Convert an estimate into crimes prevented per thousand searches

Takes an elasticity or a treatment effect and expresses it as the number of crimes prevented per thousand searches at the sample mean, which is the form in which the question is usually asked. The conversion is arithmetic, not evidence: it inherits every assumption of the estimate it is given, and adds more of its own. The assumption chain is returned with the number and printed with it.

Usage

lamp_crimes_prevented(
  estimate,
  panel,
  per_stops = 1000,
  stops_added = NULL,
  outcome_column = NULL,
  n_boot = 2000,
  seed = NULL
)

Arguments

estimate

A lamp_estimate from lamp_elasticity(), lamp_twfe(), lamp_did_staggered() or lamp_event_study().

panel

The panel the estimate was built from, for the sample means.

per_stops

Searches to express the result per, default 1000.

stops_added

For a treatment effect: the searches the intervention added per area-month. Required unless the estimate is an elasticity.

outcome_column

The crime column to take the mean of; defaults to the estimate's outcome.

n_boot

Retained for compatibility. Intervals now transform the coefficient interval directly and require no simulation.

seed

Retained for compatibility; the conversion is deterministic.

Value

A list of class lamp_crimes_prevented with crimes_prevented, conf_low, conf_high, the inputs used, and assumptions, a character vector naming every step from the estimate to the number.

Details

For an elasticity e, a proportional change in searches dS/S changes crime by e * dS/S, so at mean monthly crime C and mean searches S the crimes prevented by an extra per_stops searches are -e * C * per_stops / S. The elasticity estimators use log(1 + stops), so their derivative has denominator S + 1. The count-mean model uses C in the numerator; the legacy log-one-plus outcome approximation uses C + 1. For a treatment effect in log points b, the effect on crime is C * (exp(b) - 1), and it is divided by the searches the intervention actually added, which you must supply as stops_added because a binary treatment does not say how much searching it involved.

What this number does not include

It counts recorded crime only, so crimes not reported to the police are invisible to it, and any change in recording practice is counted as a change in crime. It assumes the effect is linear in searches over the range considered, and that the average effect applies at the margin, which is the opposite of what diminishing returns implies. It says nothing about the costs of searching, which fall on the people searched.

See also

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

Examples

sim <- lamp_simulate(n_areas = 30, n_months = 30, design = "continuous", seed = 1)
el <- lamp_elasticity(sim, "crime_total", lags = 0:1)
lamp_crimes_prevented(el, sim)
#> 
#> ── Crimes prevented per 1000 searches 
#> 90.2 [-0.615, 181] on crime_total
#> 
#> ── Assumption chain 
#> 1. The log-one-plus stops slope is -0.0982, summed over lags 0, 1.
#> 2. The denominator is mean stops plus one; legacy OLS also uses mean crime plus
#> one.
#> 3. The effect is proportional, so it scales with the mean level of crime.
#> 4. At the sample mean of 7.12 crimes and 6.76 searches per area-month.
#> 5. The association between searching and recorded crime, net of area and month
#> effects. Causal only if the variation in searching has a source outside the
#> crime process; see lamp_allocation().
#> 6. Recorded crime only: unreported crime and recording changes are not
#> separated.
#> 7. The average effect is applied at the margin, which ignores diminishing
#> returns.