Some limits on taxing sin: cigarette taxation and health care finance.

• Author: Jackson, John D.

1. Introduction

   Politicians have long known the advantages of levying excises on items that the electorial majority view with disfavor. Discriminating against the consumption of these goods appeals to the puritanical prejudices of the majority. In addition, these "sinful" goods typically have an inelastic demand which makes them excellent instruments for raising governmental revenue. Although, historically, the individual state governments have been the major promulgators of these taxes, the federal government, faced with projected revenue short falls in many social programs, has been considering expanding their participation in this type of tax. Independent of the many arguments for or against such taxation policies, is the question of how much additional revenues can be generated by instituting new taxes or increasing existing taxes. Even a difference as small as .2 percent in projected revenue growth can lead to billions of dollars differences between projected and actual tax revenues.(1) In particular, problems arise in forecasting tax revenue when evaluating proposals for large discrete changes in tax rates. Using the 1993 President's Task Force on Health Care Reform's proposals to raise federal taxes on cigarettes as an example, we identify problems in forecasting revenue based on constant elasticity demand models and suggest an alternative methodology to lessen the errors.

   In early 1993, the President's Task Force on Health Care Reform led to two proposals to increase federal taxes on cigarettes. One doubled the tax from its current $.24 per pack to $.48 per pack. The other increased the tax by $2.00 to $2.24 per pack. The former policy was projected to increase revenues by $3b the first year [5]. The latter proposal, the extremism of which seems to have gotten everyone's attention, had several different scenarios. Depending on who is doing the forecasting, it will raise between $18b [5] and $28b [10] per year. Continuing the debate, Grossman [8] suggested that a $1.26 tax per pack would maximize revenue from the tax at $16b.(2) Even though the enthusiasm for national health care legislation has waned, there is still a lesson to be learned from these policy proposals. The lesson is this: there are limits to taxation, even to the taxation of sin.

   All of the tax scenarios outlined above (except Grossman's) are based on the assumption of a constant elasticity demand curve. This assumption, combined with the assumption of inelastic demand, implies that tax rate increases will lead to increased tax revenues, and hence highlights an important limitation on taxing sin: If these assumptions are correct, the revenue maximizing tax rate is infinite; because higher tax rates would always yield higher tax revenues. This reductio ad absurdum argument illustrates an important tenet of empirical demand analysis: the assumption of constant elasticity of demand beyond some limited, often small, range of price-quantity combinations is analytically untenable.

   A second problem arises due to interstate variation in state level cigarette taxes. These rates, which account for most of cigarette price variation across the states, are quite high in some states and comparatively low in others. Assuming smoking preferences do not vary from state to state, a sizeable increase in the federal tax on cigarettes could price smokers in some (high tax) states out of the market while leaving smokers in other (low tax) states only slightly affected. The import of this observation becomes clear once we consider the equity aspects of using the federal tax revenues to finance national health care. Even if the aggregate forecasts of federal tax revenue were correct, a large increase in the federal levy in combination with existing state taxes could end up pricing smokers in numerous states out of the market so that national health care would be financed only by smokers in a few low tax states.(3) Furthermore, these types of problems arising from variation in state level taxes are completely ignored when the analysis of federal cigarette taxation is conducted at the aggregate national level.

   The object of this paper is to address these two problems and thereby provide some insight into the limits of sin taxation. Specifically, we estimate a cigarette demand function in which the consumer can be priced out of the market, and we compute all tax effects at the state level and aggregate them to find the national revenue impact of federal cigarette tax increases. The paper proceeds as follows: In section II, we attempt to model cigarette demanded by integrating the procedures that Becker, Grossman, and Murphy [2] use to estimate a rational addiction model of smoking behavior with bootlegging predictions from the endogenous smuggling model of Saba, Beard, Ekelund, and Ressler [17]. The resulting model is estimated as a fixed effects (combined time series-cross section data with state dummies) model using two stage least squares. In section III we conduct two experiments, using the estimates of section II, to illustrate the limits of federal cigarette taxation. First we provide interval estimates of the choke price of cigarettes by state. The upper limits of these estimates range from a low of $3.59 per pack for Utah to a high of $7.57 per pack for New Hampshire. In addition, we consider the question of how much federal tax revenue would be generated, by state, under alternative tax rate scenarios. At least two interesting results come out of these experiments. First, if federal taxes are raised by $2.00 per pack (to $2.24/pack), representative individual demand would be choked off in thirteen states, resulting in the generation of less than 80% of current federal tax revenue from that source. Second, our estimates suggest that the revenue maximizing tax is about fifteen cents lower than Grossman's, i.e., about $1.10 per pack, for a $13.5b federal tax yield. In the concluding section of the paper we provide caveats concerning our analysis and present our conclusions concerning the limits of taxing sin.

2. Estimating the Demand for Cigarettes

   Our introductory remarks suggest that a crucial element in deriving accurate forecasts of the revenue attributable to an increase in cigarette excises is a reliable estimate of the demand function for cigarettes. There have been numerous attempts to estimate the demand for cigarettes. Some of the earlier efforts are reviewed in Baltagi and Levin [1]; salient aspects of more recent efforts are discussed by Grossman, et al. [9]. However, two recent advances in the estimation of cigarette demand lead us to submit that there may be room for yet another estimated model. The two advances are estimates of the rational addiction model by Becker, Grossman, and Murphy [2] and the endogenous smuggling model of Saba, Beard, Ekelund, and Ressler [17]. The remainder of this section integrates these two views into an empirical model of cigarette demand which incorporates the strengths of both approaches.

   The Rational Addiction Empirical Formulation

   Becker, Grossman, and Murphy [2], hereafter BGM, assume that the current utility of the representative individual is determined by current and lagged cigarette consumption, a composite good whose price is normalized to unity, and some unmeasured life cycle variables. The individual attempts to consume cigarettes and "all other goods" so as to maximize the discounted present value of his utility subject to two constraints, one specifying the initial value of cigarette consumption, the other stating that the current value of his wealth holdings must equal the discounted present value of his future income stream. The first order conditions for maximization are intuitively appealing: The marginal utility of consuming all other goods must equal the marginal utility of wealth, and the sum of the marginal utility of current cigarette consumption and the discounted marginal effect of current consumption on next period's utility must equal current cigarette price weighted by the marginal utility of wealth.(4)

   BGM derive a cigarette demand function based on this general model by assuming a quadratic utility function and substituting the first order conditions for consuming all other goods into the first order conditions for consuming cigarettes. The resulting second order linear difference equation expresses current cigarette consumption ([Q.sub.t]) in terms of future ([Q.sub.t+1]) and past cigarette consumption ([Q.sub.t-1]), current cigarette price ([P.sub.t]), and current and future life cycle effects. They further operationalize the model by proxying life cycle (and other exogenous) effects by (per capita) income ([Y.sub.t]), fixed state effects (state dummy variables), and some time dummies indicating dissemination of information on the health hazards of smoking. Finally, because the available data is on cigarette sales rather than cigarette consumption (by state), BGM create several measures to account for bootlegging.

   Although the BGM model is an improvement over prior efforts in virtually all areas, its measures of bootlegging remain ad hoc. BGM propose three proxy measures for smuggling: short distance importing (SDBLIM[P.sub.it]), short distance exporting (SDBLEX[P.sub.it]), and long distance smuggling. Each of these measures is a function of the relevant interstate tobacco tax differences weighted by a measure of market penetration for the importing state. These weights are determined by the percent of population living within an arbitrarily determined market area, 20 miles from the low tax state in...