Have you ever wondered how the tax policy in your local area might be influenced by what neighbouring places are doing? Or why certain trends seem to spread across cities, states and regions in unexpected patterns? The answer often lies in hidden networks of influence that shape decisions in ways that we rarely see.
In a world where everything seems connected, understanding these invisible networks has become crucial. But here’s the challenge: most of the time, we don’t actually know who influences whom. We see the outcomes – such as tax rates, policy changes or economic decisions – but the underlying web of relationships remains hidden.
The network detective problem
Imagine you’re a detective trying to solve a mystery, but instead of finding a criminal, you’re trying to map an invisible network of influence. You have clues – in the United States, for example, in how different states change their tax policies over time – but you don’t know who’s actually talking to whom or whose decisions matter to whom.
This is exactly the challenge that researchers face when studying ‘social interactions’ in economics and policy when measurements of such direct connections are not available. Traditional approaches have relied on assumptions: maybe states only care about their geographical neighbours, or perhaps they follow similar states economically. But what if these assumptions are wrong?
The mathematics behind the magic
In research with Imran Rasul (UCL) and Pedro Souza (Queen Mary University of London), published recently in the Review of Economic Studies, we develop a method for identifying these hidden networks using only the outcomes we can observe – such as tax rates, spending levels or policy changes – tracked over time (de Paula et al, 2025). Think of it as reverse-engineering the network from its effects.
The key insight is surprisingly elegant: when State A influences State B’s tax policy, and State B influences State C, this creates a chain reaction that leaves mathematical fingerprints in the data. By analysing these patterns across many years, we can work backwards to figure out who actually influences whom.
The method relies on an observation about how influences propagate through networks. When one state changes its tax rate, it doesn’t just affect its immediate ‘neighbours’ – it creates ripple effects that bounce around the entire network. These ripples have different strengths and travel through different paths depending on the network’s structure.
By watching how policy changes in one location eventually affect outcomes everywhere else, and how these effects evolve over time, we can essentially reconstruct the hidden map of influences. It’s like figuring out the shape of a pond by watching how waves travel across its surface.
Putting theory to the test
To prove that our method works, we test it on simulated networks where we know the ‘true’ connections. The results are positive: even with relatively short time periods (as few as five years of data), the method correctly identifies most strong connections and avoids false positives.
We test it on various network types – from simple friendship networks in schools to complex village social structures – and consistently find that the approach can recover the essential features of the hidden networks (see Figure 1).
Figure 1: Simulated and true networks
Source: de Paula et al, 2025
The tax competition revelation
The real excitement comes when applying this method to US state tax competition. For decades, economists assumed that states primarily compete with their geographical neighbours – if Colorado raises taxes, neighbouring states like Kansas or Utah might respond.
Figure 2: Network of US states, identified by economic neighbours. (A) kept and removed edges only; (B) all edges
Source: de Paula et al, 2025
The hidden network reveals a dramatically different story. Geographical proximity turns out to be an incomplete predictor of tax competition. Instead, states influence each other through more complex economic and political relationships that span across the continent (see Figure 2).
For example, South Carolina emerges as affecting policy decisions in places as distant as Missouri and Montana – states it doesn’t even border (see Figure 3).
Figure 3: General equilibrium impacts of South Carolina (SC) tax rises. (A) economic network state’s reaction to 10% increase in SC taxes; (B) economic network relative to to geographic network state’s reaction to 10% increase in SC taxes, relative to geographic network
Beyond geography: what really drives influence
The research uncovers fascinating patterns about what actually creates influence between states:
- Political opposition matters: surprisingly, states are more likely to influence each other when they have had governors from different political parties. This suggests that voters might be comparing their governor’s performance to opposition governors in other states – a form of ‘yardstick competition’.
- Distance still counts: while not geographical neighbours per se, influential relationships are more likely between states in similar regions, suggesting that some proximity still matters.
- Tax havens stay isolated: states known to be tax havens – such as Delaware and Nevada – show little influence over others, potentially easing concerns about a ‘race to the bottom’ in tax policy.
The ripple effect
When South Carolina raises its taxes by 10%, the hidden network shows that this creates policy responses across dozens of other states – many of which wouldn’t be affected at all if we only considered geographical neighbours. The total economic impact is roughly three times larger than traditional models would predict.
Why this matters
Our research opens up new ways of understanding how influence spreads through society. The applications extend far beyond tax policy:
- Financial crisis prevention: understanding hidden connections between banks and firms could help to prevent future financial contagions.
- Policy design: knowing the real networks of influence could help policy-makers to design more effective interventions.
- Social media and information: the same techniques could reveal how information and opinions actually spread online.
- Business strategy: companies could develop a better understanding of their competitive landscape and market influences.
The bigger picture
Perhaps most importantly, our research reveals how often our assumptions about influence networks are wrong. We tend to think geographically or organisationally – assuming influence follows obvious boundaries like state borders or industry categories. But real influence networks are often more complex, surprising and powerful than we imagine.
As our world becomes increasingly connected, tools like this become essential for understanding how changes in one corner of society ripple through to affect everyone else. Whether we’re talking about tax policy, financial markets or social movements, the hidden networks of influence shape our world in ways we’re only beginning to understand.
The next time you see a policy change in your local area, remember: the real story of why it happened might involve connections and influences stretching across the country in ways that no one ever imagined.
