Panel Cointegration Tests Based on Westerlund (2007)

Implements a functional approximation of the four panel cointegration tests developed by Westerlund (2007) . The tests are based on structural rather than residual dynamics and allow for heterogeneity in both the long-run cointegrating relationship and the short-run dynamics. The package includes logic for automated lag and lead selection via AIC/BIC, Bartlett kernel long-run variance estimation, and a bootstrap procedure to handle cross-sectional dependence. It also includes a bootstrapping distribution visualization function for diagnostic purposes.

Westerlund: Panel Cointegration Testing in R

Westerlund is an R package implementing the four error-correction-based panel cointegration tests developed by Westerlund (2007). The test evaluates the null hypothesis of no cointegration by testing whether the error-correction term in a conditional panel ECM is equal to zero. Rejection of the null provides evidence of a long-run equilibrium relationship between the variables.

The implementation is designed to reproduce the logic of the Stata xtwest command while providing an R-native interface, reusable result objects, plotting, and summary methods.

Key Features

The package provides:

• Four Test Statistics: Computes $G_t$, $G_a$, $P_t$, and $P_a$.
• Flexible Dynamics: Supports fixed or unit-specific lag and lead lengths.
• Automated Selection: Built-in AIC/BIC selection and the Westerlund-specific information criterion.
• Bootstrap Inference: Residual-based bootstrap inference with synchronized time-cluster resampling to preserve contemporaneous cross-sectional dependence.
• Reproducible Bootstrap Runs: Optional seed argument.
• Unbalanced Panels: Supports unequal panel lengths while requiring continuous time within each unit.
• Kernel Estimation: Bartlett-kernel long-run variance estimation.
• Strict Time-Series Handling: Gap-aware lags, leads, and differences.
• Individual ECM Output: Optional unit-level regression output with indiv.ecm = TRUE.
• Rich Result Objects: Returns raw statistics, standardized Z-scores, asymptotic and bootstrap p-values, unit-level estimates, mean-group estimates, settings, and bootstrap distributions.
• S3 Methods: Includes print(), summary(), and plot() methods for fitted results.
• Bootstrap Visualization: Configurable critical level, robust-p annotations, and optional direct file export.

Installation

You can install the development version of Westerlund from GitHub using the devtools package:

# Install devtools if you haven't already
# install.packages("devtools")

# Install Westerlund
devtools::install_github("bosco-hung/Westerlund/R", build_vignettes = TRUE)

Quick Start

library(Westerlund)

results <- westerlund_test(
  data = my_data,
  yvar = "ln_gdp",
  xvars = c("ln_energy", "ln_capital"),
  idvar = "country",
  timevar = "year",
  constant = TRUE,
  trend = FALSE,
  lags = c(1, 3),      # AIC search between 1 and 3 lags
  leads = c(0, 2),     # AIC search between 0 and 2 leads
  bootstrap = 100,     # Run 100 bootstrap replications
  lrwindow = 3,        # Bartlett kernel window size
  seed = 123           # Reproducible bootstrap
)

# Main results
print(results)

# Extended summary
summary(results)

# Bootstrap distributions and critical values
plot(
  results,
  conf_level = 0.05,
  show_robust_p = TRUE
)

If no lag specification is supplied, lags = 1 is used. If leads = NULL, the lead order defaults to zero.

For individual-unit ECM output, set:

results <- westerlund_test(
  data = my_data,
  yvar = "ln_gdp",
  xvars = "ln_energy",
  idvar = "country",
  timevar = "year",
  constant = TRUE,
  indiv.ecm = TRUE
)

results$unit_data
results$indiv_reg

References

Westerlund, J. (2007). Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and Statistics, 69(6), 709-748.

Persyn, D., & Westerlund, J. (2008). Error-Correction-Based Cointegration Tests for Panel Data. Stata Journal, 8(2), 232-241.