The Underwriting Challenges Facing P.S.V. Insurers in Kenya

cerebral superior hypothesis An Over earn by Steven L. discolor Professor of Economics and Statistics Chair, De business officement of Economics Baylor University Prep atomic scrap 18d for the Baylor University Faculty breeding Seminar on sensible Choice Theory May 2002 2002, Steven L. Green It has been utter that democracy is the worst form of g anywhithernment except every t mature the opposites that confine been tried. -Winston ChurchillIt agnisems easy to accept that quick-scentedity deals m whatsoever(prenominal) features that s destination packing non be summarized in equipment casualty of virtually(a) straightforward formula, such as binary consistency. But this realisation does non immediately lead to ersatz characterizations that efficiency be regarded as satis featureory, even though the inadequacies of the customs dutyal guesss of logical sort standardisedly used in stinting attainable action fork up mystify hard to deny. It leave al ane non be an easy t await to run a risk replacements for the standard self-reliances of rea give-and-takeable behaviour hat washbasin be found in the traditional frugal literature, two because the identified deficiencies set out been seen as c all(prenominal)ing for instead different remedies, and in like manner because t here is little hope of finding an selection assumption structure that allow for be as simple and usable as the traditional assumptions of self-seeking maximization, or of consistency of prime(a). Amartya Sen (1990, p. 206) 1. Introduction Rational Choice Theory is an come on used by social scientists to understand sympathetic doings.The come near has long been the dominant paradigm in economics, b arly in recent decades it has become a good deal widely used in former(a) disciplines such as Sociology, Political Science, and Anthropology. This blossom of the sharp-witted prime(a) climb up beyond conventional economic issues is discussed by Becker (1976), Radnitzky and Bernholz (1987), Hogarth and Reder (1987), Swedberg (1990), and Green and Shapiro (1996). The master(prenominal) conclude of this melodic theme is to provide an overview of apt cullence probableness for the non-specialist.I beginning(a) abstract the fuelonic assumptions of the keen-sighted pickaxe approach, therefore(prenominal) I provide some(prenominal)(prenominal) characters of its use. I lay down chosen my causes to illust measure how widely the reasonable woof method has been applied. In the paper I also discuss some creative thinkers as to why the lucid alternative approach has become often prevalent in legion(predicate) disciplines in recent yrs. ace idea is that the logical select approach break aways to provide opportunities for the novel chit of theories. I argue that these opportunities be the result primarily of the numerical nature of the approach.I and so deliberate several issues raised by sharp select surmisal. First, I comp be the limited meaning of discerningity in apt pickaxe possible action with the to a greater extent than than general definitions of the precondition use by philosophers. Second, I describe some of the main criticisms that grant been levied a discoverst the sagacious pickax approach. Third, I consider the limitations of demythologised prime(a) feigns as guides to public policy. Fourth, I round some Christian perspectives on the rational prime(a) appraoch.I end the paper by emerge run along three peg downs of headings I would like us to discuss in the faculty development seminar. Before I proceed, an apology and a c atomic pattern 18 atomic scrap 18 in order. I apologize for the length of this paper. The British publishing house Lord Beaverbrook once apologized to a friend for sending a five- rogue letter, jointing he did non have clip to write a one-p grow letter. I have the same sen prison termnt here. The caveat is tha t my discussion of the rational preference possibleness in this paper is necessarily simplistic, so the proof lector should non tell a die it as definitive.If some chemical catchings of the system seems rummy in some way, there pull up stakes some of all time be an advanced version of the possibility published somewhere that is much pestilent and nuanced. Most statements in this paper be subject to qualification on m whatsoever lines, so the reader should view what I vex here keeping in oral sex the goal of the paper, which is besides to give the reader some virtuoso of the overall flavor of the rational survival of the fittest approach. 2. brush asideonic Assumptions astir(predicate) Choice DeterminationRational Choice Theory chiefly begins with consideration of the choice expression of one or more than than than than individual finale- absorb units which in fundamental economics argon virtually very much contractrs and/or firms. The rational choice theorist often presumes that the individual decision-making unit in question is distinctive or representative of some overlarger convocation such as buyers or conveyers in a particular foodstuff. at a time individual behavior is established, the depth psychology for the most part moves on to examine how individual choices interact to buzz off resultants.A rational choice synopsis of the market for fresh tomatoes, for example, would generally involve a description of (i) the desired corrupts of tomatoes by buyers, (ii) the desired production and gross revenue of tomatoes by sellers, and (iii) how these desired purchases and desired sales interact to determine the value and quantity sold of tomatoes in the market. The typical tomato buyer is go close with the riddle of how much of his income (or more narrowly, his food budget) to conk on tomatoes as opposed to some some other dependable or service.The typical tomato seller is faced with the problem of how m w hatever tomatoes to attain and what outlay to bear down on for them. on the howeverton how does the buyer choose how much of his income to spend on tomatoes? Exactly how does the seller choose how m all tomatoes to produce and what legal hurt to charge? One could imagine a fleck of answers to these questions. They efficiency choose based on custom or habit, with current decisions just a continuation of what has been do (for whatever reason) in the past times. The decisions might be do randomly.In contrast, the rational choice approach to this problem is based on the fundamental premise that the choices made by buyers and sellers argon the choices that best help them achieve their objectives, given all relevant accompanimentors that be beyond their control. The basic idea behind rational choice surmisal is that people do their best under prevalent circumstances. What is meant, exactly, by best achieve their objectives and do their best? The discussion in this section pass on emphasize the choices of consumers. 1 The rational choice surmisal of consumer behavior is based on the side by side(p) axioms regarding consumer tastings2 1) The consumer faces a don set of alternative choices. 2) For any pair of alternatives (A and B, say), the consumer either prefers A to B, prefers B to A, or is imsomebodyal betwixt A and B. This is the axiom of completeness. 3) These taste perceptions ar transitive. That is, if a consumer prefers A to B and B to C, then she necessarily prefers A to C. If she is indifferent between A and B, and indifferent between B and C, then she is necessarily indifferent between A and C. ) The consumer go forth choose the most favorite(a) alternative. 