Hungarian Historical Phonology haj
haj 'hair'
First attestation/Old Hungarian data
[coming]
Important dialectal forms
[coming]
Uralic/Ugric/Pre-Hungarian reconstruction
*kajə
Aikio 2013, 2015: PU *kaji 'grass, stalk, awn'
UEW: PUg *kajɜ 'hair; Haar'
Status of the Ugric etymology
Plausible, but probably derived from PU (see below)
Loan etymology
None suggested so far
Cognates suggested in earlier research
UEW:
Mansi: South (TJ) χōj: päŋkχōj 'Haar', West (P) kōj 'Kopfhaut', North (N) χåj 'hajüstök, hajfürt, hajcsomó az ember fején; Haartolle, Locke, Haarbüschel am Kopf des Menschen' < PMs *kāj (Aikio 2015)
Aikio 2013, 2015:
Mansi: South (TJ) χōj: päŋkχōj 'Haar', West (P) kōj 'Kopfhaut', North (N) χåj 'hajüstök, hajfürt, hajcsomó az ember fején; Haartolle, Locke, Haarbüschel am Kopf des Menschen' < PMs *kāj (Aikio 2015)
Saami: N guodja 'seed shell of a sedge'
Komi: ki̮ 'awn'
Udmurt: ki̮ 'awn'
Samoyed: Selkup Taz qu 'stalk, stem, oblong or slender object' < PSam *kåǝ
Commentary
The Ugric etymology presented in the UEW is regular. However, Aikio (2013: 166–167) has presented phonologically regular cognates also in Saami, Permic and Samoyed (Selkup). It seems thus quite clear that both the Hungarian and the Mansi word go back to Proto-Uralic *kajə, and the word is not confined to Ugric.
However, it should be noted here that the meaning 'grass, stalk, awn' reconstructed by Aikio is based on Saami, Permic and Samoyed evidence, and only Hungarian and Mansi show the meaning 'hair'. 'stalk' > 'hair' a plausible semantic change, so semantics are not an obstacle to the Proto-Uralic etymology. It can be assumed, however, that the meaning 'hair' in Hungarian and Mansi reflects a common semantic innovation that took place either in Proto-Ugric or in a Sprachbund formed by Pre-Hungarian and Pre-Mansi.
Conclusion
The Proto-Uralic etymology is convincing. The meaning 'hair' in Hungarian and Mansi might reflect a common semantic innovation.
References
Aikio 2013: 166–167: PU
Aikio 2015: 52: PU
UEW s.v. kajɜ: Proto-Ugric Uralonet