The problem with New Keynesian models of optimal policy rules

Many New Keynesians point out that there is a class of flexible inflation targeting rules that perform better (from a welfare perspective) than NGDP targeting.  This is true.  In a previous post I pointed out that I agreed with Woodford’s claim that NGDPLT is not in general the “optimal” policy rule.  After reading some comments I realize that I need to amend that post.  That’s because I don’t accept the validity of the New Keynesian models that show flexible inflation targeting is superior to NGDPLT, and should not have implied that I did.  I view a completely different rule—nominal wage targeting—as being the theoretical ideal.

[My first line was poorly worded--I meant "a class of models with flexible inflation targeting rules that perform better . . .]

I just noticed that George Selgin left a comment that nicely characterizes my objection to new Keynesian monetary models:

I think that Scott and others are granting far too easily the “nominal GDP targeting isn’t optimal but it’s a good pragmatic solution” argument. Having looked closely at Woodford’s work, and at other work in the same vein, I find that somewhere there is always a loss function, not always implicit, that treats fluctuations in P as “bad,” but without supplying any compelling justification for doing so. Instead, there’s some rather transparent hand-waving that amounts to saying that this treatment itself is “not optimal but pragmatically justified” or something like that. (The same, by the way, can be said of Wicksell’s own argument for treating zero inflation as optimal–that is, for equating a policy that achieved it with one that kept interest rates at their “natural” levels. In fact his argument here goes through only if productivity growth is constant, which of course it usually isn’t.)

Of course, it’s almost certainly true that no particular NGDP (or nominal income) target is “optimal.” But it doesn’t follow that it isn’t at least as optimal as the usual alternatives. And there are now a number of studies, DSGE and otherwise, supporting this conclusion.

I agree with George 100%.  I’ve often argued that the supposed “welfare costs of inflation” are better thought of as the welfare costs of volatile or excessive NGDP growth.  This also has implications for the supposed “lack of models” in the market monetarist camp.  I believe that I have provided models, but that other economists don’t recognize them because they don’t know what a model is.  They think (wrongly) that a model is a bunch of equations.  Don’t get me wrong; equations can be useful.  I once published a model with equations showing the optimality of wage targeting.  Another time I did the same for NGDP futures targeting.  But in all truthfulness the equations in those papers merely demonstrated what was already intuitively obvious given the model’s assumptions.

Here’s what a lot of economists don’t realize.  We aren’t yet at the stage where mathematical models can show which policy is best.  We simply don’t know enough about the welfare costs of inflation.  Obviously if you think the CPI is a good proxy for the welfare costs of inflation, then inflation is likely to play a role in your optimal policy rule.  And if you think (as George and I do) that NGDP is a better proxy for the welfare costs of inflation then NGDP may play a role in your policy rule.  That’s just common sense.

In the 1970s Milton Friedman argued that macroeconomics had advanced beyond Hume in one respect only—we now know how to deal with the first derivative of nominal changes.  In the 1920s economists debated macro issues using words, not equations.  There’s something to be said for going back to that approach.


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32 Responses to “The problem with New Keynesian models of optimal policy rules”

  1. Gravatar of Andy Harless Andy Harless
    16. September 2012 at 15:22

    It seems to me, even if you accept Woodford’s type of loss function, that there could be a class of models in which the optimal rules use NGDP targeting. Surely, in the real world, the credibility of a rule is inversely related to the number of parameters. If this feature were part of the model, then there would be a benefit to constraining the inflation and output parameters to be equal. (And one could also try to model the way having to estimate potential output reduces credibility relative to a rule that incorporates a constant growth rate.)

  2. Gravatar of Morgan Warstler Morgan Warstler
    16. September 2012 at 15:31

    Undiscussed:

    1. DeKrugman primarily supports NGDPLT because it means immediate QE.

    2. Sumner if pushed, will take NGDPLT with no make-up… he’s willing to roll dice, on if after we raise rates, we slow down enough to need QE in future.

    Since we know it is not discussed, and it is the FUNDAMENTAL difference between them…

    Why is it not discussed?

  3. Gravatar of George Selgin George Selgin
    16. September 2012 at 16:03

    Some things that formal models need to allow for if they are to be useful in comparing the performance of nominal income targets with inflation or mixed inflation-output targets:

    1) no nominal magnitudes in loss function, implicit or otherwise;
    2) real output, and especially total factor productivity, innovations;
    3) if price stickiness is allowed for, e.g., by Calvo pricing or something like it, different degrees of stickiness for AD vs. AS innovations (see Okun for intuition);
    4) “full information” or equivalent (e.g., Walrasian pricing) counter-factual for welfare comparisons.

