Einstein in Sweezy's Mag

Albert Einstein had an article in the inaugural issue of Monthly Review. I don't know if there is a story here. Did Paul Sweezy, the publisher of the magazine ask Einstein for this article? Did Einstein merely answer a call for papers?

When I first found out about existence of this article, I expected Einstein to merely put forward comments about how we should all try to get along. (I'm never quite sure if I understand the word "Bien-pensant". I know enough French to translate it, but I think I've stumbled on the concept here.) But when I read Einstein's article I found out that he accepts Marx as having made scientific claims:

"The owner of the means of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. Insofar as the labor contract is 'free', what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists' requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product." -- Albert Einstein (1949) "Why Socialism?", Monthly Review (May), as reprinted in Out of My Later Years

A Perspective on the Coase "Theorem"

"'Coase's Theorem' says that once we determine who can legally do what, externalities will vanish as actors pay one another off. This methodology - either the victims bribe the perpetrator to stop the distasteful behavior (when the perpetrator has the legal right to do it) or the perpetrator bribes the victim to put up with the distasteful outcome (when the victims have a right not to suffer the pain) - is considered an epochal innovation in American economics and jurisprudence. Even without understanding all the details and context, this tells us a great deal about our intellectual culture since, in fact, Coase's methodology doesn't work.

1. Bargains made with only two parties, perpetrator and victim, will rarely if ever be efficient.
2. Whenever the perpetrator is a corporation and the victim a far-flung collection of disparate individuals, the latter is at such a disadvantage in seeking recompense that without intervention correction rarely takes place at all.
3. Coase's methodology provides a 'bully incentive' for anyone able to muster the courts on their behalf. Suppose Z owns a train. If we have the legal right to spew sparks, we should create the most spark-spewing train we can. If we have the right to be noisy, we should create a decibel demon. Whenever anyone with the means to pursue legal claims has a right that could cause others pain, they should threaten to exercise it and then extort bribery payments to desist. In the absence of a specific legal prohibition, a bully walking down the street should spit on everyone, claiming that he will only suffer the pains of stopping if his vitims bribe him to do so.

Not surprisingly, Coase's 'extort the victim,' 'empower the powerful' analysis was welcome as soon as economists could understand its utility to elites able to make legal claims here, there, and everywhere, thereby profitably spitting this way and that with impunity.

Why the hoopla for Coase? First, Coase's Theorem, better named the Bully Theorem, reinstates markets and privatization as optimal, even providing an argument against unwanted government regulation. Second, it elevates 'property rights' to the defining position in jurisprudence and establishes a logic for dealing with externalities perfectly suited to co-optation by capital." -- Michael Albert (November 1991)

Soros on Historical Time

The New York Times a couple of weeks ago profiled George Soros, the billionaire financial speculator, philanthropist, and student of Karl Popper's ideas. According to this profile, Soros would like to have an impact on the discipline of economics:

"Now in his eighth decade, [Soros] yearns to be remembered not only as a great trader but also as a great thinker. The market theory he has promoted for two decades and espoused most of his life - something he calls 'reflexivity' - is still dismissed by many economists. The idea is that people's biases and actions can affect the direction of the underlying economy, undermining the conventional theory that markets tend toward some sort of equilibrium." -- Louise Story (2008)

Stiglitz is quoted as saying that Soros might become successful at his goal:

"But Joseph E. Stiglitz, a professor at Columbia who won the Nobel for economics in 2001, said Mr. Soros might still meet success. 'With a slightly different vocabulary these ideas, I think, are going to become more and more part of the center,' said Mr. Stiglitz, a longtime friend of Mr. Soros." -- Louise Story (2008)

I suppose one could debate about whether mainstream economics is as open to these ideas as Stiglitz suggests.

About a decade ago is the first time Soros put these ideas into print, as far as I aware. Here is his then definition of reflexivity:

"In the case of scientists, there is only a one-way connection between statements and facts. The facts about the natural world are independent of the statements that scientists make about them... If a statement corresponds to the facts, it is true; if not, it is false. Not so in the case of thinking participants. There is a two-way connection. On the one hand, participants seek to understand the situation in which they participate. They seek to form a picture that corresponds to reality. I call this the passive or cognitive function. On the other hand, they seek to make an impact, to mold reality to their desires. I call this the active or participating function. When both functions are active at the same time, I call the situation reflexive...

