We provide a Keynesian growth theory in which pessimistic expectations can lead to very persistent, or even permanent, slumps characterized by high unemployment and weak growth. We refer to these episodes as stagnation traps, because they consist in the joint occurrence of a liquidity and a growth trap. In a stagnation trap, the central bank is unable to restore full employment because weak growth depresses aggregate demand and pushes the policy rate against the zero lower bound, while growth is weak because low aggregate demand results in low profits, limiting firms' investment in innovation. Aggressive policies aiming at restoring growth, such as subsidies to investment, can successfully lead the economy out of a stagnation trap by generating a regime shift in agents' growth expectations.