Neat! This site from Helmer Aslaksen of the National University of Singapore describes how to calculate the Lunar New Year and other important Chinese holidays, based on the movements of the moon. In Ancient China, there used to be a government body, the Board of Mathematics, to carry out this function, though in the modern age, calendar-making has been privatized. My parents bring back a stack of lunar calendars from Taiwan every year, to distribute to family and friends.
If the goal is preserving tradition in daily life, it seems like it would be extremely useful for a society to have institutions whose sole cause is planning cultural affairs and defining and maintaining customs. That's why an executive ministry to govern cultural issues, with a real commitment to tradition, would be so interesting! (Not to sound monarchist, but an imperial body that claims a centuries-long legacy would potentially have more investment in cultural preservation and the esprit de corps to match).
Then again, in setting dates, the Board of Mathematics did not simply pinpoint occasional, optional celebrations. Lives and livelihoods were in the balance, as farmers relied on the agricultural calendar to time the sowing of crops. It was a genuine public service; the creation of the calendar helped to frame the activities of a whole year. So perhaps this is more like an NBER or an EIA, but with cultural implications.