...When both functions are at work at the same time, they may interfere with each other. Through the participating function, people may influence the situation that is supposed to serve as an independent variable for the cognitive function. Consequently, the participants' understanding cannot qualify as objective knowledge...

...Our expectations about future events do not wait for the events themselves; they may change at any time, altering the outcome. That is what happens in financial markets all the time... But reflexivity is not confined to financial markets; it is present in every historical process. Indeed, it is reflexivity that makes a process truly historical...

A truly historical event does not just change the world; it changes our understanding of the world - and that new understanding, in turn, has a new an unpredictable impact on how the world works."-- George Soros (1998: 6-8)

And Soros uses these ideas to criticize the use of equilibrium models in economics.

To me, Soros is expressing the same concept that Post Keynesians call historical time. Post Keynesians reject neoclassical economics. In the failed neoclassical approach, the economy tends towards an economic equilibrium pre-determined by the objective data of tastes, technology, and endowments. Both Soros and the Post Keynesians, with their emphases on expectations, question the objectivity of the data. Today, I turn to Jan Kregel for a statement of the Post Keynesian position:

"There can be no tendency to equilibrium based on a relation between expectations and the objective data of what the consumer will demand and the price he will pay which describes the conditions of equilibrium because the incomes available to consumers will be determined ultimately by the very decisions taken by entrepreneurs on the basis of these expectations.

The post Keynesian approach is thus influenced by Keynes' insistence that the level of output and employment cannot be considered as objective data determining the conditions of equilibrium because they will be endogenously determined by entrepreneurs' decisions... Keynes is concerned with the role of expectations in the coordination of individual production plans in a society consisting of several independent producers whose expectations determine the means available to satisfy an uncertain multiplicity of future demands. Expectations themselves determine the objective facts of the conditions of equilibrium... The problem is not whether the objective data necessary to achieve equilibrium will be reflected in subjective data available to the individual, but the very definition of the objective data. Indeed, even its objectivity is questioned." -- Jan Kregel (1986).

And these ideas accompany an concern with processes set in history. (I have previously mentioned Paul Davidson's use of the concept of non-ergodicity in a formalization of the idea of a process set in history.)

Soros and Post Keynesians like Davidson draw similar practical conclusions from developments of these ideas. The financial system, including internationally, can be a source of economic instability. We need to design new international institutions and conventions to govern finance. The system that has evolved since Richard Nixon abolished the Bretton Woods system doesn't work, as international economic crisis succeeds international economic crisis.

References

• J. A. Kregel (1986). "Conceptions of Equilibrium: The Logic of Choice and the Logic of Production", in Subjectivism, Intelligibility, and Economic Understanding: Essays in Honor of Ludwig M. Lachmann on his Eightieth Birthday (ed. by Israel M. Kirzner), New York University Press.
• George Soros (1998). The Crisis of Global Capitalism: Open Society Endangered, Public Affairs
• Louise Story (2008). "The Face of a Prophet: Soros Craves Respect for His Theories, Not Just His Money", New York Times (11 April) Business, p. 1

Foundations of Probability: No Decided Opinion

Over at Good Math, Bad Math, Mark Chu-Carroll has brought up the disagreement between frequentists and Bayesians. Here's a highly technical and theoretical argument, conducted with a great deal of vitriol, and perhaps with practical consequences. You might think this is the sort of thing I would have a decided opinion on. Yet I don't, perhaps because I don't know enough about Bayesianism in practice.

I have sometimes applied Neyman-Pearson hypothesis testing, sometimes in the context of the design of experiments. I think it useful to have a decision rule before looking at the data, but I try not to get hung up on ontological commitments. I am not sure that my practice is compatible only with some position on these arguments. I generally explain the math with frequentist arguments.

I did have some thoughts on the comments. I wondered whether more schools should be distinguished than Mark or his commentators have done. The first comment supports what might be called a formalist or axiomatic approach: Probability is a mathematical theory of certain measures on sigma algebras. Somewhere in the comments, E. T. Jaynes is mentioned. Is Jaynes' entropy-maximization approach co-extensive with Bayesianism? Somewhere else, personalism is mentioned. Is this also a synonym of Bayesianism? I think some approaches are about objective properties of propositions. I gather this is Keynes' position is his book on probability. Can the non-frequentist school be further decomposed into objective and subjective branches? Somewhere I seem to vaguely recall a fidicual approach, which I understood even less. Where does this fit? I suppose I also ought to ask where Savage fits in.

