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Home , Gary Becker, Paul Samuelson, Sunspots (economics)

A FEMINIST CHALLENGE TO PAUL A. SAMUELSON’S OVERLAPPING GENERATIONS MODEL

KARIN SCHÖNPFLUG and DORIS A. BEHRENS University of Klagenfurt, Department of

We look at Paul A. Samuelson’s 1958 article “An Exact -Loan Model of With or Without the Social Contrivance of ” as an exemplary, Neo-classically misconstructed model of nowadays society and its economic activities. The failure to notice the existence of unpaid labor in the framework of the model, and the implicit dependence of the outcomes on unpaid (omitted) reproduction work has apparently gone un- challenged so far. The logical inconsistencies of the model and their androcentric backgrounds are discussed in this paper. Furthermore, we aim to debate (but not explicitly formulate) an alternative modeling approach based on the use of Genetic Algorithms to include – at least some – crucial features of modern society in its whole heterogeneity.

Keywords: OLG, feminism, critique, Genetic Algorithms, retirement contributions.

men and women from a gender3 point of view rather n the one hand, ’s 1958 article O than explaining the occurrence of unpaid work via the “An Exact Consumption-Loan Model of Interest With existence of (possibly racist) discrimination – or Without the Social Contrivance of Money” appears extending to slavery4-like conditions, i.e. working to be a paradigmatic misconstruction of nowadays conditions of illegal immigrants or prisoners in pri- society and its economic activities, but on the other vate detention centers. hand, it is still the uncriticized core of numerous economic theories in various fields. Men as Hobbe- 1.2 THE CONCEPT OF INTEREST RATES AND THE sian Mushrooms, Robinson-Crusoe-Individuals, and ORIGINS OF MECHANICAL BELIEFS Mother Earth are the agents populating Samuelson’s The origins of the use of interest rates are closely analogy. Though often challenged, e.g. by Hahn and related to the invention of devices to measure time. If Solow (1995), Samuelson’s overlapping generations a society does not keep track of time, interest rates are (OLG) model also explains the basics of monetary without any meaning. With the invention of mechani- theory and social contrivance. The androcentric bias cal clocks around 1300 AD, mechanical concepts have become characteristic for natural as well as for in Samuelson’s assumptions leads to partially bizarre 5 results which have apparently gone unchallenged so socio-economic sciences. Nowadays, the principle of far. Among these assumptions are (1) the failure to interest rates is usually not questioned, on the con- acknowledge the existence of unpaid labor in the trary, it seems to be one of the most normal concepts framework of the OLG model, and (2) the fact that of everyday life. Students are trained to cope with the model outcomes implicitly depend on the (unpaid) them in school, the influence of interest payments on “reproduction work” (of women). The logical incon- private acts as source of joy (or threat), sistencies in the assumption- relations – in and the government’s indebtedness may bring contrast to the wide recognition of Samuelson’s OLG or to its citizens. Note that nonetheless, a model – are discussed in this paper. 3 “Gender, as the word is used by many feminists, means 1. THE THEORETICAL CONTEXT FOR AN something quite different from biological sex. Gender is the APPROACH TO SAMUELSON’S OLG MODEL social meaning given to biological differences between the sexes; it refers to cultural constraints rather than to bio- 1.1 DEFINITION OF THE BASIC KEYWORDS logical givens.” (Ferber and Nelson, 1993). The critique of the OLG model presented in this pa- 4 1 Notions of racism imbedded in rational economic theory per is based on a feminist background , and the lay for example in the use of Robinson Crusoe’s persona as 2 awareness of androcentric biases inherent in the an anchor for the agents populating Samuelson’s modeled model. We focus on the social inequalities between world (see Grapard, 1995). 5 The belief in mechanics as the most successful approach 1 to science is meanwhile widely challenged by feminist “... common to virtually all feminist views [...] is the belief scientists in almost all fields of research. E.g. Wertheim that women are subordinated to men to a degree that is (1997) describes physics as a male dominated religious morally wrong and unnecessary.” (England, 1993). clique, and relates the witch hunts in Europe and the de- 2 The term androcentric refers to a system of any sort, struction of wise women’s wisdom during the Middle-ages where everything is related to men. to the boom of mechanistic sciences.

