In the context of a standard one‐sector AK model of endogenous growth, we show that the economy exhibits equilibrium indeterminacy and belief‐driven aggregate fluctuations under progressive taxation of income. When the tax schedule is regressive or flat, the economy's balanced growth path displays saddle‐path stability and equilibrium uniqueness. These results imply that in sharp contrast to a conventional automatic stabilizer, progressive income taxation may destabilize an endogenously growing macroeconomy by generating cyclical fluctuations driven by agents' self‐fulfilling expectations or sunspots.