Improvements to the test for balanced growth path

— Raise the default tolerance for cross-derivatives to 1e-6, to reduce the
  number of false positives

— New option “balanced_growth_test_tol” to the “model” block for changing that
  tolerance

— Turn back test failures into errors. Since there is now an option for
  controlling the tolerance, the user always has the possibility of making the
  test pass.

Closes: dynare#1389

src/DynamicModel.cc

@@ -100,6 +100,7 @@ DynamicModel::DynamicModel(const DynamicModel &m) :
   ModelTree {m},
   trend_component_model_table {m.trend_component_model_table},
   var_model_table {m.var_model_table},
+  balanced_growth_test_tol {m.balanced_growth_test_tol},
   static_only_equations_lineno {m.static_only_equations_lineno},
   static_only_equations_equation_tags {m.static_only_equations_equation_tags},
   deriv_id_table {m.deriv_id_table},
@@ -160,6 +161,7 @@ DynamicModel::operator=(const DynamicModel &m)
 
   assert(&trend_component_model_table == &m.trend_component_model_table);
   assert(&var_model_table == &m.var_model_table);
+  balanced_growth_test_tol = m.balanced_growth_test_tol;
 
   static_only_equations_lineno = m.static_only_equations_lineno;
   static_only_equations_equation_tags = m.static_only_equations_equation_tags;
@@ -5800,13 +5802,14 @@ DynamicModel::testTrendDerivativesEqualToZero(const eval_context_t &eval_context
                 if (symbol_table.getType(endogit->first.first) == SymbolType::endogenous)
                   {
                     double nearZero = testeq->getDerivative(endogit->second)->eval(eval_context); // eval d F / d Trend d Endog
-                    if (fabs(nearZero) > zero_band)
+                    if (fabs(nearZero) > balanced_growth_test_tol)
                       {
-                        cerr << "WARNING: trends not compatible with balanced growth path; the second-order cross partial of equation " << eq + 1 << " (line "
+                        cerr << "ERROR: trends not compatible with balanced growth path; the second-order cross partial of equation " << eq + 1 << " (line "
                              << equations_lineno[eq] << ") w.r.t. trend variable "
                              << symbol_table.getName(it->first.first) << " and endogenous variable "
-                             << symbol_table.getName(endogit->first.first) << " is not null. " << endl;
-                        // Changed to warning. See discussion in #1389
+                             << symbol_table.getName(endogit->first.first) << " is not null (abs. value = "
+                             << fabs(nearZero) << "). If you are confident that your trends are correctly specified, you can raise the value of option 'balanced_growth_test_tol' in the 'model' block." << endl;
+                        exit(EXIT_FAILURE);
                       }
                   }
             }

src/DynamicModel.hh

@@ -35,7 +35,15 @@ public:
   TrendComponentModelTable &trend_component_model_table;
   //! A reference to the VAR model table
   VarModelTable &var_model_table;
+  /* Used in the balanced growth test, for determining whether the
+     cross-derivative of a given equation, w.r.t. an endogenous and a trend
+     variable is zero. Controlled by option “balanced_growth_test_tol” of the
+     “model” block. The default should not be too small (see dynare#1389). */
+  double balanced_growth_test_tol{1e-6};
 private:
+  /* Used in the balanced growth test, for skipping equations where the test
+     cannot be performed (i.e. when LHS=RHS at the initial values). Should not
+     be too large, otherwise the test becomes less powerful. */
   constexpr static double zero_band{1e-8};
 
   //! Stores equations declared as [static]

src/DynareBison.yy

@@ -73,7 +73,7 @@ class ParsingDriver;
 }
 
 %token AIM_SOLVER ANALYTIC_DERIVATION ANALYTIC_DERIVATION_MODE AR POSTERIOR_SAMPLING_METHOD
-%token BAYESIAN_IRF BETA_PDF BLOCK USE_CALIBRATION SILENT_OPTIMIZER
+%token BALANCED_GROWTH_TEST_TOL BAYESIAN_IRF BETA_PDF BLOCK USE_CALIBRATION SILENT_OPTIMIZER
 %token BVAR_DENSITY BVAR_FORECAST NODECOMPOSITION DR_DISPLAY_TOL HUGE_NUMBER FIG_NAME WRITE_XLS
 %token BVAR_PRIOR_DECAY BVAR_PRIOR_FLAT BVAR_PRIOR_LAMBDA INTERACTIVE SCREEN_SHOCKS STEADYSTATE
 %token BVAR_PRIOR_MU BVAR_PRIOR_OMEGA BVAR_PRIOR_TAU BVAR_PRIOR_TRAIN DETAIL_PLOT TYPE
@@ -900,6 +900,7 @@ model_options : BLOCK { driver.block(); }
               | o_linear
               | PARALLEL_LOCAL_FILES EQUAL '(' parallel_local_filename_list ')'
               | LINEAR_DECOMPOSITION { driver.linear_decomposition(); }
+              | BALANCED_GROWTH_TEST_TOL EQUAL non_negative_number { driver.balanced_growth_test_tol($3); }
               ;
 
 model_options_list : model_options_list COMMA model_options

src/DynareFlex.ll

@@ -706,6 +706,7 @@ DATE -?[0-9]+([ya]|m([1-9]|1[0-2])|q[1-4]|w([1-9]{1}|[1-4][0-9]|5[0-2]))
 <DYNARE_BLOCK>periods {return token::PERIODS;}
 <DYNARE_BLOCK>cutoff {return token::CUTOFF;}
 <DYNARE_BLOCK>mfs	{return token::MFS;}
+<DYNARE_BLOCK>balanced_growth_test_tol {return token::BALANCED_GROWTH_TEST_TOL;}
 <DYNARE_BLOCK>gamma_pdf {return token::GAMMA_PDF;}
 <DYNARE_BLOCK>beta_pdf {return token::BETA_PDF;}
 <DYNARE_BLOCK>normal_pdf {return token::NORMAL_PDF;}

src/ParsingDriver.cc

@@ -793,6 +793,12 @@ ParsingDriver::mfs(const string &value)
   mod_file->static_model.mfs = val;
 }
 
+void
+ParsingDriver::balanced_growth_test_tol(const string &value)
+{
+  mod_file->dynamic_model.balanced_growth_test_tol = stod(value);
+}
+
 void
 ParsingDriver::end_initval(bool all_values_required)
 {

src/ParsingDriver.hh

@@ -356,6 +356,8 @@ public:
   void cutoff(const string &value);
   //! mfs option of model block
   void mfs(const string &value);
+  //! balanced_growth_test_tol option of model block
+  void balanced_growth_test_tol(const string &value);
   //! Sets the FILENAME for the initial value in initval
   void initval_file(const string &filename);
   //! Declares an endogenous variable