Some Financial Analysis in Software Engineering

Warning: Lots of navel-gazing in this post.

Example of Financial Analysis of Two Methods for Detecting Software Bugs (from Vienneau 1995)

Consider a specific industry, namely the production of software. (This industry would correspond to a column in an input-output matrix.) Many methods have been proposed for improving the productivity, the quality, and management control in software development, operations, and management. And, as software became a more important component in, for example, embedded systems, various measures, and various methods for choosing among possible measures, have been proposed for software processes and products. Some time ago, some researchers argued that analyses of such metrics should be oriented towards economic analysis of, for example, efforts to introduce new methods into the software lifecycle. I think of the following two articles as early exponents of this thesis:

• Sandra A. Slaughter, Donald E. Harter, and Mayuram S. Krishnan. Evaluating the Cost of Software Quality, Communications of the ACM. V. 41, No. 8 (Aug. 1998): pp. 67-73.
• Robert L. Vienneau. The Present Value of Software Maintenance, Journal of Parametrics (April 1995).

Slaughter et al. is more high level and is published in a more prestigious journal. My article is more a tutorial.

One can apply economics to analyze specific decisions during the software lifecycle. For instance, the following article looks at when testing should stop and software should be released:

• Robert L. Vienneau. The Cost of Testing Software, Proceedings of the Annual Reliability and Maintainability Symposium, Orlando, FL (29-31 Jan. 1991).

The optimal release date can be justified by a simple marginal rule: the final phase of testing should stop, and software should be released, when the cost of an increment of testing reaches or exceeds the marginal benefit to gained from that increment of testing. The marginal benefit can be conceptualized as the product of the expected number of bugs to be observed during that increment of time and the savings in finding those bugs during test, instead of operations. (Various software reliability models exist for estimating the parameters needed to implement this rule.)

I have not been aggressive in promoting my work in software engineering economics. Once in a while, I search the web to see who, if anybody, is referencing this stuff. This post concludes with a number of papers, theses, and selected technical reports citing one or the other of the above papers, or related work from me. I do not know why so many of these references are so recent; perhaps software processes must attain a certain level of maturity before these financial analyses become useful.

• Majed Alyahya, Rodina Ahmad, and Sai Peck Lee. Impact of CMMI-Based Process Maturity Levels on Effort, Productivity and Diseconomy of Scale, International Arab Journal of Information Technology. V. 9, No. 4 (Jul. 2012): pp. 352-360
• Hanna Farnstrand. Introducing Structured Testing, Lund University (16 Jun. 2008).
• Matt Ganis. Agile Methods: Fact or Fiction, Trenton Computer Festival. (Apr. 2010).
• Warren Harrison, David Raffo, John Settle, Nancy Eickelmann. Technology Review: Adapting Financial Measures: Making a Business Case for Software Process Improvement, Software Quality Journal. V. 8, No. 3 (1999): pp. 211-231.
• Chin-Yu Huang, Jung-Hua Lo, Sy-Yen Kuo, and Michael R. Lyu. Optimal Allocation of Testing-Resource Considering Cost, Reliability, and Testing Effort, Proceedings of the 10th IEEE Pacific Rim International Symposium on Dependable Computing (PRDC'04) (2004): pp. 103-112.
• Chin-Yu Huang and Jung-Hua Lo. Optimal Resource Allocation for Cost and Reliability of Modular Software Systems in the Testing Phase, Journal of Systems and Software. V. 79, Iss. 5 (May 2006): pp. 653-664.
• Zhengrui Jiang, Sumit Sarkar, and Varghese S. Jacob. Postrelease Testing and Software Release Policy for Enterprise-Level Systems, Information Systems Research. V. 23, No. 4 (Dec. 2012).
• J. Dennis Lawrence. Software Reliability and Safety in Nuclear Reactor Protection Systems, Lawrence Livermore National Laboratory, UCRL-ID-114839 (11 Jun. 1993).
• Tuomas Paasonen. Methods for Improving the Maintainability of Application Software. Master Thesis, Aalto University (13 April 2012).
• David Raffo and Tim Menzies. Evaluating the Impact of a New Technology Using Simulation: The Case for Mining Software Repositories. [I am unsure of the status of this paper].
• Tobias Scherner and Lothar Fritsch. Early Evaluation of Security Functionality in Software Projects - some Experience on using the Common Criteria in a Quality Management Process, Johann Wolfgang Goethe - Universitat, Franfurt am Main (2007).
• Leon van Delft. Automated GUI Testing in Industry. Master Thesis, Delft University of Technology (28 Dec. 2011).

Update (28 February 2013): Added Huang and Lo (2006) to remind me to check if my search with Google Scholar yielded an accurate reference.

Update (13 March 2013): Added Huang et al. (2004).

Empirical Bifurcation Diagram For Kaldor Model

Figure 1: An Empirically-Constructed Bifurcation Diagram

I thought I would try to summarize what I have learned about the qualitative behavior of Kaldor's business cycle model. (Although I had some preparation, I learned much of the mathematics in this post during this analysis.) Figure 1, above, shows (mostly) bifurcations found empirically, while Figure 2 below shows bifurcations that can be found analytically. The normalized model is specified by four parameters, the speed of adjustment of national income to the difference between aggregate demand and supply, the depreciation rate of capital, the (average and marginal) propensity to save out of income, and the cost of adjusting the capital stock to the desired level. Figures 1 and 2 are drawn for a constant depreciation rate (δ = 1/5) and a constant cost of adjustment (γ = 3/5). The abscissa in the figures represents different levels of the speed of adjustment (α), while the ordinate represents different levels of the propensity to save (σ).

