Sunday, December 9, 2012

Gaps and Triangles

James Tobin once said:
It takes a heap of Harberger triangles to fill an Okun gap.
Gregory Mankiw once discussed gaps versus triangles in the context of fiscal policy issues (the 2009 stimulus package). According to Mankiw, Keynesians think of Harberger triangles as small potatoes, and output gaps as large potatoes; non-Keynesians think the opposite. That's certainly consistent with Paul Krugman's view of the world. Krugman quotes Tobin in his post, and states:’s a more general observation that even bad microeconomic policies, which lead to substantial distortions in the use of resources, have a hard time doing remotely as much damage as a severe economic slump, which doesn’t misallocate resources — it simply wastes them.

What's a Harberger triangle? It's a partial equilibrium measure of the welfare loss from a distortion - a tax or monopoly power for example. Total welfare from the production and consumption of a given good or service can be measured as consumer surplus plus producer surplus, which is the area under the demand curve minus the area under the supply curve, calculated given the quantity traded in the market. Total welfare is maximized at the competitive equilibrium quantity and price, but a proportional tax, for example, reduces the quantity traded, and the welfare loss (when we include the revenue generated from the tax) is a triangle - indeed a Harberger triangle.

In the 1950s, Harberger measured the welfare loss from monopoly in the United States, essentially by adding up these triangles for monopolized industries. He came up with a small number - about 0.1% of GDP. Thus, if we were to use Harberger's methods to add up the heap of Harberger triangles arising from tax distortions, monopoly, various trade restrictions, and other synthetic obstacles to exchange, the welfare loss we obtain should be small.

Are output gaps large? Certainly Paul Krugman thinks so.
Right now the U.S. economy is operating something like 6 percent below capacity.
A 6% output gap is what you get if you use the Congressional Budget Office's (CBO's) measure of potential output. The chart shows this measure, along with actual real GDP. Suppose we take the CBO output gap of 6% of GDP as an accurate measure of what could be achieved if the fiscal and monetary authorities in the United States behaved appropriately. Also suppose that 0.1% is a good part of the heap of Harberger triangles in existence in the US economy. Then, indeed, the heap of triangles looks trivial relative to the gap.

But this isn't as obvious as it might look to some of you. Let's go back to Tobin's article ("How Dead is Keynes?"), where the quote comes from, and try to figure out what he was trying to say. Perhaps surprisingly, he wasn't comparing the welfare cost of business cycles to the welfare costs of "micro" distortions. In his article, Tobin said that 1977 policymakers were between the rock and the hard place. To achieve disinflation would require some sacrifice in terms of lost output. But further monetary accommodation would just lead to self-fulfilling increases in inflation. According to Tobin, "the way out, the only way out, is incomes policy." Then he states:
Most of you will, I'm sure, have no idea what "incomes policy" is, and that's a wonderful thing. "Incomes policy" sounds innocuous. What could be wrong with a government policy that looks after our incomes, presumably making them larger? Well, incomes policy is actually wage and price controls. In the pre-Volcker era, wage-price controls were very much on the table as a means for controlling inflation. Wage and price controls were introduced by the Nixon administration, and were in effect from 1971 to 1974 in the United States. I had the misfortune to live through the era of the Anti-Inflation Board in Canada, 1975-1978. The key achievement of Milton Friedman and the Old Monetarists was to convince everyone that inflation control is the job of the central bank. It's hard to find anyone today who disagrees with that view, and I think that's a good.

The funny, and I think key, point comes out of Tobin's confusion about gaps and triangles. Relative to what he's discussing, the gap and the triangles are actually exactly the same thing. Early in his paper, Tobin discusses the "central propositions" of Keynes's General Theory. To start:
So, inefficiencies arise because prices and wages are not at their market-clearing values, and quantities traded are demand-determined. In this context, how would we measure the efficiency loss in a particular market? Guess what, it's a Harberger triangle. The inefficiencies Tobin envisions arising from wage and price controls arise from what? From wages and prices that deviate from their market clearing values. What's the efficiency loss? It's a Harberger triangle. It takes a heap of Harberger triangles to fill a heap of Harberger triangles.

