The big difference between the official deficit and standard accounting: Congress exempts itself from including the cost of promised retirement benefits. Yet companies, states and local governments must include retirement commitments in financial statements, as required by federal law and private boards that set accounting rules.

The deficit was $5 trillion last year under those rules. The official number was $1.3 trillion. Liabilities for Social Security, Medicare and other retirement programs rose by $3.7 trillion in 2011, according to government actuaries, but the amount was not registered on the government’s books.

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