Figure 2: An Analytically-Constructed Bifurcation Diagram

The Kaldor model has two (endogenously determined) state variables, the normalized level of the capital stock (k_t) and the normalized flow of national income (y_t). A bifurcation analysis determines regions in the parameter space in which the flows for the state variables qualitatively differ. A bifurcation is a manifold in the parameter space in which some such qualitative difference arises. The figures above show selected bifurcations, where each bifurcation is represented by a line or curve in the figure. (I do not claim that the bifurcations shown are the complete set of bifurcations that arises, even in the part of the parameter space shown. For example, I ignore homoclinic bifurcations of points along a limit cycle with the (in)stability of a saddle point.)

The horizontal line near the top of Figure 1 is shown near the bottom of Figure 2. This line represents a pitchfork bifurcation. The model has one fixed point (stationary state), at the origin of the state space, above the line. The model has three fixed points below the line, one at the origin, and the other two symmetrically located around the origin in the first and third quadrants. As I understand it, the origin always has saddle-point (in)stability below this line.

The blue curve in Figure 2 arcing upward to the right from the horizontal line is a Neimark-Sacker bifurcation. (The Neimark-Sacker bifurcation is the discrete time analog to the Hopf bifurcation.) To the left of this curve, the fixed point at the origin is stable. The origin loses its stability at the Niemark-Sacker bifurcation, and it throws out a stable limit cycle to the right. A limit cycle corresponds to a business cycle in the modeled economy.

I think that the bifurcations in the region with three fixed points, below the horizontal line representing the pitchfork bifurcation, are more complicated and more difficult to understand. In the lower left of Figure 1, the two symmetrical fixed points not at the origin are stable. One can find each fixed point's basin of attraction in the state space, that is, those values of the state variables such that a trajectory in the state space started with those values converges to the given fixed point. As I understand it the two basins of attraction cover the entire state space in this region of the parameter space.

Figure 1 shows three (hard to distinguish) curves coming down from the horizontal line and curving to the right. All of these curves intersect the horizontal line at the same point. And that point is also the intersection with that horizontal line of the curve above the horizontal line representing the Neimark-Sacker bifurcation I have previously described. (I have no idea how you would formally prove this.)

The lowest of these curves sloping downward to the right represents a bifurcation in which a limit cycle with saddle point stability appears. Along this curve in the parameter space, a region exists in the state space in which trajectories approach the limit cycle, only to ultimately diverge to one of the fixed points away from the origin.

The next higher curve sloping downward to the right in Figure 1 is almost impossible to tell apart from the curve that I have just described. This curve represents a homoclinic bifurcation. The basins of attraction of the fixed points away from the origin no longer combine to cover the state space. At the homoclinic bifurcation, the stable and unstable sets of the origin merge. Between the lower curve and this curve, the limit cycle with saddle-point stability bifurcates to form (at least) two limit cycles, one stable and one unstable. The unstable limit cycle is the boundary of the union of the basins of attraction of the two stable fixed points. Just above this curve, the border of the basins of attraction bifurcates, to form two disjoint unstable limit cycles. The stable limit cycle remains in the state space, enclosing the fixed point at the origin and these unstable limit cycles.

The highest curve sloping downward to the right in Figure 1 is another Neimark-Sacker bifurcation. The fixed points away from the origin lose their stability at this bifurcation. Their basins of attraction disappear. The unstable limit cycles forming the border of each basin of attraction are absorbed into the corresponding limit point. A stable limit cycle remains. So on the right of Figure 1, both above and below the horizontal line, a stable limit cycle exists, even though the number of fixed points varies with the propensity to save.

I was surprised at the diverse and complex behavior that economists have found in the Kaldor model, a model of the business cycle that is nearly three-quarters of a century old.

Inconsistencies In Keynes's General Theory And In General Equilibrium Theory?

1.0 Introduction

In this post, I raise some questions about how short-period and long-period equilibrium relate. I consider this issue in two frameworks:

• Keynes's General Theory.
• The Arrow-Debreu model of intertemporal equilibrium.

The issue in the first framework is at least partly a question of hermeneutics - can one read Keynes such that his theory is internally consistent? The issue in the second framework is, as I understand it, a question of mathematics.

2.0 Keynes's General Theory

It seems to me, Keynes, in his definition of long-period equilibrium simultaneously postulates that agents have common and divergent expectations. Can one find a consistent long-period equilibrium concept in the General Theory that includes both production and financial markets? I think of Post Keynesians, such as Joan Robinson, as having emphasized the extension of the General Theory to the long period. But I am not sure I can find a good resolution in the literature. I think my question is close to Jan Kregel's (1985) point.

Keynes defines long period equilibrium in Chapter 5, "Expectation as Determining Output and Employment":

"If we suppose a state of expectation to continue for a sufficient length of time for the effect on employment to have worked itself out so completely that there is, broadly speaking, no piece of employment going on which would not have taken place if the new state of expectation had always existed, the steady level of employment thus attained may be called the long-period employment¹ corresponding to that state of expectation. It follows that, although expectation may change so frequently that the actual level of employment has never had time to reach the long-period employment corresponding to the existing state of expectation, nevertheless every state of expectation has its definite corresponding level of long-period employment...

...past expectations, which have not yet worked themselves out, are embodied in the to-day's capital equipment with reference to which the entrepreneur has to make to-day's decisions, and only influence his decisions in so far as they are so embodied. It follows, therefore..., to-day's employment can be correctly described as being governed by to-day's expectations taken in conjunction with to-day's capital equipment.

¹ it is not necessary that the level of long-period employment should be constant, i.e. long-period conditions are not necessarily static. For example, a steady increase in wealth or population may constitute a part of the unchanging expectation. The only condition is that the existing expectations should have been foreseen sufficiently far ahead." -- John Maynard Keyes (1936): pp. 48-50.

