Estimating elasticities of substitution for sin goods

Own-price and cross-price elasticities of substitution are estimated for the six ‘sin’ goods of spirits, beer, wine, casino gambling and lotteries using aggregate U.S. quarterly national data. The own-price and cross-price elasticities of substitution are not constrained to be constant over the sample and are estimated using the Fourier flexible form. There is evidence of much variation in substitution over the sample, including during the recessions. All ‘sin’ goods, except lotteries, have inelastic demands. Beer and tobacco have the most inelastic demands which are consistent with the evidence that beer is the most popular type of spirit while tobacco products are often considered addictive commodities. The three types of alcohol of spirits, beer, and wine are Morishima cross-price substitutes. Casino gambling and lotteries are Morishima cross-price substitutes having an elastic response to price changes in casino gambling but have and inelastic response for price changes of lotteries. Estimates show that the remaining ‘sin’ goods are complements in use. Policy makers must consider how a tax on a ‘sin’ good will impact demand for the good partially based on its own-price elasticity of demand as well as the cross-price elasticity of substitution or complementarity relationships with other ‘sin’ goods.