  Input-Output analysis describes the dependence of production, demand and
trade between sectors and regions and allows to understand the propagation of
economic shocks through economic networks. A central challenge in practical
applications is the availability of data. Observations may be limited to the
impact of the shocks in few sectors, but a complete picture of the origin and
impacts would be highly desirable to guide political countermeasures. In this
article we demonstrate that a shock in the final demand in few sectors can be
fully reconstructed from limited observations of production changes. We adapt
three algorithms from sparse signal recovery and evaluate their performance and
their robustness to observation uncertainties.
