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

Rational Choice Theory: An Overview by Steven L. Green Professor of Economics and Statistics Chair, Department of Economics Baylor University Prepared for the Baylor University Faculty Development Seminar on Rational Choice Theory May 2002  © 2002, Steven L. Green It has been said that democracy is the worst form of government except all the others that have been tried. -Winston ChurchillIt seems easy to accept that rationality involves many features that cannot be summarized in terms of some straightforward formula, such as binary consistency. But this recognition does not immediately lead to alternative characterizations that might be regarded as satisfactory, even though the inadequacies of the traditional assumptions of rational behaviour standardly used in economic theory have become hard to deny. It will not be an easy task to find replacements for the standard assumptions of rational behaviour †¦ hat can be found in the traditional economic literature, both because the identified deficiencies have been seen as calling for rather divergent remedies, and also because there is little hope of finding an alternative assumption structure that will be as simple and usable as the traditional assumptions of self-interest maximization, or of consistency of choice. – Amartya Sen (1990, p. 206) 1. Introduction Rational Choice Theory is an approach used by social scientists to understand human behavior.The approach has long been the dominant paradigm in economics, but in recent decades it has become more widely used in other disciplines such as Sociology, Political Science, and Anthropology. This spread of the rational choice approach 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 main purpose of this paper is to provide an overview of rational choice theory for the non-specialist.I first outline the basic assumptions of the ra tional choice approach, then I provide several examples of its use. I have chosen my examples to illustrate how widely the rational choice method has been applied. In the paper I also discuss some ideas as to why the rational choice approach has become more prevalent in many disciplines in recent years. One idea is that the rational choice approach tends to provide opportunities for the novel confirmation of theories. I argue that these opportunities are the result primarily of the mathematical nature of the approach.I then consider several issues raised by rational choice theory. First, I compare the limited meaning of â€Å"rationality† in rational choice theory with the more general definitions of the term use by philosophers. Second, I describe some of the main criticisms that have been levied against the rational choice approach. Third, I consider the limitations of rational choice models as guides to public policy. Fourth, I review some Christian perspectives on the rat ional choice appraoch.I end the paper by outlining three sets of questions I would like us to discuss in the faculty development seminar. Before I proceed, an apology and a caveat are in order. I apologize for the length of this paper. The British publisher Lord Beaverbrook once apologized to a friend for sending a five- page letter, saying he did not have time to write a one-page letter. I have the same sentiment here. The caveat is that my discussion of the rational choice theory in this paper is necessarily simplistic, so the reader should not take it as definitive.If some element of the theory seems suspect in some way, there will nearly always be an advanced version of the theory published somewhere that is more subtle and nuanced. Most statements in this paper are subject to qualification along many lines, so the reader should view what I present here keeping in mind the goal of the paper, which is only to give the reader some sense of the overall flavor of the rational choice approach. 2. Basic Assumptions about Choice DeterminationRational Choice Theory generally begins with consideration of the choice behavior of one or more individual decision-making units – which in basic economics are most often consumers and/or firms. The rational choice theorist often presumes that the individual decision-making unit in question is â€Å"typical† or â€Å"representative† of some larger group such as buyers or sellers in a particular market. Once individual behavior is established, the analysis generally moves on to examine how individual choices interact to produce outcomes.A rational choice analysis of the market for fresh tomatoes, for example, would generally involve a description of (i) the desired purchases of tomatoes by buyers, (ii) the desired production and sales of tomatoes by sellers, and (iii) how these desired purchases and desired sales interact to determine the price and quantity sold of tomatoes in the market. The typical toma to buyer is faced with the problem of how much of his income (or more narrowly, his food budget) to spend on tomatoes as opposed to some other good or service.The typical tomato seller is faced with the problem of how many tomatoes to produce and what price to charge for them. Exactly how does the buyer choose how much of his income to spend on tomatoes? Exactly how does the seller choose how many tomatoes to produce and what price to charge? One could imagine a number of answers to these questions. They might choose based on custom or habit, with current decisions simply a continuation of what has been done (for whatever reason) in the past. The decisions might be made randomly.In contrast, the rational choice approach to this problem is based on the fundamental premise that the choices made by buyers and sellers are the choices that best help them achieve their objectives, given all relevant factors that are beyond their control. The basic idea behind rational choice theory is tha t people do their best under prevailing circumstances. What is meant, exactly, by â€Å"best achieve their objectives† and â€Å"do their best? † The discussion in this section will emphasize the choices of consumers. 1] The rational choice theory of consumer behavior is based on the following axioms regarding consumer preferences:[2] 1) The consumer faces a known 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 indifferent between A and B. This is the axiom of completeness. 