{
  "schema_version": "var-residual-diagnostic-layerB-selection-decomposition-v1.851",
  "classification": "derived_from_frozen_v1_85_simulation",
  "not_new_research_draws": true,
  "generated_at": "2026-09-28",
  "source": {
    "path": "src/data/macro/var_residual_diagnostic_simulation_results.json",
    "source_sha256": "04cc4ad5f8395f894a4c9c164fc8374841b6eb20c97dc4a8c4d7098dc6912a7e",
    "schema_version": "var-residual-diagnostic-simulation-results-v1.85"
  },
  "derivation_script": "scripts/var-residual-diagnostics/decompose_selection.py",
  "derivation_command": "pnpm var:residual-decompose",
  "new_random_draws": 0,
  "simulation_reruns": 0,
  "var_reestimations": 0,
  "actual_country_data_read": false,
  "diagnostic_horizon": 12,
  "selection_categories": {
    "correct": "selected lag == true lag",
    "underselection": "selected lag < true lag",
    "overselection": "selected lag > true lag"
  },
  "replication_level_joint_crosstab_available": false,
  "conditional_rejection_rates_reconstructable": false,
  "joint_distribution_note": "Cell-level selected-lag frequencies and overall rejection rates are observed, but their replication-level joint distribution was not retained; conditional rejection rates cannot be reconstructed from the frozen aggregate artifact.",
  "metric_semantics": {
    "layer_A": "conditional_diagnostic_size",
    "layer_B": "selection_plus_specification_plus_diagnostic_procedure_rejection",
    "layer_B_pure_size_identified": false,
    "reason": "Layer A estimates the true lag, so under the null DGP each rejection is a Type-I error of the diagnostic. Layer B first selects the lag by BIC; when the selected lag is below the true lag the fitted VAR is underfitted and residual whiteness need not hold, so Layer B rejections are not all Type-I errors."
  },
  "layer_A_summary": {
    "pt_adjusted": {
      "cell_count": 36,
      "cells_inside_0_035_to_0_065": 18,
      "minimum_rejection_rate": 0.0406,
      "maximum_rejection_rate": 0.25,
      "all_cells_at_or_below_0_075": false,
      "layer_A_gate_components_met": false
    },
    "bg_lm": {
      "cell_count": 36,
      "cells_inside_0_035_to_0_065": 14,
      "minimum_rejection_rate": 0.0306,
      "maximum_rejection_rate": 0.362,
      "all_cells_at_or_below_0_075": false,
      "layer_A_gate_components_met": false
    },
    "edgerton_shukur_f": {
      "cell_count": 36,
      "cells_inside_0_035_to_0_065": 36,
      "minimum_rejection_rate": 0.0353,
      "maximum_rejection_rate": 0.0599,
      "all_cells_at_or_below_0_075": true,
      "layer_A_gate_components_met": true
    }
  },
  "layer_B_cell_count": 36,
  "layer_B_cells": [
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      "cell_id": "primary_LB_T120_p1_r0.50_det-constant_innov-gaussian_iid",
      "sample_size": 120,
      "true_lag": 1,
      "persistence": 0.5,
      "deterministic_spec": "constant",
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      "selected_lag_counts": {
        "1": 10000
      },
      "correct_selection_count": 10000,
      "underselection_count": 0,
      "overselection_count": 0,
      "correct_selection_rate": 1.0,
      "underselection_rate": 0.0,
      "overselection_rate": 0.0,
      "parameter_gate_passed": 10000,
      "h12_rejection": {
        "pt_adjusted": {
          "rejections": 468,
          "tested": 10000,
          "rate": 0.0468
        },
        "bg_lm": {
          "rejections": 335,
          "tested": 10000,
          "rate": 0.0335
        },
        "edgerton_shukur_f": {
          "rejections": 375,
          "tested": 10000,
          "rate": 0.0375
        }
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      "pt_h12_rejection_rate": 0.0468,
      "bg_h12_rejection_rate": 0.0335,
      "es_h12_rejection_rate": 0.0375
    },
    {
      "cell_id": "primary_LB_T120_p1_r0.50_det-constant_plus_11_month_dummies_innov-gaussian_iid",
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      "persistence": 0.5,
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        "2": 1
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      "correct_selection_count": 9999,
      "underselection_count": 0,
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          "rejections": 2167,
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          "rate": 0.2167
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          "rate": 0.2448
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          "rate": 0.0522
        }
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      "pt_h12_rejection_rate": 0.2167,
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    },
    {
      "cell_id": "primary_LB_T120_p1_r0.80_det-constant_innov-gaussian_iid",
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    {
      "cell_id": "primary_LB_T120_p1_r0.80_det-constant_plus_11_month_dummies_innov-gaussian_iid",
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          "rate": 0.2506
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    {
      "cell_id": "primary_LB_T120_p1_r0.95_det-constant_innov-gaussian_iid",
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    {
      "cell_id": "primary_LB_T120_p1_r0.95_det-constant_plus_11_month_dummies_innov-gaussian_iid",
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          "rejections": 2481,
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          "rate": 0.2481
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    {
      "cell_id": "primary_LB_T120_p2_r0.50_det-constant_innov-gaussian_iid",
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      "cell_overselection_rate_range": [
        0.0,
        0.0002
      ],
      "h12_rejection_rate_range": {
        "pt_adjusted": [
          0.0433,
          0.2481
        ],
        "bg_lm": [
          0.0335,
          0.2553
        ],
        "edgerton_shukur_f": [
          0.0366,
          0.0592
        ]
      },
      "h12_cells_inside_0_035_to_0_065": {
        "pt_adjusted": 9,
        "bg_lm": 5,
        "edgerton_shukur_f": 18
      },
      "by_deterministic_spec": {
        "constant": {
          "cell_count": 9,
          "replications": 90000,
          "pooled_correct_selection_rate": 1.0,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            1.0,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0433,
              0.0635
            ],
            "bg_lm": [
