PAC: rethink the relation between PacModelTable and DynamicModel classes

pac-components
Sébastien Villemot 2021-10-27 18:17:14 +02:00
parent 127361971f
commit 37a6ed6261
No known key found for this signature in database
GPG Key ID: 2CECE9350ECEBE4A
4 changed files with 444 additions and 444 deletions

View File

@ -50,9 +50,6 @@ DynamicModel::copyHelper(const DynamicModel &m)
blocks_derivatives_exo.emplace_back(convert_block_derivative(it));
for (const auto &it : m.blocks_derivatives_exo_det)
blocks_derivatives_exo_det.emplace_back(convert_block_derivative(it));
for (const auto &[key, expr] : m.pac_expectation_substitution)
pac_expectation_substitution.emplace(key, f(expr));
}
DynamicModel::DynamicModel(SymbolTable &symbol_table_arg,
@ -108,15 +105,7 @@ DynamicModel::DynamicModel(const DynamicModel &m) :
blocks_jacob_cols_other_endo{m.blocks_jacob_cols_other_endo},
blocks_jacob_cols_exo{m.blocks_jacob_cols_exo},
blocks_jacob_cols_exo_det{m.blocks_jacob_cols_exo_det},
var_expectation_functions_to_write{m.var_expectation_functions_to_write},
pac_mce_alpha_symb_ids{m.pac_mce_alpha_symb_ids},
pac_h0_indices{m.pac_h0_indices},
pac_h1_indices{m.pac_h1_indices},
pac_mce_z1_symb_ids{m.pac_mce_z1_symb_ids},
pac_eqtag_and_lag{m.pac_eqtag_and_lag},
pac_growth_neutrality_params{m.pac_growth_neutrality_params},
pac_model_info{m.pac_model_info},
pac_equation_info{m.pac_equation_info}
var_expectation_functions_to_write{m.var_expectation_functions_to_write}
{
copyHelper(m);
}
@ -173,16 +162,6 @@ DynamicModel::operator=(const DynamicModel &m)
var_expectation_functions_to_write = m.var_expectation_functions_to_write;
pac_mce_alpha_symb_ids = m.pac_mce_alpha_symb_ids;
pac_h0_indices = m.pac_h0_indices;
pac_h1_indices = m.pac_h1_indices;
pac_mce_z1_symb_ids = m.pac_mce_z1_symb_ids;
pac_eqtag_and_lag = m.pac_eqtag_and_lag;
pac_expectation_substitution.clear();
pac_growth_neutrality_params = m.pac_growth_neutrality_params;
pac_model_info = m.pac_model_info;
pac_equation_info = m.pac_equation_info;
copyHelper(m);
return *this;
@ -3003,237 +2982,6 @@ DynamicModel::writeDriverOutput(ostream &output, const string &basename, bool bl
for (int i = 1; i < static_cast<int>(NNZDerivatives.size()); i++)
output << (i > computed_derivs_order ? -1 : NNZDerivatives[i]) << "; ";
output << "];" << endl;
// Write Pac Model Consistent Expectation parameter info
for (auto &it : pac_mce_alpha_symb_ids)
{
output << "M_.pac." << it.first.first << ".equations." << it.first.second << ".mce.alpha = [";
for (auto it : it.second)
output << symbol_table.getTypeSpecificID(it) + 1 << " ";
output << "];" << endl;
}
// Write Pac Model Consistent Expectation Z1 info
for (auto &it : pac_mce_z1_symb_ids)
output << "M_.pac." << it.first.first << ".equations." << it.first.second << ".mce.z1 = "
<< symbol_table.getTypeSpecificID(it.second) + 1 << ";" << endl;
// Write Pac lag info
for (auto &it : pac_eqtag_and_lag)
output << "M_.pac." << it.first.first << ".equations." << it.second.first << ".max_lag = " << it.second.second << ";" << endl;
// Write Pac equation tag info
map<string, vector<pair<string, string>>> for_writing;
for (auto &it : pac_eqtag_and_lag)
for_writing[it.first.first].emplace_back(it.first.second, it.second.first);
for (auto &it : for_writing)
{
output << "M_.pac." << it.first << ".tag_map = [";
for (auto &it1 : it.second)
output << "{'" << it1.first << "', '" << it1.second << "'};";
output << "];" << endl;
}
for (auto &[model, growth_neutrality_param_index] : pac_growth_neutrality_params)
output << "M_.pac." << model << ".growth_neutrality_param_index = "
<< symbol_table.getTypeSpecificID(growth_neutrality_param_index) + 1 << ";" << endl;
for (auto &[model, values] : pac_model_info)
{
auto &[lhs, aux_model_type] = values;
output << "M_.pac." << model << ".lhs = [";
for (auto it : lhs)
output << it + 1 << " ";
output << "];" << endl;
output << "M_.pac." << model << ".auxiliary_model_type = '" << aux_model_type << "';" << endl;
}
for (auto &pit : pac_equation_info)
{
auto [lhs_pac_var, optim_share_index, ar_params_and_vars, ec_params_and_vars, non_optim_vars_params_and_constants, additive_vars_params_and_constants, optim_additive_vars_params_and_constants] = pit.second;
string substruct = pit.first.first + ".equations." + pit.first.second + ".";
output << "M_.pac." << substruct << "lhs_var = "
<< symbol_table.getTypeSpecificID(lhs_pac_var.first) + 1 << ";" << endl;
if (optim_share_index >= 0)
output << "M_.pac." << substruct << "share_of_optimizing_agents_index = "
<< symbol_table.getTypeSpecificID(optim_share_index) + 1 << ";" << endl;
output << "M_.pac." << substruct << "ec.params = "
<< symbol_table.getTypeSpecificID(ec_params_and_vars.first) + 1 << ";" << endl
<< "M_.pac." << substruct << "ec.vars = [";
for (auto it : ec_params_and_vars.second)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ec.istarget = [";
for (auto it : ec_params_and_vars.second)
output << (get<1>(it) ? "true " : "false ");
output << "];" << endl
<< "M_.pac." << substruct << "ec.scale = [";
for (auto it : ec_params_and_vars.second)
