Global factors for local shocks in a data-scarce environment: with an application to regional fiscal multipliers in Italy

We propose a novel econometric methodology for structural vector autoregressions with external instruments ('proxy-SVARs' or 'SVAR-IVs') in panel data characterized by strong cross-sectional dependence, dynamic heterogeneity, and limited availability of direct external instruments for the shocks of interest. For each unit, we specify a factor-augmented proxy-SVAR ('proxy-FA-SVAR') that incorporates factors summarizing cross-sectional information from the non-policy variables of the system. The effects of the policy shocks are then recovered indirectly by estimating unit-specific policy reaction functions through a minimum-distance approach. Identification relies on global instruments for the non-policy shocks; that is, proxies common to all units in the panel, internally constructed from a separate SVAR estimated on factors for the policy and non-policy variables. These global instruments can be complemented with local (idiosyncratic) instruments constructed from auxiliary unit-level SVARs. Their joint use renders the proxy-FA-SVARs overidentified and therefore statistically testable. We illustrate the methodology by estimating government spending multipliers for Italian NUTS-2 regions using annual data. The global and local instruments for the regional output shocks are obtained from Blanchard-Perotti-type SVARs.