Thompson’s Reformulation of Macroeconomic Theory, Part V: A Neoclassical Black Hole

It’s been over three years since I posted the fourth of my four previous installments in this series about Earl Thompson’s unpublished paper “A Reformulation of Macroeconomic Theory,” Thompson’s strictly neoclassical alternative to the standard Keynesian IS-LM model. Given the long hiatus, a short recapitulation seems in order.

The first installment was an introduction summarizing Thompson’s two main criticisms of the Keynesian model: 1) the disconnect between the standard neoclassical marginal productivity theory of production and factor pricing and the Keynesian assertion that labor receives a wage equal to its marginal product, thereby implying the existence of a second scarce factor of production (capital), but with the market for capital services replaced in the IS-LM model by the Keynesian expenditure functions, creating a potential inconsistency between the IS-LM model and a deep property of neoclassical theory; 2) the market for capital services having been excluded from the IS-LM model, the model lacks a variable that equilibrates the choice between holding money or real assets, so that the Keynesian investment function is incompletely specified, the Keynesian equilibrium condition for spending – equality between savings and investment – taking no account of the incentive for capital accumulation or the relationship, explicitly discussed by Keynes, between current investment and the (expected) future price level. Excluding the dependence of the equilibrium rate of spending on (expected) inflation from the IS-LM model renders the model logically incomplete.

The second installment was a discussion of the Hicksian temporary-equilibrium method used by Thompson to rationalize the existence of involuntary unemployment. For Thompson involuntary unemployment means unemployment caused by overly optimistic expectations by workers of wage offers, leading them to mistakenly set reservation wages too high. The key idea of advantage of the temporary-equilibrium method is that it reconciles the convention of allowing a market-clearing price to equilibrate supply and demand with the phenomenon of substantial involuntary unemployment in business-cycle downturns. Because workers have an incentive to withhold their services in order to engage in further job search or job training or leisure, their actual short-run supply of labor services in a given time period is highly elastic at the expected wage. If wage offers are below expectations, workers (mistakenly = involuntarily) choose unemployment, but given those mistaken expectations, the labor market is cleared with the observed wage equilibrating the demand for labor services and supply of labor services. There are clearly problems with this way of modeling the labor market, but it does provide an analytical technique that can account for cyclical fluctuations in unemployment within a standard microeconomic framework.

In the third installment, I showed how Thompson derived his FF curve, representing combinations of price levels and interest rates consistent with (temporary) equilibrium in both factor markets (labor services and capital services) and two versions of the LM curve, representing price levels and interest rates consistent with equilibrium in the money market. The two versions of the LM curve (analogous, but not identical, to the Keynesian LM curve) correspond to different monetary regimes. In what Thompson called the classical case, the price level is fixed by convertibility of output into cash at a fixed exchange rate, with money being supplied by a competitive banking system paying competitive interest on cash balances. The LM curve in this case is vertical at the fixed price level, with any nominal rate of interest being consistent with equilibrium in the money market, inasmuch as the amount of money demanded depends not on the nominal interest rate, but on the difference between the nominal interest rate and the competitively determined interest rate paid on cash. In the modern case, cash is non-interest bearing and supplied monopolistically by the monetary authority, so the LM curve is upward-sloping, with the cost of holding cash rising with the rate of interest, thereby reducing the amount of money demanded and increasing the price level for a given quantity of money supplied by the monetary authority. The solution of the model corresponds to the intersection of the FF and LM curves. For the classical case, the intersection is unique, but in the modern case since both curves are upward sloping, multiple intersections are possible.

The focus of the fourth installment was on setting up a model analogous to the Keynesian model by replacing the market for capital services excluded by Walras’s Law with something similar to the Keynesian expenditure functions (consumption, investment, government spending, etc.). The key point is that the FF and LM curves implicitly define a corresponding CC curve (shown in Figure 4 of the third installment) with the property that, at all points on the CC curve, the excess demand for (supply of) money exactly equals the excess supply of (demand for) labor. Thus, the CC curve represents a stock equilibrium in the market for commodities (i.e., a single consumption/capital good) rather than a flow rate of expenditure and income as represented by the conventional IS curve. But the inconsistency between the upward-sloping CC curve and the downward sloping IS curve reflects the underlying inconsistency between the neoclassical and the Keynesian paradigms.

In this installment, I am going to work through Thompson’s argument about the potential for an unstable equilibrium in the version of his model with an upward-sloping LM curve corresponding to the case in which non-interest bearing money is monopolistically supplied by a central bank. Thompson makes the argument using Figure 5, a phase diagram showing the potential equilibria for such an economy in terms of the FF curve (representing price levels and nominal interest rates consistent with equilibrium in the markets for labor and capital services) and the CC curve (representing price levels and nominal interest rates consistent with equilibrium in the output market).