Keynes analyzes financial markets in Chapter 12, "The State of Long-Term Expectation". It is in this chapter that he introduces his distinction between speculation and enterprise, as well as likening the markets for shares (stocks) and bonds to a beauty contest in which participants are not trying to pick the prettiest entrant, but rather the entrant who will be thought prettiest by common opinion, when all who are picking the entrant are looking at their choice from this perspective.

My claim is that the Chapter 5 definition requires common expectations, while the chapter 12 analysis presumes a diversity of expectations. In fact, according to Keynes, the momentary stability of financial markets depends on a balance of bulls and bears and, thus, divergent expectations.

3.0 General Equilibrium Theory

In the Arrow-Debreu model, an equilibrium can be considered a path through (logical) time. Some of those paths, in some simplified models, are steady states, in which each industry expands at the same rate of growth. One can read Von Neumann as setting forth the production side of such a model of a stationary state, if one so chooses.

In general, an equilibrium path in the Arrow-Debreu model is a (very) short-period equilibrium. The initial endowment of capital goods is taken as given, and expectations of the agents in the model are pre-reconciled. (Questions, perhaps unanswerable, exist about how such an equilibrium can be achieved.) One can ask about the limit behavior of each equilibrium path, as time increases without bound. Some of these paths might converge to stationary states, and some might diverge.

I associate the Turnpike Theorem with Paul Samuelson. I turn to either Dorfman, Samuelson, and Solow (1958) or, for example, Dixit (1976), when I want to read an exposition of this theorem. As I understand it, this theorem implies that stationary states, generically, have saddle point (in)stability in the Arrow-Debreu model.

I am also aware of the Sonnenschein-Mantel-Debreu theorem. As I understand it, this theorem implies almost any dynamics are possible in the Arrow-Debreu model. Some such dynamics, then, should be consistent with stationary states that are locally stable. Another dynamics in the model should be consistent with stationary states that are locally unstable. And some configuration of parameters should be consistent with multiple equilibrium mixing any combination of stable steady states, unstable steady states, and saddle-point steady states.

My understanding of the implications of the Turnpike and Sonnenschein-Mantel-Debreu theorems seems to be inconsistent. Where do I go wrong?

References

• A. K. Dixit (1976). The Theory of Equilibrium Growth. Oxford University Press.
• Robert Dorfman, Paul A. Samuelson and Robert M. Solow (1958). Linear Programming and Economic Analysis, Dover.
• John Maynard Keynes (1936).The General Theory of Employment, Interest and Money. Harcourt, Brace and Company.
• J. A. Kregel (1985). Hamlet without the Prince: Cambridge Macroeconomics without Money, American Economic Review. V. 75, No. 2 (May): pp. 133-139.
• J. Von Neumann (1945-1946). A Model of General Economic Equilibrium, Review of Economic Studies. V. 13, No. 1: pp. 1-9.

Against "Science", "Reality", And "Free Will"

1.0 Introduction

You may have noticed. I am not overly fond of neoclassical economics. But today I thought I would talk about criticisms you might find in the blogosphere that I find unpersuasive. That is, I do not like certain one-line assertions, without additional elaborations. I make no attempt to demonstrate here that some make these assertions.

2.0 "Economics Is Not Science"

If you are not arguing about the history, philosophy, or sociology of science, why would you care if a particular field is a science? Should you not be more concerned if the arguments in a field tend to be persuasive, if the norms in the field lead to such arguments? I can see a role here for classifying types of assumptions. One can argue about whether economists put forth supposedly substantial theories that cannot be falsified by any logical or empirical findings. Likewise, perhaps some communities of economics are not as quick as they should be to discard empirically falsified theories. Or one could ask if whatever laws are supposed to be embedded in economic models are restricted to certain institutional and historical instances of capitalism. I hope in putting forth criticisms along these lines, I try to provide concrete examples, not just abstract claims.

3.0 "Economic Theory Does Not Correspond To Reality"

What does use of the word "reality" add to an argument about the persuasiveness or non-persuasiveness of a certain set of doctrines? (I do not mean here to downgrade Tony Lawson's research into ontology and economics. In particular, I do not have a problem with the idea that economic systems are invariably open systems. I guess this idea is in tension with my simultaneous interest in natural experiments.)

4.0 "People Have Free-Will; Thus, Economies Cannot Be Modeled With Mathematics"

I am also not fond of the claim that, since people have free will, one cannot apply mathematics to economics. First, I think at least some applications of mathematics in economics are about algorithms and accounting conventions. I do not see how ideas about consumer choice are relevant to much of this work. Second, I tend to think of the distinction between free will versus determinism as one of those tired dualisms that the linguistic turn in philosophy should have dissolved. I usually cite work drawing on Ludwig Wittgenstein for this sort of point. But let me mention J. L. Austin's "A Plea For Excuses" as being directly relevant for an analysis of when an action is voluntary and of when an agent is responsible or blameworthy for what they do. Austin argues for distinctions that you might not initially see. Third, I agree that describing agents as if they calculate how to obtain a maximum utility curve, given preferences and constraints does not leave room for genuine individual choice. One might try to problematize individual choice and seek more sophisticated models. Such an approach does not necessitate the rejection of mathematics.

Distinctive Elements of Keynes' General Theory

I suggest the following are distinctive features¹ of Keynes' General Theory:

• An investment function, independent of savings (as in these examples).
• An argument for the possible existence of an equilibrium with widespread unemployment.
• A setting in historical time, not logical time.
• A claim that interest rates are to be explained by monetary and financial markets, not by causes in the "real" economy.

Paul Davidson rightly notes that Keynes strove to make his theory compatible with any degree of monopoly. This differs from Michal Kalecki, who just assumed the degree of monopoly empirically existing. But Kalecki and Keynes had different objectives; Kalecki was not as interested in internal criticism of existing neoclassical theory. Nevertheless, I think Keynes' assumption of an independent investment function may have reflected existing corporate structures. In particular, Keynes was aware of the separation of ownership from control in joint stock companies. This awareness has something to do with what Keynes meant by the "socialization of investment." Maybe it also facilitated his awareness of the possibility of investment decisions as an independent driving force for the economy.

