Econometric Evaluation of Rational Belief Models

The paper proposes a method for construction, estimation, and testing the Rational Beliefs (RB) models. RB models, due to Kurz, 1994, allow agents' beliefs to differ from the Rational Expectations (RE), but require that beliefs cannot be contradicted by past data. By implication, RB and RE must agree in strictly stationary worlds, while a disagreement is allowed in non-stationary setting. The estimation method involves sample counterparts to the conditional and unconditional moment restrictions formed from the Euler equations and rationality conditions. In essence, the method deduces systems of conditional beliefs consistent with the conditional moment restriction posed by the Euler equations. Consistent test statistics then discriminates the rationality from non-rationality. The attractive features are (i) the estimation and testing procedures are implemented without solving explicitly for RB equilibria, (ii) learning is permitted, and (iii) both the econometrician and the economic agents are put on the ``equal footing'' in the sense of Muth, 1961 and ``down to earth''. Under flexible regularity conditions, the test statistics are shown to converge in distribution to the continuous functionals of generalized Brownian bridges, whose coordinates are projections on the space of moment functions that are used to phrase the rationality conditions. As a result, the limit distributions are non-standard or standard, depending on whether the test statistic is itself a function of finite-dimensional projection or a functional of the whole process, respectively. The resampling and simulation methods allow for valid approximation of either distribution. A simple estimated model of aggregate consumption and stock market behavior, populated by investors with rational beliefs, points to the variation in agents' sentiments as a dominant source of asset price volatility.