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Professor Sanchirico’s Institute for Law and Economics research paper demystifies an influential model of optimal capital and wealth taxation

May 06, 2020

Professor Sanchirico’s paper aims to demystify the influential but oracular Judd model – both Judd’s original findings and Straub & Werning’s important recent revision.

Samuel A. Blank Professor of Law, Business, and Public Policy Chris William Sanchirico has published “Why the Optimal Long-Run Tax Rate on Capital is Zero … or Very High: The Missing Explanation” in the University of Pennsylvania’s Institute for Law and Economics (ILE) Research Paper Series.

The original Judd model prescribes a zero rate of tax on capital in the long run. In an article published just this year, Straub and Werning, using the same model, find that the long-run tax rate should be positive, and potentially very high.

In his new research paper, Professor Sanchirico concludes that despite playing an important role in practical policy debates, the Judd model and the findings derived from it remain largely oracular. The reader attempting to grasp why the optimal long-run rate of tax on capital is zero — or potentially very positive — reaches out to find only tightly wound proofs and loosely twisted “intuitions.” Here, Professor Sanchirico has attempted to provide something between those two extremes, an explanation.

More than this, the paper argues that once the key moving parts of the Judd model are understood, it becomes clear that its findings, both new and old, are largely driven by quirks in the mathematical concept of infinity and are not properly included in any practical brief on optimal capital taxation, whether for or against.

From the introduction:

A bimodality of black-hole proofs and nebulous intuitions produces a special problem when the target of mathematical analysis is public policy. The Judd model, after all, is not like a model in physics or engineering wherein the rocket makes it to the moon or not, or wherein the bridge collapses or not. No one reading a description of the Judd model would believe that it is somehow ready to be run on the real economy, to be verified or not. Rather the findings derived in the Judd model are policy arguments—nothing more, nothing less—and they should be evaluated as such. On the one hand, the too obvious objection that the Judd model is artificial just amounts to the assertion that the arguments made within its frame are not comprehensive. But no argument is. The comparatively self-evident incompleteness of the Judd model ought to be regarded as a virtue. On the other hand, the fact that findings derived from the Judd model cite mathematical reasoning as authority cannot be the end of the conversation. Like any authority, the mathematical reasoning needs to probed, and the argument that is being made, essentially comprehended.

Providing an explanation of Judd model findings is this paper’s primary, and less contestable goal. Its secondary goal is more controversial. The explanation that is offered in this paper calls into question the Judd model’s relevance. It reveals that the findings of both model variants are driven by an oddity of infinite-horizon reasoning that cannot be regarded as connected to any real public policy consideration.

Professor Sanchirico is also the Co-Director of the Center for Tax Law and Policy at the Law School.

Read the full paper here.