Thompson_Figure5A phase diagram shows the direction of price adjustment when the economy is not in equilibrium (one of the two points of intersection between the FF and the CC curves). A disequilibrium implies a price change in response to an excess supply or excess demand in some market. All points above and to the left of the FF curve correspond to an excess supply of capital services, implying a falling nominal interest rate; points below and to the right of the FF curve correspond to excess demand for capital services, implying a rising interest rate. Points above and to the left of the CC curve correspond to an excess demand for output, implying a rising price level; points below and to the right of the CC curve correspond to an excess supply of output, implying a falling price level. Points in between the FF and CC curves correspond either to an excess demand for commodities and for capital services, implying a rising price level and a rising nominal interest rate (in the region between the two points of intersection – Eu and Es — between the CC and FF curves) or to an excess supply of both capital services and commodities, implying a falling interest rate and a falling price level (in the regions below the lower intersection Eu and above the upper intersection Es). The arrows in the diagram indicate the direction in which the price level and the nominal interest rate are changing at any point in the diagram.

Given the direction of price change corresponding to points off the CC and FF curves, the upper intersection is shown to be a stable equilibrium, while the lower intersection is unstable. Moreover, the instability corresponding to the lower intersection is very dangerous, because entering the region between the CC and FF curves below Eu means getting sucked into a vicious downward spiral of prices and interest rates that can only be prevented by a policy intervention to shift the CC curve to the right, either directly by way of increased government spending or tax cuts, or indirectly, through monetary policy aimed at raising the price level and expected inflation, shifting the LM curve, and thereby the CC curve, to the right. It’s like stepping off a cliff into a black hole.

Although I have a lot of reservations about the practical relevance of this model as an analytical tool for understanding cyclical fluctuations and counter-cyclical policy, which I plan to discuss in a future post, the model does resonate with me, and it does so especially after my recent posts about the representative-agent modeling strategy in New Classical economics (here, here, and here). Representative-agent models, I argued, are inherently unable to serve as analytical tools in macroeconomics, because their reductionist approach implies that all relevant decision making can be reduced to the optimization of a single agent, insulating the analysis from any interactions between decision-makers. But it is precisely the interaction effects between decision makers that create analytical problems that constitute the subject matter of the discipline or sub-discipline known as macroeconomics. That Robert Lucas has made it his life’s work to annihilate this field of study is a sad commentary on his contribution, Nobel Prize or no Nobel Prize, as an economic theorist.

That is one reason why I regard Thompson’s model, despite its oversimplifications, as important: it is constructed on a highly aggregated, yet strictly neoclassical, foundation, including continuous market-clearing, arriving at the remarkable conclusion that not only is there an unstable equilibrium, but it is at least possible for an economy in the neighborhood of the unstable equilibrium to be caught in a vicious downward deflationary spiral in which falling prices do not restore equilibrium but, instead, suck the economy into a zero-output black hole. That result seems to me to be a major conceptual breakthrough, showing that the strict rationality assumptions of neoclassical theory can lead to aoutcome that is totally at odds with the usual presumption that the standard neoclassical assumptions inevitably generate a unique stable equilibrium and render macroeconomics superfluous.

8 Responses to “Thompson’s Reformulation of Macroeconomic Theory, Part V: A Neoclassical Black Hole”


  1. 1 Lord November 23, 2015 at 10:56 am

    Sounds like a start, ignoring the misleading labor analysis, but still seems only half a story. If only fiscal/monetary policy can prevent black holes, why haven’t we seen them, or is there some limit to them, possibly between assets and income, that creates a third lower equilibrium from which growth proceeds again.

  2. 2 Egmont Kakarot-Handtke November 23, 2015 at 11:36 am

    Black hole economics
    Comment on ‘Thompson’s Reformulation of Macroeconomic Theory, Part V: A Neoclassical Black Hole’

    Thompson rejected the IS-LM model for various reasons but overlooked the lethal flaw, that is, the implicit equality/equilibrium of saving/investment. In this he was by no means unique. From the utterances of the mouthpieces of the major economics sects one can safely conclude that the representative economist has not gotten the point until this very day (2014; 2011).* Because the lethal flaw of IS-LM escaped Thompson he set out to repair non-existing or inconsequential defects.

    The flaw of IS-LM and all its recent variants is that no such thing as an IS schedule exists because saving and investment are never equal. This is a testable proposition, so there is no need for further debate.

