Adaptive Green Subsidy Design Under Carbon Border Adjustments—A Stochastic Stackelberg Differential Game with Bayesian Learning About Foreign Compliance Standards, with Application to Indian Manufacturing Exports

Abstract

The European Union’s Carbon Border Adjustment Mechanism imposes a levy on the embedded emissions of imports in covered sectors. Verification rules, the trajectory of the foreign carbon price, and the embedded emissions reference are still moving targets that exporting economies cannot perfectly forecast. Developing economies that export to the European Union face a strategic question with operational consequences. Should the home government subsidise emissions abatement at home so that domestic exporters preserve market access without paying the levy abroad, and if so, how should the subsidy schedule respond to learning about how the levy itself will evolve. We pose the problem as a continuous time Stackelberg differential game between a government and a continuum of heterogeneous exporting firms. The government holds a Bayesian prior over the path of the foreign carbon price and updates the prior as new policy signals arrive. Firms differ in baseline emissions intensity and choose abatement investment to maximize expected discounted profit. We prove existence and uniqueness of the firm best response, characterize it through a three-region threshold rule that distinguishes firms that abate fully, firms that target the embedded emissions reference exactly, and firms that abate partially while paying a residual levy. We then derive the optimal subsidy schedule as a function of the government’s posterior belief and demonstrate that the schedule is increasing in the posterior expected foreign carbon price and convex in the posterior variance, which produces a precautionary subsidy channel. A numerical study calibrated to Indian steel exports to the European Union shows that adaptive subsidies recover most of the welfare loss caused by border exposure when the prior on foreign standards is reasonably informative, and roughly half of the loss under a diffuse prior. Static policies, computed under a point estimate of the foreign carbon price, leave substantial welfare on the table because they cannot respond to posterior shifts. The framework speaks to industrial policy design in any open economy whose export structure is exposed to unilaterally evolving foreign environmental standards.