output << get<2>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ec.isendo = [";
for (auto it : ec_params_and_vars.second)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "ar.params = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << (pid != -1 ? symbol_table.getTypeSpecificID(pid) + 1 : -1) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ar.vars = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << (vid != -1 ? symbol_table.getTypeSpecificID(vid) + 1 : -1) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ar.lags = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << vlag << " ";
output << "];" << endl;
if (!non_optim_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "non_optimizing_behaviour.params = [";
for (auto &it : non_optim_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.vars = [";
for (auto &it : non_optim_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.isendo = [";
for (auto &it : non_optim_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.lags = [";
for (auto &it : non_optim_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.scaling_factor = [";
for (auto &it : non_optim_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
if (!additive_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "additive.params = [";
for (auto &it : additive_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.vars = [";
for (auto &it : additive_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.isendo = [";
for (auto &it : additive_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "additive.lags = [";
for (auto &it : additive_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.scaling_factor = [";
for (auto &it : additive_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
if (!optim_additive_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "optim_additive.params = [";
for (auto &it : optim_additive_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.vars = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.isendo = [";
for (auto &it : optim_additive_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.lags = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.scaling_factor = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
// Create empty h0 and h1 substructures that will be overwritten later if not empty
output << "M_.pac." << substruct << "h0_param_indices = [];" << endl
<< "M_.pac." << substruct << "h1_param_indices = [];" << endl;
}
for (auto &it : pac_h0_indices)
{
output << "M_.pac." << it.first.first << ".equations." << it.first.second << ".h0_param_indices = [";
for (auto it1 : it.second)
output << symbol_table.getTypeSpecificID(it1) + 1 << " ";
output << "];" << endl;
}
for (auto &it : pac_h1_indices)
{
output << "M_.pac." << it.first.first << ".equations." << it.first.second << ".h1_param_indices = [";
for (auto it1 : it.second)
output << symbol_table.getTypeSpecificID(it1) + 1 << " ";
output << "];" << endl;
}
}
void
@ -3899,11 +3647,9 @@ DynamicModel::getUndiffLHSForPac(const string &aux_model_name,
return lhs;
}
map<pair<string, string>, pair<string, int>>
DynamicModel::walkPacParameters(const string &name)
void
DynamicModel::analyzePacEquationStructure(const string &name, map<pair<string, string>, pair<string, int>> &eqtag_and_lag, PacModelTable::equation_info_t &pac_equation_info)
{
map<pair<string, string>, pair<string, int>> eqtag_and_lag;
int i = 0;
for (auto &equation : equations)
{
@ -3978,12 +3724,12 @@ DynamicModel::walkPacParameters(const string &name)
}
if (lhs.first == -1)
{
cerr << "walkPacParameters: error obtaining LHS variable." << endl;
cerr << "analyzePacEquationStructure: error obtaining LHS variable." << endl;
exit(EXIT_FAILURE);
}
if (ec_params_and_vars.second.empty())
{
cerr << "walkPacParameters: error obtaining RHS parameters." << endl;
cerr << "analyzePacEquationStructure: error obtaining RHS parameters." << endl;
exit(EXIT_FAILURE);
}
string eq = "eq" + to_string(i++);
@ -3996,7 +3742,6 @@ DynamicModel::walkPacParameters(const string &name)
eqtag_and_lag[{name, eqtag}] = {eq, max_lag};
}
}
return eqtag_and_lag;
}
int
@ -4038,37 +3783,12 @@ DynamicModel::getPacTargetSymbId(const string &pac_model_name) const
throw PacTargetNotIdentifiedException{pac_model_name, "No equation with the corresponding pac_expectation operator"};
}
void
DynamicModel::declarePacModelConsistentExpectationEndogs(const string &name)
{
int i = 0;
for (auto &equation : equations)
if (equation->containsPacExpectation(name))
{
if (!equation_tags.exists(&equation - &equations[0], "name"))
{
cerr << "Every equation with a pac expectation must have been assigned an equation tag name" << endl;
exit(EXIT_FAILURE);
}
string standard_eqtag = "eq" + to_string(i++);
try
{
pac_mce_z1_symb_ids[{name, standard_eqtag}]
= symbol_table.addSymbol("mce_Z1_" + name + "_" + standard_eqtag, SymbolType::endogenous);
}
catch (SymbolTable::AlreadyDeclaredException &e)
{
cerr << "Variable name needed by PAC (mce_Z1_" << name << "_" << standard_eqtag << endl;
exit(EXIT_FAILURE);
}
}
}
void
