I Am Even More Confused Now…

By Richard Posner’s math…On August 25th he wrote, regarding Dr. Romer’s August 6 speech:

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. [emphasis added]

For those readers new to this debate (which I had thought had been clearly resolved by explicit math), see the previous posts here: [1] [2] [3].


There’s a moving window on the Recovery.com, so I can’t see the cumulative $60 billion figure for end-June, but I do recall it. Better yet, Donald Marron recalls it. No one else has disputed the $60 billion figure.


In any case, apparently in this latest attempt to salvage his argument, Mr. Posner has given up on accusing Dr. Romer of deliberately lying about the $40 billion figure, and has moved on to redefining those funds. (By the way, I’m not sure I’ve seen him explicitly admit that dividing a quarterly figure by annualized GDP, as he does in his original post, is a mistake.)
Specifically, he is saying that the $40 billion is partly decreased withholding, or shifting around of tax liabilities, and not entirely rebates. Mr. Posner does not provide any source for this assertion, and the language in Dr. Romer’s speech (and footnote 4) seems to indicate otherwise.


Let’s assume absolutely none of the $40 billion took the form of rebates. As I showed in my math in this post, assuming zero spending out of the tax component, one can easily obtain 4 ppts growth in 2009Q2 GDP, given that the “transfers” to the states are largely helping support continued spending on goods and services like teachers, civil servants, health services, etc.


I am of course working in the “old-fashioned” Keynesian mode that Mr. Posner says he prefers. If one hews to a real business cycle approach, or other approaches were the economy does not systematically deviate from full-employment, then none of the foregoing is relevant.


Update 8/28 12:20pm Pacific: See also Justin Wolfer’s take on Posner.

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17 thoughts on “I Am Even More Confused Now…

  1. antoniusb

    I still believe that Dr. Chinn is incorrect in annualizing the impact of the stimulus spending in Q2 2009. I have found an alternate way that will unequivocally demonstrate this to be true.
    Let us assume that there is no dispute that the impact of the stimulus spending in Q2 of 2009 was $32.4 billion. Let us also assume that the spending has a one time effect and does not permanently lift the level of GDP in succeeding quarters (I assume this to be the case though if I am wrong this would explain some of the difference in results obtained).
    ANNUAL US GDP is ~13 trillion so that $32.4 trillion represents 0.25% of the ANNUAL US GDP figure. On an ANNUALIZED basis, the impact of the stimulus of $32.4 billion in Q2 would be 1% (1 + 0.25) ^ 4 -1.
    Because the stimulus spending is a one time effect, the impact on annual GDP is 0.25% (32.4/ 13,000). For every $100 billion in annual stimulus spending, we should expect to see an increase of 0.3%.
    I am not an economist so if there are some type of lag effects or unexplained multipliers that were not explained in the various posts on the topic then this changes the situation.
    However, if the stimulus effect is accurately described as a one time effect in the quarter it is spent, I do not see how I can possibly be incorrect.

  2. Mark A. Sadowski

    Everyone who has followed this remembers the figures. I googled and found this image of the cumulative spending as of June 26th:
    http://picasaweb.google.com/lh/photo/IxLMoHa1yhg2s79U0kyYuQ?authkey=Gv1sRgCOWcs5m5waORKw&feat=embedwebsite
    Note that it was $56.3 billion on that date. Furthermore I have no idea where Posner is getting the $61 billion figure because when you go yo the site you can clearly see as of last week it was $84.6 billion:
    http://www.recovery.gov/?q=content/report-progress

  3. Menzie Chinn

    antoniusb: You are confusing annual impact with annualizing a quarterly impact. You might wish to consult, in addition, this post, and acquaint yourself with the concept of a dynamic multiplier.

  4. Mark A. Sadowski

    I’ve been researching the $40 billion second quarter tax cut figure. It is actually quite plausible that that money ended up in people’s hands. Here’s why.
    Approximately 52 million people received a $250 Economic Recovery Payment in May. That comes to $13 billion. Reduced payroll deductions for the Make Work Pay Tax Credit started at the beginning of April. $58 billion of this credit was budgeted for FY 2009. Thus $29 billion probably went out in the second quarter. The total sum is thus $42 billion. Not much of a mystery.

  5. MPO

    I’m not exactly a fan of Posner, but with everything going on does he really warrant four entries in one week?

