Panel Cointegration Tests with Structural Breaks

Implements panel cointegration tests allowing for structural breaks and cross-section dependence following the methodology of Banerjee and Carrion-i-Silvestre (2015) . The package provides iterative factor-break estimation, individual ADF tests on defactored residuals, standardized panel test statistics, and the Bai and Ng (2004) MQ test for identifying common stochastic trends. Supports five model specifications with varying deterministic components and break structures.

xtbreakcoint

Panel cointegration tests allowing for structural breaks and cross-section dependence, implementing the methodology of Banerjee and Carrion-i-Silvestre (2015).

Installation

You can install the development version from GitHub:

# install.packages("devtools")

Overview

The xtbreakcoint package tests for panel cointegration when:

• Structural breaks may be present in the cointegrating relationship
• Cross-section dependence exists through common factors

The methodology follows four steps:

1. Iterative Factor-Break Estimation: Jointly estimates common factors and individual break dates
2. Individual ADF Tests: Applies ADF tests to defactored residuals
3. Panel Test Statistic: Combines individual statistics into a standardized panel statistic
4. MQ Test: Tests whether common factors are I(1) stochastic trends

Example

library(xtbreakcoint)

# Generate example panel data
set.seed(42)
N <- 10   # panels
T <- 50   # time periods

panel_data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  y = NA,
  x = NA
)

# Create cointegrated data with a structural break at t=25
for (i in 1:N) {
  idx <- panel_data$id == i
  x <- cumsum(rnorm(T))
  u <- rnorm(T, sd = 0.5)
  beta <- ifelse(1:T <= 25, 1, 1.5)  # Break in slope
  y <- 1 + beta * x + u
  panel_data$x[idx] <- x
  panel_data$y[idx] <- y
}

# Test for cointegration
result <- xtbreakcoint(y ~ x, data = panel_data, id = "id", time = "time")
print(result)

Model Specifications

References

• Banerjee, A., & Carrion-i-Silvestre, J. L. (2015). Cointegration in panel data with structural breaks and cross-section dependence. Journal of Applied Econometrics, 30(1), 1-22. doi:10.1002/jae.2348

• Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127-1177. doi:10.1111/j.1468-0262.2004.00528.x

• Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221. doi:10.1111/1468-0262.00273

Author

Based on original GAUSS code by A. Banerjee and J.L. Carrion-i-Silvestre.

License

GPL (>= 3)