We develop a methodology to estimate DSGE models with incomplete information, free of parametric restrictions on information structures. First, we define a "primal" economy in which deviations from full information are captured by wedges in agents' equilibrium expectations. Second, we provide implementability conditions, which ensure the existence of an information structure that implements these wedges. We apply the approach to estimate a New Keynesian model in which firms, households and the monetary authority have dispersed information about business conditions and productivity is the only aggregate fundamental. The estimated model fits the data remarkably well, with informational shocks able to account for the majority of U.S. business cycles. Output is driven mainly by household sentiments, whereas firm errors largely determine inflation. Our estimation indicates that firms and the central bank learn the aggregate state of the economy quickly, while household confusion about aggregate conditions is sizable and persistent.