In this paper, we develop solutions for linearized models with forward-looking expectations and structural changes under a variety of assumptions regarding agents' beliefs about those structural changes. For each solution, we show how its associated likelihood function can be constructed by using a backward-forward algorithm. We illustrate the techniques with two examples. The first considers an inflationary program in which beliefs about the inflation target evolve differently from the inflation target itself, and the second applies the techniques to estimate a new Keynesian model through the Volcker disinflation. We compare our methodology with the alternative in which structural change is captured by switching between regimes via a Markov switching process. We show that our method can produce accurate results much faster than the Markov switching method as well as being easily adapted to handle beliefs departing from reality.