Title: Bootstrap Slope Heterogeneity Test for Panel Data
Version: 1.0.1
Description: Implements the bootstrap slope heterogeneity test for panel data based on Blomquist and Westerlund (2015) <doi:10.1007/s00181-015-0978-z>. Tests the null hypothesis that slope coefficients are homogeneous across cross-sectional units. Provides both standard and adjusted Delta statistics with bootstrap p-values. Supports partialling out of control variables and cross-sectional averages for dealing with cross-sectional dependence.
License: GPL-3
URL: https://github.com/muhammedalkhalaf/xtbhst
BugReports: https://github.com/muhammedalkhalaf/xtbhst/issues
Encoding: UTF-8
RoxygenNote: 7.3.3
Depends: R (≥ 3.5.0)
Imports: stats, graphics, grDevices
Suggests: testthat (≥ 3.0.0), plm
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-03-09 17:14:06 UTC; acad_
Author: Muhammad Alkhalaf ORCID iD [aut, cre, cph], Tore Bersvendsen [ctb], Jan Ditzen [ctb]
Maintainer: Muhammad Alkhalaf <muhammedalkhalaf@gmail.com>
Repository: CRAN
Date/Publication: 2026-03-13 13:30:02 UTC

xtbhst: Bootstrap Slope Heterogeneity Test for Panel Data

Description

Implements the bootstrap slope heterogeneity test for panel data based on Blomquist and Westerlund (2015). The test examines whether slope coefficients are homogeneous across cross-sectional units in a panel regression.

Main Function

xtbhst

Performs the bootstrap slope heterogeneity test.

Methods

print.xtbhst

Print test results.

summary.xtbhst

Detailed summary of test results.

plot.xtbhst

Diagnostic plots for the bootstrap test.

Test Details

The null hypothesis is that all cross-sectional units share the same slope coefficients (H0: homogeneous slopes). Rejection indicates significant slope heterogeneity, suggesting that pooled or fixed effects estimators may be inappropriate.

The test is based on the Delta statistic:

\Delta = \sqrt{N} \frac{\tilde{S}/N - K}{\sqrt{2K}}

where \tilde{S} measures the weighted sum of squared deviations of individual slope estimates from the weighted pooled estimate.

The bootstrap procedure uses a block bootstrap to preserve serial correlation in the residuals.

Cross-Sectional Dependence

The package supports handling cross-sectional dependence through cross-sectional averages (CSA), following the approach of Pesaran (2006). Users can specify variables for which CSA should be computed and partialled out.

Author(s)

Maintainer:

Other contributors:

References

Blomquist, J., & Westerlund, J. (2015). Panel bootstrap tests of slope homogeneity. Empirical Economics, 48(1), 1191-1204. doi:10.1007/s00181-015-0978-z

Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 74(4), 967-1012. doi:10.1111/j.1468-0262.2006.00692.x

Swamy, P. A. V. B. (1970). Efficient inference in a random coefficient regression model. Econometrica, 38(2), 311-323. doi:10.2307/1913012

See Also

Useful links:

Plot method for xtbhst objects

Description

Produces diagnostic plots for the bootstrap slope heterogeneity test.

Usage

## S3 method for class 'xtbhst'
plot(x, which = c(1L, 2L), ask = NULL, ...)

Arguments

x

An object of class "xtbhst".

which

Integer vector specifying which plots to produce: 1 = Bootstrap distribution of Delta, 2 = Bootstrap distribution of adjusted Delta, 3+ = Individual coefficient distributions. Default is c(1, 2).

ask

Logical. If TRUE, prompt before each plot (default: TRUE if multiple plots and interactive session).

...

Additional arguments passed to plotting functions.

Value

Invisibly returns NULL.

Print method for xtbhst objects

Description

Print method for xtbhst objects

Usage

## S3 method for class 'xtbhst'
print(x, digits = 4L, ...)

Arguments

x

An object of class "xtbhst".

digits

Number of digits to display (default: 4).

...

Additional arguments (ignored).

Value

Invisibly returns the input object.

