This article investigates a partial equilibrium production model with dynamic information aggregation. Firms apply Bayesian learning to estimate the unknown model parameter. In the baseline setting, where prices and quantities are supported by the real line and the noise term is Gaussian, convergence of the limited information to the full information setting is obtained. Deviating from Gaussian noise need not result in consistent Bayes estimates.In addition, imposing a non-negativity constraint on quantities also destroys the convergence results obtained in the baseline model. With the constraints firms learning an unknown demand intercept parameter exit with strictly positive probability, even when the true value of this parameter would induce production in the full information setting. Parts of the model can be rescued by assuming bounded support for the stochastic noise term. However, even with bounded support the forecasts of the agents have to fulfill some regularity conditions to obtain convergence.