We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in (...) which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance. (shrink)

To understand how small business entrepreneurs respond to government policy one has to know their risk and time preferences. Are they risk averse, or have high discount rates, such that they are hard to motivate? We have conducted a set of field experiments in Denmark that will allow a direct characterization of small business entrepreneurs in terms of these traits. We build on experimental tasks that are well established in the literature. The results do not suggest that small business entrepreneurs (...) are more or less risk averse than the general population under the assumption of Expected Utility Theory. However, we generally find an S-shaped probability weighting function for both small business entrepreneurs and non-entrepreneurs, with entrepreneurs being more optimistic about the chance of occurrence for the best outcome in lotteries with real monetary outcomes. The results also point to a significant difference in individual discount rates between entrepreneurs and non-entrepreneurs: entrepreneurs are willing to wait longer for certain rewards than the general population. (shrink)