xtbreakcoint: Panel Cointegration Test with Structural Breaks

In xtbreakcoint: Panel Cointegration Tests with Structural Breaks

Panel Cointegration Test with Structural Breaks

Description

Implements the panel cointegration test of Banerjee and Carrion-i-Silvestre (2015), allowing for structural breaks and cross-section dependence through common factors.

Usage

xtbreakcoint(
  formula,
  data,
  id,

  time,
  model = "trendshift",
  max_factors = 5,
  max_lag = 4,

  lag_method = c("auto", "fixed"),
  trim = 0.15,
  max_iter = 20,
  tolerance = 0.001
)

Arguments

formula	A formula of the form y ~ x1 + x2 + ... specifying the cointegrating relationship.
data	A data frame containing panel data with columns for the panel identifier, time identifier, and all variables in the formula.
id	Character string naming the panel (cross-section) identifier.
time	Character string naming the time identifier.
model	Model specification for deterministic components. One of: "constant" (1), "trend" (2), "levelshift" (3), "trendshift" (4, default), or "regimeshift" (5). Can also specify as integer 1-5.
max_factors	Maximum number of common factors to estimate (default: 5). Set to 0 to skip factor estimation.
max_lag	Maximum lag order for ADF tests (default: 4).
lag_method	Method for selecting ADF lag order: "auto" for automatic selection via BIC (default) or "fixed" to use max_lag.
trim	Trimming parameter for break estimation, proportion of sample excluded from endpoints (default: 0.15). Must be in (0, 0.5).
max_iter	Maximum iterations for factor-break estimation (default: 20).
tolerance	Convergence tolerance for iterative estimation (default: 0.001).

Details

This function tests for panel cointegration in the presence of structural breaks and cross-sectional dependence. The methodology follows these steps:

1. Iterative Factor-Break Estimation: Jointly estimates common factors and individual break dates using an iterative procedure.

2. Individual ADF Tests: Applies ADF tests to the defactored (idiosyncratic) residuals for each cross-section unit.

3. Panel Test Statistic: Combines individual ADF statistics into a standardized panel statistic using Monte Carlo moments.

4. MQ Test: If factors are detected, tests whether they are stationary or represent stochastic trends (Bai & Ng, 2004).

Value

An object of class "xtbreakcoint" containing:

Z_t

Panel test statistic (standard normal under H0)

p_value

One-sided p-value for Z_t

tbar

Average of individual ADF t-statistics

mean_t

Expected value of t-statistic under H0

var_t

Variance of t-statistic under H0

N

Number of cross-section units

T

Number of time periods

n_factors

Number of estimated common factors

n_trends

Number of stochastic trends (from MQ test)

MQ_np

Non-parametric MQ test statistic

MQ_p

Parametric MQ test statistic

iterations

Number of iterations for factor-break convergence

reject_pct

Percentage of individual units rejecting H0 at 5%

adf_stats

Vector of individual ADF t-statistics

lag_orders

Vector of selected lag orders for each unit

breaks

Vector of estimated break dates (periods from start)

factors

Matrix of estimated common factors (T-1 x n_factors)

model

Model specification used

call

The matched call

Model Specifications

1 - constant

Constant only

2 - trend

Constant plus linear trend

3 - levelshift

Constant plus level shift at break

4 - trendshift

Constant, trend, plus level shift (default)

5 - regimeshift

Constant, trend, level shift, plus slope shift

Author(s)

Muhammad Alkhalaf

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jae.2348")}

Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127-1177. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1468-0262.2004.00528.x")}

Examples

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

# Create cointegrated data with a structural break
panel_data <- data.frame(
  id = rep(1:N, each = T),
  time = rep(1:T, N),
  y = NA,
  x = NA
)

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

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

xtbreakcoint documentation built on March 16, 2026, 5:09 p.m.