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) of 5.77 ppm/K, whereas the contemporaneous temperature response (CTR) is statistically indistinguishable from zero. Accounting for lagged feedbacks, the cumulative temperature response within one millennium of CO$_2$ doubling reaches 11.8 K.