how are the Degrees of freedom calculated in plm:::vcovDC.plm?

I use a fixed effect model with time and group fixed effects. Further, I want to calculate robust clustered standard errors. Therefore, I use coeftest(model, vcov = vcovDC(model))

I do not understand how the degrees of freedom are calculated for the provided t-statistics. Does it use the same degrees of freedom like the in the provided plm-fixed-effect model or are they adjusted. Probably my question is rather; are the degrees of freedom adjusted when one uses clustered standard errors for a two-way fixed effect model, or do they remain the same?

Solution

plm calculates an ordinary variance–covariance matrix (VCOV). When you use summary on your plm object (what you probably mean by "provided plm-fixed-effect model"), actually the plm:::summary.plm method is applied, which uses ordinary standard errors (SE) without degrees-of-freedom correction, until you change the vcov= argument defaulting to NULL to another VCOV calculated differently, e.g. with vcovCL or vcovDC.

You can do lmtest::coeftest(fit, vcov.=...), or directly summary(fit, vcov=...), as I show you below in an example.

Example

library(plm)
data(Cigar)
fit <- plm(sales ~ price, data=Cigar, effect="twoways", model="within", 
           index=c("state", "year"))

summary(fit)$coe   
# same:
summary(fit, vcov=NULL)$coe  ## default, ordinary SE
#        Estimate Std. Error   t-value     Pr(>|t|)
# price -1.084712 0.07554847 -14.35782 1.640552e-43

Now, to get robust standard errors (without adjustment for clustering), we may use vcovCL and consider the type= argument. In ?sandwich::vcovCL we may read:

HC0 applies no small sample bias adjustment. HC1 applies a degrees of freedom-based correction, (n-1)/(n-k) where n is the number of observations and k is the number of explanatory or predictor variables in the model.

summary(fit, vcov=vcovHC)$coe
# same:
summary(fit, vcov=vcovHC(fit, type="HC0"))$coe  ## robust SE
#        Estimate Std. Error   t-value     Pr(>|t|)
# price -1.084712  0.2406786 -4.506889 7.168418e-06

summary(fit, vcov=vcovHC(fit, type="HC1"))$coe  ## robust SE, df-corrected
#        Estimate Std. Error   t-value    Pr(>|t|)
# price -1.084712  0.2407658 -4.505256 7.22292e-06

The same applies to vcovDC and its type= argument for robust standard errors, doubly adjusted for clustering on group and time:

summary(fit, vcov=vcovDC(fit))$coe 
# same:
summary(fit, vcov=vcovDC(fit, type="HC0"))$coe  ## double-cluster-robust SE
#        Estimate Std. Error  t-value     Pr(>|t|)
# price -1.084712  0.2923507 -3.71031 0.0002157146

summary(fit, vcov=vcovDC(fit, type="HC1"))$coe  ## double-cluster-robust SE, df-corrected 
#        Estimate Std. Error   t-value     Pr(>|t|)
# price -1.084712  0.2924567 -3.708966 0.0002168511