3) These preferences are 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 will choose the most preferred alternative. [3] If the consumer is indifferent between two or more alternatives that are preferred to all others, he or sh e will choose one of those alternatives — with the specific choice from among them remaining indeterminate. When economists speak of â€Å"rational† behavior, they usually mean only behavior that is in accord with the above axioms. I consider the definition of â€Å"rationality† in more detail near the end of the paper below. Rational choice theories usually represent preferences with a utility function.This is a mathematical function that assigns a numerical value to each possible alternative facing the decision maker. As a simple example, suppose a consumer purchases two goods. Let x denote the number of units of good 1 consumed and y denote the number of units of good 2 consumed. The consumer’s utility function is given by U = U(x,y), where the function U( ·, ·) assigns a number (â€Å"utility†) 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] Th e analysis is by no means restricted to two goods, though in many cases the analyst finds it convenient to assume that x is the good of interest is and y is a â€Å"composite good† representing consumption of everything but good x. The function U( ·, ·) is normally assumed to have certain properties. First, it is generally assumed that more is preferred to less – so that U rises with increases in x and with increases in y. Another way of saying this is to say that marginal utility is positive – where the term â€Å"marginal utility† is the change in utility associated with a small increase in the quantity of a good consumed.The second property of U( ·, ·) is that of diminishing marginal utility, which means that the (positive) marginal utility of each good gets smaller and smaller the more of the good that is being consumed in the first place. One’s first Dr. Pepper after a workout yields quite a lot of satisfaction. By the fifth or sixth, the additional satisfaction, while still positive, is much smaller. An important result in consumer theory is that a preference relationship can be represented by a utility function only if the relationship satisfies completeness and transitivity.The converse (that any complete and transitive preference relation may 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 may not be possible to represent the preference relation with a utility function. Rational choice analysis generally begins with the premise that some agent, or group of agents, is [are] maximizing utility – that is, choosing the preferred alternative. This is only part of the story, however.Another important element of the choice process is the presence of constraints. The presence of constraints makes choice necessary, and one virtue of rational c hoice theory is that it makes the trade-offs between alternative choices very explicit. A typical constraint in a simple one-period consumer choice problem is the budget constraint, which says that the consumer cannot spend more than her income. Multi-period models allow for borrowing, but in that case the constraint is that the consumer must be able to repay the loan in the future.The use of utility functions means the idea of agents making the preferred choices from among available alternatives is translated into a mathematical exercise in constrained optimization. That is, an agent is assumed 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 well developed in mathematics. The solution to the constrained optimization problem generally leads to a decision rule.The decision rule shows how uti lity-maximizing choices vary with changes in circumstances such as changes in income or in the prices of goods. A third element of rational choice analysis involves assumptions about the environment in which choices are made. Simple economic models are often restricted to choices made in markets, with emphasis on how much of each good or service consumers want 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 consistent with one another.A situation with consistent choices in which each agent is optimizing subject to constraints is called equilibrium. 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 price is equal to the quantity that firms want to produce and sell at that price. In this as in other simple market models, price pl ays a key role in the establishment of equilibrium. If consumers want to purchase more than firms are producing, the price will be bid upward, which will induce more production by firms and reduce 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 of strong 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 model are adequate representations of what actually happens in the real world.This means, in the above example, that a rational choice theorist would explain 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 model. Extensions The basic rational choice theory des cribed above has been extended 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 only for choice at a given time – that is, the model is static.In contrast, a dynamic (or intertemporal) model allows the agent to plan 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 only 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 case, it may well be â€Å"rational† to sacrifice (e. g. , consume less or work more) today in order to obtain some better outcome tomorrow. The dynamic formulation is an essential element of theories of saving and investment.One issue that arises in dynamic models is that of discounting. In most dynamic models, the agents under consideration are assumed to prefer (other things equal) a given level of consumption in the present to a given level of consumption in the future. Consider a model with two periods, 1 and 2. Let U1 denote the agent’s 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 formulate a plan for periods 1 and 2 to maximize the sum V = U1 + ?  ·U2, where 0 < ? < 1 is the â€Å"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 â€Å"positive rate of time preference† or simply â€Å"time preference. † A justification for time preference is given by Olson and Bailey (1981). Elster (1984, pp. 66ff) summarizes the opposing view that â€Å"†¦ for an individual the very fact of having time preferences, over and above what is justif ied by the fact that we are mortal, is irrational and perhaps immoral as well. † In any 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 extension of the basic model involves explicit treatment of uncertainty. 