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Networked risk perception and behavioral bubbles: the case of a pandemic
\email{[email removed]}
\affil*[1]{\orgname{Northeastern University}, \orgaddress{\city{Boston}, \state{MA}, \country{USA}}}
\affil[2]{\orgname{University of Paris-Saclay}, \orgaddress{\city{Paris}, \country{France}}}
\affil[3]{\orgname{Paris School of Economics}, \orgaddress{\city{Paris}, \country{France}}}
\abstract{ Risk perception is typically modeled as an individual cognitive readout of objective hazard. Yet during crises what people judge as risky is shaped by what their peers do, making risk perception in part a property of communities, not just individuals. Using weekly mobility data from 313 Massachusetts municipalities over the first year of the COVID-19 pandemic and a pre-pandemic inter-town mobility network that fixes interaction structure before the shock, we estimate two-way fixed-effects panel regressions that separate the response to local case incidence, inter-town behavioral spillover along the mobility network, and within-town behavioral inertia; the pre-shock network and a lagged peer signal address the standard reflection and endogenous-group concerns. Inter-town behavioral spillovers are substantial and localize almost entirely within mobility-defined communities (the empirical referent of behavioral bubbles), with effectively no propagation across community boundaries. The within-community spillover carries behavioral content beyond what peer-town case information alone would predict: when network-exposure-to-cases and network-exposure-to-behavior are raced, the behavioral channel survives and the case-exposure channel goes null. A four-way decomposition by mobility and demographic similarity shows the spillover requires both, concentrating where towns are routinely connected and socioeconomically similar and vanishing between similar towns that are not connected, which points to an observational and normative channel rather than a purely informational one. These results recast risk perception as a networked phenomenon and identify mobility-defined communities, rather than administrative units, as the operative scale of behavioral response. The pattern should generalize wherever exposure is uncertain, evolving, and socially negotiated, including climate adaptation and financial contagion. }
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Low-probability, high-impact risks such as pandemics, climate shocks, and financial crises pose a persistent puzzle for science and policy kunreuther2013risk,aven2010risk. Their objective properties can increasingly be quantified, yet societies routinely under-react to some threats and over-react to others KahnemanTversky1979,slovic2016perception,tversky1974judgment,slovic1987perception. Even communities facing the same pathogen or physical hazard differ widely in how far they change daily routines, whether they trust institutions, and how much they invest in protection. During the COVID-19 pandemic, places with comparable age structures, health systems, and policy environments followed sharply different trajectories of behavior and mortality flaxman2020estimating,hsiang2020effect,haug2020ranking,brauner2021inferring,aboukheydari2021immediate. Comparative work finds that even after demographics, comorbidities, socioeconomic composition, and the timing and stringency of interventions are accounted for, much of the cross-sectional variation in outcomes is left unexplained. That residual points to something systematic in how communities perceive and respond to risk that current models do not capture.
We argue that the missing structure is the social construction of risk perception at the community level. Work in psychology, sociology, and behavioral economics has long shown that perceived risk is not a direct readout of objective probabilities but the product of cognitive heuristics, cultural frames, and social influence slovic1988risk,douglas1982can,KahnemanTversky1979,finucane2000affect,loewenstein2001risk,flynn1994gender. The social amplification of risk framework describes how media, institutions, and interpersonal communication amplify or dampen hazard signals and so set off cascades of concern or complacency kasperson1988social,pidgeon2003social. A parallel literature on social norms shows that people read their peers to judge what is safe, appropriate, or necessary, and adjust accordingly cialdini2004social,bicchieri2005grammar,fehr2004social,cialdini1990focus. Perceived risk, on this view, is negotiated and reinforced within communities, and it can stay sticky or path-dependent even as objective conditions move brewer2007meta,savadori2021risk,lavell2020social,tsoy2021role. Yet most formal models of behavior under risk, whether in economics, epidemiology, or policy analysis, still treat risk perception as an individual attribute bauch2013social,reluga2010game,funk2010modelling,fenichel2011adaptive. They picture individuals weighing costs against local risk, sometimes with bounded rationality or prospect-theoretic distortions, and leave the social processes that generate perceived risk implicit. This abstracts away a regularity that crises make hard to ignore: much of what people do is coordinated and constrained at the group level centola2010spread,centola2018behavior,caoheydari2022micro.
Here we give direct empirical evidence that community-level peer effects matter for behavior under risk. People do not meet pandemic, climate, or financial risk alone. They meet it as members of communities whose members watch one another, trade information, and settle on implicit thresholds of how much caution is enough bavel2020using,betsch2020behavioural. Using high-frequency mobility data from 313 Massachusetts municipalities across the first pandemic year, we show that a town's behavior responds to its local infection rate and, to a substantial degree, to what its mobility-linked peers are doing kraemer2020effect,chang2021mobility,chan2020risk,barbieri2021impact,lawal2022movement,galasso2020gender. We build a pre-pandemic mobility network from device-level travel flows recorded before the state's first COVID-19 case and treat it as an exogenous structure along which behavioral norms can travel colizza2007reaction,balcan2009multiscale,brockmann2013hidden,meloni2011modeling,pastor2015epidemic. The design separates three forces acting on town mobility. The first is local objective risk, the response of a town's behavior to its own weekly incidence. The second is within-town inertia, which at the town level folds residents' own-behavior persistence together with within-town peer reinforcement into one lagged-outcome channel. The third is across-town spillover, carried by pre-existing interaction patterns and, as we show, gated by demographic similarity.
