Panel Estimators

Panel estimators create fixed-effect style design variables before compression. This keeps the compressed table small when \(N\) is large and \(T\) is modest.

Mundlak

DBMundlak augments the original covariates with unit means and, optionally, time means. For a covariate \(W_{it}\), the two-way design contains

\[ W_{it}, \qquad \bar{W}_{i\cdot}, \qquad \bar{W}_{\cdot t}. \]

The fitted model is

\[ Y_{it} = \alpha + W_{it}'\beta + \bar{W}_{i\cdot}'\gamma + \bar{W}_{\cdot t}'\delta + u_{it}. \]

from duckreg import DBMundlak

model = DBMundlak(
    db_name="panel.db",
    table_name="panel_data",
    outcome_var="Y",
    covariates=["D", "X"],
    unit_col="unit",
    time_col="time",
    cluster_col="unit",
    seed=42,
    n_bootstraps=100,
)
model.fit()
model.summary()

The right-hand side is ordered as:

["Intercept", "D", "X", "avg_D_unit", "avg_X_unit", "avg_D_time", "avg_X_time"]

Double Demeaning

DBDoubleDemeaning constructs the two-way residualized treatment

\[ \ddot{W}_{it} = W_{it} - \bar{W}_{i\cdot} - \bar{W}_{\cdot t} + \bar{W}_{\cdot\cdot}. \]

It then fits

\[ Y_{it} = \alpha + \tau \ddot{W}_{it} + u_{it} \]

on the compressed residualized treatment values.

from duckreg import DBDoubleDemeaning

model = DBDoubleDemeaning(
    db_name="panel.db",
    table_name="panel_data",
    outcome_var="Y",
    treatment_var="D",
    unit_col="unit",
    time_col="time",
    cluster_col="unit",
    seed=42,
    n_bootstraps=0,
)
model.fit()
model.summary()

This estimator is useful when the target is a two-way fixed-effect style coefficient on one treatment variable.

Event Study

DBMundlakEventStudy builds cohort indicators, time indicators, and cohort-by-time treatment interactions. It estimates event-study profiles by cohort after compression.

from duckreg import DBMundlakEventStudy

model = DBMundlakEventStudy(
    db_name="event.db",
    table_name="panel_data",
    outcome_var="Y",
    treatment_col="D",
    unit_col="unit",
    time_col="time",
    cluster_col="unit",
    seed=42,
    pre_treat_interactions=True,
    n_bootstraps=50,
)
model.fit()
model.summary()

If pre_treat_interactions=False, the treatment interaction columns are zeroed outside treated periods. If it is True, the design keeps a full cohort-by-time profile.

Implementation Pattern

The panel estimators avoid formula-level fixed effects in DBRegression. They use ordinary database operations:

Estimator	Preparation
DBMundlak	Group by unit/time to compute covariate means, then join them to the raw table.
DBDoubleDemeaning	Join unit means, time means, and the overall treatment mean, then compute \(\ddot{W}_{it}\).
DBMundlakEventStudy	Infer treatment cohorts, create indicator columns, and compress the generated design.

The compatibility Duck* panel classes expose the same statistical designs but use older SQL-string internals.