To mitigate climate change, states must make significant investments into energy and other related sectors. To solve this problem, scholars emphasize the importance of leveraging private capital. If states create institutional mechanisms that promote private investment, they can reduce the fiscal cost of carbon abatement. We examine the ability of different international institutional designs to leverage private capital in the context of the Kyoto Protocol's Clean Development Mechanism (CDM). Empirically, we analyze private capital investment in 3,749 climate mitigation projects under the CDM, 2003-2011. Since the CDM allows both bilateral and unilateral implementation, we can compare the two modes of contracting within one context. Our model analyzes equilibrium private investment in climate mitigation. When the cost of mitigation is high, unilateral project implementation in one host country, without foreign collaboration, draws more investment than bilateral contracting, whereby foreign investors participate in the project. * This paper was written during a research stay funded by an ERP fellowship of the Studienstiftung des deutschen Volkes. Patrick Bayer gratefully acknowledges this generous funding and is thankful for the hospitality of Columbia University. We thank Michaël Aklin, Paula Castro, Kyle Meng, and Martin Stadelmann for helpful comments on a previous draft.