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 of BTtest from GitHub with:
# install.packages('devtools')
devtools::install_github('Paul-Haimerl/BTtest')
#> Skipping install of 'BTtest' from a github remote, the SHA1 (b1262865) has not changed since last install.
#> Use `force = TRUE` to force installation
library(BTtest)
The stable version is available on CRAN:
The BTtest
packages includes a function that automatically simulates a panel with common nonstationary trends:
# 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 2
Differences 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.
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: