Rational Addiction and Smoking when there are Legal and Illegal Cigarettes

We propose an extension of the often used rational addiction model. Our model includes both legal and illegal cigarettes. The model is tested on a Swedish data set covering the aggregate legal and illegal cigarette markets. When we treat legal and illegal cigarettes as independent demand equations, we find no addiction, but rationality for legal cigarettes, and rational addiction for illegal cigarettes. Since the demand for legal and illegal cigarettes is probably best considered as simultaneously determined, we have also estimated a "semi-reduced" system. Legal cigarettes are negatively related to their price while illegal cigarettes are positively related to the legal price. This indicates that, as expected, the drawback of excise duty on legal cigarettes is that more agents are attracted into the illegal cigarette market. When testing the hypothesis of a common habit stock for legal and illegal cigarettes, the results are mixed. It cannot be ruled out that legal and illegal cigarettes accumulate two separate habit stocks. The proposed model is applicable to any situation with two a addictive consumption goods.