Posner, Redux

The confusing spectacle of Judge Posner blogging about macro continues. His latest missive appears particularly misguided.
To recap, Posner attacked CEA Chair Christina Romer for being too optimistic about the effects that fiscal stimulus had on second-quarter growth. According to Romer, the better performance of the economy in Q2 relative to Q1 was largely attributable to the economic stimulus. But Posner argues that $100 billion in stimulus spending in that quarter is simply too small relative to the size of the economy to make much of a difference. Throw in accusations of unethical or irresponsible behavior, and you have yourself an academic brouhaha.
But the error was Posner’s. As it turned out, he was comparing apples and oranges. Actually, he was comparing a quarter of an apple with a whole apple: by contrasting the amount of stimulus spending in one quarter with an annual measure of gross domestic product, he understated the relative size of the stimulus by a factor of four. He then multiplied his error by comparing it with the change in an annualized growth rate, which overstates the change in quarterly GDP growth by a factor of four. Yes, he was right that his numbers suggested the stimulus was too small to make this much of a difference. But that’s because his numbers understated the relative size of the stimulus by a factor of four and overstated the claimed consequences by a factor of four. And so Posner was wrong by a factor of sixteen. (See if you can spot his correction or apology in his follow-up.)
But now Posner is back, talking about “Christina Romer’s More Than $300 Billion Mistake.” That $300 billion? Beyond stating that number in a headline, he never returns to it, so we don’t know if it’s a typo or a calculation. But reading the full piece, it becomes clear that his real target is that we’ve all been wrong in taking Romer at her word that in Q2 around $100 billion of the stimulus money went out the door. Posner now thinks that it was “too high.” To cut through some confusion, note that this reflects that $60 billion is direct government spending and $40 billion comes in tax reductions. But Posner says:

The figure of $60 billion of [sic] $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 … the number for the second quarter is undoubtedly significantly lower.

You can see the data from recovery.gov, here.
The chart plainly shows that seven weeks after the end of Q2, $84.6 billion had been paid out, not $61 billion. But Romer’s claims are about the quarter that ended on June 30, and while I don’t have data for precisely that day (although I’m sure Romer does), you can extrapolate the green line backwards. By July 17, $67.4 billion had been spent, and it looks like about $3 to $4 billion per week is being spent. Extrapolating backwards two to three weeks to June 30, the total was probably right around, ummm … $60 billion.
And the other $40 billion? As Menzie Chinn rightly notes, Posner doesn’t think that taxpayers have received it, but he doesn’t say why.
I’m glad that there are folks who are going to monitor the claims of government economists closely, but unfortunately Posner has generated more heat than light. John Maynard Keynes reportedly said, “When the facts change, I change my mind.” My advice to Posner: when your understanding of the facts change, don’t keep attacking the facts, change your mind.