Want to read Slashdot from your mobile device? Point it at m.slashdot.org and keep reading!

 



Forgot your password?
typodupeerror
×
Stats The Almighty Buck

Excel Error Contributes To Problems With Austerity Study 476

quarterbuck writes "Many politicians, especially in Europe, have used the idea that economic growth is impeded by debt levels above 90% of GDP to justify austerity measures. The academic justification came from a paper and a book by Kenneth Rogoff and Carmen Reinhart. Now researchers at U Mass at Amherst have refuted the study — they find that not only was the data tainted by bad statistics, it also had an Excel error. Apparently when averaging a few GDP numbers in an excel sheet, they did not drag down the cell ranges down properly, excluding Belgium. The supporting website for the book, 'This time it is different,' has lots of financial information if a reader might want to replicate some of the results." The Excel error is making the rounds as the cause of the problems with the study, but it's actually a minor component. The study also ignores some post-WWII data for countries that had a high debt load and high growth, and there's some fishy weighting going on: "The U.K. has 19 years (1946-1964) above 90 percent debt-to-GDP with an average 2.4 percent growth rate. New Zealand has one year in their sample above 90 percent debt-to-GDP with a growth rate of -7.6. These two numbers, 2.4 and -7.6 percent, are given equal weight in the final calculation, as they average the countries equally. Even though there are 19 times as many data points for the U.K."
This discussion has been archived. No new comments can be posted.

Excel Error Contributes To Problems With Austerity Study

Comments Filter:
  • by BlackPignouf ( 1017012 ) on Wednesday April 17, 2013 @05:09AM (#43470317)

    Does High Public Debt Consistently Stifle Economic Growth?

    No, finite resources do.

    • by Taco Cowboy ( 5327 ) on Wednesday April 17, 2013 @05:54AM (#43470461) Journal

      Does High Public Debt Consistently Stifle Economic Growth?

      No, finite resources do.

      High public debt drains away valuable resources faster than low public debt
       
      Given the same amount of initial resource, a country with high public debt will have smaller chances for recovery
       
      But then again, most economies (other than that of North Korea) are dynamic, and the amount of resource fluctuates

      • by mcgrew ( 92797 ) * on Wednesday April 17, 2013 @06:08AM (#43470525) Homepage Journal

        But then again, most economies (other than that of North Korea) are dynamic, and the amount of resource fluctuates

        That depends on what you mean by "resources." An MBA Romney-style corporate raider considers "resources" to mean "cash and credit" while someone who isn't a rent-seeking parasite considers things like timber, ore, fuel, and available labor to be resources. The only real resources that fluctuate are labor and renewables.

      • by gutnor ( 872759 ) on Wednesday April 17, 2013 @09:12AM (#43471463)

        At some point the country with more debt has had more money than the other one. What matters is what the country is doing with that extra-resource. As a example, in June 1999, Google was 25 millions in debt, a considerably worst shape than my local kebab place.

        Debt is just an indicator. That's what's wrong with the current austerity measure in Europe. It does not matter what a Country is doing with its money, Europe only cares about the yearly balance sheet and does not give a damn about the future of the country.

  • Excel error? (Score:5, Insightful)

    by Richard_at_work ( 517087 ) on Wednesday April 17, 2013 @05:11AM (#43470321)

    When I read the title, I expected a calculation or rounding issue, or an internal range issue from built in components and not "dumb ass user didn't set the range correctly when averaging". That's not an Excel error, that's a user error - Excel did exactly what it was told to do.

    • GDP = 77.1*850

    • When I read the title, I expected a calculation or rounding issue, or an internal range issue from built in components and not "dumb ass user didn't set the range correctly when averaging". That's not an Excel error, that's a user error - Excel did exactly what it was told to do.

      Not to mention that if you use a reasonably recent version of Excel (at least 2003, which is nearly 10 years old), it'll warn you if you're doing something with a range of cells and it thinks you've missed a bunch of them out.

      It's n

    • by u38cg ( 607297 )
      I agree it is user error, but I feel very strongly that this is the fault of Excel, not the user. My job is effectively being a professional spreadsheet driver and you eventually learn to become rigid about range checking, row counting, balancing totals, etc, because the structure of Excel makes these errors inevitable.
    • There are two factors in play here.