Keynes offers a theory of a (Marshallian) short run equilibrium. For most of the book, capacity is given. Keynes analysis addresses the question of what level that capacity will be operated at. (In chapter 5, he does offer a theory of a long run equilibrium, in which the expectations that guided the installation of the present array of capital equipment have persisted since their production and are currently being satisfied.) In offering a theory of equilibrium, he needs to answer why the multiplier process does not create a cumulative process that goes on unceasingly. Somewhere I have read that Keynes' ability to answer this question distinguishes him from some potential precursors.

The distinction between historical time and logical time includes the distinction between uncertainty and risk. If I recall correctly, Hyman Minsky describes Keynes setting as having a business cycle background.

I am deliberately not putting forth the liquidity preference theory of interest as a distinctive feature. Keynes needed liquidity preference to explain why interest was a monetary phenomenon, not a matter of bringing the real economy into equilibrium. And the theory certainly generated lots of discussion. But once you see that interest rates are a monetary feature, must you retain that specific theory? Can I not think of the long run interest rate as what emerges from a succession of short runs, where the interest rate emerges in those short runs from speculators disagreeing over their views of the long run? In others words, cannot one accept interest rates as some mixture of being held up by its own bootstraps and of conventions, perhaps supported by the monetary authority?

1. I do not here make any claim about originality. This post was inspired by reading Daniel Kuehn and Jonathan Catalan noodling over the question of what was original in The General Theory.

Frank Hahn (1925-2013)

Frank Hahn's 1982 article, "The Neo-Ricardians", in the Cambridge Journal of Economics is important in my understanding of Sraffa's economics, even though I think it was misdirected in many ways. Here are some posts where I have mentioned Hahn's work:

• Geoff Harcourt reminiscing about an oral debate with Hahn.
• Wondering if macroeconomists have yet met Hahn's challenge to make money matter in General Equilibrium Theory.
• Quoting Hahn on intellectual regression in macroeconomics.

Books That I Find Sad

• Judea Pearl (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Judea is the father of Danny Pearl, the Wall Street Journal reporter who was kidnapped in Pakistan and beheaded on YouTube.
• Philippe Petit (2002). To Reach the Clouds: My High Wire Walk Between the Twin Towers. Petit performed an illegal tightrope walk between the twin towers of the World Trade Center when they were still under construction. Of course, they are gone now.
• Gary Kasparov (2003). On My Great Predecessors, Part 1. As I understand it, his childhood home in Azerbaijan was destroyed in the post-Soviet war with Armenia. At the time, I tried to follow his two tournaments with the Deep Blue computer, both played on top of one of the towers at the World Trade Center.
• Lawrence Lessig (2004). Free Culture: How Big Media Uses Technology and the Law to Lock Down Culture and Control Creativity. Everything he writes will now always remind me of Aaron Swartz.

These days, neither mathematics, nor clowning, nor games seem to be reliable escapism.

Selected Principles Of Microeconomics

This post presents a series of claims, without argument, references, or empirical evidence.

1. Raw materials & agricultural products, commodities produced by industry, and services are priced differently by firms producing each in advanced capitalist countries.
• Undeveloped, industrial, and post-industrial economies systematically vary in which of these three types of commodities they mainly produce.
• Thus, these economies may differ in their microeconomic and macroeconomic behavior.
• And even the performance of a single economy may vary among regions in that economy.
2. The prices and quantities produced of raw materials and agricultural products are mediated by supply and demand, in some sense.
• These commodities are traded on organized commodity markets.
• These markets have definite rules for matching bids and asks.
• Some speculators in these markets are willing to take either side of an exchange.
• Some firms in these markets are tasked with "making" the market.
3. The prices of industrial products are administrated, with firms setting a markup over cost.
• Typically, the ownership of a firm producing industrial commodities is separated from its control.
• Typically, such a firm operates multiple plants and produces multiple products, often in more than one industry.
• The allocation of overhead costs among the produced products is a challenge, and is mediated by accounting conventions.
• Plants typically face constant average variable costs, up to some maximum.
• Firms in these industries plan plants to operate at some average capacity below this maximum, so as to have room to respond to unforeseen demand.
• Firms in these industries respond to short-run fluctuations in demand more by varying output than by varying quoted prices.
• Firms set their markup over cost to generate internal finance for a planned rate of growth.
4. I should say something about the quantities produced and prices of services here.
• The concept of dual economies, in which some parts of a modern economy behave like an undeveloped economy, seems particularly appropriate for analyzing firms providing services.
5. Piero Sraffa's model, suitably modified, provides a framework to analyze how markets for these different kinds of commodities fit together.
• One modification involves dropping the assumption that the same rate of profits is earned in all industries.
• The absence of barriers to entry in an industry is the relevant notion of a competitive industry.
• One might consider how firm reaction functions or old Industrial Organization theory fit in here.

Charlatanism On The Theory Of Foreign Trade

I’ve noticed some foolish things said about free trade in the news recently. Yes, Ricardo showed that trade in two goods generates surplus for both countries under free trade. Samuelson later gave a more formal, general proof of the benefits of Ricardian trade for a nation, though his theorem with Stopler explains which individuals may be made worse off. Samuelson also showed that even when individuals are worse off, there is enough surplus that transfers can be made to the harmed individuals such that free trade is a Pareto improvement on autarky. Note that the last sentence is absolutely not implied by Ricardo, and how could it have been: he didn’t have the apparatus of ordinal utility nor the concept of Pareto improvement nor the idea of the Hicksian demand curve.

All of the above is true, but ..."