    Some models get pretty close, e.g., Schmitt-Grohe and Uribe’s “Medium Scale” one–but no one has done (3) yet (kindly give me at least a footnote if you take it on–I’d do it myself but I’m hopelessly addicted to words).

  4. Gravatar of Bill Woolsey Bill Woolsey
    16. September 2012 at 16:42

    I think nominal GDP level targeting is less than perfect largely because it allows too little change in the price level in response to aggregate supply shocks. If demand is not unit elastic, then spending in the rest of the economy must shift if total spending is held constant. While this shift in spending could signal a need to shift resources, the appropriate amount depends on supply elasticity, or more fundamentally, on resource subsitutability.

    For example, suppose the demand for gasoline is inelastic and the supply is pefectly inelastic. Supply shifts to the left, the price level rises, and total spending on gasoline rises. The rule requires spending in the rest of the economy. While this properly signals the need to shift production to gasoline in some general sense, the supply is perfectly elastic. No resources from the rest of the economy can be absorbed into the production of gasoline. Spending, prices, an nominal incomes in the rest of the economy drop to offset the increase in prices, spending, and nominal incomes in the gasoline industry.

    It seems to me that in this situation, it would be better for nominal GDP to rise. Spending in everything else but gasoline would stay the same, and spending on gasoline rises.

    The prices of everything else stays the same, and the price of gasoline rises.

    If the demand for gasoline is elastic, then a decrease in supply results in less spending on gasoline. With total spending fixed, this implies more spending on everything else. Spending, prices, and nominal incomes in the rest of the economy must rise.

    So, the central bank should examine each supply shock, determine the elasticity of demand and adjust the target for nominal GDP accordingly. It should simply be to allow total spending to change by the change in spending in the industry with the supply shock, because supply isn’t perfectly inelastic. Some adjustment in spending in the rest of the economy is appropriate.

    Now, if the disruption in the rest of the economy could be summarized by an “output gap,” then adjusting the target for the price level according to the gap appears to solve the problem.

    For example, the supply of gasoline falls and the price of gasoline rises. With a price level target, nominal GDP would need to fall enough to push down other prices enough to offset the increase in the price of gasoline. But this reduction of demand would open up an output gap, and the target for the price level would be increased until the output gap closes.

    Now, I think that if the demand for gasoline is unit elastic, the result would be the exact same as a nominal GDP target (perhaps with perfectly inelastic supply.) In other words, the target for the price level would rise to a level where nominal GDP is the same. However, the price level would actually rise to the level needed to close the output gap. Presumably, with inelastic demand for the good with the decrease in supply, this would involve bringing spending on everything else up to where it started less any resources that can and should be shifted to producing the good with the adverse supply shock. (That is the increase in quantity supplied due to the higher price.)

    Now, do I really have much faith in estimates of potential output? No.

    What I know is that the price level and inflation rates are the wrong target. Presumably, adjusted the target for the growth path of nominal GDP according to the output gap would do better than starting with a price level target.

  5. Gravatar of Benjamin Cole Benjamin Cole
    16. September 2012 at 17:28

    Economists and their models remind me of anthropologist Ruth Benedict, and the rap on her—that she always found what she was looking for. If she was in a “matriarchal society” kick, sure enough the tribe under observation was a matriarchy.

    Having constructed a few models in my hard school days, everyone knows that can be jiggered by choosing the right time frame, or budging coefficients, or whatever.

    Long time ago there was a famous economist who put together and published model proving Social Security depressed savings rates, and then someone went through the model and found a denominator/numerator was flipped.

  6. Gravatar of D.Gibson D.Gibson
    16. September 2012 at 17:53

    Are there other factors for what is “optimal” like the inaccuracy of measuring inflation or the political difficulties of a policy that require elaborate re-targeting of inflation rates?

    There are certain conditions where F=ma doesn’t hold, but it is good for anything I need. Same with NGDPLT.

  7. Gravatar of ssumner ssumner
    16. September 2012 at 17:59

    All good points. In my view the labor market is the number one macro problem–by far. If monetary policy leads to steady growth in nominal wages (at say 3% per year) it means the labor market is (roughly) in equilibrium. And if that’s true, everything else is basically a micro problem by comparison.

