This paper argues that endogenous growth requires not merely savings and investment, but institutions that ensure investment is productivity-enhancing. We develop a model in which agents choose between productive entrepreneurship and rent-seeking, with institutional quality governing the relative returns to each activity. The fraction of productive investment, λ, is determined endogenously by this occupational choice, and interacts with precautionary liquidity demand to generate multiple equilibria. Below a critical institutional threshold, the economy is trapped in stagnation even when markets clear and savings are high. We derive closed-form conditions for the existence of the stagnation trap and show that the trap is more likely when savings rates are low, speculative returns are high, and uncertainty is elevated. These results distinguish two empirically relevant failure modes: savings-abundant economies such as Japan, where the primary constraint is institutional quality, and savings-scarce economies such as the United Kingdom, where low savings and poor institutional quality constitute a dual failure requiring distinct policy responses.