Subjective Expectations: Test for Bias and Implications for Choices

In expected utility models, individuals' choices critically depend on their subjective expectations of future events (Manski 2004). A common approach in the literature is to evoke the rational expectations assumption and substitute objectively estimated state transitions in the data for the subjective probabilities that individuals assign to future events. This methodology takes a strong stand that individuals' subjective expectations should coincide with objective estimates in the data, which rules out the possibility of biased expectations. This restriction might not be warranted in empirical work, and may lead to misspecification of the model and misleading conclusions regarding individuals' behaviors and the effectiveness of different public policies. In this paper, I relax the rational expectations assumption by directly using subjective expectations elicited from individuals. I theoretically show that the data on subjective expectations can identify the distribution of individuals' expectation bias. Combined with individuals' choices, the subjective expectations data can further be used to identify the structural parameters of binary choice models. In the empirical part of the paper, I focus on individuals' subjective survival probabilities available from the survey data, show how the mortality expectations affect individuals' smoking decisions and discuss policy implications. The theoretical methods developed in this paper provide the tools to quantitatively understand individuals' subjective expectations and their relation to the objective counterparts in the data. In particular, non-parametric identification of individuals' expectation bias can be used to test the rational expectations assumption, assess the extent of individuals' unobserved heterogeneity, and identify the difference in relative importance of factors for subjective versus objective probabilities in the data. In empirical analysis, I propose a new dynamic approach to the formation of subjective expectations, which allows me to back out, in a forward-looking fashion, the one-period ahead subjective expectations of the agents from their expectations of multi-step ahead events elicited in the survey. Applying this method to the subjective longevity expectations from the Health and Retirement Study, I find that while the factors that individuals take into consideration are similar to those identified in the objective mortality data, the relative weights placed on factors can be quite different in the two approaches. For instance, high income and good health tend to increase expected longevity, both objectively and subjectively, However, I find that individuals subjectively put a disproportionately large weight on genetic information and small weight on their health-related choices, relative to the objective estimation. Subjective expectations are further used in a structural dynamic model of smoking choice. I find that individuals subjectively care more about their health and are more forward-looking than estimated based purely on objective data. Hence, the reason that people smoke is not that they do not care about their health or that they are myopic, but that they put much more weight on their genetic makeup and too little weight on their health-related behaviors. The direct implication of these results for public policy is to design information campaigns in a more personalized way to decrease this bias in individuals' subjective expectations.

Risk Behavior

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