-- Kevin Bryan, "'Gains From Trade Without Lump-Sum Compensation'"

I have yet to read the paper referenced in the blog post linked to above. But contrast the following two quotations with the above:

"We have examined a version of the familiar H-O-S analysis, with two countries, two commodities and two factors; we have made all the normal assumptions except that, instead of a common zero rate of profit, we have assumed a common positive rate of profit. Since the existence of a positive profit rate does not affect the properties of the familiar relationship between commodity-prices and factor-prices it does not affect the factor-price-equalisation and Stolper-Samuelson theorems. In general, however, nothing can be said a priori about the relationship between factor-prices and the factor-intensity of production methods, when the profit rate is positive, and it follows that nothing can be said a priori about the shape of the relative supply curve. This does not prevent the H-O-S theorem about the pattern of trade from holding in its 'quantity' form, but does make the theorem invalid in its 'price' form, does mean that trade need not 'harm' a country's scarce factor, and does mean that uniqueness of international equilibrium is to be regarded as a special case when the common rate of profit is positive."

-- Ian Steedman and J. S. Metcalfe (1977). "Reswitching, Primary Inputs and the Heckscher-Ohlin-Samuelson Theory of Trade", Journal of International Economics

"7.5. The idea that the opening of foreign trade bears a close resemblance to technical progress, in that in both cases additional processes of production are made available to the economy, is clearly expressed in Ricardo's Principles in the chapter 'On Foreign Trade'... Ricardo in fact compares the extension of trade to improvements in machinery, and, taking the real wage rate as given, investigates whether trade or improved machinery will have an impact on the general rate of profit. He concludes that if 'by the extension of foreign trade, or by improvements in machinery, the food and necessaries of the labourer can be brought to market at a reduced price, profits will rise,' whereas 'if the commodities obtained at a cheaper rate... be exclusively the commodities consumed by the rich, no alteration will take place in the rate of profits'...

7.6. In recent years the pure theory of trade has been reformulated, using a 'classical' approach to the theory of value and distribution and paying special attention to the fact that capital consists of produced means of production. A start was made by Parrinello (1970), followed by several contributions by Steedman, Metcalfe and Steedman, and Mainwaring... It was shown that several of the traditional trade theorems, derived within the Heckscher-Ohlin-Samuelson model, do not carry over to a framework with a positive rate of profit (interest) and produced inputs (capital goods). (As is well known, the Heckscher-Ohlin-Samuelson model of international trade assumes two countries producing the same two commodities by means of the same constant returns to scale technology, using the same two primary inputs, each of which is taken to be homogeneous across countries.) With a positive rate of interest that is uniform across countries some, though not all, of the standard theorems are undermined (including the 'factor price equalization theorem'), while with different rates of interest in different countries all standard theorems except the Rybczynski theorem turn out to be untenable. The 'gains' from trade for the single small open economy need not be positive. When in the Heckscher-Ohlin-Samuelson theory one of the two primary factors (land) is replaced by a factor called 'capital', the 'quantity' of which is represented in terms of a given total value of capital, then the theory is deprived of its logical coherence..."

-- Heinz D. Kurz and Neri Salvadori, Theory of Production: A Long-Period Analysis, Cambridge University Press, 1995.

I happen to know the factor price theorem is false, once one takes into account the existence of capital.

My post here was inspired by a comment on Noah Smith's query, "Why do people think economists are charlatans"? Empirically, I expect most mainstreams economists to not give a fair overview of the literature, whether from incapacity or dishonesty. In this case, the author of the blog, "A Fine Theorem", does not even seem to be aware of the existence of work on international trade by such authors as L. Mainwaring, J. S. Metcalfe, Sergio Parrinello, Ian Steedman. Instead he just blithely claims ideas to be true that I consider to have been falsified a third of a century ago. Thus, he cannot refute their conclusions or quickly evaluate any literature on the topic.

I consider the point of this example to be general.

Elsewhere

• Dean Baker notes problems created by the Cambridge Capital Controversy (CCC) for Krugman's position on capital-intensive technological change. Most of Dean Baker's blog does not have a theoretical flavor, but is more practical.
• Matt Yglesias notes CCC problems for Krugman's position.
• A macroeconomist tells the readers to ask him anything on Reddit. (Paul Krugman once did one of these Ask-Me-Anythings.)
• Maybe one might want to occasionally look at the Ask Social Science and Academic Economics reddits.

Functions For Fashion

How might a concern with being up on current fashions in mainstream economics models help perpetuate the current sociology of economics?

Economists could study various economies in various regions and at various stages of development, economic history, the history of economics, epistemology and methodology, various alternative theories (Austrian, Feminist, Institutionalist, Marxist, Post Keynesian, ...), and other social sciences. Studying varieties of mathematical models takes up their time and provides an excuse for remaining ignorant of so much.

If you want to argue against mainstream economics, a mainstream economist can dismiss you as ignorant of some model variation and as attacking a strawperson. Furthermore, this dismissal could be "justified" by just checking whether you have a degree from a small number of schools, and, if you do, just mocking you as not having fully learned what they are teaching. Thus, your time can be taken up with argument about whether you know what you are talking about. The mainstream economist never need get to the point of engaging a critique.

With all these varieties of models, surely one will do better than another in some specific historical circumstance or when applied to some specific time series. But likely another will do better in a different circumstance. Thus, one need never empirically assess mainstream economics as a whole in some prominent field or empirically compare and contrast a mainstream theory to a non-mainstream theory.

Economics Of The Steady State

A steady state is characterized by the economy having a constant rate of growth. I here select a number of expositions of analyses of steady state I have made on this blog:

• The Harrod-Domar model of warranted and natural rates of growth.
• Karl Marx's volume 2 model of simple and expanded reproduction.
• An extension of the Kahn-Kaldor-Pasinetti-Robinson macroeconomic model of income distribution.
• Explanations of aspects of the non-substitution theorem.
• Neoclassical Overlapping Generations (OLG) models with intertemporal utility maximization.

