– I am not the Messiah, would you please listen, I am not the Messiah, do you understand? Honestly!
– Only the true Messiah denies his divinity.
– What? Well, what sort of chance does that give me? All right! I am the Messiah!
– He is! He is the Messiah!
(Monty Python's Life of Brian)1. INTRODUCTION
One side effect of the growing popularity and influence of behavioural economics has been the profusion of discussions of the methodology and rhetoric of economic theory (see Caplin and Schotter Reference Caplin and Schotter2008, for a representative collection of essays, as well as Rabin Reference Rabin2002; Rubinstein Reference Rubinstein2006; Bernheim Reference Bernheim2009; Dekel and Lipman Reference Dekel and Lipman2009; Binmore and Shaked Reference Binmore and Shaked2010). This paper aims to add a dimension to this debate.
To motivate the discussion, think of the following familiar situation. You are sitting in the audience of an economic theory seminar. The speaker is presenting a model of a certain economic phenomenon, in which some of the economic agents are boundedly rational in some way. As the speaker is going through her model, you are beginning to sense that although this may be an interesting exercise, the model could be entirely recast in terms of a standard model with rational agents, possibly with an added conventional source of friction such as imperfect information or search costs. You are about to raise your hand . . .
This paper is about what happens next – or, to be more precise, about what should happen next. How should we conduct our debates about explanations of economic behaviour that are based on non-standard behavioural assumptions? How should we evaluate these explanations in comparison with more conventional explanations based on rational choice? In particular, should we devalue a bounded-rationality model (BRM henceforth) when the economic phenomenon it addresses seems to be explicable by a rational-choice model?
As the above not-so-imaginary scenario suggests, these questions are not motivated by abstract philosophizing, but on my own direct experience both as a member of seminar audiences and as a theorist who has been preoccupied with economic models in which at least some agents are boundedly rational. From this experience (as well as others' – see Rabin Reference Rabin2002), a major share of the comments contributed by referees and seminar audiences in response to a BRM can be read as attempts to ‘rationalize’ the model. As an inventor of BRMs, I often feel an internal need to compare such models with more conventional ones based on rational choice. And when I do not feel this need myself, I can always count on seminar audiences, referees and coffee-machine conversation partners to fill the gap.
The audience's basic criticism can be summarized as follows:
Although BRMs may shed some light on economic phenomena, in many cases one could think of a rational-choice model that could account for these phenomena. And if we can ‘get the same thing’ with a standard model, why should we depart from the rational-choice paradigm? Moreover, since rational-choice models and BRMs tend to have dramatically different welfare implications, a switch from rational-choice models to BRMs is not only problematic methodologically, but also carries a significant cost in terms of its implied policy prescriptions.
This paper is an attempt to come to terms with this ‘can't we get the same thing with a standard model’ critique. The methodological problem at hand involves theory selection under observational equivalence: how should we choose from a number of competing models that provide different explanations for a given phenomenon? The need to choose is only magnified by the models' diverging welfare implications. The normatively scientific way of making this choice is to tease out cases in which the models generate different predictions, and subject these predictions to an empirical test. However, economics being the dismal science that it is, such empirical tests are difficult and rare. Indeed, the whole point of the ‘can't we get the same thing’ critique is that since the two types of explanations are empirically hard to distinguish, the conventional rational-choice explanation should be given priority.
Therefore, for the purpose of our discussion here, I will set aside the question of empirical tests and take it for granted that the account a BRM in question provides for a given collection of economic phenomena is sound: the ‘story’ it tells ‘rings true’; its behavioural assumptions seem to fit generally known psychological principles as well as the market situation in question; and its predictions are broadly consistent with known (stylized) facts. What the ‘can't we get the same thing with a standard model’ critique maintains is that for the purpose of making these predictions, one does not have to abandon conventional behavioural assumptions, and therefore one ought not to; even if there is some truth in the bounded-rationality story, the same truth could be captured equally well by a rational-choice model. I refer to such a rational-choice model that is offered in refutation of a BRM as a ‘rationalization’, or as a ‘rationalizing model’. My objective in this paper is to demonstrate several difficulties with this type of refutation-by-rationalization critique.
I should emphasize that I do not ask how to select between competing explanations conditional on accepting the validity of the ‘can't we get the same thing with a standard model’ critique of BRM; my focus is on questioning that very validity. In particular, my discomfort with this particular critique does not imply a rejection of other criticisms of BRMs: their scope tends to be limited in comparison with the impressive generality of the basic rational-choice models; they are perceived as arbitrary and post-hoc relative to their rational-choice counterparts; and they tend to violate the principle of revealed preferences. These concerns are often justified but have been debated elsewhere.Footnote 1 In contrast, the ‘can't we get the same thing’ observational-equivalence critique has not been subjected to careful methodological scrutiny.
My discussion so far may have given the impression that every BRM faces a single, well-defined rationalization. This is obviously not the case. The rational-choice paradigm is famously flexible, and there is a variety of conventional models that can be offered in refutation of any given BRM. Rationalizing models tend to come in one of the following three forms:
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Rationalization via modified information. The rationalizing model modifies the BRM by replacing the boundedly rational agents with conventionally rational agents who happen to have different information.
