Bill Eskridge and Connor Raso have posted this draft on SSRN. Here is the abstract:

Legal scholars almost universally believe that federal judges defer to agency interpretations of statutes. The debate has therefore focused on when judges should defer and how judges should operationalize a deference regime doctrinally. Such normative debates about deference rest upon factual assumptions that have not been rigorously tested; drawing from the entire population of Supreme Court cases (1984-2006) our empirical finds that Supreme Court Justices do not generally afford deference precedents stare decisis effect, but that the policies underlying the major deference regimes do have bite at the Supreme Court level. We also find that judicial ideology affects the Justices’ applications of deference regimes but does not explain why different Justices prefer different doctrinal formulations; we advance the hypothesis that the Justices’ expressed preferences are genuine, but do not dominate ideology and other context based factors in actual cases. Deference regimes are more like canons of statutory construction, applied episodically but reflecting deeper judicial commitments, than binding precedents, pretty faithfully applied or distinguished. Our study suggests that most academic proposals to “reform” deference doctrines would have little or no bite at the Supreme Court level; more modest proposals to clarify such doctrines would probably be (modestly) helpful, however.