{
  "generated_at": "2026-07-20T03:23:06.118Z",
  "study_design": "Unbalanced country-year panel with within estimator",
  "sample": {
    "n": 4406,
    "countries": 186,
    "years": 24,
    "first_year": 2000,
    "last_year": 2023,
    "balanced_countries": 177,
    "balanced_observations": 4248,
    "observations_per_country_min": 11,
    "observations_per_country_median": 24,
    "observations_per_country_max": 24,
    "within_country_pm25_sd": 3.4056
  },
  "method": {
    "estimator": "Alternating-projection within transformation for country and year fixed effects",
    "uncertainty": "Country-clustered CR1 standard errors; 95% normal-approximation confidence intervals",
    "outcome": "Life expectancy at birth",
    "controls": [
      "Log GDP per capita PPP",
      "Urban population per 10 pp",
      "Age 65+ per 5 pp",
      "Log health spending per capita PPP"
    ]
  },
  "models": [
    {
      "id": "P1",
      "label": "Country FE",
      "exposure_name": "PM2.5 current per 10 µg/m³",
      "n": 4406,
      "countries": 186,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3"
      ],
      "within_r_squared": 0.0477,
      "rmse_within": 2.4313,
      "demeaning_iterations": 2,
      "demeaning_maximum_change": 2.5461114698070258e-14,
      "absorbed_fixed_effect_rank": 186,
      "estimated_parameter_count": 187,
      "residual_degrees_freedom": 4219,
      "clustered_by": "country",
      "cluster_correction": 1.04973,
      "coefficients": {
        "PM2.5 current per 10 µg/m³": {
          "estimate": -1.5986,
          "cluster_se": 0.2791,
          "test_statistic": -5.728,
          "p_value": 0,
          "ci95_low": -2.1456,
          "ci95_high": -1.0516
        }
      }
    },
    {
      "id": "P2",
      "label": "Country + year FE",
      "exposure_name": "PM2.5 current per 10 µg/m³",
      "n": 4406,
      "countries": 186,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.0053,
      "rmse_within": 1.6745,
      "demeaning_iterations": 8,
      "demeaning_maximum_change": 1.6084507463305768e-12,
      "absorbed_fixed_effect_rank": 209,
      "estimated_parameter_count": 210,
      "residual_degrees_freedom": 4196,
      "clustered_by": "country",
      "cluster_correction": 1.055484,
      "coefficients": {
        "PM2.5 current per 10 µg/m³": {
          "estimate": 0.3906,
          "cluster_se": 0.1448,
          "test_statistic": 2.697,
          "p_value": 0.007,
          "ci95_low": 0.1067,
          "ci95_high": 0.6745
        }
      }
    },
    {
      "id": "P3",
      "label": "Two-way FE + controls",
      "exposure_name": "PM2.5 current per 10 µg/m³",
      "n": 4406,
      "countries": 186,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.1342,
      "rmse_within": 1.5629,
      "demeaning_iterations": 8,
      "demeaning_maximum_change": 1.6084507463305768e-12,
      "absorbed_fixed_effect_rank": 209,
      "estimated_parameter_count": 214,
      "residual_degrees_freedom": 4192,
      "clustered_by": "country",
      "cluster_correction": 1.056491,
      "coefficients": {
        "PM2.5 current per 10 µg/m³": {
          "estimate": 0.0471,
          "cluster_se": 0.1349,
          "test_statistic": 0.349,
          "p_value": 0.7271,
          "ci95_low": -0.2174,
          "ci95_high": 0.3116
        },
        "Log GDP per capita PPP": {
          "estimate": 2.0787,
          "cluster_se": 0.7127,
          "test_statistic": 2.917,
          "p_value": 0.0035,
          "ci95_low": 0.6819,
          "ci95_high": 3.4756
        },
        "Urban population per 10 pp": {
          "estimate": 0.6473,
          "cluster_se": 0.3675,
          "test_statistic": 1.761,
          "p_value": 0.0782,
          "ci95_low": -0.0729,
          "ci95_high": 1.3676
        },
        "Age 65+ per 5 pp": {
          "estimate": -2.8654,
          "cluster_se": 0.5059,
          "test_statistic": -5.664,
          "p_value": 0,