I was not aware that those that worry about these sorts of things have tended to swing from frequentists to Bayesians with the growth in computing power. I was taught a frequentist approach, with an acknowledgement of the existence of debate. I'm aware that the growth of computing power has led to greater popularity of bootstrap/jackknife/resampling methods since I received my undergraduate degree. Perhaps that's another topic.

Some comments at Mark's go down what I think is a blind alley - they suggest the Monte Hall Problem is an illustration of the strength of Bayesianism. While Bayes' theorem is useful in calculating the correct solution, I don't see the problem as connected strongly to foundational principles. Perhaps, use of Bayes' theorem emphasizes. that Monte's decision rules must be precisely specified beforehand.

There is a discussion of confidence intervals and the correct way of thinking about them from the frequentist perspective. One of my colleagues once suggested to me that constructing a confidence interval is like trying to throw a hat over, say, an apple. The apple is at some position, and you don't know whether it is or is not under the hat after it is thrown. If your hat is a sombero - like a 99% confidence interval - you are more likely to catch the apple. If your hat is a English derby - like a 90% confidence interval - you are less likely to catch the apple. But when you have caught it, you've more precisely specified where the apple is.

I Pity The Fool

Apparently, Philip Mirowski is currently researching how economics can inform science and technology policy. Mirowski (2007) is a step in this enterprise. This paper reviews Warsh (2006). Warsh's book is a popular account of economics organized around the history of the idea of increasing returns. Paul Romer is the hero of Warsh's story. Warsh praises, specifically, Romer (1990).

Mirowksi concludes that neither Solovian growth theory nor so-called new growth theory can legitimately say much for science and technology policy, since they are so defective. Basically, Mirowski agrees with me (for example, look here).

Some quotes from Mirowski follow:

"...the entire book is so lacking in any skeptical perspective that would ideally derive from a deep background familiarity with the history of economics, not to mention some modicum of philosophical humility..., that one has to wonder just what Warsh was thinking.

I want to be clear about this, since I honestly think that David Warsh is the best we have in terms of economics journalism in America."

"The problem is not simply a secondary matter of aggregation, as some suggested back during the capital controversies of the 1970s. The entire motivation behind early production functions was to posit a sharp distinction between factor substitution and something more dynamic and pervasive, which for lack of a better term, is still commonly called technological change."

"Yet, economists and journalists alike extol the new growth theory, and there is no denying its popularity in certain circles. ... Rigorous mathematics and assiduous empiricism had little to do with it."

"I pity the poor student of modern economics, trying to make some sense of what can only appear to the outsider as cryptic oracular pronouncements emitted from people who claim to be experts in the nature and validity of knowledge. But when you get your news from Jon Stewart, your history from Paul Krugman, and your research facts from Wikipedia, maybe the nature of knowledge has itself changed.

References

• Mirowski, Philip (2007) "Review Essay: Did the (Returns to) Scales Fall From Their Eyes?", Journal of the History of Economic Thought, V. 29, N. 4 (Dec): 481-494
• Romer, Paul M. (1990) "Endogenous Technological Change", Journal of Political Economy V. 98, N. 5 (Oct): S71-S102.
• Warsh, David (2006) Knowledge and the Wealth of Nations: A Story of Economic Discovery, Norton

A Reswitching Example With Fixed Capital

1.0 Introduction
This post presents an example of reswitching with fixed capital. This is Example 5 in Chapter 9 of J. E. Woods, The Production of Commodities: An Introduction To Sraffa (Humanities Press, 1990). Fixed capital is a special case of joint production. I often analyze the choice of technique in circulating capital models by constructing the so-called factor-price frontier as the outer envelope of factor-price curves for each technique. This method of analysis does not generalize to general models of joint production. I confine myself in this post to methods of analysis that apply generally to joint production. This example illustrates the reswitching of techniques. A manifestation of reswitching in this example is the non-monotonic dependence of the economic life of machinery on the rate of profits.

2.0 Technology
The example is of a vertically-integrated industry producing a net output of corn with inputs of corn, machines, and labor. Machines can last for two yearly cycles of production, while corn inputs are entirely used up each year in production. Firms have available the three Constant-Returns-to-Scale (CRS) processes shown in Figure 1. New machines are produced by the first process, while corn is produced by both of the two remaining processes. The third process uses a one-year old machine as an input. The one-year old machine is produced jointly with corn by the second process.

