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WASHINGTON — The Supreme Court passed up an opportunity to clarify a key doctrine underpinning corporate tax law Tuesday, as it declined to hear two cases brought by Dow Chemical Co. and a former subsidiary of Goodrich Corp.

Both cases involved tax shelters the two companies pursued in the 1990s. The Court's decision lets stand two lower court rulings that were in favor of the Internal Revenue Service.

Dow was seeking a refund of approximately $22 million and Goodrich a refund of approximately $82 million in taxes they paid after tax strategies they pursued were disallowed by the IRS.

The two cases, while technical, involved several aspects of the "economic substance" doctrine, which holds that for a company to claim a tax deduction for a specific transaction, that transaction must yield a profit or have some other clear economic benefit separate from the tax effect.

All transactions must satisfy the economic substance test to successfully claim a tax deduction or other benefit, meaning any change to the doctrine would have had a widespread impact.

The cases were Dow Chemical v. United States, 06-478 and Coltec Industries Inc. v. the United States, 06-659. Coltec, now owned by EnPro Industries Inc., was bought by Goodrich and subsequently spun off. Goodrich retained its claim to any tax refund that might have arisen from the case, an attorney for Coltec said.

Shares of Dow Chemical dropped 8 cents to $43.36 in midday trading, while Goodrich's stock rose 73 cents to $51.58 and EnPro shares jumped $1.18, or 3 percent, to $40.56, all on the New York Stock Exchange.