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 criminal act. The rational choice model is extended to allow for uncertainty by assuming the agent maximizes expected utility. Uncertainty is characterized by a probability distribution that assigns a likelihood (probability) to each possible outcome.Suppose 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 occur pB denote the probability of outcome B. With these as the only 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 agent’s utility with outcome A and U(B) be the agent’s 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 = pA ·U(A) + pB ·U(B). In general, the choices of the agent can affect pA and pB as well as U(A) and U(B). A related (and third) area in which the rational choice model is extended involves incomplete information. 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 information.A university generally does not have full information about the future rese arch productivity of a new assistant professor, for example, and a used car buyer cannot be certain that he is not driving a â€Å"lemon† off the lot. The fourth area in which the basic rational choice model is extended involves strategic 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 effect 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 kind of interaction involves the crude-oil production decisions of the Organization of Petroleum Exporting Countries (OPEC). Acting collectively, OPEC members have an incentive to restrict production to keep the world price of crude-oil high. Thus each OPEC country is given a production quota – a limit on the amount it can produce. Each country acting individually, however, has an incentive to â€Å"cheat† on its quota and thereby be able to sell more crude-oil at the high price. This will only be successful if the other countries maintain their 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 Description of the Rational Choice Method Like most scholarship, rational choice analysis usually begins with a question. What determines church attendance? Are suicide rates affected by the state of the economy? Do seat belt laws make highways safer? Under what circumstances are â€Å"cold turkey† methods necessary to end addictions?Why are drivers of certain minority groups more likely to be pulled over by police? Which soldiers are most likely to suffer casualties in a war? Why can’t Yasser Arafat and Ariel Sharon just get along? Why did large mammals become extinct in the Pelistocene era? When are workers most likely to â€Å"shirk† their job responsibilities? Does a reported decline in â€Å"consumer confidence† portend a slowdown in the economy? Varian (1997, p. 4) describes the model-building process as follows: †¦ all economic models are pretty much the same. There are some economic agents. They make choices in order to advance their objectives.The choices have to satisfy various constraints so there’s 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 aren’t mutually consistent? I will provide a slightly more detailed description here. Rational choice analysis may be characterized as working through the following steps: 1) Identify the relevant agents and make assumptions about their objectives. 2) Identify the constraints faced by each agent. ) Determine the â⠂¬Å"decision rules† of each agent, which characterize how an agent’s choices respond to changes of one kind or another – 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 anal ysis of data and can involve sophisticated techniques (to control sample selection bias, for example). 7) Draw conclusions and any implications (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 Specification 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 â€Å"says rational people consider only costs and benefits that accrue directly to themselves. † The presen t-aim standard of rationality â€Å"says rational people act efficiently in pursuit of whatever objectives they hold at the moment of choice. † Frank contends 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 probably 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): Suppose, for example, that we see someone drink a gallon of used crankcase oil and keel over dead. The present-aim approach can â€Å"explain† this behavior by saying that the person 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 th at utility depends only on the consumption of material goods and services 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 successful 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 â€Å"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 observable predictions. In particular, models in w hich 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 should include concerns for others. Bergstrom (1999) explores some possible solutions to the â€Å"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 attempt 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 brief discussion here. Suppose a theory T has prediction P, when in fact available 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 rather than P. My impression is that most economists would much rather change assumptions about constraints rather than change assumptions about preferences. 9] This viewpoint reflects a desire to avoid meaningless tautologies such as â€Å"he consumed more tomatoes because his preferences changed in such a way that he wanted to consume more tomatoes. † One can explain any choice in this way. Hausman (1984) summarizes the thinking of Lakatos (1970) as follows: A modification 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 testable implications at all. Lakatos regards such modifications as completely empty and unscientific.Modifications that are not ad hoc in this sense are â€Å"theoretically progressive. † It may be, however, that the testable implications of the theoretically progressive mod ifications are not confirmed by experiments or observations. In that case modifications are theoretically progressive but not empirically 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 one’s 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 claim 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 thir d sense. One needs to recognize the role of something like a Kuhnian â€Å"paradigm. † Modifications of theories must be made in the â€Å"right† way. (p. 23) I believe that most rational choice theorists would adhere to these criteria for effective theory modification. As Stigler and Becker (1977) note: What we assert is not that we are clever 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 appearance 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 generate 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 ca refully. 