learn_within_vs_lsdv

source

learn_within_vs_lsdv(
    n_units=30,
    n_periods=6,
    beta=2.0,
    unit_effect_corr=0.8,
    noise_sd=0.5,
    seed=0,
)

Show that within (demeaning) and least-squares dummy variables give the same slope.

Simulates a panel with a unit fixed effect and recovers the slope two ways: the within transformation (demeaning, via absorbed fixed effects) and least-squares dummy variables (one dummy per unit in OLS). By the Frisch-Waugh-Lovell theorem the two slopes are identical for any number of periods — demeaning and unit dummies do the same job.

Parameters

Name	Type	Description	Default
n_units	int	Panel dimensions (kept modest so LSDV’s one-dummy-per-unit design stays cheap).	`30`
n_periods	int	Panel dimensions (kept modest so LSDV’s one-dummy-per-unit design stays cheap).	`30`
beta	float	True within-unit slope.	`2.0`
unit_effect_corr	float	Correlation between `x` and the unit effect.	`0.8`
noise_sd	float	Idiosyncratic noise standard deviation.	`0.5`
seed	int	Random seed.	`0`

Returns

Name	Type	Description
	SandboxResult	`df` (within vs LSDV vs true slope), `fig`, `summary` and `topic`.

Examples

This sandbox simulates its own panel, so the call needs no DataFrame:

import expdpy as ex

res = ex.learn_within_vs_lsdv()
res.fig