Nonparametric robust covariance matrix estimators a la Newey and West for panel models with serial correlation.
vcovNW(x, ...)
# S3 method for class 'plm'
vcovNW(
x,
type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
maxlag = NULL,
wj = function(j, maxlag) 1 - j/(maxlag + 1),
...
)
# S3 method for class 'pcce'
vcovNW(
x,
type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
maxlag = NULL,
wj = function(j, maxlag) 1 - j/(maxlag + 1),
...
)An object of class "matrix" containing the estimate of
the covariance matrix of coefficients.
vcovNW is a function for estimating a robust covariance matrix of
parameters for a panel model according to the
Newey and West (1987)
method. The function works
as a restriction of the Driscoll and Kraay (1998)
covariance (see
vcovSCC()) to no 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)
(see Zeileis 2004)
.
The main use of vcovNW (and the other variance-covariance estimators
provided in the package vcovHC, vcovBK, 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 (see also Zeileis 2004)
, 4.1-2, and examples below.
Cribari–Neto F (2004). “Asymptotic Inference Under Heteroskedasticity of Unknown Form.” Computational Statistics & Data Analysis, 45, 215–233.
Driscoll JC, Kraay AC (1998). “Consistent covariance matrix estimation with spatially dependent panel data.” Review of economics and statistics, 80(4), 549–560.
MacKinnon JG, White H (1985). “Some Heteroskedasticity–Consistent Covariance Matrix Estimators With Improved Finite Sample Properties.” Journal of Econometrics, 29, 305–325.
Newey WK, West KD (1987). “A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55(3), 703–08.
Zeileis A (2004). “Econometric Computing With HC and HAC Covariance Matrix Estimators.” Journal of Statistical Software, 11(10), 1–17. https://www.jstatsoft.org/article/view/v011i10.
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="pooling")
## as function input to plm's summary method (with and without additional arguments):
summary(zz, vcov = vcovNW)
#> Pooling Model
#>
#> Note: Coefficient variance-covariance matrix supplied: vcovNW
#>
#> Call:
#> plm(formula = log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
#> data = Produc, model = "pooling")
#>
#> Balanced Panel: n = 48, T = 17, N = 816
#>
#> Residuals:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> -0.23176215 -0.06103699 -0.00010248 0.05085197 0.35111348
#>
#> Coefficients:
#> Estimate Std. Error t-value Pr(>|t|)
#> (Intercept) 1.6433023 0.1143540 14.3703 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0299283 5.1793 2.812e-07 ***
#> log(pc) 0.3091902 0.0206394 14.9806 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0316213 18.7827 < 2.2e-16 ***
#> unemp -0.0067330 0.0020247 -3.3254 0.0009225 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Total Sum of Squares: 849.81
#> Residual Sum of Squares: 6.2942
#> R-Squared: 0.99259
#> Adj. R-Squared: 0.99256
#> F-statistic: 12659.9 on 4 and 16 DF, p-value: < 2.22e-16
summary(zz, vcov = function(x) vcovNW(x, method="arellano", type="HC1"))
#> Pooling Model
#>
#> Note: Coefficient variance-covariance matrix supplied: function(x) vcovNW(x, method = "arellano", type = "HC1")
#>
#> Call:
#> plm(formula = log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
#> data = Produc, model = "pooling")
#>
#> Balanced Panel: n = 48, T = 17, N = 816
#>
#> Residuals:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> -0.23176215 -0.06103699 -0.00010248 0.05085197 0.35111348
#>
#> Coefficients:
#> Estimate Std. Error t-value Pr(>|t|)
#> (Intercept) 1.6433023 0.1147060 14.3262 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0300204 5.1634 3.053e-07 ***
#> log(pc) 0.3091902 0.0207029 14.9346 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0317186 18.7251 < 2.2e-16 ***
#> unemp -0.0067330 0.0020309 -3.3152 0.0009563 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Total Sum of Squares: 849.81
#> Residual Sum of Squares: 6.2942
#> R-Squared: 0.99259
#> Adj. R-Squared: 0.99256
#> F-statistic: 12582.3 on 4 and 16 DF, p-value: < 2.22e-16
## standard coefficient significance test
library(lmtest)
coeftest(zz)
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.6433023 0.0575873 28.5359 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0171538 9.0363 < 2.2e-16 ***
#> log(pc) 0.3091902 0.0102720 30.1003 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0137475 43.2032 < 2.2e-16 ***
#> unemp -0.0067330 0.0014164 -4.7537 2.363e-06 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
## NW robust significance test, default
coeftest(zz, vcov.=vcovNW)
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.6433023 0.1143540 14.3703 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0299283 5.1793 2.812e-07 ***
#> log(pc) 0.3091902 0.0206394 14.9806 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0316213 18.7827 < 2.2e-16 ***
#> unemp -0.0067330 0.0020247 -3.3254 0.0009225 ***
#> ---
#> 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) vcovNW(x, type="HC1", maxlag=4))
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.6433023 0.1399123 11.7452 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0367023 4.2234 2.679e-05 ***
#> log(pc) 0.3091902 0.0256858 12.0374 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0388977 15.2691 < 2.2e-16 ***
#> unemp -0.0067330 0.0023634 -2.8488 0.004499 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
## joint restriction test
waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovNW)
#> 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 -2 480.18 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
if (FALSE) { # \dontrun{
## test of hyp.: 2*log(pc)=log(emp)
library(car)
linearHypothesis(zz, "2*log(pc)=log(emp)", vcov.=vcovNW)
} # }