New estimates of the optimal tax on alcohol.

Kenkel, Donald S.

I. INTRODUCTION

Over the past decade, federal taxes on alcoholic beverages have been increased twice, first in 1984 and again in 1990, to raise revenue and reduce the federal deficit. Many states also increased alcohol taxes, again usually prompted by revenue concerns. The recent experience is in sharp contrast with the long-term trend of declining real alcohol taxes, due to inflation eroding the real value of excise taxes fixed in nominal terms. Figure 1 shows the average tax rate on alcoholic beverages, including federal, state, and local taxes.(1) The average tax rate was over 50 percent of the net-of-tax price (that is, the price exclusive of taxes) in 1954, but declined to below 25 percent by the beginning of the 1980s. Nominal increases during the 1980s only served to keep the real tax rate roughly constant at slightly above 20 percent.

Aside from revenue concerns, taxing alcohol is possibly justified on Pigovian grounds because of the external costs associated with excessive alcohol consumption. The most dramatic external costs are the thousands of non-drinkers killed by drunk drivers each year. Most of the remaining external costs stem from the adverse health effects of heavy drinking, which create medical and other costs that are only partly borne by the drinker. In light of the external costs, a number of economists have supported alcohol tax increases, some via a petition to Congress. Several recent empirical estimates suggest that the optimal tax rate is about double the current rate, but the range of estimates has been extremely wide, from 19 to 306 percent.(2)

In this paper I use a new data set to estimate most of the key determinants of the optimal alcohol tax rate, in an attempt to narrow the range of plausible estimates. Choosing the optimal alcohol tax involves balancing the deadweight welfare losses taxation creates as moderate drinking falls with the welfare gains created as socially costly heavy drinking is reduced. The relative price elasticities of the demand for moderate and heavy drinking are therefore key determinants of the optimal tax rate, but empirical evidence on these elasticities is limited.(3) An important contribution of this paper is to estimate separately the price elasticities of the demand for moderate drinking and the demand for heavy drinking. The demand for heavy drinking is estimated to be at least as price elastic as the demand for moderate drinking, implying there is considerable scope for alcohol taxation to improve social welfare.

As a benchmark, the empirical results imply that the optimal tax rate is over 100 percent of the net-of-tax price, higher than many other recent estimates, and about five times the current average rate. However, in the framework used alcohol taxation is a second-best solution to some of the social costs created by heavy drinking. An important question is the extent to which the optimal tax would fall if other, more direct policies were also used. The analysis therefore turns to estimating the optimal tax rate under alternative policy scenarios.

In this and other studies, a large portion of the external costs of heavy drinking actually stem from drunk driving. The most direct policy response is to increase the certainty and severity of drunk driving penalties. If penalties for drunk driving were certain and severe enough to force drunk drivers to see the full social costs of their actions, the estimated optimal alcohol tax rate falls to 42 percent, less than half the benchmark estimate and much closer to current rates. This suggests that stricter drunk driving laws deserve consideration as policy substitutes for alcohol taxation.

This paper also incorporates imperfect consumer information as an additional reason alcohol taxation may be a desirable second-best policy.(4) Heavy drinking has serious health effects, but many drinkers are unaware of at least some of these (for evidence on this point, see Kenkel [1991]). This means some internal health costs are in fact uninternalized, so taxation creates welfare gains for uninformed heavy drinkers. Government provision of information about the health consequences of heavy drinking would remove part of the rationale for alcohol taxes. The empirical analysis concludes that correcting the problem of imperfect consumer information (leaving drunk driving penalties at current levels) would cause the optimal tax rate to drop to 78 percent.

The next section uses a simple framework to derive a formula for the optimal tax rate. Section III describes the new empirical estimates of the demand for alcohol. Section IV describes the sources used to estimate the remaining determinants of the optimal tax rate. Section V presents new estimates of the optimal tax rate under alternative policy scenarios and compares the results to previous estimates. Section VI concludes.

II. FRAMEWORK FOR OPTIMAL ALCOHOL TAXATION

This section develops the framework for optimal alcohol taxation to be empirically implemented below. The framework is based on that developed by Pogue and Sgontz [1989], but it has been extended to incorporate (i) the relationship between drunk driving deterrence policies and the optimal tax rate, and (ii) imperfect consumer information.(5)

The Framework and Assumptions

It is assumed there are at least three types of drinking: moderate drinking, heavy drinking by informed consumers, and heavy drinking by uninformed consumers. The empirical analysis below will distinguish several categories of imperfectly informed consumers, but this only represents a slight complication for the analysis and formulas. Figure 2 shows compensated alcohol demand schedules for moderate drinking ([D.sub.A]), informed heavy drinking ([D.sub.B]), and uninformed heavy drinking ([D.sub.C]).(6) The distinctions between types of drinking are on practical grounds: heavy drinking is used here to describe consumption at high enough levels to generate costs for the drinker and society. The distinction applies to drinking, not drinkers. For example, even a typically moderate drinker creates costs for himself and others if he drinks heavily one evening. Similarly, the same consumer may display different price elasticities when drinking heavily than when drinking moderately.(7)

The uninformed heavy drinking demand schedule reflects the consumer's failure to internalize all of the health costs of heavy drinking. The vertical distance between [D.sub.B] and [D.sub.C] is the dollar value of the internal health costs, H.(8) There are several types of mistakes poorly informed consumers can make. The case shown in Figure 2 results if consumers are unaware of some health risks, underestimate the risk levels, or overestimate the rates of cure for some conditions. Other consumers may incorrectly believe that alcohol creates more health costs than it actually does. The demand schedule for this type of consumer is not shown in Figure 2, but would lie below [D.sub.B], reflecting the consumer's internalization of nonexistent health costs. Viscusi [1990] suggests this is not a far-fetched possibility: he estimates that both smokers and nonsmokers greatly overestimate the lung cancer risks of smoking, perhaps because of the extensive publicity about these risks. The empirical importance of this type of poor information about the health risks of drinking is explored below.