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 predicts 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 inadequate 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 some possibility 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 thought is no doubt full of bad theories (â€Å"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 other 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 t o 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 â€Å"only when we see that we can explain in terms 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 evidence is ‘novel’. The verification of an unusual prediction, for example, tends to provide much stronger confirmation than the explanation of something already known of something the theory was designed to account for. This view is so familiar that Michael Gardner has r ecently 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 quote implies. Campbell and Vinci (1983) also note that â€Å"†¦ the notion of novel confirmation is beset with a theoretical puzzle 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 â€Å"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 error 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 improbable in the absence of the theory. There is of course a question over the proper definition of â€Å"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 novelty 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 exposure to alternative social science methodologies not based on rational choice and my limited knowledge of the philosophy of s cience.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 safety regulation, addiction, racial profiling, Congressional influence on military assignments, political 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 â€Å"†¦ the first formal model for religious participation (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 household consisting of two members, a husband and a wife, is given by: (1)U = U(C1, s1, C2, s2, †¦ , Ct, st, †¦ Cn, sn, q), where Ci is the household’s consumption of market goods and services in period i (i = 1, †¦ n), and si denotes religious participation in period i. The model assumes â€Å"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 t he household cares about future as well as current consumption. The remaining variable in the household utility function, q, is the â€Å"expected value of the household’s afterlife consumption. Azzi and Ehrenberg assume that church attendance follows from a â€Å"salvation motive† (the desire to increase afterlife consumption) and a â€Å"social pressure motive† (where church membership and participation increases the chances that an individual will be successful in business), rather than necessarily a pure â€Å"consumption motive† (people simply enjoy 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 devoted by the husband and wife, respectively, to market-based consumption. The idea here is that satisfaction involves not only the purc hase 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 time 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 â€Å"Our household’s 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 equation (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 couple 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, the couple cannot spend more than their combined income. â€Å"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 t he wage rate each is paid.The model also allows for â€Å"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 Ehrenberg’s 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 â€Å"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 â€Å"supply side. † That is, the model simply assumes that the household can â€Å"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 frequently 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 increases church attendance; (ix) Females’ hours devoted to religious activities will rise more rapidly 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 aging from 40 to 50 will be greater among women than among men. Item (ii) follows directly 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): â€Å"†¦ nce an individual is faced with a relatively high probabilit y 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 â€Å"consumption† and negatively on â€Å"a technological relation describing the cost each period of maintaining [oneself] at some minimum level of subsistence. † (p. 85) â€Å"Consumption† is a function of age a nd of â€Å"permanent income,† which is a measure of current and expected future income. Individuals are assumed to vary 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 â€Å"†¦ 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 â€Å"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 income[13] and decreases in the unemp loyment 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 person is earning $50,000 to begin with than if the person 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 â€Å"legally mandated installation of various safety devices[14] on automobiles. †[15] The devices in question for the most part were designed to reduce the damages caused by accidents rather than to reduce the likelihood that accidents occur. Peltzm an 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 â€Å"[t]echnological 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 traffic accidents – or, equivalently, that he or she benefits from safety. Peltzman also assumes, however, that the driver benefits from what he calls â€Å"driving intensity,† by which he means â€Å"more speed, thrills, etc. † (p. 681). Other 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 giving up some of the other.This kind of trade-off is in standard fare 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 consumer’s 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 â€Å"spread aro und† 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 accidents[16] should rise because of increased driving intensity, while the average amount of damage per accident – 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 mandates!This 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 testing based on several data sets, Peltzman concludes that â€Å"regulation appears not to have reduced highway deaths. † (p. 714). There is indeed some evidence that the number of deaths increased, but in most cases that ev