Three findings anchor the paper. The first is that once we condition on local case incidence, time-invariant town characteristics, and common weekly shocks, the cross-community variation that remains in protective behavior is itself organized along the pre-pandemic mobility network. The second is that this structure is local: a Louvain partition of the network blondel2008fast splits the spillover into a within-community component that carries the signal and a across-community component statistically indistinguishable from zero, the empirical referent of what we call behavioral bubbles. The third characterizes when the spillover operates. Crossing the mobility partition with a near-orthogonal partition on demographic similarity shows that the channel requires both. It is concentrated among towns that are routinely connected and demographically similar, it is absent across mobility-community boundaries even when the towns on either side resemble one another, and it is only partial among connected towns that differ demographically. Two things follow. Routine connection is necessary but not sufficient, so demographic similarity gates the network channel rather than acting as a separate driver. And the pattern rules out the most natural alternative to social influence, that demographically similar places simply react alike to similar objective conditions: were that the case, similar but unconnected towns would co-move, and they do not. Two further results round out the picture. Towns respond to local risk in the direction any precautionary model predicts. And behavior is persistent at the town level, so the lagged-outcome channel, working together with the peer channel, hardens early differences into lasting divergence; a community that settles into caution, or into normality, tends to stay there absent a substantial local or network shock manski1993identification,bramoulle2009identification,jackson2008social.
We read these results as micro-level evidence that risk perception is socially constructed at the community level. Rather than respond only to its own epidemiological situation, a community appears to infer how much caution is warranted from its interaction network, aligning in part with what its mobility-linked and demographically similar peers do. This helps explain why so much cross-place variation in pandemic outcomes resists demographics, institutions, and formal policy flaxman2020estimating,hsiang2020effect. It also suggests that models of collective response to systemic risk should treat perceived risk as a property of interacting communities rather than of isolated individuals bavel2020using,betsch2020behavioural, and that interventions built around administrative units, or on an assumption of independent response, can miss the channels through which perception and behavior actually move.
COVID-19 is our setting, but the mechanism is not specific to it. Behavioral spillovers along social and spatial networks should arise whenever risks are uncertain, evolving, and socially contested, conditions that describe climate adaptation, financial contagion, and technological hazards as much as infectious disease. The pandemic simply supplies an unusually rich, high-frequency record of both behavior and exposure. What it reveals is portable, and the sections that follow make the case that perceived risk has a measurable community-level structure that current models leave out.
We test the social-construction hypothesis on town-level mobility data from Massachusetts during the first year of the COVID-19 pandemic. The setting offers cross-sectional variation across 313 municipalities while holding the state-level legal and institutional environment fixed, and weekly device-flow data make it possible to track behavior at a frequency comparable to the timescale at which information and norms diffuse. The outcome $Y^{adj}_{i,t}$ is the median daily non-home dwell time in town $i$ during week $t$, expressed as a deviation from the town's last two pre-pandemic weeks: positive values mean residents spent longer outside the home than they did pre-COVID, negative values the reverse. Local hazard is captured by the weekly case rate per 10{,}000 residents, $X_{i,t}$.
The empirical strategy hinges on a pre-determined network along which behavioral signals can propagate. We construct $\mathrm{PreG}$ from the same device-flow data restricted to the last two weeks of January 2020 (before the first confirmed case in the state) and normalize each row by its outflow total, so that $\mathrm{PreG}_{ij}$ is the share of town $i$'s routine outflow directed toward town $j$. Because the network predates any pandemic exposure, it captures the state's standing travel structure of commuting corridors, retail catchments, and social ties without itself being shaped by the pandemic, and it serves as a pre-determined channel along which behavioral signals can cross between towns. The principal spillover regressor is
the network-weighted lagged behavior of town $i$'s routine peers. Throughout we estimate two-way fixed-effects panel regressions with town fixed effects (absorbing time-invariant municipal characteristics) and week fixed effects (absorbing common shocks such as state-wide policy and national news), with standard errors clustered at the town level. Methodological detail is deferred to Methods.
Table (ref) (columns 1--2) and Fig. (ref)a,b report the three structural coefficients of Eq. (ref): $\alpha$ on local hazard $X_{i,t}$, $\beta$ on the inter-town peer signal $S^{\mathrm{PreG}}_{i,t-1}$, and $\gamma$ on the own lag $Y^{adj}_{i,t-1}$. Each coefficient is significant in the headline specification, and each plays a distinct role.
Towns do respond to local risk in the direction any precautionary model predicts: $\hat\alpha < 0$, with higher case rates predicting reduced non-home dwell time. At the winter 2020--21 peaks, when weekly incidence in the worst-hit towns ran above $100$ cases per $10{,}000$, the implied hazard-driven reduction in non-home dwell time is on the order of a few minutes per day relative to a town with near-zero incidence.
