Indigenous Territories (ITs) with less centralized forest governance than Protected Areas (PAs) may represent cost-effective natural climate solutions to meet the Paris agreement. However, the literature has been limited to examining the effect of ITs on deforestation, despite the influence of anthropogenic degradation. Thus, little is known about the temporal and spatial effect of allocating ITs on carbon stocks dynamics that account for losses from deforestation and degradation. Using Amazon Basin countries and Panama, this study aims to estimate the temporal and spatial effects of ITs and PAs on carbon stocks. To estimate the temporal effects, we use annual carbon density maps, matching analysis, and linear mixed models. Furthermore, we explore the spatial heterogeneity of these estimates through geographic discontinuity designs, allowing us to assess the spatial effect of ITs and PAs boundaries on carbon stocks. The temporal effects highlight that allocating ITs preserves carbon stocks and buffer losses as well as allocating PAs in Panama and Amazon Basin countries. The geographic discontinuity designs reveal that ITs' boundaries secure more extensive carbon stocks than their surroundings, and this difference tends to increase towards the least accessible areas, suggesting that indigenous land use in neotropical forests may have a temporarily and spatially stable impact on carbon stocks. Our findings imply that ITs in neotropical forests support Nationally Determined Contributions (NDCs) under the Paris Agreement. Thus, Indigenous peoples must become recipients of countries' results-based payments.