If I were a hardcore Keynesian - New, Old, whatever - how would I measure the costs of business cycles? Well, to start, I would accept Tobin's first central proposition from the General Theory. Inefficiencies arise because wages and prices are misaligned. To calculate welfare losses I would add up Harberger triangles across markets. The inefficiencies that arise in New Keynesian models are indeed identical to the ones which would be generated by a set of good-specific taxes.

What's the conclusion? Keynesians - Paul Krugman in particular - can't have it both ways. Macro does not "trump" micro. This is a no-trump world. If I argue that Keynesian sticky wage/price distortions are large, and that tax distortions are small, that's a contradiction.

But it's not a contradiction to say that sticky wage/price distortions are small, and other inefficiencies that we face are large. Is 6% of GDP a serious measure of the current effects of sticky wage/price distortions? Of course not. Read this document and see if you think the CBO measures potential output the way any sensible macroeconomist would measure it. Yikes. I don't think so.

There are of course plenty of models around now that take wage and price stickiness seriously, and also contain a multitude of shocks that allow those models to fit the data. Christiano/Eichenbaum/Evans is one of those. It seems straightforward to take a model like that, turn off the wage/price rigidity, compare business cycles without the wage/price rigidity to those with it, and ask what the agents in the model would pay to live without the wage-price rigidity (this is with monetary and fiscal policies that are not correcting the inefficiencies). I don't know if that has ever been done.

We could think of such an experiment as giving us an upper bound on the welfare loss from wage/price rigidity. There are plenty of reasons to think that standard New Keynesian models exaggerate the effects of wage/price stickiness. For example, Calvo pricing is suspect. If the losses from wage/price rigidity are such a big deal, there are large surpluses left on the table that inventive buyers and sellers of labor, goods, and services, would be happy to have.

So, there are good reasons to think that the welfare losses from wage/price rigidity are small. There is also plenty of evidence that other inefficiencies matter a great deal. This paper by Hsieh and Klenow shows how the misallocation of resources in China and India is a big deal - for aggregate TFP (total factor productivity) and GDP. There is an upcoming special issue of the Review of Economic Dynamics on misallocation and productivity. This includes a paper by Greenwood, Sanchez, and Wang, showing that financial misallocation can be big-time. In the United States, we have experienced a decade where resources were apparently reallocated, inefficiently, to the housing and mortgage markets, with disastrous results. We understand more about that episode than we used to, but we have a lot to learn. What people should come to terms with, is that wage and price rigidity likely had little to do with that experience, and the sooner economists recognize that, the more progress we'll make.


  1. This comment has been removed by the author.

  2. Prof. Williamson writes, "In the United States, we have experienced a decade where resources were apparently reallocated, inefficiently, to the housing and mortgage markets, with disastrous results."

    If this is true, into what assets should these resources have been allocated?

    How did you make that determination?

    How does your thesis square up to the efficient market hypothesis? What if, for example and argument, people realized that because of the earnings manipulations and fraud in the stock market made possible and encouraged by Central Bank of Denver case (1995) that putting resources into corporate stocks or bonds was not a good idea.

    1. "If this is true, into what assets should these resources have been allocated?"

      We don't think of resources being allocated into assets. In the United States, roughly post-2000, incentive problems in the mortgage and housing markets led to an inefficient allocation of resources to housing investment (on top of the inefficiency that already existed due to the mortgage interest deduction among other government interventions).

      "How did you make that determination?"

      I read, look at the evidence, sit and think, ...

      "How does your thesis square up to the efficient market hypothesis?"

      It's consistent with rational behavior.

    2. Assets v. Investments

      I'll accept your word, that you honestly see a difference.

      Into what investments should the resources have been allocated?

      Or, is this a Feynman problem for you. You believe to a level of certainty sufficient to make it scientific to you, either by experience or observation, that there was "an inefficient allocation of resources to housing investment."

      However, you lack a a level of certainty sufficient to make it scientific, either by experience or observation, to state what an efficient allocation of the resources would have been?

      It doesn't bother me that you are look at the evidence, sitting and thinking. That puts you well past a lot of economists, at worst, and at times I think it could put you in a league of your own.