1 prevailing strain in economic theory aims at ex- science of political are naively masculine. plaining and legitimizing the phenomenon of using They assume as unquestionably that the “economic interest rates. E.g., Samuelson (1958) defines interest man” will never do anything unless he has to; will rates as the “intertemporal terms of between only do it to escape pain or attain pleasure; and will generations”. They will spring up spontaneously in inevitably take all he can get and do all he can to ideally competitive markets. outwit, overcome, and if necessary destroy his an- tagonist”. Samuelson’s consumption-loan model of 1.3 THE DIFFICULTIES OF MATHEMATICAL MODELING interest perfectly mirrors this belief and the basic Closely intertwined with the origins of all modern features of mechanical thinking. We will try to ex- sciences (and the belief in mechanics) is the tech- tract these “mechanical beliefs”, their consequences, nique of mathematical modeling, a tool which is and their applications, from the implicit assumptions excessively used to describe the generations’ interac- of Samuelson’s OLG model – since these beliefs are tions in Samuelson’s model. Whenever we set up a used as an instrumentality of the justification of op- mathematical model of a real world process, we have pression and exploitation of women (or slaves) deeply to pay particular attention to the fact whether the rooted within them. aspired features of real world behavior carry over to the mathematical model which is subject to restric- 2. SAMUELSON’S OLG MODEL AND ITS tions caused by the choice of the methodology – in CURRENT APPLICATIONS IN ECONOMICS terms of Albert Einstein “we should make models as In his famous 1958 paper Paul A. Samuelson intends simple as possible, but not simpler”. Since these to develop equilibrium conditions for lifetime con- limitations caused by the choice of methodology do sumption- patterns determined by the not only restrict the model’s input, but also the interest rates in a society of rational consumers. Actu- model’s output, it is essential for further discussion to ally, Samuelson seeks to explain the survival of a be aware of the degree of real world’s alienation due single group of (currently) non-productive agents in to the modeling procedure. Note that “the information an ideally competitive world. As a pioneer in this we omit from our stories reveals as much, if not more, field of research, Samuelson develops a brand new of our values and beliefs than the information we model including “some interesting mathematical choose to include.” (Grapard, 1995). Symptomati- boundary problems, a little like those in the modern cally, this applies, in particular, as soon as we attempt theories of dynamic programming” (Samuelson, to involve the principle of into a mathematical 1958), and he contributes to the current theories of modeling approach. money and interest. But beyond these clearly specified 1.4 THE THEORY OF RATIONAL CHOICE (AND LABOR) issues a hidden agenda influences the choice of the Economics was (and still is) regarded as the “science assumptions, of the methodology, and, finally, of the of rational choice”. With respect to scarce resources outcomes of the mathematical analysis of Samuel- individuals are supposed to maximize their son’s OLG model. (and/or minimize their pain) in a rational way. These Figure 1 seeks to visualize Samuelson’s construc- rational optimality decisions are treated like scientific tion, i.e. its explicit and its implicit assumptions (ex- (Samuelson, 1947), and, hence, economics may plained in detail in Section 3), its conclusions (dis- be regarded as a physical-mathematical science (Wal- cussed in Sections 3 and 4), and their relations among ras, 1881). Relying on the theory of rational choice, each other. Additionally, the diagram shows a few the models used to describe the phenomenons of extensions of the last decades to adapt and to improve physical mechanics are often precisely copied and the model’s fit to real-world behavior. applied to economic problems (using the identical Though Samuelson’s article was published more mathematical approaches) – “Under the assumption than 40 years ago, still each working in the that is based on geometry, geometrical field of intertemporary interactions (between genera- rules can be applied to situations in economics.” tions) seems to stumble over Samuelson’s OLG (Debreu, 1959). model, because the application of this model emerges The majority of rational decisions in economic life in various areas – ranging from the most obvious ones arise from the demand for labor in order to satisfy the like retirement contribution systems, social policies, desire for consumption. Labor is related to its utility taxation, income , financial and monetary and the value or wage, respectively, associated with theory to , and economics of it. Traditionally, view labor as painful war and peace, see e.g. Bommier and Lee (1995), experience. (1778) defines labor as an Brunner (1997, 1999), Galor (1989), Goenka and activity which forces a worker to give up “his tran- Spear (1994), John et al. (1993), Koskela and Ol- quility, his freedom and his happiness”. Charlotte likainen (1998), Macher et al. (1999), Manne (1999), Perkins Gilman (1964) links “that pitiful conception McCallum (1983), Nishimura and Shimomura of labor as a curse to the very old and androcentric (1997), Pingle and Tesfation (1993), Raut (1989), habit of despising it as belonging to women and then Rutherford (1999), Spiegel (1998), Wallace (1978), to slaves. [...] Our current teachings of the infant Weizsäcker (1996) to mention only some of them. 2 EXPLICIT ASSUMPTIONS OF THE OVERLAPPING EXTENSIONS TO SAMUELSON´S GENERATIONS MODEL (SAMUELSON, 1958) ASSUMPTIONS A1 All agents in the model are supposed to behave uni- Ø allowing non-identical individu- formly over time, with identical preferences regard- als, e.g. Arifovic (1995, 1996), ing their consumption behavior and with identical Dawid (1996), Bullard and production capacities. Duffy (1998), A2 All agents live equally long. The birth rate is as- Ø introducing irregular mortality sumed to be geometrically growing with respect to patterns, e.g. Rutherford (1999), the magnitude of the labor force (or constant). Ø including different views about A3 Life is divided into 3 periods, where the first two children’s consumption, e.g. Ro- periods are devoted to work and the last period is senzweig and Wolpin (1994), spent in retirement. This leaves us with the young Ø introducing the existence of fiat workers (20–42), the middle aged workers (42–65) money, e.g. Wallace (1978), and the aged people in retirement (65–80). Note that Ø restricting to a finite time children (up to the age of 20) “are part of their par- framework, e.g. John et al. ents’ consumption, and we take no note of them” (1993), Bommier and Lee (Samuelson, 1958). (1995), A4 The economic agents produce one unit of a good Ø allowing imperfect markets, e.g. when they are young workers, one unit of the good Hahn and Solow (1995). when they are middle-aged workers, and nothing at all when they are retired. A5 The good produced has a constant and is as- IMPLICIT ASSUMPTIONS sumed to be renewable but not storable at all. Com- A11 All agents in the model are of munity’s total saving per period equals zero. male gender. A6 Absence of comprehensive social security. A12 Women are part of the male A7 The time horizon is regarded to be infinite. individuals´ consumption. A8 Negation of Boehm-Bawerk’s (1924) three causes: A13 The modeled economy in- 1. Society doesn’t get more prosperous over time cludes the unpaid labor of women in non-market do- 2. Time- is non systematic mains. 3. Technological progress is non existent A14 The number of females in the A9 Markets are ideally competitive; Neo-Walrasian modeled economy leaves the concept of a general competitive equilibrium (Wal- birth rate unaffected. ras, 1881). A15 Value depends on A10 Non-slave economy.

