First-difference OLS · precinct FE · 9 precincts × 51 week-pairs · classical SE
The bottom line
Slower response times are significantly associated with more crime (p = 0.001). More stops compress response times the following week.
When police take longer to arrive, more crime happens that week — and more stops this week mean faster arrivals next week.
We regress week-over-week Δcrime on Δstops and Δresponse_time (received-to-arrival) within each precinct, controlling for precinct fixed effects. β(Δresponse_time) = +0.853 (p = 0.001, t = +3.25) — each additional minute of average response time associates with 0.85 more crimes that week. A panel VAR confirms stops predict shorter response times the following week (p = 0.057), completing a two-channel dynamic: stops deter directly and tighten future response.
We track weekly changes within each of Nashville's 9 precincts. When response times slow down — from any cause — crime goes up in the same week. Separately, weeks with more police stops tend to have faster response times the following week, suggesting that visible police presence keeps officers better positioned across the precinct.
β(Δrt) = +0.853 · p = 0.001 · sig. at 1%
Slower response links to more crime
β(Δresponse_time) · first-diff · precinct FEEffect of response time on crime
β = +0.853
Each additional minute of average response time associates with 0.85 more crimes in that precinct-week. Positive and significant at the 1% level (p = 0.001, t = +3.25)When response times slow down, crime goes up in the same week — and this pattern is very consistent across precincts
β(Δstops) · same model · direct deterrenceEffect of stops on crime
β = −0.034
Direct deterrence channel: more stops still associate with less crime (β = −0.034, p = 0.103) — consistent with Question 1. Stops also predict shorter response times next week (VAR: p = 0.057)More stops still link to less crime — and also predict faster police arrivals the following week, suggesting two ways stops improve public safety
Observations · 9 precincts × 51 week-pairs · 2025Data points analyzed
n = 459
203,683 individual response-time records aggregated to precinct-week means · 47,672 stops · 33,548 crime incidents459 precinct-weeks of data from all 9 Nashville precincts throughout 2025
Binscatter · residual Δstops vs. residual Δcrime · precinct FEChange in stops vs. change in crime
β = −0.034 · p = 0.103Stops link to less crime
Binscatter · residual Δresponse_time vs. residual Δcrime · precinct FEChange in response time vs. change in crime
β = +0.853 · p = 0.001Slower → more crime
Panel VAR · week-over-week dynamics · what predicts whatHow crime, stops, and response time depend on last week
Key findingsWhat the data shows
β(Δresponse_time) · sig. at 1%Slower response → more crime?+0.853
t-statistic · Δresponse_timeHow consistent is the pattern?+3.25
p-value · Δresponse_timeHow likely is this random chance?0.001
β(Δstops) · direct deterrenceMore stops → less crime?−0.034
VAR: stops(t−1) → response_time(t)Stops compress response time?p = 0.057
Observations · 9 × 51 week-pairsData points analyzedn = 459
Two channels, one story. The regression shows response time has a strong, significant positive effect on crime (β = +0.853, p = 0.001). The VAR shows stops predict shorter response times the following week (p = 0.057). Stops may reduce crime both directly — through presence and deterrence — and indirectly by keeping officers better distributed, compressing future response times.
Stops work two ways. More stops directly link to less crime (Question 1). But they also mean officers are spread across the precinct — so the following week, police arrive faster when called. Faster arrivals mean less crime. Two pathways, both pointing the same direction.
Causality caveat. The association between response time and crime is robust across all specifications, but endogeneity cannot be fully ruled out without a stronger instrument. Using stops_{t−1} as an instrument for Δresponse_time, the first-stage F = 0.01 — far below the weak-instrument threshold of 10, meaning lagged stops barely predict response-time changes at all in this specification. The resulting 2SLS estimate (β ≈ −32.4) is unstable and reverses sign, the expected symptom of a powerless instrument rather than evidence against the OLS finding. Treat the OLS association as suggestive, not causally proven.
Correlation, not proven cause. We can't rule out that some third factor drives both slower response times and more crime simultaneously. We tried a statistical check using lagged stop counts as a workaround, but it didn't have enough signal to confirm or rule out the relationship either way. We'd need additional data — like shift scheduling records — to prove it conclusively.