📈 economics

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

This paper proposes a novel Factor-Augmented proxy-SVAR methodology for panel data with strong cross-sectional dependence and limited instruments, which identifies regional policy shocks using global and local instruments to estimate government spending multipliers in Italian regions.

Original authors: Giuseppe Cavaliere, Luca Fanelli, Marco Mazzali

Published 2026-07-16

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CC BY 4.0

Original authors: Giuseppe Cavaliere, Luca Fanelli, Marco Mazzali

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to figure out why a specific neighborhood in a giant city suddenly got a burst of energy. Maybe a new park opened, or a factory started hiring. You want to know: did that specific event cause the neighborhood to boom, or was the whole city just having a good week anyway? This is the daily puzzle for economists who study "multipliers." A multiplier is a simple idea: if the government spends one dollar, how many dollars of extra economic activity does that one dollar create? It's like throwing a pebble in a pond and counting how many ripples it makes.

Usually, economists look at the whole country to answer this. But what if you want to know why your town reacted differently than the town next door? That's where things get tricky. In the world of data, some places are like well-documented libraries with endless records, while others are like dusty attics where you can only find a few old receipts. This is called a "data-scarce" environment. Furthermore, neighborhoods don't exist in a vacuum; they are connected. If the city center has a party, the suburbs might get noisy too. This "cross-sectional dependence" means you can't just look at one town in isolation without getting confused by the noise from its neighbors. The big question is: how do you measure the true effect of a local spending decision when you don't have perfect data and everything is connected?

This paper, written by Giuseppe Cavaliere, Luca Fanelli, and Marco Mazzali, is like a new, clever detective kit designed specifically for these messy, data-poor neighborhoods. The authors propose a method to figure out how much government spending actually boosts local economies in Italy, a country where the north is wealthy and the south often struggles, creating a patchwork of very different local economies.

The core problem they tackle is that for small regions, it's almost impossible to find a "perfect" external tool (an instrument) to prove that a change in spending caused a change in growth. Usually, you'd need a magical variable that only affects spending and nothing else, but those are rare in local data. To solve this, the authors invent a two-step magic trick. First, they look at all the regions together to find the "common heartbeat" of the economy—the parts of the data that move together because of big, shared forces like national trends. They call these "global factors." Then, they look at what's left over for each specific region, the unique "local quirks."

They build their solution by creating two types of "clues" (instruments) for each region. One clue is the "Global Instrument," which captures the common economic waves affecting everyone. The other is a "Local Instrument," which captures the unique, weird stuff happening only in that specific town. By combining these two clues, they can mathematically separate the signal (the real effect of spending) from the noise (random local events or national trends). It's like having a microphone that can filter out the roar of the crowd (global factors) and the specific chatter of the person next to you (local factors) to hear exactly what the speaker said.

They tested this method on 20 regions in Italy (called NUTS-2 regions) using annual data from 1995 to 2021. The results were fascinating and revealed a clear divide. In the wealthy North-West regions (like Lombardia and Piemonte), the government spending multiplier was huge. For every euro spent, the economy grew by about 3.5 euros in the short term. It was as if the money hit a trampoline and bounced back with massive energy. However, as they moved South and to the Islands (the "Mezzogiorno"), the effect dropped significantly. In places like Calabria or Basilicata, the multiplier was much smaller, often hovering around 1 or even less, meaning the money didn't generate much extra growth.

The authors are careful to note that while their method works, the data isn't perfect. They only have 27 years of data for 20 regions, which is a bit like trying to predict the weather with only a month of history. Because of this, they can't be 100% certain about every single number, and their "confidence intervals" (the range where the true answer likely sits) are sometimes quite wide. For some southern regions, the data is so fuzzy that they can't even be sure if the spending helped or hurt. But despite this uncertainty, the pattern is clear: the same policy doesn't work the same way everywhere.

In short, the paper suggests that "one size fits all" economic policies are a myth. A spending plan that supercharges a rich, industrialized region might barely make a dent in a struggling one. By using their new "Global and Local Instrument" method, the authors show that we can finally start measuring these differences, even when the data is scarce and the regions are all tangled up with each other. It's a new way to listen to the local economy without getting lost in the global noise.

Technical Summary: Global Factors for Local Shocks in a Data-Scarce Environment

Problem Statement
Empirical macroeconomists face significant challenges when attempting to identify dynamic causal effects, such as fiscal multipliers, in local settings (e.g., regions or sectors) rather than aggregate national economies. Two primary obstacles hinder standard approaches in these contexts:

Cross-sectional Heterogeneity and Dependence: Local units often exhibit heterogeneous dynamic responses to policy shocks and are interdependent. Standard panel instrumental variable methods often fail under these conditions, particularly when assuming homogeneity in dynamic responses, which can lead to biased estimates (Canova, 2024; Canova and Pappa, 2025).
Instrument Scarcity: Credible external instruments for local policy shocks (e.g., exogenous innovations in regional fiscal spending) are frequently unavailable, limited, or measured imprecisely. This "data-scarce" environment prevents the direct application of conventional Proxy-SVAR (or SVAR-IV) methodologies, which rely on strong, exogenous external instruments for the shocks of interest.

These issues are particularly acute in the estimation of fiscal multipliers for Italian regions, where administrative data is less informative than at the national level, yet the need for region-specific analysis is critical due to persistent territorial disparities.

