Beck and Katz Robust Covariance Matrix Estimators

Description

Unconditional Robust covariance matrix estimators a la Beck and Katz for panel models.

Usage

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

Arguments

Details

vcovBK is a function for estimating a robust covariance matrix of parameters for a panel model according to the Beck and Katz (1995) 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 nondiagonal 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 are analogous to those in vcovHC in package sandwich and are justified theoretically (although in the context of the standard linear model) by MacKinnon and White (1985) and Cribari-Neto (2004) (see Zeileis, 2004).

The main use of vcovBK is to be an argument to other functions, e.g. for Wald-type testing: as vcov to coeftest(), waldtest() and other methods in the lmtest package; and as vcov to linearHypothesis() in the car package (see the examples). Notice that the vcov argument may be supplied a function (which is the safest) or a matrix (see Zeileis (2004), 4.1-2 and examples below).

Value

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

Author(s)

Giovanni Millo

References

Beck, N. and Katz, J. (1995) What to do (and not to do) with time-series-cross-section data in comparative politics. American Political Science Review, 89(3), 634–647.

Greene, W. H. (2003) Econometric Analysis, 5th ed. Macmillan Publishing Company, New York, 323.

Examples

library(lmtest)
library(car)
data("Produc", package="plm")
zz <- plm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc, model="random")
## standard coefficient significance test
coeftest(zz)
## 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)
## test of hyp.: 2*log(pc)=log(emp)
linearHypothesis(zz, "2*log(pc)=log(emp)", vcov=vcovBK)