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Rationalization via modified preferences. The rationalizing model modifies the BRM by replacing the boundedly rational agents with conventionally rational agents who happen to have different preferences.
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Rationalization via endogenization. The rationalizing model refuses to take the behavioural rule assumed by the BRM as truly exogenous, and instead derives it as a rational equilibrium response in a larger model that introduces frictions which are not explicitly included in the original model.
I could illustrate the difficulties of these forms of rationalization with any number of BRMs from the literature. For expositional effectiveness, however, I adopt a case study approach and restrict attention to a single model, due to Spiegler (Reference Spiegler2006a), of price competition in markets for credence goods when profit-maximizing firms face consumers who use naive anecdotal reasoning to evaluate stochastic variables. This model was proposed to highlight aspects of industries such as alternative medicine, consulting and mutual funds. There are two reasons for this expositional strategy, beyond my obvious familiarity with the model. First, a case study approach is useful because fine details turn out to matter. Second, the model in question is extremely simple to begin with. This facilitates the formulation of explicit rationalizing models and enables an intelligible comparison with the original model. Were the BRM itself more complex to begin with, detailed comparison with its rationalizations would quickly become intractable. The sparseness of the original model makes it a particularly easy target for the ‘can't we get the same thing with a standard model’ critique, because it is easy to think of conventional frictions that are excluded from the original model. Nevertheless, I show that even in this ideal case, the ‘can't we get the same thing with a standard model’ criticism is plagued with several difficulties, which can be summarized as follows:
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• The rationalizing model changes not only assumptions regarding individual behaviour, but also assumptions regarding the external environment that individuals face.
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• The rationalizing model introduces new parameters into the model. Replication of the original BRM's predictions hinges on proper selection of parameter values.
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• The rationalizing model may give rise to multiple equilibria, whereas the original BRM has a unique equilibrium. Replication of the BRM's predictions hinges on proper selection of equilibrium.
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• Changed assumptions about individual behaviour mandated by the rationalizing model may be implausible in the context of applications of the original BRM.
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• Natural extensions of the original BRM can be meaningless under the rationalizing model.
These are essentially problems of how to assign burden of proof in a debate: which desiderata should the rationalizing model satisfy in order to count as a successful refutation of the BRM? For instance, when the rationalization introduces new unobservable parameters and replicates the original BRM's predictions under a suitable selection of parameter values, does this diminish its power as a ‘devastating criticism’ of the BRM? In the concluding section, I offer my own opinion about how we should regard ‘rational explanations’ that are offered as a criticism of BRMs. But my main objective in this paper is simply to expose the burden-of-proof problems themselves, because I believe that heightened awareness of these problems could improve the quality of our debates over BRMs.
I wish to make two clarifying comments that emphasize the limited scope of this paper. First, we need to distinguish the programme of rationalizing models of economic behaviour that depart from the rational-choice paradigm from the time-honoured tradition of rationalizing observed economic behaviour. This paper is entirely about the former. Second, the methodological questions explored here are not unique to selection between rational-choice and bounded-rationality economic models. They could be raised in the contexts of other problems of theory selection in economics and other sciences, e.g. debates between ‘New Keynesian’ and ‘New Classical’ macroeconomists. Because I am not a professional philosopher myself, I prefer to stick to the concrete debate I am familiar with as a practicing economic theorist, in the hope that professional philosophers of economics might be able to draw more general lessons.
The remainder of the paper is structured as follows. Section 2 presents the simplest version of the model due to Spiegler (Reference Spiegler2006a). Sections 3–5 subject this model to the three forms of the ‘can't we get the same thing with a standard model’ critique. I discuss my lessons from these rationalization exercises in Section 6.
2. A MARKET MODEL WITH BOUNDEDLY RATIONAL CONSUMERS
Imagine a market that consists of a continuum of consumers and n identical firms. Consumers enter the market with some problem. The value of fixing it is 1. Each firm i sells at zero cost a product that fixes the problem with probability α ∈ (0,1), independently across firms. Consumers also have an outside option (‘doing nothing’), labelled i = 0, which fixes their problem with the same probability α. Firms are standard profit maximizers. They compete by choosing prices simultaneously. Let p i ∈ [0,1] denote the price chosen by firm i. Assume that p 0 = 0 – that is, ‘doing nothing’ costs nothing to consumers.
I will refer to the firms as ‘quacks’, as they display no skills relative to ‘doing nothing’. There are several real-life situations that seem to fit this specification. Actively managed mutual funds are a case in point. According to the Efficient Market Hypothesis, prices in financial markets fully reveal private information. Consequently, an actively managed mutual fund cannot generate (risk-adjusted) returns in excess of the market portfolio. Thus, under the Efficient Market Hypothesis, the market for actively managed mutual funds is a ‘market for quacks’. And of course, as the term ‘quacks’ indicates, practitioners of non-scientific medicine often fall into this category.