DynamicModel::addPacModelConsistentExpectationEquation(const string &name, int discount_symb_id,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
ExprNode::subst_table_t &diff_subst_table,
expr_t growth)
map<pair<string, string>, int> &pac_mce_z1_symb_ids,
map<pair<string, string>, vector<int>> &pac_mce_alpha_symb_ids)
{
int pac_target_symb_id;
try
@ -4080,43 +3800,53 @@ DynamicModel::addPacModelConsistentExpectationEquation(const string &name, int d
cerr << "Can't identify target for PAC model " << name << ": " << e.message;
exit(EXIT_FAILURE);
}
pac_eqtag_and_lag.insert(eqtag_and_lag.begin(), eqtag_and_lag.end());
int neqs = 0;
for (auto &it : eqtag_and_lag)
for (const auto &[key, val] : eqtag_and_lag)
{
assert(it.first.first == name);
string eqtag = it.first.second;
string standard_eqtag = it.second.first;
int pac_max_lag_m = it.second.second + 1;
auto &[name2, eqtag] = key;
if (name2 != name)
continue;
auto &standard_eqtag = val.first;
int pac_max_lag_m = val.second + 1;
string append_to_name = name + "_" + standard_eqtag;
if (pac_mce_z1_symb_ids.find({name, standard_eqtag}) == pac_mce_z1_symb_ids.end())
// Create the endogenous representing Z₁
int mce_z1_symb_id;
string varname = "mce_Z1_" + append_to_name;
try
{
cerr << "Error finding pac MCE Z1 symb id" << endl;
mce_z1_symb_id = symbol_table.addSymbol(varname, SymbolType::endogenous);
}
catch (SymbolTable::AlreadyDeclaredException &e)
{
cerr << "The variable/parameter '" << varname << "' conflicts with the variable that will be generated for the Z_1 variable of the '" << name << "' PAC model. Please rename it." << endl;
exit(EXIT_FAILURE);
}
int mce_z1_symb_id = pac_mce_z1_symb_ids[{name, standard_eqtag}];
pac_mce_z1_symb_ids[{name, standard_eqtag}] = mce_z1_symb_id;
expr_t A = One;
expr_t fp = Zero;
expr_t beta = AddVariable(discount_symb_id);
for (int i = 1; i <= pac_max_lag_m; i++)
try
{
int alpha_i_symb_id = symbol_table.addSymbol("mce_alpha_" + append_to_name + "_" + to_string(i),
SymbolType::parameter);
pac_mce_alpha_symb_ids[{name, standard_eqtag}].push_back(alpha_i_symb_id);
A = AddPlus(A, AddVariable(alpha_i_symb_id));
fp = AddPlus(fp,
AddTimes(AddTimes(AddVariable(alpha_i_symb_id),
AddPower(beta, AddPossiblyNegativeConstant(i))),
AddVariable(mce_z1_symb_id, i)));
}
catch (SymbolTable::AlreadyDeclaredException &e)
{
cerr << "Variable name needed by PAC (mce_alpha_" << append_to_name << "_" << i << ")" << endl;
exit(EXIT_FAILURE);
}
{
string param_name = "mce_alpha_" + append_to_name + "_" + to_string(i);
try
{
int alpha_i_symb_id = symbol_table.addSymbol(param_name, SymbolType::parameter);
pac_mce_alpha_symb_ids[{name, standard_eqtag}].push_back(alpha_i_symb_id);
A = AddPlus(A, AddVariable(alpha_i_symb_id));
fp = AddPlus(fp,
AddTimes(AddTimes(AddVariable(alpha_i_symb_id),
AddPower(beta, AddPossiblyNegativeConstant(i))),
AddVariable(mce_z1_symb_id, i)));
}
catch (SymbolTable::AlreadyDeclaredException &e)
{
cerr << "The variable/parameter '" << param_name << "' conflicts with a parameter that will be generated for the '" << name << "' PAC model. Please rename it." << endl;
exit(EXIT_FAILURE);
}
}
// Add diff nodes and eqs for pac_target_symb_id
const VariableNode *target_base_diff_node;
@ -4173,14 +3903,14 @@ DynamicModel::addPacModelConsistentExpectationEquation(const string &name, int d
for (int j = k+1; j <= pac_max_lag_m; j++)
{
int alpha_j_symb_id = -1;
string varname = "mce_alpha_" + append_to_name + "_" + to_string(j);
string param_name = "mce_alpha_" + append_to_name + "_" + to_string(j);
try
{
alpha_j_symb_id = symbol_table.getID(varname);
alpha_j_symb_id = symbol_table.getID(param_name);
}
catch (SymbolTable::UnknownSymbolNameException &e)
{
alpha_j_symb_id = symbol_table.addSymbol(varname, SymbolType::parameter);
alpha_j_symb_id = symbol_table.addSymbol(param_name, SymbolType::parameter);
}
ssum = AddPlus(ssum,
AddTimes(AddVariable(alpha_j_symb_id), AddPower(beta, AddPossiblyNegativeConstant(j))));
@ -4191,51 +3921,56 @@ DynamicModel::addPacModelConsistentExpectationEquation(const string &name, int d
AddMinus(AddTimes(A, AddMinus(const_cast<VariableNode *>(target_base_diff_node), fs)), fp));
addEquation(neweq, -1);
neqs++;
}
cout << "PAC Model Consistent Expectation: added " << neqs << " auxiliary variables and equations for model " << name << "." << endl;
}
void
DynamicModel::computePacModelConsistentExpectationSubstitution(const string &name,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
expr_t growth,
const map<string, int> &pac_growth_neutrality_params,
const map<pair<string, string>, int> &pac_mce_z1_symb_ids,
map<pair<string, string>, expr_t> &pac_expectation_substitution)
{
for (const auto &[key, val] : eqtag_and_lag)
{
auto &[name2, eqtag] = key;
if (name2 != name)
continue;
int mce_z1_symb_id = pac_mce_z1_symb_ids.at({name, val.first});
/* The growth correction term is not added to the definition of Z₁
because the latter is recursive. Rather put it at the level of the
substition of pac_expectation operator. */
expr_t growth_correction = growth ? AddTimes(AddVariable(pac_growth_neutrality_params.at(name)), growth) : Zero;
