learn_omitted_spatial_lag

learn_omitted_spatial_lag(side=10, beta=1.0, rho=0.7, noise=0.5, seed=0)

Show why ignoring spatial dependence biases OLS — and how SAR repairs it.

Simulates y = (I - rho W)^-1 (beta x + eps): outcomes spill over through the spatial multiplier, so OLS on y ~ x (which omits the spatial lag Wy) absorbs the feedback into its slope and overstates β. The ML spatial-lag (SAR) estimator models the dependence and recovers both β and ρ.

Parameters

Name	Type	Description	Default
side	int	Lattice side length (n = side²).	10
beta	float	Planted coefficient on x.	1.0
rho	float	Planted spatial-lag parameter, |ρ| < 1 (drives the OLS bias).	0.7
noise	float	Standard deviation of the innovation.	0.5
seed	int	Random seed.	0

Returns

Name	Type	Description
	SandboxResult	df (OLS vs SAR vs true coefficient), fig, summary, topic and the simulated cross-section in data.

Examples

import geometrics as gm

res = gm.learn_omitted_spatial_lag(rho=0.7)
print(res.summary["ols_coef"], res.summary["sar_beta"])