    The corrections/improvements of Thompson are spurious because he methodologically falls back into pre-Keynesian darkness. Keynes realized that the neoclassical approach was fundamentally (=axiomatically) flawed. “For if orthodox economics is at fault, the error is to be found not in the superstructure, which has been erected with great care for logical consistency, but in a lack of clearness and of generality in the premises.” (1973, p. xxi) And, by consequence “there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required to-day in economics.” (1973, p. 16)

    What Keynes meant with ‘to throw over the axiom of parallels’ is now called a paradigm shift. Most economists erroneously think that it is enough to replace one model by another model or to replace a patently weird assumption, e.g. perfect wage/price flexibility, with something more ‘realistic’, e.g. sticky wages. Those marginal corrections are insufficient, a paradigm shift goes to the root.

    Thompson’s attempt is misguided because the whole neoclassical approach is misguided because its axiomatic basis is forever unacceptable. The common denominator of all neoclassical models is given with these hard core propositions: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states. (Weintraub, 1985, p. 147)

    Or, as Krugman put it on his blog “most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point …”. This is the root mistake.

    What can be said with certainty is that the set of five neoclassical hard core propositions has proven its worthlessness. More specifically ALL sorta-kinda maximization-and-equilibrium models are “inherently unable to serve as analytical tools in macroeconomics” (See intro).

    This includes Thompson’s approach. Note in particular that the distinction between stable and unstable equilibrium does not make the concept of equilibrium more acceptable — just as the distinction between female/male angels does not make the concept of angel more acceptable. Equilibrium is a nonentity. Because of this, HC5 has to be rejected. The same holds for HC2. And this means that all sorta-kinda maximization-and-equilibrium models have to be rejected. From wrong premises nothing of any value ever follows: garbage in, garbage out.**

    We can agree with Thompson that Keynesian IS-LM models are unacceptable. We can agree with Keynes that all Walrasian models are unacceptable. This has the dire consequence that the policy proposals with regard to monetary and fiscal policy of both sects have no sound theoretical foundation. Where the true economic theory should reside there is a scientific black hole.

    Egmont Kakarot-Handtke

    References
    Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–20. URL http://ssrn.com/abstract=1966438.
    Kakarot-Handtke, E. (2014). Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It. SSRN Working Paper Series, 2392856: 1–19. URL
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2392856.
    Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.
    Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL
    http://www.jstor.org/stable/1805586

    * See also I=S: Mark of the Incompetent
    http://axecorg.blogspot.de/2015/10/is-mark-of-incompetent.html
    ** The replacement of HC1 to HC5 for the correct reformulation of macroeconomics is given here

  3. 3 elwailly November 24, 2015 at 3:09 pm

    A question to increase my understanding..

    “For Thompson involuntary unemployment means unemployment caused by overly optimistic expectations by workers of wage offers, leading them to mistakenly set reservation wages too high”.

    Isn’t the cause more than just the expectations of out of work workers when contemplating wage offers? Isn’t the cause the general nominal price level being too high for the amount of money in the economy, part of which is the wage level of all workers, employed or unemployed?

    Ignoring the fact that a new hire would feel it is very unfair to work for a lower wage when others doing his exact same job are being paid more; it doesn’t seem likely to me that hiring 10% more workers at a lower wage, because these new workers are flexible enough to accept a lower wage, is enough to fully change the general nominal price level in the economy.

    Employers would have to lower the price they charge for all their products and convince all their employees to accept the lower wage (or replace them all with new workers).

    I’ve always wondered why economist think the solution to unemployment is personally in the hands of each of the unemployed persons if only they were flexible.

  4. 4 Egmont Kakarot-Handtke November 25, 2015 at 5:51 am

    ICYMI (elwailly Nov 24)

    The correct employment theory states that — for the economy as a whole — the average wage rate must rise in order to prevent unemployment and deflation.

    With the provably false standard employment theory economists bear the intellectual responsibility for the social devastation of unemployment. Since Keynes gave his diagnosis in ‘The Great Slump of 1930’ every economist could know that ‘what we economists have all learned, and many of us teach’ (Tobin) about the relationship between wage rate and employment for the economy as a whole is dead wrong.

    For more details and references see the post ‘The key relationship between employment and wage rate’
    http://axecorg.blogspot.de/2015/11/the-key-relationship-between-employment.html

    For the bigger picture see ‘Profit and the collective failure of economists’
    http://axecorg.blogspot.de/2015/11/profit-and-collective-failure-of.html

  5. 5 TravisV November 27, 2015 at 9:38 am

    Dr. Glasner, you might be interested in this new book review:

    http://www.nytimes.com/2015/11/22/books/review/the-money-makers-by-eric-rauchway.html

    Jeffry Frieden: Book Review: ‘The Money Makers’ by Eric Rauchway


  1. 1 Eric Rauschway on the Gold Standard | Uneasy Money Trackback on December 1, 2015 at 6:24 pm
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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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