Table 1: The Technology

	Machine Industry	Corn Industry
Inputs
Labor	1/10 Person-Year	43/40 Person-Year	1 Person-Year
Corn	1/16 Bushel	1/16 Bushel	1/4 Bushel
New Machines		1	0
Old Machines		0	1
Outputs
Corn	0 Bushels	1 Bushel	1 Bushel
New Machines	1	0	0
Old Machines	0	1	0

3.0 Quantity Flows
A choice of technique arises over the economic life of the machine. A firm might choose to discard the machine after the first year and never use the third process, whether in conjunction with the other processes or not. (I assume that machines can be freely disposed of after both one and two years of operation.)

The proportions in which processes are operated varies, depending on how many years the machine is used. Table 2 shows the first two process being used to produced a net output of one bushel corn. Notice that when these processes are operated in parallel new machines are simultaneously produced by the first process and used up by the second process. (I suppose I could scale up the processes in Tables 2 and 3 by 91 so that an integral number of machines is used in each technique and the net output of both is the same quantity of bushels of corn.)

Table 2: Use Of Machine For One Year

	Machine Industry	Corn Industry
Inputs
Labor	4/35 Person-Year	43/35 Person-Year
Corn	1/14 Bushel	1/14 Bushel
New Machines	0	8/7
Outputs
Corn	0 Bushels	8/7 Bushel
New Machines	8/7	0

Table 3 shows how all three processes must be scaled when machines are used for two years and the net output is one bushel corn. Tables 2 and 3 can be used to calculate the flow of labor inputs and capital goods required to produce a net output of one bushel corn for each technique. Table 4 exhibits the result of this calculation. If machines are junked after one year, 2/455 person-years more labor is hired per bushel corn net, as compared to machines being junked after two years.

Table 3: Use Of Machine For Two Years

	Machine Industry	Corn Industry
Inputs
Labor	4/65 Person-Year	43/65 Person-Year	8/13 Person-Year
Corn	1/26 Bushel	1/26 Bushel	2/13 Bushel
New Machines	0	8/13	0
Old Machines	0	0	8/13
Outputs
Corn	0 Bushels	8/13 Bushel	8/13 Bushel
New Machines	8/13	0	0
Old Machines	0	8/13	0

Table 4: Inputs Per Net Output of 1 Bushel Corn

	Years Machine Is Operated
	1 Year	2 Years
Labor	47/35 Person-Years	87/65 Person-Years
Capital	1/7 Bushel, 8/7 New Machines	3/13 Bushel, 8/13 New Machines, 8/13 Old Machines

4.0 Prices and the Choice of Technique
Firms choose the technique - that is how long machines are used - based on profitability. Hence, an analysis of the choice of technique requires an analysis of prices.

4.1 Prices When Machine is Operated One Year
Suppose, to begin with, that the machine is operated for one year only. Prices are such that no pure economic profits can be earned in producing new machines or in operating machines for the first year. Furthermore, costs (inclusive of a charge on capital goods advanced) do not exceed revenues in either of these two processes. These assumptions imply two equalities are met:

(1/16) (1 + r) + (1/10) w_α = p_{0, α}

[(1/16) + p_{0, α}](1 + r) + (43/40) w_α = 1,

where a bushel corn is the numeraire, p_{0, α} is the price of a new machine, w_α is the wage, and r is the rate of profits. These equations embody the implicit assumption that wages are paid after the laborers have been working for a year. The price of a year-old machine is zero.

This is a system of two equations in three unknowns. If the rate of profits is taken as given outside this system, the other two variables can be found as a function of the rate of profits:

w_α(r) = (5/2)(14 - 3 r - r²)/(4 r + 47)

p_{0, α}(r) = (1/16)(103 + 39 r)/(4 r + 47)

The larger is the wage, the smaller is the rate of profits. The maximum rate of profits in this system arises for a wage of zero. That maximum is approximately 253.11%.

The above solution can be used to analyze the profitability of operating the machine for another year. Figure 1 shows the costs and revenues (in bushels corn) for producing a bushel of corn by operating the third process in Table 1. Inputs are valued at the prices given by the above solution. Note that revenues would exceed costs if the rate of profits were below approximately 33%. Likewise, revenues would exceed costs if the rate of profits were above 50% and below the maximum. In these regions, firms would choose to operate the machines for a second year, and the prices would not be equilibrium prices.

