Own-area and neighbour effects estimated together

Adds the treatment of an area's neighbours to the specification, so that the effect on the area itself and the effect on its neighbours are estimated in one model. This is what separates a reduction in crime from its displacement next door: if searching an area pushes offending into the surrounding areas, the own-area coefficient is negative and the neighbour coefficient positive, and the net effect is their sum.

Usage

lamp_spillover(
  panel,
  outcome = "crime_total",
  treatment,
  adjacency = NULL,
  rings = 1:2,
  cluster = c("area", "force"),
  family = c("poisson", "negbin", "ols_log", "ols_ihs"),
  controls = NULL
)

Arguments

panel

A lamp_panel from lamp_panel().

outcome

The outcome column, for example "crime_total" or a crime type key from lamp_crime_types().

treatment

A lamp_treatment() object, or the name of a panel column.

adjacency

A lamp_adjacency() object; taken from the panel's contract when not given.

rings

Contiguity rings to include, default first and second order.

cluster

"area" (default) or "force".

family

"poisson" (default, a Poisson pseudo-likelihood suited to counts), "negbin", "ols_log" or "ols_ihs".

controls

Optional panel columns to include as covariates.

Value

A lamp_estimate of class lamp_spillover, whose coefficients hold the own-area effect and one neighbour effect per ring, and whose diagnostics$net gives the implied net effect (own plus neighbours) with a standard error from the full covariance matrix.

Identifying assumption

Parallel trends as in two-way fixed effects, and in addition that the treatment reaches an area only through its own treatment and that of the rings included. If spillovers extend beyond the last ring, the areas used as controls are themselves affected, and every coefficient is biased toward zero.

See also

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

Examples

sim <- lamp_simulate(
  n_areas = 49, n_months = 20, design = "spillover",
  effect = -0.3, spillover_effect = 0.15, seed = 1
)
adj <- lamp_adjacency_from_nb(attr(sim, "truth")$nb, attr(sim, "truth")$lattice$area)
truth <- attr(sim, "truth")
tr <- lamp_treatment(sim, "event", date = truth$event_date, scope = truth$treated_areas)
fit <- lamp_spillover(sim, "crime_total", tr, adjacency = adj, rings = 1)
fit
#> 
#> ── streetlamp estimate: lamp_spillover 
#> Outcome: crime_total; family: Poisson pseudo-likelihood on counts
#> Treatment: event; clustered by area
#> Identifying assumption: Parallel trends, and no spillover beyond the rings
#> included: if there is any, control areas are treated too and every coefficient
#> is pulled toward zero.
#> Sample: 980 area-months in 49 areas; 0 rows dropped for coverage.
#> Dispersion: 0.951
#>   Term                Estimate  Std. error           95% CI      p
#>   ──────────────────  ────────  ──────────  ───────────────  ─────
#>   Own area              −0.123       0.206   [−0.526, 0.28]  0.550
#>   Neighbours, ring 1   −0.0902       0.221  [−0.523, 0.342]  0.683
#> Net effect (own plus neighbours): -0.213 [-0.306, -0.12]