In this paper, we propose a novel concept of path consistency to learn robust object matching without using manual object identity supervision. Our key idea is that, to track a object through frames, we can obtain multiple different association results from a model by varying the frames it can observe, i.e., skipping frames in observation. As the differences in observations do not alter the identities of objects, the obtained association results should be consistent. Based on this rationale, we generate multiple observation paths, each specifying a different set of frames to be skipped, and formulate the Path Consistency Loss that enforces the association results are consistent across different observation paths. We use the proposed loss to train our object matching model with only self-supervision. By extensive experiments on three tracking datasets (MOT17, PersonPath22, KITTI), we demonstrate that our method outperforms existing unsupervised methods with consistent margins on various evaluation metrics, and even achieves performance close to supervised methods.