pac_expectation_substitution[{name, eqtag}] = AddPlus(AddVariable(mce_z1_symb_id), growth_correction);
}
cout << "Pac Model Consistent Expectation: added " << neqs << " auxiliary variables and equations for model " << name << "." << endl;
}
void
DynamicModel::createPacGrowthNeutralityParameter(const string &pac_model_name)
DynamicModel::computePacBackwardExpectationSubstitution(const string &name,
const vector<int> &lhs,
int max_lag,
const string &aux_model_type,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
const vector<bool> &nonstationary,
expr_t growth,
const map<string, int> &pac_growth_neutrality_params,
map<pair<string, string>, vector<int>> &pac_h0_indices,
map<pair<string, string>, vector<int>> &pac_h1_indices,
map<pair<string, string>, expr_t> &pac_expectation_substitution)
{
string param_name = pac_model_name + "_pac_growth_neutrality_correction";
try
{
int param_idx = symbol_table.addSymbol(param_name, SymbolType::parameter);
pac_growth_neutrality_params[pac_model_name] = param_idx;
}
catch (SymbolTable::AlreadyDeclaredException)
{
cerr << "The parameter '" << param_name << "' conflicts with the auxiliary parameter that will be generated for the growth neutrality correction of the '" << pac_model_name << "' PAC model. Please rename that parameter." << endl;
exit(EXIT_FAILURE);
}
}
void
DynamicModel::fillPacModelInfo(const string &pac_model_name,
vector<int> lhs,
int max_lag,
string aux_model_type,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
const vector<bool> &nonstationary,
expr_t growth)
{
pac_eqtag_and_lag.insert(eqtag_and_lag.begin(), eqtag_and_lag.end());
bool stationary_vars_present = any_of(nonstationary.begin(), nonstationary.end(), logical_not<bool>());
bool nonstationary_vars_present = any_of(nonstationary.begin(), nonstationary.end(), [](bool b) { return b; }); // FIXME: use std::identity instead of an anonymous function when we upgrade to C++20
for (auto pac_models_and_eqtags : pac_eqtag_and_lag)
for (const auto &[key, val] : eqtag_and_lag)
{
if (pac_models_and_eqtags.first.first != pac_model_name)
auto &[name2, eqtag] = key;
if (name2 != name)
continue;
string eqtag = pac_models_and_eqtags.first.second;
string standard_eqtag = pac_models_and_eqtags.second.first;
auto &standard_eqtag = val.first;
expr_t subExpr = Zero;
if (stationary_vars_present)
{
@ -4243,21 +3978,21 @@ DynamicModel::fillPacModelInfo(const string &pac_model_name,
{
/* If the auxiliary model is a VAR, add a parameter corresponding
to the constant. */
string param_name_h0 = "h0_" + pac_model_name + "_" + standard_eqtag + "_constant";
string param_name_h0 = "h0_" + name + "_" + standard_eqtag + "_constant";
int new_param_symb_id = symbol_table.addSymbol(param_name_h0, SymbolType::parameter);
pac_h0_indices[{pac_model_name, standard_eqtag}].push_back(new_param_symb_id);
pac_h0_indices[{name, standard_eqtag}].push_back(new_param_symb_id);
subExpr = AddPlus(subExpr, AddVariable(new_param_symb_id));
}
for (int i = 1; i < max_lag + 1; i++)
for (auto lhsit : lhs)
{
stringstream param_name_h0;
param_name_h0 << "h0_" << pac_model_name
param_name_h0 << "h0_" << name
<< "_" << standard_eqtag
<< "_var_" << symbol_table.getName(lhsit)
<< "_lag_" << i;
int new_param_symb_id = symbol_table.addSymbol(param_name_h0.str(), SymbolType::parameter);
pac_h0_indices[{pac_model_name, standard_eqtag}].push_back(new_param_symb_id);
pac_h0_indices[{name, standard_eqtag}].push_back(new_param_symb_id);
subExpr = AddPlus(subExpr,
AddTimes(AddVariable(new_param_symb_id),
AddVariable(lhsit, -i)));
@ -4270,21 +4005,21 @@ DynamicModel::fillPacModelInfo(const string &pac_model_name,
{
/* If the auxiliary model is a VAR, add a parameter corresponding
to the constant. */
string param_name_h1 = "h1_" + pac_model_name + "_" + standard_eqtag + "_constant";
string param_name_h1 = "h1_" + name + "_" + standard_eqtag + "_constant";
int new_param_symb_id = symbol_table.addSymbol(param_name_h1, SymbolType::parameter);
pac_h1_indices[{pac_model_name, standard_eqtag}].push_back(new_param_symb_id);
pac_h1_indices[{name, standard_eqtag}].push_back(new_param_symb_id);
subExpr = AddPlus(subExpr, AddVariable(new_param_symb_id));
}
for (int i = 1; i < max_lag + 1; i++)
for (auto lhsit : lhs)
{
stringstream param_name_h1;
param_name_h1 << "h1_" << pac_model_name
param_name_h1 << "h1_" << name
<< "_" << standard_eqtag
<< "_var_" << symbol_table.getName(lhsit)
<< "_lag_" << i;
int new_param_symb_id = symbol_table.addSymbol(param_name_h1.str(), SymbolType::parameter);
pac_h1_indices[{pac_model_name, standard_eqtag}].push_back(new_param_symb_id);
pac_h1_indices[{name, standard_eqtag}].push_back(new_param_symb_id);
subExpr = AddPlus(subExpr,
AddTimes(AddVariable(new_param_symb_id),
AddVariable(lhsit, -i)));
@ -4293,29 +4028,26 @@ DynamicModel::fillPacModelInfo(const string &pac_model_name,
if (growth)
{
int growth_param_index = pac_growth_neutrality_params.at(pac_model_name);
int growth_param_index = pac_growth_neutrality_params.at(name);
subExpr = AddPlus(subExpr,
