We develop a general equilibrium business cycle model with imperfectly observed neutral and investment-specific technology shocks, which agents learn from noisy signals. Estimated using US data, the model implies that neutral technology shocks generate more volatile responses than in an environment with perfect information, whereas investment-specific shocks have more persistent impact. Noise accounts for substantial variation in investment, and alters agents’ behavior persistently through its influence on beliefs — even when the underlying fundamentals are unchanged and the noise itself is not persistent. Further implications for business cycle analysis are explored.