Nonfundamentalness in structural econometric models: a review

Economic theory typically assumes the existence of few unobserved unpredictable stochastic disturbances, called structural shocks, driving the whole economy. Would the economy be representable as a very high dimensional stochastic vector process, those shocks would be the reduced rank innovation of that process. In practice, however, only a few components of that process are observable, the innovation of which, in general, does not coincide with the structural shocks. As a result, a MA representation of the observed process in terms of the structural shocks will be a noninvertible one. In other words, the structural shocks driving the economy do not belong to the past of the observed series, but also involve their future, i.e. they are nonfundamental for the observed process. It follows that the present values of those structural shocks cannot be recovered from the observations; in particular, fitting causal VARs to the observed series can be extremely misleading. We review economic literature on VARs and we provide many examples of small size economic models that imply nonfundamentalness. If fundamental shocks nevertheless are to be recovered, the only solution consists in enlarging the space of observations, that is, in considering a very large panel of related time series. Among several alternatives, we consider the dynamic factor model methodology, which requires very little additional assumptions. We review first their economic interpretation and then we show how fundamentalness of the shocks is always guaranteed in this framework. Finally, by means of structural dynamic factor models we provide new empirical evidence on the relation between hours worked and technology shocks and we compare it with traditional VAR results.