diff --git a/doc/manual/source/the-model-file.rst b/doc/manual/source/the-model-file.rst
index 1616d5b3ce193cdcebf1c0bc190bff632648fdea..b77d1320c4f9de35accc0b02ae79864f87350ec7 100644
--- a/doc/manual/source/the-model-file.rst
+++ b/doc/manual/source/the-model-file.rst
@@ -14709,7 +14709,7 @@ simply add the exogenous variables to the PAC equation (without the weight
``trend_component_model``, to compute the VAR based expectations for the
expected changes in the target, *i.e.* to evaluate
:math:`\sum_{i=0}^{\infty} d_i \Delta y^{\star}_{t+i}`. The infinite sum
- will then be replaced by a linear combination of the variables involved in
+ will then be replaced by a linear combination, defined by a vector :math:`h`, of the variables involved in
the companion representation of the auxiliary model. The weights defining
the linear combination are nonlinear functions of the
:math:`(a_i)_{i=0}^{m-1}` coefficients in the PAC equation. This option is
@@ -14729,6 +14729,16 @@ simply add the exogenous variables to the PAC equation (without the weight
or expression is given) is consistent with the asymptotic growth rate of the
endogenous variable.
+ .. option:: kind = dd | dl
+
+ Instructs Dynare how to compute the vector :math:`h`, the weights
+ defining the linear combination of the companion VAR
+ variables. The default value ``dd`` must be used if the target
+ appears in first difference in the auxiliary model, see equation
+ (A.79) in *Brayton et alii (2000)*, while value ``dl`` must be
+ used if the target shows up in level in the auxiliary model,
+ equation (A.74) in *Brayton et alii (2000)*.
+
.. operator:: pac_expectation (NAME_OF_PAC_MODEL);
@@ -14739,7 +14749,89 @@ simply add the exogenous variables to the PAC equation (without the weight
the variables involved in the companion representation of the auxiliary model
or by a recursive forward equation.
- |br|
+
+The PAC equation target can be composite and defined as a weighted sum
+of stationary and non stationary components. Such a target requires an
+additional equation in the model block, with the target variable on
+the left hand-side and the components in the right hand-side. Each
+component must be an endogenous variable in the auxiliary model. The
+characteristics of each component must be described in the
+``pac_target_info`` block, see below, and the
+``pac_target_nonstationary`` operator must be used in the error
+correction term of the PAC equation to link the target to the provided
+description. Note that composite targets make only sense if the
+auxiliary model is not a trend component model (where all the
+variables are non stationary).
+
+.. block:: pac_target_info (NAME_OF_PAC_MODEL);
+
+ |br| This block enables the user to provide the properties of each
+ component of a target in PAC models with a composite target. The
+ ``NAME_OF_PAC_MODEL`` argument refers to a PAC model (must match
+ the value of option ``model_name`` in the declaration of a PAC
+ model).
+
+ On the first line of the block, the name of the composite target
+ variable must be provided using the following syntax::
+
+ target VARIABLE_NAME ;
+
+ where ``VARIABLE_NAME`` is a declared endogenous variable, its
+ associated equation is not part of the auxiliary model but all the
+ components (the variables on the right hand-side) must be defined
+ in the auxiliary model. Next, the following line declares the name
+ of the auxilary variable that will appear in the error correction
+ term, this variable contains only the non stationary components of
+ the target::
+
+ auxname_target_nonstationary NAME ;
+
+ The block should contain the following group of lines for each
+ stationary component::
+
+ component STATIONARY_VARIABLE_NAME ;
+ kind ll ;
+ auxname AUX_VAR_NAME ;
+
+
+ where ``STATIONARY_VARIABLE_NAME`` is the name of a stationary
+ variable appearing in the right hand-side of the equation defining
+ the target ``VARIABLE_NAME``. The second line instructs Dynare that
+ the component appears in levels in the auxiliary model and in the
+ PAC expectations. The third line specifies the name of the
+ auxiliary variable created by Dynare for the component of the PAC
+ expectation related to ``STATIONARY_VARIABLE_NAME``.
+
+ The block should contain the following group of lines for each
+ nonstationary component::
+
+ component NONSTATIONARY_VARIABLE_NAME ;
+ kind dd | dl ;
+ auxname AUX_VAR_NAME ;
+ growth PARAMETER_NAME | VARIABLE_NAME | EXPRESSION | DOUBLE ;
+
+ where ``NONSTATIONARY_VARIABLE_NAME`` is the name of a
+ nonstationary variable appearing in the right hand-side of the
+ equation defining the target ``VARIABLE_NAME``. The second line
+ instructs Dynare on how to calculate the weights that define the linear
+ combination of the companion VAR variables. Use value ``dd`` if the
+ target appears in first difference in the auxiliary model, or
+ ``dl`` if the target shows up in level in the auxiliary model. The
+ third line sets the name of the auxiliary variable created by
+ Dynare for the component of the PAC expectation related to
+ ``NONSTATIONARY_VARIABLE_NAME``. The fourth line is mandatory if a
+ growth neutrality correction is required. The provided value for
+ this option must be consistent with the asymptotic growth rate of
+ the PAC endogenous variable.