    I’m not too concerned by things like the price of magazines moving temporarily away from the equilibrium price due to stickiness–it’s a trivial problem if we keep the overall labor market in equilibrium.

  8. Gravatar of Morgan Warstler Morgan Warstler
    16. September 2012 at 20:14

    Undiscussed. Why?

  9. Gravatar of Saturos Saturos
    16. September 2012 at 22:31

    “I believe that I have provided models, but that other economists don’t recognize them because they don’t know what a model is. They think (wrongly) that a model is a bunch of equations.

    … But in all truthfulness the equations in those papers merely demonstrated what was already intuitively obvious given the model’s assumptions.”

    It’s remarks like these that reassure me that Scott truly is a really smart guy.

  10. Gravatar of Morgan Warstler Morgan Warstler
    16. September 2012 at 22:53

    Saturos +1

  11. Gravatar of Luis Pedro Coelho Luis Pedro Coelho
    16. September 2012 at 23:45

    The real estate market can suffer from zero-lower-bounds too and it, too, is an important market in people’s lives (Lisbon is full of “for sale” adds on apartments and the market does not move; some apartments have been on the market for years before the owners drop the nominal price by 10%).

    Nominal wages are definable in theory, but very hard to measure (and likely to move due to tax-changes in non-monetarily relevant ways as compensation shifts between wage and non-wage forms). Is this your reason for not pushing harder for nominal wage targets? Or are you worried about the public choice mess that would ensue?

  12. Gravatar of Peter N Peter N
    17. September 2012 at 02:15

    An NGDP rule is certainly an improvement over an inflation rule, but it neglects asset prices. Research seems to show that when the distribution of economic results is fat tailed, a boom in asset prices, particularly real estate prices (because real estate is less tradeable?) increases the probability of an extreme fluctuation in GDP or CPI.

    This is exacerbated by the peculiarities of NIPA which was not designed for the purposes to which you propose to put it. In particular, if you look at published mathematical models, you’ll find that they often use an adjusted form of GDP that corrects for whatever they perceive to be its problems (for example, undoing imputed real estate income is a common adjustment).

    This paper looks at the effect of asset booms on the probability of extreme GDP and CPI results with different lags. This is a bit from it:

    “A recent study by Cecchetti [2006], however, provides a compelling rationale as to why asset prices ought to matter for monetary policy (and why central bankers ought to sleep less soundly at night), quite apart from any possible effects such asset prices may have on the mean values of variables of interest. The empirical evidence he provides is that housing and equity price booms raise the risk of particularly bad macroeconomic outcomes occurring in his sample of developed countries, whose price-level and output gaps are characterized by so called ‘fat tails’. A distribution characterized by such ‘fat tails’ is one in which the probability of being in the tail of bad outcomes, for example, is higher than if the distribution were normal. Hence, if asset price booms significantly raise the risk of extreme bad events occurring, i.e., being in the tail of bad outcomes of a distribution, the existence of ‘fat tails’ will worsen the expected losses from asset booms.

    This may have potentially important implications for the conduct of monetary policy. It may be myopic and counterproductive for a central banker to focus exclusively on minimizing a quadratic loss function around the mean values of variables of interest to the neglect of the risk of extreme events occurring if asset booms make such tail events more likely. An approach that is ex-ante more actively compatible with risk management may be appropriate.”

    http://www.bis.org/repofficepubl/arpresearch200802.2.pdf

    There is also an element of moral hazard to confining central bank bubble policy to compensating for the damage after the fact. This gives financial institutions an implicit put from the government. We’ve already seen signs of this, and actions such as the government’s assuming the banks’ counter-party risk in the AIG case, however necessary it may have been can hardly help. This transfer of risk from the financial sector is very undesirable viewed from a utility perspective, and logically leads to a concentration of resources in the sector because of the superior returns from transferring risk (The government’s implicit guarantee of the major banks has been estimated to be worth 1/2%, which is huge).

  13. Gravatar of Bill Woolsey Bill Woolsey
    17. September 2012 at 03:42

    Peter N.

    At first pass, I would say that we now know that an interest rate instrument and an inflation rate target (even when combined with an output gap target) is not robust against the finanical instability.

    What evidence do you have that a base money instrument and a nominal GDP level target has the same problem?

