Krugman’s Second Best

A couple of days ago Paul Krugman discussed “Second-best Macroeconomics” on his blog. I have no real quarrel with anything he said, but I would like to amplify his discussion of what is sometimes called the problem of second-best, because I think the problem of second best has some really important implications for macroeconomics beyond the limited application of the problem that Krugman addressed. The basic idea underlying the problem of second best is not that complicated, but it has many applications, and what made the 1956 paper (“The General Theory of Second Best”) by R. G. Lipsey and Kelvin Lancaster a classic was that it showed how a number of seemingly disparate problems were really all applications of a single unifying principle. Here’s how Krugman frames his application of the second-best problem.

[T]he whole western world has spent years suffering from a severe shortfall of aggregate demand; in Europe a severe misalignment of national costs and prices has been overlaid on this aggregate problem. These aren’t hard problems to diagnose, and simple macroeconomic models — which have worked very well, although nobody believes it — tell us how to solve them. Conventional monetary policy is unavailable thanks to the zero lower bound, but fiscal policy is still on tap, as is the possibility of raising the inflation target. As for misaligned costs, that’s where exchange rate adjustments come in. So no worries: just hit the big macroeconomic That Was Easy button, and soon the troubles will be over.

Except that all the natural answers to our problems have been ruled out politically. Austerians not only block the use of fiscal policy, they drive it in the wrong direction; a rise in the inflation target is impossible given both central-banker prejudices and the power of the goldbug right. Exchange rate adjustment is blocked by the disappearance of European national currencies, plus extreme fear over technical difficulties in reintroducing them.

As a result, we’re stuck with highly problematic second-best policies like quantitative easing and internal devaluation.

I might quibble with Krugman about the quality of the available macroeconomic models, by which I am less impressed than he, but that’s really beside the point of this post, so I won’t even go there. But I can’t let the comment about the inflation target pass without observing that it’s not just “central-banker prejudices” and the “goldbug right” that are to blame for the failure to raise the inflation target; for reasons that I don’t claim to understand myself, the political consensus in both Europe and the US in favor of perpetually low or zero inflation has been supported with scarcely any less fervor by the left than the right. It’s only some eccentric economists – from diverse positions on the political spectrum – that have been making the case for inflation as a recovery strategy. So the political failure has been uniform across the political spectrum.

OK, having registered my factual disagreement with Krugman about the source of our anti-inflationary intransigence, I can now get to the main point. Here’s Krugman:

“[S]econd best” is an economic term of art. It comes from a classic 1956 paper by Lipsey and Lancaster, which showed that policies which might seem to distort markets may nonetheless help the economy if markets are already distorted by other factors. For example, suppose that a developing country’s poorly functioning capital markets are failing to channel savings into manufacturing, even though it’s a highly profitable sector. Then tariffs that protect manufacturing from foreign competition, raise profits, and therefore make more investment possible can improve economic welfare.

The problems with second best as a policy rationale are familiar. For one thing, it’s always better to address existing distortions directly, if you can — second best policies generally have undesirable side effects (e.g., protecting manufacturing from foreign competition discourages consumption of industrial goods, may reduce effective domestic competition, and so on). . . .

But here we are, with anything resembling first-best macroeconomic policy ruled out by political prejudice, and the distortions we’re trying to correct are huge — one global depression can ruin your whole day. So we have quantitative easing, which is of uncertain effectiveness, probably distorts financial markets at least a bit, and gets trashed all the time by people stressing its real or presumed faults; someone like me is then put in the position of having to defend a policy I would never have chosen if there seemed to be a viable alternative.

In a deep sense, I think the same thing is involved in trying to come up with less terrible policies in the euro area. The deal that Greece and its creditors should have reached — large-scale debt relief, primary surpluses kept small and not ramped up over time — is a far cry from what Greece should and probably would have done if it still had the drachma: big devaluation now. The only way to defend the kind of thing that was actually on the table was as the least-worst option given that the right response was ruled out.

