Hate crime is hostility or bias directed at a person, or their property, because of their race, religion, national origin, disability or other identity — and it is often more violent than it needs to be, because the aggressor is not only attacking a victim but sending a message to everyone who shares the victim’s characteristics. Now a provocative new statistical study argues that across much of the United States, this violence may be anchored to a level that law enforcement alone cannot reach. Analyzing annual hate crime data from 36 states over three decades, researchers report that in 17 of them, the hate crime rate behaves as though it gravitates toward a “natural rate” — an equilibrium toward which the series keeps reverting no matter how hard authorities push. In those states, spending on deterrence can suppress offending only in the short run; over the long run the rate rebounds to its underlying level. Only “corrective” policies that change the baseline itself — educating potential offenders, rehabilitating convicted ones, and attacking the poverty and inequality that feed social tension — can deliver a permanent reduction, the authors conclude.

The study, published in the International Review of Economics by Sakiru Adebola Solarin of Multimedia University in Malaysia, Luis Alberiko Gil-Alana of the University of Navarra and Universidad Francisco de Vitoria in Spain, and Chris Stewart of Kingston University in the United Kingdom, is the first to pose this question for hate crime anywhere, and the first to test it for individual U.S. states rather than the country as a whole. Its intellectual scaffolding is imported from macroeconomics. Just as economists long debated whether unemployment is pulled back toward a “natural rate” — the logic behind the Phillips curve — crime economists have argued that some offenses revert to a structural level after shocks. If a natural crime rate exists, crackdowns buy temporary relief before the rate creeps back. If instead the rate exhibits hysteresis — the statistical signature of a random walk with no anchor — shocks never wash out, and enforcement can reshape crime permanently. Earlier work tested this idea for burglary, robbery, homicide and other conventional crimes in the United States, the United Kingdom, India and emerging economies. Hate crime had never been tested.

The stakes of that technical distinction are visible in federal statistics. According to the FBI’s Crime Data Explorer, reported hate crime incidents climbed from 11,129 in 2020 to 13,377 in 2022, lifting the rate from 3.357 to 4.018 incidents per 100,000 people. These are not rare or remote events: 26.8 percent of 2022 incidents occurred near residences or homes, and another 15.7 percent on roads, highways, streets, alleys and sidewalks. Roughly two-thirds of 2022 incidents were committed against people rather than property. Against that backdrop, the question of whether the trend can be bent — and by which policy instrument — is anything but academic.

To settle it, the team deployed fractional integration, a technique considerably more flexible than the standard unit-root tests used in earlier crime research. A time series is said to be integrated of order d — written I(d) — if it must be differenced d times to become stationary, and crucially, d need not be a whole number. That single parameter traces a spectrum of behavior. When d equals zero, the series has only short memory and shocks vanish almost instantly. Between zero and 0.5 it is stationary but long-memory, with shocks decaying slowly. Between 0.5 and 1 the series is nonstationary yet still mean- or trend-reverting, so disturbances are transitory even if they fade slowly. At d equal to 1 the process is a classic unit root — hysteresis, in criminological terms — and above 1 it is explosive. The higher the value of d, the more persistent the series and the longer the shadow each shock casts. The authors estimated d by maximum likelihood in the frequency domain using a testing approach developed by econometrician P. M. Robinson, fitting each state’s series under three specifications — no deterministic terms, a constant only, and a constant plus a linear trend — so that reversion to an evolving, trended natural rate could be distinguished from reversion to a fixed mean. The data run from 1993 through 2022, drawn from the FBI’s Crime Data Explorer and population figures from the U.S. Bureau of Economic Analysis; fifteen states had to be excluded for missing records.

The verdicts defy any single national narrative. Nine states — Indiana, Iowa, Maine, Nevada, New Jersey, New Mexico, South Carolina, South Dakota and Tennessee — showed hate crime rates reverting to a constant mean, the cleanest signature of a fixed natural rate, with estimated d values ranging from 0.27 in Nevada to 0.67 in New Jersey. Five states — Kentucky, Louisiana, North Carolina, Ohio and Vermont — revert to an upward trend, implying an evolving natural rate that rises through the sample, though the authors caution this may partly reflect improving hate crime reporting and compliance over time. Three states — Idaho, Oklahoma and Rhode Island — revert to a downward trend, which may indicate corrective policies already at work or the wage-driven effects predicted by earlier economic models of hateful behavior. No state showed anti-persistence, and the confidence intervals — wide, given the limited number of annual observations per state — matter: the District of Columbia and Utah are genuinely ambiguous, with data that cannot distinguish a trend-reverting process from a full-blown unit root.