    As for the “moral hazard” this would generate, a monetary regime that is subject to Great Depressions from time to time should make people more careful about bidding up asset prices. So?

    The notion that central banks should be focused on regulating financial markets, chiefly preventing speculation, and considering recessions to be the inevitable result of past speculation is the conventional wisdom of the ages. And it is entirely wrong. It is based upon a confusion of money and credit.

    Central banks create money, and an imbalance between the quantity of money and the demand to hold it generate changes in spending on output.

    An individual bank that makes bad loans will lose money and maybe fail. Avoiding making loans into speculator bubbles is wise. If a bank has already made such loans, continuing to lend more and more rather than just “liquidate” and take the losses is a mistake.

    For a small open economy with a fixed exchange rate, there are some parellels and we can imagine a “central bank” regulating the banking system along those lines and perhaps doing some good.

    But when we are speaking of a central bank that creates the money for the economy, this approach is compeltely wrongheaded.

  14. Gravatar of Brano Brano
    17. September 2012 at 04:24

    “In the 1920s economists debated macro issues using words, not equations. There’s something to be said for going back to that approach.”
    -
    Perhaps there is, but I think you can afford this because you have an experience with equations in economics. The equations helped you to build up your big picture, so now you do not need equations anymore.
    -
    The approach “without equations” is actually nothing new in Central and Eastern Europe. This is how they teach economics all the time. But nothing good came out of it.

  15. Gravatar of Saturos Saturos
    17. September 2012 at 04:43

    Brano, so we have to go back to the general power of reason, which predates written mathematics. Intelligent debate has always been employed to separate good ideas from bad. Mathematics helps to settle the debates by stating things in logical form, incorporating them into an edifice of mathematical truth – but for those who can already reason well mathematics is sometimes just a distraction. It’s mathematics that is there to capture our ideas, not the other way around.

    I suspect you didn’t need much mathematics to see what was wrong with some of the teachings you were getting in Eastern Europe. Neither does a smart person need a lot of mathematics to see that e.g. old Keynesian economics doesn’t make enough sense.

  16. Gravatar of W. Peden W. Peden
    17. September 2012 at 04:54

    Peter N,

    Since (a) PT doesn’t equal PY and the relation between the two has become unpredictably distant over the past 30 years or so, (b) one instrument can only hit one target in one time period, and (c) and since the central bank has one instrument (the supply of base money) it cannot control both PT and PY at the same time.

    Insofar as asset prices are a problem, they are a problem for regulatory (or lack thereof) policy.

    Governments have four broad sets of economic policy tools, which can hit a maximum of four objectives, e.g. -

    1. Monetary policy: stabilise nominal expenditure by adjusting the money supply in line with the demand for money.

    2. Fiscal policy: stabilise private financial expansion contraction by stabilising government saving/borrowing.

    3. Labour market policy: lower the natural rate of unemployment so as to minimise secular unemployment.

    4. Financial regulatory policy: remove externalities from asset price swings, so that right to profits = liability for losses for any given asset.

    (That’s based on a slight expansion of Nick Rowe’s framework from an excellent blog post a while back where he described the difference between the Old Keynesian policy framework that was popular in the 1960s & 1970s and the modern post-monetarist policy framework.)

  17. Gravatar of Mike Sax Mike Sax
    17. September 2012 at 05:19

    Morgan don’t you get the idea that the window for the time to get a pissing war between Scott and Delong has bascially closed.

    At this point nobdoy really cares in the post New Frontier we now live in.

  18. Gravatar of B B
    17. September 2012 at 05:48

    “But in all truthfulness the equations in those papers merely demonstrated what was already intuitively obvious given the model’s assumptions.”

    Not everyone’s intuition is as good as yours. (That’s not snark, that’s a compliment.) I think without equations, economists would have an even harder time convincing each other. You can refute an obnoxious seminar attendant by pointing to the equations and the black and white results they offer.

  19. Gravatar of Andy Rowell Andy Rowell
    17. September 2012 at 06:02

    On the FAQ http://www.themoneyillusion.com/?page_id=3447

    which is also quoted in http://www.businessinsider.com/who-is-scott-sumner-2012-9
    there is a typo:
    The “less” is missing.

    The spread is currently *less* than 1/2% on two year bonds, which means inflation expectations are far too low for a vigorous recovery. It should be closer to 2%.