Summary method for xtbhst objects

Description

Summary method for xtbhst objects

Usage

## S3 method for class 'xtbhst'
summary(object, digits = 4L, ...)

Arguments

object

An object of class "xtbhst".

digits

Number of digits to display (default: 4).

...

Additional arguments (ignored).

Value

Invisibly returns a list with summary statistics.

Bootstrap Slope Heterogeneity Test for Panel Data

Description

Implements the bootstrap slope heterogeneity test based on Blomquist and Westerlund (2015). Tests the null hypothesis that slope coefficients are homogeneous across cross-sectional units.

Usage

xtbhst(
  formula,
  data,
  id,
  time,
  reps = 999L,
  blocklength = NULL,
  partial = NULL,
  csa = NULL,
  csa_lags = 0L,
  constant = TRUE,
  seed = NULL
)

Arguments

formula

A formula of the form y ~ x1 + x2 + ... specifying the dependent variable and regressors.

data

A data frame containing the panel data.

id

A character string specifying the name of the cross-sectional identifier variable.

time

A character string specifying the name of the time variable.

reps

Integer. Number of bootstrap replications (default: 999).

blocklength

Integer. Block length for the block bootstrap. If NULL (default), set automatically to floor(2 * T^(1/3)) where T is the number of time periods.

partial

Optional formula specifying variables to be partialled out. For example, ~ z1 + z2.

csa

Optional formula specifying variables for which cross-sectional averages should be computed and included. Used to handle cross-sectional dependence following Pesaran (2006).

csa_lags

Integer. Number of lags of the cross-sectional averages to include (default: 0).

constant

Logical. If TRUE (default), include a constant (partialled out).

seed

Optional integer seed for reproducibility.

Details

The test is based on the following Delta statistic:

\Delta = \sqrt{N} \frac{\tilde{S}/N - K}{\sqrt{2K}}

where \tilde{S} is a weighted sum of squared deviations of individual slope estimates from the weighted pooled estimate.

The adjusted Delta statistic corrects for small sample bias:

\Delta_{adj} = \sqrt{N} \frac{\tilde{S}/N - K}{\sqrt{V}}

where V = 2K(T-K-K_{partial}-1)/(T-K_{partial}+1).

Under the null hypothesis of slope homogeneity, both statistics are asymptotically standard normal. The bootstrap procedure provides finite-sample p-values.

The function requires a strongly balanced panel (all units observed for all time periods).

Value

An object of class "xtbhst" containing:

delta

The Delta test statistic.

delta_adj

The adjusted Delta test statistic.

pval

Bootstrap p-value for the Delta statistic.

pval_adj

Bootstrap p-value for the adjusted Delta statistic.

blocklength

The block length used in the bootstrap.

reps

Number of bootstrap replications.

N

Number of cross-sectional units.

T

Number of time periods.

K

Number of regressors.

beta_i

Matrix of individual slope estimates (N x K).

beta_fe

Vector of weighted fixed effects (pooled) estimates.

delta_stars

Vector of bootstrap Delta statistics.

delta_adj_stars

Vector of bootstrap adjusted Delta statistics.

call

The matched call.

References

Blomquist, J., & Westerlund, J. (2015). Panel bootstrap tests of slope homogeneity. Empirical Economics, 48(1), 1191-1204. doi:10.1007/s00181-015-0978-z

Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 74(4), 967-1012. doi:10.1111/j.1468-0262.2006.00692.x

Examples


# Generate example panel data
set.seed(123)
N <- 20  # cross-sectional units
T_periods <- 30  # time periods

# Homogeneous slopes (H0 is true)
data_hom <- data.frame(
  id = rep(1:N, each = T_periods),
  time = rep(1:T_periods, N),
  x = rnorm(N * T_periods)
)
data_hom$y <- 1 + 0.5 * data_hom$x + rnorm(N * T_periods)

# Test for slope heterogeneity
result <- xtbhst(y ~ x, data = data_hom, id = "id", time = "time",
                 reps = 199, seed = 42)
print(result)
summary(result)