Structural Cointegration of the Climate-Carbon Feedback: Evidence from the Last 130,000 Years

Using a gap-free, millennial-resolution ice-core record spanning the last 130,000 years, we identify the feedback architecture between Antarctic temperature and atmospheric CO$_2$. The series are found to be cointegrated, justifying estimation with a Vector Error Correction Model (VECM). The estimated long-run relationship yields a temperature change of 13.0 K per CO$_2$ doubling. Structural identification combining Milankovitch-cycle instrumental variables with the VECM residuals yields a contemporaneous carbon response (CCR) that closely aligns with the thermodynamic bounds of Henry's Law. For the contemporaneous temperature response (CTR), the estimated confidence interval fully encompasses the theoretical Planck response. Accounting for structural lags and error correction, the cumulative temperature response within one millennium of CO$_2$ doubling reaches 11.8 K, successfully quantifying the delayed manifestation of the greenhouse effect.