      It just seems to me that you have opened the door pretty wide and it is fair to ask

      My problem with your POV is that, for micro reasons, I cannot make the case that for it being a rational investment for the people buying houses to put the money in stocks or bonds. Stocks, in particular feel worse than housing, as I recall. I suspect, depending on the year you pick, that housing may still be outperforming stocks.

      Thus, I believe it legitimate to ask where

      This seems, to me, to have a lot of practical considerations, like the mortgage interest deduction.

      If the government permitted inefficient allocation of resources to housing, is it now fair to limit or take away the interest deduction? Not answering the question, just putting it out there.

    3. After your self-debunking performance at Uneasy Money, I'm surprised you have the gall to show up at any economics blogs at all.

    4. I clicked through on the link.

      Apparently some people have the good sense to object to a man who supported a dictator who was at the same time and earlier dropping people out of helicopters.

      I checked into Missouri's view on moral and civil liability. Seems that in Missouri a person who who does not guard
      against reasonably foreseeable wrong, who counsels, abets, encourages such by cooperation is liable even when the defendant did not personally participate. O’Brien v. B.L.C. Ins. Co., 768 S.W.2d 64, 68-69 (Mo. 1989) (insurance
      company liable for failing to obtain salvage title prior to selling wrecked car to
      a dealer, because it knew dealer was unlikely to disclose to true condition of the car).

      If you approve of a person who supported a dictator who dropped people out of helicopters, I am surprised you have the gall to show up on an economics blog, but then you don't, you post anonymously.

      If a reader is interested in learning about Pinchot I would suggest that they simply go to Wikipedia, where the scope and extent of the number of people murdered and tortured is documented, including American Journalists Charles Horman and Frank Teruggi. There is very substantial evidence that the CIA was involved in Horman's disappearance in 1973, so Hayek knew exactly what he was ratifying and encouraging.

    5. Prof. Williamson, having been interrupted, if we can now get back to my questions to you.

      In the meantime, Noah has up a new blog where he argues, "thus the financial system was broken for a long, long time." It seems to me he has a good point.

      I am attempting to make the two points of view fit together. I guess where I am coming out is that how do we tell inefficient allocation from broken financial markets?

      If there is no where to invest, where does one invest?

    6. Now you're attaching your last name too. John D., you sure are persistent. Now if you'd only be absent.

    7. Williamson wrote, "We understand more about that episode than we used to, but we have a lot to learn."

      The longer I wait for an answer for my question the more I begin to doubt that is what economists, including this blog, are really about.

      All I can discern is that they are about B.S. about thought experiments of dead people, save for Noah, Brad, and Nick Rowe (sometimes).

      Of here, a way to express jealously over more public members of the club.

      It seems to me that Noah raised a very interesting question, basically asserting that banking may be broken.

      Prof. Williamson, based on experience, sees a bigger picture and interprets such as inefficient resource allocation

      Krugman just argued that the problem may be too much efficiency, the rise of the robots.

      Now it seems that we have room for a very useful and healthy debate, which I know will never take place.

      For example, there are experiments that could be run to test Noah's suggestion (real experiments, not thought experiments). Instead of arguing over thought experiments of dead people, why doesn't the profession actually act like a science and propose to the government that we have some real experiments.

      And, of course, the answer is jealously, again. Someone else might be picked to run the experiment. It is therefore better that we have no real experiments.

      For example, we should draw stocks by lot and subject them to a different regulatory regimes (like making the brokers, attorneys, and accountants liable for fraud for aiding and abetting, or changing the business judgment rule)

      I could go on, but having ready too many comments on too many blogs it is apparent that economists are perhaps the most conservative set in their way people around, for which the American public has been badly served and greatly and I fear irreparably damaged. For sure, they are rarely scientists.

