We review, under a historical perspective, the developement of the problem of non-fundamentalness of Moving Average (MA) representations of economic models, starting from the work by Hansen and Sargent . Nonfundamentalness typically arises when agents' information space is larger than the econometrican's one. Therefore it is impossible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We re-state the conditions under which it is possible to invert an MA representation in order to get an ordinary VAR, and we consider how the latter is used in the literature to assess the validity of Dynamic Stochastic General Equilibrium models, providing some interesting examples. We believe that possible nonfundamental representations of considered models are too often neglected in the literature. We consider how factor models can be seen as an alternative to VAR for assessing the validity of an economic model without having to deal with the problem of nonfundamentalness. We then review the works by Lippi and Reichlin  and Lippi and Reichlin  which are the first attempts to give to nonfundamental representations the economic relevance that they deserve, and to outline a method to obtain such representations starting from an estimated VAR.
Nonfundamentalness Structural VAR Dynamic Stochastic General Equilibrium Models Factor Models