Consider the hypothesis that a consumer's decision to save should be viewed as a choice between current consumption and future consumption so as to maximize an utility function. Except in the last case above, I have no need of that hypothesis. Alternative theories of value and distribution exist. (Does Nick Rowe imagine that I am in his intended audience for this post?)

Krugman Confused About His Profession, Preferences

Paul Krugman has explained on several occasions that he was inspired to become an economist by Isaac Asimov's Foundation triology. The collapse of a galaxy-wide civilization into an interim dark age, before the revival of a second galactic empire, provides the background setting of the novels. The organizing conceit is that Hari Seldon, the expert founder of the discipline of psychohistory, has figured out how to set up initial conditions such that the intervening and unpleasant dark ages will last for only a millennium, instead of 30 millennia. In Asimov's telling, psychohistory is an explicitly mathematical discipline.

It turns out that Asimov was not the only science fiction author in that era writing about mathematical psychology:

"So? The greatest mathematical psychologist of our time, a man who always wrote his own ticket even to retiring when it suited him..." -- Robert A. Heinlein (1958).

Heinlein's character has written a book titled, On the Statistical Interpretation of Imperfect Data, and his colleagues are at the Institute for Advanced Study, in Princeton, New Jersey.

When people referred to "Mathematical psychology" during the 1950s, what were they talking about? I suggest that they had in mind cybernetics, as invented by Norbert Wiener, and later developments. For example, consider the 1960 book, Developments in Mathematical Psychology, with contributions from R. Duncan Luce, Robert R. Bush, and J. C. R. Licklider.

Many have built on this work over the last half-century, in a variety of disciplinary settings. A few years ago, one could find the label Command, Control, Communications, and Intelligence (C³I) used to refer to much of this work. Departments and ministries of defense provided quite a bit of funding for research in these areas. And if you want to find current research on these topics, you could do worse than read such journals as IEEE Transactions on Communications, IEEE Transactions on Control Systems Technology, and IEEE Transactions on Signal Processing. These journals are all put out by the Institute of Electrical and Electronics Engineers (IEEE).

Thus, Paul Krugman wanted to be a electrical engineer, although he does not know it.

References

• Isaac Asimov (1953). Second Foundation. [I happen to have this book in the trilogy handy.]
• Robert R. Bush (1960). "A Survey of Mathematical Learning Theory", in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
• Robert A. Heinlein (1958). Have Space Suit-Will Travel.
• J. C. R. Licklider (1960). "Quasi-Linear Operator Models in the Study of Manual Tracking", in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
• R. Duncan Luce (1960). "The Theory of Selective Information and Some of Its Behavioral Applications, in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
• Norbert Wiener (1948). Cybernetics: Or Control and Communication in the Animal and The Machine.

Money Missing From Mainstream Economics

"In practice, of course, the purists were unable to deliver, and the new tricks involve the 'modern macroeconomists' in ad hoc assumptions of their own that are at least as objectionable as the Keynesian macroeconomic generalizations that [Michael] Wickens objected to. We have already encountered one example, the 'Gorman preferences' needed to make the representative agent at least minimally plausible... Two others are equally incredible. The first is the 'no-bankruptcies' assumption in Walrasian models and the related 'No Ponzi' conditon that is imposed on D[ynamic] S[tochastic] G[eneral] E[quilibrium] models. This eliminates the possibility of default, and hence the fear of default (since these are agents with rational expectations, who know the correct model, and hence know that there is no possibility of default), and hence the need for money, since if your promise to pay is 'as good as gold', it would be pointless for me to demand gold (or any other form of money) from you. Money would be at most a unit of account, but never a store of value. The second is the unobtrusive postulate of 'complete financial markets', smuggled into Michael Woodford's Interest and Prices (Woodford 2003, p. 64), which means that all possible future states of the world are known, probabilistically, and can be insured against: this eliminates uncertainty, and hence the need for finance..." -- J. E. King, The Microfoundations Delusion: Metaphor and Dogma in the History of Macroeconomics (2012: p. 228)

Can General Equilibrium Theory find a role for money? Consider Frank Hahn's "On some problems of proving the existence of an equilibrium in a monetary economy" (1965). He considered the question posed above to be an unmet challenge at the time. Hahn did not think, for example, Don Patinkin's attempt to justify the use of money through the inconvenience of indirect transactions and through transactions cost fit comfortably in a General Equilibrium model. Hahn wanted to find a model in which the existence of money was essential, in some sense, in which an equilibrium with money differed from one without.

mainstream macroeconomists claim to base their approach on General Equilibrium Theory. Experts on GE (for example, Alan Kirman) have been saying for decades that this claim is dubious. The critiques that I am most aware of are based on price theory.

These modern macroeconomists claim to have available models incorporating money and finance. This availability does not mean that they are unwilling to deploy models without money in some contexts for some purposes. As far as I am aware, Woodford is widely cited and widely respected in current mainstream monetary economics.

I have wondered how and if mainstream macroeconomists address the problems highlighted by Hahn in incorporating money in General Equilibrium Theory. But I have not wondered enough to read much. If I take King as an authority, I can spare myself the trouble of establishing that mainstream macroeconomists are basically confused about their own monetary theory. Is this a sound conclusion?

(Colin Rogers is an expert on how the Cambridge Capital Controversies can be used to critique Wicksellian theories of money and of the natural rate of interest. Woodford and Rogers had an exchange of views in the Cambridge Journal of Economics a number of years ago.)

