xtfifevd implements fixed effects estimators for time-invariant variables in panel data models. Standard fixed effects (FE) estimation cannot identify coefficients on time-invariant regressors because they are collinear with the individual fixed effects. This package provides three methods to estimate these coefficients:
- FEVD: Fixed Effects Vector Decomposition (Plümper & Troeger, 2007)
- FEF: Fixed Effects Filtered (Pesaran & Zhou, 2018)
- FEF-IV: FEF with instrumental variables for endogenous regressors
All methods use the correct Pesaran-Zhou (2018) variance estimators that account for generated regressor uncertainty, avoiding the severe size distortions documented in the literature.
# Install from CRAN (when available)
install.packages("xtfifevd")
# Or install development version from GitHub
# install.packages("remotes")library(xtfifevd)
# Simulate panel data
set.seed(123)
N <- 100 # panels
T <- 10 # time periods
n <- N * T
id <- rep(1:N, each = T)
time <- rep(1:T, N)
alpha_i <- rep(rnorm(N), each = T) # Fixed effects
z <- rep(rnorm(N), each = T) # Time-invariant variable
x <- rnorm(n) # Time-varying variable
y <- 1 + 2 * x + 0.5 * z + alpha_i + rnorm(n, sd = 0.5)
data <- data.frame(id = id, time = time, y = y, x = x, z = z)
# Formula: y ~ time_varying_vars | time_invariant_vars
fit <- xtfifevd(y ~ x | z, data = data, id = "id", time = "time")
summary(fit)Output:
======================================================================
FEVD Estimation Results xtfifevd 1.0.0
======================================================================
Dep. variable: y
Method: FEVD
Variance: Pesaran-Zhou (2016)
Observations: 1000 Groups: 100
T (average): 10.00
----------------------------------------------------------------------
Estimate Std. Error z value Pr(>|z|)
x 1.99842 0.01621 123.283 < 2e-16 ***
z 0.51247 0.10834 4.731 2.23e-06 ***
_cons 0.98123 0.10521 9.326 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
----------------------------------------------------------------------
Time-varying (FE): x
Time-invariant: z
sigma_e: 0.5012 sigma_u: 0.9834
======================================================================
# All three methods
fit_fevd <- fevd(y ~ x | z, data, id = "id", time = "time")
fit_fef <- fef(y ~ x | z, data, id = "id", time = "time")
# FEF and FEVD produce identical point estimates (Proposition 3)
all.equal(coef(fit_fevd), coef(fit_fef))
# [1] TRUE
# With instruments (when z may be endogenous)
data$iv <- data$z + rnorm(n, sd = 0.3) # Instrument
fit_iv <- fef_iv(y ~ x | z, data, id = "id", time = "time",
instruments = ~ iv)# Between/Within variance ratio
# High ratios suggest FEVD/FEF may improve on standard FE
bw_ratio(data, c("z", "x"), id = "id")
# Between/Within Variance Ratios
# ------------------------------------------------------------
# Variable Between SD Within SD B/W Ratio
# ------------------------------------------------------------
# z 1.0234 0.0000 Inf
# x 0.1023 0.9876 0.10
# ------------------------------------------------------------
# Note: B/W > 1.7 suggests FEVD/FEF may improve on FEStandard FE estimation "absorbs" time-invariant variables into the fixed effects, making their coefficients unidentified. Researchers often want to estimate effects of variables like:
- Gender, ethnicity, geographic region
- Institutional characteristics
- Baseline/entry values
- Hausman-Taylor: Requires valid instruments, often hard to justify
- Naive FEVD Stage 3 SEs: Severely understated (factors of 2-5x!)
- Ignoring the problem: Biased pooled OLS
FEVD/FEF methods with Pesaran-Zhou corrected standard errors provide:
- Consistent point estimates under standard FE assumptions
- Valid inference that accounts for generated regressor uncertainty
- Better efficiency than FE for variables with high between/within ratio
-
Plümper, T., & Troeger, V. E. (2007). Efficient Estimation of Time-Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects. Political Analysis, 15(2), 124-139. doi:10.1093/pan/mpm002
-
Pesaran, M. H., & Zhou, Q. (2018). Estimation of time-invariant effects in static panel data models. Econometric Reviews, 37(10), 1137-1171. doi:10.1080/07474938.2016.1222225
-
Greene, W. H. (2011). Fixed Effects Vector Decomposition: A Magical Solution to the Problem of Time-Invariant Variables in Fixed Effects Models? Political Analysis, 19(2), 135-146. doi:10.1093/pan/mpq034
GPL-3