Saturday, November 27, 2010

Continued Balderdash From Liebowitz And Margolis

Joan Robinson, drawing on John Maynard Keynes, famously distinguished between models set in historical and logical time. Geoffrey Hodgson, now an institutionalist economist, has written extensively about evolutionary models in economics. Given my interest in such economists, I also find of interest how to formalize the notion that "history matters". I think mathematical models of nonergodic processes is one way of formally setting a model in historical time.

Brian Arthur and Paul David, two economists, have developed a parallel idea, that of path dependence. This post is about false statements Stan Liebowitz and Stephen Margolis like to make about this work. Liebowitz and Margolis quote Paul David:
"The foregoing account of what the term 'path dependence' means may now be compared with the rather different ways in which it has come to be explicitly and implicitly defined in some parts of the economics literature. For the moment we may put aside all of the many instances in which the phrases 'history matters' and 'path dependence' are simply interchanged, so that some loose and general connotations are suggested without actually defining either term. Unfortunately much of the non-technical literature seems bent upon avoiding explicit definitions, resorting either to analogies, or to the description of a syndrome - the set of phenomena with whose occurrences the writers associate path dependence. [Rather than telling you what path dependence is, they tell you some of the symptomology - things that may, or must happen when the condition is present. It is rather like saying that the common cold is sneezing, watering eyes and a runny nose.]" -- Paul David
Liebowitz and Margolis somehow think you will be persuaded to believe the following:
"So here we see David disqualifying, at least from others, any efforts to connect path dependence to observable phenomena. David would have path dependence discussed only in the context of the most severe abstraction, an immaculate concept immune from criticism: it is a dynamic stochastic process that is non-ergodic." -- Stan Liebowitz and Stephen Margolis
Notice Paul David never says that path dependence, under a rigorous definition, never will be manifested in observable empirical phenomena. Elsewhere Paul David notes that Markov processes can be non-ergodic, that is, path dependent. And he notes that economists have connect Markov processes, not all of which need be path-dependent, to observable penomena:
"Homogeneous Markov chains are familiar constructs in economic models of the evolving distribution of workers among employment states, firms among size categories, family lineages among wealth-classes or socio-economic (occupational) strata, and the rankings of whole economies among in the international distribution of per capita income levels." -- Paul David
Why are certain economists so willing to tell untruths?

  • W. Brian Arthur (1989) "Competing Technologies and Lock-In by Historical Small Events", Economic Journal, V. 99, N. 1: pp. 116-131.
  • W. Brian Arthur (2009) The Nature of Technology: What It Is and How It Evolves, The Free Press. [I haven’t read this]
  • Paul A. David (1985) "Clio and the Economics of QWERTY", American Economic Review. V. 75, N. 2 (May): pp. 332-337.
  • Paul A. David (2000) "Path Dependence, It's Critics and the Quest for 'Historical Economics'"
  • Paul A. David (2007) "Path Dependence - A Foundational Concept for Historical Social Science", Cliometrica, V. 1, N. 2: pp. 91-114 (working copy)
  • Stan J. Liebowitz and Stephen E. Margolis (2010) "How the Lock-In Movement Went off the Tracks"

Sunday, November 14, 2010

On "A Splendid Contribution"

The appendix of Omkarnath's aprreciation of Bharadwaj's review of Sraffa's book contains an exchange of letters between Bharadwaj and Sraffa. Here's Sraffa's letter:
"As from Trinity College, Cambridge
Sabzburg, Austria
September 8, 1963

Dear Mrs. Bharadwaj,

Thank you so much for your kind letter, which I receive abroad, just as I am about to return to Cambridge.

I am delighted with your excellent article, which will be of great help to many who have been puzzled by my book. I have no doubt that you have correctly grasped the main lines of the argument and also guessed some of the directions in which, in my view the criticism of marginalism should be developed.

There are only one or two minor points in which I think your exposition is perhaps not as lucid as it is in general. One (p. 1452, col 3, first para), on deriving 'land theory of value'. I suppose this is an echo of Samuelson, but I do not see the implications. (I have the impression that you somewhat underestimate the historical importance of the labour theory of value: in my view much of modern theory is, whether consciously or not, a polemic against it.) Another one is p. 1453, col 1, from 'To a particular wage' to the end of the paragraph: I find this obscure and have some doubts about what I seem to understand. Also, a small point of disagreement is the very last words of your final footnote. I insist that the construction of a subsystem is a purely bookkeeping operation!

These, however, are very minor blemishes and the article remains a splendid contribution for which I am most grateful. I hope very much you will continue to work on these lines.

With kind regards,

Yours sincerely,
Piero Sraffa"

Sraffa criticizes three passages in Bharadwaj's review. I agree the second passage is not well written:
"To a particular wage, given in any standard, there may correspond several alternative rates of profits. This shows the absolute necessity of measuring the wage in terms of the Standard commodity, if unequivocal conclusions regarding the movements of the rate of profits given the wage rate are to be drawn. Measurement of the wage in terms of the Standard commodity gives us definite information regarding both the direction as well as the extent of change in the rate of profits, consequent upon a change in the wage rate. No other standard possesses this predictive value." -- Krishna Bharadwaj (1963)
The wage is only defined in terms of some standard. Once the standard is specified, a unique rate of profits corresponds to that wage, no matter what the standard. A different rate of profits may correspond to the same numeric value in a different standard. But one would not expect the same properties to be displayed by a substance at zero degrees Celsius and zero degrees Fahrenheit.

I think Sraffa's criticism of the third passage is a disagreement about the level of emphasis. Here is that passage:
"Nevertheless, while reading the paragraphs relating to the construction of the Standard system (pp. 23-4) and more particularly the subsystems (p. 89), one gets a feeling as though the assumption of constant returns-to-scale is necessary. Such doubts could easily be warded off since the Standard commodity is purely an auxiliary construction having no physical existence in production relations. Similar is the case of the subsystems which are used to derive the direct and indirect labour content of commodities (at zero profit rate)." -- Krishna Bharadwaj (1963)

  • Krishna Bharadwaj (1963) "Value Through Exogenous Distribution", The Economic Weekly, (August 24): pp. 1450-1454.
  • G. Omkarnath (2005) "'Value Through Exogenous Distribution': A Review Article in 1963", Economic and Political Weekly, (January 29): pp. 459-464.

Tuesday, November 09, 2010

Do Angeletos And La'O Know What They Are Talking About?

Some comic gives some stupid and vile economists an opportunity to comment on some of Cosma Shalizi's ideas [1]. (I find particularly stupid the commentator that cites Amazon, a Web 2.0 exemplar, for an example of agents interacting only through prices.) Eventually, one respondent says that George-Marios Angeletos and Jennifer La'O show how to embed animal spirits in Dynamic Stochastic General Equilibrium (DSGE) models. I'm not sure which paper they are talking about, but I did download their paper Sentiments (with accompanying slides.) I do not object to how Angeletos and La'O model shocks, although in this setting I don’t see why I should care.

I was quickly stopped in reading this paper at the first footnote:
"By 'mainstream' we mean the prototypical RBC and New-Keynesian models, as well as the more recent DSGE models. This excludes models with multiple equilibria or irrational agents, which we discuss in due course."
How are models with multiple equilibria non-mainstream? They continue in this vein throughout their paper:
"In our model, agents are fully rational; preferences and technologies are standard; markets are Walrasian; there are no nominal frictions, no externalities, and no non-convexities; the equilibrium is unique; and there is no room for correlation devices or lotteries. In these respects, our theory has squarely neoclassical foundations."
"This extrinsic uncertainty has very similar flavor as the one encountered in models with multiple equilibria: it captures the self-fulfilling nature of short-run fluctuations. Importantly, though, it does not rest on the severe externalities, non-convexities and missing markets that are most often needed to sustain multiple equilibria-nor does it come with the usual difficulties in conducting policy analysis."
It is my understanding that the Sonnenschein-Mantel-Debreu theorem is proved in a Walrasian model with no externalities, non-convexities, or missing markets. The excitement over the theorem comes from being derived with the same sort of assumptions that are used in Debreu's Theory of Value to derive the existence of an equilibrium. So I find it hard to believe the authors know what they are talking about when they suggest multiple equilibria are non-Walrasian or non-neoclassical.

By the way, I happen to have available a model with multiple equilibria. Figures 1 and 2 below illustrate. I'd like somebody to point out to me how agents in this model are not fully rational; how preferences and technologies are non-standard; or where nominal frictions, externalities, and non-convexities exist in this model. I suppose one can say some markets do not exist in an overlapping generations model. Agents cannot buy commodities or sell their labor before they are born or after they are dead. I did not think such an assumption made a model heterodox or non-neoclassical.
Figure 1: Equilibrium Interest Rates as a Function of One Parameter in the Utility Function
Figure 2: Equilibrium Wages as a Function of Another Parameter

[1] Cosma Shalizi is on a team of three that has recently received a grant awarded by the Institute for New Economic Thinking.

