This study aims to estimate the scientific productivity of collective subjects. The objective is to build a method for evaluating scientific productivity that allows calculating productivity, including for new collective subjects with a small citation network—the paper purposes the Time-Weighted PageRank method with citation intensity (TWPR-CI). The Citation Network Dataset (ver. 13) has been analyzed to verify the method. The dataset includes more than 5 million scientific publications and 48 million citations. There have been allocated four classes of collective subjects (more than 27,000 collective subjects in total). For each class, scientific productivity estimates from 2000 to 2021 were calculated using the PageRank, Time-Weighted PageRank, and TWPR-CI methods. It is shown that the advantage of the TWPR-CI method is the higher sensitivity of the scientific productivity estimates for new collective subjects on average during the first ten years of observation. At the same time, the assessment of scientific productivity for other collective subjects according to this method is stable. However, the small citation network of the new collective subjects does not allow an adequate assessment of scientific productivity during the first years of its operation. Therefore, the TWPR-CI method can be used to assess the scientific productivity of collective subjects, in particular the productivity of new ones.