That’s one example of a second-best problem, but it’s only one of a variety of problems, and not, it seems to me, the most macroeconomically interesting. So here’s the second-best problem that I want to discuss: given one distortion (i.e., a departure from one of the conditions for Pareto-optimality), reaching a second-best sub-optimum requires violating other – likely all the other – conditions for reaching the first-best (Pareto) optimum. The strategy for getting to the second-best suboptimum cannot be to achieve as many of the conditions for reaching the first-best optimum as possible; the conditions for reaching the second-best optimum are in general totally different from the conditions for reaching the first-best optimum.

So what’s the deeper macroeconomic significance of the second-best principle?

I would put it this way. Suppose there’s a pre-existing macroeconomic equilibrium, all necessary optimality conditions between marginal rates of substitution in production and consumption and relative prices being satisfied. Let the initial equilibrium be subjected to a macoreconomic disturbance. The disturbance will immediately affect a range — possibly all — of the individual markets, and all optimality conditions will change, so that no market will be unaffected when a new optimum is realized. But while optimality for the system as a whole requires that prices adjust in such a way that the optimality conditions are satisfied in all markets simultaneously, each price adjustment that actually occurs is a response to the conditions in a single market – the relationship between amounts demanded and supplied at the existing price. Each price adjustment being a response to a supply-demand imbalance in an individual market, there is no theory to explain how a process of price adjustment in real time will ever restore an equilibrium in which all optimality conditions are simultaneously satisfied.

Invoking a general Smithian invisible-hand theorem won’t work, because, in this context, the invisible-hand theorem tells us only that if an equilibrium price vector were reached, the system would be in an optimal state of rest with no tendency to change. The invisible-hand theorem provides no account of how the equilibrium price vector is discovered by any price-adjustment process in real time. (And even tatonnement, a non-real-time process, is not guaranteed to work as shown by the Sonnenschein-Mantel-Debreu Theorem). With price adjustment in each market entirely governed by the demand-supply imbalance in that market, market prices determined in individual markets need not ensure that all markets clear simultaneously or satisfy the optimality conditions.

Now it’s true that we have a simple theory of price adjustment for single markets: prices rise if there’s an excess demand and fall if there’s an excess supply. If demand and supply curves have normal slopes, the simple price adjustment rule moves the price toward equilibrium. But that partial-equilibriuim story is contingent on the implicit assumption that all other markets are in equilibrium. When all markets are in disequilibrium, moving toward equilibrium in one market will have repercussions on other markets, and the simple story of how price adjustment in response to a disequilibrium restores equilibrium breaks down, because market conditions in every market depend on market conditions in every other market. So unless all markets arrive at equilibrium simultaneously, there’s no guarantee that equilibrium will obtain in any of the markets. Disequilibrium in any market can mean disequilibrium in every market. And if a single market is out of kilter, the second-best, suboptimal solution for the system is totally different from the first-best solution for all markets.

In the standard microeconomics we are taught in econ 1 and econ 101, all these complications are assumed away by restricting the analysis of price adjustment to a single market. In other words, as I have pointed out in a number of previous posts (here and here), standard microeconomics is built on macroeconomic foundations, and the currently fashionable demand for macroeconomics to be microfounded turns out to be based on question-begging circular reasoning. Partial equilibrium is a wonderful pedagogical device, and it is an essential tool in applied microeconomics, but its limitations are often misunderstood or ignored.

An early macroeconomic application of the theory of second is the statement by the quintessentially orthodox pre-Keynesian Cambridge economist Frederick Lavington who wrote in his book The Trade Cycle “the inactivity of all is the cause of the inactivity of each.” Each successive departure from the conditions for second-, third-, fourth-, and eventually nth-best sub-optima has additional negative feedback effects on the rest of the economy, moving it further and further away from a Pareto-optimal equilibrium with maximum output and full employment. The fewer people that are employed, the more difficult it becomes for anyone to find employment.