  6. antoniusb

    Dr Chinn: The concept of a dynamic multiplier spreading the effects of the stimulus across quarters is not disputable.
    It was not referenced in any of the posts on this topic nor did you mention this effect in either of your email responses to my inquiry.
    The lag effect in the link is stated in terms of years and not quarters. To measure the estimated effect of Q2 stimulus spending in Q3 and Q4 and Q1 2010, one would need to know the value of the dynamic multipliers on a quarterly scale and then apply the expected residual impact from those quarters into the second quarter.
    In order to achieve a four percent effect on GDP, one would need roughly $484 in residual stimulus spending in the upcoming quarters to get to reach a 4% annual effect ($12.9 trillion x 4% = $516 billion less the $32 billion recognized in Q2).
    That seems to be a very aggressive assumption but economics is not my field of expertise. I will defer to you that the stimulus impact in the following three quarters will be more than 15x the effect in the quarter it was spent.
    I still not see the justification for annualizing numbers that are presented on the same quarterly scale. For example, if I pay quarterly taxes of 20% of my income, my annual income tax rate is 20% and not (1.2 ^ 4)-1.
    I also do not understand the justification for pushing future effects of the stimulus into the current time frame for the purpose of explaining a gap occurring in the current quarter.
    Suppose I proposed to my boss to spend $100K for a marketing campaign that was expected to bring in an additional $100K in revenue on a quarterly basis over the next four quarters. In the following quarter, the campaign performs as expected bringing in $100K in revenue.
    Our company experiences an overall increase of $400K and my boss asks me how much of this was due to the aforementioned marketing campaign. An answer of 100% would be impossible to justify. The correct answer would be 25%.
    I cannot see how my example differs materially from the ongoing dispute between you and Prof Posner. I thought the crux of his argument was that the impact of the stimulus spent in Q2 could only explain 25% of a theoretical gap while your claim was that it explained substantially all of it.

  7. Mark A. Sadowski

    @MPO,
    I find the Posner debate incredibly compelling. (And I’m extemely gratified that Menzie has chosen to take a stand.) For one thing I believe he is being exposed as a gigantic hypocrite in his accusation that Romer has been intellectually dishonest. For another I perceive his attack on macroeconomists who study business cycles as a stealth “concern troll” attack by the Chicago freshwater RBC/Neo-Classicists with whom he shares academic halls and who are clearly on the defensive since the economy imploded late last year.

  8. Menzie Chinn

    antoniusb: I didn’t reference dynamic multipliers before because I was only talking about 2009Q2 before…(although I did talk about impact multipliers before — which you should have understood to mean something different than the cumulative effect).

  9. antoniusb

    OK. I now understand where I went wrong. In estimating the impact of the stimulus spending in Q2, I assumed the $32 billion stimulus impact was was the only effect on Q2 GDP.
    I neglected the factor of government spending itself as a component of the GDP in itself. When added together they are consistent with covering the gap between the two scenarios of ~4% of GDP on a quarterly basis.
    I sure hope this is the explanation for my numbers adding up or I will start pulling my hair out.

  10. mike

    Me thinks Dr. Posner isn’t the type to eat crow.
    Sadly, few as famous as him are. Most that famous make up for their insecurity by being extremely careful.
    I’m in no way excusing his behavior.

  11. rana

    Menzie,
    From recovery.gov you can get a $60 billion figure for expenditures through end of June, but a small amount of those were during the first quarter–basically Medicaid payments. On the tax side you have several things going on. First, lower withholding, from the Make Work Pay tax cut is reducing taxes by about $4 billion per month since April and a bit in March (see BEA’s personal income statement for April–which puts it at $48 billion, saar). In addition, the COBRA payments by the govt to businesses is showing up as lower withholding, probably about $1 billion per month. Moreover, first-time home buyers tax credit may be reducing withholding (families should reduce their withholding to zero when they by a qualifying house–maybe another $1 billion per month, but usually not included in these calculations because JCT assumed that this provision would show up as refunds next year. Finally, corporate provisions–bonus depreciation and temporary defferal of income from debt writedowns–may be reducing taxes they pay by about $5 billion per quarter. None of this is at an annual rate

  12. antoniusb

    OK, I am an idiot. I was using comparable quarter for the previous year to determine the size of the gap and not sequential.
    As it turns out, this happens to overstate the size of the gap by a factor of 16 ($8.2 billion compared to $132 billion). Where have I seen that number recently?
    My apologies to Dr. Chinn for wasting his time on something that I should have brushed up on before posting.