      (1) Likely, they didn't use drag-and-drop to copy the cells, but double-clicking on the fill handle (the same widget used for drag&drop copying) which stops extending the range up to but not including the first neighboring empty cell, not at the end of the table. As such it's perfectly possible to not include the entire cell range while realizing that.
      (2) Having said that, one would expect that whoever makes a model with that much impact double checks their model a
    • Re:Excel error? (Score:5, Insightful)

      by toxicafunk ( 1367319 ) on Wednesday April 17, 2013 @07:06AM (#43470745)
      The real news to me is that academic, world-famous, policy-influencing researchers use Excel instead of, say, R or SPSS, etc.
      • And you should be frightened by that news. Very frightened. Oops, didn't mean to destroy that country's economy. Sorry about the mistake.
      • Re:Excel error? (Score:4, Insightful)

        by tehcyder ( 746570 ) on Wednesday April 17, 2013 @11:45AM (#43473113) Journal

        The real news to me is that academic, world-famous, policy-influencing researchers use Excel instead of, say, R or SPSS, etc.

        Excel is perfectly capable of adding up a few hundred numbers and making a basic chart out of the results.

        Anyway, do you really think that someone who can't copy and paste numbers/formulas on a spreadhseet properly (or, more relevantly, build a model that incorporates some sort of checking of the results to the base data) is going to learn a programming language?

  • Economics. The social "science" with a pretension and envy of physics, practiced by those who couldn't cut it at math or physics.
    • Not sure how you draw the conclusion that it has any desire to be physics.

      If you want to associate economics with another form of science, then you'd probably best compare it to psychology. For example, something simple like supply and demand play directly into somebody's thought process about what something is worth.

    • Re: (Score:3, Insightful)

      by mcgrew ( 92797 ) *

      Wow, what a horrible moderation. Troll? Really? Looks like the idiots from 4chan have mod points today, or maybe a disgruntled MBA. You are entirely correct, I had an undergrad psychology prof say that there isn't a psychologist that there's another calling him a gold-studded liar, the same could be said for economists, who seem to ignore results. Example: Cut taxes on the rich for job creation, ignoring all of history. Even after the Bush cuts (among other mistakes) ruined the economy.

      However, rather than

  • by srussia ( 884021 ) on Wednesday April 17, 2013 @05:25AM (#43470361)
    It's about what you spend it on.

    If you spend it on capital goods that allow you to produce more, that's investment.

    If you spend it on final use goods, that's consumption

    Simple concepts: consumption is not production and not all spending is investment. And yet, look at how Gross Domestic Product is calculated.

    GDP = private consumption + gross investment + government spending + (exports - imports)
    • That is a simple accounting identity, a way to avoid double counting. Income (output, GDP, whichever term you choose) is just the flow of value, and it would be stupid not to include how much value went toward consumption. An economy produces x amount of value in a given year, and those are simply how the value is divvyed up. Some production goes to satisfying consumer demand, and some is held back to build more productive capacity. You're just off base not conflating your own personal semantics for what "p
      • More than that: according to his logic, an "investment" should only count as such it is is successful. I'll leave it as an exercise to the reader to determine how you can possibly decide that, and when.

  • by SmallFurryCreature ( 593017 ) on Wednesday April 17, 2013 @05:32AM (#43470379) Journal

    In Holland at least, financial products must carry a legal disclaimer stating that past performance is no indication for the future.

    What is this entire flawed study? Trying to predict the future, from past performance.

    The Dutch economy is an open economy heavily dependent on the performance of the rest of the world. It doesn't much matter what our leaders do, the rest of the world dictates the state of the Dutch economy. So how do you compare its performance with the rest of world? It doesn't matter what our debt is, it matter how many products Germany ships through Rotterdam. But still, these economists try to compare how The Netherlands fared with X debt against the US which has a totally different economy. How different? The US is one of the bigger countries and is #1 in agri culture. The Netherlands is one of the smallest countries and is #2 in agri culture. Why? Every American black and white cow was created by a dutch boy sticking his arm up a cow. And jerking of a bull. The US exports low value agri cultural products, the Netherlands high value.

    But it means the SAME industry, is COMPLETELY different. Baby cow production US style is cowboys and homo sexuality in the prairy. Dutch baby cow production is bestiality and high tech in the desolate north.

