Panel Fixed Effects Filtered and Variance Decomposition Estimation.

xtfifevd

Overview

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.

Installation

# Install from CRAN (when available)
install.packages("xtfifevd")

# Or install development version from GitHub
# install.packages("remotes")

Usage

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
======================================================================

Methods Comparison

# 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)

Diagnostics

# 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 FE

Why Use This Package?

The Problem

Standard 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

Common (Wrong) Solutions

1. Hausman-Taylor: Requires valid instruments, often hard to justify
2. Naive FEVD Stage 3 SEs: Severely understated (factors of 2-5x!)
3. Ignoring the problem: Biased pooled OLS

The Right Solution

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

References

• 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

License

GPL-3