Those "labels" are actually attributes that apparently get lost during conversion. You can try to reassign them to your pdata.frame. Example:
dat <- data.frame(matrix(1:12, 3, 4)) ## toy df
dat[] <- Map(`attr<-`, dat, 'foo', 1:4) ## assign some labels named 'foo'
str(dat) ## check structure
# 'data.frame': 3 obs. of 4 variables:
# $ X1: int 1 2 3
# ..- attr(*, "foo")= int 1
# $ X2: int 4 5 6
# ..- attr(*, "foo")= int 2
# $ X3: int 7 8 9
# ..- attr(*, "foo")= int 3
pdat <- plm::pdata.frame(dat) ## convert to pdata.frame
str(pdat) ## check for attributes
# Classes ‘pdata.frame’ and 'data.frame': 3 obs. of 3 variables:
# $ X1: Factor w/ 3 levels "1","2","3": 1 2 3
# ..- attr(*, "names")= chr [1:3] "1-4" "2-5" "3-6"
# ..- attr(*, "index")=Classes ‘pindex’ and 'data.frame': 3 obs. of 2 variables:
# .. ..$ X1: Factor w/ 3 levels "1","2","3": 1 2 3
# .. ..$ X2: Factor w/ 3 levels "4","5","6": 1 2 3
# $ X2: Factor w/ 3 levels "4","5","6": 1 2 3
# ..- attr(*, "names")= chr [1:3] "1-4" "2-5" "3-6"
# ..- attr(*, "index")=Classes ‘pindex’ and 'data.frame': 3 obs. of 2 variables:
# .. ..$ X1: Factor w/ 3 levels "1","2","3": 1 2 3
# .. ..$ X2: Factor w/ 3 levels "4","5","6": 1 2 3
# ...
Now we can see, that there are new attributes, but the old are lost. However we can reassign them easily using `attributes<-`():
pdat[] <- Map(`attributes<-`, dat, lapply(dat, attributes))
str(pdat)
# Classes ‘pdata.frame’ and 'data.frame': 3 obs. of 3 variables:
# $ X1: 'pseries' Named int 1 2 3
# ..- attr(*, "foo")= int 1
# ..- attr(*, "names")= chr [1:3] "1-4" "2-5" "3-6"
# ..- attr(*, "index")=Classes ‘pindex’ and 'data.frame': 3 obs. of 2 variables:
# .. ..$ X1: Factor w/ 3 levels "1","2","3": 1 2 3
# .. ..$ X2: Factor w/ 3 levels "4","5","6": 1 2 3
# $ X2: 'pseries' Named int 4 5 6
# ..- attr(*, "foo")= int 2
# ..- attr(*, "names")= chr [1:3] "1-4" "2-5" "3-6"
# ..- attr(*, "index")=Classes ‘pindex’ and 'data.frame': 3 obs. of 2 variables:
# .. ..$ X1: Factor w/ 3 levels "1","2","3": 1 2 3
# .. ..$ X2: Factor w/ 3 levels "4","5","6": 1 2 3
# ...
`attributes<-`() will assign all attributes of dat to pdat. To only select specific labels, use `attr<-`() with the label name.
Notice that your attributes probably called "labeled" not "foo", I don't use labelled. See if this works and your labels show up in the summary.