Ebook Structural Econometric Tests Of General Equilibrium Theory On Data From Large-Scale Experimental Financial Markets
The purpose of this paper is to develop and implement structural econometric tests of general equilibrium asset pricing theory on data from large-scale experimental financial markets. These tests differ from standard tests on field data in two significant ways. First, the tests use cross-sectional portfolio holdings data, and therefore, verify the consistency between securities prices and allocations. In field studies, one generally only verifies whether prices (price dynamics) satisfy some necessary conditions for equilibrium. Second, unlike tests on field data, the joint distribution of asset returns is not treated as unknown, because it is one of the design parameters, and hence, known to the experimentor. This also implies that the sampling error in the estimation of the joint distribution of asset returns cannot be the source of the uncertainty on which the structural econometric tests are built.
Econometric tests of asset pricing theory on field data almost invariably focus on prices, ignoring the allocational predictions of the same theory. Tests of the Capital Asset Pricing Model (CAPM), for instance, have merely verified whether prices are such that the market portfolio (supply of risky securities) is mean-variance optimal. The allocational prediction of the CAPM, namely, that all investors should hold the same portfolio of risky securities (a result which has been referred to as portfolio separation), is rarely if ever verified. Yet economists are not directly interested in prices. They are mostly interested in allocations, and whether competitive markets manage to indeed generate optimal allocations (the first welfare theorem).
To be sure, the allocational predictions of standard asset pricing theory are extreme and a quick look at any evidence makes one reject them off hand. Investors do not hold risky securities in the same proportions, unlike predicted by the CAPM, for instance. One wonders what the meaning is of the multitude of tests of asset pricing theory that have been performed solely on prices if the allocations are plainly at odds with the theory and if, as is widely believed, prices depend crucially on allocations. This paper will provide a constructive answer.
It is our view that any realistic theory of general equilibrium ought to allow for discrepancies between the tight theoretical allocational predictions and the observed outcomes. There are a variety of reasons why allocations may not be exactly as predicted. Determination and implementation of optimal portfolio holdings requires a subtantial amount of computational ability and trading skill. Investors may be satisfied with near-optimal holdings if there are no further incentives (an issue that many have brought up in the context of financial markets experiments, where potential earnings, while generous, are nevertheless limited). In addition, prices are observed at a relatively arbitrary point in time (e.g., the end of a trading period), and it is not clear whether any/many/all investors could have retraded at those prices if they had to in order to obtain optimal holdings. Also, the preference assumptions needed to operationalize the theory (e.g., quadratic preferences) may only be correct as an approximation. Even if optimal for the true preferences, actual holdings may deviate from those computed on the basis of the hypothesized preferences. Finally, even if subjects are mean-variance optimizers, their risk aversion may change randomly over time, in which case the strict predictions of the theory (based on constant risk aversion) will fail.
To accommodate these discrepancies, we opted to introduce investor-specific perturbation terms at the demand level. These perturbations terms are meant to capture unmodeled features of the problem so as to render realism to the outcomes. Stochastic structure is imposed on the perturbation terms so as to generate falsifiable predictions. The specific stochastic structure used in the present paper is such that, through the law of large numbers, exact CAPM pricing is recovered when the number of investors (subjects) is large, even if no investor’s portfolio holdings satisfies strict portfolio separation. Deviations from exact CAPM pricing with a small number of subjects are then to be explained as a standard small-sample effect.
The latter result is not only of interest as a basis for formal econometric tests of the CAPM. It also teaches that strict portfolio separation is not crucial for CAPM pricing, unlike widely believed. The market portfolio (supply of risky securities) can be mean-variance optimal even if nobody demands a fully optimal portfolio, i.e., even if everybody demands a portfolio below the frontier of mean-variance efficient portfolios.
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