The inter-town peer signal $\beta$ carries the main result, and its magnitude depends on whether own-town persistence is controlled, so the two pooled columns must be read together. Without the own lag (column 1) $\hat\beta = 0.51$; with it (column 2) $\hat\beta = 0.23$ ($p<0.01$). The drop is not the peer effect weakening under scrutiny but the removal of a known upward bias: the omitted own-town behavior $Y^{adj}_{i,t-1}$ is positively correlated with the peer signal, because connected towns co-move, so the static estimate absorbs part of a town's own persistence and overstates the across-town channel. The FE+AR(1) estimate $\hat\beta = 0.23$ is the clean across-town response, the share of a one-unit shift in the network-weighted lagged behavior of a town's routine peers that passes into its own behavior the following week, holding own-town momentum, contemporaneous hazard, and time-invariant town characteristics fixed. This partialed estimate is the one that carries the interpretation, and it is a lower-bound measure of social influence: it captures only the across-town channel, because any peer reinforcement within the focal town has nowhere to go and is absorbed into the lagged-outcome term $\gamma\,Y^{adj}_{i,t-1}$, since the town aggregation cannot separate residents' own persistence from within-town peer adjustment manski1993identification,bramoulle2009identification,jackson2008social.
The within-town channel $\gamma$ supplies the matching upper bound. With $\hat\gamma = 0.46$, the lagged-outcome term folds individual persistence together with within-town peer reinforcement at the town level, so the sum $\hat\beta + \hat\gamma = 0.68$ is an upper-bound measure of behavior-on-behavior coupling per unit lagged behavior, taking in every within-town and across-town peer channel along with the residual individual persistence that cannot be separated out without individual-level ties. The true social-influence response per unit peer behavior therefore lies between $\hat\beta = 0.23$ (across-town only) and $\hat\beta + \hat\gamma = 0.68$. These are one-week responses. Because the own lag re-injects part of last week's peer-driven shift, the cumulative own-town response to a sustained change in peer behavior is the dynamic multiplier $\hat\beta / (1 - \hat\gamma) \approx 0.42$, larger than the one-step $\hat\beta$ but still below the inflated static estimate of $0.51$, which therefore overstates even the long-run peer effect and is not itself a bound.
Taken together, the headline specification isolates a substantial network-mediated channel in the cross-community variation that local hazard and town characteristics leave unexplained. We take up what this residual structure implies for behavioral science, for adaptive epidemic models, and for intervention design in the Discussion.
Behavior is also persistent at the town level, and the persistence carries content. The within-town channel $\gamma$ implies an own-town-shock half-life of about a week on its own, and the inter-town channel lengthens that decay because lagged peer behavior re-injects last week's shock at each step. The effective half-life of a community-level shock, governed by the dominant eigenvalue of $\hat\gamma\,I + \hat\beta\,\mathrm{PreG}$ acting on the within-mobility-community block, runs materially longer than the AR(1) parameter alone would suggest. Two towns with nearly identical objective exposure but different early shocks then settle onto persistently divergent trajectories. Once a community converges on caution or on normality, the joint action of within-town inertia and the within-community peer effect $\beta^{w}$ holds it there.
Where does the inter-town peer effect travel? A Louvain modularity partition of the symmetrized origin-normalized $\mathrm{PreG}$ recovers seven mobility communities (Fig. (ref)a). They are spatially coherent, picking out a Greater Boston cluster, a Cape Cod and South Coast cluster, a Pioneer Valley cluster, a Berkshires cluster, and so on, yet they do not track the Massachusetts county boundaries overlaid as dashed lines. The partition is organized by routine flow, not by jurisdictional design.
The mobility partition matters for behavior as well as for connectivity. Within-community $\mathrm{PreG}$ edges are markedly heavier than across-community edges (Fig. (ref)b), and the same partition organizes behavioral co-movement, not connectivity alone. After we remove the common pandemic shock by week-demeaning each town's $Y^{adj}$ trajectory, the pairwise Pearson correlations across towns, ordered by community membership, fall into a clear block-diagonal pattern (Fig. (ref)e): positive within mobility communities and essentially zero across them. A partition recovered from pre-pandemic flows alone, with no reference to outcomes, thus accounts for a meaningful share of behavioral co-movement during the pandemic.
A complementary Louvain partition on four widely used town-level demographic indicators, namely median age, net worth, diversity index, and population density, recovers eight demographic communities (Fig. (ref)c). Two properties matter for what follows. First, these communities are not connectivity-coherent: within-demographic-community pairs are no heavier in $\mathrm{PreG}$ than across-community pairs (Fig. (ref)d), so demographically similar towns are not the towns that travel between one another. Second, on the 313-town intersection the mobility and demographic partitions are close to orthogonal ($\mathrm{ARI} = 0.08$, $\mathrm{NMI} = 0.14$; Fig. (ref)f), so membership in a demographic community is not redundant with membership in a mobility community. Crossing the two therefore produces four genuinely distinct kinds of inter-town pair rather than a relabeling of the mobility split, which is the structural basis for the four-way decomposition below.
The mobility partition cleanly splits the inter-town peer effect. Masking $\mathrm{PreG}$ element-wise with the within- and across-community indicators (Methods §(ref)) gives two spillover regressors that enter as separate terms (Table (ref), columns 3--4; Fig. (ref)b). The within-community coefficient $\beta^{w}$ is large and significant; the across-community coefficient $\beta^{a}$ is statistically indistinguishable from zero. The split holds once within-town inertia is absorbed in column 4, and auxiliary specifications that re-introduce the unsplit $S^{\mathrm{PreG}}_{i,t-1}$ alongside the masked components confirm that the within-community pairs carry the channel (SI Table (ref)). The peer effect, already a lower-bound measure of social influence, runs almost entirely along edges inside the same routine-interaction community. This is the empirical referent of a behavioral bubble centola2010spread,centola2018behavior.
