You are analyzing a panel data set and want to determine if the cross-sectional units share a linear trend as well as any \(I(1)\) or \(I(0)\) dynamics?
Conveniently test for the number and type of common factors in large nonstationary panels using the routine by Barigozzi & Trapani (2022).
You can install the development version (0.10.3) of BTtest from GitHub with:
# install.packages('devtools')
devtools::install_github('Paul-Haimerl/BTtest')
library(BTtest)The stable version (0.10.2) is available on CRAN:
install.packages('BTtest')The BTtest packages includes a function that
automatically simulates a panel with common nonstationary trends:
set.seed(1)
# Simulate a DGP containing a factor with a linear drift (r1 = 1, d1 = 1 -> drift = TRUE) and
# I(1) process (d2 = 1 -> drift_I1 = TRUE), one zero-mean I(1) factor
# (r2 = 1 -> r_I1 = 2; since drift_I1 = TRUE) and two zero-mean I(0) factors (r3 = 2 -> r_I0 = 2)
X <- sim_DGP(N = 100, n_Periods = 200, drift = TRUE, drift_I1 = TRUE, r_I1 = 2, r_I0 = 2)For specifics on the DGP, I refer to Barigozzi & Trapani (2022, sec. 5).
To run the test, the user only needs to pass a \(T \times N\) data matrix X and
specify an upper limit on the number of factors (r_max), a
significance level (alpha) and whether to use a less
(BT1 = TRUE) or more conservative
(BT1 = FALSE) eigenvalue scaling scheme:
BTresult <- BTtest(X = X, r_max = 10, alpha = 0.05, BT1 = TRUE)
print(BTresult)
#> r_1_hat r_2_hat r_3_hat
#> 1 1 2Differences between BT1 = TRUE/ FALSE, where
BT1 = TRUE tends to identify more factors compared to
BT1 = FALSE, quickly vanish when the panel includes more
than 200 time periods (Barigozzi &
Trapani 2022, sec. 5; Trapani, 2018,
sec. 3).
BTtest returns a vector indicating the existence of (i)
a factor subject to a linear trend (\(r_1\)), the number of (ii) zero-mean \(I(1)\) factors (\(r_2\)) and the number of (iii) zero-mean
\(I(0)\) factors (\(r_3\)). Note that only one factor with a
linear trend can be identified.
The test statistic is constructed from R draws of an
i.i.d. standard normal random variable. Consequently, the test
results are nondeterministic and may vary slightly between executions,
particularly when R is small. However, in practical
applications this randomness can be eliminated by specifying a random
seed set.seed() before invoking BTtest().
An alternative way of estimating the total number of factors in a nonstationary panel are the Integrated Information Criteria by Bai (2004). The package also contains a function to easily evaluate this measure:
IPCresult <- BaiIPC(X = X, r_max = 10)
print(IPCresult)
#> IPC_1 IPC_2 IPC_3
#> 2 2 2