OUTCOMES OF THE OVERLAPPING GENERATIONS MODEL (SAMUELSON, 1958) Samuelson’s final conclusions, after his mathematical approach of regarding the dilemma of the collision between the desire for consumption in retirement and the inability to store remains of former production, come to form following statements: · “Every geometrically growing consumption-loan economy has an equilibrium market rate of interest exactly equal to its biological percentage growth rate.” (Samuelson, 1958), i.e. in ab- sence of the output is merely determined by the number of workers – which explains the importance of human reproduction. · The biological market interest rates are related to growth, but are not socially optimal. · The will install money as an institution to achieve a socially optimal biological configuration. Money becomes an invention of a social arrangement to store wealth, optimize saving and consumption in productive periods, reach pareto-efficient out- comes, and to guarantee optimal old age benefits (Samuelson, 1958).

Figure 1: Samuelson’s modeled world including extensions to his assumptions.

3 The OLG model, however, is not only used as a major labor market (and of society in general) would not requisite in most economists’ toolkit, it also serves as have fit white, middle-class surroundings at all. It a rigid philosophical framework for economic and seems unlikely, that Samuelson aimed to model a political activities in , e.g. new situation opposite to the real-life situation he was classical economists, like , are still facing -especially, according to ’s opin- building their theories on the dogmatic opinions ion (1993) which says that an economist’s (or scien- stemming from Samuelson-like models. The difficul- tist’s) subjective view of a real-world problem inevi- ties arising from this traditional (ab)use of exclusively tably emerges in the corresponding : male economic theories as propaganda instruments to “, in thinking about the economy, strengthen male advantages combined with the naive is inevitably thinking about herself or himself. gender-blindness inherent in such models, often lead Introspection plays no part in the framing of hy- to logical dead-ends and paradoxes in the model out- potheses about chemistry or molecular biology, comes. This is why we carefully have to answer the but I do not see how it can be wholly avoided in question whether or not Samuelson’s analogy is an framing hypotheses about economic behavior.” appropriate and, especially, a technically correct (Solow, 1993) reflection of real-world behavior – particularly of nowadays real-world behavior. Therefore, we can assume that Samuelson was refer- ring to (male) men only. Then his assumptions with 3. THE HIDDEN AGENDA IN SAMUELSON’S respect to the agents populating his model make more OLG MODEL sense (though these assumptions are, nonetheless, a 3.1 THE ECONOMIC AGENTS’ GENDER (ASSUMPTION A11) considerable simplification of human behavior): The A major bifurcation in the logical motivation of the (male) individuals amongst each other can be thought overlapping generations model already arises due to of as “far more identical” than in the previous sce- Samuelson’s (1958) first assumption, nario which tends to satisfy assumption A1. The life “... men enter the labor market at about the age cycles are quite similar, work life starts at around the of twenty ...” age of 20 and is not interrupted till retirement which fulfils assumption A3. The levels of and Does men stand for male persons only or does Sa- are more equal in a group of workers consist- muelson refer to the second meaning of the word men ing out of men only as outlined by assumption A4; which includes all humans in a common manhood? duties or responsibilities aside from professional labor This distinction between the corresponding scenarios are not an issue. But now the role of women in the is absolutely necessary, since the very essence of the context of the OLG model is quite unclear. model, and all its implications have to be looked at differently in either way. 3.2 THE ROLE OF WOMEN IN SAMUELSON’S OLG Let us assume that Samuelson was indeed taking MODEL (ASSUMPTIONS A12–A14) an inclusive approach, referring to men and women We know that females have to exist somewhere in the by the use of the term “men”. Then men and women OLG model, since the existence of children is inevi- are considered to have identical production patterns tably necessary for the outcomes of Samuelson’s and identical possibilities according to assumption model – and, indeed, Samuelson does not forget fe- A1. They produce identical , get paid identical males as he refers to the importance of the reproduc- wages, are equally present in the labor market, and tivity of human mothers (and even “Mother Earth” equally share work among both sexes. The birth of a herself as a metaphor for fertility). Since the labor child, however, is “a women’s job” – and the exis- market is not accessible for females according to tence of children is essential for the outcomes of the Section 3.1, women must be (working) somewhere OLG model (see Figure 1). But the time invested into else. But where? If they are “simply at home”, we the so-called “reproduction phase” does not cut back have to continue our inquiry: What is their occupa- the labor force at any time. Consequently, either “re- tion? Who pays their expenses? Are they – just like production work” is assigned a market price which children – part of their parents’ (or husbands’) con- would be a real innovation and should have caused sumption, and “we take no further note of them”? Do some discussions, or women are not included to act as mothers solely serve as a source for the Hobbesian economic agents in the OLG model. men6, or are women only existing in the form of chil- Furthermore, considering the OLG model in its dren and mothers? historical context -the late 1950ies- one has to admit, that the “men-and-women-are-identical-individuals- 6 “Let us consider men ... as if but even now sprung out of with-respect-to-labor-and-wages”description of the the earth, and suddenly, like mushrooms, come to full

