Bootstrap Slope Heterogeneity Test for Panel Data

Implements the bootstrap slope heterogeneity test for panel data of Blomquist and Westerlund (2016) . Tests the null hypothesis that slope coefficients are homogeneous across cross-sectional units using a block bootstrap of the Swamy-type statistic, with the unit-specific variance estimator of the paper or that of Pesaran and Yamagata (2008) , whose Delta and adjusted Delta statistics are reported with asymptotic p-values. Supports partialling out of control variables and cross-sectional averages.

xtbhst: Bootstrap Slope Heterogeneity Test for Panel Data

Overview

xtbhst implements the bootstrap slope heterogeneity test for panel data based on Blomquist and Westerlund (2016). The test examines whether slope coefficients are homogeneous across cross-sectional units.

Reference: Blomquist, J. and Westerlund, J. (2016). Panel bootstrap tests of slope homogeneity. Empirical Economics, 50(4), 1359-1381. doi:10.1007/s00181-015-0978-z

The Delta and adjusted Delta statistics reported alongside the bootstrap test are those of Pesaran, M. H. and Yamagata, T. (2008). Testing slope homogeneity in large panels. Journal of Econometrics, 142(1), 50-93. doi:10.1016/j.jeconom.2007.05.010

Installation

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

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

Usage

Basic Example

library(xtbhst)

# Generate panel data with homogeneous slopes
set.seed(123)
N <- 20   # cross-sectional units
T <- 30   # time periods

data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  x = rnorm(N * T)
)
data$y <- 1 + 0.5 * data$x + rnorm(N * T)

# Test for slope heterogeneity
result <- xtbhst(y ~ x, data = data, id = "id", time = "time",
                 reps = 999, seed = 42)
print(result)

The printed output reports the statistic S with its bootstrap p-value (the test of the paper), and the Delta and adjusted Delta statistics of Pesaran and Yamagata (2008) with asymptotic p-values, together with the bootstrap settings and the panel dimensions.

Variance estimator

# Default: unit-specific residual variance of Blomquist and Westerlund (2016)
result_bw <- xtbhst(y ~ x, data = data, id = "id", time = "time", variance = "bw")

# Alternative: Pesaran and Yamagata (2008) estimator from pooled FE residuals
result_py <- xtbhst(y ~ x, data = data, id = "id", time = "time", variance = "py")

With Control Variables

# Partial out control variables
data$z <- rnorm(N * T)
result <- xtbhst(y ~ x, data = data, id = "id", time = "time",
                 partial = ~ z, reps = 999)

Cross-Sectional Averages (extension)

The block bootstrap of the paper is itself robust to cross-sectional dependence. As an extension not covered by Blomquist and Westerlund (2016), cross-sectional averages (in the spirit of Pesaran, 2006) can be partialled out. With csa_lags > 0 the first csa_lags periods are dropped for all units.

result <- xtbhst(y ~ x, data = data, id = "id", time = "time",
                 csa = ~ x, csa_lags = 2, reps = 999)

Diagnostic Plots

# Plot bootstrap distributions
plot(result)

# Plot all diagnostics including individual slopes
plot(result, which = 1:4)

Interpretation

• Null hypothesis (H0): Slope coefficients are homogeneous across all cross-sectional units
• Alternative (H1): Slopes differ across units

If the bootstrap p-value of S is small (e.g., < 0.05), reject H0 and conclude there is evidence of slope heterogeneity. This suggests that pooled OLS or standard fixed effects estimators may be inappropriate, and heterogeneous coefficient models (e.g., mean group estimator) should be considered.

Requirements

• Strongly balanced panel (all units observed for all time periods); rows with missing values are dropped before this is checked
• At least one regressor beyond the constant

Citation

If you use this package, please cite:

Blomquist, J. and Westerlund, J. (2016). Panel bootstrap tests of slope
homogeneity. Empirical Economics, 50(4), 1359-1381.
https://doi.org/10.1007/s00181-015-0978-z

How to cite

If you use xtbhst in your work, please cite the package as:

Alkhalaf, M.A. (2026). xtbhst: Bootstrap Slope Heterogeneity Test for Panel Data. R package version 1.1.0. https://CRAN.R-project.org/package=xtbhst. doi:10.32614/CRAN.package.xtbhst

In R, the suggested citation is also available via citation("xtbhst").

The R port is based on the Stata xthst command; please also cite the original Stata implementation when relevant.

License

GPL (>= 3)

Author

R port based on the Stata implementation xtbhst, which was adapted from the Stata xthst command.