    It is interesting to note that politicians who claim to want the best for big business are NEVER themselves successful big business owners AND that the successful big business owners never ever agree with them. Wallstreet likes the Republicans supposedly (but the two top financial newspapers advised voting against Romney because even a socialist in the white house would be better) but people like Warren Buffet and Richard Branson sing a very different tune. They think the best way to beat a recession is to spend. Not spend recklessly but invest in the future not in handing out tax cuts to buy votes.

    Be wary of any leader who leads out of an ideology and not what is needed right now. Would you go to a doctor whose every answer is "lets amputate"? No? Then why vote for a politician whose every answer is "cut taxes, spend less, except on the pork project I need to get re-elected"? Real leadership is looking at what needs to be done and then do it. Not just have a one size fits all slogan.

    • by 3.5 stripes ( 578410 ) on Wednesday April 17, 2013 @05:47AM (#43470431)

      " a dutch boy sticking his arm up a cow. And jerking of a bull."

      The red light district has changed since I was last there..

    • The US is one of the bigger countries and is #1 in agri culture. The Netherlands is one of the smallest countries and is #2 in agri culture. Why? Every American black and white cow was created by a dutch boy sticking his arm up a cow. And jerking of a bull. The US exports low value agri cultural products, the Netherlands high value.

      But it means the SAME industry, is COMPLETELY different. Baby cow production US style is cowboys and homo sexuality in the prairy. Dutch baby cow production is bestiality and high tech in the desolate north.

      I think the high value of Dutch agricultural products has more to do with the gigantic high-yield flower industry than with jerking of cows. Go over the Dutch border and try to find Dutch cheese. Famous as it is, you will not find the entire dairy island stacked with Dutch cheese outside the Benelux. Visit any flower store in the world, and it's a different picture: you're likely to find a good amount of Dutch flowers. My ghetto neighborhood supermarket sells more packets with Dutch flower seeds than it sel

    • Re: (Score:2, Troll)

      They think the best way to beat a recession is to spend.

      This is mainly because they subscribe to Keynesian thought. The new deal was probably the greatest example of Keynesian theory being applied, and it didn't benefit anything. The war did because it displaced millions of otherwise non-working Americans overseas, which offset the supply of labor in a way that inadvertently triggered a recovery. Keynesian thought was later shattered when stagflation happened in the 80's, which under Keynesian theory is impossible, and demonstrated rather conclusively that gover

  • by Anonymous Coward

    """
    Paul Ryan's Path to Prosperity budget states their study "found conclusive empirical evidence that [debt] exceeding 90 percent of the economy has a significant negative effect on economic growth."
    """

    Nope. "has a[n] effect" is a claim of causation. In reality, all they found was a correlation. And by "reality", I of course mean "made up fantasy land where they can't use excel properly".

    -- FatPhil (AC, as I'm away from home and don't remember my password)

  • About the authors: (Score:5, Informative)

    by oduesp ( 1302043 ) on Wednesday April 17, 2013 @05:47AM (#43470433)

    Carmen Reinhart: (Chief Economist) Bear Stearns -> IMF -> Harvard
                                                \-> married with Vincent Reinhart: FED -> (Chief US Economist) Morgan Stanley.
                                                          famous quote: "Secretary Paulson Makes the Right Call" The Wall Street Journal, Sept. 16, 2008:
    "In other words, some government aid might ultimately have to be directed toward financial firms whose failure would otherwise threaten the financial system.
    The politicians now running for office should also appreciate that their grand ambitions for new spending programs or tax cuts may have to be tempered by the need to rescue financial firms."

    Kenneth Rogoff: IMF -> Harvard

  • by explosivejared ( 1186049 ) * <hagan@jared.gmail@com> on Wednesday April 17, 2013 @05:54AM (#43470459)
    Reinhart and Rogoff have certainly been warning of high debt levels, but it's wrong to give this study too much credit for what "austerity" there has been across Europe. Most cuts in places like Greece and Spain were fait accompli, once it was clear that the ECB was not going to budge on its inflation target to neither try and boost nominal growth nor to crudely relieve nominal debt levels.

    I will grant that the 90% debt/gdp trigger is most likely non-existent, but the rest of their book does yeoman's work in cataloging financial crises. It's a useful antidote to the mass psychological amnesia that is perpetually recurring. "Our new investments our safe and returns will never fall" inevitably leads to "what perfidy caused this?" The cycle has been repeated in remarkably similar ways for nearly a millenium now. We should appreciate the detailed financial history they have created, and chide them for the dubious massaging of the data. Just don't overstate its political implications.
    • by SomeKDEUser ( 1243392 ) on Wednesday April 17, 2013 @07:16AM (#43470783)

      Crises which happened in a world without central banks are profoundly different than those after. In that what was ignorance and foolishness is now malign or incompetence.

