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Current economic theory typically assumes that all the macroeconomic variables belonging to a given economy are driven by a small number of structural shocks. As recently argued, apart from negligible cases, the structural shocks can be recovered if the information set contains current and past values of a large, potentially infinite, set of macroeconomic variables. However, the usual practice of estimating small size causal Vector AutoRegressions can be extremely misleading as in many cases such models could fully recover the structural shocks only if future values of the few variables considered were observable. In other words, the structural shocks may be non-fundamental with respect to the small dimensional vector used in current macroeconomic practice. By reviewing a recent strand of econometric literature, we show that, as a solution, econometricians should enlarge the space of observations, and thus consider models able to handle very large panels of related time series. Among several alternatives, we review dynamic factor models together with their economic interpretation, and we show how non-fundamentalness is non-generic in this framework. Finally, using a factor model, we provide new empirical evidence on the effect of technology shocks on labour productivity and hours worked. © 2011 The Authors. International Statistical Review © 2011 International Statistical Institute.