4 Even though the scenario of excluding women – ac- blind for.8 The homo oeconomicus is the personifica- cording to assumption A11 – piles up an enormous tion of a white, middle-class male; people less privi- amount of questions with respect to the argumenta- leged are not mentioned at all in this context. On the tion in Section 3.1 it still is the one Samuelson had in contrary, as a component of historical tradition (see mind with respect to his modeling process. This fact e.g. Mies, 1988), these people are regarded as con- is embarrassing, but not new or special in the field of sumption goods rather than as agents, just like it economic theory. When trying to explain the different seems to be the case in Samuelson’s analogy. approaches of “individuals” with respect to their 3.2.1 RETIREMENT BENEFITS FOR WOMEN actions on the compared to their altruism To exclude women from the modeling process ac- at home, Gary Becker (1995) walks in Adam Smith’s cording to assumption A11 mirrors the (often) op- (1778) boots just like Paul Samuelson by continuing pressive real-life conditions. A practical example is the Neo-classical tradition of male bias7: delivered by the retirement contribution insurance: “Every man feels his own pleasures and pains The core problem in Samuelson’s modeled world is more sensibly than those of other people. ... After the desire of the aged men to consume once they are himself, the members of his own , those retired. To guarantee retirement incomes it is neces- who usually live in the same house with him, his sary to have worked and produced beforehand. parents, his children, his brothers and sisters, are Women are not mentioned in this context; they are naturally the objects of his warmest affections. not even considered as intertemporary trading part- They are naturally and usually the persons upon ners with respect to retirement benefits. This happens whose happiness or misery his conduct must have because women, who are not working in the labor the greatest influence.” (Smith, 1778). market, but e.g. operating solely as mothers – being part of their husbands’ consumption which satisfies Here, we may witness the typical, symptomatic Neo- assumption A12 – will not produce anything in the classical blindness for the role and for the status of framework of the OLG model. If a housewife’s hus- women: In the long list of nearest and dearest people band dies after a long marriage she will receive a in a man’s , neither Smith, nor Becker, nor retirement income since the insurance has guaranteed Samuelson realize that the inclusion of a beloved him to care for his wife in case he dies first. But if the partner, and/or wife who cares for her husband’s husband leaves his wife after a whole life of house- physical and emotional needs, and/or a mother of work he will receive his retirement benefits – while joint children, and/or a woman who does the house- she will not. Just like in Samuelson’s model world the work, is not accomplished. wife does not exist in the retirement contribution Behind this obvious insufficiency lurks the vehe- scheme. Generally, the consumption of “Samuelson’s ment discussion whether it is correct to reduce the women” of any age depends entirely on the altruism agents populating an economic model to the (mathe- of a male relative as expressed by assumption A12. matically tractable) paradigm of the homo oeconomi- cus. This construction dates back to 3.2.2 WOMEN’S REPRODUCTION WORK (1869), and seeks to describe seemingly objectified The imperfection of the conditions for women in real personae, which should create the objectivity needed life does not start in retirement age. Economic theory by scientists. The concept has been source of a wide dismisses a whole segment of production, namely the dispute, where the heart of the discussion was the unpaid reproduction work in the household as out- debate whether the homo oeconomicus is an idealized lined by assumption A13. The reluctance to acknowl- picture of human rationality, or a ruthless ego- edge women’s traditional work results in low wages if maniac. Another interesting controversy arises from these duties are performed on the labor market, and the question, whether this “device for objectivity” in no wages if performed at home. Women and their reflects the sexism and racism most economists are work go unnoticed and the value of their work is disclaimed.9 The fact that women receive lower-level

8 maturity, without all kind of engagement to each other” “There are androcentric biases in the deep theoretical (Nelson, 1996a). Nowadays the Hobbesian mushroom structure of Neo-. [...] It presumes that theory is replaced by the more popular technocratic ap- humans are autonomous, impervious to social influences, proach of parachuters, who fall from the skies with their and lack sufficient emotional connection to each other to full supplies. make empathy possible [...] in the market. [But] in the 7 Feminists who are criticizing some obvious inequalities, family, individuals (particularly men) are presumed to be e.g. discrimination via wages, are constantly facing theo- altruistic.” (Mies, 1988). retical rationalizations originating from such economic 9 “Men’s are furthered because analyses pro- basics. In order to falsify theories like that, it is indispensa- ceeding from these [biased] assumptions direct our atten- ble to look into the reasoning which justified the slip from tion away from the ways in which typical arrangements the reality which theories sought to portray. between men and women perpetuate women’s disadvantage 5 wages is often justified by the dubious argument that and the new workers – and Samuelson (1958) this is a necessary condition to increase welfare himself realizes and acknowledges that “the in- (Maier, 1993). Diane Elson (1993) points out that, terest rate is related to the reproductivity of hu- though (or even because), “economics does not dis- man