The present invention provides a novel carboxylic acid derivative, a salt thereof or a hydrate of them which is useful as an insulin sensitizer, and a medicament comprising the derivative as the effective ingredient. More specifically, it provides a carboxylic acid compound represented by the formula (I), a salt thereof or a hydrate of them. ##STR00001## In the formula, Ar represents a 6- to 14-membered aromatic ring group which may have at least one substituent; R.sup.1, R.sup.2, R.sup.3, R.sup.4, R.sup.5, R.sup.6, R.sup.7 and R.sup.8 are the same as or different from each other and each represents a hydrogen atom, a halogen atom, a hydroxyl group, a C.sub.1-6 alkyl group or a C.sub.1-6 alkoxy group; X represents an oxygen atom or a methylene group; Y represents a group represented by the formula (II) or (III): ##STR00002## (wherein Z represents a group represented by the formula (IV): ##STR00003## (wherein R.sup.9, R.sup.10, R.sup.11 and R.sup.12 are the same as or different from each other and each represents a hydrogen atom, a halogen atom, a hydroxyl group, a C.sub.1-6 alkyl group or a C.sub.1-6 alkoxy group)); m is 0 or 1; and n is 0 or 1.