Methodology: The Proxy-FA-SVAR Framework
The authors propose a novel econometric framework for Structural Vector Autoregressions with external instruments (Proxy-SVARs) in panel data, termed Factor-Augmented Proxy-SVAR (Proxy-FA-SVAR). This methodology addresses the dual challenges of heterogeneity and instrument scarcity through a three-step indirect identification strategy:

Factor Augmentation: To account for cross-sectional dependence while preserving unit-specific heterogeneity, the authors augment each region-specific VAR with a vector of common factors ( $F^o_t$ ) extracted from the non-policy variables of the entire panel. This results in $R$ region-specific Proxy-FA-SVARs. The factors capture the common co-movements across regions, effectively modeling interdependence without imposing homogeneity on the dynamic parameters.
Indirect Identification via Global and Local Instruments: Since direct external instruments for the target policy shocks are unavailable, the authors recover the policy shocks indirectly. They estimate region-specific policy reaction functions using a Minimum Distance (MD) approach.
- Global Instruments: Proxies common to all units in the panel, constructed from a separate SVAR estimated on the global factors (summarizing policy and non-policy variables across the panel).
- Local (Idiosyncratic) Instruments: Region-specific proxies constructed from separate SVARs estimated on the idiosyncratic components of the variables.
- Overidentification: The joint use of global and local instruments renders the regional models overidentified. This allows for statistical testing of the validity of the identifying restrictions and the instruments themselves.
Instrument Construction: The global and local instruments are not drawn from external datasets but are internally constructed. They are derived from auxiliary SVARs estimated on the extracted factors. These auxiliary SVARs are identified using standard restrictions (e.g., recursive schemes like Blanchard-Perotti) to ensure the resulting instruments for the non-policy shocks are orthogonal to the policy shocks. The policy shocks are then recovered as the residual structural errors in the estimated reaction functions.

Key Contributions
The paper contributes to the literature on panel data econometrics and structural identification in three specific ways:

Region-Specific Causal Effects: It delivers dynamic causal effects for individual regions while explicitly accounting for cross-sectional heterogeneity and dependence, avoiding the biases associated with standard panel estimators.
Solution to Instrument Scarcity: It provides a general framework for settings where direct external instruments for local policy shocks are unavailable. By constructing instruments internally from the panel data itself (via factors and auxiliary SVARs), it enables structural analysis in data-scarce environments.
Testable Structural Models: Unlike many existing approaches that rely on untestable exclusion restrictions, the proposed method produces overidentified models. The joint use of global and local instruments allows for empirical testing of the overidentifying restrictions, providing a check on the validity of the identification strategy.

Empirical Application: Regional Fiscal Multipliers in Italy
The methodology is applied to estimate government spending multipliers for 20 Italian NUTS-2 regions using annual data from 1995 to 2021 ( $T=27, R=20$ ).

Data: The analysis uses real per-capita GDP and total government expenditure. Global factors are extracted from regional GDP series.
Instrument Construction: Global and local instruments for regional output shocks are obtained from Blanchard-Perotti-type SVARs estimated on the global and idiosyncratic factors, respectively. First-stage F-statistics confirm the instruments are strong.
Results:
- Heterogeneity: There is marked geographical heterogeneity in fiscal multipliers. Northern regions (e.g., Piemonte, Lombardia, Veneto) exhibit large and persistent multipliers (impact multipliers around 3.5, long-run multipliers above 2).
- North-South Gradient: Southern regions and Islands display significantly smaller multipliers. While some southern regions show positive multipliers, others (e.g., Abruzzo, Basilicata) show estimates below one or imprecisely estimated effects with wide confidence intervals.
- National Aggregate: The national multiplier is estimated at approximately 2.6 on impact and 2.3 in the long run, but the authors emphasize that this aggregate figure masks substantial regional variation.
- Uncertainty: The study highlights substantial uncertainty surrounding the estimates, particularly for regions with weaker data or more complex dynamics, necessitating caution in interpretation given the limited time dimension ( $T=27$ ).

Significance and Claims
The paper claims to offer a general econometric framework for identifying dynamic causal effects in panel data characterized by heterogeneous local responses, cross-sectional interdependence, and limited availability of valid external instruments.

Methodological Rigor: The authors position their approach as a transparent alternative to Bartik-type (shift-share) instruments, achieving exogeneity through structural identification in auxiliary SVARs rather than relying on the assumption that initial local shares are uncorrelated with subsequent unobserved factors.
Practical Utility: The framework is designed to be applicable in environments where direct external instruments are missing, allowing researchers to leverage the informational content of the panel data itself.
Empirical Insight: In the context of Italian regions, the study demonstrates that aggregate fiscal multipliers can be misleading. The effectiveness of government spending is geographically uneven, with the South and Islands struggling to translate fiscal resources into medium-term growth compared to the North.
Caveats: The authors explicitly acknowledge limitations, particularly the finite-sample properties given the ratio of time periods to cross-sectional units ( $T/R \approx 1.35$ ). They note that their confidence intervals, derived via Moving Block Bootstrap (MBB) in the final step, do not fully account for the uncertainty generated in the earlier steps of factor extraction and instrument construction, potentially understating true sampling uncertainty. They also clarify that the identified shocks represent local structural innovations conditional on common macroeconomic factors, rather than purely idiosyncratic disturbances or aggregate national shocks.

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