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xtife: Interactive Fixed Effects Estimator for Panel Data

xtife provides a pure base-R implementation of the Interactive Fixed Effects (IFE) panel estimator for both balanced and unbalanced panels. It delivers full analytical standard errors, asymptotic bias correction, and factor number selection with no external dependencies beyond base R.

For a comprehensive review of interactive fixed effects, see Ditzen & Karavias (2025).

The Model

Standard two-way fixed effects (TWFE) assumes unobserved heterogeneity enters additively. IFE generalises this by allowing unobserved confounders to interact across units and time:

\[y_{it} = \alpha_i + \xi_t + X_{it}'\beta + \lambda_i'F_t + u_{it}\]

where \(F_t \in \mathbb{R}^r\) are common factors and \(\lambda_i \in \mathbb{R}^r\) are unit-specific loadings. Setting \(r = 0\) reduces the model to standard TWFE. For unbalanced panels, ife_unbalanced() supports the same additive fixed effects via its force argument ("none", "unit", "time", "two-way"), estimated jointly with the factors by EM on the imputed panel — robust to informative (factor-correlated) missingness. Its default is force = "none" (the intercept-free interactive model); use force = "two-way" for data with level or trend structure.

Features

Installation

# From CRAN
install.packages("xtife")

# Development version from GitHub
# install.packages("remotes")
remotes::install_github("Rickchen0910/xtife")

Balanced Panel: Quick Start

library(xtife)
data(cigar)   # 46 US states x 30 years cigarette panel (Baltagi 1995)

# Fit IFE with r = 2 factors, two-way FE, cluster-robust SE
fit <- ife(sales ~ price, data = cigar,
           index  = c("state", "year"),
           r      = 2,
           force  = "two-way",
           se     = "cluster")
print(fit)

Interactive Fixed Effects (Bai 2009, Econometrica)
-------------------------------------------------------
        Estimate Std.Error  t.value   Pr(>|t|) CI.lower CI.upper
price    -0.5242    0.0802  -6.5360     0.0000  -0.6814  -0.3670

Converged: TRUE  (10 iterations)
N = 46  T = 30  r = 2  force = two-way  se = cluster

Standard error types

fit_std <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "standard")
fit_rob <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "robust")
fit_cl  <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "cluster")

Factor number selection

sel <- ife_select_r(sales ~ price, data = cigar,
                    index = c("state", "year"),
                    r_max = 6, force = "two-way")

Prints a table of IC1, IC2, IC3 (Bai & Ng 2002), IC(BIC), and PC (Bai 2009) for each candidate \(r\). IC(BIC) is recommended for panels with \(\min(N, T) < 60\).

Asymptotic bias correction

# Static bias correction — Bai (2009)
fit_bc <- ife(sales ~ price, data = cigar,
              index = c("state", "year"), r = 2, bias_corr = TRUE)

# Dynamic bias correction — Moon & Weidner (2017)
# Use when regressors include lagged dependent variables
fit_dyn <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2,
               method = "dynamic", bias_corr = TRUE, M1 = 1L)

For the cigar panel (\(N = 46\), \(T = 30\), \(T/N \approx 0.65\)):

Comparison with TWFE

Setting r = 0 recovers the standard two-way FE estimator, identical to lm() with unit and time dummies at machine precision:

fit0 <- ife(sales ~ price, data = cigar,
            index = c("state", "year"), r = 0)
# Equivalent to plm(..., model = "within", effect = "twoways")

Unbalanced Panel: Quick Start

ife_unbalanced() fits the IFE model on genuinely unbalanced panels following the estimation and inference theory of Su, Wang & Wang (2025), which extends the interactive fixed effects estimator of Bai (2009) to the unbalanced case using the missing-data factor analysis / matrix completion of Bai & Ng (2021). The core algorithm is an alternating outer loop that updates β and the structure \((\hat\alpha, \hat\xi, \hat\lambda, \hat F)\) until convergence, with an expectation-maximisation inner loop that imputes the unobserved cells from the current structure. Initialisation is via plain OLS (init = "ols", the default) or nuclear-norm-regularised soft-impute (Mazumder, Hastie & Tibshirani 2010; init = "nnr", recommended when the panel is severely unbalanced or \(r \geq 3\)). The resulting estimator is \(\sqrt{NT}\)-consistent and asymptotically normal.

