Implements the four error-correction-based panel cointegration tests of Westerlund (2007): two group-mean statistics (Ga, Gt) and two panel statistics (Pa, Pt). The null hypothesis is no cointegration between the dependent variable and the regressors.
cointegration_test(
data,
unit_index,
time_index,
formula,
lags = 1L,
leads = 1L,
test = c("ga", "gt", "pa", "pt"),
n_bootstrap = 0L,
seed = NULL,
show_progress = FALSE
)An object of class dcce_cointegration with elements
statistics (a tibble with columns test, statistic,
p_value, method), lags, leads, N,
T_bar, and call.
A panel data.frame.
Character scalar: unit identifier column.
Character scalar: time identifier column.
Two-sided formula of the form y ~ x1 + x2 in
levels (not first differences).
Integer scalar: ADF lag order for \(\Delta y\) lags in the
ECM regression. Default 1L.
Integer scalar: number of leads of \(\Delta x\). Default
1L.
Character vector: which statistics to compute. Subset of
c("ga", "gt", "pa", "pt"). Default: all four.
Integer: number of bootstrap replications for
p-values. Default 0L (asymptotic p-values).
Integer: random seed for the bootstrap.
Logical: print progress? Default FALSE.
For each unit \(i\), an error-correction regression is fitted $$\Delta y_{it} = \delta_i d_t + \alpha_i y_{i,t-1} + \lambda_i' x_{i,t-1} + \sum_{j=1}^{p_i} \alpha_{ij} \Delta y_{i,t-j} + \sum_{j=-q_i}^{p_i} \gamma_{ij}' \Delta x_{i,t-j} + e_{it},$$ and the t-statistic for \(\alpha_i = 0\) is used to construct the four test statistics:
Gt: group-mean of the \(\hat\alpha_i / SE(\hat\alpha_i)\).
Ga: group-mean of \(T \hat\alpha_i / \hat\alpha_i(1)\) (unnormalised form).
Pt: pooled t-statistic.
Pa: pooled alpha-statistic.
A negative, large-magnitude statistic rejects the null of no
cointegration. Asymptotic p-values are obtained by linear interpolation
on the critical values in Westerlund (2007, Table 3). A bootstrap path
(n_bootstrap > 0) is also provided, resampling cross-sectional
units with replacement to account for cross-sectional dependence.
Westerlund, J. (2007). Testing for Error Correction in Panel Data. Oxford Bulletin of Economics and Statistics, 69(6), 709-748.
data(pwt8)
result <- cointegration_test(
data = pwt8,
unit_index = "country",
time_index = "year",
formula = log_rgdpo ~ log_hc + log_ck,
test = c("ga", "gt"),
lags = 1L
)
print(result)
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