آیا مدل های رفتاری قیمت گذاری دارایی، ساختاری است؟

The recent increase in interest in so-called behavioral models of asset-pricing is motivated partly by the desire to have models that appear realistic in light of experimental evidence, and partly by their success in moment-matching exercises. This paper argues that the attention given to these two criteria misses perhaps the most important aspect of the modeling exercises. That is, the search for parameters that are invariant to changes in the economic environment. It is precisely this invariance that motivates the use of a tightly parameterized general equilibrium model. Assessing a model on this dimension is difficult and, as the paper argues through the use of suggestive examples, will undoubtedly require strong subjective judgments about the reasonableness of preference assumptions. Such judgments are routinely made about the reasonableness of assumptions about stochastic endowments. The paper suggests that more effort be applied to understanding aggregation in these models and to the exploration of behavioral assumptions in a less flexible but less corruptible time-stationary recursive class of preferences.

The recent successes of behavioral asset-pricing models provide new hope for the quantitative research program started by Mehra and Prescott (1985) following the theoretical work of Lucas (1978). That is, there is a renewed interest in the ability of a tightly parameterized, representative-agent, general-equilibrium model to explain the salient features of historical asset-market data (e.g., large equity premium, excess volatility, etc.). What makes an asset-pricing model “behavioral” can itself be the subject of debate. For the purposes of this paper, I will lump all asset-pricing models that endow agents with preferences that do not adhere to the assumption of time-stationary expected utility (i.e., “Savage rationality”), into the category of “behavioral”. Many of these preference assumptions are directly motivated by evidence from experimental psychology and behavioral decision theory, e.g., loss aversion (Epstein and Zin, 1990; Benartzi and Thaler, 1995; Barberis et al., 1999), or hyperbolic discounting (Luttmer and Mariotti, 2000; Krusell and Smith, 2000). Also falling within this broad definition, however, are models that may depart from classical assumption by allowing for state-dependent utility functions, but that are less formally motivated by behavioral evidence, e.g., habit formation (Abel, 1990; Constantinides, 1990; Campbell and Cochrane, 1995; Wachter, 2001). These examples are suggestive and are in no way an exhaustive list of behavioral asset-pricing models. Indeed as more experimental evidence filters into economics from various fields of psychology, this list continues to grow at a rapid rate. This paper takes a sympathetic view of these recent behavioral approaches and tries to identify what these models have yet to accomplish before they can claim success and presumably supplant more traditional approaches. Particular attention is paid to the need for structural models, and whether behavioral models are more or less likely to achieve the sort of “deep structural excavation” called for by the rational expectations revolution in dynamic macroeconomics. The methodological guidelines laid out by Friedman and Lucas in the two quotes above, cast a very different light on the current debate about the usefulness of behavioral versus more traditional models of asset markets, than what one might hear in academic circles and even in the popular press. From this perspective, traditional models cannot be viewed as inherently better because of their reliance on well-understood Savage rationality. Likewise, behavioral models cannot claim superiority simply based on experimental evidence of individual departures from this definition of rationality, and the sense of modeling realism that this evidence invokes. If this debate can be settled, then following Lucas’ advice, it can only be settled by determining which approach to building a mechanical, imitation economy provides “better imitations” of real asset markets. It is now common for behavioral models to adopt the dynamic stochastic general equilibrium approach of Lucas (1978) and Mehra and Prescott (1985) as a framework for understanding the consequences of alternative behavioral assumptions on observables in asset markets. In other words, the basic difference between the two approaches can be thought of as differences in assumptions about agents’ preferences — most often a hypothetical representative agent. Therefore, the common use of dynamic general equilibrium endowment economies by both approaches provides a common framework for comparison. The use of these general equilibrium models highlights an implicit desire to obtain structural models. In this case, “structural” is used to differentiate between purely statistical descriptions of empirical evidence (which may or may not use economic theory to suggest functional forms and factors), from models that derive their empirical predictions directly from the structure of a parametric version of an economic theory. The obvious implication being that like more traditional models, behavioral models can potentially provide useful guidance for understanding the likely consequences of changes in the economic environment. That is, they can be used to make forecasts about situations in which we have no (or at least very little) historical evidence. If that was not the desire of behavioralists in finance, then behavioral arguments could be safely relegated to a relatively minor role in the design and interpretation of reduced-form econometric models. Predicting responses to changes in the economic environment, e.g., changes in government policy, therefore, are precisely the “particular questions” for which we seek “better imitations”, using Lucas’ words, or the “sufficiently accurate predictions”, using Friedman's words. The primary reason for using tightly parameterized general equilibrium models to characterize asset-market outcomes is precisely the need for identifying policy-invariant structural parameters. Behavioral models have an obvious and important advantage over traditional models: their parameters can be calibrated so that various moments of particular interest of the distribution of asset prices generated by these models, will closely match their sample counterparts in historical data. That is, they do a better job imitating the large equity premiums, volatility, and persistent dynamics that are so puzzling from the perspective of traditional models. Clearly, this data-fitting exercise seems like a necessary condition for evaluating the usefulness of any equilibrium model. We would have little confidence in any model's ability to forecast outcomes in new environments when it is incapable of forecasting in the current environment. These conclusions, however, require a fair bit of judgment on the part of the modeler. Section 2 outlines judgments that modeler's working in this area typically make about the reasonableness of assumptions about the stochastic properties of exogenous variables. A simple example demonstrates that poorly fitting Savage-rational models can be made to fit empirical evidence by making assumptions about higher-order moments of the distribution of endowments. Most people would object to this strategy, however, since these assumptions might not seem reasonable given their prior beliefs. Where these beliefs come from is unspecified. They may derive from beliefs about the deeper micro-foundations of production, or they may derive from personal experience, or they may be purely whimsical. Direct statistical evidence about these higher-order-moment assumptions is likely to be misleading, or at best inconclusive, so we are left with non-sample-based judgments about the reasonableness of these assumptions. Section 3 of the paper looks at a similar sort of reasonableness criterion for preference assumptions. Unfortunately, unlike the case of assumptions about endowments, we are not yet at the stage where there is a consensus about what types of preference assumptions are unreasonable. The examples in Section 3 demonstrate that virtually any well-fitting, reduced-form empirical model of asset pricing can be incorporated into the representative agent's preferences so that a purely statistical model could be viewed as the outcome of what one could claim to be a structural general equilibrium model. Naturally, there is no guarantee that a model constructed in this way will have parameters that are invariant to the types of structural change for which these models must provide guidance. Analogous to the case for reasonableness of endowments, the modeler is forced to make judgments about the reasonableness of the preference assumptions. It is clear that fitting historical data is not a sufficient criterion for determining the usefulness of particular preference assumptions for delivering a structurally stable model. Likewise, without some explicit aggregation results, individual-level experimental evidence will also be insufficient. The main conclusion of this paper is straightforward: the parameters of asset-pricing models including behavioral models must be invariant to changes in the economic environment. This is not a very original conclusion and it is not likely to be very controversial. What is controversial and quite difficult, is assessing whether this goal has been met. Econometric testing for structural stability is notoriously problematic, especially in small samples. Moreover if the type of structural change under investigation has no historical counterpart, then purely statistical testing will be uninformative. The examples in 2 and 3 of the paper suggest that any assessment of the structural stability of a model will require the use of both non-sample information and the researcher's judgment. Accounting for historical evidence is not enough. The researcher is forced to evaluate the reasonableness of the assumptions on preferences and technologies under which the asset-pricing model can both account for historical evidence and maintain its basic structure in the face of significant changes in the economic environment. If aggregation results are available, then preferences of the representative agent that appear unreasonable given individual-level evidence would certainly be a cause for concern. These results also suggest that maintaining time-consistency as a basic axiom for preferences, and avoiding the introduction of arbitrary state variables in the utility function, will help eliminate much of the scope for well-fitting but non-structural empirical asset-pricing models to pass as deeper structural models.

