We provide a production‐based asset pricing model with dispersed information and small deviations from full rational expectations. In the model, aggregate output and equity prices depend on the higher‐order beliefs about aggregate demand and individual stochastic discount factors. We prove that equity price volatility becomes arbitrarily large as the volatility of idiosyncratic shocks diverges to infinity due to the interaction of signal extraction with idiosyncratic trading decisions, while aggregate output volatility falls. We propose a two‐step spectral factorization method that permits closed‐form solutions in the frequency domain applicable to a wide range of models with more hidden states than signals. Our model can quantitatively match output and equity volatilities observed in U.S. data.