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Fixed ordering of variables in error correction term of PAC equation 

PAC equation has to be written as

diff(x) = a0*(xstar(-1)-x(-1)) + a1*diff(x(-1)) + ... + ap*diff(x(-p)) + PAC_EXPECTATION(pacmodelname) + ...;

In the error correction term, a0*(xstar(-1)-x(-1)), we must have the difference
between the target (the trend xstar(-1)) and the level of the endogenous
variable (x(-1)). To ensure stability around the trend, the parameter a0 needs
to be positive.

REMARKS

 [1] In the TREND_COMPONENT_MODEL the error correction terms are written in
 reverse order, ie as the difference betwwen the level of the endogenous
 variable and the trend variable.

 [2] In the estimation routine we do not constrain a0 to be positive, but is
 would surely help to satisfy this condition in the initial condition.
time-shift
Stéphane Adjemian(Charybdis) 2018-09-06 22:07:31 +02:00
parent 74ef4d2131
commit 0f3678ec4a
4 changed files with 21 additions and 8 deletions
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11
matlab/+pac/+estimate/iterative_ols.m
View File

@ -83,9 +83,18 @@ if ~isempty(M_.pac.(pacmodl).h1_param_indices)
end
end
% Reorder ec.vars locally if necessary. Second variable must be the
% endogenous variable, while the first must be the associated trend.
if M_.pac.(pacmodl).ec.isendo(2)
ecvars = M_.pac.(pacmodl).ec.vars;
else
ecvars = flip(M_.pac.(pacmodl).ec.vars);
end
% Build matrix for EC and AR terms.
DataForOLS = dseries();
DataForOLS{'ec-term'} = data{M_.endo_names{M_.pac.(pacmodl).ec.vars(2)}}.lag(1)-data{M_.endo_names{M_.pac.(pacmodl).ec.vars(1)}}.lag(1);
% Error correction term is trend minus the level of the endogenous variable.
DataForOLS{'ec-term'} = data{M_.endo_names{ecvars(1)}}.lag(1)-data{M_.endo_names{ecvars(2)}}.lag(1);
listofvariables3 = {'ec-term'};
xparm = { M_.param_names(M_.pac.(pacmodl).ec.params(1))};
for i = 1:length(M_.pac.(pacmodl).ar.params)

7
matlab/+pac/+estimate/nls.m
View File

@ -44,6 +44,13 @@ global M_ oo_
[pacmodl, lhs, rhs, pnames, enames, xnames, pid, eid, xid, ~, ipnames_, params, data, islaggedvariables] = ...
pac.estimate.init(M_, oo_, eqname, params, data, range);
% Check that the error correction term is correct.
if M_.pac.(pacmodl).ec.isendo(1)
error(['\nThe error correction term in PAC equation (%s) is not correct.\nThe ' ...
'error correction term should be the difference between a trend\n' ...
'and the level of the endogenous variable.'], pacmodl);
end
% List of objects to be replaced
objNames = [pnames; enames; xnames];
objIndex = [pid; eid; xid];

9
matlab/+pac/+update/parameters.m
View File

@ -65,7 +65,7 @@ end
pacvalues = DynareModel.params([pacmodel.ec.params; pacmodel.ar.params(1:pacmodel.max_lag)']);
% Get the indices for the stationary/nonstationary variables in the VAR system.
id = find(strcmp(DynareModel.endo_names{pacmodel.ec.vars(2)}, varmodel.list_of_variables_in_companion_var));
id = find(strcmp(DynareModel.endo_names{pacmodel.ec.vars(find(~pacmodel.ec.isendo))}, varmodel.list_of_variables_in_companion_var));
if isempty(id)
% Find the auxiliary variables if any
@ -75,14 +75,11 @@ if isempty(id)
else
for i=1:length(ad)
auxinfo = DynareModel.aux_vars(get_aux_variable_id(varmodel.list_of_variables_in_companion_var{ad(i)}));
if isequal(auxinfo.endo_index, pacmodel.ec.vars(2))
% /!\ First element of ec.vars is the level of the endogenous
% variable in the PAC equation, the second element
% is the target variable.
if isequal(auxinfo.endo_index, pacmodel.ec.vars(find(~pacmodel.ec.isendo)))
id = ad(i);
break
end
if isequal(auxinfo.type, 8) && isequal(auxinfo.orig_index, pacmodel.ec.vars(2))
if isequal(auxinfo.type, 8) && isequal(auxinfo.orig_index, pacmodel.ec.vars(find(~pacmodel.ec.isendo)))
id = ad(i);
break
end

2
preprocessor

@ -1 +1 @@
Subproject commit 27c9a9a5e03e05396b3df1a69351e44b11e5993b
Subproject commit e19a14869eae4f2ed1571446c543ee39726421d8