If consumers chose rationally with respect to a correct understanding of the above market model, the market for quacks would be inactive, as all consumers would choose the outside option.Footnote 2 I refer to this outcome as the rational-consumer benchmark. Instead, let us assume that consumers choose according to the following procedure. Each consumer independently draws one sample point from each alternative (including the outside option). For every i = 0,1,. . ., n, let x i denote the outcome of the consumer's sampling of alternative i: x i = 1 (the problem is fixed) with probability α and x i = 0 (the problem is not fixed) with probability 1 − α. Given a sample, the consumer chooses an alternative i that maximizes x i − p i . (Let us ignore the case of ties.) The outcome of the consumer's choice i is a new, independent draw; therefore, his expected payoff is α − p i .
The consumers' choice procedure captures an element of bounded rationality which may be referred to as anecdotal reasoning. Rather than forming probabilistic assessments of the quality of products, consumers evaluate them on the basis of randomly generated anecdotes. When the result of the sample of alternative i is x i = 1 (0), this is interpreted as a good (bad) anecdote. Because consumers take their anecdotes at face value and regard them as perfect representations of the products' quality, the term ‘anecdotal reasoning’ is apt.
This model of consumer behaviour induces a complete-information, simultaneous-move game played by the firms. To illustrate the firms' payoff function, suppose that p n > p n−1 > ⋅⋅⋅ > p 1 > p 0 = 0. Then, firm k's expected payoff is
The reason is that the firm's clientele consists of all consumers who obtained a good anecdote about the firm's product and a bad anecdote about all of the cheaper alternatives.
When all firms play the same mixed pricing strategy given by a continuous cdf G over some interval [p L , p H ], the clientele size that a price p in the support of G generates for an individual firm is
The reason is that the firm's clientele consists of consumers who obtained a good anecdote about the firm's product (the probability of this event for a given consumer is α), a bad anecdote about the outside option (the probability of this event for a given consumer is 1 – α), and a bad anecdote about every rival firm that charges a lower price (the probability of this event is (1 − α) · G(p) + (1 − G(p)) = 1 − α G(p) for a given consumer and a given rival firm). It follows that the expected payoff that a price p in the support of G generates for an individual firm is
The max-min payoff in this game is α (1 − α) n , for the following reason. The worst-case scenario for an individual firm is that all other firms charge p = 0. In this case, when the firm charges any p > 0, its clientele consists of consumers who obtained a good anecdote about the firm and a bad anecdote about every other alternative. The probability of this event for a given consumer is α (1 − α) n . Therefore, the firm's best-reply against the worst-case scenario is to charge the monopoly price p = 1, yielding a payoff of α (1 − α) n .
This game has a unique Nash equilibrium. The equilibrium is symmetric: each firm plays a mixed strategy given by the following cdf:
defined over the support [(1 − α) n − 1, 1]. Recall that by a basic property of mixed-strategy Nash equilibrium, every price in the support of the equilibrium strategy is a best-reply. Therefore, since the monopoly price p = 1 is in the support of the equilibrium strategy, each firm earns its max-min payoff α(1 − α) n in equilibrium. As a result, equilibrium industry profits are
The equilibrium has several noteworthy features:
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Consumer behaviour. The market for quacks is active and consumers pay positive prices for what is ultimately a useless product. Moreover, there is a positive clientele for each firm, including the most expensive one. Given a realization of the strategy profile, the size of the clientele of the firm that charges the k th -lowest price is α · (1 − α) k .
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Comparative statics: prices. Expected price goes up as α goes down, and converges to the monopoly level p = 1 as α tends to zero. The reason is that as α gets closer to zero, the probability of multiple successes in the consumer's sample goes down, and therefore each firm is effectively unlikely to face competition.
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Comparative statics: industry profits. Industry profits are hump-shaped with respect to the number of competitors n. The intuition for this effect is straightforward. On one hand, a greater number of firms increases the incentive to cut prices. This is a standard ‘competitive’ effect. On the other hand, a greater number of market alternatives increases demand for the industry as a whole, because there is a higher chance of hearing a good anecdote about some product. This is an ‘exploitative’ effect. Fixing α, the exploitative effect outweighs the competitive effect when n is relatively small (the critical value of n for which this is overturned increases as α decreases). Note that industry profits are a pure transfer from consumers to firms, given our assumption that the probability that the consumer's problem gets fixed is independent of his decision. Thus, all the statements regarding industry profits are at the same time statements about consumer welfare.
Having presented the basic BRM, let us turn to its rationalizations.
3. RATIONALIZATION VIA MODIFIED INFORMATION
Replacing imperfect rationality with imperfect information is perhaps the most immediate and common of traditional responses to models of bounded rationality. The idea is to replace what seems like a decision error resulting from bounded rationality with a rational response to limited information. For instance, choosing a low-quality product over an identically priced, high-quality product can be interpreted as evidence of imperfect information regarding product characteristics.
