Pesaran's CD or Breusch--Pagan's LM (local or global) tests for cross sectional dependence in panel models

`pcdtest(x, ...)`# S3 method for formula
pcdtest(
x,
data,
index = NULL,
model = NULL,
test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"),
w = NULL,
...
)

# S3 method for panelmodel
pcdtest(
x,
test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"),
w = NULL,
...
)

# S3 method for pseries
pcdtest(
x,
test = c("cd", "sclm", "bcsclm", "lm", "rho", "absrho"),
w = NULL,
...
)

x

an object of class `formula`

, `panelmodel`

, or `pseries`

(depending on the respective interface) describing the model to
be tested,

…

further arguments to be passed on for model estimation to `plm`

,
such as `effect`

or `random.method`

.

data

a `data.frame`

,

index

an optional numerical index, if `NULL`

, the first two
columns of the data.frame provided in argument `data`

are
assumed to be the index variables; for further details see
`pdata.frame()`

,

model

an optional character string indicating which type of
model to estimate; if left to `NULL`

, the original
heterogeneous specification of Pesaran is used,

test

the type of test statistic to be returned. One of

`"cd"`

for Pesaran's CD statistic,`"lm"`

for Breusch and Pagan's original LM statistic,`"sclm"`

for the scaled version of Breusch and Pagan's LM statistic,`"bcsclm"`

for the bias-corrected scaled version of Breusch and Pagan's LM statistic,`"rho"`

for the average correlation coefficient,`"absrho"`

for the average absolute correlation coefficient,

w

either `NULL`

(default) for the global tests or -- for the
local versions of the statistics -- a `n x n`

`matrix`

describing proximity between individuals, with \(w_ij = a\)
where \(a\) is any number such that `as.logical(a)==TRUE`

, if
\(i,j\) are neighbours, \(0\) or any number \(b\) such
that `as.logical(b)==FALSE`

elsewhere. Only the lower
triangular part (without diagonal) of `w`

after coercing by
`as.logical()`

is evaluated for neighbouring information (but
`w`

can be symmetric). See also **Details** and
**Examples**,

An object of class `"htest"`

.

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 (`model = NULL`

).
If a different model specification (`model = "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 `data frame`

; 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`

(except for `test = "bcsclm"`

which
requires a within model with either individual or two-ways 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 PESA:04;textualplm (and complemented by
Pesaran (2005)). The bias-corrected scaled test (`test="bcsclm"`

)
is due to BALT:FENG:KAO:12plm and only valid for
within models including the individual effect (it's unbalanced
version uses max(Tij) for T) in the bias-correction term).
BREU:PAGA:80;textualplm 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`

.

BALT:FENG:KAO:12plm

BREU:PAGA:80plm

PESA:04plm

PESA:15plm

# NOT RUN { 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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