Understanding how poverty persists and how this affects environmental reliance has policy implications for poverty reduction and environmental conservation. Employing a panel dataset from rural Nepal, we shed light on this issue, using a combination of parametric and nonparametric models. Results show that, as a population, households will converge at a single equilibrium point in the long term, hence indicating the absence of a poverty trap. The exact asset level of this single equilibrium point, which indicates the absence of a poverty trap, varies between groups of households (e.g. based on location, marital status). Based on the convergence point of the entire study population, two groups of households are identified: one situated above the convergence point and another situated below the point. Total environmental income, i.e. all income from forest and non-forest environments, is very important to households below the convergence point. Although total environmental income is not a major contributor to asset accumulation, its non-forest component is a significant and positive contributor. We attribute the importance to their looser restriction to access, than for forest resources. Hence, securing greater access to forests without affecting the conservation priorities will help improve the contribution of forest resources to poverty reduction.