The goal of this article is to apply panel data approach to the analysis of claim frequency in automobile insurance. The model which is constructed estimates the influence of particular characteristics of the insured on their insurance loss number, but it also enables identification of the hunger for bonus effect. Panel data approach allows for identification of drivers' individual effects that influence their driving quality, but cannot be quantified directly, such as for example tendency to drive fast. This is done thanks to repetitive observation of the same individuals. Having information on their number of losses claimed in different bonus-malus system classes, it is possible to separate their individual skills from the hunger for bonus phenomenon, as well as identify the scale of the latter, which differs in particular classes. Chapter one is an introduction. In chapter two main benefits from the use of panel data have been described. Recent publications considering the topic are mentioned as well, with emphasis on the differences between other authors' approaches and this one. Chapter three contains a brief description of the methods applied, which are Poisson regression mixed models. In chapter four the basic model is adjusted to the conditions of hunger for bonus and it is shown, how this phenomenon is identified. In chapter five empirical analysis based on the real market data of approximately 21 thousand observations is done. The model is estimated and the conclusions are discussed with a short simulation study of the insurance company financial state.