In the case of the market-for-quacks model, this rationalization is very naturally suggested by the sampling-based procedure itself. Instead of viewing the samples as part of the choice procedure in a complete-information model, we can re-interpret the samples as information sets in a model in which consumers are imperfectly informed. The rationalization turns the model into an incomplete-information extensive-form game: firms move first (making simultaneous pricing decisions) and consumers move second, after receiving partially informative signals of the firms' success rates. This model's predictions are given by applying the solution concept of sequential equilibrium to the incomplete-information game. In the BRM, consumers confront their market environment with a decision procedure that generates systematic inference errors. In contrast, the imperfect-information rationalizing model rules out systematic inference errors because the solution concept of sequential equilibrium embodies ‘rational expectations’.
This rationalization sounds highly plausible. As we shall see, it gives rise to symmetric Nash equilibria in which firms play mixed pricing strategies and a positive fraction of consumers choose firms over the outside option. Nevertheless, the rationalization suffers from a number of difficulties.
Changed assumptions about the external environment
In order for consumers' imperfect information to have any relevance, we must assume that firms have multiple payoff-relevant types – e.g., a high-quality firm and a low-quality firm. Thus, in order to apply the rationalization, we also need to modify our assumptions about the external market environment.
This is not an innocuous modification. For example, consider the market for homeopaths. A homeopathic medicine is based on a solution so diluted that it is, to an excellent approximation, pure water. To claim that there are high-quality and low-quality homeopaths is to claim that different types of water have different therapeutic properties.Footnote 3
In another context, if we consider the money-management application of the model, the assumption that there are high-quality and low-quality money managers means that some managers can systematically beat the market. This is an important substantive assumption, which is not taken lightly by financial economists. One should continue not to take it lightly when using it to rationalize models of money management markets with boundedly rational investors.
New unobservable parameters
The incomplete-information game designed to rationalize the market-for-quacks model requires us to introduce new parameters that describe the distribution of firm types and the consumers' signal structure. The following specification is minimalistic in this regard. Each market alternative (the firms as well as the outside option) has a type t ∈ {L, H}. The prior probability of L is λ, independently across market alternatives. When a consumer chooses an alternative of type t, his need is satisfied with probability α t , where 1 ≥ α H > α L > 0. Thus, each alternative's ex-ante success rate is α = λα L + (1 − λ)α H . Each consumer observes a signal s i ∈ {L, H} about each alternative. The signals are distributed independently across market alternatives and across consumers. Let q ts denote the probability that the consumer observes the signal s conditional on the alternative's type being t. Assume that q LL > q LH and q HH > q HL – i.e. signals have some informational content.
Notice how many new parameters have been introduced, even in such a minimalistic two-type, two-signal rationalization: α L , α H , q LL , q LH , q HL , q HH (λ is not an independent parameter, as it is determined by α L , α H and α.) In contrast, the market-for-quacks model essentially had a single parameter, namely the firms' ex-ante success rate α. Also, note that if α H = α L , consumers know with certainty that they are in a market for quacks, and the model collapses to what I referred to as the rational-consumer benchmark. Therefore, in what follows we must insist that α H > α L .
A similar dilemma caused by the enrichment of the informational structure of the game pertains to the firms' information. When firms were assumed to be homogeneous, as in the original market-for-quacks model, this issue was irrelevant. However, when firm quality is assumed to be heterogeneous, we need to make an explicit assumption about what each firm knows about its rivals. Once again, we see that the rationalizing model generates new degrees of freedom. For the rest of this section, I will assume that firms are uninformed of their opponents' types. This assumption fits an interpretation by which the n firms that compete for the consumer are drawn from a general population, such that all that firms know is the distribution over types from which its opponents are drawn. This assumption is made for simplicity – if I assumed that each firm is informed of its opponents' types, the analysis would grow vastly more complicated, thus bolstering my point even further.
Does the rationalizing model replicate the original model's key predictions?
Let us explore sequential equilibria in this incomplete-information game, and compare them to the unique Nash equilibrium in the market-for-quacks model. Formal near-equivalence between the original model and its rationalization is attained for the following parameter values: α H = 1, α L = 0, and q HH = q LL = 1. That is, high-quality (low-quality) alternatives satisfy the consumer's need with probability one (zero), and the consumer is perfectly informed of the alternative's type. The equilibrium strategy for high type firms is the same as in the basic model. Low types are always recognized as such and are never chosen, and so their pricing strategy is indeterminate as well as irrelevant for the market outcome.
The reason I refer to this as ‘near-equivalence’ is two-fold. First, we should have compared the firms' ex-ante pricing strategy in the rationalizing model to the equilibrium strategy in the original market-for-quacks model. Instead, we compared the latter to the equilibrium behaviour of high-quality firms in the rationalizing model. Second, and more importantly, the two models generate different consumer behaviour. In the rationalizing model, all consumers make the same decision in equilibrium. They are all informed of the firms' types, and since firms play continuous pricing strategies, price ties occur with probability zero. Therefore, all consumers make the same choice: they select the cheapest high-quality alternative (or the outside option, if no high-quality alternative is available). In contrast, recall that a salient feature of the market-for-quacks model was that each firm – including the most expensive one – had a positive clientele. Here, the most expensive firm ends up with either no clients or with all clients. In light of this discrepancy in the predictions that these two models make regarding consumer behaviour, should we view this rationalization as successful?
The parameter values in this specification of the rationalizing model are also problematic in terms of interpretation. They imply that consumers are perfectly informed of the types of all market alternatives, while firms receive no signal about their opponents' types. It is not easy to think of market situations for which this would be a plausible assumption. And in any case, recall that our motivation was to replace imperfect rationality with imperfect information about firms' types, yet consumers turn out to be perfectly informed under these parameter values.
When we turn to more plausible parameter specifications, the rationalizing model fails to reproduce salient features of firm behaviour in the original model. Recall that in the market-for-quacks model, the firms' equilibrium pricing strategy is a continuously increasing cdf over the interval [(1 − α) n − 1, 1]. That is, firms charge prices that range all the way up to consumers' willingness to pay for guaranteed satisfaction of their need, and these prices generate a positive clientele. Can sequential equilibrium in the rationalizing model reproduce this effect?
When consumers are imperfectly informed of the firms' types, the firms' pricing strategy in equilibrium is independent of their type, because there is nothing in the incentive structure in the model that enables firms to signal their type. In other words, equilibrium must be pooling. (Note, however, that in other cases, rationalization via modified information does introduce signalling issues that give rise to multiple equilibria. In this case, the rationalizing model's ability to replicate the predictions of the target BRM relies on suitable equilibrium selection, thus raising a burden-of-proof problem similar to the parameter selection problem discussed here.)
By Bayes' rule:
Therefore, when a consumer observes a good signal about an alternative, the alternative's posterior success rate is
Similarly, when a consumer observes a bad signal about an alternative, the alternative's posterior success rate is
In order for a consumer to be willing to pay a positive price for a firm, it must be the case that he received a bad signal about the outside option. This is just as in the market-for-quacks model. The reason is that all market alternatives are symmetric in terms of ex-ante quality, but the outside option comes free whereas firms charge positive prices. Therefore, the maximal price that consumers are willing to pay to firms is (α|H) − (α|L). This has to be the maximal price in the support of the marginal equilibrium pricing strategy. It is easy to see that (α|H)−(α|L) ≤ 1. This inequality is strict unless q HH = α H = 1 and q HL = α L = 0, which is the case we already covered above. Thus, the price range cannot be replicated under reasonable assumptions on the signal structure.
It could be argued that the range of equilibrium prices is not a key prediction of the original model, because of the difficulty of observing the consumers' underlying willingness to pay. But the rationalizing model also fails to reproduce the market-for-quacks model's comparative statics. As α L and α H go down, it is easy to see that since q LL > q LH and q HH > q LH , (α|H)−(α|L) decreases as well. Therefore, the maximal price that consumers are willing to pay in the rationalizing model goes down. In the limit, as α L and α H tend to zero, the maximal price converges to zero. This is in marked contrast to the effect of lowering ex-ante success rates on equilibrium prices in the original market-for-quacks model.Footnote 4
To summarize, in the zoo of new parameters that are needed to specify the rationalizing model, there is a configuration of parameter values that roughly replicates the firms' equilibrium behaviour in the market-for-quacks model. However, this configuration is inconsistent with the motivation of imperfect informed consumers. Indeed, it has a difficult-to-interpret property that consumers are fully informed of firms' quality, while firms do not receive any signal about their opponents' quality. Furthermore, consumer behaviour in equilibrium differs from the market-for-quacks model. For all other configurations of parameter values, the rationalizing model fails to replicate the original model's range of equilibrium prices, and the comparative statics of expected prices with respect to the ex-ante success rate are diametrically opposed to what the original model predicts.
Summary
Our analysis has raised several questions regarding the burden of proof we may wish to impose on the rationalizing model. How should we evaluate a rationalization when it requires us to modify assumptions about the external environment, particularly when these are essential to the ‘moral’ of the original story? Should we discount the rationalizing model if it forces us to introduce a number of new degrees of freedom (e.g., new parameters)? Is it enough to replicate the firms' behaviour, or do we need to reproduce consumer behaviour as well, in order for the rationalization to count as a success? Is it enough to find particular parameter values that replicate certain aspects of the original model's equilibrium? Or should the replication hold for a large range of parameter values? What is the interpretational burden on the parameter values that are used for replicating the original model's predictions?
4. RATIONALIZATION VIA MODIFIED PREFERENCES
When a certain choice pattern appears like a decision error that results from bounded rationality, we should entertain the possibility that what seems like an error is in fact a perfectly rational decision, and the only reason it seems erroneous is that we, as outside observers, attribute the wrong preferences to the agent. For instance, a manager's failure to choose a profit-maximizing project can be interpreted as evidence of a career concern. Replacing a behavioural model based on boundedly rational reasoning with a rational-choice model in which the consumer's preferences are re-specified is another common form of rationalizing BRMs.
Unlike the rationalization via modified information, rationalization via modified preferences turns out to be extremely effective in the case of the market-for-quacks model. Drop the assumption that consumers are interested in the firms' products only because they expect it to fix their problem. Instead, assume that there is an idiosyncratic value for each consumer-firm match. Specifically, a consumer's evaluation of each alternative i ∈ {0, 1,. . ., n} is u i − p i , where u i gets the values 1 or 0, with probabilities α and 1 − α, independently across alternatives and consumers.
Rational consumers with this specification of independent private values behave exactly like boundedly rational consumers who evaluate alternatives according to the sampling procedure. Therefore, the rationalizing model is formally – and therefore behaviourally – equivalent to the market-for-quacks model. This is an extreme case of the methodological dilemma which motivated this paper. The formal equivalence between the two models means that every prediction about market outcomes that we make in one model is perfectlymimicked by the other. However, the welfare implications are radically different. The BRM implies that in a ‘market for quacks’ (where the success rate of any product traded in the market is no different from the outside option of doing nothing), industry profits are a pure welfare loss for consumers. This loss can grow with the number of competitors. In contrast, in the rationalization, the market serves genuine consumer needs. It is welfare enhancing, and a greater number of firms is unambiguously better for consumers because it gives consumers access to a greater set of alternatives to choose from, while lowering their prices.
How should we compare these two accounts?
Prior plausibility of behavioural assumptions
I do not see any escape from the need to judge the prior plausibility of the behavioural assumptions that underlie two formally equivalent models, in the context of their intended application. For instance, when the market in question is for forecasting services, then assuming independent private values makes little sense: every rational consumer should prefer a forecaster who makes more accurate predictions. In contrast, when the market in question is for self-help guides, both explanations are plausible. On one hand, independent private values make sense because different self-help guides may contain different pieces of advice that fit different people. On the other hand, casual observation suggests that people extrapolate naively from anecdotal evidence to evaluate self-help guides.
The only reason that I mention this obvious point is that there is a strong tradition in economic methodology (following Friedman Reference Friedman1953) that is opposed to a priori judgements of behavioural assumptions and preaches that we evaluate models exclusively by their predictive success. However, when we need to choose between two formally equivalent models having different welfare implications, Friedman's positivistic criterion is too weak, and we may want to take into account the plausibility of behavioural assumptions in the context of the model.
Extended models
Even when two different models appear equivalent, they may differ when we move outside the original environment for which they were formulated. That is because different models tend to suggest different extensions. For example, Spiegler (Reference Spiegler2006b) extends the model of market competition with consumers who follow the sampling procedure, by allowing firms to randomize over prices. Each consumer evaluates a firm's price distribution on the basis of a single sample point, and selects the cheapest firm in his sample. However, the actual price he pays is a new, independent draw from the distribution associated with the firm he ends up choosing.
Thus, the extended model presupposes that the same element of bounded rationality that made consumers extrapolate naively from small samples when evaluating the random performance of credence goods is going to make them extrapolate naively from small samples to evaluate random pricing strategies. Spiegler (Reference Spiegler2006b) shows that this behavioural model implies a strict incentive for firms to randomize over prices. Moreover, a greater number of competitors results in a mean-preserving spread in the equilibrium price distribution that firms adopt. In contrast, it is hard to think of an organic extension of the differentiated-taste rationalization of the market-for-quacks model that will generate these effects. Should the observation that the BRM and its rationalization become behaviourally distinct in an enlarged domain affect our judgement of the rationalizing model in the original domain?
Although the idea that extensions can break formal equivalence between two models is familiar, it has certain subtleties. Consider another extension of the market-for-quacks model, discussed in Spiegler (Reference Spiegler2006a), in which firms choose not only prices but also (simultaneously) whether to disclose their success rates to consumers. Disclosure is meaningless under the differentiated-taste rationalization, because its premise is that consumers are better informed than firms, and not the other way around. One could argue that this by itself provides a meaningful distinction between the sampling-based model and its differentiated-taste rationalization. However, it turns out that the equilibrium prediction of the extended model is that firms choose not to disclose their success rates. Therefore, as far as equilibrium behaviour is concerned, the two models are equivalent after all. In the sampling-based model, disclosure is meaningful but fails to occur in equilibrium, while in the differentiated-taste rationalization, disclosure does not occur because it is meaningless in the first place. Can we legitimately say that the differentiated-taste rationalization replicates the sampling-based model's predictions in the extended domain that includes disclosure?
Summary
In this section we examined a rationalization that looks perfect at first glance, as it is formally equivalent to the original BRM. However, we identified two burden-of-proof issues. First, the behavioural assumptions underlying the rationalizing model may be implausible in the context of the original model's intended domain applications. Second, the original model has natural extensions that are either nonsensical from the point of view of the rationalizing model, or generate predictions which are distinct from those of an analogous similar extension of the rationalizing model. How should we evaluate the rationalizing model in light of these observations?