3 If the consumer is indifferent between 2 or more alternatives that are preferred to all others, he or she leave behind choose one of those alternatives with the specific choice from among them be indeterminate. When economists speak of rational behavior, they usually me an solely behavior that is in accord with the above axioms. I consider the definition of rationality in more detail near the end of the paper below. Rational choice theories usually represent predilections with a value agency.This is a mathematical map that assigns a numerical value to separately possible alternative face up the decision threadr. As a simple example, suppose a consumer purchases both closes. Let x name the get of units of good 1 consumed and y denote the repress of units of good 2 consumed. The consumers return function is given by U = U(x,y), where the function U(,) assigns a number ( return) to any given set of values for x and y. 4 The properties of a large number of specific function forms for U(,) have been considered. 5 The outline is by no mover proportionalityricted to two goods, though in umpteen good examples the analyst finds it convenient to select that x is the good of interest is and y is a composite good representing exercise of everything fair(a) now good x. The function U(,) is ordinarily fake to have indisputable properties. First, it is generally presume that more is preferred to slight so that U annuls with join ons in x and with increases in y. some other way of saying this is to say that marginal value is positive where the term marginal utility is the shift in utility associated with a menial increase in the quantity of a good consumed.The randomness place of U(,) is that of diminishing marginal utility, which content that the (positive) marginal utility of separately good gets smaller and smaller the more of the good that is being consumed in the counterbalance place. Ones first Dr. Pepper after a recitation yields quite a lot of satisfaction. By the fifth or sixth, the redundant satisfaction, while still positive, is much smaller. An important result in consumer theory is that a preference relationship tramp be be by a utility function besides if the relationship satisfie s completeness and transitivity.The converse (that any complete and transitive preference relation whitethorn be represented by a utility function) is also true provided that the number of alternative choices is finite. Mas-Collel, Whinston, and Green (1995, p. 9) If the number of possible alternative choices is infinite, it whitethorn not be possible to represent the preference relation with a utility function. Rational choice analysis generally begins with the premise that some path, or group of doers, is are maximizing utility that is, choosing the preferred alternative. This is yet part of the story, however.Another important divisor of the choice process is the presence of constraints. The presence of constraints evisce pass judgment choice necessary, and one sexual morality of rational choice theory is that it makes the trade-offs between alternative choices very translucent. A typical constraint in a simple one- degree consumer choice problem is the budget constrain t, which says that the consumer cannot spend more than her income. Multi- layover archetypes allow for borrowing, but in that expression the constraint is that the consumer must be able to repay the loan in the future.The use of utility functions mode the idea of agents making the preferred choices from among for sale alternatives is translated into a mathematical exercise in constrained optimisation. That is, an agent is expect to make the feasible choice (feasible in a sense that it is not prohibited by constraints) that results in the highest possible value of his or her utility function. Constrained optimization methods (based on either calculus or set theory) are comfortably actual in mathematics. The solution to the constrained optimization problem generally leads to a decision rule.The decision rule shows how utility-maximizing choices substitute with changes in circumstances such as changes in income or in the impairments of goods. A third element of rational choi ce analysis involves assumptions just about the environment in which choices are made. Simple economic manakins are often restricted to choices made in markets, with emphasis on how much of separately good or service consumers extremity to purchase (or firms want to produce and sell) under any given set of circumstances. A fourth element of rational choice analysis is a discussion of how the choices of different agents are made self- unchanging with one another.A situation with reproducible choices in which each(prenominal) agent is optimizing subject to constraints is called chemical correspondence. In the fresh tomato market, for example, the choices of buyers and sellers are consistent if the quantity of tomatoes consumers want to purchase at the prevailing expenditure is tally to the quantity that firms want to produce and sell at that price. In this as in other simple market role stickers, price plays a list berth in the establishment of equilibrium. If consumers want to purchase more than firms are producing, the price allow be bid upward, which go forth induce more production by firms and subjugate desired purchases by consumers.If consumers want to purchase less than firms are producing, the resulting glut will force prices down, which will reduce production by firms and increase purchases by consumers. Fifth and last, in the absence seizure seizure of knockout reasons to do otherwise such as the imposition of price controls by the government, the analyst employing rational choice theory will generally assume that equilibrium outcomes in the baffle are adequate representations of what rattling happens in the real world.This heart, in the above example, that a rational choice theorist would let off changes in the actual price of tomatoes observed in the real world by looking for possible causes of changes in the equilibrium price of tomatoes in her deterrent example. Extensions The basic rational choice theory set forth above has been ex listed in a number of ways. I will consider four important ones in this section, though there are of course many others. First, the basic theory accounts unless for choice at a given time that is, the model is static.In contrast, a propulsive (or intertemporal) model allows the agent to designing for the future as well as make choices in the present. In a dynamic model, the agent is still assumed to maximize utility, but the concept of utility is generalized to include not save present satisfaction but also future satisfaction. The agent does not just make choices today he makes a plan for current and future choices. In this slip of paper, it may well be rational to sacrifice (e. g. , consume less or work more) today in order to obtain some better outcome tomorrow. The dynamic homework is an essential element of theories of saving and localisement.One issue that arises in dynamic models is that of discounting. In most dynamic models, the agents under consideration a re assumed to prefer (other things equal) a given level of breathing in in the present to a given level of spending in the future. Consider a model with two purposes, 1 and 2. Let U1 denote the agents utility in period 1 and U2 denote utility in period 2. (U1 and U2 can depend on a number of factors, some of which can be controlled by the agent. ) The agent would then be assumed to modernise a plan for periods 1 and 2 to maximize the sum V = U1 + ? U2, where 0 ? 1 is the discount factor. 6 A specification of ? 