kernel of a dsge model using a non linear filter.
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item xparam1
%! Vector of doubles, current values for the estimated parameters.
%! @item DynareDataset
%! Matlab's structure describing the dataset (initialized by dynare, see @ref{dataset_}).
%! @item DynareOptions
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
%! @item Model
%! Matlab's structure describing the Model (initialized by dynare, see @ref{M_}).
%! @item EstimatedParamemeters
%! Matlab's structure describing the estimated_parameters (initialized by dynare, see @ref{estim_params_}).
%! @item BayesInfo
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
%! @item DynareResults
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
%! @end table
%! @sp 2
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item fval
%! Double scalar, value of (minus) the likelihood.
%! @item exit_flag
%! Integer scalar, equal to zero if the routine return with a penalty (one otherwise).
%! @item ys
%! Vector of doubles, steady state level for the endogenous variables.
%! @item trend_coeffs
%! Matrix of doubles, coefficients of the deterministic trend in the measurement equation.
%! @item info
%! Integer scalar, error code.
%! @table @ @code
%! @item info==0
%! No error.
%! @item info==1
%! The model doesn't determine the current variables uniquely.
%! @item info==2
%! MJDGGES returned an error code.
%! @item info==3
%! Blanchard & Kahn conditions are not satisfied: no stable equilibrium.
%! @item info==4
%! Blanchard & Kahn conditions are not satisfied: indeterminacy.
%! @item info==5
%! Blanchard & Kahn conditions are not satisfied: indeterminacy due to rank failure.
%! @item info==6
%! The jacobian evaluated at the deterministic steady state is complex.
%! @item info==19
%! The steadystate routine thrown an exception (inconsistent deep parameters).
%! @item info==20
%! Cannot find the steady state, info(2) contains the sum of square residuals (of the static equations).
%! @item info==21
%! The steady state is complex, info(2) contains the sum of square of imaginary parts of the steady state.
%! @item info==22
%! The steady has NaNs.
%! @item info==23
%! M_.params has been updated in the steadystate routine and has complex valued scalars.
%! @item info==24
%! M_.params has been updated in the steadystate routine and has some NaNs.
%! @item info==30
%! Ergodic variance can't be computed.
%! @item info==41
%! At least one parameter is violating a lower bound condition.
%! @item info==42
%! At least one parameter is violating an upper bound condition.
%! @item info==43
%! The covariance matrix of the structural innovations is not positive definite.
%! @item info==44
%! The covariance matrix of the measurement errors is not positive definite.
%! @item info==45
%! Likelihood is not a number (NaN).
%! @item info==45
%! Likelihood is a complex valued number.
%! @end table
%! @item Model
%! Matlab's structure describing the model (initialized by dynare, see @ref{M_}).
%! @item DynareOptions
%! Matlab's structure describing the options (initialized by dynare, see @ref{options_}).
%! @item BayesInfo
%! Matlab's structure describing the priors (initialized by dynare, see @ref{bayesopt_}).
%! @item DynareResults
%! Matlab's structure gathering the results (initialized by dynare, see @ref{oo_}).
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 1
%! @ref{dynare_estimation_1}, @ref{mode_check}
%! @sp 2
%! @strong{This function calls:}
%! @sp 1
%! @ref{dynare_resolve}, @ref{lyapunov_symm}, @ref{priordens}
%! @end deftypefn
%@eod:

Houtan Bastani's avatar
Houtan Bastani committed
104
% Copyright (C) 2013 Dynare Team
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.

% AUTHOR(S) stephane DOT adjemian AT univ DASH lemans DOT fr
%           frederic DOT karame AT univ DASH lemans DOT fr

%global objective_function_penalty_base
% Declaration of the penalty as a persistent variable.
persistent init_flag
persistent restrict_variables_idx observed_variables_idx state_variables_idx mf0 mf1
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations

% Initialization of the returned arguments.
fval            = [];
ys              = [];
trend_coeff     = [];
exit_flag       = 1;

% Set the number of observed variables
nvobs = DynareDataset.info.nvobs;

%------------------------------------------------------------------------------
% 1. Get the structural parameters & define penalties
%------------------------------------------------------------------------------

