This methodological note describes the econometric methodology used to produce the result summarized in the Policy Brief “Understanding Italian Regional Fiscal Multiplier: Policy Insight for Enhancing Fiscal Policy Effectiveness” by Cavaliere G., Fanelli L., and Mazzali M., which documents the effectiveness of Italian local fiscal policy through the estimation of regional government spending multipliers at the NUTS-2 and NUTS-1 levels.
The analysis is based on Factor-Augmented Vector Autoregressive (FA-VAR) models estimated region-wise, intended to capture the heterogeneous responses to regional fiscal policy, while accounting for cross-sectional dependence. 
To circumvent the use of fiscal instruments for fiscal shocks in a context of limited cross-sectional data, a single external instrument constructed from factor analysis is used to identify regional output shocks and estimate regional fiscal reaction functions. 
This non-fiscal instrument captures the “common” (national) component driving Italian regional output and is by construction orthogonal to regional government spending shocks.