Disclosed are a method for producing a polymer by a polymerization of a mixture at a temperature of 210° C. or lower, wherein the mixture comprises 0.01 to 35 mol % of a monomer or a polymer thereof which has a piperidine skeleton represented by formula (1), and a molded body thereof. R1 represents a hydrogen atom or a methyl group, X represents an oxygen atom, an imino group, or a specific oxygen atom containing a hydrocarbon group, and R2 and R3 represent a hydrogen atom, a linear alkyl group with C1 to C8, a branched alkyl group with C1 to C8, an alicyclic hydrocarbon with C6 to C8, or an aryl group, wherein R2 and R3 may also form a cyclic structure.