pwaldtest function

Wald-style Chi-square Test and F Test

Wald-style Chi-square test and F test of slope coefficients being zero jointly, including robust versions of the tests.

pwaldtest(x, ...)

## S3 method for class 'plm'
pwaldtest(
  x,
  test = c("Chisq", "F"),
  vcov = NULL,
  df2adj = (test == "F" && !is.null(vcov) && missing(.df2)),
  .df1,
  .df2,
  ...
)

## S3 method for class 'pvcm'
pwaldtest(x, ...)

## S3 method for class 'pgmm'
pwaldtest(x, param = c("coef", "time", "all"), vcov = NULL, ...)

Arguments

• x: an estimated model of which the coefficients should be tested (usually of class "plm"/"pvcm"/"pgmm")`,
• ...: further arguments (currently none).
• test: a character, indicating the test to be performed, may be either "Chisq" or "F" for the Wald-style Chi-square test or F test, respectively,
• vcov: NULL by default; a matrix giving a variance--covariance matrix or a function which computes such; if supplied (non NULL), the test is carried out using the variance--covariance matrix indicated resulting in a robust test,
• df2adj: logical, only relevant for test = "F", indicating whether the adjustment for clustered standard errors for the second degrees of freedom parameter should be performed (see Details , also for further requirements regarding the variance--covariance matrix in vcov for the adjustment to be performed),
• .df1: a numeric, used if one wants to overwrite the first degrees of freedom parameter in the performed test (usually not used),
• .df2: a numeric, used if one wants to overwrite the second degrees of freedom parameter for the F test (usually not used),
• param: (for pgmm method only): select the parameters to be tested: "coef", "time", or `"all"``.

Returns

An object of class "htest", except for pvcm's within model for which a data.frame with results of the Wald chi-square tests and F tests per regression is returned.

Details

pwaldtest can be used stand--alone with a plm object, a pvcm object, and a pgmm object (for pvcm objects only the 'random' type is valid and no further arguments are processed; for pgmm objects only arguments param

and vcov are valid). It is also used in summary.plm() to produce the F statistic and the Chi-square statistic for the joint test of coefficients and in summary.pgmm().

pwaldtest performs the test if the slope coefficients of a panel regression are jointly zero. It does not perform general purpose Wald-style tests (for those, see lmtest::waldtest() (from package list("lmtest")) or car::linearHypothesis() (from package list("car"))).

If a user specified variance-covariance matrix/function is given in argument vcov, the robust version of the tests are carried out. In that case, if the F test is requested (test = "F") and no overwriting of the second degrees of freedom parameter is given (by supplying argument (.df2)), the adjustment of the second degrees of freedom parameter is performed by default. The second degrees of freedom parameter is adjusted to be the number of unique elements of the cluster variable - 1, e. g., the number of individuals minus 1. For the degrees of freedom adjustment of the F test in general, see e. g. \insertCite CAME:MILL:15;textualplm, section VII; \insertCite ANDR:GOLS:SCMI:13plm, pp. 126, footnote 4.

The degrees of freedom adjustment requires the vcov object supplied or created by a supplied function to carry an attribute called "cluster" with a known clustering described as a character (for now this could be either "group" or "time"). The vcovXX functions of the package plm provide such an attribute for their returned variance--covariance matrices. No adjustment is done for unknown descriptions given in the attribute "cluster" or when the attribute "cluster" is not present. Robust vcov objects/functions from package list("clubSandwich") work as inputs to pwaldtest's F test because a they are translated internally to match the needs described above.

Examples

data("Grunfeld", package = "plm")
mod_fe <- plm(inv ~ value + capital, data = Grunfeld, model = "within")
mod_re <- plm(inv ~ value + capital, data = Grunfeld, model = "random")
pwaldtest(mod_fe, test = "F")
pwaldtest(mod_re, test = "Chisq")

# with robust vcov (matrix, function)
pwaldtest(mod_fe, vcov = vcovHC(mod_fe))
pwaldtest(mod_fe, vcov = function(x) vcovHC(x, type = "HC3"))

pwaldtest(mod_fe, vcov = vcovHC(mod_fe), df2adj = FALSE) # w/o df2 adjustment

# example without attribute "cluster" in the vcov
vcov_mat <- vcovHC(mod_fe)
attr(vcov_mat, "cluster") <- NULL  # remove attribute
pwaldtest(mod_fe, vcov = vcov_mat) # no df2 adjustment performed

References

\insertRef WOOL:10plm

\insertRef ANDR:GOLS:SCMI:13plm

\insertRef CAME:MILL:15plm

See Also

vcovHC() for an example of the vcovXX functions, a robust estimation for the variance--covariance matrix; summary.plm()

Author(s)

Yves Croissant (initial implementation) and Kevin Tappe (extensions: vcov argument and F test's df2 adjustment)