    8. Hayek's support for Pinochet surely merits condemnation. But it doesn't merit making up stuff about his economic/political thought, which is what Glasner called you out on. You tend to cite Mark Twain or the early Federalists (like Hamilton) to make some non-sequitur about contemporary disputes, but you screwed you trying to use Coase to deny Hayek's status as a legit thinker when we have Coase's actual words to the contrary. Earlier in the thread you were aghast that anyone could take Hayek seriously (usually justified by ascribing to him positions he didn't actually hold, as if he was Murray Rothbard). Normally there is a basic presumption that one's dialogue partner is an honest interlocutor, which you have plainly proven yourself not to be. So why should anyone bother talking with you at all? Maybe if you want to be accepted into conversation you should think about how you behaved, adopt a new identity, and then write in such a way that nobody figures out you're the same person who wrote as John D/Alexander Hamilton.

    9. Well, this is a pretty weird discussion. I was only looking at what was happening below. To answer your basic question, John D., the financial crisis and what led up to it is all about economic efficiency - regulations that permitted socially wasteful behavior, leading to asset price movements amplified through the financial system as costly default and disruption.

    10. It appears the conversation with David was stopped for the reasons there is no good reason to talk about thought experiments of dead people and based on the consensus that Hayek is dark as he has become the tool of Glen Beck.

      TCCP, are your really Glen Beck?

      Regarding your assertion that Hayek was a legit thinker, you have not made that case.

      As evidence, Hayek does not even get a chapter in Coase's book.

      The HBR essay by Coase rejects Hayek's reliance on price, albeit not by name. David's response is a red herring as is David's reliance on events in the early 1930s. The "Dark" Hayek emerged later and, as you write, "Hayek's support for Pinochet surely merits condemnation."

      Exactly what condemnation do you support?

      At page 19 in the work cited by David Coase wrote, "As far as I can see, the Hayekian analysis did not make predictions . . ."

      A fundamental test of science is whether it makes predictions. Hayek, as per Coase, was not a scientist, not a legit thinker.

      Coase then immediately writes about Lionel Robbins writing a book based on Hayek, as I read the passage, which he subsequently wrote was the only book he ever regretted writing.

      Now you may draw whatever inferences you want from these passages but so may any other reader.

      It is unfortunate Prof Williamson choose not to answer my questions.

    11. "It is unfortunate Prof Williamson choose not to answer my questions."

      But fortunate for the rest of us! Please people, stop feeding this troll.

    12. Prof. Williamson

      Thank you for your answer.

      It is very informative. The entire piece was very informative. It is the first time that I can recall you writing across several decades, connecting events.

      Nor do I recall ever reading anyone asking this question, "If I were a hardcore Keynesian - New, Old, whatever - how would I measure the costs of business cycles?"

      I also notice you used the word Krugman, not followed by a curse.

      Perhaps, someday, I will ask another question and get a similar response.

    13. No, I am not Glenn Beck. I regarded him as a clown when I first saw him on CNN, from what I hear he became no less clownish as time went on. Nevertheless, it is blatantly illogical to say that Hayek's ideas are worthless because Glenn Beck likes to talk about him. "The Road to Serfdom" endorses universal health care, and we cannot conclude it is a bad idea merely because Beck or even Hayek are bad people. I'm sure Beck also lauds the Founding Fathers. You frequently do the same thing (misrepresenting them just as you do Coase). What can we conclude about the founders based on that? Nothing.

      If every legit thinker merited a chapter in every book by Coase, he would be unable to focus on the chosen topic of his book. You again make complete non sequiturs.

      Milton Friedman in his essay on positivism said that economic theories should be judged based on their predictions rather than their realism. The passage by Coase in which he said that Hayek (and Keynes!) lacked predictive power is part of his critique of Friedman, at least if Friedman's essay is itself interpreted as a positive account of how economists behave rather than a normative one of how Friedman wants them to. Unlike Friedman, Coase is not known for doing things like predicting that the Phillips Curve will break down, but for coming up with ideas (theory of the firm, "Coase theorem" bargaining vs transaction costs, spectrum should be sold off) that economists found sensible. That's just the characteristic he ascribes to Hayek & Keynes' theories on the depression.

      I should say that I don't have a very high opinion of Hayek's writings on the depression (even if officially that's part of what he won his Econ nobel for). "The Use of Knowledge in Society", "The Sensory Order", "The Denationalization of Money" and his writings on how law & norms can evolve like language are more interesting to me.