  13. Tom

    If recovery.gov said stimulus spending was $60 billion at end-June and $61 billion seven weeks later, then the reliability of both figures is in question. But in the big picture this hardly matters.
    To measure the impact of stimulus on GDP, one needs to know not only how much of it was spent on consumption, but also how much of it would otherwise have been spent on consumption, had the government not borrowed the money, or in this odd case, created it, which in effect is a tax on all dollars. I haven’t seen any serious estimates, from Romer or anyone else, only arbitrary guesses.
    My sense is the stimulus bill had a small impact on 2q gdp growth, on the order of one or 1.5 points, while Fed purchases of mortgage securities probably provided a similar boost. The combined negative impacts on future growth will be greater.

  14. Simon van Norden

    Menzie;
    Thanks for taking a stand on this; I think Posner merits it.
    1) He has important academic credentials.
    2) He’s blogging in mainstream media.
    3) He’s accusing others of abusing their academic credentials in mainstream media.
    4) They’re not.
    5) He is.
    6) You’re not.
    I feel I’m benefiting from your public service (and I’m not even American!)

  15. rana

    Tom,
    Recovery.gov does not have$61 billion seven weeks later, it has $85 billion; see /www.recovery.gov/?q=content/report-progress (go to recovery.gov, click on investments, then by agency and it has a short time series from july 17 (67 billion) to now (85 billion).
    Simon, unfortunately you are 100% correct. Menzie tried to show Posner the simple math but he was too arrogant to try to understand.

  16. Mark A. Sadowski

    I’ve been researching the $40 billion tax figure and realize I made two *major* mistake earlier. 1) The Economic Recovery Payments appear on the spending side and so are included in the recovery.gov figures.
    2) Only $23.4 billion is budgeted for he Make Work Pay Credit in FY 2009.
    On July 8th in congressional testimony Robert L. Nabors Deputy Director of the OMB stated:
    “As of June 30, almost $201 billion, or approximately 26 percent, of all Recovery Act funding had been obligated or distributed. This includes $157.7 billion of obligations, representing all major agenciesof which over a third has been outlaidand $43.2 billion of tax relief.”
    http://www.whitehouse.gov/omb/assets/testimony/deputy_070809_arra.pdf
    On August 7th the Democratic Policy Committee stated:
    “The Department of Treasury’s Office of Tax Analysis estimates that, through the end of June, approximately $43.2 billion in tax relief has already been made available through Recovery Act tax provisions for Making Work Pay, other individual credits, energy incentives, tax incentives for businesses, and COBRA. [The White House, 7/15/09]”
    http://dpc.senate.gov/docs/fs-111-1-109.pdf
    Let’s look at each of these provisions separately. Evidently, based on Treasury/IRS/Congressional websites, all start paying out more or less immediately through a refund or through reduced withholding. Here are my best guesses on how much was obligated or distributed through the end of the second quarter based on congressional testimony, BEA data and JCT analysis.
    1) Make Work Pay
    Nabors said that $15 billion in Make Work Pay went out by the end of June. However according to the BEA $0.93 billion went out in March and $4.15 billion went out in each of the three following months for a total of $13.4 billion.
    2)Other Individual Incentives
    a) Expanded Tax Break for 2009 First-time Buyers
    $1.4 billion
    b) Sales Tax Deduction for Vehicle Purchases $340 million
    c) Exclude up to $2,400 of unemployment
    insurance benefits from gross income.
    $470 million
    3)Energy Incentives
    $160 million
    4)Tax Incentives for Business
    a)Bonus Depreciation
    $320 million
    b)Carryback of Net operating Losses
    $16.25 billion
    c)Deferral of Income from Debt Writedowns
    $4.0 billion
    5)Cobra
    $4.8 billion
    The JCT analysis is here:
    http://www.jct.gov/publications.html?func=startdown&id=1231
    So the total equals $42.8 billion (using Nabor’s Make Work Pay figure)which is pretty close to the official $43.2 billion figure.
    I wish the administration would be as transparent with the tax expenditure figures as they have been with the direct spending figures. This is only aiding critics like Posner.
    I notice that rana has some similar calculations. If she or anyone else has better information please let me know.

  17. dilbert dogbert

    Re: Salt Water vs Fresh Water Economics
    Maybe we need more estrogen vs testosterone economics.

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