Double clustered standard errors for panel data

11
votes

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).

4
rregressionstandard-errorpanel-dataplm

4 Answers

4
votes

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.
10
votes

This is an old question. But seeing as people still appear to be landing on it, I thought I'd provide some modern approaches to multiway clustering in R:

Option 1 (fastest): fixest::feols()

library(fixest)

nlswork = haven::read_dta("http://www.stata-press.com/data/r14/nlswork.dta")

est_feols = feols(ln_wage ~ age | race + year, cluster = ~race+year, data = nlswork)
est_feols

## An important feature of fixest: We can _instantaneously_ compute other
## VCOV matrices / SEs on the fly with summary.fixest(). No need to re-run
## the model!
summary(est_feols, se = 'standard') ## vanilla SEs
summary(est_feols, se = 'hetero') ## robust SEs
summary(est_feols, se = 'twoway') ## diff syntax, but same as original model
summary(est_feols, cluster = c('race', 'year')) ## ditto
summary(est_feols, cluster = ~race^year) ## interacted cluster vars
summary(est_feols, cluster = ~ race + year + idcode)  ## add third cluster var (not in original model call)
## etc.

Option 2 (fast): lfe::felm()

library(lfe)

## Note the third "| 0 " slot means we're not using IV

est_felm = felm(ln_wage ~ age | race + year | 0 | race + year, data = nlswork)
summary(est_felm)

Option 3 (slower, but flexible): sandwich

library(sandwich)
library(lmtest)

est_sandwich = lm(ln_wage ~ age + factor(race) + factor(year), data = nlswork) 
coeftest(est_sandwich, vcov = vcovCL, cluster = ~ race + year)

Benchmark

Aaaand, just to belabour the point about speed. Here's a benchmark of the three different approaches (using two fixed FEs and twoway clustering).

est_feols = function() feols(ln_wage ~ age | race + year, cluster = ~race+year, data = nlswork) 
est_felm = function() felm(ln_wage ~ age | race + year | 0 | race + year, data = nlswork)
est_standwich = function() {coeftest(lm(ln_wage ~ age + factor(race) + factor(year), data = nlswork), 
                                     vcov = vcovCL, cluster = ~ race + year)}

microbenchmark(est_feols(), est_felm(), est_standwich(), times = 3)

#> Unit: milliseconds
#>             expr       min        lq      mean    median        uq       max neval cld
#>      est_feols()  11.94122  11.96158  12.55835  11.98193  12.86692  13.75191     3 a  
#>       est_felm()  87.18064  95.89905 100.69589 104.61746 107.45352 110.28957     3  b 
#>  est_standwich() 176.43502 183.95964 188.50271 191.48425 194.53656 197.58886     3   c
7
votes

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:

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
5
votes

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: