Pocketful of Multipliers (II): Options for Stimulus Packages

As the debate over the nature and size of a stimulus package wends its way through the Congress [0], [1], [2], I thought it would be useful to bring numbers into the debate, especially as we are considering fiscal stimulus in a time when the Bush Administration has constrained, by dint of previous profligacy, our options. In particular, I want to return to the issue of multipliers, discussed in nearly a year ago. Here, I want to provide a little more specificity, regarding the impact depending upon the type of outlays.

From the testimony of Economy.com’s Mark Zandi back in July (thanks to Chad Stone for the pointer):

Chart from Excerpts of comments by Mark Zandi, chief economist of Moody’s Economy.com, testimony before the U.S. House Committee on Small Business on July 24, 2008.

What is a multiplier? It’s:




where Y and Z are measured in real dollars. Note that in principle, one can re-write the multiplier in terms of percentage point change of income relative to baseline income for a given percentage point change of the Z-to-Y baseline ratio.


What is apparent is that some tax cuts, or really rebates, can have a substantial effect. But in most cases, tax policies will have a relatively minor impact on aggregate demand, relative to increases in spending on goods and services. That’s because the first round of injection of the dollar into the economy via tax reductions or transfer increases initially augments disposable income, and then, by indirectly increasing consumption, increases GDP over time. In other words, for an increase in transfers, the impact of one dollar increase in outlays by the government is:


(c(1-t)) + (c(1-t)) 2 + (c(1-t)) 3 + …. = c(1-t)/(1-c(1-t))


Whereas for spending on goods and services:


1 + (c(1-t)) + (c(1-t)) 2 + (c(1-t)) 3 + …. = 1/(1-c(1-t))


Where c is the marginal propensity to consume (MPC) out of disposable income, and t is the marginal tax rate.


Why is the increase in extending unemployment insurance so large (and similarly for increaseing food stamps), when these are increases in transfers, and not increases in spending for goods and services? Look back to first series, and notice that if on the first round, the marginal tax rate is zero (which is definitely true for food stamps, and might be for unemployment benefits depending on the tax bracket), and the marginal propensity to consume is nearly unity, then the first term becomes close to 1. Hence, transfers to the lowest income households that have the highest MPC will have the biggest impact (of course on the 2nd and 3rd rounds, the standard fractions apply).


Increases for infrastructure spending will have a relatively large multiplier as well, exactly because these are expenditures for goods and services. To the extent that most of the input (concrete, labor) is domestically sourced, then on the first round impact, the increase in GDP is almost dollar for dollar (I’ve suppressed the marginal propensity to import in the above calculations to simplify the algebra and to provide the clearest intuition).


The above discussion explains why in my previous post on fiscal policy, I stressed that if we were to undertake any fiscal stimulus aimed at stabilizing the economy at the short to medium run, we should aim for aid to the states and localities, increases in unemployment insurance, and buttressing infrastructure spending.


One big caveat to the argument for infrastructure spending is that it usually takes a long time to plan such projects. Hence, it is not clear when the spending for such projects would actually occur, and hence the stimulus to the economy (this is called an outside policy lag, in the jargon). The “one-year horizon” shown in the table is for the horizon of one year from beginning of spending, not the beginning of planning and appropriation.


I have two observations here. First, if the spending could be directed to the states which had construction about to start, but hindered by financing or state revenue issues, then the problem of timing could be partly mitigated. I admit that it is unlikely that there are a tremendous number of such projects (although I am happy to be corrected). That leads me to my second observation.


The CBO study Options for Responding to Short-Term Economic Weakness (January 2008) laid out three principles for effective stimulus, loosely characterized as “timely, targetted, and temporary”. Spending on infrastructure is problematic on this first count if one believes the recession will be short. If one believes that it will be prolonged (in the now outdated lingo, “L-shaped” instead of “V-shaped”), then this drawback is not so significant. So, what’s the outlook? I reprise this graph from an October 18th post:

Figure 1: Log GDP, from 26 Sep release (blue line), and implied GDP gaps from WSJ survey (3-7 October survey, green x) Deutsche Bank (3-7 October forecast, teal +), and Deutsche Bank (17 October forecast, red square). Source: BEA, CBO [xls], WSJ [xls], Mayer, Hooper, Slok and Wall, “WO Update: From Financial Crisis to Global Recession,” Global Economic Perspectives (Deutsche Bank, 17 October 2008),
and author’s calculations.

