We establish the energy estimate for higher order linear Schrödinger type equations on the torus. The proof is based on the energy method with correction terms, but some derivative losses cannot be recovered and they may have an affect on the well-posedness. As a corollary, we can classify the Cauchy problem into three types: dispersive type, parabolic type and ill-posed type. This talk is based on the joint work with Professor Kotaro Tsugawa (Chuo univ.).