mothers”. Nevertheless, Samuelson relies on tinguish between men and women, economics is not an everlasting constant fertility rate or a birth neutral with respect to gender. The overestimation of rate geometrically growing with the size of the the importance of issues like GDP, growth, imports, labor force, respectively. The fact that women – exports, optimization of resource allocation, prizes, whose number is exogenously determined, and and so on, elucidates the male bias in economics”. who are treated to be outside the modeled labor The sphere of household and household production is force – are at least as important for the determi- terribly neglected, even though most economists nation of the birth rate as (working) men are. But should be aware of the fact that (women’s) reproduc- the model assumptions are confusing: Does the tion work emerges as the basis of all economic activi- extent of the labor force (A2) determine the birth ties. Economic theories assume implicitly that repro- rate or is the fertility of women dependent on duction work is independent of all other economic their number to keep the population growth con- activities (so does Samuelson in assumption A13), i.e. stant? (A14) reproduction work will always be available to an (2) The second hint comes up when Samuelson adds extent that ensures that the remaining economic ac- the statement to his astonishing discovery about tivities will never be negatively influenced by a short- the relation between interest rates and biological age of production due to reproduction. For instance, growth that his results are imbedded in a mod- Samuelson simply assumes: “... let us [...] keep births eled world “outside a slave economy” according forever constant.” (Samuelson, 1958). Remarkable, to assumption A10. This is more than a gentle however, is the fact that the birth rate is completely push for examining whether there is really no independent of the number of women as outlined by unpaid work hidden somewhere in the depths of assumption A14. We pay attention to this paradox in the unspoken model assumptions – or in other the following section. words, whether a contradiction between explicit (A10) and implicit (A13) assumptions exists. 3.3 SUMMARIZING THE CHANCES OMITTED FOR THE IMPROVEMENT OF THE OLG MODEL Samuelson ignores these hints and sets up the story of PERFORMANCE the Hobbesian young men who pay for (and nurse?) When Samuelson discovers that interest rates are the old. This simplification follows a long tradition, related to the growth of the population in the frame- and is usually regarded with a congenial smile, but it work of his OLG model the track of ignorance begins: is essential not to play down this practice. “I seem to be the first, outside a slave economy to “Well socialized economists, however, in practice develop a biological theory of interest relating it to tend to view their simplifications - especially those the reproductivity of human mothers.” (Samuelson, required by the core assumptions of self-interested 1958). and contractual exchange - as rela- tively innocent. The prevalence of jokes about Samuelson emphasizes his surprise about his discov- economists forgetting that assumptions are just as- ery with the words, sumptions is no accident. The of “Is there a common-sense market explanation of economic theory are seen as being approximately this (to me at least) astonishing result?” (Samuelson true rather than as only partially true. The notion 1958), of modeling as approximation however, disguises the value judgements hidden behind the decision to and proceeds to solve the mystery. He finds the count some phenomena as more important than seemingly sufficient explanation that an increment in others.” (Strassmann, 1993). the number of younger workers makes the life of the old more pleasant. Rigorous examination of the If Samuelson decided to follow the hints mentioned model assumptions and its conclusions, however, above, he would have had to allow unorthodox and yields a different answer. Instead of sticking to the unwanted economic truths, namely that the reproduc- dogma, one might follow the two blatant hints arising tivity of human mothers allows positive interest rates from Samuelson’s analysis. and that incident causes an increase of well being for (1) The existence of a biological interest rate already part of the population – contradicting assumption A8. strongly points towards the source of children But then he would have had to conclude that child- birth must have some kind of value (this principle will be discussed in the next section) instead of taking both in their and in labor markets.” (England, it for granted and not valuing it at all. These contra- 1993). dicting issues associated with a monetary valuing 6 system lead to even more questions: Does money trary. The field of responsibility of the woman worker really create socially optimal outcomes for all indi- is still somewhat blurred. Bosses often feel they have viduals (either existing implicitly or outspokenly a right to special services of their female employees – within the modeled world)? Why does economic the- just think about the coffee ritual. Sexual harassment ory deny the importance of women’s work? Does this at the working place is partly resulting from tradi- denial mirror the subjectivity and real political inter- tionally far-reaching boundaries for women’s working ests of economic theory? Is the discrimination faced domains. Hence, for women money often creates by women and by people who are non-white and/or dependence instead of the desirable independence. members of “lower social classes” a consequence of The creation of money to preserve typically male concepts like Samuelson’s contribution to Neo- values in a men’s world is an androcentric tool to classical theory? Some of these questions will be maintain power. answered in what follows. 