5. RATIONALIZATION VIA ENDOGENIZATION
Another way of rationalizing a BRM is to argue that the behaviour it generates appears to be non-rational only because the model leaves out certain costs associated with the decision process. Once these are explicitly incorporated into the model, rationality is restored. In the extended model, the consumer chooses how much mental resources to spend on the decision problem, on the basis of ‘rational expectations’ of the benefits of information processing. Note that it is not so much the friction as its formal treatment that is conventional. Decision costs are rarely incorporated into standard economic models. However, the type of extended model described above is conventional in that it treats decision costs as if they were search costs, or costs of acquiring information.
The following example has become almost canonical in methodological discussions of BRMs (see Caplin and Schotter Reference Caplin and Schotter2008). An American tourist visits London (the tourist is invariably American in tellings of this story). Before crossing a street, he looks left, sees that the road is clear, starts walking, and gets hit by a car coming from his right. The bounded-rationality interpretation of the tourist's behaviour is that he does not deliberate over his decision problem (when to cross the street). Instead, he follows an automatic rule that may be optimal in his home environment. A rationalization that incorporates information-processing costs would proceed as follows. The tourist realizes that he is on foreign soil and that he needs some time to remember which side the cars are coming from. However, spending time on this mental task is costly. The tourist rationally trades off this cost against the benefit of safe crossing.
As this example is only meant to illustrate a methodological dilemma, I will not get into a detailed discussion of the plausibility of the rationalization of the tourist's behaviour. I will only comment that the two explanations of the tourist's behaviour are in principle distinguishable. For instance, one could put up a sign for pedestrians saying ‘don't cross the street without thinking first’. This intervention would have an impact only under the bounded-rationality interpretation.
Let us turn back to the market-for-quacks model. The consumer's procedure of sampling each market alternative and selecting the best alternative in the sample can be viewed as an optimal strategy in a larger model, in which we introduce search costs. In such an extended model, there is an arbitrarily large number of firms. The consumer optimally designs a sample, taking into account the cost of obtaining information about the firms' quality and pricing decision. In this way we endogenize n as the size of the consumers' sample, given their correct expectation of the firms' equilibrium pricing strategy.
This rationalization shares all the problems of the rationalization method discussed in Section 3. In particular, the equilibrium pricing strategy can be replicated only if we assume that when a consumer samples a firm, he obtains perfect information about its type (whereas the firm's opponents are uninformed). We have already commented on the implausibility of this informational assumption. At any rate, in this case, it is easy to come up with a cost of obtaining a single sample point, for which the number of firms that the consumer samples will be optimal ex-ante, given their pricing strategy. However, the assumption that the consumer commits ex-ante to the size of his sample is problematic. Suppose that the consumer has sampled n firms, and all of them - as well as the outside option - turned out to be of low quality. As the cost of obtaining these sample points is sunk, what prevents the consumer from obtaining new sample points?
Rationalization via endogenization is an interesting modelling exercise. However, as a criticism of a BRM, it suffers from several methodological difficulties.
When should we endogenize informational constraints?
Any informational constraint in any economic model could be endogenized, by enabling agents to invest resources that help them relax their constraint. Economists address this endogeneity only when they wish to focus on the information acquisition process, and in most applications they are happy to treat the informational limitations as exogenous, because this is a good modelling strategy. The same standard should hold for rationality constraints. If the modeller has good reasons for certain restrictions on the process by which the consumer receives word-of-mouth information in the form of anecdotes, and a much fuzzier notion of the restrictions that could be imposed on the costs of actively looking for such anecdotes, then it is a good modelling strategy to take the sampling procedure as primitive.
At which scale should we endogenize informational constraints?
Even if the sampling procedure is a result of some optimizing process that takes into account information-processing costs, the optimization often takes place not on a case-by-case basis, but at a ‘general equilibrium’ level, or on an ‘evolutionary’ time scale. Consumers devise heuristics and calculational short-cuts that are meant to work well on average across a large number of market (as well as non-market) situations. The sampling procedure is such a calculational short-cut. For the kind of partial equilibrium analysis that economists apply in industrial organization, taking the consumer's decision rule as given is a good approximation.
A ‘Lucas critique’
In order for rationalization via endogenization to be operational, the consumer's optimization must be made on the basis of correct knowledge of the market equilibrium. Otherwise, we are not dealing with a rationalization, but merely shifting the element of bounded rationality to another level. The rational-expectations restriction often restricts the class of behavioural parameters of the original model which can be derived. For example, in the case of the market for quacks, we could imagine that certain pairs of parameter values (α, n) are simply inconsistent with equilibrium under the rationalizing model. In contrast, the market-for-quacks model does not impose any constraint on the range of values that they can get.
