fect_iden: Over-identification test for causal moderation (cm)

In fect: Fixed Effects Counterfactual Estimators

Over-identification test for causal moderation (cm)

Description

Implements the over-identification test described in the slide: run two auxiliary regressions of residualized outcomes on the moderator and covariates (including quadratic and interaction terms) with unit and time fixed effects, then test using n \times R^2 \sim \chi^2(df), where df is the number of *nonlinear* (quadratic + interaction) terms that remain in the fitted model.

Usage

fect_iden(
  x,
  moderator,
  covariates = NULL,
  quadratic = TRUE,
  interaction = TRUE
)

Arguments

x	A 'fect' object. Must be estimated with 'cm=TRUE' so that 'x$est.cm' exists.
moderator	Character scalar. Name of the moderator M_{it} (must be in 'x$X').
covariates	Optional character vector. Names of other covariates X_{it}. Default is all covariates in 'x$X' except 'moderator'.
quadratic	Logical. Include quadratic terms M_{it}^2 and X_{it}^2. Default TRUE.
interaction	Logical. Include interaction terms M_{it} \times X_{it}. Default TRUE.

Value

A list with elements 'e1' and 'e0', each containing: - 'n': sample size used in the auxiliary regression - 'r2': R-squared of the auxiliary regression - 'stat': n \times R^2 - 'df': degrees of freedom (# nonlinear terms kept) - 'p': p-value from chi-square test - 'model': the fitted 'fixest' model

fect documentation built on April 30, 2026, 9:06 a.m.