"Many of the theoretical equations in DSGE models take a form in which a variable today, say incomes (denoted as yt), depends inter alia on its ‘expected future value’. (In formal terms, this is written as Etyt+1], where the ‘t’ after the ‘E’ indicates the date at which the expectation is formed, and the ‘t+1’ after the ‘y’ indicates the date of the variable). For example, yt may be the log-difference between a de-trended level and its steady-state value. Implicitly, such a formulation assumes some form of stationarity is achieved by de-trending.1
Unfortunately, in most economies, the underlying distributions can shift unexpectedly. This vitiates any assumption of stationarity. The consequences for DSGEs are profound. As we explain below, the mathematical basis of a DSGE model fails when distributions shift (Hendry and Mizon 2014). This would be like a fire station automatically burning down at every outbreak of a fire. Economic agents are affected by, and notice such shifts. They consequently change their plans, and perhaps the way they form their expectations. When they do so, they violate the key assumptions on which DSGEs are built."