One point of view is that such a failure to rationalize certain specifications of the BRM should be regarded as a criticism of the BRM, akin to the famous Lucas critique of traditional Keynesian macroeconomic models (Lucas Reference Lucas1976). According to this interpretation, the fact that certain specifications cannot be justified as equilibrium responses in a larger model that incorporates explicit information-processing costs means that these specifications are illegitimate. Note the rhetorical cunning at play here. So far, we have viewed success at rationalizing BRMs as a vindication of the ‘can't we get the same thing with a standard model’ critique. Now, the ‘Lucas critique’ turns the rationalization program on its head, and sees its failure as a reason to detract the BRM. Nothing better illustrates the trickiness of debates over BRMs.
Comment: Rationalization via incorrect subjective models
Throughout this paper, I have refrained from considering rationalizations that restore the rationality of an agent's behaviour by describing it as an optimal response to an incorrect subjective model. The reason is simple: I do not view such rationalizations as being standard at all. Conventional economic models invariably assume common understanding of the economic model, such that any asymmetry in the agents' beliefs is fully embedded in the model itself. The only subjectivity that standard models admit is non-common priors (something that would probably have been considered highly ‘non-standard’ 20 years ago).
6. DISCUSSION
This paper has been concerned with the following dilemma: what is the burden of proof that should be imposed on a rational-choice model (referred to as RM in the sequel) that is offered in refutation of a given BRM? The following scenarios abstract from the details of the specific case study we examined. Each scenario raises a difficulty in the evaluation of RM as a successful rationalization/refutation of BRM.
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• RM mimics key predictions of BRM, but RM differs from BRM not only in behavioural assumptions, but also in assumptions about the external environment.
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• RM introduces new parameters that were not included in BRM. Whether RM mimics key predictions of BRM depends on a suitable selection of parameter values.
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• BRM and RM are observationally equivalent in a certain domain, but BRM is based on behavioural assumptions that appear more plausible in this particular domain.
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• BRM and RM are observationally equivalent in a certain domain of market situations, but become distinct when we extend (in a ‘natural’ way) the behavioural models underlying BRM and RM to a broader domain.
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• BRM and RM are observationally distinct out of equilibrium, but they imply identical equilibrium behaviour. An extreme case is where a certain action is meaningful in BRM yet not taken in equilibrium, while the same action is meaningless and inconceivable a priori in RM.
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• RM has multiple equilibria whereas BRM has a unique equilibrium. Whether RM mimics the predictions of BRM depends on a suitable equilibrium selection.
In light of these difficulties, I argue that we should impose stricter burden-of-proof requirements on the ‘can't we get the same thing with a standard model’ critique. The predictions of most rational-choice models are qualified by restrictions on parameter values or the external environment. We usually take these qualifications very seriously when assessing a rational-choice model that is advanced in a constructive attempt to capture an economic phenomenon. Yet at the same time we exhibit a tendency to ignore the same qualifications when the rational-choice model is offered in refutation of a BRM. I object to this double burden-of-proof standard.
We should also be reluctant to tamper with assumptions of a BRM that concern the domain of market situations that agents face. Whether a model is static or dynamic, whether its informational constraints are endogenous or exogenous, whether agents are assumed to be homogeneous or heterogeneous – these are all modelling choices that the theorist makes to define the limits of the theoretical exercise he wishes to pursue. We are not forced to respect these assumptions when discussing the model's merits and drawbacks, but we should try to accept them as given when advancing alternative ‘rational explanations’.
But if the ‘can't we get the same thing with a standard model’ criticism is so problematic, what explains its popularity? I believe that as economists, we are simply used to looking for ‘rational explanations’. It is what we do for a living. The programme of rationalizing human behaviour is an important part of what defines economic theory, and it has had great successes (Gary Becker's theories of marriage and criminal behaviour are spectacular extreme points along this line). Rationalizations of superficially non-rational behaviour continue to be the subject of very interesting works (e.g. Samuelson Reference Samuelson2001; Compte and Postelwaite Reference Compte and Postelwaite2005; Kamenica Reference Kamenica2008; Baliga and Ely Reference Baliga and Ely2009). The ‘can't we get the same thing with a standard model’ critique simply extends this type of reasoning. We are so effortless in our search for rational explanations that we tend to overlook the rough edges, especially when we have a prior inclination to reject explanations of economic behaviour that depart from the rational-choice paradigm. However, as I hope this paper has shown, a modelling approach can be very useful for understanding phenomena, and yet quite weak as a basis for criticizing an alternative modelling approach. This is probably the chief general lesson from this paper.
As the reader may have noticed, nothing in the methodological points made in this paper relies on the distinction between rational-choice and bounded-rationality economic models. Similar arguments could be made in the context of other debates between proponents of theories that are regarded by a community of researchers as ‘standard’ and ‘non-standard’, and are hard to distinguish empirically. Replace RM and BRM in the bullet list earlier in this section with arbitrary ‘standard’ and ‘non-standard’ models, and many of the statements would still make sense. I have not attempted to generalize beyond the concrete case of debates over BRMs, because I am not a professional philosopher myself, and I thought that the philosophically inclined reader would benefit more from a close analysis of a concrete example taken from a contemporary debate with which I am familiar. I do hope that the questions that this paper raises will be taken up by professional philosophers and interpreted against conventional discussions of observationally equivalent theories.
