Heinrich's pyramid, which postulates that the severity distribution of occupational accidents is relatively constant, is one of the main tools for management of occupational safety. However, existing evidence suggests that decreases in minor accidents have not always been followed by similar decreases in serious and fatal accidents. To test the statistical validity of the pyramid, we propose a Bayesian two-part model: the first part estimates accident rates using a Poisson-gamma distribution, and the second part estimates the proportion of minor, serious and fatal accidents using a Multinomial-Dirichlet distribution. If this proportion does not change when the accident rate is reduced, then the statistical validity of the pyramid is confirmed, but if it changes, then its validity is refuted. Our data cover more than 50,000 companies observed over 28 months in Chile. Heinrich's pyramid is confirmed to be statistically invalid for different economic activity sectors and geographic regions, but the discrepancy is so small that, for practical purposes, the pyramid is valid. We thus conclude that the occurrence of minor accidents is a useful signal for assessing and forecasting the overall safety performance of a firm.
Economists have become increasingly interested in using attention to explain behavioral patterns both on the micro and macro level. This has resulted in several disparate theoretical approaches. Some, like rational inattention, assume a "top-down" model of executive optimization. Others, like salience theory, assume a "bottom-up" influence where attention is driven by contextual factors. This distinction is fundamental for the economic implications of attention, but so far there is little understanding of their relative importance. We propose a multi-attribute random utility model that unifies prior theoretical approaches by distinguishing between the impact of top-down and bottom-up attention. We accomplish this by separating agent-specific and decisionspecific variation in attention and verify our framework in an eye-tracking experiment on risky choice. We find that both top-down and bottom-up attention are connected to important choice variables: both are associated with the weighting of the attributes of choice options, while top-down attention is additionally associated with measures of loss aversion. We discuss the insights regarding the nature of attention and its role in economic theory.
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