  20. Gravatar of Brano Brano
    17. September 2012 at 06:23

    Saturos,
    I almost completely agree with this: “mathematics helps to settle the debates by stating things in logical form… and It’s mathematics that is there to capture our ideas, not the other way around.” (almost completely, because I think there are situations when you can come up with a new idea just by knowing some mathematical theorem)

    But does it imply that we should go back to economics without equations? Most of the economists are not that smart to solve for the equilibrium in words. And isn’t it the same as saying that we shall stop using graphs? Yes, using graphs in a bad way can be misleading, but that is not an argument to stop using them.

    “I suspect you didn’t need much mathematics to see what was wrong with some of the teachings you were getting in Eastern Europe.”

    Yes, part was an obvious non-sense. But you realize that almost all of the stuff is non-sense only after you study abroad.

  21. Gravatar of W. Peden W. Peden
    17. September 2012 at 07:26

    As an example of a model being only as good as its assumptions, Alec Cairncross once waited patiently as someone scrawled a long, long series of equations on a blackboard until they’d covered most of it, before asking-

    “While all that’s happening down here, what effect is it having on everything up here?”

  22. Gravatar of johnleemk johnleemk
    17. September 2012 at 11:07

    Re the politics of the Fed, Matt O’Brien calls for markets in central bankers: http://www.theatlantic.com/business/archive/2012/04/how-much-is-a-good-central-banker-worth/256089/

    It wouldn’t be enough just to import Svensson. As L.A. Galaxy fans can tell you, bringing in one (albeit, overrated) superstar like David Beckham doesn’t help much if his teammates are only mediocre. We’d need to create a Federal Reserve board equivalent of the Super Friends for Svensson to make the biggest difference. We might even find out that we already have a superstar in Bernanke in that scenario.

  23. Gravatar of Saturos Saturos
    17. September 2012 at 11:20

    Brano, I absolutely agree that mathematics can be very helpful in clarifying our thought. In fact I’d go further: there simply isn’t a sharp distinction between mathematics and non-mathematics, when it comes to sufficiently advanced mental activity. My point is simply that it is regrettable we are in a place today where journals (indeed, even college tutors) will reject you for explicating a good argument or “model” of a situation (which can approximately be described as just a “clear and communicable mental picture”) through good verbal reasoning, but will happily accept the same thing when stated “formally” i.e. as a series of algebraic expressions. Which is ridiculous, I mean it’s not as if they would be interested in a full derivation from first-order logic. Anyway, my point is that pieces like what Scott and some of the other MMers have been blogging not only deserve to be in journals, but also should not be “sidelined” to journals reserved for qualitative pieces (JEP). If most economists aren’t reading stuff like what’s on this blog, it’s their loss. Because the thinking and content here is as intelligent as anything being written by any other economist right now, and most would learn more from reading this – even if only to disagree with. As many (David Andolfatto, Miles Kimball, Noah Smith) have already found.

  24. Gravatar of Patrick R. Sullivan Patrick R. Sullivan
    17. September 2012 at 11:24

    ‘…there was a famous economist who put together and published model proving Social Security depressed savings rates….’

    According Tom Sargent that was the purpose of SS; to counter the capital glut many believed existed at the time.

  25. Gravatar of Saturos Saturos
    17. September 2012 at 11:31

    Garett Jones’ latest is very interesting:
    http://econlog.econlib.org/archives/2012/09/bad_balance_she.html

  26. Gravatar of Greg Ransom Greg Ransom
    17. September 2012 at 12:41

    How is that government sector intervention in the labor market working out for you macro guys? Sticky & unsustainable government union worker compensation contracts, rockets-to-the-moon minimum wage rate increases in major U.S. labor markets, pathological compensation mandates and regulatory nightmares in the labor sector, eg pathological workers comp in California, pathological health care & insurance mandates, tax schemes & general chaos, etc.

    What you are admitting, Scott, is that the microeconomics of labor markets is the functional core of macroeconomics.

    “In my view the labor market is the number one macro problem–by far.”

  27. Gravatar of RebelEconomist RebelEconomist
    17. September 2012 at 14:26

    I agree; expressing models in equations often obscures the vacuous nature of the assumptions that drive the conclusions and gives the work a false air of precision, as well as wasting everyones’ time creating and decipering such a tedious style of communication, but economics has got itself into a “emperor’s new clothes” rut in which to protest against equations is taken to suggest intellectual weakness, which automatically discredits the criticism. I sometimes wonder whether, for all his reputation, the contribution of the likes of Woodford to the understanding of monetary policy is actually negative.