% Return, with endogenous penalty, if some parameters are smaller than the lower bound of the prior domain.
%if (DynareOptions.mode_compute~=1) && any(xparam1<BayesInfo.lb)
%    k = find(xparam1(:) < BayesInfo.lb);
%    fval = objective_function_penalty_base+sum((BayesInfo.lb(k)-xparam1(k)).^2);
%    exit_flag = 0;
%    info = 41;
%    return
%end

% Return, with endogenous penalty, if some parameters are greater than the upper bound of the prior domain.
%if (DynareOptions.mode_compute~=1) && any(xparam1>BayesInfo.ub)
%    k = find(xparam1(:)>BayesInfo.ub);
%    fval = objective_function_penalty_base+sum((xparam1(k)-BayesInfo.ub(k)).^2);
%    exit_flag = 0;
%    info = 42;
%    return
%end

% Get the diagonal elements of the covariance matrices for the structural innovations (Q) and the measurement error (H).
Q = Model.Sigma_e;
H = Model.H;
for i=1:EstimatedParameters.nvx
    k =EstimatedParameters.var_exo(i,1);
    Q(k,k) = xparam1(i)*xparam1(i);
end
offset = EstimatedParameters.nvx;
if EstimatedParameters.nvn
    for i=1:EstimatedParameters.nvn
        k = EstimatedParameters.var_endo(i,1);
        H(k,k) = xparam1(i+offset)*xparam1(i+offset);
    end
    offset = offset+EstimatedParameters.nvn;
else
    H = zeros(nvobs);
end

% Get the off-diagonal elements of the covariance matrix for the structural innovations. Test if Q is positive definite.
if EstimatedParameters.ncx
    for i=1:EstimatedParameters.ncx
        k1 =EstimatedParameters.corrx(i,1);
        k2 =EstimatedParameters.corrx(i,2);
        Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
        Q(k2,k1) = Q(k1,k2);
    end
    % Try to compute the cholesky decomposition of Q (possible iff Q is positive definite)
%    [CholQ,testQ] = chol(Q);
%    if testQ
        % The variance-covariance matrix of the structural innovations is not definite positive. We have to compute the eigenvalues of this matrix in order to build the endogenous penalty.
%        a = diag(eig(Q));
%        k = find(a < 0);
%        if k > 0
%            fval = objective_function_penalty_base+sum(-a(k));
%            exit_flag = 0;
%            info = 43;
%            return
%        end
%    end
    offset = offset+EstimatedParameters.ncx;
end

% Get the off-diagonal elements of the covariance matrix for the measurement errors. Test if H is positive definite.
if EstimatedParameters.ncn
    for i=1:EstimatedParameters.ncn
        k1 = DynareOptions.lgyidx2varobs(EstimatedParameters.corrn(i,1));
        k2 = DynareOptions.lgyidx2varobs(EstimatedParameters.corrn(i,2));
        H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
        H(k2,k1) = H(k1,k2);
    end
    % Try to compute the cholesky decomposition of H (possible iff H is positive definite)
%    [CholH,testH] = chol(H);
%    if testH
        % The variance-covariance matrix of the measurement errors is not definite positive. We have to compute the eigenvalues of this matrix in order to build the endogenous penalty.
%        a = diag(eig(H));
%        k = find(a < 0);
%        if k > 0
%            fval = objective_function_penalty_base+sum(-a(k));
%            exit_flag = 0;
%            info = 44;
%            return
%        end
%    end
    offset = offset+EstimatedParameters.ncn;
end

% Update estimated structural parameters in Mode.params.
if EstimatedParameters.np > 0
    Model.params(EstimatedParameters.param_vals(:,1)) = xparam1(offset+1:end);
end

% Update Model.Sigma_e and Model.H.
Model.Sigma_e = Q;
Model.H = H;

%------------------------------------------------------------------------------
% 2. call model setup & reduction program
%------------------------------------------------------------------------------

% Linearize the model around the deterministic sdteadystate and extract the matrices of the state equation (T and R).
[T,R,SteadyState,info,Model,DynareOptions,DynareResults] = dynare_resolve(Model,DynareOptions,DynareResults,'restrict');

%if info(1) == 1 || info(1) == 2 || info(1) == 5
%    fval = objective_function_penalty_base+1;
%    exit_flag = 0;
%    return
%elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21
%    fval = objective_function_penalty_base+info(2);
%    exit_flag = 0;
%    return
%end