          "ci95_low": -3.857,
          "ci95_high": -1.8738
        },
        "Log health spending per capita PPP": {
          "estimate": 0.0736,
          "cluster_se": 0.4168,
          "test_statistic": 0.177,
          "p_value": 0.8599,
          "ci95_low": -0.7434,
          "ci95_high": 0.8906
        }
      }
    },
    {
      "id": "P4",
      "label": "Lag 1 year + controls",
      "exposure_name": "PM2.5 lag 1 year per 10 µg/m³",
      "n": 4406,
      "countries": 186,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.1347,
      "rmse_within": 1.5625,
      "demeaning_iterations": 8,
      "demeaning_maximum_change": 1.6084507463305768e-12,
      "absorbed_fixed_effect_rank": 209,
      "estimated_parameter_count": 214,
      "residual_degrees_freedom": 4192,
      "clustered_by": "country",
      "cluster_correction": 1.056491,
      "coefficients": {
        "PM2.5 lag 1 year per 10 µg/m³": {
          "estimate": 0.1247,
          "cluster_se": 0.1367,
          "test_statistic": 0.912,
          "p_value": 0.3615,
          "ci95_low": -0.1431,
          "ci95_high": 0.3925
        },
        "Log GDP per capita PPP": {
          "estimate": 2.0829,
          "cluster_se": 0.7115,
          "test_statistic": 2.927,
          "p_value": 0.0034,
          "ci95_low": 0.6883,
          "ci95_high": 3.4775
        },
        "Urban population per 10 pp": {
          "estimate": 0.6431,
          "cluster_se": 0.368,
          "test_statistic": 1.748,
          "p_value": 0.0805,
          "ci95_low": -0.0782,
          "ci95_high": 1.3644
        },
        "Age 65+ per 5 pp": {
          "estimate": -2.8352,
          "cluster_se": 0.4977,
          "test_statistic": -5.696,
          "p_value": 0,
          "ci95_low": -3.8107,
          "ci95_high": -1.8596
        },
        "Log health spending per capita PPP": {
          "estimate": 0.0844,
          "cluster_se": 0.419,
          "test_statistic": 0.202,
          "p_value": 0.8403,
          "ci95_low": -0.7368,
          "ci95_high": 0.9057
        }
      }
    },
    {
      "id": "P5",
      "label": "3-year mean + controls",
      "exposure_name": "PM2.5 3-year mean per 10 µg/m³",
      "n": 4406,
      "countries": 186,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.1347,
      "rmse_within": 1.5625,
      "demeaning_iterations": 8,
      "demeaning_maximum_change": 1.6084507463305768e-12,
      "absorbed_fixed_effect_rank": 209,
      "estimated_parameter_count": 214,
      "residual_degrees_freedom": 4192,
      "clustered_by": "country",
      "cluster_correction": 1.056491,
      "coefficients": {
        "PM2.5 3-year mean per 10 µg/m³": {
          "estimate": 0.1407,
          "cluster_se": 0.1798,
          "test_statistic": 0.782,
          "p_value": 0.4341,
          "ci95_low": -0.2118,
          "ci95_high": 0.4931
        },
        "Log GDP per capita PPP": {
          "estimate": 2.0828,
          "cluster_se": 0.7116,
          "test_statistic": 2.927,
          "p_value": 0.0034,
          "ci95_low": 0.688,
          "ci95_high": 3.4775
        },
        "Urban population per 10 pp": {
          "estimate": 0.6419,
          "cluster_se": 0.3684,
          "test_statistic": 1.742,
          "p_value": 0.0814,
          "ci95_low": -0.0802,
          "ci95_high": 1.364
        },
        "Age 65+ per 5 pp": {
          "estimate": -2.8296,
          "cluster_se": 0.5006,
          "test_statistic": -5.653,
          "p_value": 0,
          "ci95_low": -3.8107,
          "ci95_high": -1.8485
        },
        "Log health spending per capita PPP": {
          "estimate": 0.0862,
          "cluster_se": 0.4194,
          "test_statistic": 0.206,
          "p_value": 0.8372,
          "ci95_low": -0.7357,
          "ci95_high": 0.9081
        }
      }
    }
  ],
  "sensitivity": [
    {
      "id": "S1",
      "label": "Balanced 24-year countries",
      "exposure_name": "PM2.5 current per 10 µg/m³",
