This is a replication for the simple model from Blanchard, L'Huillier and Lorenzoni(2013), "News, Noise, and Fluctuations: An Empirical Exploration." American Economic Review, vol 103, no. 7, 3045-070. This is a dynamic model where the assumption is that the agents have to solve a signal extraction problem, so the dynamic model solved by the econometrician includes embedded Kalman filtering. The one slightly tricky part about setting up the equations is that the "X" variable isn't observed by the agents, but the solution of their problem requires the expectation of X(t-1) given information through t. That requires setting up a separate variable (called XLAGE) for that expectation and creating a Kalman filter update equation specifically for that.