              0.0335,
              0.0395
            ],
            "edgerton_shukur_f": [
              0.0366,
              0.0435
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 9,
            "bg_lm": 5,
            "edgerton_shukur_f": 9
          }
        },
        "constant_plus_11_month_dummies": {
          "cell_count": 9,
          "replications": 90000,
          "pooled_correct_selection_rate": 0.9999222222222223,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 7.777777777777778e-05,
          "cell_correct_selection_rate_range": [
            0.9998,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0002
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.1787,
              0.2481
            ],
            "bg_lm": [
              0.1831,
              0.2553
            ],
            "edgerton_shukur_f": [
              0.05,
              0.0592
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 0,
            "edgerton_shukur_f": 9
          }
        }
      },
      "by_sample_size": {
        "120": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.9999666666666667,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 3.3333333333333335e-05,
          "cell_correct_selection_rate_range": [
            0.9999,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0001
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0468,
              0.2481
            ],
            "bg_lm": [
              0.0335,
              0.2553
            ],
            "edgerton_shukur_f": [
              0.0366,
              0.0568
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 0,
            "edgerton_shukur_f": 6
          }
        },
        "132": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.99995,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 5e-05,
          "cell_correct_selection_rate_range": [
            0.9998,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0002
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0455,
              0.2307
            ],
            "bg_lm": [
              0.0348,
              0.2235
            ],
            "edgerton_shukur_f": [
              0.0392,
              0.0592
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 2,
            "edgerton_shukur_f": 6
          }
        },
        "144": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.9999666666666667,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 3.3333333333333335e-05,
          "cell_correct_selection_rate_range": [
            0.9999,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0001
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0433,
              0.2008
            ],
            "bg_lm": [
              0.0373,
              0.197
            ],
            "edgerton_shukur_f": [
              0.04,
              0.0578
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 3,
            "edgerton_shukur_f": 6
          }
        }
      },
      "by_persistence": {
        "0.5": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.9999833333333333,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 1.6666666666666667e-05,
          "cell_correct_selection_rate_range": [
            0.9999,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0001
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0433,
              0.2167
            ],
            "bg_lm": [
              0.0335,
              0.2448
            ],
            "edgerton_shukur_f": [
              0.0375,
              0.0522
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 1,
            "edgerton_shukur_f": 6
          }
        },
        "0.8": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.99995,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 5e-05,
          "cell_correct_selection_rate_range": [
            0.9999,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0001
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0468,
              0.2303
            ],
            "bg_lm": [
              0.0337,
              0.2506
            ],
            "edgerton_shukur_f": [
              0.0366,
              0.0521
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 2,
            "edgerton_shukur_f": 6
          }
        },
        "0.95": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.99995,
          "pooled_underselection_rate": 0.0,
          "pooled_overselection_rate": 5e-05,
          "cell_correct_selection_rate_range": [
            0.9998,
            1.0
          ],
          "cell_underselection_rate_range": [
            0.0,
            0.0
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0002
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0595,
              0.2481
            ],
            "bg_lm": [
              0.034,
              0.2553
            ],
            "edgerton_shukur_f": [
              0.0381,
              0.0592
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 3,
            "bg_lm": 2,
            "edgerton_shukur_f": 6
          }
        }
      }
    },
    "2": {
      "cell_count": 18,
      "replications": 180000,
      "pooled_correct_selection_rate": 0.0024833333333333335,
      "pooled_underselection_rate": 0.9975166666666667,
      "pooled_overselection_rate": 0.0,
      "cell_correct_selection_rate_range": [
        0.0001,
        0.0071
      ],
      "cell_underselection_rate_range": [
        0.9929,
        0.9999
      ],
      "cell_overselection_rate_range": [
        0.0,
        0.0
      ],
      "h12_rejection_rate_range": {
        "pt_adjusted": [
          0.0844,
          0.4523
        ],
        "bg_lm": [
          0.0481,
          0.3781
        ],
        "edgerton_shukur_f": [
          0.0534,
          0.1288
        ]
      },
      "h12_cells_inside_0_035_to_0_065": {
        "pt_adjusted": 0,
        "bg_lm": 3,
        "edgerton_shukur_f": 3
      },
      "by_deterministic_spec": {
        "constant": {
          "cell_count": 9,
          "replications": 90000,
          "pooled_correct_selection_rate": 0.0019222222222222223,
          "pooled_underselection_rate": 0.9980777777777777,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0001,
            0.0047
          ],
          "cell_underselection_rate_range": [
            0.9953,
            0.9999
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0844,
