learn_spatial_spillovers

learn_spatial_spillovers(
    side=10,
    beta=1.0,
    gamma=0.5,
    rho=0.5,
    noise=0.5,
    n_draws=5000,
    seed=0,
)

Plant direct and indirect effects, then recover them as LeSage-Pace impacts.

Simulates y = (I - rho W)^-1 (beta x + gamma Wx + eps) on a lattice, so the true impacts are known in closed form — direct = tr[(I-ρW)⁻¹(βI+γW)]/n and total = (β+γ)/(1-ρ) — then estimates a spatial Durbin model with :func:geometrics.analyze_spatial_model and compares its Monte-Carlo impact decomposition against the truth. This is why spatial-model coefficients are read through impacts: β alone is not the marginal effect once feedback via ρ exists.

Parameters

Name	Type	Description	Default
side	int	Lattice side length (n = side²).	10
beta	float	Planted own-place coefficient on x.	1.0
gamma	float	Planted neighbor coefficient on Wx (drives spillovers alongside ρ).	0.5
rho	float	Planted spatial-lag parameter, |ρ| < 1.	0.5
noise	float	Standard deviation of the innovation.	0.5
n_draws	int	Monte-Carlo draws behind the estimated impact standard errors.	5000
seed	int	Random seed (also passed to the estimator’s Monte-Carlo step).	0

Returns

Name	Type	Description
	SandboxResult	df (direct/indirect/total, estimated vs true), fig, summary, topic and the simulated cross-section in data.

Examples

import geometrics as gm

res = gm.learn_spatial_spillovers(rho=0.7)
res.df