Several last observations.


  • It’s not clear that these policies would do much good if the financial system is not restored to some semblance of working order (so, I’m in agreement with Jim). Hence, fiscal stimulus is not a substitute for financial triage. By the same token, even with an effective rescue of the financial system, deleveraging is going to be a long, drawn out process which will tend to depress aggregate demand; it seems that some fiscal stimulus should be emplaced to mitigate those contractionary effects.


  • Those who are familiar with multipliers will recognize that implicit in my discussion is accomodative monetary policy (i.e., there is no transactions- and portfolio-crowding out). I think this assumption is, in usual times, not a defensible assumption. However, the times hardly seem usual; and as we get closer to the zero bound on nominal interest rates, the assumption seems ever less problematic.
  • I know the preceding has been a pretty old fashioned Keynesian discussion. If I thought that the economy were near full employment and/or prices were fully flexible [3], I wouldn’t be propounding these ideas. But it seems to me we’re more in a world with some underutilized resources, requiring some sort of coordination mechanism, than an monetarist world.

    Greater discussion of these options, and how to allocate the monies across states, is contained in this brief by CBPP (September 26, 2008). See also Economix and National Journal blog.

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31 thoughts on “Pocketful of Multipliers (II): Options for Stimulus Packages

  1. ndk

    I dunno. I’m Keynesian to the point of reading and loving his General Theory — sentences were bigger back then — but this time is trying my soul.
    I’m getting pretty worried about government backstops and alternatives disincentivizing private expenditure and investment. We’ve seen many fundamental markets touched by the well-meaning hand of government become completely dysfunctional: mortgage lending, commercial paper, money markets, and even inter-bank lending. The Treasury and currency markets are also heavily touched, though the government players here are not the U.S.
    This intervention might have effects contrary to those intended. When government steps into a market, private players may withdraw, because they know full well they can’t compete on economic terms with a government. Governments are not economic, profit-maximizing entities, and they can borrow at rates with which no private enterprise can ever compete. This results in the government gradually assuming more and more control of the market, with active intention of stabilization, but the opposite effect in practice. Also, as this occurs in more and more markets, private players may become suspicious of further action, causing a chilling effect which itself causes intervention to become more necessary.
    Anyway, back to intervention sans acronym: the fiscal sort. Expenditures with obvious common benefits that no individual enterprise could undertake, such as the highway system and much basic research, are an obvious longer-term win. They create opportunities and incentives for private enterprise while introducing a positive demand shock for labor and materials.
    Unemployment and food benefits, while desperately needed from a humanitarian point of view, are only consumptive and create no private incentives. I don’t believe they create a foundation for longer-term recovery.
    Finally, we have to be really careful of crowding out demand for capital. While nominal yields are showing no warning, real interest rates on T-bonds as measured by TIPS differential for 5 years hit 3.74% tonight. That’s really high, the highest it’s been in many years. This is a strong further disincentive to any private investment.
    Personally, I favor monetization above Keynesian intervention at this point. But that’s only because I’m nuts.

  2. ndk

    P.S. More on topic, apologies, aren’t there significant limits on the gross amount of stimulus we can provide via food stamps and unemployment? Food is a small portion of GDP and household budgets these days, while unemployment (by U-3, at least) is still only a percent or two over long-run averages. Those ain’t going to close much of an output gap.

  3. DickF

    I am amused and amazed that anyone actually still believes this stuff. If the government gives a dollar (food stamps) to a homeless person holding a sign saying, “Will work for food” it will save our economy because he will go buy wine (with his now disposable income) and everyone will be better off.
    But where did that dollar come from? The homeless person is supported in his homelessness and will go sleep under a tree rather than getting a job taking out someone’s trash, so have we increased productivity? That dollar and all of the other dollars given the same way are taken from those who actually produce. So what this does is reduce production on both sides of the transaction. The multiplier actually multiplies waste and malinvestment.
    The whole idea of a multiplier is fraught with inefficiency. A portion of consumption goes to inflation, a portion goes to waste, and in the end the whole economy is pushed into disequilibrium and must expend capital to overcome the distortions.
    When I was in grad school none of this made sense but I could not articulate why. The interesting thing is that neither could my teacher. His assumptions were so great as to be foolish. I passed the class by regurgitating what I was fed but only later did I understand that this kind of foolishness is what contributed to the unemployment of the Great Depression.
    As is so often the problem the assumption is that government spending is magic so any deeper analysis is unnecessary.
    Welcome back to the past.

