Description Usage Arguments Details Value Author(s) References See Also Examples

Robust covariance matrix estimators *a la White* for panel models.

1 2 3 4 5 6 |

`x` |
an object of class |

`method` |
one of |

`type` |
the weighting scheme used, one of |

`cluster` |
one of |

`...` |
further arguments. |

`vcovHC`

is a function for estimating a robust covariance matrix of
parameters for a fixed effects or random effects panel model according
to the White method (White 1980, 1984; Arellano 1987). Observations may
be clustered by `"group"`

(`"time"`

) to account for serial
(cross-sectional) correlation.

All types assume no intragroup (serial) correlation between errors and
allow for heteroskedasticity across groups (time periods). As for the
error covariance matrix of every single group of observations,
`"white1"`

allows for general heteroskedasticity but no serial
(cross–sectional) correlation; `"white2"`

is `"white1"`

restricted to a common variance inside every group (time period) (see
Greene (2003, Sec. 13.7.1-2; 2012, Sec. 11.6.1-2) and Wooldridge (2002), Sec. 10.7.2);
`"arellano"`

(see ibid. and the original ref. Arellano (1987))
allows a fully general structure w.r.t. heteroskedasticity and serial
(cross–sectional) correlation.

Weighting schemes specified by `type`

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)).
`type = "sss"`

employs the small sample correction as used by Stata.

The main use of `vcovHC`

is to be an argument to other functions,
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). Notice that the `vcov`

and `vcov.`

arguments allow to supply a
function (which is the safest) or a matrix (see Zeileis (2004), 4.1-2
and examples below).

A special procedure for `pgmm`

objects, proposed by Windmeijer
(2005), is also provided.

An object of class `"matrix"`

containing the estimate of the asymptotic covariance matrix of coefficients.

Giovanni Millo & Yves Croissant

Arellano, M. (1987) Computing robust standard errors for within-group estimators,
*Oxford Bulletin of Economics and Statistics*, **49(4)**, pp. 431–434.

Cribari-Neto, F. (2004) Asymptotic inference under heteroskedasticity
of unknown form. *Computational Statistics & Data Analysis*
**45(2)**, pp. 215–233.

Greene, W. H. (2003) *Econometric Analysis*, 5th ed., Prentice Hall/Pearson,
Upper Saddle River, New Jersey.

Greene, W. H. (2012) *Econometric Analysis*, 7th ed., Prentice Hall/Pearson,
Upper Saddle River, New Jersey.

MacKinnon, J. G. and White, H. (1985) Some heteroskedasticity-consistent
covariance matrix estimators with improved finite sample properties.
*Journal of Econometrics* **29(3)**, pp. 305–325.

Windmeijer, F. (2005) A finite sample correction for the variance of
linear efficient two–step GMM estimators, *Journal of
Econometrics*, **126(1)**, pp. 25–51.

White, H. (1980) *Asymptotic Theory for Econometricians*, Ch. 6, Academic Press, Orlando (FL).

White, H. (1984) A heteroskedasticity-consistent covariance matrix and
a direct test for heteroskedasticity. *Econometrica* **48(4)**, pp. 817–838.

Wooldridge, J. M. (2002) *Econometric Analysis of Cross Section and
Panel Data*, MIT Press, Cambridge (MA).

Zeileis, A. (2004) Econometric Computing with HC and HAC Covariance Matrix
Estimators. *Journal of Statistical Software*, **11**(10), pp. 1–17.
URL http://www.jstatsoft.org/v11/i10/.

`vcovHC`

from the sandwich package for weighting schemes (`type`

argument).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | ```
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)
coeftest(zz, vcov.=vcovHC)
## idem with parameters, pass vcov as a function argument
coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano", type="HC1"))
## idem, cluster by time period
## (robust vs. cross-sectional correlation)
coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano",
type="HC1", cluster="group"))
## idem with parameters, pass vcov as a matrix argument
coeftest(zz, vcov.=vcovHC(zz, method="arellano", type="HC1"))
## joint restriction test
waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovHC)
## test of hyp.: 2*log(pc)=log(emp)
linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovHC)
## Robust inference for GMM models
data("EmplUK", package="plm")
ar <- pgmm(dynformula(log(emp) ~ log(wage) + log(capital) + log(output),
list(2, 1, 2, 2)), data = EmplUK, effect = "twoways",
model = "twosteps", gmm.inst = ~ log(emp),
lag.gmm = list(c(2, 99)))
rv <- vcovHC(ar)
mtest(ar, order = 2, vcov = rv)
``` |

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