Short answers, pulled from the story.
Ricardian equivalence is the hypothesis that it makes no difference to the economy whether a government finances its spending through current taxes or by issuing debt. Forward-looking consumers anticipate the future taxes needed to repay government bonds and save the equivalent amount today, leaving total demand unchanged.
David Ricardo first proposed the idea in his 1820 essay "Essay on the Funding System," though he doubted it had practical relevance. Antonio de Viti de Marco elaborated on it in the 1890s, and Robert J. Barro gave it a formal theoretical foundation in 1974.
Barro assumed that families act as infinitely lived dynasties due to intergenerational altruism, that capital markets are perfect so everyone borrows and lends at a single rate, and that the path of government expenditures is fixed. Under these conditions, families would increase bequests to cover the future tax burden from government bonds.
The evidence contradicts Ricardian equivalence. After the Reagan tax cuts, net private saving as a percentage of GNP fell from 8.55 in the 1976-1980 period to 7.47 percent in the 1981-1986 period, while consumption as a share of GNP rose from 62.96 percent to 64.72 percent. Research by Chris Carroll, James Poterba, and Lawrence Summers confirmed that government deficits were followed by lower, not higher, private saving.
Martin Feldstein argued in 1976 that Barro ignored economic and population growth and demonstrated that public debt creation depresses savings in a growing economy. James M. Buchanan, in the same journal issue, noted that the underlying question was an age-old problem in public finance already raised by Ricardo and extended by de Viti de Marco.
Ricardo expressed doubt immediately after proposing the idea in 1820. He argued that individuals do not actually evaluate taxes in a forward-looking manner and instead take a myopic view of the tax path. Gerald P. O'Driscoll noted in 1977 that Ricardo's subsequent Encyclopaedia Britannica article changed so many features of his argument that it effectively became a Ricardian Nonequivalence Theorem.