vcovHC.plm.RdRobust covariance matrix estimators a la White for panel models.
# S3 method for plm vcovHC(x, method = c("arellano", "white1", "white2"), type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"), cluster = c("group", "time"), ...) # S3 method for pgmm vcovHC(x, ...)
| x | an object of class |
|---|---|
| method | one of |
| type | the weighting scheme used, one of |
| cluster | one of |
| … | further arguments. |
An object of class "matrix" containing the estimate of
the asymptotic covariance matrix of coefficients.
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, Greene 2012, Sec. 11.6.1-2
)
; "arellano" (see
)
allows a fully general
structure w.r.t. heteroskedasticity and serial (cross--sectional)
correlation.
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 MacKinnon and White (1985)
and
Cribari--Neto (2004)
(Zeileis 2004)
. type = "sss" employs the small sample
correction as used by Stata.
elaborate why different result for FE models (intercept)
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
(ZEIL:04, 4.1-2 and examples below)
.
A special procedure for pgmm objects, proposed by
Windmeijer (2005)
, is also provided.
The function pvcovHC is deprecated. Use vcovHC for the
same functionality.
Arellano M (1987). “Computing Robust Standard Errors for Within-groups Estimators.” Oxford bulletin of Economics and Statistics, 49(4), 431--434.
Cribari--Neto F (2004). “Asymptotic Inference Under Heteroskedasticity of Unknown Form.” Computational Statistics \& Data Analysis, 45, 215--233.
Greene W (2003). Econometric Analysis, 5th edition. Prentice Hall.
Greene W (2012). Econometric Analysis, 7th edition. Prentice Hall.
MacKinnon J, White H (1985). “Some Heteroskedasticity--Consistent Covariance Matrix Estimators With Improved Finite Sample Properties.” Journal of Econometrics, 29, 305--325.
Windmeijer F (2005). “A Finite Sample Correction for the Variance of Linear Efficient Two--Steps GMM Estimators.” Journal of Econometrics, 126, 25--51.
White H (1984). Asymptotic Theory for Econometricians. New York: Academic press. chap. 6
White H (1980). “A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.” Econometrica, 48(4), 817--838.
Wooldridge J (2002). Econometric Analysis of Cross--Section and Panel Data. MIT press.
Zeileis A (2004). “Econometric Computing With HC and HAC Covariance Matrix Estimators.” Journal of Statistical Software, 11(10), 1--17. http://www.jstatsoft.org/v11/i10/.
sandwich::vcovHC() from the sandwich
package for weighting schemes (type argument).
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)#> #> t test of coefficients: #> #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 2.13541100 0.13346149 16.0002 < 2.2e-16 *** #> log(pcap) 0.00443859 0.02341732 0.1895 0.8497 #> log(pc) 0.31054843 0.01980475 15.6805 < 2.2e-16 *** #> log(emp) 0.72967053 0.02492022 29.2803 < 2.2e-16 *** #> unemp -0.00617247 0.00090728 -6.8033 1.986e-11 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>## robust significance test, cluster by group ## (robust vs. serial correlation) coeftest(zz, vcov.=vcovHC)#> #> t test of coefficients: #> #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 2.1354110 0.2386676 8.9472 < 2.2e-16 *** #> log(pcap) 0.0044386 0.0545970 0.0813 0.935226 #> log(pc) 0.3105484 0.0435922 7.1239 2.317e-12 *** #> log(emp) 0.7296705 0.0699680 10.4286 < 2.2e-16 *** #> unemp -0.0061725 0.0023326 -2.6461 0.008299 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>## idem with parameters, pass vcov as a function argument coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano", type="HC1"))#> #> t test of coefficients: #> #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 2.1354110 0.2394021 8.9198 < 2.2e-16 *** #> log(pcap) 0.0044386 0.0547651 0.0810 0.935424 #> log(pc) 0.3105484 0.0437264 7.1021 2.689e-12 *** #> log(emp) 0.7296705 0.0701833 10.3966 < 2.2e-16 *** #> unemp -0.0061725 0.0023398 -2.6380 0.008499 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>## idem, cluster by time period ## (robust vs. cross-sectional correlation) coeftest(zz, vcov.=function(x) vcovHC(x, method="arellano", type="HC1", cluster="group"))#> #> t test of coefficients: #> #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 2.1354110 0.2394021 8.9198 < 2.2e-16 *** #> log(pcap) 0.0044386 0.0547651 0.0810 0.935424 #> log(pc) 0.3105484 0.0437264 7.1021 2.689e-12 *** #> log(emp) 0.7296705 0.0701833 10.3966 < 2.2e-16 *** #> unemp -0.0061725 0.0023398 -2.6380 0.008499 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>## idem with parameters, pass vcov as a matrix argument coeftest(zz, vcov.=vcovHC(zz, method="arellano", type="HC1"))#> #> t test of coefficients: #> #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 2.1354110 0.2394021 8.9198 < 2.2e-16 *** #> log(pcap) 0.0044386 0.0547651 0.0810 0.935424 #> log(pc) 0.3105484 0.0437264 7.1021 2.689e-12 *** #> log(emp) 0.7296705 0.0701833 10.3966 < 2.2e-16 *** #> unemp -0.0061725 0.0023398 -2.6380 0.008499 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>#> Wald test #> #> Model 1: log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp #> Model 2: log(gsp) ~ log(pcap) + log(pc) #> Res.Df Df Chisq Pr(>Chisq) #> 1 811 #> 2 813 -2 404.16 < 2.2e-16 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1#> Linear hypothesis test #> #> Hypothesis: #> 2 log(pc) - log(emp) = 0 #> #> Model 1: restricted model #> Model 2: log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp #> #> Note: Coefficient covariance matrix supplied. #> #> Res.Df Df Chisq Pr(>Chisq) #> 1 812 #> 2 811 1 0.5878 0.4433## Robust inference for GMM models data("EmplUK", package="plm") ar <- pgmm(log(emp) ~ lag(log(emp), 1:2) + lag(log(wage), 0:1) + log(capital) + lag(log(capital), 2) + log(output) + lag(log(output),2) | lag(log(emp), 2:99), data = EmplUK, effect = "twoways", model = "twosteps") rv <- vcovHC(ar) mtest(ar, order = 2, vcov = rv)#> #> Autocorrelation test of degree 2 #> #> data: log(emp) ~ lag(log(emp), 1:2) + lag(log(wage), 0:1) + log(capital) + ... #> normal = -0.1165, p-value = 0.9073 #>