For the remaining 17 states — among them California, Texas, New York, Florida, Georgia, Illinois, Michigan, Pennsylvania and Washington — there is no natural rate at all. The hate crime rate in these states is unambiguously non-reverting: shocks are permanent and hysteresis rules. In California and Georgia the estimated d even exceeded 1, hinting at a potentially explosive process. Paradoxically, this is the more hopeful category from an enforcement standpoint, because where shocks never fade, deterrence — more policing, longer jail terms, stricter bail conditions — can lower hate crime in the long run rather than merely postponing it.

Why would hate crime, which is rarely committed for money, obey a natural rate in the first place? The authors build on sociologist Donald Black’s account of violence as “self-help” social control: unilateral acts justified as punishment for a perceived wrongdoing, often under a logic of collective responsibility in which any member of a group can be made to answer for the acts of others. Where perpetrators believe their actions are morally warranted — a matter of honor rather than gain — the deterrent power of criminal law is weakened at its core. The paper also revives an economist’s utility-maximizing model of hateful behavior, which found hate crimes rising with unemployment and falling with market wages while law enforcement effort showed no statistically significant effect. In the cold arithmetic of rational choice, an offense is committed whenever the expected satisfaction exceeds the expected cost of apprehension and sanction; where the act is felt to be morally owed, no realistic price may suffice. Different blends of such motives across states, the authors argue, may explain why some states produce a natural rate while others do not.

The findings also collide with an uncomfortable measurement problem. The 1990 Hate Crime Statistics Act requires reporting at the federal and state level but does not compel individual police agencies to report — a uniquely American loophole. Recent research found that only about 24 percent of U.S. police agencies show “true compliance” with reporting requirements, while others fail to report altogether or practice “ceremonious compliance,” filing unvarying zeroes that are unlikely to reflect reality. Compliance is weakest in the Confederate South and in counties with histories of racial terror lynchings, and is shaped by political context and resources. The upward trends detected in the five trend-reverting states could therefore signal genuine deterioration — or simply agencies becoming more diligent about reporting a problem that was always there.

The researchers stress-tested their conclusions against this data quagmire. Using the Brennan Center for Justice’s inventory of state hate crime statutes, they identified three states in their sample — Indiana, North Dakota and South Carolina — with no genuine hate crime laws, and nine more — Colorado, Delaware, Georgia, Missouri, Nevada, Ohio, South Dakota, Tennessee and Vermont — whose laws do not mandate data collection. Excluding all twelve, the picture barely changed: among the remaining 24 states, ten showed a natural rate, six of them trend-reverting, twelve showed hysteresis, and two remained ambiguous. Even among the states with the most consistently participating agencies in federal reporting — Texas, Iowa and New York — the verdicts diverged. The heterogeneity, the authors argue, is a feature of the phenomenon itself, not an artifact of sloppy bookkeeping.

The study’s descriptive statistics underline how uneven the terrain is. The District of Columbia posted the highest mean hate crime rate in the sample at 9.694 per 100,000, with New Jersey close behind at 8.024, while Louisiana, Georgia and Florida sat at the bottom with means below one. For the 17 natural-rate states, the prescription is a shift of resources away from deterrence, which buys only temporary relief, and toward correcting the motives that generate hate — education, rehabilitation, and policies that reduce poverty and inequality. In the 17 hysteresis states, by contrast, enforcement spending can work in both the short and long run. For the two ambiguous cases, more research is urgent, especially in the District of Columbia, which pairs the nation’s highest mean hate crime rate with unresolved questions about which policy lever would actually move it. The deeper lesson is methodological as much as practical: national aggregates concealed a patchwork that only state-by-state analysis could expose. Hate crime in America, the results insist, is not one problem but thirty-six — and in half of them, the invisible equilibrium will outlast any crackdown.