Method library WORKFLOW / 069

Research workflow/5 steps

Entropy balancing for covariate overlap (ebal)

@guido_imbens D · Jun 29, 2026 · 946 views

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Method mapInput → 5 steps → output

START WITHInput data

ARRIVE ATResults

Read step 01

Inside the methodReasoning, equations & implementation

Data prep

Assemble treatment indicator and covariates

Step notesField note & discussion1

Data preparation — shapes the raw inputs into what the estimator expects.

What happens here

Build a binary treatment vector and the covariate set whose means you want the reweighted controls to match the treated group on.

Reads fromNot specified Feeds into#2

Key code

# Install:  install.packages("ebal")
library(ebal)
set.seed(42)
n_t <- 75; n_c <- 250
df <- data.frame(
  treat  = c(rep(1,n_t), rep(0,n_c)),
  age    = c(rnorm(n_t,45,8),  rnorm(n_c,38,10)),
  educ   = c(rnorm(n_t,16,2.5),rnorm(n_c,13,3)),
  income = c(rnorm(n_t,65,12), rnorm(n_c,50,15)))
df$y <- 0.1*df$age + 0.3*df$educ + 0.05*df$income + 5*df$treat + rnorm(nrow(df),0,3)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Estimation

Run entropy balancing

Step notesField note & discussion1

The core estimate — where the causal quantity itself is computed.

What happens here

ebalance() solves for control weights that exactly reproduce the treated-group covariate moments under maximum entropy.

Formula

\min_{w_i}\sum_{i\in C} w_i\log\frac{w_i}{q_i}\;\;\text{s.t.}\;\sum_{i\in C} w_i c_{ri}(X_i)=m_r,\;\sum_i w_i=1

Reads from#1 Feeds into#3

Key code

fit <- ebalance(treat ~ age + educ + income, data = df)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Diagnostic / pre-tests

Check exact moment balance

Step notesField note & discussion1

A pre-flight check — run this before trusting any estimate downstream.

What happens here

summary(fit) prints treated vs control covariate means before and after weighting; post-weighting means coincide with the treated means.

Reads from#2 Feeds into#4

Key code

summary(fit)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Estimation

Weighted ATT estimate

Step notesField note & discussion1

The core estimate — where the causal quantity itself is computed.

What happens here

Pass the balancing weights to a weighted regression of the outcome on treatment to recover the ATT (true value 5).

Formula

\hat\tau_{ATT} = \bar Y_{1} - \sum_{i\in C} w_i\, Y_i

Reads from#3 Feeds into#5

Key code

df$w <- weights(fit)
coef(lm(y ~ treat, data = df, weights = w))["treat"]

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Reporting

Love plot of standardized differences

Step notesField note & discussion1

Reporting — turn the numbers into a figure or table a reader can act on.

What happens here

plot(fit) draws a base-R Love plot of standardized differences before vs after weighting, one row per covariate.

Reads from#4 Feeds intoNot specified

Key code

plot(fit)

Reference / docs ↗

Discussion on this step (0)

StatsOtterDiscussion starter · Editorial note

Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.

Questions to explore

Which assumption matters most here, and what evidence could challenge it?
What would you check before passing this output to the next step?

Peer discussion

Bring your experience, a question, or a different perspective.

Data contract

Inputs & data

A binary treatment indicator and a matrix of covariates to balance.

Show data format & exampleHide example

treat	age	income	educ
1	40	52000	16
0	38	47000	12
1	45	61000	18
0	33	41000	11

Read the evidence

Results & interpretation

1 figure Workflow discussion 0

01FigureStandardized covariate differences before vs after entropy balancing — exact moment balance.

Result figure rendered by StatsOtter from the package's documented example — unofficial community showcase; all credit to the original authors.

The estimate

\min_{w}\ \sum_i w_i\log\frac{w_i}{q_i}\quad\text{s.t.}\quad \sum_{i:\,Z_i=0} w_i\,c_r(X_i)=\bar c_r^{\,\text{treated}}

Context & interpretation

⚠️ Unofficial community showcase of ebal (docs). Not affiliated with the authors — all credit to Guido Imbens & coauthors; this summarizes public documentation.

What it does. ebal computes weights that make the reweighted control group's covariate means (and higher moments) exactly equal the treated group's, so you can estimate effects on balanced samples. How it works. It solves a maximum-entropy optimization that finds weights staying as close as possible to uniform while satisfying the user's balance constraints—replacing the usual 'estimate propensity score, check balance, respecify' loop with a single calibration step. Assumptions. Unconfoundedness and overlap; balance constraints must be feasible given the data. Imbens's contribution. Entropy balancing (Hainmueller 2012) sits squarely in the propensity-score / overlap-weighting tradition that Imbens systematized in his influential review, Nonparametric Estimation of Average Treatment Effects Under Exogeneity (Imbens 2004, Review of Economics and Statistics), which framed balancing and overlap as central to observational causal estimation.

What you get — A vector of balancing weights for control units that equalize covariate moments with the treated group.

Example output

Entropy balancing

Means on covariates: treatment group vs. weighted control group

          Treated Control(pre) Control(post) StdDiff(pre) StdDiff(post)
age        45.213       37.842        45.213        0.793         0.000
educ       15.987       12.948        15.987        1.064         0.000
income     64.512       49.871        64.512        0.987         0.000

Constraints converged: TRUE
Max. moment deviation: 1.21e-07
N treated = 75   N control = 250   (effective = 213.4)

Links: package · paper

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Inputs & data

Results & interpretation

∑The estimate

Example output

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The estimate