The macroeconomic literature on belief-driven business cycles treats news and noise as distinct representations of people's beliefs about economic fundamentals. We prove that these two representations are actually observationally equivalent. This means that the decision to use one representation or the other must be made on theoretical, and not empirical, grounds. Our result allows us to determine the importance of beliefs as an independent source of fluctuations. Using three prominent models from this literature, we show that existing research has understated the importance of independent shocks to beliefs. This is because representations with anticipated and unanticipated shocks mix the fluctuations due independently to beliefs with the fluctuations due to fundamentals. We also argue that the observational equivalence of news and noise representations implies that structural vector auto-regression analysis is equally appropriate for recovering both news and noise shocks.