    And, in this spirit of seeing the wood for the trees, I would point out that this whole idea of optimal policy rules is based on the questionable assumption that the central bank is the only institution running economic policy. In my view, the central bank should stick to a relatively narrow role of providing the right amount of money to facilitate transactions, which should be judged by price stability, because their are other institutions, principally the government, that should be concerned with real economic peformance. I would say that central bankers have foolishly allowed themselves to become regarded by the public as “controlling the economy” in general, which has allowed the politicians to avoid tackling contentious structural reform such as taxation changes, education and labour laws etc.

  28. Gravatar of John Larison John Larison
    17. September 2012 at 15:05

    Here’s my two cents as someone from a “hard” science (comp sci and physics) and math background. The point of the math in a model is to allow the model to easily make clear predictions. A model that does not make clear and accurate predictions is of no use. As Scott said, “…the equations in those papers merely demonstrated what was already intuitively obvious given the model’s assumptions.” Every model makes assumptions. What validates those assumptions is the models predictive power, not how much the assumptions “make sense”. What “makes sense” can change depending on who is thinking about it. The number of unemployed Americans, or the average price of a house in California, does not change depending on who is looking at the numbers.

  29. Gravatar of Bill Woolsey Bill Woolsey
    17. September 2012 at 15:15

    Well, I messed up the analysis above. Said elastic instead of inelastic.

    If a particular good suffers an adverse supply shock, and demand is inelastic, then a nominal GDP rule requires spending in the rest of the economy to fall. This signals a need to free up resources in the rest of the economy. If the supply of the good with the adverse supply shock is perfectly inelastic, then there is no need to free up resources in the rest of the economy, since no more resources can be used to produce the good with the adverse supply shock.That is what perfectly inelastic supply means.

    It would be better, I think, if nominal GDP increased, leaving spending in the rest of the economy unchanged, while spending rises in the industry with the decrease in supply. Real income falls, of course, because the unchanged nominal income in the rest of the economy buys less of the good with reduced supply.

    I think it is certain that the optimal change in the price level (and nominal GDP) depends on the elasticity of supply and demand for the particular good with the shift in supply.

    Nominal GDP targeting would be optimal if elasticity of demand is unit elastic and supply is perfectly inelastic. The shift in supply leaves spending on the good with the supply shock unchanged. It leaves spending in the rest of the economy unchanged. There is no need to shift resources between the industry with the shift of the supply and the rest of the economy because the supply is inelastic.

    There is going to be a set of conditions where the shift in spending between the good with the supply shock and the rest of the economy just matches the appropriate shift in resources. Otherwise, it would seem that some shift in nominal GDP would be better.

    However, there is no possible monetary regime that will vary the quantity of money, spending on output, and the price level different amounts depending on the elasticies of the supply and demand of the particular good that has a supply shock. Or, at least, I have my doubts.

    Nominal GDP level targeting is better than price level targeting for supply shocks. Nominal GDP targeting is better than inflation targeting for demand shocks and anticipated supply shocks. Nominal GDP targeting is better than quantity of money targeting for changes in money demand.

    When we look at realistic alternatives, nominal GDP targeting looks good.

  30. Gravatar of Peter N Peter N
    17. September 2012 at 20:47

    @ W Peden

    Unfortunately the fiscal authority is asleep at the switch and probably drunk to boot.

    I’d add another item to your list legal/tax policy – providing the correct incentives.

    This, I think is at the root of our problems. Why, for instance does debt have a tax advantage over equity?

    What can be done with monetary policy, of course depends on where you draw its boundaries. Bernanke has drawn them quite broadly. Is QE3 really monetary policy? Is the Fed going to offer the homeowners loan modifications?

    And, of course, the Fed is a regulatory agency (which it seems occasionally to forget), with newly enhanced powers.

  31. Gravatar of "Most economists don’t know what a model is. They think (wrongly) that a model is a bunch of equations." « Economics Info "Most economists don’t know what a model is. They think (wrongly) that a model is a bunch of equations." « Economics Info
    18. September 2012 at 06:02

    [...] Source [...]

  32. Gravatar of Saturos Saturos
    21. September 2012 at 02:14

    Here is another kind of model, no less than the models in our econ textbooks: http://www.periodicvideos.com/videos/006.htm

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