The aim of the article is to discuss a model used to determine the number of losses in automobile insurance. The model is based on panel data. Although the aim is to model the number of losses, due to hunger for bonus not all the losses are revealed. Thus the data on the number and also the value of claims are used. Common use of these two types of data enables estimation of the true number of losses that occur (not just those that are claimed). This is done with the use of true data from the Polish market. The discussion of particular factors that influence the severity of losses (moral hazard, hunger for bonus, observed and unobserved characteristics of the insured) is included.