      If you read the re-analysis of RR, with the correct data, you see that there is nearly no correlation between debt level and growth. And indeed, crises happen randomly, and so do the rise and fall in debt level. sometimes they meet, but it turns out that most of the time it's just bad luck.

      Should you pile on any amount of debt? probably not. But you also should not worry much about it.

  • by dltaylor ( 7510 ) on Wednesday April 17, 2013 @05:59AM (#43470485)

    When you're cooking the data, try not to make too many obvious mistakes. Of course, had the original propaganda piece, I mean "study", been peer-reviewed by someone who "could do the math" (obviously NOT any economists), this would have been pointed out as total nonsense in the first place.

  • Confirmation Bias (Score:5, Interesting)

    by MetricT ( 128876 ) on Wednesday April 17, 2013 @06:15AM (#43470563)

    http://en.wikipedia.org/wiki/Confirmation_bias [wikipedia.org]

    The researchers got the result they wanted, so they didn't bother to check if they were actually correct.

    And actually, that's being kind.

  • "fishy" (Score:5, Insightful)

    by khallow ( 566160 ) on Wednesday April 17, 2013 @06:17AM (#43470565)

    These two numbers, 2.4 and -7.6 percent, are given equal weight in the final calculation, as they average the countries equally. Even though there are 19 times as many data points for the U.K."

    Why should the UK be given more weight? There's only one such country, not 19 such countries. And the UK data in question is highly correlated (it all comes from the same debt over the same span of time, not 19 different points in the UK's history).

    In addition, the rebuttal ignores two stretches of data:

    RR examines three data samples: 20 advanced economies over 1946{2009; the same 20 economies over roughly 200 years; and 20 emerging market economies 1970{2009. We repli- cate the results only from the first sample as these are the most relevant to current U.S. and European policy debates, and they require the least splicing of data from multiple sources. We focus exclusively on their results regarding means because these have generated the most widespread attention. On their website, Reinhart and Rogo provide public access to coun- try historical data for public debt and GDP growth in spreadsheets with complete source documentation.3 However, the spreadsheets do not include guidance on the exact data series, years, and methods used in RR.

    It's worth noting here that the rebuttal is willing to take data from the period just after the Second World War where a number of countries had high debt and were transitioning from a total war economy (that is, an economy totally focused on winning a particular war to exclusion of everything else, including economic growth) to a normal one - including the 19 year series of the UK mentioned above, and periods of excluded (excluded that is from the original study for unknown reasons) data from Australia, New Zealand, and Canada. All of these incidentally show high economic growth combined with high debt.

    If we're excluding data series due to their irrelevance to current economies, why should these be counted? The US and Europe haven't been in a total war economy since the end of the Second World War. So it is to be expected that one would not see the economic gain (whether or not the debt is present) that one saw in the immediate post-war period.

    The original research seems weak for a number of reasons, but I'm not willing to call it "fishy" on the basis of a rebuttal which makes its own "fishy" assumptions.

    • Re: (Score:3, Informative)

      Comment removed based on user account deletion
      • and you probably ought to weight the figures relative to the size of the coutrys economy to stop outliers having a disproportionate effect
        • by khallow ( 566160 )

          and you probably ought to weight the figures relative to the size of the coutrys economy to stop outliers having a disproportionate effect

          Unless, of course, the large economy is the outlier. Then you made the disproportionate effect worse.

      • by khallow ( 566160 )

        At the very least, you should be comparing growth of (1.024^20 * 100 - 100) = ~60% to -7.6%, rather than 2.4% to -7.6%.

        Which is even more of an exaggeration than taking the same data point 19 times.

  • High debt is bad. (Score:3, Insightful)

    by Karmashock ( 2415832 ) on Wednesday April 17, 2013 @06:20AM (#43470585)

    It means less flexibility.
    More liability.
    Less freedom.
    More waste.

    Say what you will about this study, the governments of the western world are living beyond their means.

    The US government for example is spending about 50k per US household.

    The median income of US households is about 49k.

