Abstract: Accurate measurement of global CO2 shadow prices is conducive to judging the carbon emission reduction costs of different countries and regions, and then provides a basis for resolving international climate disputes, formulating and implementing carbon tax policies, and establishing bilateral or multilateral carbon trading markets. Based on the quadratic directional distance function and the stochastic frontier analysis model, the shadow price of carbon dioxide in 167 countries in the world from 1992~2018 was calculated, and then its spatiotemporal evolution characteristics were analyzed from three perspectives: national, regional and income level. The results show that the global average CO2 shadow price shows a fluctuating upward trend. There are huge differences in shadow prices between different countries, but the degree of discretization between different countries is decreasing, and shadow prices are showing convergence. There are also large differences in shadow prices between different regions, and the degree of differentiation between regions is increasing; Shadow prices between countries at different income levels are generally characterized by "low-income countries> lower-middle-income countries> upper-middle-income countries >high-income countries". 

Keywords: marginal abatement costs; shadow prices; directional distance function; Stochastic frontier analysis