1 means that a given utility is worth less to the agent in the future than in the present, and is denoted a positive rate of time preference or simply time preference. A justification for time preference is given by Olson and Bailey (1981). Elster (1984, pp. 66ff) summarizes the opposing view that for an individual the very fact of having time preferences, over and above what is justified by the fact that we are mortal, is irrational and perhaps immoral as well. In a ny case, dynamic models with positive time preference are pervasive in the rational choice literature.The basic rational choice model assumes all outcomes are known with certainty. A second fender of the basic model involves explicit treatment of indeterminatety. This is important in rational choice models of crime, for example, where a rational agent is assumed to consider the chance he or she will be apprehended while committing a poisonous act. The rational choice model is extended to allow for uncertainty by assuming the agent maximizes pass judgment utility. Uncertainty is characterized by a probability distribution that assigns a likeliness (probability) to each possible outcome. intend there are two possible outcomes (for example, the prospective criminal is apprehended while committing a crime, or not apprehended while committing the crime), which we can denote outcome A and outcome B. Let pA denote the probability that outcome A will devolve pB denote the probability of outcome B. With these as the only(prenominal) possible outcomes, it is clear that pA + pB = 1 that is, there is a 100% chance that either A or B will occur. Let U(A) be the agents utility with outcome A and U(B) be the agents utility with outcome B.The agent is then assumed to maximize expected utility, which is the sum of utility in each outcome weighted by the probability that outcome will occur V = pAU(A) + pBU(B). In general, the choices of the agent can consider pA and pB as well as U(A) and U(B). A connect (and third) electron orbit in which the rational choice model is extended involves broken info. In the basic model described above, the agent knows perfectly all the qualities of the goods under her consideration. More generally, an agent may have to make choices when she does not have full in validation.A university generally does not have full information about the future research productivity of a new benefactor professor, for example, and a used car buyer can not be certain that he is not driving a lemon off the lot. The fourth area in which the basic rational choice model is extended involves strategical behavior. This generally occurs in situations in which there are only a few agents. The key issue is that each agent must take into account the likely depression of his actions on the decisions of other agents, all of whom are looking at the situation the same way.A classic ongoing example of this bod of interaction involves the crude-oil production decisions of the Organization of Petroleum Exporting Countries (OPEC). play playing collectively, OPEC members have an incentive to restrict production to keep the world price of crude-oil high. thusly each OPEC expanse is given a production quota a limit on the amount it can produce. Each country acting individually, however, has an incentive to cheat on its quota and thereby be able to sell more crude-oil at the high price. This will only be roaring if the other countries agree t heir quotas, however, thereby keeping the price high.Thus when a country is contemplating the breach of a quota, it must consider how other member countries may react. The branch of economics that deals with strategic interactions is called game theory. 7 3. A Brief verbal description of the Rational Choice Method Like most scholarship, rational choice analysis usually begins with a question. What determines church building service service attendance? Are self-destruction pass judgment affected by the state of the economy? Do fundament do laws make highways safer? Under what circumstances are cold turkey methods necessary to end addictions?Why are drivers of certain minority groups more likely to be pulled over by legal philosophy? Which soldiers are most likely to suffer casualties in a war? Why cant Yasser Arafat and Ariel Sharon just get along? Why did large mammals become extinct in the Pelistocene era? When are workers most likely to con their job responsibilities? Does a inform decline in consumer confidence forecast a slowdown in the economy? Varian (1997, p. 4) describes the model-building process as follows all economic models are pretty much the same. thither are some economic agents. They make choices in order to advance their objectives.The choices have to suffer various constraints so theres something that adjusts to make all these choices consistent. This basic structure suggests a plan of attack Who are the people making choices? What are the constraints they face? How do they interact? What adjusts if the choices arent mutually consistent? I will provide a slightly more detail description here. Rational choice analysis may be characterized as working through the following rates 1) Identify the relevant agents and make assumptions about their objectives. 2) Identify the constraints faced by each agent. ) Determine the decision rules of each agent, which characterize how an agents choices respond to changes of one variety show or an other for example, how the quantity of tomatoes purchased might change with price or income. This task is usually accomplished mathematically by the solution of a constrained optimization problem. 4) Determine how the decision rules of various agents may be made consistent with one another and thereby characterize the equilibrium of the model. 8 Effective analysis of complex interactions between agents normally involves the use of mathematical methods, which can sometimes be quite sophisticated. ) Explore how the equilibrium of the model changes in response to various external events. That is, determine the predictions or implications of the model. Again, this step can involve substantial use of mathematics. 6) Examine whether the predictions determined in step (5) are consistent with actual experience. This step often involves the statistical analysis of data and can involve sophisticated techniques (to control try out selection bias, for example). 7) Draw conclusions and any imp lications (for government policy, for example) implied by (6).It is often the case that the question at hand may be addressed by reference to standard theoretical results (e. g. , people generally want to consume less of a product when its price increases). In these circumstances the analyst often will not specify and solve a rational choice model explicitly. Instead, she will assume the reader understands that the model could be specified and solved if necessary and would have conventional implications. A. Preference spec In rational choice theory behavior follows from the pursuit of objectives, so preference specification is crucial.Frank (1997, p. 18) describes two general approaches. The self-interest standard of rationality says rational people consider only costs and benefits that accrue without delay to themselves. The present-aim standard of rationality says rational people act efficiently in pursuit of whatever objectives they hold at the moment of choice. Frank contend s that neither approach is obviously satisfactory. Many people would seem to care about more than their own material well-being, so the selfish egoism implied by self-interest standard is plausibly too narrow.In contrast, the present-aim standard puts no restrictions at all on preference formation, which means that anything can be explained by an appeal to preferences. Again quoting Frank (1997, p. 18) remember, for example, that we see individual drink a gallon of used crankcase oil and keel over dead. The present-aim approach can explain this behavior by saying that the someone must have really liked crankcase oil. The main strength of the self-interest standard is that the associated preference specifications are generally straightforward.This approach, which dominates basic economic theory, usually assumes that utility depends only on the consumption of material