% Define a vector of indices for the observed variables. Is this really usefull?...
BayesInfo.mf = BayesInfo.mf1;

% Define the deterministic linear trend of the measurement equation.
if DynareOptions.noconstant
    constant = zeros(nvobs,1);
else
    if DynareOptions.loglinear
        constant = log(SteadyState(BayesInfo.mfys));
    else
        constant = SteadyState(BayesInfo.mfys);
    end
end

% Define the deterministic linear trend of the measurement equation.
if BayesInfo.with_trend
    trend_coeff = zeros(DynareDataset.info.nvobs,1);
    t = DynareOptions.trend_coeffs;
    for i=1:length(t)
        if ~isempty(t{i})
            trend_coeff(i) = evalin('base',t{i});
        end
    end
    trend = repmat(constant,1,DynareDataset.info.ntobs)+trend_coeff*[1:DynareDataset.info.ntobs];
else
    trend = repmat(constant,1,DynareDataset.info.ntobs);
end

% Get needed informations for kalman filter routines.
start = DynareOptions.presample+1;
np    = size(T,1);
mf    = BayesInfo.mf;
Y     = transpose(DynareDataset.rawdata);

%------------------------------------------------------------------------------
% 3. Initial condition of the Kalman filter
%------------------------------------------------------------------------------

% Get decision rules and transition equations.
dr = DynareResults.dr;

% Set persistent variables (first call).
if isempty(init_flag)
    mf0 = BayesInfo.mf0;
    mf1 = BayesInfo.mf1;
    restrict_variables_idx  = BayesInfo.restrict_var_list;
    observed_variables_idx  = restrict_variables_idx(mf1);
    state_variables_idx     = restrict_variables_idx(mf0);
    sample_size = size(Y,2);
    number_of_state_variables = length(mf0);
    number_of_observed_variables = length(mf1);
    number_of_structural_innovations = length(Q);
    init_flag = 1;
end

ReducedForm.ghx  = dr.ghx(restrict_variables_idx,:);
ReducedForm.ghu  = dr.ghu(restrict_variables_idx,:);
ReducedForm.ghxx = dr.ghxx(restrict_variables_idx,:);
ReducedForm.ghuu = dr.ghuu(restrict_variables_idx,:);
ReducedForm.ghxu = dr.ghxu(restrict_variables_idx,:);
ReducedForm.steadystate = dr.ys(dr.order_var(restrict_variables_idx));
ReducedForm.constant = ReducedForm.steadystate + .5*dr.ghs2(restrict_variables_idx);
ReducedForm.state_variables_steady_state = dr.ys(dr.order_var(state_variables_idx));
ReducedForm.Q = Q;
ReducedForm.H = H;
ReducedForm.mf0 = mf0;
ReducedForm.mf1 = mf1;

% Set initial condition for t=1
if observation_number==1 
    switch DynareOptions.particle.initialization
      case 1% Initial state vector covariance is the ergodic variance associated to the first order Taylor-approximation of the model.
        StateVectorMean = ReducedForm.constant(mf0);
        StateVectorVariance = lyapunov_symm(ReducedForm.ghx(mf0,:),ReducedForm.ghu(mf0,:)*ReducedForm.Q*ReducedForm.ghu(mf0,:)',1e-12,1e-12);
      case 2% Initial state vector covariance is a monte-carlo based estimate of the ergodic variance (consistent with a k-order Taylor-approximation of the model).
        StateVectorMean = ReducedForm.constant(mf0);
        old_DynareOptionsperiods = DynareOptions.periods;
        DynareOptions.periods = 5000;
        y_ = simult(oo_.steady_state, dr,Model,DynareOptions,DynareResults);
        y_ = y_(state_variables_idx,2001:5000);
        StateVectorVariance = cov(y_');
        DynareOptions.periods = old_DynareOptionsperiods;
        clear('old_DynareOptionsperiods','y_');
      case 3% Initial state vector covariance is a diagonal matrix.
        StateVectorMean = ReducedForm.constant(mf0);
        StateVectorVariance = DynareOptions.particle.initial_state_prior_std*eye(number_of_state_variables);
      otherwise
        error('Unknown initialization option!')
    end
    ReducedForm.StateVectorMean = StateVectorMean;
    ReducedForm.StateVectorVariance = StateVectorVariance;
end