    That alone should tell you there is a problem.

    To paraphrase Emperor Augustus: "things that can't go on forever - don't."

    These governments are spending well beyond their means and the only way they can presume to maintain it even for a time is through massive inflation. Which will harm the economy, raise interest rates, and generally transition any country that chooses this path into a second world country.

    And even this won't be enough because having destroyed your credit and dealing with increasingly higher interest rates it will only be a matter of time before you can't inflate the currency fast enough to paper over your debt.

    And when that happens... anarchy... blood... social collapse.

    People need to stop deluding themselves that they can magic the debt away as if it won't exist if you don't believe in it.

    It isn't a six year old's imaginary monster. It's our civilization's very real debt. And it will bring us low if we don't bring it under control.

    I also love that they're whining about these austarity measures when many of these countries are still increasing the amount of debt they owe. In many cases, they're simply slowing down... not reversing course.

    If a country can at least tread water without building additional net debt then it's got the situation under control.

    But many do not. The US does not. We spend more every year and the tax recipes and economic growth are not remotely keeping up.

    I know I'm going to get hate mail for this... It's what comes of having an open forum.

    But you can't wish the numbers away through denial. It's like arguing with the Sun.

    • Re:High debt is bad. (Score:5, Informative)

      by Anonymous Coward on Wednesday April 17, 2013 @08:47AM (#43471249)

      "The US government for example is spending about 50k per US household. The median income of US households is about 49k."

      These statements do a great job of conflating median and mean. If you're comparing per household spending to per household income, you don't want median because a small proportion of American households take home a huge amount of income.

      The mean per capita income in 2012 was $42,693 [1]. Per capita spending by the federal government was $11,260 [2]. Total spending including state and local government spending was $19,015.7 [2]. This means that the federal government would be fully fundable with only revenue increases, even with lower taxes than much of western europe.

      The US has a long-term health care problem. In the short term, the US has a small revenue problem and a very large austerity problem (which is actually causing long term harm to the economy). The US, currently, does not have a spending problem from an economic point of view.

      If you want to argue that the US has a moral spending problem like many austerity/deficit hawks, feel free, but don't conflate that with an actual economic argument.

      [1] http://bber.unm.edu/econ/us-pci.htm
      [2] http://www.usgovernmentspending.com/year_spending_2012USdn_14ds1n_F0#usgs302

    • Say what you will about this study, the governments of the western world are living beyond their means.

      Interesting assertion. Now, fire up Excel, and prove it.

    • Re:High debt is bad. (Score:5, Informative)

      by deanklear ( 2529024 ) on Wednesday April 17, 2013 @12:06PM (#43473319)

      You're not going to get hate mail. But you will be told you are wrong, because using the simplistic idea that "debt is bad" to plan an economy is ridiculous How would you explain how startups are successful? When they start, their income to debt levels are completely off the mark, but with investment of capital to improve efficiency and drive sales, eventually they can be profitable regardless of how much their debt to income ratio was.

      With large economies, the principles are the same. If you borrow money to fight wars, there's very little chance of receiving a return on the initial investment, as the Iraq War has proved: over three trillion dollars spent, and nothing but one million veterans with a lifetime of expensive treatments to care for it. If America had instead spent that money on infrastructure improvements, like renewable energy, fiber-to-the-home, or even an improved commuter rail network and efforts to modernize the government itself, we would all be doing very well just as we did during the Space Race. Even making common sense changes, like decriminalizing harmless drugs and ending our for-profit prison system and replacing it with a reasonable mental health infrastructure would not only save us money through simple budget changes, but it would also have extensive monetary effects by reducing recidivism, which frees up police to focus on actual crimes instead of trying to continue functioning as a moral goon squad.

      If you want to understand why America is in such deep trouble financially, all you have to understand is that we lowered taxes for everyone, especially the super wealthy, at a time when we also spent three trillion dollars we did not have on unnecessary wars.

      That's why it's so frustrating to see rambling nonsense like yours modded as insightful. Debt it not scary. It's a concept that we have invented and one that we can redefine or simply do away with using a debt jubilee, or a national reorganization as done by Iceland. Paper money only causes anarchic collapse when people go hungry. And even when there is a massive economic collapse, like the Great Depression, America did not devolve into cruelty. FDR told the rich to pay back the money they swallowed up, and they did, and our economy was further assisted by a massive government spending program, including complete takeovers of private industry for a brief period of time. And that's fine because private enterprises are usually massively inefficient hierarchies controlled by internal politics rather than innovation (see: Microsoft).