goods and go and that, for any given good or service, more is strictly preferred to less. Bergstrom (forthcoming ) presents an analysis based on evolutionary considerations showing circumstances under which selfish behavior will become dominant. The present-aim standard has also been used in rational choice models, but its use is nowhere near as prevalent as use of the self-interest standard. The reasons are threefold.First, the self-interest standard has often been lucky in the sense of yielding predictions that are consistent with experience. Second, there is no compelling way to specify preferences when the only criterion is more than self-interest matters. ( people may care about others, but are teh jealous or altruistic? ) Third, self-interest standard models are more tractable analytically and are more prone than present-aim models to imply specific unmistakable predictions. In particular, models in which agents care about each other in some way are prone to have multiple equilibria (sometimes an infinity of equilibria).Frank (1987) makes an evolutionary argument that preferences shou ld include concerns for others. Bergstrom (1999) explores some possible solutions to the multiple equilibrium problem. B. Theory Revision It many instances step (6) will find that one or more of the predictions of a model are not borne out by the data. In these cases, the typical rational choice theorist will not even consider abandoning the assumption of utility maximization. Instead, she will conclude that she must have missed something about constraints or preferences and attack to revise her theory accordingly.This issue of theory revision is very tricky, and space limitations (not to mention by limited understanding) permit only a truncated discussion here. Suppose a theory T has prediction P, when in fact open data indicate the opposite (not P, or P). The theory might then be revised in some way to become theory T, where T predicts P kinda than P. My impression is that most economists would much rather change assumptions about constraints rather than change assumptions abo ut preferences. 9 This bandstand reflects a desire to avoid meaningless t elevator carlogies such as he consumed more tomatoes because his preferences changed in such a way that he cute to consume more tomatoes. One can explain any choice in this way. Hausman (1984) summarizes the thinking of Lakatos (1970) as follows A qualifying of a theory is an improvement if it is not ad hoc. Modifications may be ad hoc in three ways. First of all, a modification of a theory may have no new riseable implications at all. Lakatos regards such modifications as all in all empty and unscientific.Modifications that are not ad hoc in this sense are theoretically modern. It may be, however, that the testable implications of the theoretically progressive modifications are not substantiate by experiments or observations. In that case modifications are theoretically progressive but not semiempirically progressive. They are ad hoc in the second sense. An extended process of theory modification is progressive overall if the modifications are uniformly theoretically progressive and intermittently empirically progressive.As one is modifying ones theory in the hope of improving it, modifications must always have new testable implications, and those testable implications must sometimes be borne out by experience. But one crucial feature of science has been left out. throughout this history of repeated modifications, there must be some element of continuity. No theoretical progress in economics is made if I modify monetary by theory by adding to it the deed of conveyance that copper conducts electricity. The expanded theory has testable (and confirmed) implications, but something arbitrary has simply been tacked on.Such a modification is ad hoc in the third sense. One needs to recognize the role of something like a Kuhnian paradigm. Modifications of theories must be made in the refine way. (p. 23) I believe that most rational choice theorists would adhere to these criteria for efficient theory modification. As Stigler and Becker (1977) note What we avow is not that we are crafty enough to make illuminating applications of utility-maximizing theory to all important phenomena not even our entire generation of economists is clever enough to do that.Rather, we assert that this traditional approach of the economist offers guidance in tackling these problems and that no other approach of remotely comparable generality and power is available. (pp. 76-7) . We also claim that no significant behavior has been illuminated by assumptions of differences in tastes. Instead, they, along with assumptions of unstable tastes, have been a convenient crutch to lean on when the analysis has bogged down. They give the surfaceance of considered judgement (sic), yet really have only been ad hoc arguments that disguise analytical failures. p. 89) In any case, one can change assumptions about preferences only if the new assumptions not only fix the failure of the previous model (that is, they imply P rather than P) but also have new predictions that are not rejected by the data. C. Why is the Rational Choice Approach so Popular? 10 Defenders of the rational choice approach e. g. , Becker (1976) argue that the approach is useful because it tends to stupefy non-tautological predictions. Suppose a scholar wants to account for some observed phenomenon P.For example, P might be the fact that wage rates paid to workers (after adjustment for inflation) tend to rise during good economic times expansions and fall during bad economic times recessions. It is generally quite easy to develop a theory T that predicts P, especially for someone who has studied P carefully. In fact, many such theories can be constructed. Importantly, however, it is generally not good scientific practice to use the same data to both formulate and test a hypothesis or theory. If so, all theories would be confirmed.Instead, good methodology will develop a theory T that not only pred icts P, but that also has other predictions Q1, Q2, Q3, Ideally, many of these predictions will be observable that is, one should be able to determine if Q1, Q2, Q3 . do or do not in fact occur. If these predictions are not observed say not Q1 (Q1) is observed rather than Q1 the theory may be judged pitiful and either revised or discarded. If I may be allowed a lapse into imprecise language, a theory can never be right if there is not at least(prenominal) some adventure in the first place for it to be wrong. 11 This is not to say that rational choice theorists are pristine with respect to this requirement. The history of economic model is no doubt full of bad theories (bad in the sense that one or more key predictions are not consistent with the data) that have been saved by ad hoc modifications. It is to say that proponents of the rational choice approach contend that ad hoc theorizing and the resulting empty tautologies may be less prevalent with their approach than with o ther approaches.I certainly agree that the rational choice method does in fact tend to generate many testable predictions, and in Sections 4 and 5 below I discuss several illustrative examples. Despite the fact that advocates of rational choice theory justify their approach in this way, I know of no study that explicitly compares methodologies along these lines. Is it really the case that rational choice models have more non-tautological implications than the models implied by other approaches? I am not sure anyone has examined this issue carefully.I believe the rational choice methodology is gaining in popularity not just because it tends to generate lots of observable predictions, but also because it tends to generate novel predictions. This is an extension of