Between Estimator

The Between Estimator regresses on the unit means of the variables — exploiting between-unit variation rather than the within (time) variation used by Fixed Effects. It answers "do units with a higher average $X$ have a higher average $Y$".

When to use

Use Between when you care about long-run differences across units (e.g. comparing countries/firms by their averages). RE is essentially a weighted average of Between and Within.

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Model specification

$$\bar{Y}_i = \beta_0 + \bar{X}_i \beta + \bar{\varepsilon}_i, \qquad \bar{Y}_i = \frac{1}{T}\sum_t Y_{it}$$

OLS on the unit-averaged data.

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Running in EcoLab

1. Modeling module → Linear panel data family → Between.
2. Declare entity/time, $Y$, $X$.
3. Run; contrast with FE (within) to analyze the source of variation; export the replication code.

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Replication code

Stata

* ---- Between Estimator ----
use "panel_data.dta", clear
xtset id time

* Between estimator (regression on unit means)
xtreg y x1 x2, be

R

# ---- Between Estimator ----
library(plm)

# Load panel data (illustrative)
df <- read.csv("panel_data.csv")
pdata <- pdata.frame(df, index = c("id", "time"))

# Between estimator
model_be <- plm(y ~ x1 + x2, data = pdata, model = "between")
summary(model_be)

Python

# ---- Between Estimator ----
import pandas as pd
from linearmodels.panel import BetweenOLS

# Load panel data (illustrative)
df = pd.read_csv("panel_data.csv")
df = df.set_index(["id", "time"])

y = df["y"]
X = df[["x1", "x2"]]

model_be = BetweenOLS(y, X).fit()
print(model_be)

Limitations

• Ignores time variation; does not control for individual effects like FE.
• Loses dynamic information.

Video tutorial

Video Tutorial: Running the Between estimator in EcoLab

See also

• FEM/REM · Pooled OLS · Catalog