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.