4.2 VALUES 4. MONETARY UNITS AND THEIR VALUE Both the use of the technique of mathematical mod- eling and the invention of money allow to combine 4.1 MONEY AS A SOCIAL CONTRIVANCE TO ENSURE and to measure groups of durable and non-durable SOCIAL OPTIMALITY goods (which have different values) over time, how- The third outcome of Samuelson’s analysis is “to see ever, one “function” of money from a new slant – as a social compact that can provide optimal old age “One of the great metaphysical ideas in eco- social security.” (Samuelson, 1958). Indeed, money nomics is expressed by the word “value”. ... It serves as a deposit of goods’ values, as an instrument does not mean market , which vary from to shift individual saving from productive periods to time to time under the influence of casual acci- non-productive (future) periods, and, consequently, as dents; nor is it just an historical average of ac- a medium to guarantee consumption in retirement. tual prices. Indeed, it is not simply a price; it is Economists love to tell stories about the origins of something which will explain, how prices come to money in different cultures. Kauri shells, stone- be what they are. What is it? Where shall we find wheels, elephants’ tails, pressed tea, or dogs’ teeth, it? Like all metaphysical concepts, when you try are curious examples of prehistoric . These to pin it down it turns out to be just a word.” paradigms are often used to make us believe that (Robinson, 1979) every advanced culture is obliged to invent money to Most crucial is the very basic assumption A15. Goods store wealth. But what is the nature of the “values” which are rare are most valuable: e.g. gold charms. which need to be preserved and stored for the future? Others which are easily available are of less value: While women perform “non-monetary” (actually non- e.g. bricks. The usefulness of those rare items com- measurable) activities like reproduction work, child- pared to widespread articles does not influence the care, taking care of the sick and old, household work, evaluation process. With regard to services, Adam work on the family’s fields, etc. for free, other (meas- Smith was the first economist to connect moral values urable) values become non-perishable as monetary to market values. In doing so he scientifically founded units. Money seems to be an invention by men to the arrangement that men’s doings are valuable and preserve values for men. Symptomatically, the inven- non-altruistic and therefore need to be paid for, while tion of money pops up in Samuelson’s model, when women’s doings are nothing of that sort. In the free we try to answer the question of how to preserve market the homo oeconomicus is operating as fol- men’s production (of goods) for their old age. lows: These observations are consistent with women’s experiences having to face (a lot of) money. For men “It is not from the benevolence of the butcher, the the ownership of money clearly means independence, brewer or the baker, that we expect our dinner, but for women it often indicates an ambivalent situation: from their regard to their own interest.” (Adam Historically, women’s access to money was via men. Smith, 1778). Receiving money was never associated with a deal of The wife’s provision of a dinner is not so clearly neutral nature; the interpersonal relationships accom- founded on her own interest. Altruistic motives and panying monetary transfers were (and are) usually emotional ties are believed to be the driving force of quite complicated. The husband provides physical interactions in the family. Not only women, but also things and money to satisfy the family’s needs, in men are in this context unselfishly straining to make return the wife produces children and emotional sup- each others´ and their children’s lives more happy: port and other monetarily invaluable deeds. The diffi- culty to measure the wife’s performance in monetary “Becker refers to the altruistic head [of the family] units leads to arbitrary rewards for her duties. On the as male and to the beneficiaries as women and labor market the rewards (i.e. wages) are less arbi- children, although he claims that he used masculine 7 and feminine pronouns only to distinguish the al- However not the lack of contact, but the dramatic truist from the beneficiary. Since Becker certainly influence of such programs on the real world and knows that it is generally men who have greater ac- their strategy to maintain the status quo is crucial. cess to money, we must be suspicious of his claim Economists systematically omit information about that his choice of the male pronoun to denote the women and their spheres of life to emphasize the altruist was arbitrary. Yet Becker never discusses importance of male interests. To give up this strategy the effects of such differential power in the family. would also mean to give up male privileges in real [...] It is particularly ironic that altruism, in which life. women seem to specialize more than men, gets credited to men!” (England, 1993). 5. GENETIC ALGORITHMS AS AN ALTERNATIVE MODELING APPROACH TO As mentioned above, like birth of CONSIDER NOWADAYS SOCIETY? a child and motherhood, childcare, emotional sup- A possible way to overcome the troublesome “repre- port, relief of aged people, etc. can hardly be meas- sentative agent” assumption, A1, (and also the neo- ured in monetary units because these goods are not Walrasian concept of a general competitive equilib- produced and purchased in a free market. Since rium expressed by assumption A9), is the use of women traditionally (re)produce in their families, Computational Intelligence (CI) techniques like neu- most of their deeds – whether regarded as valuable or ral networks, genetic algorithms and/or cellular not – are performed (altruistically) without orienta- automata. All of these approaches from computer tion on compensation. But remembering the connec- sciences are used lately to describe the adaptive be- tion of value to scarcity it would be interesting to find havior of heterogeneous individuals in economic out if reproduction work became more valuable if systems, see e.g. the survey in (Dawid, 1999a). CI