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Christina Romer, in her speech that I have been blogging critically about, said that the government had by the end of the second quarter of this year (June 30) "spent" more than $100 billion in stimulus money. The official stimulus web site, recovery.gov, has $61 billion, and one of my critics says "about $60 billion." Other critics say that the official figure is too low, because it omits "tax reductions," which one critic calls "tax rebates." These critics say that the missing figure for tax relief is $40 billion, so gets Romer up to at least the $100 billion of her "more than $100 billion."

The figure of $60 billion of $61 billion is too high. According to recovery.gov, the $61  billion figure is as of last week--seven weeks after the end of the second quarter. Since the rate of stimulus expenditures is said to be accelerating, the number for the second quarter is undoubtedly significantly lower. This makes the $40 billion in tax relief all the more important to Romer's argumente And if that figure consisted of actual rebate checks, or reductions in current withholding, then of course it should be included in the total outlays of the stimulus program. But in fact very little of it consists of rebates, which is why it is not recorded on the government's website as stimulus money spent and is why Romer should not have said that by the end of the second quarter the government had "spent" "more than $100 billion" in stimulus money. Almost all the tax relief provided for in the stimulus bill consists of reductions in taxes by individuals and businesses. The question is how many of those reductions have resulted in increased cash flow to taxpayers. If, for example, the reduction is reflected in reduced withholding, or a reduced payment of estimated tax by people who filed estimated returns on April 15, it should be counted as stimulus spending; it puts money in people's pockets. If it merely reduces their future tax liability, it does not. All that is certain is that not all that $40 billion in tax relief is stimulus money; not all, and, at a guess, not most, put money in people's pockets before the second quarter ended.

That is a surprising oversight of Romer and her allied macroeconomists, and I am guessing that they will regroup and argue that just the prospect of greater after-tax income in the future can have a stimulus effect. And I agree! As I have said repeatedly, I support the stimulus. My criticism of Romer's speech, and of her defenders (apart from their incivility, surprising in those of my critics who are university professors), is that it and they exaggerate the probable effect on the economy of the limited amount of stimulus spending as of the end of the second quarter. To me, the significance of the stimulus is its effect on the confidence of business and consumers (that is a Keynesian point, and I am an "old Keynesian," which is to say a fan of the General Theory), and that effect is to a considerable degree, I should think, independent of the schedule of stimulus spending. So yes, if businesses and consumers know that they are getting tax reductions, this may well affect their current spending, because they know their after-tax income will rise. The effect, however, cannot be quantified.

So what would be the most accurate statement about the effect of the stimulus is as follows: since the financial collapse of last September, the government has taken a number of steps to arrest the economic decline. The joint effect of these steps (credit easing, bank bailouts, auto bailouts, stimulus package, mortgage relief, etc.) has almost certainly been positive, and I would guess strongly positive. But the separate effect of each of the components cannot be quantified. The stimulus package is a major component of the government's overall recovery program, and there are theoretical reasons for believing that it had a signficant effect in advance of actual expenditures of stimulus funds by the recipients. Our inability to quantify its effect should not be a ground of criticism.

Paul Krugman has now chimed in, concurring with Professor DeLong's claim that I understated the effect of stimulus sending through June 30 by a factor of 16. DeLong's analysis of the effect of the stimulus was based on the premise that $100 billion dollars of stimulus moneys were not only received through June 30 but actually spent by the recipients; and we now know that that is a wild exaggeration. On the assumption that all that money was spent in the second quarter, the stimulus was approximately 2.9 percent of GDP for that quarter (he uses the figure 2.6 percent). Considering that an unknown but probably significant fraction of the so-called $60 billion in state aid was not even disbursed in the second quarter and that of the fraction that was disbursed only a modest fraction in all likelihood was actually spent by recipients of the aid rather than retained in state treasuries or saved by the individual or business recipients, and that an even smaller fraction of the $40 billion in tax relief was actually received by taxpayers rather than accrued or, again, saved, the assumption that $100 billion (let alone more than $100 billion) was actually spent on goods and services is a gross exaggeration. (DeLong reversed the fractions; he thought that $60 billion was tax relief--of course if that were right, his assumption that $100 billion was actually spent in the second quarter would be even more extravagant. But it is wrong.)

Remember that Romer herself speculated "that households are initially using the tax cut mainly to increase their saving and pay off debt." Yet all the stimulus money disbursed in the second quarter similarly consisted of transfers, not of investments, and no one seems to know how much was actually spent rather than squirreled away during the second quarter. People tend to save rather than spend transitory (i.e., windfall) income (the tendency Romer herself acknowledged with reference to tax relief), and all the transfer payments authorized by the stimulus program are transitory. Romer says that public works (she calls them "direct investments," but the meaning is the same) "have short-run effects roughly 60 percent larger than tax cuts." She doesn't indicate where she gets the number, but it is further evidence that she believes that transfer payments are not as efficient in stimulating economic activity as public works are. And there was not yet any significant spending of stimulus moneys on public works in the second quarter.

Moreover, given the inevitable lag between the disbursement and the expenditure of disbursed funds by the recipient of the disbursement, disbursements made toward the end of the second quarter could not possibly have affected output and employment in that quarter, other than psychologically, and hence unquantifiably.

No one seems to know the true figure of stimulus money actually spent (not saved, not sitting state treasuries, not accrued) in the second quarter. If it was as much as $25 billion, which is roughly two-thirds of one percent of that quarter's GDP, I would be surprised. That is not a negligible amount, but whether it would explain much or all or a little of the reduction in the rate of decline of GDP from the first to the second quarter is unproved, and probably unprovable. So much else was happening in the economy in the second quarter; separating out the causal effect of one development that may have contributed to the decline in the rate of decline of output in the second quarter is probably impossible, but in any event has not been attempted. The one thing we can be certain of is that, Christina Romer and her phalanx of defenders to the contrary notwithstanding, "more than $100 billion" of the stimulus money had not been "spent" ("absolutely going out the door," as she also put it) when the second quarter of 2009 ended on June 30.