  3. Could rising monopoly power, particularly in the financial sector, be a source of the decline in trend growth ? This is another source of triangles.

    1. In the chart, you would get more or less the same picture by replacing the CBO potential output series with a linear time trend fit to post-WWII real GDP, except the time trend would be higher. Given the data we have to date, it looks like there is a downward level change in real GDP, and we're growing at roughly the post-WWII average rate (a little on the low side perhaps). For monopoly power to explain that, we would have had to have a one-time increase in it around the time of the financial crisis.

  4. Nice catch on the Tobin quote.

    I have to defend Tobin a little, though. Essentially, he was saying that macro declines in output create first-order welfare losses, while other "micro" distortions tend to create second-order welfare losses. This is false in the context of the typical NK model, as you point out: there, when the economy's output is depressed, the distortion of the representative agent's intratemporal EE creates a second-order welfare loss, in exactly the same way that a "micro" distortion does.

    My view, however, is that this is a serious flaw in the baseline NK model, which does a horrible job of dealing with labor markets. If, rather than saying that a decline in output pushes workers down a little away from the optimum on the intensive margin, we take the (more realistic) view that most of the adjustment is done on the extensive margin, and that this process is something akin to job rationing, then declines in output in the NK model will have first-order welfare consequences. I think that this is probably what Tobin had in mind.

    (You might quibble with my characterization of unemployment during a recession as job rationing. This is, of course, a caricature, but I suspect it is a more accurate caricature of the labor market than most of the other prevailing approaches. See Pascal Michaillat's recent AER, for instance.)

    1. How are you thinking of modeling the choice at the extensive margin? Indivisible labor? Where's the inefficiency coming from?

  5. "If the losses from wage/price rigidity are such a big deal, there are large surpluses left on the table that inventive buyers and sellers of labor, goods, and services, would be happy to have."

    Employers could just say, hey unemployed, I'll hire you for this far lower wage, and you'll have a job, and I’ll make a profit Harbergernon-style, but then:

    1) Huge information problems–Workers don’t know if their new market wage is now so pathetic, and it may not come close to paying for the kind of lifestyle, and of course positional externalities, their family has grown accustomed to. The doom of having to tell your family you now have to live permanently, or at least for years, in a way you’ve grown to consider poor, you have to sell the home, cars, etc., and buy “poor people” ones, can be devastating and take years to accept. (but of course positional externalities are zero, so I guess not – on planet Zenon)

    2) Workers may be very disgruntled at this NOMINAL wage; the quality wage phenomena can be big.

    3) If everyone started doing this, then the costs of hiring to you, even at this much lower wage, would be offset by the new spending power from all of the new employees economy-wide from all of the other companies likewise hiring. But if everyone else didn’t go along, then you’d be left hanging. You wouldn’t get the increased economy-wide spending to justify your hiring.

    If everyone hires at once, then hiring becomes a lot more worth it, because there is increased spending power from all these new hires economy-wide to buy what your particular new hires produce. But if you can’t coordinate with the bulk of the companies nationwide in your hiring decisions (and obviously you can’t in the real world), then it may be too risky for you to act alone in hiring. Vast coordination across independent companies may be a huge problem – something you really learn at the top business schools when you talk about all the fantastic potential joint ventures among companies that will never occur because of the huge real world problems and costs.

    1. 4) It's hard to cut the wage a lot that you offer the unemployed guy to get this Harberger win-win, and yet keep the wage of all of the other workers the same. You've now got resentment which can be very bad for business. If you cut all workers wages – nominally – as you'd have to with inflation so low, now you've really got resentment. Even you have to admit the mountain of evidence and psychology on the difficulty and reluctance of nominal wage cuts.

  6. Love the post.

    Regarding misallocation, however, didn't TFP rise throughout the recession? I know that Prescott argues that it didn't if measured correctly, but interested to get your thoughts on this general observation.

    1. Yes, Prescott argues that if you take account of intangible investment, then his model makes sense. Clearly we want a theory that can account for the data, including the rise in TFP during the last recession, as conventionally measured. If misallocation of various kinds is important in thinking about recent history, it's clearly not the sort of mechanism that gives you a direct route to measured TFP.

