Eliciting Beliefs: Theory and Experiments

Subjective beliefs play a role in many economic decisions. There is a large theoretical literature on the elicitation of beliefs, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover beliefs, but stresses the need to make strong auxiliary assumptions or “calibrating adjustments” to elicited reports in order to recover the latent belief. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We make three contributions to bridge this gulf. First, we offer a general theoretical framework in which the belief elicitation task can be viewed as an exchange of state-dependent commodities between two traders. Second, we provide a specific elicitation procedure which has clear counterparts in field betting environments, and that is directly motivated by our theoretical framework. Finally, we illustrate how one can jointly estimate risk attitudes and subjective beliefs using structural maximum likelihood methods. This allows the observer to make inferences about the latent subjective belief, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with an experiment in which we elicit subjective probabilities over three future events and one fact. † Department of Economics and Centre for Economic and Business Research, Copenhagen Business School, Copenhagen, Denmark (Andersen); Department of Economics, University of Canterbury, Christchurch, New Zealand (Fountain); and Department of Economics, College of Business Administration, University of Central Florida, USA (Harrison and Rutström). Harrison is also affiliated with the Durham Business School, Durham University, UK. E-mail contacts: sa.eco@cbs.dk, john.fountain@canterbury.ac.nz, gharrison@research.bus.ucf.edu and erutstrom@bus.ucf.edu. We thank the U.S. National Science Foundation for research support under grants NSF/IIS 9817518, NSF/HSD 0527675 and NSF/SES 0616746, and the Danish Social Science Research Council for research support under project #24-02-0124. We are grateful to Peter Wakker for many helpful discussions. All instructions and statistical code are available at the ExLab Digital Library at http://exlab.bus.ucf.edu.