              0.2133
            ],
            "bg_lm": [
              0.0481,
              0.1101
            ],
            "edgerton_shukur_f": [
              0.0534,
              0.1187
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 3,
            "edgerton_shukur_f": 3
          }
        },
        "constant_plus_11_month_dummies": {
          "cell_count": 9,
          "replications": 90000,
          "pooled_correct_selection_rate": 0.0030444444444444442,
          "pooled_underselection_rate": 0.9969555555555556,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0003,
            0.0071
          ],
          "cell_underselection_rate_range": [
            0.9929,
            0.9997
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.2601,
              0.4523
            ],
            "bg_lm": [
              0.2361,
              0.3781
            ],
            "edgerton_shukur_f": [
              0.0658,
              0.1288
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 0,
            "edgerton_shukur_f": 0
          }
        }
      },
      "by_sample_size": {
        "120": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.002616666666666667,
          "pooled_underselection_rate": 0.9973833333333333,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0001,
            0.0071
          ],
          "cell_underselection_rate_range": [
            0.9929,
            0.9999
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0844,
              0.4523
            ],
            "bg_lm": [
              0.0481,
              0.3781
            ],
            "edgerton_shukur_f": [
              0.0534,
              0.1057
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 1,
            "edgerton_shukur_f": 1
          }
        },
        "132": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.002533333333333333,
          "pooled_underselection_rate": 0.9974666666666666,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0001,
            0.0059
          ],
          "cell_underselection_rate_range": [
            0.9941,
            0.9999
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0872,
              0.4477
            ],
            "bg_lm": [
              0.0507,
              0.365
            ],
            "edgerton_shukur_f": [
              0.0559,
              0.1234
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 1,
            "edgerton_shukur_f": 1
          }
        },
        "144": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.0023,
          "pooled_underselection_rate": 0.9977,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0002,
            0.0058
          ],
          "cell_underselection_rate_range": [
            0.9942,
            0.9998
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0893,
              0.4321
            ],
            "bg_lm": [
              0.0564,
              0.3405
            ],
            "edgerton_shukur_f": [
              0.0611,
              0.1288
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 1,
            "edgerton_shukur_f": 1
          }
        }
      },
      "by_persistence": {
        "0.5": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.0002666666666666667,
          "pooled_underselection_rate": 0.9997333333333334,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0001,
            0.0005
          ],
          "cell_underselection_rate_range": [
            0.9995,
            0.9999
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.0844,
              0.2923
            ],
            "bg_lm": [
              0.0481,
              0.2769
            ],
            "edgerton_shukur_f": [
              0.0534,
              0.0767
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 3,
            "edgerton_shukur_f": 3
          }
        },
        "0.8": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.0018666666666666666,
          "pooled_underselection_rate": 0.9981333333333333,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0011,
            0.0033
          ],
          "cell_underselection_rate_range": [
            0.9967,
            0.9989
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.1425,
              0.3823
            ],
            "bg_lm": [
              0.066,
              0.3375
            ],
            "edgerton_shukur_f": [
              0.0736,
              0.0988
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 0,
            "edgerton_shukur_f": 0
          }
        },
        "0.95": {
          "cell_count": 6,
          "replications": 60000,
          "pooled_correct_selection_rate": 0.005316666666666667,
          "pooled_underselection_rate": 0.9946833333333334,
          "pooled_overselection_rate": 0.0,
          "cell_correct_selection_rate_range": [
            0.0042,
            0.0071
          ],
          "cell_underselection_rate_range": [
            0.9929,
            0.9958
          ],
          "cell_overselection_rate_range": [
            0.0,
            0.0
          ],
          "h12_rejection_rate_range": {
            "pt_adjusted": [
              0.1953,
              0.4523
            ],
            "bg_lm": [
              0.0888,
              0.3781
            ],
            "edgerton_shukur_f": [
              0.0962,
              0.1288
            ]
          },
          "h12_cells_inside_0_035_to_0_065": {
            "pt_adjusted": 0,
            "bg_lm": 0,
            "edgerton_shukur_f": 0
          }
        }
      }
    }
  },
  "worst_layer_B_es_cell": {
    "cell_id": "primary_LB_T144_p2_r0.95_det-constant_plus_11_month_dummies_innov-gaussian_iid",
    "selected_lag_counts": {
      "1": 9942,
      "2": 58
    },
    "underselection_rate": 0.9942,
    "es_h12_rejection_rate": 0.1288,
    "interpretation": "该 cell 的高 rejection frequency 与几乎完全的 lag underselection 同时出现。No share of ES rejections can be attributed to underselection because the replication-level joint distribution was not retained."
  },
  "decision_boundary": {
    "v1_85_method_decision_changed": false,
    "disposition": "no_eligible_replacement",
    "phase_B_authorized": false,
    "es_activated": false,
    "note": "The preregistered selection rule requires the joint Layer A + Layer B procedure gate. This decomposition clarifies interpretation only and cannot change eligibility."
  }
}