Figure 1: Costs and Revenues for Operating Machine for Second Year

On the other hand, the above solution gives equilibrium prices if the rate of profits lies between approximately 33% and 50%. In this region, the costs of operating the machine for a second year exceed the revenues. Firms would only operate the machine for one year, consistently with the hypothesis for this case.

4.2 Prices When Machine is Operated Two Years
The other case arises when prices are consistent with the machine being operated for two years. By assumption, pure economic profits cannot be earned in any of the three processes in the technology. Likewise, costs do not exceed revenues for any of the three processes. These assumptions yield a system of three equations:

(1/16) (1 + r) + (1/10) w_β = p_{0, β}

[(1/16) + p_{0, β}](1 + r) + (43/40) w_β = 1 + p_{1, β}

[(1/4) + p_{1, β}](1 + r) + w_β = 1

where p_{0, β} is the price of a new machine, p_{1, β} is the price of a machine after operating for one year, w_β is the wage, and r is once again the exogeneously specified rate of profits.

This system has one more equation than the system in Section 4.1. But it contains one more variable also. Thus, the wage and the prices of the new and one year-old machine can be found in terms of the rate of profits:

w_β(r) = (5/2)(26 + 7r - 4r² - r³)/(87 + 51r + 4 r²)

p_{0, β}(r) = (1/80)(135 - 166 w_β - 86 w_β r + 50 r - 5 r²)/(1 + r)²

p_{1, β}(r) = (1/4)(3 - 4 w_β - r)/(1 + r)

In this case also, the maximum rate of profits arises when the wage is zero. The maximum rate of profits is approximately 258.77%

The analysis of the choice of technique in this case is based on examining the price of the year-old machine (Figure 2). Only non-negative prices are consistent with equilibria. The price of an used machine becoming negative is a sign that it is cheaper to truncate the use of a machine after it is used for one year. That is, for a rate of profits between approximately 33% and 50%, firms will junk the machine after one year of operation.

Figure 2: Price of One-Year Old Machine

4.3 Choice of Years of Operation
The analysis of the choice of technique is consistent, whether one begins with the price system for machines being used for one or two years. When the rate of profits is below approximately 33%, but non-negative, machines are used for two years. When the rate of profits exceeds 50% and below the maximum, machines are also used for two years. When the rate of profits exceed approximately 33% and are below 50%, machines are discarded after one year of operation.

5.0 Conclusion
Suppose one incorrectly accepts pre-Sraffian neoclassical or Austrian intuition. Then one would believe that a low rate of profits reflects capital, in some sense, being relatively less scarce than labor. And one would expect firms to adopt a more capital-intensive technique at a lower rate of profits. In this context, one would expect the economic lives of machines to be longer at a lower rate of profits. But, as shown by Figure 3, such a belief is incorrect, in general.

Figure 3: Economic Life of Machine versus Rate of Profit

If one had such incorrect pre-Sraffian neoclassical or Austrian intuition, one would likewise expect firms to hire more workers at lower wages, also under conditions of perfect competition. Figure 4 demonstrates this belief is false as well. So much for the idea that wages and employment are determined by the interaction of well-behaved supply and demand functions.

Figure 4: Labor Intensity versus Wage

Madrick on the End of an Age

Jeff Madrick has a Huffington Post column titled, "The End of the Age of Milton Friedman".

Since this is short and popular, one could think up lots of caveats. I'll go first. "Crisis in the 1970s" does not explain why Friedman's ideas became popular. Economists had available another account of stagflation. Something else remains of Friedman's academic contributions other than "the overstated natural rate of unemployment philosophy". I think most working economists would still echo something of Friedman's views on methodology, despite their rejection by specialists in the field.

A Photo of Barkley Rosser

I stumbled upon the following photo accompanying an interview with Albert Tucker (Maurer 1985).



The 3rd man from the left in the first row is the father of Barkley Rosser, Jr.

I have tried reading Rosser (1936), but I did not really understand the proof. As I understand it, Rosser puts some theorems of the time together to alter a theorem of Gödel's so that it's statement seems more natural. It is a very concise paper. Gödel shows that ω-consistency implies the existence of undecidable propositions. Rosser discarded the ω; he showed that consistency implies the existence of undecidable propositions. I guess there can be consistent systems that are not ω-consistent. Consistency is a syntactical property, and it does not require intuitions about universal quantification over all natural numbers.

