Brian Broughman and Deborah Widiss have written this important article for the Journal of Legal Studies. Here is the abstract:

Congressional overrides of prior judicial interpretations of statutory language are typically defined as equivalent to judicial overrulings, and they are presumed to play a central role in maintaining legislative supremacy. Our study is the first to empirically test these assumptions. Using a differences-in-differences research design, we find that citation levels decrease far less after legislative overrides than after judicial overrulings. This pattern holds true even when controlling for depth of the superseding event or considering only the specific proposition that was superseded. Moreover, contrary to what one might expect, citation levels decrease more quickly after restorative overrides—in which Congress repudiates the prior Supreme Court decision as incorrect—than after overrides intended to update or clarify the law. This suggests that ongoing citation of overridden precedents, what we call shadow precedents, may be driven more by information failure or ambiguity than by ideological disagreements between the branches of government.