This insight was actually admirably, if inexactly, expressed by Say’s Law: supply creates its own demand. The cause of the cumulative contraction of output in a depression is not, as was often suggested, that too much output had been produced, but a breakdown of coordination in which disequilibrium spreads in epidemic fashion from market to market, leaving individual transactors unable to compensate by altering the terms on which they are prepared to supply goods and services. The idea that a partial-equilibrium response, a fall in money wages, can by itself remedy a general-disequilibrium disorder is untenable. Keynes and the Keynesians were therefore completely wrong to accuse Say of committing a fallacy in diagnosing the cause of depressions. The only fallacy lay in the assumption that market adjustments would automatically ensure the restoration of something resembling full-employment equilibrium.

18 Responses to “Krugman’s Second Best”


  1. 1 WaltFrench July 30, 2015 at 1:56 pm

    Isn’t this the same question as how the economy responds to any new shock? I.e., not really about “second best” at all?

  2. 2 David Glasner July 30, 2015 at 8:57 pm

    Walt, I should have made the point more clearly. Let me quote from the Lipsey-Lancaster article:

    “The general theorem of the second best states that if one of the Paretian optimum conditions cannot be fulfilled a second best optimum situation is achieved only by departing from all other optimum conditions. It is important to note that in general, nothing can be said about the direction or the magnitude of the secondary departures from optimum conditions made necessary by the original non-fulfillment of one condition.”

    What that says, I believe, is that the price changes dictated by market forces in a situation in which not all optimum conditions are satisfied do not necessarily bring prices closer to their general equilibrium values. With high unemployment, there is pressure on nominal, and presumably real, wages to fall, but the real wage in general equilibrium might turn out to be much higher. So, it is not strictly correct to say that in a depression if there is mass unemployment, it is because the real wage is too high and workers are unwilling to accept the wage reductions needed to restore full employment.

  3. 3 Nick Zbinden July 31, 2015 at 3:51 am

    > Conventional monetary policy is unavailable thanks to the zero lower bound, but fiscal policy is still on tap, as is the possibility of raising the inflation target.

    Its funny how langauge frames the debate. He uses ‘conventional’ as ‘short term interest rates’ but before the new keynsian revolution it was not unconventional to use other tools. I would argue that using the exchange rate is also a pretty conventional.

    Why do we need the raise the inflation target? Hitting the target in 2008 and 2009 would have done most of the job already. Leveling the target could have been done by the fed, if they had wanted to. The ZLB is no excuse at all.

  4. 5 Tom Brown July 31, 2015 at 8:14 am

    Interesting post David.

  5. 6 jm July 31, 2015 at 10:02 am

    Regarding your use of “negative feedback”, note that in the realm of control theory negative feedback stabilizes a system*; technically, what you are describing is a consequence of “positive feedback”, in which feedback of a change in system output in a particular direction causes the output to move increasingly in that direction.

    * (as long as the gain around the feedback loop is less than 1.0 at that frequency where lags and pure delays around the loop equate to a 180-degree phase shift, in which case it leads to instability and limit cycling at that frequency between whatever external constraints exist — as we see in real estate markets, for example).

  6. 7 Tom Brown July 31, 2015 at 11:00 am

    jm… lol, after reading your first phrase I wanted to say exactly what you did say in your footnote.

    David, from my limited understanding of all things economics, your post here reminds me a little of some criticisms of macro that I’ve seen Steve Keen make years ago. Sorry, I didn’t mean to ruin your day… you can chalk my misapprehension (if it is one) to my ignorance.

    Would it be wrong to conclude from your post that skepticism of the claim that markets are always “self correcting” may well be warranted?

  7. 8 Frank Restly August 2, 2015 at 9:39 am

    David,

    Before you can get to a first best versus a second best solution to a problem, you have to build a consensus on what the problem is.

    And since guys like Krugman aren’t able to build that consensus, arguing over a first best versus second best solution to a problem that Krugman believes to exist is a mute point.

    If Paul would adopt the position that debt levels can and have become problematic, then first and second best solutions to “the problem” become more easily identified.

    Solutions to a debt problem:
    1. Convert debt to equity
    2. Debt forgiveness
    3. Mass defaults
    4. Run surpluses instead of deficits

    In a macroeconomic system it is impossible for all parties (public and private) to run surpluses simultaneously. That leaves solutions #1, #2, and #3.