  4. kharris

    You may be right that food stamps and jobless benefits won’t generate as much spending as we need, but their ability to generate lots of spending for a dollar of cost to the Treasury suggests we should err on the side of generosity in those programs. They should be first on the list of fiscal stimulus efforts every time.
    Note that a FICA holiday is also very efficient, and we can have as much of that as we want. The problem there is accounting. The drive to end Social Security in its current form has been relentless, and there is every chance that the SS hit-squad would argue that any FICA holiday should be chargable to the Trust Fund, so that, “Oh, Look! The Trust will be insolvent (sic) even sooner.”
    As for big infrastructure projects, heck let’s toss in a big old national green goal and build a national public transit system.

  5. SvN

    NDK: “I dunno. I’m Keynesian to the point of reading and loving his General Theory …I’m getting pretty worried about government backstops and alternatives disincentivizing private expenditure and investment. We’ve seen many fundamental markets touched by the well-meaning hand of government become completely dysfunctional: mortgage lending, commercial paper, money markets, and even inter-bank lending.”
    I feel I’m in an Orwellian nightmare when the word “Keynesian” has been warped to this degree.

  6. SvN

    Menzie Chinn: “… if we were to undertake any fiscal stimulus aimed at stabilizing the economy at the short to medium run, we should aim for aid to the states and localities, increases in unemployment insurance, and buttressing infrastructure spending.”
    I’m just wondering about the assumptions underlying the multiplier on transfers to state governments. I suspect how they use the funds makes a difference; i.e. is it used to reduce their primary deficit, offer tax cuts, invest in infrastructure, hire more economics professors at state universities, etc.

  7. James Kwak

    I believe ndk is right that food stamps and unemployment benefits, while desirable for the reasons Menzie cites, are not going to be good for large increases in GDP. The Center on Budget and Policy Priorities is recommending an outlay of $5-12 billion on increased food stamps and $6.5 billion on extended unemployment benefits. (See Robert Greenstein’s comment on http://economy.nationaljournal.com/2008/10/what-should-the-stimulus-plan.php.) Therefore I think that the bulk of the stimulus will have to come in other forms, such as state/local government aid and infrastructure spending. Within the latter category, I think it is appropriate to at least consider large infrastructure projects that will help move us partially off of fossil fuels; there’s no rule that says we can’t make long-term investments that also have a stimulative (or should that be “stimulating” effect?). Larry Summers argued something like this in the FT: http://www.ft.com/cms/s/0/d775399a-a38e-11dd-942c-000077b07658.html.

  8. EorrFU

    The aid to state and local municipalities would directly increase spending. It would either stand in for bond issues that are having a hard time in the current crdit market or would directly augment spending. Many states and municipalities aren’t allowed to run heavy deficits by law and in these states/localities any funding would immediately buttress spending and thus provide a healthy multiplier.

  9. mickslam

    Note that while the multipliers for list 4 are very high, the first two will not have a large enough total effect to stimulate the economy, and the other two have substantial lag times before the stimulus will hit.
    The best solution we have in the short run is a payroll tax holiday.
    DickF, money doesn’t have to be borrowed. It can just be printed. Plus, it doesn’t have to go to homeless people, it can go to working people through a payroll tax holiday.

  10. GNP

    Are Mark Zandi’s multipliers derived using an open or closed input-output model or some synthesis era macro model? If the model is an input-output model, and most of the multipliers exceed the value of one (1), then the I-O model is likely closed.

    Input-output or old synthesis macro model multipliers are sensitive to domestic subsidy levels.

    Multipliers tend to appeal to policy-makers with little or no understanding of national accounting or large macro-level economic models.

    There are plenty of other economic policy criteria that can be used in place of multipliers for targeting counter-cyclical expenditures.

  11. Menzie Chinn

    A Cassel: Thanks for the link — very useful!

    DickF: If you could make a plausible case that we were at an efficient equilibrium now, I think your arguments against the prescriptions I make would be more persuasive. Are you contending that we are currently at an efficient equilibrium?

