Beauty contests under private information and diverse beliefs: How different?
The paper contrasts theories that explain diverse belief by asymmetric private information (PI) with theories which postulate agents use subjective heterogenous beliefs (HB). We focus on problems where agents forecast aggregates such as profit rate of the S&P500 and our model is similar to the one used in the literature on asset pricing (e.g. Brown, D., Jennings, R., 1989. On technical analysis. Review of Financial Studies 2, 527-551; Grundy, B., McNichols, M., 1989. Trade and revelation of information through prices and direct disclosure. Review of Financial Studies 2, 495-526; Allen, F., Morris, S., Shin, H.S., 2006. Beauty contests and iterated expectations in asset markets. Review of Financial Studies 19, 719-752). We first argue there is no a-priori conceptual basis to assuming PI about economic aggregates. Since PI is not observed, models with PI offer no testable hypotheses, making it possible to prove anything with PI. In contrast, agents with HB reveal their forecasts hence data on market belief is used to test hypotheses of HB. We show the common knowledge assumptions of the PI theory are implausible. The theories differ on four main analytical issues. (1) The pricing theory under PI implies prices have infinite memory and at each t depend upon unobservable variables. In contrast, under HB prices have finite memory and depend only upon observable variables. (2) The "Beauty Contest" implications of the two are different. Under PI today's price depends upon today's market belief about tomorrow's mean belief as a function of the supply shock and inference from prices. Under HB it depends upon today's market belief about tomorrow's market beliefs. Tomorrow's beliefs are, in part, beliefs about future beliefs and are often mistaken. Market forecast mistakes are key to Beauty Contests, and are a central cause of market uncertainty called "endogenous uncertainty". (3) Contrary to PI, theories with HB have wide empirical implications which are testable with available data. (4) PI theories assume unobserved data and hence do not restrict behavior, while rationality conditions impose restrictions on any HB theory. We explain the tight restrictions on the model's parameters imposed by the theory of Rational Beliefs.
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