As an alternative, with GNU `date`, you can do:

    eval "$(date -r "$file" +'year=%Y month=%-m day=%-d')"

To have the modification time's year, month and day component stored in `$year`, `$month` and `$day` respectively (as decimal integers, remove the `-`s in `%-m` and `%-d` if you care for the leading zeros; see also `%y` for 2-digit years).

(note that contrary to GNU `stat`, for files of type symlink, the modification time of the target of the symlink is considered rather than that of the symlink itself. With GNU `stat`, you'd use `stat -L`).