A Behavioral Model of Forecasting: Naive Statistics on Mental Samples

Most operations models assume individuals make decisions based on a perfect understanding of random variables or stochastic processes. In reality, however, individuals are subject to cognitive limitations and make systematic errors. We leverage established psychology on sample naivete to model individuals’ forecasting errors and biases in a way that is portable to operations models. The model has one behavioral parameter and embeds perfect rationality as a special case. We use the model to mathematically characterize point and error forecast behavior, reflecting an individual’s beliefs about the mean and variance of a random variable. We then derive 10 behavioral phenomena that are inconsistent with perfect rationality assumptions but supported by existing empirical evidence. Finally, we apply the model to two operations settings, inventory management and queuing, to illustrate the model’s portability and discuss its numerous predictions. For inventory management, we characterize order decisions assuming behavioral demand forecasting. The model predicts that even under automated cost optimization, one should expect a pull-to-center effect. It also predicts that this effect can be mitigated by separating point forecasting from error forecasting. For base stock models, it predicts that safety stocks are too small (large) for short (long) lead times. We also express the steady-state behavior of a queue with balking, assuming rational joining decisions but behavioral wait-time forecasts. The model predicts that joining customers tend to be disappointed in their experienced waits. Also, for long (short) lines, it predicts customers have more (less) disperse wait-time beliefs and tend to overestimate (underestimate) the true wait-time variance.