Friday, November 05, 2010

A Slight Illness - The Doctor Jests, A King Today - Tomorrow He Is Dead

Has the global financial crisis discredited Dynamic Stochastic General Equilibrium (DSGE) models? It seems to me that that may be so, but I wonder if new criticisms of DSGE models have been put forth. It seems to me the fundamental flaws of such models have been unaddressed for decades. Cosma Shalizi describes these models in a critical way. Joseph Stiglitz is not impressed with them either:
"It is hard for non-economists to understand how peculiar the predominant macroeconomic models were. Many assumed demand had to equal supply - and that meant there could be no unemployment. (Right now a lot of people are just enjoying an extra dose of leisure; why they are unhappy is a matter for psychiatry, not economics.) Many used "representative agent models" - all individuals were assumed to be identical, and this meant there could be no meaningful financial markets (who would be lending money to whom?). Information asymmetries, the cornerstone of modern economics, also had no place: they could arise only if individuals suffered from acute schizophrenia, an assumption incompatible with another of the favoured assumptions, full rationality." -- Joseph Stiglitz

As I understand it, Smets and Wouters (2007) is an example of a DSGE model widely approved of by mainstream economists. Sbordone et al. (2010) is a recent presentation of an introductory DSGE. One can see that the output of these models is a set of stochastic processes meant to model certain time series available in empirical data. Nominal interest rates, (real) income, the inflation rate, the volume of one-period government bonds, employment, and nominal wages are all examples of such time series. The input into such models is another set of stochastic processes. These inputs are given names that suggest they are random terms in functions characterizing either government entities - e.g., monetary policy shock - or agents in microeconomic models. Examples of the latter kind of names are a household discount rate shock, productivity shock, markup shock, and firm discount rate shock. Stochastic processes are specified by parameters of certain probability distributions. As one can see from the names of these inputs, the agents are supposed to be optimizing, including across time. A story, expressed in mathematics and supposedly of microeconomic equilibrium, connects the inputs to the outputs in the model. That is, the DSGE models are supposed to have microfoundations.

But they do not have microfoundations. I look for a number of mistakes in such models:
  • Are inputs into production function measured in numeraire units? (The numeraire is often taken to be a basket of consumer goods.) Joan Robinson (1953-54) explains why measuring the quantity of capital in production functions in numeraire units is an error. Notice this is not solely a question of the aggregation of capital. A model can have a continuum of capital goods, yet still exhibit this mistake.
  • Are representative agents used? Kirman (1992) explains why the use of representative agents is unfounded.
  • Is money modeled? Frank Hahn (1965) explains why money does not matter in General Equilibrium models, even though it does seem to matter for actually existing capitalist economies. Mainstream economists have a couple of strategies for introducing money in an ad hoc way into DSGE models. But I am not convinced the typical modeler has ever managed to address Hahn's point.
  • Is the possibility of multiple equilibria taken seriously? Is it demonstrated that non-equilibrium dynamic processes converge to the modeled equilibrium? Richard Goodwin (1990) illustrates what a macroeconomics looks like that, in contrast to typical DSGE models, takes dynamics seriously. Kirman (1989) shows that ignoring muliple equilibria and stability issues was demonstrated to be unfounded by the Sonnenschein-Mantel-Debreu results. Shiller (1978) long ago raised the issues of multiple equilibria and convergence. Shiller was critiquing the tradition out of which DSGE models evolved.
I haven't read much in the literature of DSGE models. It seems to me, however, that these issues are routinely ignored by many mainstream economists. Perhaps a wider range of macroeconomic models should be considered by serious researchers.

To read:
  • Wynne Godley and Marc Lavoie (2007) Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, Palgrave MacMillan.

Tuesday, November 02, 2010

James Joyce On Identity Economics

I think that if one looked, one would be able to find in lots of depictions in literature of multiple selves. Here's an example:
"...he had heard about him the constant voices of his father and of his masters, urging him to be a gentleman above all things and urging him to be a good catholic above all things. These voices had now come to be hollow-sounding in his ears. When the gymnasium had been opened he had heard another voice urging him to be strong and manly and healthy and when the movement towards national revival had begun to be felt in the college yet another voice had bidden him to be true to his country and help to raise up her language and tradition. In the profane world, as he foresaw, a worldly voice would bid him raise up his father's fallen state by his labours and, meanwhile, the voice of his school comrades urged him to be a decent fellow, to shield others from blame or to beg them off and to do his best to get free days for the school. And it was the din of all these hollow-sounding voices that made him halt irresolutely in the pursuit of phantoms." -- James Joyce, A Portrait of the Artist as a Young Man
Does how artists depict human beings carry any weight for how economists choose to portray agent's choices? Should it?