问题
I have a panel data set in R (time and cross section) and would like to compute standard errors that are clustered by two dimensions, because my residuals are correlated both ways. Googling around I found http://thetarzan.wordpress.com/2011/06/11/clustered-standard-errors-in-r/ which provides a function to do this. It seems a bit ad-hoc so I wanted to know if there is a package that has been tested and does this?
I know sandwich does HAC standard errors, but it doesn't do double clustering (i.e. along two dimensions).
回答1:
Frank Harrell's package rms (which used to be named Design) has a function that I use often when clustering: robcov.
See this part of ?robcov, for example.
cluster: a variable indicating groupings. ‘cluster’ may be any type of
vector (factor, character, integer). NAs are not allowed.
Unique values of ‘cluster’ indicate possibly correlated
groupings of observations. Note the data used in the fit and
stored in ‘fit$x’ and ‘fit$y’ may have had observations
containing missing values deleted. It is assumed that if any
NAs were removed during the original model fitting, an
‘naresid’ function exists to restore NAs so that the rows of
the score matrix coincide with ‘cluster’. If ‘cluster’ is
omitted, it defaults to the integers 1,2,...,n to obtain the
"sandwich" robust covariance matrix estimate.
回答2:
For panel regressions, the plm package can estimate clustered SEs along two dimensions.
Using M. Petersen’s benchmark results:
require(foreign)
require(plm)
require(lmtest)
test <- read.dta("http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.dta")
##Double-clustering formula (Thompson, 2011)
vcovDC <- function(x, ...){
vcovHC(x, cluster="group", ...) + vcovHC(x, cluster="time", ...) -
vcovHC(x, method="white1", ...)
}
fpm <- plm(y ~ x, test, model='pooling', index=c('firmid', 'year'))
So that now you can obtain clustered SEs:
##Clustered by *group*
> coeftest(fpm, vcov=function(x) vcovHC(x, cluster="group", type="HC1"))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.029680 0.066952 0.4433 0.6576
x 1.034833 0.050550 20.4714 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
##Clustered by *time*
> coeftest(fpm, vcov=function(x) vcovHC(x, cluster="time", type="HC1"))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.029680 0.022189 1.3376 0.1811
x 1.034833 0.031679 32.6666 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
##Clustered by *group* and *time*
> coeftest(fpm, vcov=function(x) vcovDC(x, type="HC1"))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.029680 0.064580 0.4596 0.6458
x 1.034833 0.052465 19.7243 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
For more details see:
- Fama-MacBeth and Cluster-Robust (by Firm and Time) Standard Errors in R.
However the above works only if your data can be coerced to a pdata.frame. It will fail if you have "duplicate couples (time-id)". In this case you can still cluster, but only along one dimension.
Trick plm into thinking that you have a proper panel data set by specifying only one index:
fpm.tr <- plm(y ~ x, test, model='pooling', index=c('firmid'))
So that now you can obtain clustered SEs:
##Clustered by *group*
> coeftest(fpm.tr, vcov=function(x) vcovHC(x, cluster="group", type="HC1"))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.029680 0.066952 0.4433 0.6576
x 1.034833 0.050550 20.4714 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
You can also use this workaround to cluster by a higher dimension or at a higher level (e.g. industry or country). However in that case you won't be able to use the group (or time) effects, which is the main limit of the approach.
Another approach that works for both panel and other types of data is the multiwayvcov package. It allows double clustering, but also clustering at higher dimensions. As per the packages's website, it is an improvement upon Arai's code:
- Transparent handling of observations dropped due to missingness
- Full multi-way (or n-way, or n-dimensional, or multi-dimensional) clustering
Using the Petersen data and cluster.vcov():
library("lmtest")
library("multiwayvcov")
data(petersen)
m1 <- lm(y ~ x, data = petersen)
coeftest(m1, vcov=function(x) cluster.vcov(x, petersen[ , c("firmid", "year")]))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.029680 0.065066 0.4561 0.6483
## x 1.034833 0.053561 19.3206 <2e-16 ***
## ---
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
回答3:
Arai's function can be used for clustering standard-errors. He has another version for clustering in multiple dimensions:
mcl <- function(dat,fm, cluster1, cluster2){
attach(dat, warn.conflicts = F)
library(sandwich);library(lmtest)
cluster12 = paste(cluster1,cluster2, sep="")
M1 <- length(unique(cluster1))
M2 <- length(unique(cluster2))
M12 <- length(unique(cluster12))
N <- length(cluster1)
K <- fm$rank
dfc1 <- (M1/(M1-1))*((N-1)/(N-K))
dfc2 <- (M2/(M2-1))*((N-1)/(N-K))
dfc12 <- (M12/(M12-1))*((N-1)/(N-K))
u1j <- apply(estfun(fm), 2, function(x) tapply(x, cluster1, sum))
u2j <- apply(estfun(fm), 2, function(x) tapply(x, cluster2, sum))
u12j <- apply(estfun(fm), 2, function(x) tapply(x, cluster12, sum))
vc1 <- dfc1*sandwich(fm, meat=crossprod(u1j)/N )
vc2 <- dfc2*sandwich(fm, meat=crossprod(u2j)/N )
vc12 <- dfc12*sandwich(fm, meat=crossprod(u12j)/N)
vcovMCL <- vc1 + vc2 - vc12
coeftest(fm, vcovMCL)}
For references and usage example see:
- Clustered Standard Errors in R
来源：https://stackoverflow.com/questions/8389843/double-clustered-standard-errors-for-panel-data