the idea of novel confirmation. Novel confirmation embodies the sentiment expressed by Descartes (1644) that we know hypotheses are correct only when we see that we can explain in equipment casualty of them, not merely the effects we originally had in mind, but also all other phenomena which we did not previously think. Quoted by Musgrave (1974), p. 1) Campbell and Vinci (1983, p. 15) begin their discussion of novel confirmation as follows Philosophers of science generally agree that when observational equivalence supports a theory, the confirmation is much stronger when the establish is novel. The verification of an unusual prediction, for example, tends to provide much stronger confirmation than the comment of something already known of something the theory was designed to account for. This view is so familiar that Michael Gardner has recently described it as a lengthy tradition not to say a consensus in the philosophy of science. As seems to often be the case in the philosophy of science, the usefulness of novel confirmation is not as well established as the above commendation implies. Campbell and Vinci (1983) also note that the notion of novel confirmation is beset with a theoretical puzz le about how the degree of confirmation can change without any change in the evidence, hypothesis, or auxiliary assumptions. (p. 315) Kahn, Landsburg, and Stockman (1992) maintain that the question of novel confirmation can be addressed meaningfully only in the presence of an explicit model by which hypotheses are generated. (p. 04) They find that the idea of novel confirmation is valid if there are unobservable differences in the abilities of scientists or if there is some chance of erroneous belief in observation. 12 Campbell and Vinci (1993) distinguish between epistemic novelty and heuristic novelty. epistemic novelty occurs when a theory has an implication that would be considered highly marvelous in the absence of the theory. There is of course a question over the proper definition of highly improbable. Heuristic novelty occurs when the evidence predicted by a theory plays no heuristic role in the formation of the theory.Descartes would seem to be referring to heuristic no velty in the above quote. Rational choice theory is a useful methodology in part (perhaps in large part) because it tends to lead the researcher to novel implications, thereby making novel confirmation more likely than may be the case with other methodologies. Space and time considerations do not allow me to attempt a full-blown analysis of this conjecture, which in any case I am not really qualified to undertake because of my limited depiction to alternative social science methodologies not based on rational choice and my limited knowledge of the philosophy of science.In Sections 4 and 5 below I describe several examples of rational choice theory and some associated novel implications. I should note that the mathematical nature of rational choice theory would appear (to me) to be crucial here. Mathematics allows the theorist to make some sense out of complicated interactions between decision-making units that would otherwise be difficult or impossible to untangle. It is precisely those kinds of situations in which rational choice theories are most likely to have novel implications, because the implications are not immediately apparent even to scholars with knowledge, experience, and intuition.We now proceed to Section 4, which provides a detailed discussion of a rational choice model of church attendance. Section 5 gives shorter summaries of several other rational choice models, including models of suicide, auto prophylactic regulation, addiction, racial profiling, Congressional influence on military machine assignments, governmental revolutions, megafauna extinction, and the predictability of consumption spending. 4. A Detailed Example Church AttendanceAzzi and Ehrenberg (1975) develop a rational choice model of church attendance. This is a classic paper, which Iannaccone (1998, p. 1480) calls the first formal model for unearthly affair (within any discipline) and the foundation for nearly all subsequent economic models of religious behavior. Italics in original. Their analysis begins with the assumption that the utility of a domicile consisting of two members, a husband and a married woman, is given by (1)U = U(C1, s1, C2, s2, , Ct, st, Cn, sn, q), where Ci is the star signs consumption of market goods and services in period i (i = 1, n), and si denotes religious booking in period i. The model assumes for simplicity that both members of the household know how long they will live and that both will die at date n. This is a dynamic model, because the household cares about future as well as current consumption. The remaining variable in the household utility function, q, is the expected value of the households hereafter consumption. Azzi and Ehrenberg assume that church attendance follows from a salvation motive (the desire to increase afterlife consumption) and a social pressure motive (where church social status and participation increases the chances that an individual will be successful in business), rather than nece ssarily a pure consumption motive (people simply delight the time they spend at church). Consumption in period i (any year during which the husband and wife are alive) is given by (2)Ci = C(xt, h1t, h2t), here xt is denotes the consumption of goods and services purchases in markets, while h1t and h2t are the amounts of time accustomed by the husband and wife, respectively, to market-based consumption. The idea here is that satisfaction involves not only the purchase of a good (such as a television) but also time spent using the good. The social value of church attendance in period i, denoted by si, is determined as follows (3)si = s(r1i, r2i) where r1i and r2i denote the time spent on church-related activities by the husband and wife, respectively, in year i.People get more current satisfaction from going to church the more time they devote to church-related activities. After-life consumption q is determined as follows (3)q = q(r11, r12, r21, r22, , r1n, r2n), That is, the more t ime spent on church-related activities during all periods of life means the more the household members will enjoy their afterlife. Azzi and Ehrenberg (p. 33, fn. 7) note that Our households view of the afterlife is not one of an all-or-nothing proposition (heaven or hell), it is rather that there is a continuum of possible outcomes. The choices of the household are constrained by time and money. The two household members can allocate time in labor which generates income that can be used to purchase the goods and services denoted by xt in comparability (1) above, consumption-related activities reflected in h1t and h2t in equation (2) above, and church-related activities reflected in the r1i and r2i in equation (3) above. The constraint here is that each day has 24 hours. Hence the dyad can spend more time on church-related activities only if they spend less time earning income and/or consuming.The second constraint in the model says basically that, over the course of their lives, t he couple cannot spend more than their feature income. Over the course of their lives means that it is possible for them to borrow early in life as long as they repay the loan (with interest) later in life. It is also possible to lend early in life, which means that consumption can exceed income later. The amount of labor income the couple earns depends on the amount of time spent working by the husband and wife and the wage rate each is paid.The model also allows for non-labor income in each period, which might reflect investment returns. The distinction between labor and non-labor income turns out to be rather interesting and important with respect