# Simulate a 10% randomly missing panel
set.seed(42)
cigar_unb <- cigar[sample(nrow(cigar), size = floor(0.9 * nrow(cigar))), ]

fit_unb <- ife_unbalanced(sales ~ price,
                           data  = cigar_unb,
                           index = c("state", "year"),
                           r     = 2L,
                           se    = "cluster")
print(fit_unb)

Standard error types

Factor number selection

ife_select_r_unb() applies the singular value thresholding (SVT) rule of Su, Wang & Wang (2025) to the nuclear-norm regularised matrix \(\hat\Theta^{(0)}\) — a missing-data counterpart of the Bai & Ng (2002) information criteria:

sel_unb <- ife_select_r_unb(sales ~ price, data = cigar_unb,
                              index = c("state", "year"))
# Returns: r_hat, singular values, SVT threshold, nu_used (NNR penalty from cross-validation)

Analytical bias correction

Setting bias_corr = TRUE applies the analytical incidental-parameter correction of Su, Wang & Wang (2025), \(\hat\beta^{abc} = \hat\beta - (NT)^{-1/2}\hat W_X^{-1}\hat b\), where the bias vector \(\hat b\) depends on the exogeneity assumption:

# Strictly exogenous regressors (default): b3 + b4 + b5 + b6
fit_bc <- ife_unbalanced(sales ~ price, data = cigar_unb,
                          index = c("state", "year"), r = 2,
                          se = "standard", bias_corr = TRUE,
                          exog = "strict")

# Weakly exogenous regressors (e.g. lagged dep. var.): b2 + b3 + ... + b6
fit_dyn_unb <- ife_unbalanced(y ~ lag_y,
                               data = df_dynamic, index = c("i", "t"),
                               r = 2, se = "hac", bias_corr = TRUE,
                               exog = "weak")

Initialisation options

# Default OLS initialisation (fast; works well for fill >= 60%)
fit_ols <- ife_unbalanced(sales ~ price, data = cigar_unb,
                           index = c("state", "year"), r = 2, init = "ols")

# Nuclear-norm regularisation (recommended for fill < 60% or r >= 3)
fit_nnr <- ife_unbalanced(sales ~ price, data = cigar_unb,
                           index = c("state", "year"), r = 2, init = "nnr")

Function Reference

Key ife() arguments

Key ife_unbalanced() arguments

About

Author

Binzhi Chen (University of Essex)

Email: Binzhi.Chen9@gmail.com

Web: https://rickchen0910.github.io/

Citation

Please cite as follows:

Chen, B. (2026). xtife: Interactive Fixed Effects Estimator for Panel Data. R package version 0.1.4. https://CRAN.R-project.org/package=xtife.

@Manual{xtife,
  title  = {{xtife}: Interactive Fixed Effects Estimator for Panel Data},
  author = {Binzhi Chen},
  year   = {2026},
  note   = {R package version 0.1.4},
  url    = {https://CRAN.R-project.org/package=xtife},
}

References

Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4), 1229–1279. doi:10.3982/ECTA6135

Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221. doi:10.1111/1468-0262.00273

Bai, J. and Ng, S. (2021). Matrix completion, counterfactuals, and factor analysis of missing data. Journal of the American Statistical Association, 116(536), 1746–1763. doi:10.1080/01621459.2021.1967163

Baltagi, B.H. (1995). Econometric Analysis of Panel Data. Wiley.

Cameron, A.C., Gelbach, J.B. and Miller, D.L. (2011). Robust inference with multiway clustering. Journal of Business & Economic Statistics, 29(2), 238–249. doi:10.1198/jbes.2010.07136

Ditzen, J. and Karavias, Y. (2025). Interactive, Grouped and Non-separable Fixed Effects: A Practitioner’s Guide to the New Panel Data Econometrics. arXiv:2507.19099. doi:10.48550/arXiv.2507.19099

Mazumder, R., Hastie, T. and Tibshirani, R. (2010). Spectral regularization algorithms for learning large incomplete matrices. Journal of Machine Learning Research, 11, 2287–2322.

Moon, H.R. and Weidner, M. (2017). Dynamic linear panel regression models with interactive fixed effects. Econometric Theory, 33, 158–195. doi:10.1017/S0266466615000328

Newey, W.K. and West, K.D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708. doi:10.2307/1913610

Su, L., Wang, F. and Wang, Y. (2025). Estimation and inference for interactive fixed effects panel data models with unbalanced panels. SSRN Working Paper No. 5177283. doi:10.2139/ssrn.5177283

License

GPL-2 | GPL-3 © 2026 Binzhi Chen

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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