The Market for Lemmas: Evidence That Complex Models Rarely Operate in Our World

The market for models whose mathematical proofs are so lengthy and complex as to call for the delineation of intermediate steps with lemmas (Lemma 1, Lemma 2, etc.) expanded remarkably in prominent economic journals during the final four decades of the 20th century. However, Alfred Marshall, Paul Samuelson, and Donald Gordon explained that the worthiness of long chains of analytic reasoning depends critically on the stability or durability of the relations involved; in economic relations, the soundness of long chains are subject to “radioactive decay,†to use Samuelson’s phrase. Here we draw on this insight and provide evidence that: (1) there has been remarkable growth in the frequency of articles with lemmas published in some top general-interest journals; (2) a sample of 12 lemma-heavy articles in Journal of Economic Theory have resulted in very few operational statements; (3) articles that cited the lemma-heavy articles have generated few operational statements; (4) lemmas are rare among the most-cited articles that appeared in the top general interest journals; and (5) true to the point about “radioactive decay,†most-cited articles with lemmas are more likely to be on statistical/econometric analytics than economic analytics.