performed less frequently. techniques do not yield analytical results, but the numerical results obtained allow to suggest features of According to Marilyn Waring (1988) all our beliefs of the model, to examine the transient behavior of eco- value are strongly influenced by androcentric bias. nomic systems before they settle down in an equilib- Assigning a certain value to an economic action is rium, and to investigate features of social learning independent of the actual time or energy invested, but like imitation and communication effects which can- solely dependent on who performs the deed. The not be dealt with in a representative agent model, as value of a or good is determined by an exoge- performed in e.g. Behrens and Dawid (2000) – and nous instance and related to an abstract monetary this “heterogeneous agents” approach is absolutely value. Patriarchal ranking of values is solely con- necessary considering nowadays family demography. nected to money and based on more or less arbitrary E.g. ÖSTAT (1998) reports that a marriage lasts on cultural and androcentric standards. The implications average approximately 8-9 years due to a divorce rate for the real life of women and people from non-white of about 38%. The associated increase in the number and/or lower-class backgrounds are aggravating. of single-parent families manifests the flaws of the “Economic approaches and policies are rooted in a 1958 OLG model or any of its extensions including problematic, and often deadly, dichotomization of assumption A1. what does and does not have value.” (Waring, To illustrate the whole variety of the characteristic 1988) features of a heterogeneous society we refer to the use of Genetic Algorithm (GA)-based models,11 see e.g. The justification of androcentric valuing in economics Goldberg (1989) or Dawid (1999a). The idea to use evolves around the idea of a well-meaning monetary Genetic Algorithms to capture the basic features of 10 system. Samuelson’s 1958 paper also takes this OLG models is not new in economic theory. Azari- point of view. The insight that money creates pareto- adis (1981) and other authors show that in OLG efficient optimal conditions seems convincing, until models equilibria with random we look more closely at the hidden agenda. Actually, Donald McCloskey believes that

“after the masculinist programs of Paul Samuelson 11 Genetic Algorithms may be treated as models of adaptive [...] we know more about economic models lacking behavior in a population of boundedly rational individuals contact with the world.” (McCloskey, 1993) . and were recently used to examine adaptive behavior in several economic models, e.g. Andreoni and Miller (1995), Arifovic (1994, 1995, 1996), Dawid (1999b), Dawid and Kopel (1998), Marimon et al. (1990), especially, because in 10 The ambivalence of money creating optimal welfare several of these contributions, e.g. Arifovic (1994, 1995), it conditions on the one hand and an utterly ruthless homo is shown that Genetic Algorithms are well-suited tools to oeconomicus who uses money to cheat others and to live on describe actual human learning behavior and match ex- their expense on the other hand is reflected in Lucas and perimental results often better than standard learning rules, Stokey (1987). like least-square learning or stochastic approximation. 8 prices12 may exist though there is no lem: What is the value of a child’s birth, and what within the model. Arifovic (1995) uses GAs to learn is the value of raising that child? stationary equilibria with perfect foresight in a simple We have to find a monetary equivalent which OLG model. She extends her analysis to the case of a can be used as an equalization payment (from so- two-country OLG model in Arifovic (1996). Dawid ciety) to consumption during the repro- (1996) shows that a simple OLG model with fiat duction phase to guarantee that type F individuals money is able to learn and even cycles. Bul- are in a position which allows a rational counter- lard and Duffy (1998) deal with a n-period OLG balance between production and reproduction. model where the agents’ adaptive learning is again This may be accomplished as follows: Contra- modeled by GAs. We argue that it might be very dicting assumption A8, the reproductivity of hu- fruitful to follow this line of investigation combined man mothers allows positive interest rates which with Becker’s (1992) “Economy and Fertility” ap- causes an increase of well-being for part of the proach, and set up a “Dawid-type” OLG model (see population, namely the women having and raising Dawid, 1996), but differentiate between populations a child. of opposite genders. In spite of the GA-based exten- sions of the standard OLG model which are listed begin above, to our knowledge, no two-gender approach exists. We argue that this is a consequence of the enormous difficulty associated with the so-called selection encoding mechanism – without destroying the “con- vergence” behavior of the GA.13 We argue that a model which captures the basic crossover features of overlapping generations in nowadays soci- ety has to include at least two populations, namely, · a population of type M individuals whose produc- mutation tivity phase lasts from their, say, 20th to their 65th “birthday” without being interrupted by a repro- duction phase, followed by a retirement phase as n uniform? described by e.g. Samuelson (1958), and · a population of type F individuals who are able to y decide whether to “reproduce or to produce” end where children are assumed to be part of their consumption. But in case of reproduction these Figure 2: Structure of a Simple Genetic Algorithm individuals have to be – for a while (or for the rest of their lives) – part of the consumption of “some- Then, the modeling approach proceeds as follows: body else”. This immediately raises the well- Each single agent in the GA-based OLG model (i.e. known question: Who is somebody else? each member of one of the populations) is represented In a number of cases this could be a