    2. TFP???

      Substantively, a machine is knowledge, an intangible investment. With the arrival of Krugmanbots (a doer that reproduces itself) all investment becomes visibly intangible.

      Hence, now, all investment is intangible, some people just lack the ability to engage in abstract thinking at a higher level.

      Of course, knowledge wants to be free so we wind up with an unhappy fact. Distribution of income is revealed as totally a political question, unrelated to marginal productivity. No patents or copyright, no income, no economics.

      Perhaps the Cambridge capital controversy should come to the front at least long enough to rid us of TFP

  7. I think Krugman's point, translated, is that during recessions the Harberger triangle in the labor market trumps the sum of Harberger triangles in the markets for goods and services during "normal times". Whether this is true, I am not sure about.

  8. To add, I do agree though that the way in which he makes the argument (micro vs. micro) is counterproductive. Misalocation IS waste (using too many resources to make things people do not value as much and too few to make things people value a lot). This is no different than allocating too much time to leisure (that people value less) and too little time to the production of marker goods (that people value more). I, too, fail to see the difference. I am not sure why Krugman calls the second waste but not the first. Unless he thinks that producing anything, even of zero market value, is a better use of time than home production or leisure. Of course, that would be consistent with the worldview of some old Keynesians, but where is the justification?

    1. Exactly. Waste is waste. Some people would argue that it's better if we hire an unemployed person to dig a hole and fill it in, than if we pay that same person to stay at home and sit on the sofa. The argument seems to be that the person is happier working. The problem is that the person knows that digging the hole and filling it up is useless.

    2. I didn't think the happiness of the workers in question was relevant to the argument. I thought the theory was that hiring people to dig a hole and fill it in would increase our net income. i.e., If we assume for the sake of argument there is a savings glut, hiring useless workers will have beneficial second-order effects ... it will increase consumption by some amount without crowding out spending elsewhere.

    3. It would increase market income but not necessarily welfare. If the hole has zero social value, to get a positive effect on welfare you must assume that people would rather dig a useless hole than, say, watch TV at home or tend their garden. Wouldn't it be better to just give them a transfer payment?

      Anyway, my point was that I am not sure why Krugman attaches the word "waste" to consuming "too much" leisure and "too few" market goods, but uses the word "misallocation" for consuming, say, "too much" housing and "too little" vacation. The two cases are the same, from an economics point of view.

    4. If we accept that the fundamental problem is that the wages and prices are sticky, the social waste in a recession can be measured by some Harberger triangles. Keynesians make it seem completely natural that the way to cure that waste is to have the government spend more - on anything. I think if you think about the economics of the problem, that this is an odd way to correct the inefficiency that you're claiming is the root of the problem. Seems a goods-specific tax/subsidy mechanism would work better. Maybe you could even make that revenue-neutral.

    5. Perhaps, but if the government has for a long, long time been shamefully underspending on public investment and insurance, then it's an especially good time to finally correct that.

    6. That's a good point. Maybe Keynesians aren't actually concerned with correcting inefficiencies. They want to increase the size of government and are looking for excuses to do it. There's nothing wrong with the motivation - maybe the US government should be larger. You would rather make the case on its merits though, I think.

    7. Yes, Arnold Kling used the labels "Keynes effect" and "Galbraith effect" to break down how Kevin Murphy & Brad Delong's intuitive estimates on the stimulus differed.

    8. Right-wingers don't seem to understand the meaning of "the size of government". Practically speaking, government should be responsible for an extremely large share of the money economy. That doesn't mean it has to have enormous bureaucracies, lots of staff, and zillions of office building, which is what "size of government" means to the average person.

      Social Security is a large operation in money terms, but run as a lean, mean, low-overhead operation.

      The Department of Defense is a very high-overhead operation.

  9. Slighty off-topic. I am an economist marginally under 40. Why does Greg think I may be unfamiliar with Harberger triangles? Was my Ph.D. program so old-fashioned? :)

    1. You should find a discussion of consumer/producer surplus and deadweight loss in almost any intro micro text, though I have not looked at one lately. The author may not always call the deadweight loss a Harberger triangle, but I'm sure some do.