This link to a 43 page paper: Ricardian equivalence: an empirical application to the Portuguese economy CarlosFonseca Marinheiro
Introduction on page 3:
The fiscal policy may be used with a stabilising role if the government finance decisions are able to influence private consumption (i.e., aggregate demand) and saving. This influence depends on the degree to which consumers treat government debt as net wealth.
If Ricardian equivalence holds then the government cannot stimulate aggregate demand by increasing spending and/or reducing taxes. So history of economic debate over the effectiveness of fiscal policy includes this theory called Ricardian equivalence.
According to the Keynesian consensus consumers treat government debt as net wealth. Therefore, a substitution of debt for taxes has a positive influence on private consumption and aggregate demand. However, the consequent decrease in private and national saving, implies an increase in the real interest rate, which crowds out private investment. The reduction in the capital accumulation then leads to a reduction of the long-term growth prospects of the economy. This negative long-run effect offsets some of the positive short-term effects of the government deficit.
The Ricardian thesis has a complete opposite view. It states that, for a given expenditure path, substitution of debt for taxes has no effect on aggregate demand nor in interest rates.The government’s inter-temporal budget constraint implies that, for an unaltered level of government outlays, a tax cut now implies a tax increase in the future. As borrowing only postpone taxes for the future, consumers, who are simultaneously taxpayers, anticipating the increase in future taxes, do not consider the current tax cut and the consequent increase in disposable income as being permanent. Their inter-temporal budget restriction is left unaltered. Therefore, consumption is also unaffected. The increased disposable income is entirely saved.
Then there is another historic economic debate over the concept called "crowding out."