METHOD FOR PRODUCING POLYMERIZATION CATALYST COMPOSITION, POLYMERIZATION CATALYST COMPOSITION, MET

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Provided is a method with which it is possible to produce a polymer that is added with silica without a long kneading process. Also provided is a polymer composition which has a favorable low heat generation property. [Solution] With respect to a first element comprising a rare earth element-containing compound, a second element containing a compound represented by formula (X), and a third element containing silica, the second element and the third element are mixed and aged, and then the first element is added to react therewith to produce a polymer catalyst composition. YR1aR2bR3c ……(X) (In the formula, Y is a metal selected from groups 1, 2, 12 and 13 in the periodic table, R1 and R2 are a hydrocarbon group having 1 to 10 carbon atoms or a hydrogen atom, R3 is a hydrocarbon group having 1 to 10 carbon atoms, provided that R1, R2 and R3 may be the same or different, and when Y is a metal selected from group 1 in the periodic table, a is 1 and b and c are 0, when Y is a metal selected from groups 2 and 12 in the periodic table, a and b are 1 and c is 0, and when Y is a metal selected from group 13 in the periodic table, a, b and c are 1.)