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corrected bugs in extended path. The code works now with 

./tests/ep/linear.mod
time-shift
Michel Juillard 2012-03-04 20:59:57 +01:00
parent df324fddcc
commit bad8746e77
5 changed files with 125 additions and 82 deletions
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58
matlab/ep/extended_path.m
View File

@ -38,13 +38,25 @@ verbosity = options_.ep.verbosity+options_.ep.debug;
% Prepare a structure needed by the matlab implementation of the perfect foresight model solver
pfm.lead_lag_incidence = M_.lead_lag_incidence;
pfm.ny = M_.endo_nbr;
pfm.max_lag = M_.maximum_endo_lag;
pfm.nyp = nnz(pfm.lead_lag_incidence(1,:));
pfm.iyp = find(pfm.lead_lag_incidence(1,:)>0);
pfm.ny0 = nnz(pfm.lead_lag_incidence(2,:));
pfm.iy0 = find(pfm.lead_lag_incidence(2,:)>0);
pfm.nyf = nnz(pfm.lead_lag_incidence(3,:));
pfm.iyf = find(pfm.lead_lag_incidence(3,:)>0);
pfm.Sigma_e = M_.Sigma_e;
max_lag = M_.maximum_endo_lag;
pfm.max_lag = max_lag;
if pfm.max_lag > 0
pfm.nyp = nnz(pfm.lead_lag_incidence(1,:));
pfm.iyp = find(pfm.lead_lag_incidence(1,:)>0);
else
pfm.nyp = 0;
pfm.iyp = [];
end
pfm.ny0 = nnz(pfm.lead_lag_incidence(max_lag+1,:));
pfm.iy0 = find(pfm.lead_lag_incidence(max_lag+1,:)>0);
if M_.maximum_endo_lead
pfm.nyf = nnz(pfm.lead_lag_incidence(max_lag+2,:));
pfm.iyf = find(pfm.lead_lag_incidence(max_lag+2,:)>0);
else
pfm.nyf = 0;
pfm.iyf = [];
end
pfm.nd = pfm.nyp+pfm.ny0+pfm.nyf;
pfm.nrc = pfm.nyf+1;
pfm.isp = [1:pfm.nyp];
@ -55,9 +67,18 @@ pfm.iz = [1:pfm.ny+pfm.nyp+pfm.nyf];
pfm.periods = options_.ep.periods;
pfm.steady_state = oo_.steady_state;
pfm.params = M_.params;
pfm.i_cols_1 = nonzeros(pfm.lead_lag_incidence(2:3,:)');
pfm.i_cols_A1 = find(pfm.lead_lag_incidence(2:3,:)');
pfm.i_cols_T = nonzeros(pfm.lead_lag_incidence(1:2,:)');
if M_.maximum_endo_lead
pfm.i_cols_1 = nonzeros(pfm.lead_lag_incidence(max_lag+(1:2),:)');
pfm.i_cols_A1 = find(pfm.lead_lag_incidence(max_lag+(1:2),:)');
else
pfm.i_cols_1 = nonzeros(pfm.lead_lag_incidence(max_lag+1,:)');
pfm.i_cols_A1 = find(pfm.lead_lag_incidence(max_lag+1,:)');
end
if max_lag > 0
pfm.i_cols_T = nonzeros(pfm.lead_lag_incidence(1:2,:)');
else
pfm.i_cols_T = nonzeros(pfm.lead_lag_incidence(1,:)');
end
pfm.i_cols_j = 1:pfm.nd;
pfm.i_upd = pfm.ny+(1:pfm.periods*pfm.ny);
pfm.dynamic_model = str2func([M_.fname,'_dynamic']);
@ -239,8 +260,9 @@ while (t<sample_size)
% If the previous call to the perfect foresight model solver exited
% announcing that the routine converged, adapt the size of endo_simul_1
% and exo_simul_1.
endo_simul_1 = [ tmp , repmat(steady_state,1,ep.step) ];
exo_simul_1 = [ exo_simul_1 ; zeros(ep.step,size(shocks,2)) ];
endo_simul_1 = [endo_simul_1, repmat(steady_state,1,ep.step)];
endo_simul_1(:,t+1) = tmp;
exo_simul_1 = [exo_simul_1; zeros(ep.step,size(shocks,2))];
tmp_old = tmp;
else
% If the previous call to the perfect foresight model solver exited
@ -258,7 +280,10 @@ while (t<sample_size)
flag = 1;
end
if flag
[flag,tmp] = solve_perfect_foresight_model(endo_simul_1,exo_simul_1,pfm1);
[flag,tmp] = solve_stochastic_perfect_foresight_model(endo_simul_1,exo_simul_1,...
pfm1, ...
options_.ep.nnodes,...
options_.ep.order);
end
info_convergence = ~flag;
if info_convergence
@ -266,7 +291,7 @@ while (t<sample_size)
% change during the first periods.
% Compute the maximum deviation between old path and new path over the
% first periods
delta = max(max(abs(tmp(:,2:ep.fp)-tmp_old(:,2:ep.fp))));
delta = max(max(abs(tmp-tmp_old)));
if delta < dynatol.x
% If the maximum deviation is close enough to zero, reset the number
% of periods to ep.periods
@ -324,10 +349,7 @@ while (t<sample_size)
end
end
% Save results of the perfect foresight model solver.
time_series(:,t) = endo_simul_1(:,2);
oo_.endo_simul(:,1:end-1) = oo_.endo_simul(:,2:end);
oo_.endo_simul(:,1) = time_series(:,t);
oo_.endo_simul(:,end) = oo_.steady_state;
time_series(:,t) = tmp;
end% (while) loop over t
dyn_waitbar_close(hh);

