In most economic models of damage compensation, the indemnity is proportional to the fault and victims have to file the claim. Contrary to the tort law approach, a growing number of reparation mechanisms choose to ignore the fault ("no-fault law") to compensate damages in their entirety. The Badinter law, which regulates the compensation of damages from traffic accidents in France, is a perfect example. One particular feature of this setting is that the party paying for the damages is likely to have imperfect information on the actual value of the loss and has to make an out-of-court offer. In turn, the victim has the option to accept the offer or to go to court. This study develops a model with these particular features based on the fact that unobserved component of the damages are correlated with observed ones. Estimation of the model is conducted on AGIRA files for all settlement between 2004 to 2006. We find a negative correlation between observed and unobserved dimensions of damages. The model explains the fact that compensations for each component of the damage is higher in out-of-court settlements, while the global indemnity is higher for in-court settlements and is mainly chosen by the most injured.
