Nonparametric robust covariance matrix estimators a la Driscoll and Kraay for panel models with cross-sectional and serial correlation.
vcovSCC(x, ...)
# S3 method for class 'plm'
vcovSCC(
x,
type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster = "time",
maxlag = NULL,
inner = c("cluster", "white", "diagavg"),
wj = function(j, maxlag) 1 - j/(maxlag + 1),
...
)
# S3 method for class 'pcce'
vcovSCC(
x,
type = c("HC0", "sss", "HC1", "HC2", "HC3", "HC4"),
cluster = "time",
maxlag = NULL,
inner = c("cluster", "white", "diagavg"),
wj = function(j, maxlag) 1 - j/(maxlag + 1),
...
)an object of class "plm" or "pcce"
further arguments
the weighting scheme used, one of "HC0", "sss",
"HC1", "HC2", "HC3", "HC4", see Details,
switch for vcovG; set at "time" here,
either NULL or a positive integer specifying the
maximum lag order before truncation
the function to be applied to the residuals inside the
sandwich: "cluster" for SCC, "white" for Newey-West,
("diagavg" for compatibility reasons)
weighting function to be applied to lagged terms,
An object of class "matrix" containing the estimate of
the covariance matrix of coefficients.
vcovSCC is a function for estimating a robust covariance matrix
of parameters for a panel model according to the
Driscoll and Kraay (1998)
method, which is consistent
with cross–sectional and serial correlation in a T-asymptotic
setting and irrespective of the N dimension. The use with random
effects models is undocumented.
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 vcovSCC (and the other variance-covariance estimators
provided in the package vcovHC, vcovBK, vcovNW, vcovDC) 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 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.
Hoechle D (2007). “Robust standard errors for panel regressions with cross-sectional dependence.” Stata Journal, 7(3), 281-312. https://ideas.repec.org/a/tsj/stataj/v7y2007i3p281-312.html.
MacKinnon JG, White H (1985). “Some Heteroskedasticity–Consistent Covariance Matrix Estimators With Improved Finite Sample Properties.” Journal of Econometrics, 29, 305–325.
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 = vcovSCC)
#> Pooling Model
#>
#> Note: Coefficient variance-covariance matrix supplied: vcovSCC
#>
#> 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 0.1503485 10.9300 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0369734 4.1924 3.064e-05 ***
#> log(pc) 0.3091902 0.0076442 40.4479 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0387024 15.3462 < 2.2e-16 ***
#> unemp -0.0067330 0.0025389 -2.6520 0.008159 **
#> ---
#> 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: 363080 on 4 and 16 DF, p-value: < 2.22e-16
summary(zz, vcov = function(x) vcovSCC(x, method="arellano", type="HC1"))
#> Pooling Model
#>
#> Note: Coefficient variance-covariance matrix supplied: function(x) vcovSCC(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 0.1508112 10.8964 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0370872 4.1795 3.239e-05 ***
#> log(pc) 0.3091902 0.0076677 40.3237 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0388215 15.2991 < 2.2e-16 ***
#> unemp -0.0067330 0.0025467 -2.6438 0.008356 **
#> ---
#> 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: 360856 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
#>
## SCC robust significance test, default
coeftest(zz, vcov.=vcovSCC)
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.6433023 0.1503485 10.9300 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0369734 4.1924 3.064e-05 ***
#> log(pc) 0.3091902 0.0076442 40.4479 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0387024 15.3462 < 2.2e-16 ***
#> unemp -0.0067330 0.0025389 -2.6520 0.008159 **
#> ---
#> 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) vcovSCC(x, type="HC1", maxlag=4))
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.6433023 0.1793363 9.1632 < 2.2e-16 ***
#> log(pcap) 0.1550070 0.0441052 3.5145 0.000465 ***
#> log(pc) 0.3091902 0.0069837 44.2731 < 2.2e-16 ***
#> log(emp) 0.5939349 0.0454539 13.0668 < 2.2e-16 ***
#> unemp -0.0067330 0.0029520 -2.2808 0.022817 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
## joint restriction test
waldtest(zz, update(zz, .~.-log(emp)-unemp), vcov=vcovSCC)
#> 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 -2 531 < 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.=vcovSCC)
} # }