Latent Process Heterogeneity in Discounting Behavior

We show that observed choices in discounting experiments are consistent with roughly one-half of the subjects using exponential discounting and one-half using quasi-hyperbolic discounting. We characterize the latent data generating process using a mixture model which allows different subjects to behave consistently with each model. Our results have substantive implications for the assumptions made about discounting behavior, and also have significant methodological implications for the manner in which we evaluate alternative models when there may be complementary data generating processes.

Theory, Experimental Design and Econometrics Are Complementary (And So Are Lab and Field Experiments)

Experiments are conducted with various purposes in mind including theory testing, mechanism design and measurement of individual characteristics. In each case a careful researcher is constrained in the experimental design by prior considerations imposed either by theory, common sense or past results. We argue that the integration of the design with these elements needs to be taken even further. We view all these elements that make up the body of research methodology in experimental economics as mutually dependant and therefore take a systematic approach to the design of our experimental research program. Rather than drawing inferences from individual experiments or theories as if they were independent constructs, and then using the findings from one to attack the other, we recognize the need to constrain the inferences from one by the inferences from the other. Any data generated by an experiment needs to be interpreted jointly with considerations from theory, common sense, complementary data, econometric methods and expected applications. We illustrate this systematic approach by reference to a research program centered on large artefactual field experiments we have conducted in Denmark. An important contribution that grew out of our work is the complementarity between lab and field experiments.

Estimating Subjective Probabilities

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, 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 subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets.

Inferring Beliefs as Subjectively Uncertain Probabilities

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.