partner, by a binary string of predetermined length. The cod- say a type M individual. But who is going to pro- ing mechanism for the populations of type M and type vide consumption for an average type F individual F individuals, respectively, could work as follows. during the reproduction phase in the remaining number of cases? Certainly, we cannot use Sa- ¨ Consider a binary string, bi, of length, lM, in the muelson’s principle of the interest rate (“You get population of type M individuals. Interpret the something, because you once gave something”) to first, say, 8 bits of this binary string as the repre- guarantee consumption during the reproduction sentation of an integer, h, in the binary alphabet. phase. If we use the “trading” principle of give This value represents individual i’s consumption, and receive we have to face the well-know prob- e.g. the string, 01010100, describes an individual with a consumption of 84 units. This value should, however, be normalized, e.g. by dividing l this integer by 2 M-1, which gives a value in the 12 These equilibria, which are governed by the beliefs of the unit interval, (0,1). Additional bits might reflect individuals that an external random variable has some information about the age, the family status in- influence on the prices, are called sunspots. cluding martial status, the number of children, 13 Though, strictly speaking, GAs never converge if the etc. mutation rate is positive, we will use the term “conver- gence” to outline a state, where one strategy spreads over · Strings in the population of type F individuals are the entire groups (of both genders), and the only fluctua- of length lF> lF. The first parts of their strings may tions within the populations are due to mutations. 9 be designed equivalently to the strings in the type 6. CONCLUDING REMARKS M population, but the rest should include more Economists systematically omit information about information about children and, particularly, the women and their spheres of life to emphasize the time devoted to bringing them up, the corre- importance of male interests in economic theory. sponding working status, the income level, etc. Theories like the one developed in Samuelson’s OLG model is used scientifically to strengthen the privi- These artificially intelligent agents have much higher leged position of men in society. The androcentrically computational capabilities than the traditional eco- biased assigning of monetary values to certain actions nomic agents who react exactly to the predetermined and goods but not to others is a core strategy in that rules according to the economic model. In each pe- regard. riod each artificially intelligent agent receives some Samuelson’s OLG model creates the typical Neo- payoff for his/her choice of consumption, which de- classical world seen from the perspective of a white, fines the so-called fitness value. (These values depend male economist in the late 1950ies. To illustrate the on the situation of the artificial agents with respect to accusation of subjectivity in this paper, try to imagine their ages and their family circumstances.) Using how "the female African economist Paula Samuelson" these fitness values the transition from one generation would try to model the problems of retirement (from to the succeeding one is executed by the application of her point of view). Do you think she would have come the GA Operators which are described in detail by up with the same modeled world as Paul Samuelson? e.g. Dawid (1999a). This application, visualized by Trying to be innovative in our critique of the OLG Figure 2, is affected separately for each population. model, we briefly outline an alternative modeling The Selection Operator models an imitation effect approach based on the use of Genetic Algorithms. In within a population. Individuals with low payoffs will doing so, we follow the basic model setup of Dawid very likely imitate those with high payoffs.14 Within a (1996) but extend the model assumption to consider single population, individuals will be influenced by two populations of artificially intelligent agents of others, even if they do not imitate each one. The different gender. whole – or only notions of their – strategy are As a different approach which avoids the andro- adopted. This is accomplished by the Crossover Op- centrically biased assigning of monetary values en- erator and gives strings with high fitness a chance to tirely, Marilyn Waring advocates the use of time produce even better individuals. The Mutation Op- rather than the use of money as a more adequate and erator models some kind of innovation: Either actions equitable standard to measure the value of productive are randomly mistaken, or the agents think that the activities (Waring, 1988). But not to find a concept best strategy has not yet been found. Thus, with very for change is most problematic. To give up andro- small probability, strings come into existence, which centric strategies also means to give up male privi- can not be found in the initial generation. This proce- leges in real life, therefore a strong denial of bias or dure will be repeated until all strings are equal, (or a subjectivity usually arises when the injustices sup- predetermined number of iteration steps is reached). ported by economic theory are pointed out. The resulting uniform populations hopefully out- line the equilibrium features of a heterogeneous soci- REFERENCES ety consisting of overlapping generations of opposite gender coming close to real-world human behavior. Andreoni, J. , Miller, J.H.. 1995. "Auctions with Artificial Adaptive Agents." Games and Economic Behavior 10: 39–64. Arifovic, Jean. 1994. "Genetic Algorithm Learning and the 14 Cobweb Model." Journal of Economic Dynamics and In the setup presented here, the fitness of a string in Control 18: 3–28. either of the populations depends on the values of other strings in both populations. Such a situation, which is Arifovic, Jean. 1995. 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