to church attendance. Azzi and Ehrenbergs analysis is complicated in some respects and simple in others. It is complicated because it considers consumption over several periods rather than just one, and it allows for consumption to depend on time (the h1t and h2t) as well as purchases of goods and services in the market (xt).The model is simple in that it does not consider the supply side. That is, the model simply assumes that the household can buy any amount that it likes of consumption goods (xt) and that there are no effective limits on religious participation (st). The power of the rational choice approach is that rational choice models tend to have lots of observable implications, some of which are novel. The Azzi and Ehrenberg model implies that (i) The frequency of church attendance increases with age (ii) Females attend church more a great deal than males (iii) Nonwhites attend church more frequently than whites (iv) People who believe in an afterlife attend church more frequently (v) Having a spouse of the same major religion increases participation (vi) As health deteriorates church attendance declines (vii) An increase in the number of pre-school age children present in the household reduces church attendance (viii) An increase in the number of school-age children present in the household i ncreases church attendance (ix) Females hours devoted to religious activities will rise more apace with age than will the hours devoted by males to religious activities (x) For males who show sharp earnings increases in their 20s, religious participation may first decline with age and then increase (xi) An increase in nonlabor income will increase religious participation and (xii) The effect of a proportionate shift in wages (say, a 10% increase in the present and all future periods) on church attendance is ambiguous. Many of these implications are not surprising, but (ix) would appear to be somewhat novel.Item (ii) means that 40 year old women will attend church more frequently than 40 year old men. Item (ix) means that the change (increase) in church participation associated with age from 40 to 50 will be greater among women than among men. Item (ii) follows today from the fact that females tend to have lower wages. Thus if one could find couples in which the wife earns more than the man, the model predicts for those couples that the wife will probably not be inclined to attend church more frequently. Also, allowing for an uncertain time of death may overturn (i) nce an individual is faced with a relatively high probability of death in a period it may become optimal for him to concentrate his religious participation as early as possible, since he may not survive to invest in future periods. (p. 38) 5. Several Brief Examples This section presents a brief overview of several applications of rational choice theory. Unlike the church attendance example above, in which the form of the utility function was written out explicitly, the discussions in this section for the most part present only brief descriptions of the relevant optimization problems and some of the resulting implications. A.Suicide Hamermesh and Soss (1974) develop a rational choice theory of suicide. They assume that the utility of an individual in any given period depends positively on con sumption and negatively on a technological relation describing the cost each period of maintaining oneself at some negligible level of subsistence. (p. 85) Consumption is a function of age and of permanent income, which is a measure of current and expected future income. Individuals are assumed to substitute exogenously (according to a probability distribution) in their distastes for suicide that is, some individuals are more averse to suicide than others.This framework implies that an individual kills himself when the total discounted lifetime utility remaining to him reaches zero. (p. 85). Thus in this model we have a rational individual who is forward looking, considering not only his present utility but what his future utility is likely to be. If total utility over the rest of his life is higher with suicide and life ending in the present than it is with the continuation of life, suicide is the rational option. Here are some of the major implications of the model. (i) The suicide rate should rise with age. (ii) The suicide rate should fall with increases in permanent income13 and decreases in the unemployment rate. (iii) The marginal absolute effect of permanent income on suicide declines as permanent income increases. The first two effects are by no means surprising, but the third effect is certainly by no means obvious ex ante (at least to me). (ii) means that suicide rates will fall as income rises. (iii) means that the effect of increases in income gets smaller the larger income is to begin with.A $10,000 raise is much more likely to prevent suicide if the somebody is earning $50,000 to begin with than if the soulfulness is earning $150,000. This is quite plausible, but the point is that it is not something most analysts would think about ex ante. B. Auto Safety Regulation. Peltzman (1975) considers the likely effects of legally mandated inductance of various safety devices14 on automobiles. 15 The devices in question for the most part were designed to reduce the damages caused by separatrixs rather than to reduce the likelihood that accidents occur. Peltzman notes that the auto safety literature estimates the impact of afety mandates by assuming that (i) the mandates have no effect on the probability that an accident will occur, and (ii) the mandates have no effect on the voluntary demand for safety devices. In effect, the regulations were implemented based on analysis that assumed the same number and nature of accidents would occur, but that automobiles would be better equipped to protect drivers and passengers from injury and death. He notes that technological studies imply that annual highway deaths would be 20 percent greater without legally mandated installation of various safety devices on automobiles. (p. 677) Peltzman considers the behavior of a typical driver and postulates quite reasonably that he or she is made worse off by barter accidents or, equivalently, that he or she benefits from safety. Peltzman also assumes, however, that the driver benefits from what he calls driving intensity, by which he means more speed, thrills, etc. (p. 681). new(prenominal) things equal, the driver can obtain more driving intensity only by driving less safely. Thus the driver faces a trade-off between two goods, intensity and safety, in which more of one can be obtained only by plentiful up some of the other.This kind of trade-off is in standard practice for rational choice theorists. In basic consumer choice theory the consumer with a given income can obtain more of one good only if he or she consumes less of some other good (or goods). The standard consumer choice problem also considers what happens when the consumers income rises. Rational choice theory predicts that, in the absence of very unusual circumstances, the consumer will buy more of most goods when income rises. Put another way, it is typically not the case that a consumer will allocate one hundred percent of an increase in income to increased consumption of a single good.Income increases tend to be spread around over several goods. Peltzman argues that the imposition of mandated safety devices in automobiles is rather like an increase in income in the sense that the devices make it possible for drivers to obtain both more safety and more intensity. Technological studies in effect assume that drivers will respond by consuming only more safety, but rational choice theory indicates that drivers can also respond by consuming more intensity (that is, by driving less safely). The