It's a Japanese "trade"
tanto or dagger. The material is most likely bone (normally bovine leg bone is used, as it its naturally "hollow" and dense enough to be carved). The blades are invariably of very low quality, and by this I mean they are normally not even heat-treated, they act mainly as a support for the mountings. Their "value" lies in the carvings, the quality of which varies through a very wide range. They were made in the 19th c. and (I think) through good part of the 20th as "export" items, there was quite a demand for them as "exotica curiosa" in the west.
It indeed seems to be missing the lowest part of the sheath (
saya), they were done in "sections", carved to fit and glued together. I've seen them up to sword length. Some feature quite nice carvings.
Top quality ones exist and are indeed made of ivory, but the carving is then normally nothing less than exquisite, and in a different, more "figurative" style. I was recently handling one, "dagger" size, with the sheath carved out of a single piece off the tip of an elephant tusk. Talk about MASSIVE. The blade was really poor, also, but the carving, which was a natural-size lobster (and a big one at that), was absolutely heart taking. It brought tears to my eyes. Good quality Japanese ivory carving frequently does that to me...
Probably Dr. Stein will be able to add more information about your dagger.