    I don’t know when you went to grad school, but there’s been a lot of development of theory since the 1980’s. If you got your PhD before then, I suggest the reading
    New Keynesian Economics.

    SvN: I agree — the estimates of the multipliers provided by Zandi must build in a number of assumptions regarding what is done with the funds. Since most states have constraints (legal or otherwise) on borrowing (and are currently experience budget-shortfalls), anything that relaxes the constraint will result in like dollar-for-dollar increased expenditures. Then the question is what is the apportioning between transfers and spending on goods and services.

    EorrFU, James Kwak, ndk, and kharris: I agree that the scope for some expenditures is limited, in terms of stimulating the economy. It seems that the infrastructure and state aid channels have the biggest bang for the buck and plausibility in terms of affecting the output gap.

  12. MalibuRenter

    “One big caveat to the argument for infrastructure spending is that it usually takes a long time to plan such projects.”
    Having worked in this area, let me tell you something. There is quite a backlog of project which either (a) Are already started and could move considerably faster if financing arrived faster. (b) Have been planned for quite some time but haven’t commenced work.
    I remember several projects which were completed ahead of time and under budget because the state decided to accelerate them during construction recessions. Everything is cheaper and easier to get, from skilled labor to equipment rentals.

  13. eRobin

    Investing in food stamps is the most efficient timely (it’s way past time, in fact), targeted and temporary investment we can make to stimulate the economy, which is what we’re talking about here. I think some of the commenters are mixing short term and long term solutions, holding investment in food stamps to long term standards and finding it failing.
    I also think that after thirty years of demonizing people in need, we’re facing some of the unfortunate bias based on Reagan’s horrible Welfare Queen mythology, as evidenced by DickF’s comment.

  14. ben claassen

    Exerpts from two letters:
    A fresh start on Monday at CNN et al reporting of the money crisis may do a service to the nation. The news has been working overtime to fuel the fires of the burning of billions through Wall Street greed. The news is much less worse than what you keep reporting, though there is a problem. Here in the Big Easy, we run on a different business and fun cycle, and I am not seeing the bad news you keep pushing. Bad news invites people who were doing fine to stop spending. That leads to layoffs and creates a bigger problem.
    Case in point– last night Bourbon Street had a very good Friday crowd having fun and freely spending money– finally like pre Katrina. Last Monday, the Saints played on Monday night, the house was full and most people drank their usual 3 to 7 beers and eat freely even with beer at $7 per big cup in the sacred dome.
    Much of the money being spent kept moving since a beer vendor or a bar tender and even more so, a great house musician, get a dollar -spend a dollar. They have no money for stock accounts, 401K’s and big loans. That is where the money needs to go to get it moving–to working people who live by the day.
    The past 8 years have had more money going to rich people who invest, make big deals and spend a lower fraction of their big incomes, so money does not circulate. It is not surprising that huge flow of money for foreign oil pulled money out of the economy and made a major crash in money to the small people.
    So yes, there is a recession. It is very similar to New Orleans. When asked by visitors, How is the city, I can say it is great. Many others feel the same way. But for those who still have not replaced their home, have lived on less income and are still trying to get out of the Katrina hole, things are still bad.
    On the US scale the unemployed, the recent foreclosed due to being unemployed and the low income working poor have the hardest time and need help. Buying bad debt at the top will not stop the cycle. Reporting sad stories with no help for people to understand the hope of a new job, makes the cycle go faster.
    So have a great Monday.
    October 8, 2008
    Mr. Ben Claassen
    614 N St Patrick St
    New Orleans, Louisiana 70119
    Dear Mr. Claassen:
    Thank you for contacting my office to express your opposition to legislation that would have provided up to $700 billion to troubled financial institutions. I appreciate hearing from you on this important issue. You will be pleased to know that I voted against this bill when the Senate recently considered it. It nonetheless passed the Senate on a 74-25 vote.
    As you may know, the legislation would have enabled the Department of Treasury to purchase up to $700 billion in troubled assets, such as mortgages and mortgage backed securities, from various financial institutions. After purchasing these assets, the Treasury could have re-sold them.
    The bill would have also provided some limits on the compensation of executives who turned to the federal government for help. Although members of Congress improved the legislation since its first audacious draft, the bill was still lacking in several different ways.
    First, the bill provided an enormous amount of taxpayer money to bailout our financial institutions without creating the necessary reforms to prevent a crisis like this from happening in the future. If the people of Louisiana have learned anything in the last several years, it is that simply throwing money at a disaster doesn’t fix the problem unless paired with wise reforms to the practices that failed us. The bill also didn’t do enough to protect Louisiana taxpayers.
    For example, if the Treasury lost a significant amount of money after purchasing the troubled assets, the bill required a future president to come up with a plan as to how the federal government can recoup this money from the various financial institutions. This simply was not good enough. The bill should have provided explicit procedures for recovering the taxpayers’ money.
    Finally, the bill did not go far enough to assist families who are fighting to make ends meet. Communities across Louisiana are still struggling from the effects of the recent hurricanes. We shouldn’t be rushing to the aid of Wall Street without first addressing the challenges that families across Louisiana face.
    It is my hope that the Congress can produce a more balanced bill that protects Louisiana taxpayers while ensuring that our economy remains strong. I appreciate the opportunity to hear from you and I hope you will continue to contact me on issues of mutual concern.
    Please also feel free to visit my website at http://landrieu.senate.gov for more information on legislative affairs.
    With warmest regards, I am Sincerely,
    Mary L. Landrieu United States Senator MLL:aar
    I appreciate your email and see your points about the non-workable elements of the “bailout” as on target.
    So with the bailout likely to pass, what is next?
    You mention the root cause of the financial downturn and I believe that there are better ways for the Federal Government to act versus doing nothing.
    Simply swapping the “named owner” of bad loans from a private institution to the Federal government does nothing fundamentally to correct the problem. The upward trend in housing foreclosures, if not stopped, will lead to another bundle of bad debt for someone to take on, all with the myth that these loans will have a future value.
    If taxpayer money is to be used, a better approach is to offer work opportunities to people who are in default on mortgages with some of their “temporary pay” for their community service work used to make partial payments of their mortgage. The gradual flow of cash into the system and into the lending system will provide a longer term improvement in the economy. The program could flow the money through state unemployment office to the people who need it most. The idea is somewhat like the taxpayer rebate program but directed at people who need temporary work while the economy grows. These people will be very likely to spend the money since they are in financial trouble.
    I still would like to hear more on the $3.9B that was to help homeowners with loan problems. How did that work so far?.. money spent to date?
    Ben Claassen