Crossing the mobility and demographic Louvain partitions splits $\mathrm{PreG}$ into four Hadamard-masked components, indexed by whether each town pair is within the same or across different mobility communities and within the same or across different demographic communities (Methods §(ref)). The four spillover regressors enter Eq. (ref) as separate terms, with coefficients reported in Fig. (ref)c. The peer effect concentrates in one block: $\beta^{ww}$, on pairs sharing both a mobility community and a demographic community, is several times the pooled $\hat\beta$; $\beta^{wa}$, on pairs in the same mobility community but different demographic communities, is smaller, though still positive and significant; and the two across-mobility coefficients, $\beta^{aw}$ and $\beta^{aa}$, are statistically indistinguishable from zero. The spillover thus needs both kinds of proximity. Routine connection is necessary, since across mobility-community boundaries we detect no spillover whether or not the two towns are demographically similar. Connection on its own is not sufficient, since among connected towns the channel concentrates in the demographically similar pairs. Demographic similarity gates the mobility channel rather than carrying one of its own.
The null across-mobility coefficients also bear on identification. The most natural alternative to social influence is that demographically similar towns respond in parallel to similar objective conditions, a pattern that could masquerade as network spillover. If that were the source, demographically similar but unconnected towns would co-move; that is the $\beta^{aw}$ block, and it is indistinguishable from zero. The crossing is what isolates this test. A decomposition along demographic similarity alone loads on both its within and across blocks (Table (ref), columns 5--6), because that partition cuts across mobility communities (Fig. (ref)f), so only the joint split separates out the similar-but-unconnected pairs the confound would require. A continuous-modulator test that replaces the binary demographic mask with the town-by-town similarity matrix $D$ and races $\mathrm{PreG}\odot D$ against $\mathrm{PreG}$ (SI §(ref), SI Table (ref)) reaches the same conclusion.
Three checks address the alternative readings most likely to worry a reader. First, the pattern is not an artifact of a few large municipalities. Dropping the 32 towns above the $90^{\text{th}}$ population percentile, among them Boston, Worcester, and Springfield, leaves $281$ towns and $14{,}612$ town-weeks, and in that reduced sample the spillover signature holds in magnitude and significance across every specification in Table (ref) (SI Table (ref)). It is not driven by metropolitan heterogeneity or by Boston's unusual position in the network.
Second, the spillover is a behavioral channel rather than a cases-aware one. Replacing $S^{\mathrm{PreG}}_{i,t-1}$ with a network-exposure-to-cases term $S^{\mathrm{PreG}\cdot X}_{i,t-1} = \sum_j \mathrm{PreG}_{ij}\,X_{j,t-1}$, or entering the two together, leaves the cases term statistically indistinguishable from zero while $S^{\mathrm{PreG}}_{i,t-1}$ keeps its sign and magnitude (SI Table (ref)). Towns adjust to peer behavior, not to peer hazard, which fits norm-based and observational-learning accounts of diffusion better than a purely informational risk-news channel.
Third, the spillover is specific to the mobility network rather than a generic spatial-correlation artifact. Re-estimating it on a geographic-proximity placebo, an inverse-distance or shared-county adjacency that encodes proximity without routine interaction, in place of $\mathrm{PreG}$ separates the mobility-specific content of the channel from spatial autocorrelation; a channel that works through routine interaction predicts an attenuated placebo coefficient relative to the mobility-network estimate.
Town-level protective behavior in the first pandemic year reflects two things: a response to local case incidence, and a residual cross-community variation that local hazard and time-invariant town characteristics do not explain. That residual is the object standard models assign to individual risk perception, and our central result is that it is itself structured. It tracks peer behavior along the pre-pandemic mobility network, and it does so within mobility communities in particular: the spillover runs along edges that connect towns inside the same routine-interaction cluster and is statistically absent across community boundaries, the signature we call a behavioral bubble. The across-town coefficient $\beta$ is a lower-bound measure of social influence, since within-town peer reinforcement is absorbed into the persistence term $\gamma$, and the matching upper bound $\beta + \gamma$ points the same way. The demographic decomposition in the SI (SI §(ref)) sharpens the pattern rather than weakening it, strongest where peers are demographically as well as routinely similar.
Why does the residual take this particular shape, organized along peer behavior rather than along peer hazard or noise? The candidate inputs to community-level risk calibration are not equally legible. Local incidence is abstract, lagged, and noisily measured: a weekly case rate per ten thousand residents depends on testing intensity, arrives with delay, and is hard for any resident to turn into a felt sense of personal exposure. Peer behavior is immediate and directly visible, in whether neighbors are out, whether the center of town is busy or shuttered, whether connected communities have loosened or tightened. When residents judge how much caution is enough, they appear to anchor on the legible, continuously updated cue. Two features of our results fit this account. The channel loads on peer behavior and not on peer cases: exposure to connected towns' incidence adds nothing once their behavior is in the model, which is what an observational or normative mechanism predicts and a purely informational one does not. And the signal concentrates where peers are actually observed, inside routine-interaction communities, rather than diffusing across the state. Read this way, the shape of community-level risk perception is a reasonable response to which cue is easier to see, and it carries a cost: it locks communities onto divergent paths that their objective circumstances alone would not produce.