AddTimes(AddVariable(growth_param_index), growth));
}
pac_expectation_substitution[{pac_model_name, eqtag}] = subExpr;
pac_expectation_substitution[{name, eqtag}] = subExpr;
}
pac_model_info[pac_model_name] = {move(lhs), move(aux_model_type)};
}
void
DynamicModel::substitutePacExpectation(const string &pac_model_name)
DynamicModel::substitutePacExpectation(const map<pair<string, string>, expr_t> &pac_expectation_substitution)
{
for (auto &it : pac_expectation_substitution)
if (it.first.first == pac_model_name)
for (auto &equation : equations)
if (equation_tags.exists(&equation - &equations[0], "name", it.first.second))
{
auto substeq = dynamic_cast<BinaryOpNode *>(equation->substitutePacExpectation(pac_model_name, it.second));
assert(substeq);
equation = substeq;
break;
}
for (auto &[key, substexpr] : pac_expectation_substitution)
{
auto &[model_name, eq_name] = key;
int eq = equation_tags.getEqnByTag("name", eq_name);
auto substeq = dynamic_cast<BinaryOpNode *>(equations[eq]->substitutePacExpectation(model_name, substexpr));
assert(substeq);
equations[eq] = substeq;
}
}
void

View File

@ -122,35 +122,6 @@ private:
//! Used for var_expectation and var_model
map<string, set<int>> var_expectation_functions_to_write;
//! store symb_ids for alphas created in addPacModelConsistentExpectationEquation
//! (pac_model_name, standardized_eqtag) -> mce_alpha_symb_id
map<pair<string, string>, vector<int>> pac_mce_alpha_symb_ids;
//! store symb_ids for h0, h1 parameters
//! (pac_model_name, standardized_eqtag) -> parameter symb_ids
map<pair<string, string>, vector<int>> pac_h0_indices, pac_h1_indices;
//! store symb_ids for z1s created in addPacModelConsistentExpectationEquation
//! (pac_model_name, standardized_eqtag) -> mce_z1_symb_id
map<pair<string, string>, int> pac_mce_z1_symb_ids;
//! Store lag info for pac equations
//! (pac_model_name, equation_tag) -> (standardized_eqtag, lag)
map<pair<string, string>, pair<string, int>> pac_eqtag_and_lag;
// Store indices for growth neutrality parameters
// pac_model_name -> growth_param_index
map<string, int> pac_growth_neutrality_params;
//! (pac_model_name, equation_tag) -> expr_t
map<pair<string, string>, expr_t> pac_expectation_substitution;
//! Store info about backward PAC models:
//! pac_model_name -> (lhsvars, aux_model_type)
map<string, pair<vector<int>, string>> pac_model_info;
//! Store info about pac models specific to the equation they appear in
//! (pac_model_name, standardized_eqtag) ->
//! (lhs, optim_share_index, ar_params_and_vars, ec_params_and_vars, non_optim_vars_params_and_constants, additive_vars_params_and_constants, optim_additive_vars_params_and_constants)
map<pair<string, string>,
tuple<pair<int, int>, int, vector<tuple<int, int, int>>, pair<int, vector<tuple<int, bool, int>>>, vector<tuple<int, int, int, double>>, vector<tuple<int, int, int, double>>, vector<tuple<int, int, int, double>>>> pac_equation_info;
//! Writes dynamic model file (Matlab version)
void writeDynamicMFile(const string &basename) const;
//! Writes dynamic model file (Julia version)
@ -415,27 +386,6 @@ public:
//! in the trend_component model
void updateVarAndTrendModel() const;
//! Get Pac equation parameter info
map<pair<string, string>, pair<string, int>> walkPacParameters(const string &name);
// Create the growth neutrality parameter of a given PAC model (when the
// “growth” option has been passed)
void createPacGrowthNeutralityParameter(const string &pac_model_name);
//! Add var_model info to pac_expectation nodes
// Must be called after createPacGrowthNeutralityParameter() has been called
// on the relevant models
void fillPacModelInfo(const string &pac_model_name,
vector<int> lhs,
int max_lag,
string aux_model_type,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
const vector<bool> &nonstationary,
expr_t growth);
//! Substitutes pac_expectation operator with expectation based on auxiliary model
void substitutePacExpectation(const string &pac_model_name);
//! Writes dynamic model file
void writeDynamicFile(const string &basename, bool block, bool bytecode, bool use_dll, const string &mexext, const filesystem::path &matlabroot, const filesystem::path &dynareroot, bool julia) const;
//! Writes file containing parameters derivatives
@ -563,6 +513,8 @@ public:
//! Substitute VarExpectation operators
void substituteVarExpectation(const map<string, expr_t> &subst_table);
void analyzePacEquationStructure(const string &name, map<pair<string, string>, pair<string, int>> &eqtag_and_lag, PacModelTable::equation_info_t &pac_equation_info);
// Exception thrown by getPacTargetSymbId()
class PacTargetNotIdentifiedException
{
@ -576,13 +528,42 @@ public:
//! Return target of the pac equation
int getPacTargetSymbId(const string &pac_model_name) const;
//! Declare Z1 variables before creating aux vars so it comes right after the endo names declared by the user
void declarePacModelConsistentExpectationEndogs(const string &name);
//! Add model consistent expectation equation for pac model
/* For a PAC MCE model, add the variable and the equation defining Z₁.