The purpose of trying to characterize asset-market data using a tightly parameterized, representative-agent, general-equilibrium model is to try to uncover deep structural parameters. This is equally true of behavioral models as it is of more traditionally expected utility models. This is not a simple task and, as the examples in this paper suggest, fitting historical data is not sufficient to insure structural stability. Evaluating a model in this dimension will always require an element of subjective judgment of the reasonableness of the assumptions of the model. This is perhaps even more true of behavioral asset-pricing models than more traditionally expected utility models. The reason is that behavioral evidence may suggest the inclusion of state variables in the utility function and the relaxation of the stationarity assumption of intertemporal preferences. This exposes these models to the risk of being reverse engineered to fit the data, without serious consideration of whether the parameters of the model can be deemed structural. Econometric testing for structural stability is likely to be problematic, especially in small samples. In addition, statistical test will be uninformative if the types of change to the economic environment being contemplated has no natural analog in historical experience. A better understanding of how behavioral models aggregate provides some hope for reaching a consensus about reasonableness, since this will allow inference about the representative agent's preferences based on individual-level experimental evidence. Finally, since the use of behavioral models often opens the door for claims of reverse engineering, it seems prudent to work harder to avoid these criticisms. Maintaining assumptions on recursivity and time-stationarity of intertemporal preferences, while incorporating behavioral concepts is both feasible, as shown in Epstein and Zin (1990), and desirable given the discipline that this will naturally enforce on the modeling exercise.