Package 'xtfifevd'

Between/Within Variance Ratio for Time-Invariant Variables

Description

Computes the between-panel and within-panel standard deviations for specified variables, along with their ratio. This diagnostic helps assess whether FEVD/FEF methods may improve upon standard FE estimation.

Usage

bw_ratio(data, variables, id)

Arguments

data	A data frame containing the panel data.
variables	A character vector of variable names to analyze.
id	Character string naming the panel identifier variable.

Details

For truly time-invariant variables, the within-panel SD should be zero (or near-zero due to numerical precision), giving an infinite ratio.

According to Plümper and Troeger (2007), FEVD/FEF methods tend to improve upon standard FE when:

• The between/within ratio exceeds approximately 1.7

• The correlation between z and the unobserved unit effect is not too high

Value

A data frame with columns:

variable

Variable name

sd_between

Between-panel standard deviation

sd_within

Within-panel standard deviation

bw_ratio

Ratio of between to within SD

References

Plumper, 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

Examples

# Create example data
set.seed(42)
N <- 50
T <- 5
id <- rep(1:N, each = T)
z_invariant <- rep(rnorm(N), each = T)  # Truly time-invariant
z_slow <- rep(rnorm(N), each = T) + rnorm(N * T, sd = 0.1)  # Slowly varying
x_varying <- rnorm(N * T)  # Time-varying

data <- data.frame(id = id, z_inv = z_invariant,
                   z_slow = z_slow, x = x_varying)

bw_ratio(data, c("z_inv", "z_slow", "x"), id = "id")

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Panel Fixed Effects Estimation for Time-Invariant Variables

Description

Estimates panel models with time-invariant regressors using FEVD, FEF, or FEF-IV methods. Standard fixed effects estimation cannot identify coefficients on time-invariant variables; these methods decompose or filter the unit effects to recover these coefficients.

Usage

xtfifevd(
  formula,
  data,
  id,
  time,
  method = c("fevd", "fef", "fef_iv"),
  instruments = NULL,
  na.action = na.omit
)

fevd(formula, data, id, time, na.action = na.omit)

fef(formula, data, id, time, na.action = na.omit)

fef_iv(formula, data, id, time, instruments, na.action = na.omit)

Arguments

formula	A formula of the form y ~ x1 + x2 | z1 + z2 where variables before | are time-varying and variables after | are time-invariant.
data	A data frame containing the variables.
id	Character string naming the panel (individual) identifier variable.
time	Character string naming the time identifier variable.
method	Estimation method: "fevd" (default), "fef", or "fef_iv".
instruments	For method = "fef_iv", a one-sided formula specifying instrumental variables, e.g., ~ iv1 + iv2.
na.action	How to handle missing values. Default is na.omit.

Details

Model

The panel model is:

$y_{it} = \alpha_i + x_{it}'\beta + z_i'\gamma + \varepsilon_{it}$

where $x_{it}$ are time-varying regressors, $z_i$ are time-invariant regressors, and $\alpha_i$ are individual fixed effects.

Stage 1 (All Methods)

Fixed effects regression of $y_{it}$ on $x_{it}$ yields consistent $\hat{\beta}$ and combined residuals $\hat{u}_{it} = \hat{\alpha}_i + \hat{\varepsilon}_{it}$.

Stage 2

Time-averaged residuals $\bar{u}_i$ are regressed on $z_i$:

• FEF: OLS of $\bar{u}_i$ on $z_i$ with intercept

• FEF-IV: 2SLS using instruments $r_i$

• FEVD: Same as FEF, then Stage 3 pooled OLS (point estimates identical)

Variance Estimation

Uses Pesaran-Zhou (2016) Equation 17/51 which properly accounts for estimation uncertainty from Stage 1. The naive pooled OLS standard errors from FEVD Stage 3 are inconsistent and can understate true SEs by factors of 2-5x or more.

Value

An object of class "xtfifevd" containing:

coefficients

Named vector of all coefficients (beta, gamma, intercept)

vcov

Variance-covariance matrix using Pesaran-Zhou estimator

beta

Coefficients on time-varying variables (from FE stage)

gamma

Coefficients on time-invariant variables

intercept

Overall intercept

residuals

Idiosyncratic residuals from FE stage

fitted.values

Fitted values

sigma2_e

Variance of idiosyncratic error

sigma2_u

Variance of unit effects

N

Total number of observations

N_g

Number of groups (panels)

T_bar

Average time periods per panel

method

Estimation method used

call

The matched call

Functions

• fevd: FEVD estimation (3-stage, Plümper-Troeger)

• fef: FEF estimation (2-stage, Pesaran-Zhou)

• fef_iv: FEF-IV estimation with instruments

References

Plumper, 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

See Also

fevd, fef, fef_iv, bw_ratio

Examples

# Simulate panel data
set.seed(123)
N <- 100  # panels
T <- 10   # time periods
n <- N * T

# Generate data
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
x <- rnorm(n)                        # Time-varying
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)

# Estimate with different methods
fit_fevd <- xtfifevd(y ~ x | z, data = data, id = "id", time = "time")
summary(fit_fevd)

fit_fef <- xtfifevd(y ~ x | z, data = data, id = "id", time = "time",
                    method = "fef")
summary(fit_fef)

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