  I show that a class of Linear DSGE models with one endogenous state variable
can be represented as a three-state Markov chain. I develop a new analytical
solution method based on this representation, which amounts to solving for a
vector of Markov states and one transition probability. These two objects
constitute sufficient statistics to compute in closed form objects that have
routinely been computed numerically: impulse response function, cumulative sum,
present discount value multiplier. I apply the method to a standard New
Keynesian model that features optimal monetary policy with commitment.
