vcovBK: Beck and Katz Robust Covariance Matrix Estimators

View source: R/tool_vcovG.R

vcovBKR Documentation

Beck and Katz Robust Covariance Matrix Estimators


Unconditional Robust covariance matrix estimators a la Beck and Katz for panel models (a.k.a. Panel Corrected Standard Errors (PCSE)).


vcovBK(x, ...)

## S3 method for class 'plm'
  type = c("HC0", "HC1", "HC2", "HC3", "HC4"),
  cluster = c("group", "time"),
  diagonal = FALSE,



an object of class "plm",


further arguments.


the weighting scheme used, one of "HC0", "HC1", "HC2", "HC3", "HC4", see Details,


one of "group", "time",


a logical value specifying whether to force non-diagonal elements to zero,


vcovBK is a function for estimating a robust covariance matrix of parameters for a panel model according to the \insertCiteBECK:KATZ:95;textualplm method, a.k.a. Panel Corrected Standard Errors (PCSE), which uses an unconditional estimate of the error covariance across time periods (groups) inside the standard formula for coefficient covariance. Observations may be clustered either by "group" to account for timewise heteroskedasticity and serial correlation or by "time" to account for cross-sectional heteroskedasticity and correlation. It must be borne in mind that the Beck and Katz formula is based on N- (T-) asymptotics and will not be appropriate elsewhere.

The diagonal logical argument can be used, if set to TRUE, to force to zero all non-diagonal elements in the estimated error covariances; this is appropriate if both serial and cross–sectional correlation are assumed out, and yields a timewise- (groupwise-) heteroskedasticity–consistent estimator.

Weighting schemes specified by type are analogous to those in sandwich::vcovHC() in package sandwich and are justified theoretically (although in the context of the standard linear model) by \insertCiteMACK:WHIT:85;textualplm and \insertCiteCRIB:04;textualplm \insertCite@see @ZEIL:04plm.

The main use of vcovBK (and the other variance-covariance estimators provided in the package vcovHC, vcovNW, vcovDC, vcovSCC) is to pass it to plm's own functions like summary, pwaldtest, and phtest or together with testing functions from the lmtest and car packages. All of these typically allow passing the vcov or vcov. parameter either as a matrix or as a function, e.g., for Wald–type testing: argument vcov. to coeftest(), argument vcov to waldtest() and other methods in the lmtest package; and argument vcov. to linearHypothesis() in the car package (see the examples), see \insertCite@see also @ZEIL:04plm, 4.1-2, and examples below.


An object of class "matrix" containing the estimate of the covariance matrix of coefficients.


Giovanni Millo












See Also

sandwich::vcovHC() from the sandwich package for weighting schemes (type argument).


data("Produc", package="plm")
zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="random")
summary(zz, vcov = vcovBK)
summary(zz, vcov = function(x) vcovBK(x, type="HC1"))

## standard coefficient significance test
## robust significance test, cluster by group
## (robust vs. serial correlation), default arguments
coeftest(zz, vcov.=vcovBK)
## idem with parameters, pass vcov as a function argument
coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1"))
## idem, cluster by time period
## (robust vs. cross-sectional correlation)
coeftest(zz, vcov.=function(x) vcovBK(x, type="HC1", cluster="time"))
## idem with parameters, pass vcov as a matrix argument
coeftest(zz, vcov.=vcovBK(zz, type="HC1"))
## joint restriction test
waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovBK)
## Not run: 
## test of hyp.: 2*log(pc)=log(emp)
linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovBK)

## End(Not run)

plm documentation built on April 9, 2023, 5:06 p.m.