Definition: A system is ω-inconsistent if and only if there exists a proposition p(n), with free variable n, such that

1. p(0) is provable, p(1) is provable, p(2) is provable, and so on.
2. It is provable that not ( for all n, p(n))

Definition: A system is ω-consistent if and only if it is not ω-inconsistent.

References

• Stephen B. Maurer (1985). "Albert Tucker", in Mathematical People: Profiles and Interviews (Ed. by D. J. Albers and G. L. Alexanderson), Birkhauser
• Barkley Rosser (1936) "Extensions of some Theorems of Gödel and Church", The Journal of Symbolic Logic, 1 (3), (September): 87-91.

Murphy An Apologist For Capitalism

I lean toward the view that Marx's account of the derivation of the returns to capital from the exploitation of labor is intended to be descriptive. Marx arguably does not condemn capitalism because of its supposed injustice. And a model of steady states in which agents are modeled as maximizing utility, including intertemporally, does not challenge the validity of Morishima's fundamental theorem of Marxism. Murphy does not address these views. Yet it sounds like he disagrees:

"The Cambridge critics of the mainstream explanation of interest theory were right: only under very special conditions can interest be viewed as the marginal product of capital. However, they were wrong in condemning the marginal approach altogether. As the pioneers of the marginal revolution knew full well, the real interest rate is first and foremost a reflection of the higher subjective valuation of present versus future consumption goods. Starting from this point - rather than the dubious equality with the marginal product of capital - the ethical defense of interest payments follows quite simply." -- Robert P. Murphy (2007) "Interest and the Marginal Product of Capital: A Critique of Samuelson", Journal of the History of Economic Thought, V. 29, N. 4: 453 - 464

Murphy does not justify this conclusion. His article analyzes neither intertemporal subjective valuations nor ethics.

I also don't think Murphy really justifies his hostility to mathematics:

"I hope to convince the reader that typical mainstream neoclassicals left themselves open to their Cambridge critics ... because their fascination with mathematical models led many of them to forget the insights of earlier thinkers." -- Robert P. Murphy (2007).

Murphy does argue well that forgetfulness is displayed. He doesn't show that this is because of mathematics. One can argue that a problem with mainstream economics is not mathematics as such. It is rather the inappropriate insistence on mathematics always and a refusal to use more sophisticated mathematics for theoretical clarification in economics.

I might as well point out that I agree with Murphy on some points, in addition to his refusal to accept the equality of the rate of interest and the marginal product of capital. For example, I think Böhm-Bawerk was insightful in his criticisms of the naive productivity theory of interest. I have read neither von Thünen nor Samuelson's defense of von Thünen against Böhm-Bawerk. Murphy's presentation of Samuelson leads me to think that Samuelson's defense lost. But I don't see the problem with Samuelson's defense being necessarily the assumption of a steady-state, as opposed to the assumption of a one good model.

J. S. Mill on Method

1.0 Introduction
John Stuart Mill wrote an essay on the methodology of economics or rather, in the language of his day, Political Economy. I look at it in a Whiggish fashion to show some of his ideas are still around today, namely:

• The distinction between positive and normative propositions
• The notion of economic man as being motivated solely by monetary considerations (Homo Economicus)
• The argument that economics should be a deductive, not an inductive, science
• The complexity of society and the nature of humankind precludes controlled experimentation

(I do not claim that Mill was original with any particular concept here.) Some of these distinctions you will find critics of mainstream economics imposing on the mainstream, while mainstream economists say that they have been long rejected. I am thinking especially of Mill's claim that economics examines the logical implications of a separate economic motive. Humankind has other motives that are altruistic or not directed towards money. Lionel Robbins, for example, rejected this distinction. (Whether economists' pronouncements about what they do matches what they do is a question not examined here.)

2.0 Positive Versus Normative Propositions
J. S. Mill introduces a distinction between positive and normative propositions. He uses the terms "science" and "art". Mill thinks political economy is and should be a science.

"... the essentially distinct, though closely connected, ideas of science and art. These two ideas differ from one another as the understanding differs from the will, or as the indicative mood in grammar differs from the imperative. The one deals in facts, the other in precepts. Science is a collection of truths; art, a body of rules, or directions for conduct. The language of science is, This is, or, This is not; This does, or does not, happen. The language of art is, Do this; Avoid that. Science takes cognizance of a phenomenon, and endeavours to discover its law; art proposes to itself an end, and looks out for means to effect it.