131
matlab/solve_stochastic_perfect_foresight_model.m
View File

@ -24,15 +24,19 @@ function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model(endo_s
number_of_shocks = size(exo_simul,2);
[nodes,weights] = gauss_hermite_weights_and_nodes(nnodes);
if number_of_shocks>1
nodes = repmat(nodes,1,number_of_shocks)*chol(pfm.Sigma_e);
% to be fixed for Sigma ~= I
for i=1:number_of_shocks
rr(i) = {nodes};
rr(i) = {nodes(:,i)};
ww(i) = {weights};
end
nodes = cartesian_product_of_sets(rr{:});
weights = prod(cartesian_product_of_sets(ww{:}),2);
nnodes = nnodes^number_of_shocks;
else
nodes = nodes*sqrt(pfm.Sigma_e);
end
innovations = zeros(periods+2,number_of_shocks);
@ -58,111 +62,118 @@ function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model(endo_s
% The columns of A map the elements of Y such that
% each block of Y with ny rows are unfolded column wise
dimension = ny*(sum(nnodes.^(0:order-1),2)+(periods-order)*world_nbr);
A = sparse([],[],[],dimension,dimension,(periods+2)*world_nbr*nnz(jacobian));
res = zeros(dimension,1);
if order == 0
i_upd = ny+(1:ny*periods);
else
i_upd = zeros(dimension,1);
i_upd(1:ny) = ny+(1:ny);
i1 = ny+1;
i2 = periods*ny;
i2 = 2*ny;
n1 = 2*ny+1;
n2 = (periods+1)*ny;
for i=1:order
for j=1:nnodes
i_upd(i1:i2) = n1:n2;
n1 = n2+(i+2)*ny+1;
n2 = n2+ny*(periods+2);
n2 = 3*ny;
for i=2:periods
k = n1:n2;
for j=1:nnodes^min(i-1,order)
i_upd(i1:i2) = (n1:n2)+(j-1)*ny*(periods+2);
i1 = i2+1;
i2 = i1+n2-n1;
i2 = i2+ny;
end
n1 = n2+1;
n2 = n2+ny;
end
end
h1 = clock;
for iter = 1:maxit
h2 = clock;
A = sparse([],[],[],dimension,dimension,(periods+2)*world_nbr*nnz(jacobian));
res = zeros(dimension,1);
i_rows = 1:ny;
i_cols = find(lead_lag_incidence');
i_cols_p = i_cols(1:nyp);
i_cols_s = i_cols(nyp+1:nyp+ny);
i_cols_f = i_cols(nyp+ny+1:nyp+ny+nyf);
i_cols_s = i_cols(nyp+(1:ny));
i_cols_f = i_cols(nyp+ny+(1:nyf));
i_cols_A = i_cols;
i_cols_Ap = i_cols_p;
i_cols_As = i_cols_s;
i_cols_Af = i_cols_f;
i_cols_Af = i_cols_f - ny;
for i = 1:periods
if i <= order+1
i_w_p = 1;
i_w_f = (1:nnodes);
if i == 1
i_cols_A = i_cols_A1;
elseif i == 2
i_cols_A = [ i_cols_Ap;
i_cols_As;
i_cols_Af + (nnodes-1)*ny];
else
i_cols_A = [ i_cols_Ap + sum(nnodes^(0:i-3))*ny;
i_cols_As + (sum(nnodes^(0:i-2))-1)*ny;
i_cols_Af + (sum(nnodes^(0:i))-2)*ny];
end
for j = 1:nnodes^(i-1)
innovation = exo_simul;
if i > 1
innovation(i+1,:) = nodes(mod(j-1,nnodes)+1,:);
end
if i <= order
y = [Y(i_cols_p,i_w_p);
Y(i_cols_s,j);
Y(i_cols_f,i_w_f)*weights];
for k=1:nnodes
y = [Y(i_cols_p,i_w_p);
Y(i_cols_s,j);
Y(i_cols_f,(j-1)*nnodes+k)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A(i_rows,i_cols_A) = A(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A(i_rows,i_cols_A) = A(i_rows,i_cols_A) + weights(k)*jacobian(:,i_cols_j);
end
res(i_rows) = res(i_rows)+weights(k)*d1;
i_cols_Af = i_cols_Af + ny;
end
else
y = [Y(i_cols_p,i_w_p);
Y(i_cols_s,j);
Y(i_cols_f,j)];
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
i_cols_A = [i_cols_As - ny; i_cols_Af];
A(i_rows,i_cols_A) = jacobian(:,i_cols_1);
else
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
end
res(i_rows) = d1;
i_cols_Af = i_cols_Af + ny;
end
innovation = exo_simul;
if i > 1
innovation(i+1,:) = nodes(mod(j,nnodes)+1,:);
end
[d1,jacobian] = dynamic_model(y,innovation,params,steady_state,i+1);
if i == 1
% in first period we don't keep track of
% predetermined variables
A(i_rows,i_cols_A) = jacobian(:,i_cols_1);
else
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
end
res(i_rows) = d1;
i_rows = i_rows + ny;
i_cols_A = i_cols_A + ny;
if mod(j,nnodes) == 0
i_w_p = i_w_p + 1;
end
i_w_f = i_w_f + nnodes;
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
if i > 1
if mod(j,nnodes) == 0
i_cols_Ap = i_cols_Ap + ny;
end
i_cols_As = i_cols_As + ny;
end
end
i_cols_p = i_cols_p + ny;
i_cols_s = i_cols_s + ny;
i_cols_f = i_cols_f + ny;
elseif i == periods
if i == order+2
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
end
for j=1:world_nbr
[d1,jacobian] = dynamic_model(Y(i_cols,j),exo_simul,params,steady_state,i+1);
[d1,jacobian] = dynamic_model(Y(i_cols,j),exo_simul, ...
params,steady_state,i+1);
A(i_rows,i_cols_A(i_cols_T)) = jacobian(:,i_cols_T);
res(i_rows) = d1;
i_rows = i_rows + ny;
i_cols_A = i_cols_A + ny;
end
else
if i == 2
i_cols_A = find(lead_lag_incidence');
if i == order+2
i_cols_A = [i_cols_Ap; i_cols_As; i_cols_Af];
end
for j=1:world_nbr
[d1,jacobian] = dynamic_model(Y(i_cols,j), ...
exo_simul,params,steady_state,i+1);
if i == 1
% this happens only with order == 0
% in first period we don't keep track of
% predetermined variables
A(i_rows,i_cols_A1) = jacobian(:,i_cols_1);
else
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
end
A(i_rows,i_cols_A) = jacobian(:,i_cols_j);
res(i_rows) = d1;
i_rows = i_rows + ny;
i_cols_A = i_cols_A + ny;
@ -181,7 +192,7 @@ function [flag,endo_simul,err] = solve_stochastic_perfect_foresight_model(endo_s
fprintf('\n') ;
end
flag = 0;% Convergency obtained.
endo_simul = reshape(Y,ny,periods+2);
endo_simul = Y(ny+(1:ny),1);
break
end
dy = -A\res;