    In my opinion, debt forgiveness / mass defaults are second best solutions to a debt problem in that they have some negative incentive effects. Paul may believe otherwise.

  8. 9 David Glasner August 4, 2015 at 7:32 pm

    Nick, What do you mean by leveling the target? I do agree that using the exchange rate is conventional.

    jm, You’re right of course about “negative feedback.” I don’t know why I got mixed about that.

    Tom, I realize that I am pushing the limits of orthodoxy by emphasizing that we have no real theory of macro stability. But I am merely elaborating on an argument made long ago by Leijonhufvud about what he called the “corridor,” in which economies are relatively stable as long as they don’t deviate too far from their equilibrium time path, but can become highly unstable when they deviate a substantial distance from the equilibrium time path.

    Frank, The theory of second-best has a pretty technical meaning, and I can’t really see how your use of the term matches up with the technical meaning.

  9. 10 Frank Restly August 4, 2015 at 8:35 pm

    David,

    The crux of my post was to illustrate that if you can’t agree on what the problems are, then you have no hope of finding a Pareto optimal, second best, or even 10th best solution to those problems.

    “The theory of second-best has a pretty technical meaning…”

    The technical meaning you are referring to is in the paper that you reference:

    “The general theorem for the second best optimum states that if there is introduced into a general equilibrium system a constraint which prevents the attainment of one of the Paretian conditions, the other Paretian conditions, although still attainable, are, in general no longer desirable. In other words given that one of the Paretian optimum conditions cannot be fulfilled, then an optimum situation finally attained may be termed a second best optimum because it is achieved subject to a constraint which, by definition, prevents the attainment of a Paretian optimum”

    That’s quite a mouthful. The definition of Pareto optimal can be found here:

    https://en.wikipedia.org/wiki/Pareto_efficiency

    “Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.”

    And so, in laymen’s terms it would seem that a second best solution divvies up resources in a way that makes some people better off and some people worse off. How does Pareto optimality and second best solutions apply to a debt problem?

    A second best solution like debt forgiveness leaves the lender worse off bearing all of the costs. A second best solution like default / bankruptcy leaves both parties worse off – lender is not repaid in full and the borrower faces difficulties in borrowing any time in the future. A first best solution (though not necessarily Pareto optimal) converts debt to equity.

    I am not sure there is a Pareto optimal solution to a debt problem because it’s supply is not inherently limited. It’s like saying that there is no Pareto optimum solution to an obesity problem because changing the allocation of candy bars doesn’t change the fact that too many candy bars are being consumed. Do you fix an obesity problem by taking candy bars from Jim and giving them to Mary?

  10. 11 Tom Brown August 4, 2015 at 10:54 pm

    David, thanks for the reply. That was helpful. It sounds like there’s a “tipping point” beyond which the instability (or “unintuitive” or highly non-linear) behavior starts… and perhaps some hysteresis preventing a direct return to “stability” again until it’s run its course.

    I have in mind a relatively stable period of evolutionary history, during which you might be able to apply the predator prey equation for example, or perhaps make some successful evolutionary predictions … and then a big meteorite hits, spreading chaos throughout the gene pools, which just breeds further chaos, until eventually a new equilibrium time path is established, and we have all new sets of predators and preys.

  11. 12 JKH August 6, 2015 at 3:28 am

    “The cause of the cumulative contraction of output in a depression is not, as was often suggested, that too much output had been produced, but a breakdown of coordination in which disequilibrium spreads in epidemic fashion from market to market, leaving individual transactors unable to compensate by altering the terms on which they are prepared to supply goods and services.”

    I’m having a bit of a problem trying to understand why there should be any inconsistency between these two things – “too much output …” and “disquilibrium spreads …”

    It seems to me that the first one is a state (stock) and the second is a process (flow). I see them as compatible pictures on how the world evolves in a depression.

    For example, are you saying that depressions do not include too much inventory accumulation and forced liquidation – i.e. do not include too much output produced?

