regife

The command regife estimates linear models with interactive fixed effects following Bai (2009).

Note: Interactive fixed effects are factor models (loadings x factors). If you want interacted fixed effects (e.g., i.state#i.year), use reghdfe instead.

For an observation i, denote (j_id(i), j_time(i)) the associated pair (id x time). The command estimates models of the form

by finding the coefficients beta, factors (f1, .., fd), and loadings (lambda1, ..., lambdad) that minimize

The command is slow. A much faster implementation is available in Julia.

Installation

regife is available on SSC. It requires reghdfe. Using absorb() with multiple variables additionally requires hdfe.

ssc install reghdfe
ssc install regife

To install the latest version from GitHub:

net install regife, from("https://raw.githubusercontent.com/matthieugomez/regife/main/")

Syntax

regife

regife depvar [indepvars] [if] [in] [weight], ife(idvar timevar, d) [options]

Required option

• ife(idvar timevar, d) specifies the id variable, time variable, and the dimension d of the factor model.

Optional

• absorb(absvar [...]) absorbs standard fixed effects (passed to reghdfe). Example: absorb(state year).
• vce(vcetype) specifies the variance-covariance estimator: unadjusted (default), robust, bootstrap, or cluster clustvar. Monte Carlo evidence suggests bootstrap performs better in finite samples.
• residuals(newvar) saves residuals to a new variable.
• tolerance(#) convergence tolerance; default 1e-9.
• maxiterations(#) maximum iterations; default 10000.
• bstart(matrix) provides a starting value for the coefficient vector.

Weights (fweight, aweight, pweight) are supported but must be constant within idvar.

ife

ife extracts factors and loadings from a single variable (without regression). This is useful for 3-step estimation: extract factors from a variable, then use them as controls in a second regression.

ife varname [if] [in] [weight], factors(idvar timevar, d) [absorb(absvar) residuals(newvar)]

Examples

Basic usage

webuse nlswork
keep if id <= 100
regife ln_w tenure, ife(id year, 1)

With absorbed fixed effects

Impose id and/or time fixed effects alongside the interactive fixed effects:

regife ln_w tenure, ife(id year, 2) absorb(id year)

Save factors and loadings

Specify new variable names at the left-hand side of = inside ife():

regife ln_w tenure, ife(ife_id=id ife_year=year, 2)

This creates variables ife_id1, ife_id2 (loadings) and ife_year1, ife_year2 (factors). Similarly for absorb():

regife ln_w tenure, absorb(fe_id=id) ife(ife_id=id ife_year=year, 2)

Save residuals

regife ln_w tenure, ife(id year, 2) residuals(newres)

Bootstrap standard errors

regife ln_w tenure, ife(id year, 1) vce(bootstrap)
regife ln_w tenure, ife(id year, 1) vce(bootstrap, cluster(id))

Extract factors with ife

ife ln_w, factors(fei=id fey=year, 2) absorb(id) residuals(res)

This decomposes ln_w (after absorbing the id fixed effect) into loadings (fei1, fei2), factors (fey1, fey2), and residuals (res).

Unbalanced panels

The command handles unbalanced panels (i.e., missing observations for a given id-time pair) as described in the appendix of Bai (2009).

FAQ

When should one use interactive fixed effects models?

Interactive fixed effects are useful when unobserved heterogeneity has a factor structure -- for instance, when units respond differently to common shocks. Some applications:

• Eberhardt, Helmers, Strauss (2013) Do Spillovers Matter When Estimating Private Returns to R&D?
• Hagedorn, Karahan, Manovskii (2015) Unemployment Benefits and Unemployment in the Great Recession: The Role of Macro Effects
• Hagedorn, Karahan, Manovskii (2015) The Impact of Unemployment Benefit Extensions on Employment: The 2014 Employment Miracle?
• Totty (2015) The Effect of Minimum Wages on Employment: A Factor Model Approach

How are standard errors computed?

Standard errors are obtained by regressing y on x and covariates of the form i.id#c.factor and i.time#c.loading, as suggested in Section 6 of Bai (2009). Monte Carlo evidence suggests bootstrap standard errors (vce(bootstrap)) perform better in finite samples.

Does this command implement the bias correction in Bai (2009)?

No. In the presence of cross-sectional or time-series correlation beyond the factor structure, the estimator for beta is consistent but biased (see Theorem 3 in Bai 2009, which derives the correction term in special cases). This package does not implement any bias correction. You may want to check that your residuals are approximately i.i.d.

Changes

v0.6 (2026-03-29)

Fix cluster bootstrap. In previous versions, vce(bootstrap, cluster()) silently ignored the absorb() option and used the wrong panel id for resampling when variable names were abbreviated. Point estimates from regife without bootstrap were unaffected. Standard errors from vce(bootstrap) without cluster() were also unaffected.

v0.4 (2021-09-01)

Remove error when N < T. Preserve tsset.

v0.3 (2017-04-12)

Correct weight handling.

v0.2 (2015-07-09)

Correct normalization for loadings.

v0.1 (2015-07-08)

First release.

References

Bai, Jushan. Panel Data Models with Interactive Fixed Effects. Econometrica, 2009.

Citation

Matthieu Gomez, 2015. "REGIFE: Stata module to estimate linear models with interactive fixed effects."
Statistical Software Components, Boston College Department of Economics.
https://ideas.repec.org/c/boc/bocode/s458042.html