Unit root tests for panel data
purtest
implements several testing procedures that have been proposed
to test unit root hypotheses with panel data.
purtest( object, data = NULL, index = NULL, test = c("levinlin", "ips", "madwu", "Pm", "invnormal", "logit", "hadri"), exo = c("none", "intercept", "trend"), lags = c("SIC", "AIC", "Hall"), pmax = 10, Hcons = TRUE, q = NULL, dfcor = FALSE, fixedT = TRUE, ips.stat = NULL, ... ) ## S3 method for class 'purtest' print(x, ...) ## S3 method for class 'purtest' summary(object, ...) ## S3 method for class 'summary.purtest' print(x, ...)
object, x |
Either a |
data |
a |
index |
the indexes, |
test |
the test to be computed: one of |
exo |
the exogenous variables to introduce in the augmented
Dickey–Fuller (ADF) regressions, one of: no exogenous
variables ( |
lags |
the number of lags to be used for the augmented
Dickey-Fuller regressions: either an integer (the number of
lags for all time series), a vector of integers (one for each
time series), or a character string for an automatic
computation of the number of lags, based on the AIC
( |
pmax |
maximum number of lags (irrelevant for |
Hcons |
logical, only relevant for |
q |
the bandwidth for the estimation of the long-run variance
(only relevant for |
dfcor |
logical, indicating whether the standard deviation of the regressions is to be computed using a degrees-of-freedom correction, |
fixedT |
logical, indicating whether the individual ADF
regressions are to be computed using the same number of
observations (irrelevant for |
ips.stat |
|
... |
further arguments (can set argument |
All these tests except "hadri"
are based on the estimation of
augmented Dickey-Fuller (ADF) regressions for each time series. A
statistic is then computed using the t-statistics associated with
the lagged variable. The Hadri residual-based LM statistic is the
cross-sectional average of the individual KPSS statistics
(Kwiatkowski et al. 1992), standardized by their
asymptotic mean and standard deviation.
Several Fisher-type tests that combine p-values from tests based on ADF regressions per individual are available:
"madwu"
is the inverse chi-squared test
(Maddala and Wu 1999), also called P test by
Choi (2001).
"Pm"
is the modified P test proposed by
Choi (2001) for large N,
"invnormal"
is the inverse normal test by (Choi 2001), and
"logit"
is the logit test by (Choi 2001).
The individual p-values for the Fisher-type tests are approximated as described in MacKinnon (1996) if the package 'urca' (Pfaff (2008)) is available, otherwise as described in MacKinnon (1994).
For the test statistic tbar of the test of Im/Pesaran/Shin (2003)
(ips.stat = "tbar
), no p-value is given but 1%, 5%, and 10% critical
values are interpolated from paper's tabulated values via inverse distance
weighting (printed and contained in the returned value's element
statistic$ips.tbar.crit).
Hadri's test, the test of Levin/Lin/Chu, and the tbar statistic of
Im/Pesaran/Shin are not applicable to unbalanced panels; the tbar statistic
is not applicable when lags > 0
is given.
The exogeneous instruments of the tests (where applicable) can be specified in several ways, depending on how the data is handed over to the function:
For the formula
/data
interface (if data
is a data.frame
,
an additional index
argument should be specified); the formula
should be of the form: y ~ 0
, y ~ 1
, or y ~ trend
for a test
with no exogenous variables, with an intercept, or with individual
intercepts and time trend, respectively. The exo
argument is
ignored in this case.
For the data.frame
, matrix
, and pseries
interfaces: in
these cases, the exogenous variables are specified using the exo
argument.
With the associated summary
and print
methods, additional
information can be extracted/displayed (see also Value).
For purtest: An object of class "purtest"
: a list with the elements
"statistic"
(a "htest"
object), "call"
, "args"
,
"idres"
(containing results from the individual regressions),
and "adjval"
(containing the simulated means and variances
needed to compute the statistic, for "test = levinlin"
and "ips"
,
otherwise NULL
), "sigma2"
(short-run and long-run variance for
"test = levinlin"
, otherwise NULL).
Yves Croissant and for "Pm", "invnormal", and "logit" Kevin Tappe
Choi I (2001).
“Unit root tests for panel data.”
Journal of International Money and Finance, 20(2), 249–272.
ISSN 0261-5606, https://www.sciencedirect.com/science/article/pii/S0261560600000486.
Hadri K (2000).
“Testing for stationarity in heterogeneous panel data.”
The Econometrics Journal, 3(2), 148–161.
ISSN 13684221, 1368423X.
Hall A (1994).
“Testing for a unit root in time series with pretest data-based model selection.”
Journal of Business \& Economic Statistics, 12(4), 461–470.
Im KS, Pesaran MH, Shin Y (2003).
“Testing for unit roots in heterogenous panels.”
Journal of Econometrics, 115(1), 53–74.
Kwiatkowski D, Phillips PC, Schmidt P, Shin Y (1992).
“Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?”
Journal of Econometrics, 54(1), 159–178.
ISSN 0304-4076, https://www.sciencedirect.com/science/article/pii/030440769290104Y.
Levin A, Lin CF, Chu CSJ (2002).
“Unit root test in panel data : asymptotic and finite sample properties.”
Journal of Econometrics, 108, 1–24.
MacKinnon JG (1996).
“Numerical Distribution Functions for Unit Root and Cointegration Tests.”
Journal of Applied Econometrics, 11(6), 601–618.
ISSN 08837252.
MacKinnon JG (1994).
“Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests.”
Journal of Business & Economic Statistics, 12(2), 167–176.
ISSN 07350015.
Maddala GS, Wu S (1999).
“A comparative study of unit root tests with panel data and a new simple test.”
Oxford Bulletin of Economics and Statistics, 61, 631–52.
Pfaff B (2008).
Analysis of Integrated and Cointegrated Time Series with R, Second edition.
Springer, New York.
ISBN 0-387-27960-1, https://cran.r-project.org/package=urca.
data("Grunfeld", package = "plm") y <- data.frame(split(Grunfeld$inv, Grunfeld$firm)) # individuals in columns purtest(y, pmax = 4, exo = "intercept", test = "madwu") ## same via formula interface purtest(inv ~ 1, data = Grunfeld, index = c("firm", "year"), pmax = 4, test = "madwu")
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