      "n": 4248,
      "countries": 177,
      "years": 24,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.1403,
      "rmse_within": 1.5433,
      "demeaning_iterations": 2,
      "demeaning_maximum_change": 2.6349293117770383e-14,
      "absorbed_fixed_effect_rank": 200,
      "estimated_parameter_count": 205,
      "residual_degrees_freedom": 4043,
      "clustered_by": "country",
      "cluster_correction": 1.056426,
      "coefficients": {
        "PM2.5 current per 10 µg/m³": {
          "estimate": 0.0656,
          "cluster_se": 0.1363,
          "test_statistic": 0.481,
          "p_value": 0.6302,
          "ci95_low": -0.2016,
          "ci95_high": 0.3329
        },
        "Log GDP per capita PPP": {
          "estimate": 1.756,
          "cluster_se": 0.6688,
          "test_statistic": 2.626,
          "p_value": 0.0086,
          "ci95_low": 0.4452,
          "ci95_high": 3.0667
        },
        "Urban population per 10 pp": {
          "estimate": 0.9356,
          "cluster_se": 0.2899,
          "test_statistic": 3.227,
          "p_value": 0.0013,
          "ci95_low": 0.3673,
          "ci95_high": 1.5039
        },
        "Age 65+ per 5 pp": {
          "estimate": -2.7325,
          "cluster_se": 0.5036,
          "test_statistic": -5.426,
          "p_value": 0,
          "ci95_low": -3.7195,
          "ci95_high": -1.7454
        },
        "Log health spending per capita PPP": {
          "estimate": 0.0272,
          "cluster_se": 0.4322,
          "test_statistic": 0.063,
          "p_value": 0.9498,
          "ci95_low": -0.82,
          "ci95_high": 0.8744
        }
      }
    },
    {
      "id": "S2",
      "label": "Exclude 2020–2021",
      "exposure_name": "PM2.5 current per 10 µg/m³",
      "n": 4034,
      "countries": 186,
      "years": 22,
      "first_year": 2000,
      "last_year": 2023,
      "fixed_effects": [
        "iso3",
        "year"
      ],
      "within_r_squared": 0.1294,
      "rmse_within": 1.5279,
      "demeaning_iterations": 8,
      "demeaning_maximum_change": 2.9051329243480317e-12,
      "absorbed_fixed_effect_rank": 207,
      "estimated_parameter_count": 212,
      "residual_degrees_freedom": 3822,
      "clustered_by": "country",
      "cluster_correction": 1.060911,
      "coefficients": {
        "PM2.5 current per 10 µg/m³": {
          "estimate": 0.0339,
          "cluster_se": 0.125,
          "test_statistic": 0.271,
          "p_value": 0.7861,
          "ci95_low": -0.211,
          "ci95_high": 0.2788
        },
        "Log GDP per capita PPP": {
          "estimate": 2.0007,
          "cluster_se": 0.7397,
          "test_statistic": 2.705,
          "p_value": 0.0068,
          "ci95_low": 0.5508,
          "ci95_high": 3.4506
        },
        "Urban population per 10 pp": {
          "estimate": 0.5862,
          "cluster_se": 0.3874,
          "test_statistic": 1.513,
          "p_value": 0.1303,
          "ci95_low": -0.1731,
          "ci95_high": 1.3455
        },
        "Age 65+ per 5 pp": {
          "estimate": -2.8853,
          "cluster_se": 0.4978,
          "test_statistic": -5.797,
          "p_value": 0,
          "ci95_low": -3.8609,
          "ci95_high": -1.9097
        },
        "Log health spending per capita PPP": {
          "estimate": 0.2341,
          "cluster_se": 0.4244,
          "test_statistic": 0.552,
          "p_value": 0.5813,
          "ci95_low": -0.5978,
          "ci95_high": 1.0659
        }
      }
    }
  ],
  "ai_judgment": {
    "conclusion": "在国家和年份双向固定效应及预设控制变量模型中，PM2.5 每增加 10 µg/m³ 的估计为 0.0471 年（95% CI -0.2174 至 0.3116）。当前模型未能把该关系与零可靠地区分，因此不能确认独立关联。",
    "independent_association_evidence_grade": "E1",
    "inconclusive_result_evidence_grade": "E2",
    "direction_stable_across_key_models": true,
    "direction_stable_across_sensitivity_models": true,
    "sign_reversal_after_year_fixed_effects": true,
    "causal_claim": false
  }
}