To answer the question: no, there is no Noda Time type that you can use to directly represent the concept of "year" or "year and month."
(Well, for the sake of completeness, I should note that you could probably use Period, but I think it would be rather difficult to use calendar duration to represent the date and somewhat abuse what is Periodintended to be used.)
, , , , Noda Time LocalDate ( "2013 " 2013-01-01) , , (.. Year, YearMonth YearMonthDay), IComparer<MyPartialLocalDate>, ( LocalDate, , , , ).