Heterogeneity, Censoring and Endogeneity in Estimates of Response to Soft Drink Tax: Finite Mixture Tobit and Censored Quantile Regression Approaches

Public health advocates have suggested taxation of Sugar Sweetened Beverages (SSBs), as a strategy to tackle obesity. There is a growing literature on the issue of potential substitutions between different varieties of beverages in response to SSB tax. Yet, evidence on the heterogeneity of consumer behaviour and reaction to taxes is still lacking. We investigate this issue by identifying the heterogeneity of individual's responses to changes in SSB prices using scanner data. The main motivation of our study is that the beverages are consumed across a diverse population, and most statistical methods look at average effects across populations. Looking at averages hides information that could be crucial for public policy. This study examines the entire distribution of consumption. Large numbers of households may consume only small amounts of SSBs. The average effect may unduly reflect their reactions, while the heavy drinkers are those most prone to be obese. This study investigates (i) whether heavy consumers of SSB respond differently to a SSB tax and thereby have differing health gains, and (ii) whether light and moderate drinkers of SSBs have a higher tax burden compared to the heavy drinkers of SSBs. A key methodological contribution of this paper is to control for censored demand (when households do not consume a particular beverage), endogeneity of expenditure and prices in a single empirical framework. We use two distinct empirical approaches to address these econometric issues: The first approach a finite mixture instrumental variable Tobit model (FMM IV-Tobit) categorises consumers into latent classes based on their response to economic incentives and their consumption levels and then calculates impact of a SSB tax on each household. The second approach uses quantile regression methods incorporating endogeneity and censoring (CQIV). The SSB own-price elasticity estimates from both these approaches show a decreasing trend across increasing quantiles. For, example the elasticities at median quantile for FMM IV-Tobit and CQIV model are -1.28 and -1.62 respectively whereas they decrease substantially at the 90th quantile to -0.21 and -0.41 respectively. We use these quantile level elasticities to calculate reduction in consumption of SSBs which is then converted to kilo joules and reduction in body weight. The main finding of the study is that an increase in price of SSBs via a 20% excise tax or 20 cents per litre ad valorem tax will lead to almost same reduction in body weight of around 0.3 kgs over 50th to 75th quantiles of SSB consumption whereas for heavy drinkers (from 75^th to 100^th  quantile), the reduction in body weight for excise tax is much higher (0.41 kgs to 1.45 kgs respectively) compared to that under ad valorem tax (0.35 kgs to 0.6 kgs). The associated yearly per capita tax burden under both of these tax regimes is negligible varying from $11 to $25 across quantiles. Our findings show that heavy purchasers of SSBs (who are the main target of obesity reduction policies), will experience even greater weight reductions and face negligible tax burden as a result of SSB tax.