We consider a linear model where the coefficients -intercept and slopes -are random and independent from regressors which support is a proper subset. When the slopes do not have heavy tails, the joint density of the random coefficients is identified. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator, its rates of convergence, and a data-driven rule which delivers adaptive estimators. The corresponding R package is RandomCoefficients.
We consider a linear model where the coefficients -intercept and slopes -are random and independent from regressors which support is a proper subset. When the slopes do not have heavy tails, the joint density of the random coefficients is identified. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator, its rates of convergence, and a data-driven rule which delivers adaptive estimators. The corresponding R package is RandomCoefficients.
In this paper, we build a new test of rational expectations based on the marginal distributions of realizations and subjective beliefs. This test is widely applicable, including in the common situation where realizations and beliefs are observed in two different datasets that cannot be matched. We show that whether one can rationalize rational expectations is equivalent to the distribution of realizations being a mean-preserving spread of the distribution of beliefs. The null hypothesis can then be rewritten as a system of many moment inequality and equality constraints, for which tests have been recently developed in the literature. Next, we go beyond testing by defining the minimal deviations from rational expectations that can be rationalized by the data in the context of structural models. Building on this concept, we propose an easy-to-implement sensitivity analysis on the assumed form of expectations. Finally, we apply our framework to test for rational expectations about future earnings, and examine the consequences of such departures in the context of a life-cycle model of consumption. participants of various seminars and conferences for useful comments and suggestions. † CREST, xavier.dhaultfoeuille@ensae.fr. ‡ CREST and TSE, christophe.gaillac@tse-fr.eu.
useful comments and suggestions. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
We consider a linear model where the coefficients -intercept and slopes -are random and independent from regressors which support is a proper subset. When the slopes do not have heavy tails, the joint density of the random coefficients is identified. Lower bounds on the supremum risk for the estimation of the density are derived for this model and a related white noise model. We present an estimator, its rates of convergence, and a data-driven rule which delivers adaptive estimators. The corresponding R package is RandomCoefficients.
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