IZA DP No. 3121: Flexible Approximation of Subjective Expectations Using Probability Questions: An Application to the Investment Game
published as 2 separate articles in: Journal of Business and Economic Statistics, 2012 (Flexible Approximation of Subjective Expectations Using Probability Questions, doi:10.1198/jbes.2011.09053) and in Experimental Economics, 2010 (Bounding Preference Parameters under Different Assumptions about Beliefs: a Partial Identification Approach, doi:10.1007/s10683-010-9244-6)
We use spline interpolation to approximate the subjective cumulative distribution function of an economic agent over the future realization of a continuous (possibly censored) random variable. The method proposed exploits information collected using a small number of probability questions on expectations and requires a weak prior knowledge of the shape of the underlying distribution. We find that eliciting 4 or 5 points on the cumulative distribution function of an agent is sufficient to accurately approximate a wide variety of underlying distributions. We show that estimated moments of general functions of the random variable can be computed analytically and/or using standard simulation techniques. We illustrate the usefulness of the method by estimating a simple model to asses the impact of expectations on investment decisions in a commonly used trust game.