Combining a Theoretical Prediction with Experimental Evidence

Abstract

We propose a novel experimental design to assess how to combine predictions from a theoretical model with experimental evidence to yield new, more accurate quantitative predictions. The first step involves deriving the predictions of the theoretical model by estimating unobserved parameters. The second step involves estimating the optimal weights with which to combine the theoretical predictions with experimental evidence. This latter estimation uses a random sample of experimental tasks from the relevant space. The optimal weight to give to the theoretical prediction can be summarized by a single number - the Equivalent Number of Observations (ENO). This number has an intuitive interpretation: the prediction of the theory is as accurate as the prediction from an experiment with n = ENO observations of the task to be predicted. To demonstrate and evaluate the use of the equivalent number of observations, the paper examines popular models in two of the best-studied problems in experimental economics: individual decision-making under uncertainty and repeated play of constant sum games. The two examples show that in addition to solving applied problems, the results provide some insights concerning the interpretation of descriptive models as useful approximations.