6
tests/ep/ar.mod
View File

@ -33,6 +33,8 @@ steady;
options_.ep.verbosity = 0;
options_.ep.stochastic = 0;
options_.ep.order = 0;
options_.ep.nnodes = 0;
options_.console_mode = 0;
@ -41,9 +43,11 @@ ts = extended_path([],1000);
options_.ep.verbosity = 0;
options_.ep.stochastic = 1;
options_.ep.order = 1;
options_.ep.nnodes = 5;
options_.console_mode = 0;
sts = extended_path([],1000);
sts = extended_path([],100);
if max(max(abs(ts-sts)))>1e-12

8
tests/ep/linear.mod
View File

@ -29,12 +29,16 @@ steady;
options_.maxit_ = 100;
options_.ep.verbosity = 0;
options_.ep.stochastic.status = 0;
options_.ep.order = 0;
options_.ep.nnodes = 0;
options_.console_mode = 0;
ts = extended_path([],1000);
ts = extended_path([],100);
options_.ep.stochastic.status = 1;
sts = extended_path([],1000);
options_.ep.order = 1;
options_.ep.nnodes = 3;
sts = extended_path([],100);
if max(max(abs(ts-sts))) > 1e-12
error('extended path algorithm fails in ./tests/ep/linear.mod')

4
tests/ep/rbc.mod
View File

@ -53,6 +53,8 @@ end;
steady;
options_.ep.verbosity = 0;
options_.ep.order = 1;
options_.ep.nnodes = 2;
options_.console_mode = 0;
ts = extended_path([],1000);
ts = extended_path([],100);