Nick Rowe Knavery

So much nonsense packed into so few words:

"But the lefty Sraffian model has only labour and time as inputs." -- Nick Rowe

I do not know what politics has to do with it. I'd like to see some evidence of the political beliefs of, say, Neri Salvadori. When Sraffa states, in the preface of Production of Commodities By Means of Commodities, that "Others have ... independently taken up [similar] points of view," I think he includes John Von Neumann. Von Neumann wanted to wage an atomic war against the Soviet Union. I guess Rowe must think Von Neumann was a Trotskyite.

The Sraffa model, of course, includes non-produced inputs other than labor. "Land" is the title of Chapter 11 of Sraffa's book. I have attempted to explain some of the points in this chapter here and here. Heinz Kurz, Neri Salvadori, and Bertram Schefold are just some of the economists who have contributed to the literature building on Sraffa's analysis of land.

To address another Rowe misconception, Sraffians have also analyzed heterogeneous labor. In fact, "Heterogeneous Labor" is the title of Chapter 7 of Ian Steedman's book, Marx After Sraffa. I have an example with heterogeneous labor here.

The bit about time being an input in Sraffa's model is apparently some convex combination of a lie and begging the question. Sraffa explicitly states, in the title of his book, that he is considering production processes with inputs of commodities. These commodities include seed corn, iron, pigs, and so on. Although Sraffa assumes a yearly cycle of production for convenience, time is explicitly not an input in Sraffa's model. In fact, Sraffa can be said to have proven that "capital" cannot be reduced to time. In the case of joint production without land, the technique cannot even be reduced to labor inputs applied over time. (By the way, in the first chapter in her Essays in the Theory of Economic Growth, Joan Robinson explicitly analyzes an economy in which robots are produced by robots.)

Does anybody expect Rowe to acknowledge that he has no concern whatsoever over whether what he says is true or even makes sense?

Krugman Promoting Zombie Horror, Not SF Futures

Paul Krugman has been writing about robots lately. He explicitly cites J. R. Hicks' incoherent and mistaken 1932 book, The Theory of Wages. This is a classic statement of the neoclassical theory of factor substitution, of the choice of technique in allocating scarce factors among alternative uses.

If I want to analyze the adoption of new technology, I turn to:

• David Ricardo's chapter, "On Machinery", in the third edition of his book.
• The Von Neumann model of growth, which can be read as a model in which robots produce robots.
• The Harrod-Domar model of the warranted and natural rate of growth, along with the definition of Harrod-neutral and biased technological change.
• Joan Robinson's models of metallic ages.
• Kaldor's growth models of various vintages and his definition of the technical progress function.

I am in agreement with Krugman on the importance of Hicks' book in the development of the neoclassical canon. And I recognize the existence of a problem in empirically distinguishing between the choice of technique and the adoption of new technology in Kaldor's model(s) of economic growth.

Update: Matias Verengo has two posts on this topic.

Anti-Reductionism: An Example?

"There are three good reasons to think that reduction will fail on any likely development of social sciences: (1) multiple realizations of social events are likely; (2) individual actions have indefinitely many social descriptions depending on context; and (3) any workable individualist social theory will in all likelihood presuppose social facts. Each of these claims, if true, rules out reduction as defined here." -- Harold Kincaid (quoted in J. E. King (2012)).

Kincaid is arguing against strong methodological individualism. To help explicate his first reason, I want to consider a different domain, biology, and some literature crossing over between biology and computer science.

I suppose I ought to first state the reductionist theory I want to oppose: The theory of evolution can be reduced to the biochemistry of DNA.

A large body of literature explores the logical structure of reproduction, including reproduction with mutations, independently of consideration of the structure of DNA. I think of Von Neumann's work on celluar automata, which, despite the publication date of the work Burks edited, pre-dates the discovery of the molecular structure of DNA. As I understand it, Von Neumann described a structure in which a part simultaneously functions as a blueprint for the next generation and as a component that is duplicated in reproduction.

Von Neumann described a celluar automaton with many states, but his logic can be implemented in a particular celluar automata with only two states, namely Conway's Game of Life. Plausibility arguments that this celluar automata can be used to form a universal computer were available before Paul Rendell implemented a Turing machine in the game of life. Basically, one can identify mechanisms for implementing a memory and an array of gates (for example, AND, OR, and NOT). The gates apply to bits flowing across a wire, in some sense. Jacob Aron has create another interesting pattern in the game of life relevant to my thesis, namely a self-replicating creature.

Some researchers have also explored the role of mutations in self-replicating automata. As I understand it, they typically assume the existence of an assembly language for a virtual machine. One can imagine small programs being executed in parallel in some sort of common memory. One needs some way of introducing random changes in some of the instructions over time cycles and a way of rewarding successful programs with, say, more energy, in some sense.

The different artificially alive creatures in these simulations do not reside in separate protected memories. They have the capability of overwriting one another and resisting such overwriting. Some have even arranged tournaments, called core wars, in these simulations. In some sense, the literature I am referencing includes some bits of recreational mathematics.

I have never seen much more than what the literature says in the little bit of exploration of the above I have done. I did once write an implementation of Conway's Game of Life in which the rules were configurable. I was able to create crystal-like growth, but nothing as interesting as in the original game.

I have pointed to some work exploring a logic of reproduction above the level of the biochemistry of DNA. DNA is one means of instantiating this logic. I have not pointed out any other non-virtual mechanisms for instantiating this logic. I do not know if mitochondrial DNA differs sufficiently from regular DNA to count. Silicon-based life forms on other planets is a standard trope in science fiction. Apparently, Reaves et al. (2012) show the supposed discovery of arsenic-based life forms in certain California lakes has not worked out. But does this anti-reductionist argument require the actual existence of another instantiation, or merely the demonstration of the possible existence of one?

