Tests of cross-section dependence for panel models
Pesaran's CD or Breusch–Pagan's LM (local or global) tests for cross sectional dependence in panel models
pcdtest(x, ...) ## S3 method for class 'formula' pcdtest( x, data, index = NULL, model = NULL, test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"), w = NULL, ... ) ## S3 method for class 'panelmodel' pcdtest( x, test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"), w = NULL, ... ) ## S3 method for class 'pseries' pcdtest( x, test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"), w = NULL, ... )
x |
an object of class |
... |
further arguments to be passed on to |
data |
a |
index |
an optional numerical index, if |
model |
an optional character string indicating which type of
model to estimate; if left to |
test |
the type of test statistic to be returned. One of
|
w |
either |
These tests are originally meant to use the residuals of separate
estimation of one time–series regression for each cross-sectional
unit in order to check for cross–sectional dependence. If a
different model specification (within
, random
, ...) is
assumed consistent, one can resort to its residuals for testing
(which is common, e.g., when the time dimension's length is
insufficient for estimating the heterogeneous model). If the time
dimension is insufficient and model=NULL
, the function defaults
to estimation of a within
model and issues a warning. The main
argument of this function may be either a model of class
panelmodel
or a formula
and dataframe
; in the second case,
unless model
is set to NULL
, all usual parameters relative to
the estimation of a plm
model may be passed on. The test is
compatible with any consistent panelmodel
for the data at hand,
with any specification of effect
. E.g., specifying
effect="time"
or effect="twoways"
allows to test for residual
cross-sectional dependence after the introduction of time fixed
effects to account for common shocks.
A local version of either test can be computed by supplying a
proximity matrix (elements coercible to logical
) with argument
w
which provides information on whether any pair of individuals
are neighbours or not. If w
is supplied, only neighbouring pairs
will be used in computing the test; else, w
will default to
NULL
and all observations will be used. The matrix need not be
binary, so commonly used "row–standardized" matrices can be
employed as well. nb
objects from spdep must instead be
transformed into matrices by spdep's function nb2mat
before using.
The methods implemented are suitable also for unbalanced panels.
Pesaran's CD test (test="cd"
), Breusch and Pagan's LM test
(test="lm"
), and its scaled version (test="sclm"
) are all
described in Pesaran (2004) (and complemented by
Pesaran (2005)). The bias-corrected scaled test (test="bcsclm"
)
is due to (Baltagi et al. 2012) and only valid for
within models including the individual effect (it's unbalanced
version uses max(Tij) for T) in the bias-correction term).
Breusch and Pagan (1980) is the original source for
the LM test.
The test on a pseries
is the same as a test on a pooled
regression model of that variable on a constant, i.e.,
pcdtest(some_pseries)
is equivalent to pcdtest(plm(some_var ~ 1, data = some_pdata.frame, model = "pooling")
and also equivalent to
pcdtest(some_var ~ 1, data = some_data)
, where some_var
is
the variable name in the data which corresponds to some_pseries
.
An object of class "htest"
.
Baltagi BH, Feng Q, Kao C (2012). “A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model.” Journal of Econometrics, 170(1), 164–177. ISSN 0304-4076, https://www.sciencedirect.com/science/article/pii/S030440761200098X.
Breusch TS, Pagan AR (1980). “The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics.” Review of Economic Studies, 47, 239–253.
Pesaran MH (2004). “General Diagnostic Tests for Cross Section Dependence in Panels.” CESifo Working Paper Series, 1229.
Pesaran MH (2015). “Testing Weak Cross-Sectional Dependence in Large Panels.” Econometric Reviews, 34(6-10), 1089–1117. doi: 10.1080/07474938.2014.956623, https://doi.org/10.1080/07474938.2014.956623.
data("Grunfeld", package = "plm") ## test on heterogeneous model (separate time series regressions) pcdtest(inv ~ value + capital, data = Grunfeld, index = c("firm", "year")) ## test on two-way fixed effects homogeneous model pcdtest(inv ~ value + capital, data = Grunfeld, model = "within", effect = "twoways", index = c("firm", "year")) ## test on panelmodel object g <- plm(inv ~ value + capital, data = Grunfeld, index = c("firm", "year")) pcdtest(g) ## scaled LM test pcdtest(g, test = "sclm") ## test on pseries pGrunfeld <- pdata.frame(Grunfeld) pcdtest(pGrunfeld$value) ## local test ## define neighbours for individual 2: 1, 3, 4, 5 in lower triangular matrix w <- matrix(0, ncol= 10, nrow=10) w[2,1] <- w[3,2] <- w[4,2] <- w[5,2] <- 1 pcdtest(g, w = w)
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