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We apply a dynamic influence model to the opinions of the US federal courts to examine the role of the US Supreme Court in influencing the direction of legal discourse in the federal courts. We propose two mechanisms for how the Court affects innovation in legal language: a selection mechanism where the Court's influence primarily derives from its discretionary jurisdiction, and an authorship mechanism in which the Court's influence derives directly from its own innovations. To test these alternative hypotheses, we develop a novel influence measure based on a dynamic topic model that separates the Court's own language innovations from those of the lower courts. Applying this measure to the US federal courts, we find that the Supreme Court primarily exercises influence through the selection mechanism, with modest additional influence attributable to the authorship mechanism. This article is part of the theme issue 'A complexity science approach to law and governance'. [ABSTRACT FROM AUTHOR]