extent to which drivers choose between more safety and more intensity is ultimately an empirical question.Suppose drivers choose to increase consumption of both safety and intensity which is what economists have come to expect in these kinds of situations. In this case, the rational choice model implies that the number of total driving accidents16 should rise because of increased driving intensity, while the come amount of damage per ac cident as reflected, say in the number of fatalities among passengers should decrease because of the safety improvements. This means that it is actually possible for total traffic fatalities to rise as a result of the safety mandatesThis would happen if the increase in the number of accidents is sufficiently large relative to the decrease in average damage per accident. Once again we have an example of a rational choice model yielding implications that are not obvious ex ante. The novel predictions here are that the imposition of auto safety mandates (i) should increase the occurrence of traffic accidents, and (ii) should decrease the relative frequency of accidents involving passenger fatalities, and (iii) may increase or decrease the total number of traffic fatalities.After extensive empirical examen based on several data sets, Peltzman concludes that regulation appears not to have reduced highway deaths. (p. 714). There is indeed some evidence that the number of deaths increa sed, but in most cases that evidence is not strong. In any case, there is no evidence that the regulations decreased traffic fatalities. Peltzman also finds that the safety mandates were followed by an increase in the number of accidents involving pedestrians and by an increase in the number of accidents involving only property damage with no injury to vehicle occupants.A related paper by McCormick and Tollison (1984) considers the effect on stopover rates of an increase in the number of constabulary officers. Rational choice theory indicates that the quality of law enforcement should not be judged by arrest rates alone. If the number of natural law officers increases and as a result the probability of arrest for any given crime increases, rational prospective criminals will see the expected cost of crime rise and therefore undertake less criminal acts.Total arrests reflect both the number of criminal acts (which should fall) and the percentage of criminal acts for which an arr est is made (which should rise). Total arrests rise only if the latter effect is stronger than the former. McCormick and Tollison test their theory using data from the Atlantic Coast congregation in mens college basketball. In 1978, the conference increased the number of officials from two to three. In this context, one may think of officials as police officers and fouls called as arrests.McCormick and Tollison find that this 50 percent increase in the number of officials caused a 34 percent reduction in the number of fouls called (p. 229). When my son Aaron (now almost 5 years old) was an infant, he attended the Baylor Child growth Center during the day. In the room where the teacher changed diapers, there was a rove on the counter but no restraint of any kind (such as a belt or guard rail). When I asked the director about this, she said that there was no restraint because she (the director) did not want to give the teacher a false sense of security.With a belt or rail, the tea cher might be tempted to walk away for just a minute to check on something in the room. Whether restraints increase or decrease changing table accidents is an empirical question, though Pelzmans analysis suggests the director made the right decision. C. Addiction Stigler and Becker (1977) propose a rational choice theory of addiction, a theory subsequently elaborated by Becker and tater (1988). In this theory, a person is dominancely addicted to some good c if an increase in his current consumption of c increases his future consumption of c. (Becker and Murphy, 1988, p. 81) The key feature of these models is that a consumers utility in any given period depends not just on consumption in that period, but also on consumption metropolis. Consumption capital is essentially the consumers ability to enjoy a particular good, which depends on past consumption of the good and perhaps on other factors. If past consumption enhances current delight ability, the improver is said to be skil ful. This might be the case, for example, with listening to classical music. The more one listens to classical music, the greater ones force to appreciate it.Stigler and Becker note that in force(p) consumption capital might also be positively influenced by education. super educated people might have a greater capacity to enjoy things like classical music, opera, and art. If past consumption reduces current frolic ability, the addition is said to be catastrophic. This is the case with substances such as heroin and other substances normally considered to be habit-forming. The more heroin a person consumes in the present, the less will be his or her future enjoyment (high) from any given amount of heroin consumption in the future. 17 The formal setup in Stigler and Becker (1977, p. 78) is relatively simple. First consider beneficial addiction to, say, classical music. Consumer utility (U) depends positively on two goods, M (music appreciation) and Z (other goods) U = U(M, Z). Music appreciation depends positively on the time allocated to music listening and on music consumption capital (Sm) M = M(tm, Sm). Music consumption capital at date j, Smj, depends positively on the time allocated to music consumption in the past, Mj-1, Mj-2, . and positively (perhaps) on the persons level of education at time j (denoted Ej) Smj = S(Mj-1, Mj-2, , Ej). The addition is beneficial if Smj depends on positively on the past values of M. Alternatively, for harmful addition we may replace M with H, where H denotes the consumption of a good such as heroin. In this case, consumption capital S depends negatively on past values of H. The elaborated model of Becker and Murphy (1988) views addictive behavior as a situation in which the consumption of a particular good begins to increase rapidly. 18 Their model has a number of implications. Perhaps he most interesting is their finding that the demand for addictive goods should be quite sensitive to permanent changes in price (w here the price of illegal goods includes the expected costs associated with apprehension by authorities, as well as any foregone earnings that may result from decorous addicted and, say, unable to work), but not necessarily to temporary price changes. A second implication is that strong addictions, if they are to end, must end suddenly (cold turkey). Rational persons end stronger addictions more rapidly than weaker ones. (p. 692). Other implications are that addicts often go on binges (p. 75), present-oriented individuals are potentially more addicted to harmful goods than future-oriented individuals (p. 682), and temporary events can permanently collar rational persons to addictive goods (p. 691). Stigler and Becker (1977) and Becker and Murphy (1988) do not perform empirical tests of their models of rational addiction. Tests have been performed by other authors, however. Because good consumption data are not available for illegal substances, tests have focused on tobacco and c affein. Tests based on tobacco consumption are reported by Becker, Grossman, and Murphy (1994), and Keeler, et. l. (1993). A test based on caffeine consumption is reported by Olekalns and Bardsley (1996). These tests are generally supportive of the rational addiction theory. Becker and Murphy (1988) note that with a simple extension their model can explain cycles of overeating and dieting. Their basic analysis assumes there is only one kind of consumption capital. Suppose that with respect to food there are instead two types of consumption capital, one of which is simply the persons weight (which might be called health capital) and the other of which is eating capital. That is, eating can be both harmful and beneficial in the senses defined above. As eating increases, health capital locomote (weight gain has detrimental effects on health) and eating capital rises (the capacity to enjoy food is greater the more one eats). Under countenance conditions, utility maximization results i n cycles of dieting and binging. 