The broader contribution is to move risk perception from the individual to the community. The social-amplification-of-risk kasperson1988social,pidgeon2003social and social-norm cialdini2004social,bicchieri2005grammar traditions long held that perceived risk is socially negotiated, and network science established that behavior spreads along social ties centola2010spread,centola2018behavior,centola2007complex,christakis2007spread,granovetter1978threshold,watts2002simple,bond2012experiment,aral2012identifying,centola2011experimental. What has been missing is a way to measure that negotiation at the scale of geographic communities. Our estimates provide one: after conditioning on local hazard and town characteristics, the residual cross-community variation in behavior is organized along persistent routine-interaction channels, concentrated within mobility-defined communities and gated by demographic similarity. That the channel requires both a routine tie and demographic similarity, rather than connection alone, fits accounts in which social influence operates through perceived relevance: a community appears to weight the behavior of peers it both interacts with and resembles, reinforced among similar actors rather than transmitted by contact alone centola2007complex,centola2011experimental. Risk perception, in this sense, has a measurable community-level shape, one that can be partitioned and put to use. The pre-determined network and lagged-peer design recover the across-town spillover where the reflection problem would otherwise block identification, and they bound the within-town channel rather than discarding it manski1993identification,bramoulle2009identification,sacerdote2001peer,bramoulle2020peer,comolaprina2021.
The modeling implication is direct. Epidemic models already route pathogens along mobility networks colizza2007reaction,balcan2009multiscale,brockmann2013hidden,kraemer2020effect,chang2021mobility; our results show that the same network also routes caution, coupling disease and behavioral dynamics on one substrate. A behaviorally adaptive model should therefore carry precaution as a network-mediated state, updating on a peer-weighted average of peers' precaution with weights set by mobility flow and gated by demographic similarity, rather than as a private function of local prevalence. This is the network structure that behavioral-feedback epidemic models have so far had to assume bauch2013social,reluga2010game,fenichel2011adaptive,funk2010modelling,verelst2016behavioural,bedford2019new,rahmandad2021behavioral,rahmandad2022missing, and a model that leaves it out will misjudge the reach of communication-based interventions.
The same structure changes how interventions should be targeted. Because behavior co-moves within mobility communities that cut across county and health-district lines (Fig. (ref)a), communication organized around administrative units will miss the scale on which behavior actually moves; and because the structured part of behavior runs through peers, messaging aimed only at where cases are will reach less far than messaging aimed at where peers are. That points to a concrete lever: within a mobility community, moving a few influential towns can shift the whole cluster through the within-community channel $\beta^{w}$, whereas effort allocated on the case distribution alone is spent on towns whose behavior is being set by peers outside the targeting unit. It also gives a readable diagnostic. The share of cross-place outcome variation left unexplained by demographics, comorbidities, and formal policy flaxman2020estimating,hsiang2020effect,allcott2020polarization,goolsbee2021fear,painter2021political,holtz2020interdependence,devaan2021social,caoheydari2022micro depends in part on where a place sits in the mobility-community structure, a quantity recoverable from device flows and census data before the next shock. Related work on the same Massachusetts towns finds that a town's mobility-network position carries out-of-sample predictive value for short-horizon case forecasts, largest where granular local case histories are coarse or delayed ilami2025network.
Two limitations bind the causal reading most tightly. First, the design is ecological: spillovers are estimated over towns, not individuals, so the town-level result is consistent with several individual mechanisms, among them observational learning, normative conformity, and shared exposure to local media, which we cannot adjudicate among, although the behavior-not-hazard and within-community patterns both lean away from a purely informational account. Second, while the lagged-peer specification and the pre-pandemic network neutralize the most direct identification threats, namely Manski reflection and endogenous group formation, they cannot rule out a time-varying unobserved shock that travels along the same edges as $\mathrm{PreG}$; the network-exposure-to-cases falsification and the geographic-proximity placebo address this where a counter-structure can be built, and the four-way decomposition adds another: a shared-conditions account, in which demographically similar towns simply react alike to correlated objective risk, would produce co-movement between similar towns whether or not they are connected, yet the similar-but-unconnected block is null. A fully causal claim would still need a behavioral instrument we do not have. The remaining caveats are narrower. Non-home dwell time is one window on protective behavior and leaves masking and contact patterns unobserved; SafeGraph coverage underweights residents without smartphones and drops 38 small rural towns; and the geography of Massachusetts, one dominant metro beside a rural west, may not carry over to states with several comparable metros, even though the empirical design itself travels wherever a pre-shock mobility panel and weekly outcomes exist.
That portability is the larger promise. The regularity we report, behavioral spillover concentrated where routine interaction and similarity overlap, should appear wherever risk is uncertain, evolving, and socially contested, and the empirical template of a pre-shock interaction network, a lagged-peer specification, and a similarity modulator applies directly. Climate adaptation is the clearest next case: heat protection, evacuation, and air-quality avoidance plausibly diffuse along the same commuter and social networks, modulated by income and demographic similarity, and the relevant mobility data are increasingly available. Whether the mechanism reaches slower-moving domains such as household finance, where formal financial access reshapes the informal risk-sharing arrangements that link households comolaprina2023, or vaccine uptake is an open question the design is built to test. The pandemic case makes the general point hard to avoid: communities do not meet risk in isolation, and models that assume they do, whether of disease, of climate, or of financial contagion, will misread which interventions move which populations and misallocate the attention that decides whether a society absorbs the next systemic shock or amplifies it.
