Measuring Revisions to Subjective Expectations

This paper develops a new metric to measure revisions to subjective expectations and proposes a survey design strategy that enables the estimation of the metric. As an application, I analyze how women update their expectations about the e¤ectiveness of contraception methods. The women interviewed exhibit substantial heterogeneity in the way they revise their expectations with receipt of the same information. When relating the heterogeneity in the updating process to observable characteristics, I …nd that schooling, having a regular sexual partner and knowledge and use of birth control methods have a large impact on the revision process about the e¤ectiveness of contraceptives. Keywords: subjective expectations, prior/posterior distribution, updating JEL classi…cation: D84, C42, J13. I am indebted to Tim Conley, Chris Taber, Luis Vasconcelos and especially Chuck Manski for extremely valuable suggestions and support. I am grateful to Ran Abramitzky, Sonia Bhalotra, Iliyan Georgiev, Joel Horowitz, Rosa Matzkin, Francesca Molinari, Joel Mokyr, Richard Spady, Joerg Stoye, and seminar participants at Northwestern University, Universidade Nova de Lisboa, University of Wisconsin, the 2005 Society for Economic Dynamics annual meeting and the Econometric Society World Congress 2005 for helpful comments. I am also grateful to the editor, W. Kip Viscusi, and an anonymous referee for comments and suggestions. All remaining errors are my own. Financial support from Northwestern University Graduate Research Grant and a grant from the Searle Fund is gratefully acknowledged. Individuals often make decisions under uncertainty. They use available information to form subjective expectations (i.e., subjective probability distributions) about the uncertain events, and rely on these expectations to make decisions. To better understand and predict behavior, it is thus essential to determine how individuals form and revise their subjective expectations. In this paper, I develop a method to measure revisions to subjective expectations about binary outcomes. The proposed method has two components: a ‡exible metric to characterize the revision process and an innovative elicitation strategy. As an application, I analyze how women update their expectations about the e¤ectiveness of contraceptives. Belief revision involves updating the probability that an event occurs when new information becomes available. Identifying the mechanisms of revisions to expectations is challenging. First, individuals receive various types of information, such as media reports or friends’opinions, that may not be generated by a simple statistical process, and leave scope for interpretation. Second, individuals may use idiosyncratic rules to revise their beliefs. Thus, an observed revision of subjective expectations can be generated by many alternative combinations of interpretation of the data and updating rules. While it is di¢ cult to identify the actual revision process, one can provide a simple structural representation of it. This representation is obtained by a procedure “reversing”Bayes’rule, i.e. by solving for the implied distribution of new information that would have led to the observed posterior distribution given the individuals’priors. Focusing on the application presented in this paper, consider a woman learning about her probability P of getting pregnant while using a particular birth control method. Following the acquisition of new information, her revision process from prior to posterior beliefs about P can be characterized by the random sample of pregnancies and no-pregnancies (i.e., the number of ones and zeros, respectively) drawn from the Bernoulli distribution of probability P; that would have generated the observed revision, had she used Bayes’rule. I call this metric the Equivalent Random Sample (ERS). Parametric assumptions on the class of distributions of beliefs ensure existence and uniqueness of the ERS, i.e. given knowledge of the parameters characterizing the prior and the posterior distributions, one can back out the random sample of zeros and ones that would have led to a Bayesian updating. The ERS is fully characterized by its sample size (the total number of zeros and ones), which re‡ects the informativeness or precision of the new information, and the proportion of ones, which represents the mean of the new information. The ERS allows full heterogeneity across individuals’ revision processes and a convenient comparison between them. Psychologists and experimental economists have analyzed how subjects update probabilities in highly stylized situations to test whether respondents rely on Bayes’ theorem when provided with observations drawn from a simple sampling process, such as balls drawn from an urn (e.g., Tversky and Kahneman, 1974; Camerer, 1987). It has been found that individuals employ certain heuristic rules to process information, rather than Bayes’ rule. In particular, individuals are claimed to be excessively conservative and fail to