19 Rational addiction theory has been applied to the analysis of religious behavior see Iannaccone (1984, 1990) and Durkin and Greeley (1991). Iannaccone (1998) summarizes this approach. Utility depends on religious commodities produced, the value of which depends on religious human capital. The stock of religious human capital depends on time and money devoted to religious activities in the past. These models have the following predictions, nearly all of which receive strong empirical support (Iannaccone, 1998, p. 1481) Individuals tend to move toward the denominations and beliefs of their parents as they mature and wampum to make their own decisions about religion People are more likely to switch denominations early in life People tend to marry within religions if they do not, one spouse is likely to sweep up the religion of the other.D. Racial Profiling Law enforcement authorities in many jurisdictions have been criticized in recent years fo r racial bias in their choice of cars to search for illegal drugs and other contraband. 20 The fact that police are more inclined to stop and search cars driven by members of certain minority groups is well established. Knowles, Persico, and Todd (2001) develop a rational choice model that suggests an empirical test for distinguishing whether this disparity is due to racial prejudice or to the polices objective to maximize arrests. In their model, the typical police officer maximizes the total number of convictions minus a cost of seek cars. (p. 209) Motorists consider the probability of being searched in deciding whether to carry contraband. (p. 209) At least some motorists perceive a benefit to carrying contraband. If they do carry, their expected benefit is positive if they are not searched and negative (that is, there is a positive expected cost) if they are searched. The model implies that if police officers are not racially biased, the frequency of guilt among motorists con ditional on being searched will be independent of race. 21 In their empirical analysis based on 1,590 searches on a stretch of Interstate 95 in doctor between January 1995 and January 1999, Knowles, Persico, and Todd find support for this proposition. They interpret this result as the absence of racial prejudice against African Americans (p. 212). The fact remains, however, that African Americans are searched more frequently than whites. If this does not arise from racial bias by police officers, then why does it occur?One possibility noted by the authors is that race may proxy for other variables that are unobservable by the policy officer and are correlated with both race and crime. manageable examples of such unobservables are the schooling level or the earnings potential of the motorist. (p. 212) While one may quibble with some elements of this study, for our present purposes the main point is that the rational choice theory, at least potentially, yielded implications that al lowed the analyst to gain some insight (if not a final resolution) into the issue of racial profiling. E. Congressional Influence on Military AssignmentsPrior to the 1960s, economic theory tended to view politicians and other government officials (bureaucrats) as disinterested observers and regulators of economic activity. A group of economics led by Nobel Laureate James Buchanan then developed a branch of economics known as public choice theory, which views government officials as self-interested maximizers. Goff and Tollison (1987) take a public choice approach to gain some understanding of casualties in the Vietnam War. The typical soldier is assumed to prefer not to be placed in risky chip situations, and this preference is shared by the soldiers family.A solider (or more likely his family) might therefore try to gain a low-risk assignment by asking for intervention in military decisions by his Senator or Representative. Senators and Representatives are assumed to desire re-ele ction, which implies a desire to please their constituencies. The ability of a Senator or Representative to have this kind of influence, however, varies according to committee assignments, ties to the military/industrial complex, etc. Goff and Tollison assume that political influence depends on seniority, with more seniority implying more influence.Taken together, all these assumptions have the straightforward implication that soldiers from states with more senior (and hence more influential) Senators and Representatives should, other things equal, have experienced few casualties in Vietnam than soldiers from states with less senior (and therefore less influential) Senators and Representatives. Their empirical analysis (using data from January 1961 to September 1972) supports the hypothesis In the House, the Mississippi delegation had an average seniority of 27. 7, while Hawaii had an average seniority of 61. . A seniority rank of 1 indicates the member had the highest seniority in his or her party. In terms of lives, this represents about 6 fewer war deaths for every 100,000 of population in Mississippi relative to Hawaii. Ceteris paribus, this difference in House seniority leads to a 55 percent higher casualty rate for Hawaii than Mississippi. In the Senate, Arkansas had an average seniority of 6. 2, and Maryland had an average seniority of 45. 4. Other things equal , this difference leads to an 86 percent higher casualty rate for Maryland than for Arkansas.In terms of lives, this translates into about 7 more war deaths for every 100,000 of population in Maryland than in Arkansas. (pp. 319-20) In this case, the value of the rational choice approach is not so much in the fact that it yields surprising answers to a well-established question, but that it suggests a unique question to ask in the first place. It is by no means obvious that someone not thinking about self-interested Senators and Representatives would even think to ask the question addressed by Goff and Tollison. F. Ideology and IntransigenceRoemer (1985) applies game theory to the analysis of political revolutions. Specifically, he presents a two-player game between Lenin and the Tsar. Lenins objective is to maximize the probability of revolution, while the Tsars objective is to minimize that probability. As in any game-theoretic setting, when making decisions each player keeps in mind how the other player might react. Lenin tries to create revolution by lining up coalescences, where people are induced to join a coalition with the promise of income redistribution.The Tsar tries to prevent revolution by promising to penalise anyone who participates in radical activities (assuming the revolution attempt is unsuccessful). Increased penalties reduce the number of individuals who are likely to join the coalition but increase the revolutionary fervor of those who do. An individual will join a coalition attempting to corrupt the Tsar if the expected benefit to him or her of doing so exceeds the expected cost. There is of course some uncertainty about the outcome. Roemers results include the following it is shown that various tyrannical aspects of the Tsars schema, and progressive aspects of Lenins strategy need not flow from ideological precommitments, but are simply good optimizi