<p>High-quality differential-shrinkage polyester combined filament yarn having good color tone and being free from fluffing can be made from a polyester polymer produced by using a catalyst comprising (1) a mixture consisting of a Ti compound component composed of one or more members selected from among titanium alkoxides of the general formula (I) and products of reaction of these alkoxides with carboxylic acids of the general formula (II) or anhydrides thereof and a P compound component consisting of a compound of the general formula (III) and/or (2) a product obtained by reacting a Ti compound component composed of one or more members selected from among titanium alkoxides of the general formula (I) and products of reaction of these alkoxides with carboxylic acids of the general formula (II) or anhydrides thereof with a P compound component consisting of a compound of the general formula (IV).</p>