  12. 13 JKH August 6, 2015 at 4:16 am

    I also found this pretty fascinating, from your linked post on Say’s Law:

    “This is where Say’s Principle kicks in; If transactors do not succeed in supplying as much as they planned to supply at prevailing prices, then, depending on the condition of their balances sheets, and the condition of credit markets, transactors may have to curtail their demands in subsequent periods; a failure to supply as much as had been planned last period will tend reduce demand in this period. If the “distance” from equilibrium is large enough, the demand failure may even be amplified in subsequent periods, rather than damped. Thus, Clower and Leijonhufvud showed that the Keynesian multiplier was, at a deep level, really just another way of expressing the insight embodied in Say’s Law (or Say’s Principle, if you insist on distinguishing what Say meant from Lange’s reformulation of it in terms of Walrasian equilibrium).”

    The idea of linking Say’s Law to the Keynesian multiplier is very intriguing.

    As I understand it, KM is demand formulated for both expansion and contraction modes.

    I think the KM process infers supply expansion and contraction in parallel with these demand iterations.

    The Say’s Law version seems to focus for example on the effect of supply contraction for subsequent demand sourced from suppliers themselves.

    I’m still trying to understand this. But I do think there has to be a deep connection between the two.

  13. 14 JKH August 6, 2015 at 6:58 am

    Sorry for the incremental comment stream, but I’ve been trying to piece together some things you’ve said in several posts.

    In your ‘What does “Keynesian” Mean?’ post:

    You seem to be saying that the correct expression of Say’s Law, rather than “supply creates demand”, is closer to “supply failure creates demand failure”.

    Is that interpretation on my part approximately right?

  14. 15 TravisV August 8, 2015 at 7:26 am

    Dr. Glasner, in case you haven’t seen it, you might be interested in reading this recent rant by John Cochrane on Europe, Greg Mankiw, sticky wages, etc:

    http://johnhcochrane.blogspot.com/2015/07/mankiw-and-conventional-wisdom-on-europe.html

    In my opinion, Cochrane is more fun to read than John Taylor (although he’s perhaps less influential).

  15. 16 Hugo André August 9, 2015 at 9:28 am

    @JKH Since I’ve read Leijonhufvud I may be able to help answer your questions about Say’s principle and law.

    The problem with Say’s law is that it’s very vague. Leijonhufvud and Clower instead formulated what they call say’s principle(SP) which states: “The net value of an individual’s planned trades is identically zero”. The aggregate version is that the net value of all individuals planned trades is zero. Note the crucial use of the word “planned”. They also use “trades” instead of supply and demand since definitions of the latter differ between the keynesian and classical traditions. When Say wrote about supply and demand he meant it for all commodities (including money, financial assets, intermediate goods etc).

    The principle should be seen as a more precise statement of Say’s reasoning although he never seems to have used the aggregate version.

    If actual prices differ from equilibrium prices in certain markets, actual spending will differ from planned purchases since some individuals will be unable to carry out their plans. This means less income for suppliers of some goods and these people will demand less in the next period. A household that fails to realise it’s sale of labour will have a consumption demand that is income-constrained which a causes knock-on effect (this is the keynesian multiplier).

    An expression of Say’s law that connects it to keynesianism might therefore be “coordination failure creates demand failure”.

  16. 18 David Glasner August 14, 2015 at 9:58 am

    Frank, I am really sorry, but trying to clear all this up for you at this point is just beyond me.

    Tom, I think you have the gist of what I was trying to say. The evolutionary story may be a good way of thinking about it, but I have never thought about intertemporal equilibrium in those terms.

    JKH, I think that the way to think about unwanted inventory accumulation is not that things would have been better if only producers had produced less of the unwanted stuff that they can’t sell. If they had anticipated that they would be unable to see what they produce, that would not have prevented the contraction from occurring. The source of the contraction was some deeper failure of coordination preventing the efficient organization of production and consumption (supply and demand).

    TravisV, Thanks for the link. I still haven’t looked at what Cochrane wrote, but I will try to read it soon.

    Hugo, Thanks for your excellent summary of Clower and Leijonhufvud.


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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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