The symbol IDs of the new endogenous and parameters are also added to
pac_mce_{z1,alpha}_symb_ids. */
void addPacModelConsistentExpectationEquation(const string &name, int discount,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
ExprNode::subst_table_t &diff_subst_table, expr_t growth);
ExprNode::subst_table_t &diff_subst_table,
map<pair<string, string>, int> &pac_mce_z1_symb_ids,
map<pair<string, string>, vector<int>> &pac_mce_alpha_symb_ids);
/* For a PAC MCE model, fill pac_expectation_substitution with the
expression that will be substituted for the pac_expectation operator */
void computePacModelConsistentExpectationSubstitution(const string &name,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
expr_t growth,
const map<string, int> &pac_growth_neutrality_params,
const map<pair<string, string>, int> &pac_mce_z1_symb_ids,
map<pair<string, string>, expr_t> &pac_expectation_substitution);
/* For a PAC backward model, fill pac_expectation_substitution with the
expression that will be substituted for the pac_expectation operator.
The symbol IDs of the new parameters are also added to pac_{h0,h1}_indices. */
void computePacBackwardExpectationSubstitution(const string &name,
const vector<int> &lhs,
int max_lag,
const string &aux_model_type,
const map<pair<string, string>, pair<string, int>> &eqtag_and_lag,
const vector<bool> &nonstationary,
expr_t growth,
const map<string, int> &pac_growth_neutrality_params,
map<pair<string, string>, vector<int>> &pac_h0_indices,
map<pair<string, string>, vector<int>> &pac_h1_indices,
map<pair<string, string>, expr_t> &pac_expectation_substitution);
//! Substitutes pac_expectation operator with expectation based on auxiliary model
void substitutePacExpectation(const map<pair<string, string>, expr_t> &pac_expectation_substitution);
//! Table to undiff LHS variables for pac vector z
vector<int> getUndiffLHSForPac(const string &aux_model_name,

View File

@ -815,6 +815,9 @@ PacModelTable::transformPass(ExprNode::subst_table_t &diff_subst_table,
DynamicModel &dynamic_model, const VarModelTable &var_model_table,
const TrendComponentModelTable &trend_component_model_table)
{
// (model name, eq_name) → expression for pac_expectation
map<pair<string, string>, expr_t> pac_expectation_substitution;
for (const auto &name : names)
{
/* Fill the growth_info structure.
@ -837,32 +840,22 @@ PacModelTable::transformPass(ExprNode::subst_table_t &diff_subst_table,
}
}
// Declare endogenous used for PAC model-consistent expectations
if (aux_model_name[name].empty())
dynamic_model.declarePacModelConsistentExpectationEndogs(name);
// Declare parameter for growth neutrality correction
if (growth[name])
dynamic_model.createPacGrowthNeutralityParameter(name);
// Substitute pac_expectation operators
// Collect some information about PAC models
int max_lag;
vector<int> lhs;
vector<bool> nonstationary;
string aux_model_type;
if (trend_component_model_table.isExistingTrendComponentModelName(aux_model_name[name]))
{
aux_model_type = "trend_component";
aux_model_type[name] = "trend_component";
max_lag = trend_component_model_table.getMaxLag(aux_model_name[name]) + 1;
lhs = dynamic_model.getUndiffLHSForPac(aux_model_name[name], diff_subst_table);
lhs[name] = dynamic_model.getUndiffLHSForPac(aux_model_name[name], diff_subst_table);
// All lhs variables in a trend component model are nonstationary
nonstationary.insert(nonstationary.end(), trend_component_model_table.getDiff(aux_model_name[name]).size(), true);
}
else if (var_model_table.isExistingVarModelName(aux_model_name[name]))
{
aux_model_type = "var";
aux_model_type[name] = "var";
max_lag = var_model_table.getMaxLag(aux_model_name[name]);
lhs = var_model_table.getLhs(aux_model_name[name]);
lhs[name] = var_model_table.getLhs(aux_model_name[name]);
// nonstationary variables in a VAR are those that are in diff
nonstationary = var_model_table.getDiff(aux_model_name[name]);
}
@ -873,19 +866,49 @@ PacModelTable::transformPass(ExprNode::subst_table_t &diff_subst_table,
cerr << "Error: aux_model_name not recognized as VAR model or Trend Component model" << endl;
exit(EXIT_FAILURE);
}
dynamic_model.analyzePacEquationStructure(name, eqtag_and_lag, equation_info);
auto eqtag_and_lag = dynamic_model.walkPacParameters(name);
// Declare parameter for growth neutrality correction
if (growth[name])
{
string param_name = name + "_pac_growth_neutrality_correction";
try
{
int param_idx = symbol_table.addSymbol(param_name, SymbolType::parameter);
growth_neutrality_params[name] = param_idx;
}
catch (SymbolTable::AlreadyDeclaredException)
{
cerr << "The variable/parameter '" << param_name << "' conflicts with the auxiliary parameter that will be generated for the growth neutrality correction of the '" << name << "' PAC model. Please rename that parameter." << endl;
exit(EXIT_FAILURE);
}
}