  15. S

    It is no surprise the idea of infrastructure spend is immediately bandied about. it is like the FT running a salvo to Keynes last weekend. Infrastructure (for the mater spend) is about as reflexive as raise taxes for the the left/right (governement generally). it is all the more ironic that back in the 30s and even the highway system per se where accretive to the national project. Repaving a road or building a bridge is nothign more than a work project. if we are going to destroy some more capital, perhaps it might make sense to do a little swat analysis and determine how that bridge increases our competitiveness in the world. Something tells me R&D grants have a higher expected value than a new 59th street bridge. This whiole exercise is like the thought exeriment in the early 30s to hold wages high so peoploe spend. The logic is so twisted it is embarrrasing.

  16. Don the libertarian Democrat

    From Alan B. Krueger this morning in the NY Times “Reforming Unemployment Benefits” :
    “In addition to extending benefits, several other potential reforms to U.I. deserve attention. ”
    1) Make employers with worse layoff records pay more.
    2) Help underfunded state programs
    3) Raise tax base cap
    4) Base extension on state problems with employment
    5) Raise benefits in certain states
    Here’s my response:
    Unemployment Insurance would be a more effective stabilizer for the economy if benefits were automatically extended in a state based on the conditions on the ground.
    You might also want to target any stimulus money to such regions as well.

  17. Charles

    So, Menzie… it sounds as if we should find Nowhere, and build as many bridges to it as possible.
    That or fire everyone and give them unemployment and Food Stamps.
    (disclaimer for the humor-impaired: just kidding)

  18. mmckinl

    Simple …
    Medicare for All …
    Re-capitalize companies, states, local governments, the self employed and the uninsured …

  19. Dean

    I’d be interested in seeing the multipliers for a longer term view. Perhaps the cumulative effect over 3 to 5 years rather than a 1 year change.