We combine three town-level data sources for 313 of the 351 Massachusetts municipalities: SafeGraph (Advan) device-flow data, weekly COVID-19 case counts from the Massachusetts Department of Public Health, and U.S. Census Bureau socioeconomic and demographic features. The 38 missing municipalities are small western and central towns absent from the SafeGraph place-level panel; their exclusion is a structural property of the device-flow source rather than an analytic choice.
The mobility data are anonymized device-level location records, originally at the census-block-group (CBG) level, aggregated to census tract and then to town using Census CBG$\to$tract and tract$\to$town crosswalks. Town is the operative unit for three reasons: COVID-19 case data are reported weekly at the town level; town aligns with public-health and municipal policy authority in Massachusetts; and place-level aggregation absorbs CBG-to-tract noise from device counts. The town panel runs weekly from early March 2020 through March 2021 (52 weeks). Boston is a single SafeGraph place; the main-text regressions treat it as one node, while the community-map figures expand it into 14 known neighborhood polygons at plot time.
Local hazard is the town-week count of weekly new cases per 10{,}000 residents, denoted $X_{i,t}$. Mortality and hospitalization counts are not used: mortality is not town-level-resolved for most of 2020, and hospitalizations conflate residence with the location of higher-capacity hospitals, biasing apparent objective risk toward urban towns regardless of behavior. Demographic features are taken at the town level: median age, household net worth, a diversity index, population density per square mile, renter share, and a seven-share race-composition vector (Hispanic, Asian, American Indian, Black, White, Mixed, Other). For the 14 Boston neighborhoods, features are population-weighted into a single Boston row to keep alignment with the SafeGraph place granularity.
The outcome variable is the within-town-demeaned median non-home dwell time. Let $D_{i,t}$ denote the median non-home dwell time of town $i$ in week $t$ (the SafeGraph published quantity, in minutes per day), and let $\bar{D}_{i}^{\mathrm{pre}}$ denote its town-specific mean over the last two pre-pandemic weeks of January 2020. The regression outcome is then
in minutes per day. Demeaning by the last two pre-pandemic weeks removes time-invariant cross-town differences in baseline mobility and lets the coefficient on $X_{i,t}$ be read directly as the change in minutes per day per unit incidence change. We use minutes per day rather than log dwell time because $Y^{adj}_{i,t}$ takes both signs and zero, and the linear scale matches the unit of SafeGraph's published median dwell-time series. The panel is indexed by town $i \in \{1,\dots,313\}$ and week $t \in \{1,\dots,52\}$, giving $N_{\text{obs}} = 16{,}276$ town-week observations unless otherwise noted; missing town-weeks are dropped pairwise.
The pre-pandemic mobility network $\mathrm{PreG}$ is the empirical scaffold along which the spillover regressions allow behavioral signals to propagate. Because it is constructed before any pandemic exposure, it is not a function of the pandemic-period outcome, which addresses the most direct simultaneity concern. The source is the town-to-town SafeGraph flow matrix, aggregated from device-level visits during the last two weeks of January 2020, the most recent pre-pandemic window for which clean data are available, before the first confirmed Massachusetts COVID-19 case.
From this matrix we derive the analytic default used throughout: the origin-normalized form $\mathrm{PreG}_{ij} = (\text{flow}_{i \to j}) / \sum_{k \ne i} \text{flow}_{i \to k}$, so that each row sums to one with the diagonal zeroed. For community detection the matrix is symmetrized to $\widetilde{\mathrm{PreG}} = (\mathrm{PreG} + \mathrm{PreG}^{\top}) / 2$ with the diagonal zeroed; the asymmetric origin-normalized form is retained for the regression-side spillover regressor, while the symmetrized form is used only for Louvain modularity optimization. The 313 SafeGraph-covered towns are held in a fixed canonical order that all subsequent matrices ($D$, the masks, and the regression panels) inherit, and the 38 SafeGraph-absent towns are excluded throughout. The spillover regressor is as in Eq. (ref), $S^{\mathrm{PreG}}_{i,t-1} = \sum_j \mathrm{PreG}_{ij}\,Y^{adj}_{j,t-1}$, with $\mathrm{PreG}_{ii} = 0$. Five flow-matrix variants (raw, summed, origin-normalized, destination-normalized, and the four with-diagonal counterparts) are produced by the public reproduction code and described in SI \S(ref).
The mobility and demographic partitions used in Figs. (ref) and (ref)c are both obtained by Louvain modularity optimization blondel2008fast of an appropriate town-by-town weighted graph. We chose Louvain over alternatives such as Clauset--Newman--Moore greedy agglomeration clauset2004finding, label propagation, and spectral cuts for three reasons: it admits a tunable resolution parameter $\gamma$ that lets us report the modularity-maximizing partition rather than fix an unobservable resolution in advance; a sweep across $\gamma$ is essentially free at this graph size ($n = 313$); and it is reproducible across runs at a fixed random seed. The Clauset--Newman--Moore algorithm is also run, on the same graphs, as a baseline check (SI §(ref)); the two algorithms agree on the broad community structure, and Louvain attains a higher modularity at the reported resolution in both the mobility and demographic settings.