      Nowhere in your diatribe against debt do you make any coherent points with supporting evidence from reality. But that's just libertarian economics in a nutshell, I guess.

  • by mjwalshe ( 1680392 ) on Wednesday April 17, 2013 @06:48AM (#43470659)
    Professionals don't use excel for data analysis
  • by Richard Kirk ( 535523 ) on Wednesday April 17, 2013 @07:22AM (#43470823)
    An error with an Excel spreadsheet looses Belgium, and the corresponding warp in the data space plays with the world economy? The only logical explanation is someone in Heaven has hired Douglas Adams to make reality 'more interesting'.
  • I don't normally support Microsoft but in this case I think they're innocent. Excel might have a small error but why isn't the work being duplicated on other statistical programs like Libre Offices spread sheet or programmed using R. For the work to be valid it has to be reproducible across a wide variety of programs and measurement techniques. I call this one in the name of bad form, just switch programs and the problem could go away.
  • Fun with statisitics (Score:4, Interesting)

    by DarkOx ( 621550 ) on Wednesday April 17, 2013 @07:47AM (#43470907) Journal

    post-WWII data for countries that had a high debt load and high growth

    It would be hard to not have had high growth after WWII for most of Europe. Given most of those economies had been pounded into next to nothing by the war. If you have a GDP of $1 in 1945 and $2 in 1946, why that is 100% year over year growth!

    Next debt load and austerity are not the same thing. The UK had a high debt load post WWII and was also rationing food. So it had high debt AND austerity. Using debt to invest in critical infrastructure like roads and basic sanitation for example you don't have or is no longer workable, and perhaps providing minimal nutrition to the needy is an entirely different proposition than making sure every dope who masters long division gets to hang out for four years at University.

    Public debt is not always bad when there is clear ROI on where the revenues for its issuance are being directed. Debt should not be used to fund blue sky efforts, nor should it be used to provide comfort. If 'austerity' today had any relationship what what it meant in the 1940s-1950s than I might be included to agree it would be going to far for the present situation to justify, but as its used today it might as well just be a synonym for 'waste'.

  • The thing to remember when hearing about all this "austerity" in Europe is that no country in Europe has tried real austerity [battleswarmblog.com].*

    Real austerity is cutting spending until outlays match receipts. As the linked chart shows, the overwhelming majority have raised taxes or continued deficit spending. Some have slightly reduced the ratio of deficit spending to GDP and called it "austerity." They're still digging a hole, they're just doing it more slowly.

    Politicians are addicted to spending to prop up an unsustainable welfare state. They've seen what the future looks like in Greece and they still refuse to stop spending. And the current government of the United States is right there digging with them.

    Austerity hasn't been tried and failed. It's been declared difficult and left untried.

    (*with the possible exception of Estonia and one or two other small countries)

    • Re: (Score:3, Insightful)

      by ljw1004 ( 764174 )

      With US defense spending at 23% of the federal budget and welfare 11%, I wonder why you choose to call it a "welfare state" rather than a "military state"?

      • You appear to have left out "health care" from the "welfare" part, because the graph you got your numbers from didn't call health care "welfare." If you put health care back in - at least, medicaid type stuff - you get an additional ~$900b. In fact, "Defense" and "Health care" have the same numbers. So, put "health care" into "welfare" and you get 24% defense vs. 35% welfare/health care.

        This only includes medical service (seniors) and "vendor payments (welfare)" ... the latter includes things like "grant

  • by the eric conspiracy ( 20178 ) on Wednesday April 17, 2013 @12:55PM (#43473935)

    The authors of the study have posted a response that refutes these criticisms.

    http://www.huffingtonpost.com/mark-gongloff/reinhart-rogoff-research-response_b_3099185.html?utm_hp_ref=tw [huffingtonpost.com]

    The real issue here is not the data which seems to be holding up, but the deeper question as to whether correlation implies causation. It clearly does not - that is low economic growth could be causing high deficits just as likely as the reverse.

    HOWEVER it does seem pretty unlikely that one can claim that high deficits cause higher economic growth. That is the real take away here.

Math is like love -- a simple idea but it can get complicated. -- R. Drabek

Working...