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We develop a stochastic, heterogeneous agent overlapping generations (OLG) model with imperfect substitutability of workers and endogenous innovation to study the effects of STEM immigration. The model incorporates detailed representations of the US immigration system, federal taxes and transfers, and the demographics of US- and foreign-born workers. Households face idiosyncratic earnings and health shocks over the life cycle and make decisions over consumption, labor, health insurance, and medical treatment. Output depends on different types of labor which vary in degree of skill complementarity or substitutability. STEM workers contribute directly to total factor productivity (TFP) through the generation of knowledge and ideas. Complementarities and innovation generate potential spillovers for US-born workers from STEM immigration. We provide new empirical estimates of the extent of these spillovers and quantify their general equilibrium effects on US economic and fiscal outcomes and the welfare of US households. After examining the historical impact of STEM immigration, we consider specific proposals such as changes to the number of H-1B visas and exempting STEM immigrants from green card caps. We quantify the welfare and fiscal impacts of alternative immigration and tax policy combinations to identify those that maximize Pareto-improving outcomes.