Louvain is run with the python-louvain implementation blondel2008fast, weight-aware, with a deterministic random seed. For each graph we sweep the resolution parameter $\gamma$ on a $20$-point grid from $0.1$ to $2.0$ in steps of $0.1$, recompute modularity $Q(\gamma)$ at every step, and adopt the partition whose modularity is maximal. The mobility sweep on $\widetilde{\mathrm{PreG}}$ has a clear global maximum at $\gamma = 0.70$ ($Q = 0.670$, $k = 7$); the demographic sweep on the RBF-kernel graph has a comparably clean maximum at $\gamma = 0.60$ ($Q = 0.859$, $k = 8$). Lower-$\gamma$ partitions collapse communities and raise modularity only mildly, while higher-$\gamma$ partitions over-fragment the network and modularity falls monotonically. We commit to these two $\gamma$ values throughout the paper; the full resolution-sweep curves (SI Fig. (ref)) and the corresponding greedy-modularity comparison are in SI \S(ref).
The mobility partition is run on $\widetilde{\mathrm{PreG}}$, the symmetrized origin-normalized pre-pandemic flow matrix with zeroed diagonal. The reported partition at $\gamma = 0.70$ has $Q = 0.670$ and $k = 7$ communities of sizes $[98, 62, 56, 40, 24, 20, 13]$. The communities are spatially coherent (Greater Boston/Northeast; Cape Cod and South Coast; Pioneer Valley; Berkshires; north-central; central; islands) but do not align with Massachusetts county boundaries, as the dashed-county overlay in Fig. (ref)a makes explicit.
The demographic partition is built from a town-by-town RBF kernel on a four-feature standardized vector: median age, household net worth, diversity index, and population density. The kernel is sparsified by mutual-$k$NN with $k = 12$ to remove the dense tail of weak similarities that would otherwise dominate the modularity computation, and Louvain is then run on the resulting sparse weighted graph over the same $\gamma$-grid. The reported partition at $\gamma = 0.60$ has $Q = 0.859$ and $k = 8$. We use this four-feature categorical partition, rather than the richer continuous demographic-similarity matrix $D$ of SI \S(ref), specifically for the four-way decomposition (Fig. (ref)c), because the four-way crossing requires a partition on each axis. The matrix $D$ enters the regressions as a continuous modulator (SI \S(ref)), and the two are complementary tests of the same structural claim. On the 313-town intersection of the two partitions, $\mathrm{ARI} = 0.082$ and $\mathrm{NMI} = 0.144$: the partitions index nearly independent dimensions of inter-town structure (Fig. (ref)f), which is the formal precondition for the four-way decomposition to carry non-redundant information. Implementation details and the corresponding greedy-modularity baseline are in SI \S(ref).
All regressions are two-way fixed-effects panel models on $N = 16{,}276$ town-weeks (313 towns $\times$ 52 weeks). The pooled headline specification (Table (ref), columns 1--2) is
where $\mu_{i}$ are town fixed effects, $\lambda_{t}$ are week fixed effects, and $\varepsilon_{i,t}$ is the disturbance. The three structural coefficients $(\alpha, \beta, \gamma)$ correspond, respectively, to the response to local objective risk, the inter-town behavioral spillover along $\mathrm{PreG}$, and within-town behavioral inertia; this $(\alpha, \beta, \gamma)$ labelling is used consistently throughout the Results and figures. Because the unit of analysis is the town, $\gamma$ does not isolate a single individual-level mechanism: at this aggregation, the lagged-outcome channel from $Y^{adj}_{i,t-1}$ to $Y^{adj}_{i,t}$ combines residents' own-behavior persistence with within-town peer reinforcement, both of which propagate intra-town from week to week. Inter-town peer effects, by contrast, enter only through $\beta$ and its mask-decomposed variants. Standard errors are clustered at the town level to allow within-town serial dependence and arbitrary intra-town heteroskedasticity.
The specification has several variants. The mobility-decomposed columns (Table (ref), cols. 3--4) replace $\beta\,S^{\mathrm{PreG}}_{i,t-1}$ with $\beta^{w}\,S^{\mathrm{PreG},w}_{i,t-1} + \beta^{b}\,S^{\mathrm{PreG},b}_{i,t-1}$, where the within/across split is the Hadamard mask of $\mathrm{PreG}$ by the mobility-Louvain partition. The demographic-decomposed columns (cols. 5--6) and the joint four-mask and continuous-modulator robustness specifications are reported in detail in SI §(ref).
Identification rests on breaking Manski's reflection problem manski1993identification, which arises when an own outcome and the contemporaneous peer mean enter the same regression and are mutually determined: $Y_{i,t} = \beta\,\mathbb{E}[Y_{j,t}\mid j \sim i] + \dots$ has no separately identified $\beta$ because the conditional mean is itself a function of $Y_{i,t}$. Two design choices break this here. First, the peer signal $S^{\mathrm{PreG}}_{i,t-1}$ is the lagged network-weighted outcome rather than the contemporaneous one, so the simultaneity that defeats $t = t$ specifications is replaced by a one-step prediction in which week-$t$ behavior of $i$ cannot mechanically drive week-$(t{-}1)$ behavior of $j$. Second, the network $\mathrm{PreG}$ is fixed in January 2020, before any case in Massachusetts, so the regressor matrix is pre-determined with respect to the pandemic-period outcome process; in the language of Bramoull\'e, Djebbari and Fortin bramoulle2009identification, $\mathrm{PreG}$ is a transitive but pre-pandemic instrument-like structure on which the lagged-peer interaction is constructed. The design is therefore identified up to the standard residual concern of correlated unobserved shocks, addressed next.