// In the MCE case, add the variable and the equation defining Z₁
if (aux_model_name[name].empty())
dynamic_model.addPacModelConsistentExpectationEquation(name, symbol_table.getID(discount[name]),
eqtag_and_lag, diff_subst_table,
growth[name]);
else
dynamic_model.fillPacModelInfo(name, lhs, max_lag, aux_model_type,
eqtag_and_lag, nonstationary, growth[name]);
mce_z1_symb_ids, mce_alpha_symb_ids);
dynamic_model.substitutePacExpectation(name);
// Compute the expressions that will be substituted for the pac_expectation operators
if (aux_model_name[name].empty())
dynamic_model.computePacModelConsistentExpectationSubstitution(name, eqtag_and_lag,
growth[name],
growth_neutrality_params,
mce_z1_symb_ids,
pac_expectation_substitution);
else
dynamic_model.computePacBackwardExpectationSubstitution(name, lhs[name], max_lag,
aux_model_type[name],
eqtag_and_lag, nonstationary,
growth[name],
growth_neutrality_params,
h0_indices, h1_indices,
pac_expectation_substitution);
}
// Actually perform the substitution of pac_expectation
dynamic_model.substitutePacExpectation(pac_expectation_substitution);
dynamic_model.checkNoRemainingPacExpectation();
}
@ -951,6 +974,237 @@ PacModelTable::writeOutput(const string &basename, ostream &output) const
}
}
}
// Write PAC Model Consistent Expectation parameter info
for (auto &[key, ids] : mce_alpha_symb_ids)
{
output << "M_.pac." << key.first << ".equations." << key.second << ".mce.alpha = [";
for (auto id : ids)
output << symbol_table.getTypeSpecificID(id) + 1 << " ";
output << "];" << endl;
}
// Write PAC Model Consistent Expectation Z1 info
for (auto &[key, id] : mce_z1_symb_ids)
output << "M_.pac." << key.first << ".equations." << key.second << ".mce.z1 = "
<< symbol_table.getTypeSpecificID(id) + 1 << ";" << endl;
// Write PAC lag info
for (auto &[key, val] : eqtag_and_lag)
output << "M_.pac." << key.first << ".equations." << val.first << ".max_lag = " << val.second << ";" << endl;
// Write PAC equation tag info
map<string, vector<pair<string, string>>> for_writing;
for (auto &[key, val] : eqtag_and_lag)
for_writing[key.first].emplace_back(key.second, val.first);
for (auto &[key, val] : for_writing)
{
output << "M_.pac." << key << ".tag_map = [";
for (auto &[eqtag, standard_eqtag] : val)
output << "{'" << eqtag << "', '" << standard_eqtag << "'};";
output << "];" << endl;
}
for (auto &[model, growth_neutrality_param_index] : growth_neutrality_params)
output << "M_.pac." << model << ".growth_neutrality_param_index = "
<< symbol_table.getTypeSpecificID(growth_neutrality_param_index) + 1 << ";" << endl;
for (auto &[model, lhs] : lhs)
{
output << "M_.pac." << model << ".lhs = [";
for (auto id : lhs)
output << id + 1 << " ";
output << "];" << endl;
}
for (auto &[model, type] : aux_model_type)
output << "M_.pac." << model << ".auxiliary_model_type = '" << type << "';" << endl;
for (auto &[key, val] : equation_info)
{
auto [lhs_pac_var, optim_share_index, ar_params_and_vars, ec_params_and_vars, non_optim_vars_params_and_constants, additive_vars_params_and_constants, optim_additive_vars_params_and_constants] = val;
string substruct = key.first + ".equations." + key.second + ".";
output << "M_.pac." << substruct << "lhs_var = "
<< symbol_table.getTypeSpecificID(lhs_pac_var.first) + 1 << ";" << endl;
if (optim_share_index >= 0)
output << "M_.pac." << substruct << "share_of_optimizing_agents_index = "
<< symbol_table.getTypeSpecificID(optim_share_index) + 1 << ";" << endl;
output << "M_.pac." << substruct << "ec.params = "
<< symbol_table.getTypeSpecificID(ec_params_and_vars.first) + 1 << ";" << endl
<< "M_.pac." << substruct << "ec.vars = [";
for (auto it : ec_params_and_vars.second)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ec.istarget = [";
for (auto it : ec_params_and_vars.second)
output << (get<1>(it) ? "true " : "false ");
output << "];" << endl
<< "M_.pac." << substruct << "ec.scale = [";
for (auto it : ec_params_and_vars.second)
output << get<2>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ec.isendo = [";
for (auto it : ec_params_and_vars.second)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "ar.params = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << (pid != -1 ? symbol_table.getTypeSpecificID(pid) + 1 : -1) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ar.vars = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << (vid != -1 ? symbol_table.getTypeSpecificID(vid) + 1 : -1) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "ar.lags = [";
for (auto &[pid, vid, vlag] : ar_params_and_vars)
output << vlag << " ";
output << "];" << endl;
if (!non_optim_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "non_optimizing_behaviour.params = [";
for (auto &it : non_optim_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.vars = [";
for (auto &it : non_optim_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.isendo = [";
