Weighted displacement quotient

Measures whether crime prevented in a treated area reappeared in the areas around it. The quotient compares the change in a buffer of surrounding areas with the change in control areas, relative to the change in the treated areas, following Bowers and Johnson (2003).

Usage

lamp_displacement_quotient(
  panel,
  outcome = "crime_total",
  treated_areas,
  buffer_areas,
  control_areas,
  pre,
  post,
  n_boot = 1000,
  seed = NULL
)

Arguments

panel

A lamp_panel.

outcome

The outcome column.

treated_areas, buffer_areas, control_areas

Area identifiers.

pre, post

Two-element vectors giving the first and last month of the before and after periods.

n_boot

Bootstrap replications over areas, default 1000.

seed

Random seed.

Value

A list of class lamp_wdq with wdq, conf_low, conf_high, the underlying totals, success (the treated area's change net of controls) and interpretation.

Details

The statistic is WDQ = ((B1/C1) - (B0/C0)) / ((A1/C1) - (A0/C0)), where A, B and C are total crime in the treated, buffer and control areas and the subscripts are the pre and post periods. Read it as:

• negative: crime moved into the buffer, so the gain in the treated area is partly or wholly displacement;

• between 0 and 1: the buffer improved too, a diffusion of benefit smaller than the treated area's gain;

• above 1: the buffer improved more than the treated area.

The quotient is a descriptive ratio, not a causal estimate: it assumes the control areas show what would have happened everywhere, and it is unstable when the treated-area change is close to zero, which the bootstrap interval will show as a very wide range.

References

Bowers, K. J. and Johnson, S. D. (2003). Measuring the geographical displacement and diffusion of benefit effects of crime prevention activity. Journal of Quantitative Criminology 19(3), 275-301.

See also

Other estimators: lamp_allocation(), lamp_crimes_prevented(), lamp_did_staggered(), lamp_elasticity(), lamp_event_study(), lamp_spillover(), lamp_synth(), lamp_twfe(), tidy.lamp_estimate()

Examples

sim <- lamp_simulate(
  n_areas = 36, n_months = 20, design = "spillover",
  effect = -0.4, spillover_effect = 0.2, seed = 2
)
truth <- attr(sim, "truth")
areas <- truth$lattice$area
lamp_displacement_quotient(
  sim, "crime_total",
  treated_areas = truth$treated_areas[1:6],
  buffer_areas = truth$treated_areas[7:12],
  control_areas = setdiff(areas, truth$treated_areas),
  pre = c("2018-01", "2018-06"), post = c("2018-12", "2019-05"), n_boot = 50
)
#> 
#> ── Weighted displacement quotient 
#> Outcome: crime_total
#> WDQ: 3.93 [-18.3, 7.91] from 50 of 50 bootstrap draws
#> Treated-area change net of controls: -0.02623
#> WDQ 3.93 is above 1: the buffer improved more than the treated areas, which is
#> hard to attribute to the intervention.