Tests of cross-section dependence for panel models

Source: R/test_cd.R

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,
  ...
)

Arguments

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,

Value

An object of class "htest".

Details

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 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.

References

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://doi.org/10.1016/j.jeconom.2012.04.004.

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.

Examples


data("Grunfeld", package = "plm")
## test on heterogeneous model (separate time series regressions)
pcdtest(inv ~ value + capital, data = Grunfeld,
        index = c("firm", "year"))
#> 
#> 	Pesaran CD test for cross-sectional dependence in panels
#> 
#> data:  inv ~ value + capital
#> z = 5.3401, p-value = 9.292e-08
#> alternative hypothesis: cross-sectional dependence
#> 

## test on two-way fixed effects homogeneous model
pcdtest(inv ~ value + capital, data = Grunfeld, model = "within",
        effect = "twoways", index = c("firm", "year"))
#> 
#> 	Pesaran CD test for cross-sectional dependence in panels
#> 
#> data:  inv ~ value + capital
#> z = 0.1162, p-value = 0.9075
#> alternative hypothesis: cross-sectional dependence
#> 

## test on panelmodel object
g <- plm(inv ~ value + capital, data = Grunfeld, index = c("firm", "year"))
pcdtest(g)
#> 
#> 	Pesaran CD test for cross-sectional dependence in panels
#> 
#> data:  inv ~ value + capital
#> z = 4.6612, p-value = 3.144e-06
#> alternative hypothesis: cross-sectional dependence
#> 

## scaled LM test
pcdtest(g, test = "sclm")
#> 
#> 	Scaled LM test for cross-sectional dependence in panels
#> 
#> data:  inv ~ value + capital
#> z = 21.222, p-value < 2.2e-16
#> alternative hypothesis: cross-sectional dependence
#> 

## test on pseries
pGrunfeld <- pdata.frame(Grunfeld)
pcdtest(pGrunfeld$value)
#> 
#> 	Pesaran CD test for cross-sectional dependence in panels
#> 
#> data:  pGrunfeld$value
#> z = 13.843, p-value < 2.2e-16
#> alternative hypothesis: cross-sectional dependence
#> 

## 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)
#> 
#> 	Pesaran CD test for local cross-sectional dependence in panels
#> 
#> data:  inv ~ value + capital
#> z = -0.87759, p-value = 0.3802
#> alternative hypothesis: cross-sectional dependence
#>