+
+
+.. operator:: pac_target_nonstationary (NAME_OF_PAC_MODEL);
+
+ |br| This operator is only required in presence of a composite
+ target in the PAC equation. The operator, used in the error
+ correction term of the PAC equation, selects the non stationary
+ components of the target.
+
.. matcomm:: pac.initialize(NAME_OF_PAC_MODEL);
.. matcomm:: pac.update(NAME_OF_PAC_MODEL);
@@ -14752,33 +14844,33 @@ simply add the exogenous variables to the PAC equation (without the weight
the infinite sum in the MCE case).
-*Example*
+*Example (trend component auxiliary model)*
::
trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']);
- pac_model(auxiliary_model_name=toto, discount=beta, growth=diff(x1(-1)), model_name=pacman);
+ pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
model;
- [name='eq:y']
- y = rho_1*y(-1) + rho_2*y(-2) + ey;
+ [name='eq:y']
+ y = (1-rho_1-rho_2)*diff(x2(-1)) + rho_1*y(-1) + rho_2*y(-2) + ey;
- [name='eq:x1']
- diff(x1) = a_x1_0*(x1(-1)-x1bar(-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:x1']
+ diff(x1) = a_x1_0*(x1(-1)-x1bar(-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']
- 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:x2']
+ 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']
- x1bar = x1bar(-1) + ex1bar;
+ [name='eq:x1bar']
+ x1bar = x1bar(-1) + ex1bar;
- [name='eq:x2bar']
- x2bar = x2bar(-1) + ex2bar;
+ [name='eq:x2bar']
+ x2bar = x2bar(-1) + ex2bar;
- [name='zpac']
- diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+ [name='zpac']
+ diff(z) = e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
end;
@@ -14787,6 +14879,51 @@ simply add the exogenous variables to the PAC equation (without the weight
pac.update.expectation('pacman');
+*Example (VAR auxiliary model and composite target)*
+
+ ::
+
+ var_model(model_name=toto, eqtags=['eq:x', 'eq:y']);
+
+ pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
+
+ pac_target_info(pacman);
+
+ target v;
+ auxname_target_nonstationary vns;
+
+ component y;
+ auxname pv_y_;
+ kind ll;
+
+ component x;
+ growth diff(x(-1));
+ auxname pv_dx_;
+ kind dd;
+
+ end;
+
+ model;
+
+ [name='eq:y']
+ y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
+
+
+ [name='eq:x']
+ diff(x) = b_x_1*y(-2) + b_x_2*diff(x(-1)) + ex ;
+
+ [name='eq:v']
+ v = x + d_y*y ; // Composite PAC target, no residuals here only variables defined in the auxiliary model.
+
+ [name='zpac']
+ diff(z) = e_c_m*(pac_target_nonstationary(pacman)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
+
+ end;
+
+ pac.initialize('pacman');
+
+ pac.update.expectation('pacman');
+
Estimation of a PAC equation
----------------------------
diff --git a/doc/manual/utils/dynare_lex.py b/doc/manual/utils/dynare_lex.py
index 855d1befea3760cf91772fa988563644d3ece3ef..be4706fe5e98a4b078f2b9f519fec588ac041cb3 100644
--- a/doc/manual/utils/dynare_lex.py
+++ b/doc/manual/utils/dynare_lex.py
@@ -60,7 +60,7 @@ class DynareLexer(RegexLexer):
"addSeries","addParagraph","addVspace","write","compile")
operators = (
- "STEADY_STATE","EXPECTATION","var_expectation","pac_expectation")
+ "STEADY_STATE","EXPECTATION","var_expectation","pac_expectation","pac_target_nonstationary")
macro_dirs = (
"@#includepath", "@#include", "@#define", "@#if",
@@ -83,7 +83,8 @@ class DynareLexer(RegexLexer):
'osr_params_bounds','ramsey_constraints','irf_calibration',
'moment_calibration','identification','svar_identification',
'matched_moments','occbin_constraints','surprise','overwrite','bind','relax',
- 'verbatim','end','node','cluster','paths','hooks'), prefix=r'\b', suffix=r'\s*\b'),Keyword.Reserved),
+ 'verbatim','end','node','cluster','paths','hooks','target','pac_target_info','auxname_target_nonstationary',
+ 'component', 'growth', 'auxname', 'kind'), prefix=r'\b', suffix=r'\s*\b'),Keyword.Reserved),
# FIXME: Commands following multiline comments are not highlighted properly.
(words(commands + report_commands,