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Few doctrines are more shrouded in mystery or litigated more often than piercing the corporate veil. We develop a new theoretical framework that posits that veil piercing is done to achieve three discrete public policy goals, each of which is consistent with economic efficiency: (1) achieving the purpose of an existing statute or regulation; (2) preventing shareholders from obtaining credit by misrepresentation; and (3) promoting the bankruptcy values of achieving the orderly, efficient resolution of a bankrupt's estate. We analyze the facts of veil-piercing cases to show how the outcomes are explained by our taxonomy. We demonstrate that a supposed justification for veil piercing--undercapitalization--in fact rarely, if ever, provides an independent basis for piercing the corporate veil. Finally, we employ modern quantitative machine learning methods never before utilized in legal scholarship to analyze the full text of 9,380judicial opinions. We demonstrate that our theories systematically predict veil-piercing outcomes, that the widely invoked rationale of "undercapitalization" of the business poorly explains these cases, and that our theories most closely reflect the actual textual structure of the opinions

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