According to the so-called Ricardian Equivalence theorem, cutting taxes or increasing transfers does not stimulate aggregate demand, because private households offset tax cuts or transfer increases by saving more.
The proof of the theorem is as follows: If the government cuts taxes (or raises transfers) by 1 euro today without cutting government spending, the public debt increases by 1 euro. To service the additional debt, the government must raise taxes by r euros, r being the interest rate, in every future period from tomorrow to infinity. The present value of those future tax payments is 1 euro (=r/r). This is the amount households need to save today to pay those future taxes.
David Ricardo was the first to lay out this simple point of arithmetic in a debate over how the British government should pay for the Napoleonic Wars. But he went on to reject the conclusion that government deficits are offset by private saving arguing that households are too short-sighted to take into account those future tax payments in their saving decisions. So David Ricardo did not believe in Ricardian Equivalence.
In preparation for my Principles of Macroeconomics class, I wanted to check if there is any correlation between government deficits and private saving. I didn’t expect to find much. So I was surprised when after a few minutes of fiddling with FRED, the awesome data base of the St. Louis Fed, I got this:
The red line is the primary government budget balance in percent of GDP, (T-G)/Y in conventional macroeconomic notation. The blue line is personal saving in percent of disposable income (Y-T-C)/(Y-T).
Look how the blue line tends to move up whenever the red line moves down, and vice versa. Your eyes do not lie. The correlation coefficient between government saving and private saving is -0.12, statistically different from zero at usual confidence levels (the t-statistic is -1.85).
Is this the most solid econometric evidence ever? No, but it is a sign that Ricardian Equivalence is not so out of touch with the data as you might think.