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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')
#> Using GitHub PAT from the git credential store.
#> Skipping install of 'BTtest' from a github remote, the SHA1 (ab5c0e4f) has not changed since last install.
#>   Use `force = TRUE` to force installation

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).

The Barigozzi & Trapani (2022) test

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)
#> 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.

The Bai (2004) Integrated Information Criterion

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)
#> IPC_1 IPC_2 IPC_3 
#>     2     2     2