for (auto &it : non_optim_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.lags = [";
for (auto &it : non_optim_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "non_optimizing_behaviour.scaling_factor = [";
for (auto &it : non_optim_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
if (!additive_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "additive.params = [";
for (auto &it : additive_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.vars = [";
for (auto &it : additive_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.isendo = [";
for (auto &it : additive_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "additive.lags = [";
for (auto &it : additive_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "additive.scaling_factor = [";
for (auto &it : additive_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
if (!optim_additive_vars_params_and_constants.empty())
{
output << "M_.pac." << substruct << "optim_additive.params = [";
for (auto &it : optim_additive_vars_params_and_constants)
if (get<2>(it) >= 0)
output << symbol_table.getTypeSpecificID(get<2>(it)) + 1 << " ";
else
output << "NaN ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.vars = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << symbol_table.getTypeSpecificID(get<0>(it)) + 1 << " ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.isendo = [";
for (auto &it : optim_additive_vars_params_and_constants)
switch (symbol_table.getType(get<0>(it)))
{
case SymbolType::endogenous:
output << "true ";
break;
case SymbolType::exogenous:
output << "false ";
break;
default:
cerr << "expecting endogenous or exogenous" << endl;
exit(EXIT_FAILURE);
}
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.lags = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << get<1>(it) << " ";
output << "];" << endl
<< "M_.pac." << substruct << "optim_additive.scaling_factor = [";
for (auto &it : optim_additive_vars_params_and_constants)
output << get<3>(it) << " ";
output << "];" << endl;
}
// Create empty h0 and h1 substructures that will be overwritten later if not empty
output << "M_.pac." << substruct << "h0_param_indices = [];" << endl
<< "M_.pac." << substruct << "h1_param_indices = [];" << endl;
}
for (auto &[model_eqtag, symb_ids] : h0_indices)
{
output << "M_.pac." << model_eqtag.first << ".equations." << model_eqtag.second << ".h0_param_indices = [";
for (auto it : symb_ids)
output << symbol_table.getTypeSpecificID(it) + 1 << " ";
output << "];" << endl;
}
for (auto &[model_eqtag, symb_ids] : h1_indices)
{
output << "M_.pac." << model_eqtag.first << ".equations." << model_eqtag.second << ".h1_param_indices = [";
for (auto it : symb_ids)
output << symbol_table.getTypeSpecificID(it) + 1 << " ";
output << "];" << endl;
}
}
void

View File

@ -200,6 +200,39 @@ private:
// The growth expressions belong to the main dynamic_model from the ModFile instance
map<string, expr_t> growth, original_growth;
map<string, vector<tuple<int, int, int, double>>> growth_info;
/* Stores symb_ids for alphas created by DynamicModel::addPacModelConsistentExpectationEquation()
(pac_model_name, standardized_eqtag) -> mce_alpha_symb_ids */
map<pair<string, string>, vector<int>> mce_alpha_symb_ids;
/* Stores symb_ids for z1s created by DynamicModel::addPacModelConsistentExpectationEquation()
(pac_model_name, standardized_eqtag) -> mce_z1_symb_id */
map<pair<string, string>, int> mce_z1_symb_ids;
/* Stores symb_ids for h0, h1 parameters
(pac_model_name, standardized_eqtag) -> parameter symb_ids */
map<pair<string, string>, vector<int>> h0_indices, h1_indices;
/* Stores indices for growth neutrality parameters
pac_model_name -> growth_neutrality_param_index */
map<string, int> growth_neutrality_params;
// Stores LHS vars (only for backward PAC models)
map<string, vector<int>> lhs;
// Stores auxiliary model type (only for backward PAC models)
map<string, string> aux_model_type;
/* Stores lag info for pac equations
(pac_model_name, equation_tag) -> (standardized_eqtag, lag) */
map<pair<string, string>, pair<string, int>> eqtag_and_lag;
public:
/* Stores info about PAC models specific to the equation they appear in
(pac_model_name, standardized_eqtag) ->
(lhs, optim_share_index, ar_params_and_vars, ec_params_and_vars, non_optim_vars_params_and_constants, additive_vars_params_and_constants, optim_additive_vars_params_and_constants)
*/
using equation_info_t = map<pair<string, string>,
tuple<pair<int, int>, int, vector<tuple<int, int, int>>, pair<int, vector<tuple<int, bool, int>>>, vector<tuple<int, int, int, double>>, vector<tuple<int, int, int, double>>, vector<tuple<int, int, int, double>>>>;
private:
equation_info_t equation_info;
public:
explicit PacModelTable(SymbolTable &symbol_table_arg);
void addPacModel(string name_arg, string aux_model_name_arg, string discount_arg, expr_t growth_arg);