References

• J. E. King (2102). The Microfoundations Delusion: Metaphor and Dogma in the History of Macroeconomics.
• Lenski, Richard E., Charles Ofra, Robert T. Pennock, and Christoph Adaml (2003). The Evolutionary Origin of Complex Features, Nature, V. 423 (May): pp. 139-144.
• Poundstone, William (1984). The Recursive Universe. William Morrow.
• M. L. Reaves et al. (2012). Absence of detectable arsenate in DNA from arsenate-grown GFAJ-1 cells.
• Thearling, Kurt and Thomas S. Ray. Evolving Multi-Cellular Artificial Life.
• Von Neumann, John (1966). Theory of Self-Reproducing Automata (ed. by A. W. Burks).

A Keen Defense

My major point in this post is to draw attention to the existence of Kapeller and Pühringer (2010).

Steve Keen's book, Debunking Economics, is mainly a compilation of well-established criticisms of textbook economics. He attempts as popular a presentation as the material will permit. These criticisms, in my opinion, leave textbook economics, both microeconomics and macroeconomics, in tatters¹.

Keen, in the first edition, also offered his own original criticism of the textbook theory of the firm under perfect competition. You can find various brouhahas on the internet over Keen's remarks. Between editions of his book, Keen has published, with others, a series of papers developing his criticism².

Some have asserted theories of perfect competition in models with a continuum of agents provide a defense of the textbook theory. As Kapeller and Pühringer point out, this is a change of subject. A non sequitur should not be a considered an adequate defense of the textbook model. Furthermore, the primary developer of models with a continuum of agents presents his approach as inconsistent with the textbook theory:

"Though writers on economic equilibrium have traditionally assumed perfect competition, they have, paradoxically, adopted a mathematical model that does not fit this assumption. Indeed, the influence of an individual participant on the economy cannot be mathematically negligible, as long as there are only finitely many participants. Thus, a mathematically model appropriate to the intuitive notion of perfect competition must contain infinitely many participants. We submit that the most natural model for this purpose contains a continuum of participants." -- Robert Aumann (1964).

It seems to me only four possibilities are open here:

1. Aumann is not talking, in his critical remarks, about the model of perfect competition taught in almost any intermediate microeconomics textbook.
2. Aumann is mistaken.
3. The economists who write and teach the self-contradictory textbook model are deliberately teaching self-contradictory models to their students.
4. The economists who write and teach the self-contradictory textbook model are ignorant.

I think only the third and fourth options are credible³. I can understand the difficulty of writing and teaching in an intellectually bankrupt discipline.

Update: Nick Rowe illustrates the willingness of some economists to teach nonsense to students: "To the individual farmer, who sees only a tiny slice of the whole demand curve, because even a 100% change in his output will cause only a tiny percentage change in total output, it will look perfectly flat." Note that in his post, even when considering the limiting case, he never considers the existence of a continuum of producers.

Update 2: Steve Keen, in the Business Spectator, re-iterates his critique of the incorrect neoclassical textbook theory of perfect competition. Tim Worstall lies to readers of Forbes. It is not true that "everyone subscribes" to the "usual basics of economics" that Keen debunks. It is not true that the bulk of Keen's book is about his "breakthroughs in showing us all the errors of our ways." One can accept almost all of Keen's demonstration of the mendacity of neoclassical textbooks without accepting any claim that Keen says is original with him. In fact, Keen notes that Stigler showed that perfectly competitive firms that are not systematically mistaken, if they produce a positive, non-infinitesimal quantity in equilibrium, will not produce at a level of output where the market price, Marginal Revenue, and Marginal Cost are all equated.

Footnotes

1. Some areas of economics, such as game theory or the recent popularity of instrumental variables and experiments (natural and otherwise), remain unaddressed by Keen.
2. Kapeller and Pühringer point to a 2008 paper published by Anglin in Physica A as a peer-reviewed response.
3. The existence of the downward-sloping part of the U-shaped average cost curve for the textbook firm hardly seems compatible with the existence of an infinite number of firms, each producing a quantity of zero units of an homogeneous good.

References

• Aumann, Robert J. (1964). Markets with a Continuum of Traders, Econometrica, V. 32, No. 1-2.
• Kapeller, Jacob and Stephan Pühringer (2010). The Internal Consistency of Perfect Competition, The Journal of Philosophical Economics, V. III, No. 2: pp. 134-152.

A Barefoot Bum Critiques Propertarianism

"Larry, the Barefoot Bum" has been refuting propertarianism¹. Crudely stated, his thesis is that if you believe taxation is unjust because it implies the initiation of force (coercion by the state), you cannot coherently also defend private property.

1. To me, what was traditionally called "libertarianism" is anarchism, that is, a kind of communism.

Widespread Incompetence In Economics

Should one try to engage with those putting forth positions refuted decades ago? Maybe one's time would be better spent on looking at arguments that come closer to reflecting the state of the art, even when those arguments are not backed up by external funding from vicious reactionaries.

Suppose the economy were a complex dynamic system. Those who have investigated this idea have long ago shown that, even if all wages and prices were perfectly flexible, no tendency need exist for the economy to tend towards an equilibrium in which all markets, including the labor market, clear. Some just do not know:

"Given the position [Casey Mulligan is] trying to defend, these are the best arguments available. And that position is widely shared, not only by economists much more famous than Mulligan but by lots of governments and policymakers. Most mainstream opponents of Keynesianism are committed, one way or another, to the view that persistent high unemployment must be caused by problems in labour markets. But it's much easier to talk in vague general terms about rigidities and structural imbalances than to present an operational explanation for the sustained high US unemployment of the last four years. Mulligan at least makes the attempt, which is more than most of the New Classical/Chicago/Real Business Cycle school have done, and necessary if there is to be any progress in the debate." -- John Quiggin

"If (Casey) Mulligan were an isolated crank, I'd ignore him. But he’s endorsed by people like Tyler Cowen who should know better. And, as I said in the opening para, most of the freshwater crowd and quite a few people who were once "New Keynesians" believe or go along with this stuff." -- John Quiggin