  20. DaveinHackensack

    A couple of thoughts:
    1) Mark Zandi’s stimulus options don’t include the injection of capital into banks (unsurprisingly, since few were considering it then). Theoretically, there ought to be more bang for the buck in that than anything else, since a bank can lend out $10 or more dollars for every $1 of capital. In practice, I think the problem here is that banks don’t charge interest rates high enough to compensate them for taking on the risk of lending in this environment. The government could probably get more bang for its buck by extending lines of credit to non-traditional lenders (e.g., American Microloan) that charge high enough rates to profitably loan to small businesses.

    2) The usual caveat about infrastructure spending — that there are long lag times involved — seems questionable, if infrastructure spending is limited to maintenance projects that already have local regulatory approval.

  21. benamery21

    I agree with pretty much everything you’ve said…
    As another category of infrastructure spending which avoids the “outside policy lag” please consider the idea of a dollar for dollar tax credit (up to reasonable cap levels) for homeowner expenditures on certain differentially qualified “distributed infrastructure” expenditures. For instance, home energy audit, home weatherization/insulation, window replacement, solar water heating, geothermal heat pumps, natural gas piping in all-electric homes, certain appliance replacements, grey water systems, energy efficient lighting retrofits, electronic thermostats, modern wood stoves, ceiling fans, landscaping retrofits for water/energy efficiency, etc.
    On financing this stuff, require banks to provide this financing (with a federal guarantee) at their cost of funds plus a minor adder (to be included in rebate) up to the cap, on presentation of an invoice, until tax returns are filed. Rebate checks to go directly to the lender.

  22. aaron

    “it sounds as if we should find Nowhere, and build as many bridges to it as possible.”

    Yes, exactly. As the song goes, “If you want to have cities, you’ve got to build roads.”

    And as I like to say, money is just a counting device, what we choose to count gives it power. Ultimately, it’s all about human interaction and what we can do to facilitate “good interactions” and prevent bad ones (e.g. violent crime and conditions endemic for disease). Well planned infastruction is a good way to do this.

  23. Charles

    Aaron, while I was kidding in my comment, I was trying to make a larger point: it matters what one spends things on. Good investments increase productivity, which is typically where their multiplier effect comes from. Building bridges to nowhere employs people but has no multiplier effect.

  24. Tom

    Targeting infrastructure dollars to the states would be a good way to get projects started quickly. Most every state has a capital improvements plan, with projects that are in design, and for which design could be completed quickly. There is a big backlog of projects to be built, and they could be started quickly.

  25. Randy Miller

    I strongly agree with those writers who say we can get infrastructure spending moving fast. In Iowa, for instance, there are quite a few highway projects and bridge projects that have been pushed back in the five year plan for lack of money. Bernanke was testifying the other day and had the same concerns about infrastructure spending taking too long, and I just started laughing, because he is out of touch on this one. Pressure your congressman to funnel the money directly to the states, with the proviso that the money has to be spent to accelerate current projects in their five year plan, and that it should not go to replace dollars from the state tax coffers. If the feds give Iowa 2 billion dollars for infrastructure, and Iowa just uses it to replace state dollars, then it is no more effective than a tax rebate.
    And….as to the idea of direct capital injections to the banks, based on the idea that for every dollar injected they will lend $10, well, we are now finding out that a lot of the direct capital injections will go for acquisitions, and to increase bank reserves. It has some effect as far as increasing confidence in the banks, but minimal stimulus effect. Allan Greenspan will rue the day he confessed to a congressional hearing that he had trusted the banks to do the right thing. He sounded naive. There are a lot of bankers out there who are responsible, and work for the best interests of their shareholders, depositors, and their communities. Unfortunately, we have seen that there are a lot out there who cannot be trusted, and will pursue improving their own paychecks to the detriment of shareholders, depositors, etc.
    We do not need heavy handed regulation that is paperwork and form intensive, where businesses pay a lot of salary money to compliance staff. We DO need rules, and we need those rules to be enforced.

  26. DickF

    House Speaker Nancy Pelosi called Wednesday for a lame-duck session of Congress that could take up a proposal for a $61 billion stimulus package the House passed Sept. 26 but which stalled in the Senate. It provides money for states, roads and bridges, unemployment insurance and food stamps. http://www.mercurynews.com/business/ci_10908504
    It looks like Pelosi hear your call.
    Interesting, not one thing said about those who actually produce.

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