idence 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 arrest rates of an increase in the number of police officers. Rational choice theory indicates that the quality of law enforcement should not be judged by arrest rates alone. If the number of police 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 fewer criminal acts.Total arrests reflect both the number of criminal acts (which should fall) and the percentage of criminal acts for which an arrest 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 Conference in men’s 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 Development Center during the day. In the room where the teacher changed diapers, there was a pad 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 teacher might be tempted to walk away for â €Å"just a minute† to check on something in the room. Whether restraints increase or decrease changing table accidents is an empirical question, though Pelzman’s 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 Murphy (1988). In this theory, â€Å"a person is potentially 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 consumer’s utility in any given period depends not just on consumption in that period, but also on â€Å"consumption capital†. Consumption capital is essentially the consumer’s ability to enjoy a particular good, which depends on past consumption of the good and perhaps on other factors. If past consumption enhances current enjoyment ability, the addition is s aid to be beneficial. This might be the case, for example, with listening to classical music. The more one listens to classical music, the greater one’s capacity to appreciate it.Stigler and Becker note that beneficial consumption capital might also be positively influenced by education. Highly educated people might have a greater capacity to enjoy things like classical music, opera, and art. If past consumption reduces current enjoyment ability, the addition is said to be harmful. This is the case with substances such as heroin and other substances normally considered to be addictive. The more heroin a person consumes in the present, the less will be his or her future enjoyment (â€Å"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 appreciat ion) and Z (other goods): U = U(M, Z). Music appreciation depends positively on the time allocated to music listening â„ ¢ 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 person’s 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 ad dictive goods should be quite sensitive to permanent changes in price (where the â€Å"price† of illegal goods includes the expected costs associated with apprehension by authorities, as well as any foregone earnings that may result from becoming 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 (â€Å"cold turkey†). â€Å"Rational persons end stronger addictions more rapidly than weaker ones. † (p. 692). Other implications are that â€Å"addicts often go on binges† (p. 75), â€Å"present-oriented individuals are potentially more addicted to harmful goods than future-oriented individuals† (p. 682), and â€Å"temporary events can permanently ‘hook’ 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 addic tion. Tests have been performed by other authors, however. Because good consumption data are not available for illegal substances, tests have focused on tobacco and caffeine. 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 person’s weight (which might be called â€Å"health capital†) and the other of which is â€Å"eating capital. That is, eating can be both harmful and beneficial in the senses defined above. As eating increases, health capital falls ( weight gain has detrimental effects on health) and eating capital rises (the capacity to enjoy food is greater the more one eats). Under appropriate conditions, utility maximization results in 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 â€Å"religious commodities† produced, the value of which depends on â€Å"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, â€Å"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 start to make their own decisions about religion; †¢ People are more likely to switch de nominations early in life; †¢ People tend to marry within religions; if they do not, one spouse is likely to adopt the religion of the other.D. Racial Profiling Law enforcement authorities in many jurisdictions have been criticized in recent years for 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 â€Å"suggests an empirical test for distinguishing whether this disparity is due to racial prejudice or to the police’s objective to maximize arrests. In their model, the typical police officer â€Å"maximizes the total number of convictions minus a cost of searching cars. † (p. 209) Motorists â€Å"consider the probability of being searched in deciding whether to carry contraband. † (p. 209) At least some motorists percei ve 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 conditional 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 Maryland between January 1995 and January 1999, Knowles, Persico, and Todd find support for this proposition. They interpret this result as â€Å"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 â€Å"race may proxy for other variables that are unobservable by the policy officer and are correlated w ith both race and crime. Possible 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 allowed 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 p refer not to be placed in risky combat situations, and this preference is shared by the soldier’s 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-election, 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 fewer 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 ranking 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 â€Å"Lenin† and the â€Å"Tsar. † Lenin’s objective is to maximize the probability of revolution, while the Tsar’s 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 coalitions, where people are induced to join a coalition with the promise of income redistribution.The Tsar tri es to prevent revolution by promising to punish anyone who participates in revolutionary 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 overthrow 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. Roemer’s results include the following: it is shown that various â€Å"tyrannical† aspects of the Tsar’s strategy, and â€Å"progressive† aspects of Lenin’s strategy need not flow from ideological precommitments, but are simply good optimizi