Optimal compulsion when behavioral biases vary and the State errs

When behavioral biases have varying sizes, and the State seeks to correct behavior through compulsion, the question is how to design optimal compulsion. One argument is that the amount of compulsion should rise with the size of the bias to be 'cured'. A contrary argument is that since compulsion affects actions, and recommended actions are independent from the bias, the amount of compulsion should not depend on the bias. This puzzle is solved for the case where individuals are affected by a bias that leads them to under-save, acknowledging that the planner predicts each individual's optimal action with error. Since only low-bias individuals are able to correct the planner's mistakes when mandated to save too little, but not in the opposite direction due to a costly spread, the optimal amount of compulsion rises with the predicted bias. As an application, the paper explores a behavioral rationale for a Maximum for Taxable Earnings (MTE). It finds that if (1) the State's information is limited to current earnings; (2) earnings do not influence the earnings ratio for old age; and (3) the bias is smaller only for the highest earnings quintile, then a MTE near the 80th percentile of the earnings distribution is optimal.