If, therefore, Political Economy be a science, it cannot be a collection of practical rules; though, unless it be altogether a useless science, practical rules must be capable of being founded upon it." -- J. S. Mill, "On the Definition of Political Economy; and on the Method of Investigation Proper to It", in Essays on Some Unsettled Questions of Political Economy (1844: 312).

This particular essay was originally published in the October 1836 issue of the London and Westminster Review. The page numbers refer to the fourth volume of The Collected Works of John Stuart Mill, from 1967.

In discussing the relationship of art to science, Mill echoes a distinction between "empirics" and "technique" (if I guess correctly from my knowledge of the greek alphabet) to be found in the "Gorgias" of Plato. Technique, in this sense, is art founded on science.

Mill, in discussing an analogy accompanying a definition of economics that he ultimately rejects, writes:

"domestic economy, so far as it is capable of being reduced to principles, is an art. It consists of rules, or maxims of prudence, for keeping the family regularly supplied with what its wants require, and securing, with any given amount of means, the greatest possible quantity of physical comfort and enjoyment." -- J. S. Mill (1844: 313)

And Mill proposes a definition for criticism:

"Political Economy [is] the science which treats of the production and distribution of wealth, so far as they depend upon the laws of human nature." -- J. S. Mill (1844: 318)

3.0 Homo Economicus
Mill says economics is a type of moral or psychological science, as opposed to a physical science (p. 316 for the distinction). Mill decomposes the subject matters of the moral sciences:

"We may inquire what belongs to man considered individually, and as if no human being existed besides himself; we may next consider him as coming into contact with other individuals; and finally, as living in a state of society, that is, forming part of a body or aggregation of human beings, systematically co-operating for common purposes." -- J. S. Mill (1844: 319)

Mill, insofar as he is interested in the social sciences, is concerned with the "laws of human nature in the social state" (p. 320). Here is an important grouping of the moral sciences:

"The science of social economy embraces every part of man's nature, in so far as influencing the conduct or condition of man in society; and therefore may it be termed speculative politics ..." -- J. S. Mill (1844: 320)

Mill then defines a part:

"'Political Economy' is not the science of speculative politics, but a branch of that science. It does not treat of the whole of man's nature as modified by the social state, nor of the whole conduct of man in society. It is concerned with him solely as a being who desires to possess wealth, and who is capable of judging of the comparative efficacy of means for obtaining that end. It predicts only such of the phenomena of the social state as take place in consequence of the pursuit of wealth. It makes entire abstraction of every other human passion or motive; except those which may be regarded as perpetually antagonizing principles to the desire of wealth, namely, aversion to labour, and desire of the present enjoyment of cosily indulgences." -- J. S. Mill (1844: 321)

"Political Economy considers mankind as occupied solely in acquiring and consuming wealth; and aims at showing what is the course of action into which mankind, living in a state of society, would be impelled, if that motive, except in the degree in which it is checked by the two perpetual counter-motives above adverted to, were absolute ruler of all their actions." -- J. S. Mill (1844: 322)

I think Mill's language here is echoed by some "libertarians":

"[Political economy] shows mankind ... establishing laws to prevent individuals from encroaching upon the property of others by force or fraud" -- J. S. Mill (1844: 322)

Mill draws an analogy between the effects of the motives treated by political economy and all other motives with the superposition of forces in Newtonian astronomy (p. 322). And he states that the motives not treated in Political Economy are "disturbing causes" resembling "frictions in mechanics" (p. 330).

Here is Mill's approved definition of Political Economy:

"The science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object." -- J. S. Mill (1844: 323)

Mill has much else to say of interest, e.g.:

"... those who are accused of despising facts and disregarding experience build and profess to build wholly upon facts and experience; while those who disavow theory cannot make one step without theorizing." -- J. S. Mill (1844: 324)

4.0 Economics as a Deductive Science
Mill characterizes Political Economy:

"as essentially an abstract science, and its method as the method a priori." -- J. S. Mill (1844: 325)

5.0 Economics as Not Supporting Controlled Experimentation

"There is a property common to almost all the moral sciences, and by which they are distinguished from many of the physical; this is, that it is seldom in our power to make experiments in them. -- J. S. Mill (1844: 327)

Mill talks about the "circumstances, moreover, of great complexity" (p. 327) in which observations for Political economy are generated. And he refers to the inability of "rarely obtain[ing] an experimentum crucis." -- J. S. Mill (1844: 328).

Economists have recently been performing controlled experiments. I refer not only to behaviorial economics, but also to field experiments.