Town fixed effects $\mu_{i}$ absorb all time-invariant municipal characteristics (geography, demographic baseline, institutional capacity), and week fixed effects $\lambda_{t}$ absorb common shocks (state-level policy stringency, national news, school-calendar effects). The residual concern is spatially patterned, time-varying unobservables that travel along the same edges as $\mathrm{PreG}$ bramoulle2009identification, for example a regional outbreak that simultaneously shocks behavior in connected towns through information rather than through peer adjustment. We address this in two ways. First, a network-exposure-to-cases falsification replaces $S^{\mathrm{PreG}}_{i,t-1}$ with $S^{\mathrm{PreG}\cdot X}_{i,t-1} = \sum_j \mathrm{PreG}_{ij}\,X_{j,t-1}$ and yields a coefficient statistically indistinguishable from zero; when both terms enter side by side, the network-exposure-to-cases coefficient remains insignificant while $S^{\mathrm{PreG}}_{i,t-1}$ retains its sign and magnitude (SI Table (ref)). A pure information-shock alternative should load on $X$-exposure rather than $Y$-exposure, and it does not. Second, a geographic-proximity placebo network replaces $\mathrm{PreG}$ with an inverse-distance or shared-county adjacency matrix; because this structure encodes spatial correlation without routine interaction, a channel specific to the mobility network predicts an attenuated placebo coefficient, isolating the mobility-specific content of the spillover from generic spatial autocorrelation.
Endogenous group formation is not a threat in this design. Because $\mathrm{PreG}$ is constructed before the pandemic, peer-group composition is exogenous to the outcome shock, so the standard concern that agents select into groups on the same unobservables that drive outcomes jackson2008social does not apply: towns that share heavy pre-pandemic flow did so for reasons set years before COVID-19, such as commuting, retail catchment, and social ties.
The within-town channel $\gamma$ and the across-town channel $\beta$ are separately identified because they load on different lagged objects: $\gamma$ on $Y^{adj}_{i,t-1}$, the focal town's own lagged outcome, and $\beta$ on $\sum_j \mathrm{PreG}_{ij}\,Y^{adj}_{j,t-1}$ with $\mathrm{PreG}_{ii} = 0$, a network-weighted sum over other towns. The two regressors are correlated at the town-week level, since towns with high lagged own outcomes tend to sit in communities whose peers also had high lagged outcomes, but they are not collinear, and the FE+AR(1) specifications in Table (ref) identify both with non-trivial standard errors. Because the two are positively correlated and $\gamma > 0$, omitting the own lag (column 1) biases the peer coefficient upward by $\gamma\,\delta$, where $\delta$ is the within-fixed-effects regression slope of $Y^{adj}_{i,t-1}$ on $S^{\mathrm{PreG}}_{i,t-1}$; this is why $\hat\beta$ falls from $0.51$ to $0.23$ once the lag enters. The FE+AR(1) estimate is therefore the partialed across-town response and the value that serves as the lower bound on social influence, while the larger static coefficient is an interior point of the $[\hat\beta,\, \hat\beta + \hat\gamma]$ interval rather than a bound on it. The substantive interpretation respects this split: $\gamma$ captures the joint persistence-plus-within-town-reinforcement that operates intra-town from week to week, and $\beta$ captures the across-town peer effect that the network can carry but the lagged-own term cannot.
Regressions are estimated with statsmodels (PanelOLS with two-way fixed effects and clustered standard errors). Community detection uses python-louvain, with networkx for graph manipulation; robust distances use the MinCovDet estimator in scikit-learn; and spatial layers use geopandas and \texttt{pyproj} (EPSG:26986). The full processing pipeline and the corresponding scripts are available in the public reproduction repository.
The within/across mask used in the main-text within-mobility-community decomposition and the four-mask cross-decomposition used in the SI demographic robustness are defined as element-wise products of $\mathrm{PreG}$ with $\{0,1\}$ indicator matrices.
For a partition $\Pi = \{C_1, \dots, C_K\}$ of the 313 towns, the within-mask and across-mask are $M^{w}_{ij}(\Pi) = \mathbf{1}[\Pi(i) = \Pi(j),\, i \neq j]$ and $M^{b}_{ij}(\Pi) = \mathbf{1}[\Pi(i) \neq \Pi(j)]$, so that $\mathrm{PreG}^{w}(\Pi) = \mathrm{PreG} \odot M^{w}(\Pi)$ and $\mathrm{PreG}^{b}(\Pi) = \mathrm{PreG} \odot M^{b}(\Pi)$, where $\odot$ is the elementwise (Hadamard) product. These are not row-renormalized after masking, so the masked-spillover coefficient is on the same scale as the pooled $S^{\mathrm{PreG}}$.
Crossing the mobility partition $\Pi^{M}$ with the demographic partition $\Pi^{D}$ yields four masks,
which sum to $\mathrm{PreG}$ off-diagonal. Each spillover regressor is then $S^{kl}_{i,t-1} = \sum_j \mathrm{PreG}^{kl}_{ij}\,Y^{adj}_{j,t-1}$ for $kl \in \{mm, ma, am, aa\}$. Finally, the matrix $D$ supports an alternative continuous-modulator spillover $S^{\mathrm{PreG}\odot D}_{i,t-1}$ used in the SI demographic robustness; its formal definition is given in SI §(ref).
\bmhead{Acknowledgements} This material is based upon work supported by the National Science Foundation under Grant No. DMS-2421289 (IHBEM: No One Lives in a Bubble: Incorporating Group Dynamics into Epidemic Models), awarded to Northeastern University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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