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We repeatedly elicit beliefs about the returns to study effort, in a large university course. A behavioral model of quasi-hyperbolic discounting and malleable beliefs predicts that the dynamics of beliefs mirrors the importance of exerting self-control, such that believed returns increase as the exam approaches, and drop post-exam. Exploiting variation in exam timing to control for common information shocks, we find this prediction confirmed: average believed study returns increase by about 20% over the period before the exam, and drop by about the same amount afterwards. Additional analyses further support the hypothesized mechanism that beliefs serve as a means of self-control.
We examine the additivity of stock-market expectations over different time intervals. When asked about a ten-year interval, survey respondents expect a stock-price change that is not equal to, but closer to zero than, the sum of their expectations over two shorter time intervals that cover the same ten years. Such sub-additivity is irrational in that it cannot stem from aggregating short-term expectations. Model estimates show that the pattern is consistent with a time perception where shorter time intervals have a proportionally larger weight. We also find that the respondents’ degree of additivity is correlated with making larger financial investments.