BTtest
Estimate the Number of Factors in Large Nonstationary Datasets
Large panel data sets are often subject to common trends. However, it can be difficult to determine the exact number of these common factors and analyse their properties.
The package implements the Barigozzi and Trapani (2022)
BTtest
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).
Installation
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')
Data
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).
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)
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.
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().
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)
print(IPCresult)
#> IPC_1 IPC_2 IPC_3
#> 2 2 2
References
- Bai, J. (2004). Estimating cross-section common stochastic trends in nonstationary panel data. Journal of Econometrics, 122(1), 137-183. DOI: 10.1016/j.jeconom.2003.10.022
- Barigozzi, M., & Trapani, L. (2022). Testing for common trends in nonstationary large datasets. Journal of Business & Economic Statistics, 40(3), 1107-1122. DOI: 10.1080/07350015.2021.1901719
- Trapani, L. (2018). A randomized sequential procedure to determine the number of factors. Journal of the American Statistical Association, 113(523), 1341-1349. DOI: 10.1080/01621459.2017.1328359