It is further assumed that there is only one alcoholic beverage and that it is produced in a competitive industry at a constant marginal cost equal to the net-of-tax price, P. Saffer and Chaloupka [1994] show that the optimal tax may vary by beverage type, but the nature of the drinking measures in the data used below requires the assumption of a single alcoholic beverage. The competitive assumption means that the alcohol tax is fully passed through to the price consumers pay. The alcoholic beverage industry is probably better described as oligopolistic, but the implications for tax incidence are unclear. Cook [1981] and Cook and Moore [1993a] suggest that under an oligopoly a tax rate of t may increase price by either less or more than t percent, instead of exactly t percent as assumed here. The results of this paper can be reinterpreted under varying assumptions about tax incidence under oligopoly. Where I conclude that the optimal tax rate is t percent, the reinterpretation is that the optimal tax rate is that rate which would cause price to increase by t percent.

Marginal external costs are assumed to be negligible for moderate drinking but to increase as the consumption level increases. Heavy drinking by both informed and uninformed consumers imposes substantial external costs on the rest of society. The social marginal cost schedule is the vertical sum of the private marginal cost P and the marginal external costs E. The external costs E measured in the alcohol market include costs drinkers impose on others through publicly financed health care programs and private insurance markets but exclude costs created by traffic fatalities due to drunk driving. In principle the included costs are also not created by alcohol consumption per se, but can be traced back to more basic failures in public programs and private insurance markets. This paper treats the design of public and private insurance as given.

The external costs of drunk driving are depicted in Figure 3. The demand schedule for drunk driving, [D.sub.y], shows the amount an individual drives drunk as a function of the expected penalty costs, Q, holding everything else, including the price of alcohol, constant. If drunk driving were not penalized (Q = 0), this typical individual would choose to drive drunk [y.sub.0] times, but at the current expected penalty cost of [Q.sub.1] the individual drives drunk less often. The potential drunk driver is assumed to be fully rational and informed, so the demand schedule reflects the internal costs created because the drunk driver is a danger to himself. Phelps [1987] presents evidence that at least young drivers typically underestimate this danger. The analysis of uninformed drunk drivers parallels the analysis of uninformed heavy drinkers, but is not undertaken here because it can not be implemented with available data.(9)

The marginal external costs of drunk driving are assumed to be constant at F, on the assumption that the probability that an occasion of drunk driving results in the death or injury of a non-drinker does not depend on the quantity of drunk driving.(10) As drawn, it is assumed that the current expected penalty costs [Q.sub.1] fall far short of F, so the external costs are not fully internalized by the drunk driver. The empirical basis for this assumption is described below in section IV.

Optimal Tax Analysis. The welfare effects of taxing alcohol are now described, beginning in the market for alcohol. When a unit tax of amount T is imposed, alcohol consumption accounted for by each type of drinking falls by an amount [Delta][x.sub.I], I = A, B, C. The deadweight consumer's surplus lost from taxing moderate drinking is given by the area a in Figure 2. The net welfare gain per informed heavy drinker is the reduction in external costs, given by [E.sub.B][Delta] [X.sub.B], less the deadweight loss of consumer surplus of area b, for a net gain given by area eb. Taxation creates private welfare gains for the uninformed heavy drinker as well as social gains.(11) The net welfare gain per uninformed heavy drinker is the reduction in external costs, [E.sub.C] [Delta] [X.sub.C] given by area [e.sub.c], plus the reduction in uninternalized internal health costs, [H.sub.C] [Delta] [X.sub.C] given by area h. The quantities [E.sub.B], [E.sub.C], and [H.sub.C] (not shown in [ILLUSTRATION FOR FIGURE 2 OMITTED]) represent the marginal external costs and health costs averaged over the relevant change in consumption.

The tax on alcohol also creates an additional welfare gain because there are uninternalized external costs of drunk driving. As the price of the complementary good alcohol increases, the amount of drunk driving decreases by [Delta]y. External costs of drunk driving are reduced, yielding a welfare gain of (F - [Q.sub.1]) [Delta]y given by the area [f.sub.1] in Figure 3. Clearly, the extent to which expected penalty costs fall short of the marginal external costs determines the size of this welfare gain. If stricter deterrence policies were enacted so that the expected penalty cost increased to [Q.sub.2], the welfare gain is the much smaller area [f.sub.2].

The aggregate welfare gain of imposing a tax T on alcohol is given by

(1) W= [([T.sup.2][[Eta].sub.A][X.sub.A])/2 P] - [([E.sub.B]T[[Eta].sub.B][X.sub.B])/P] + [([T.sup.2][[Eta].sub.B][X.sub.B])/2P] - [([E.sub.C] + [H.sub.C])T[[Eta].sub.C][X.sub.C]/P] - [(F - [Q.sub.1])T[Epsilon]Y/P].

In equation (1) [X.sub.1] is the aggregate consumption of alcohol and [[Eta].sub.I] is the price elasticity of the demand for drinking in categories I = A, B, C. The aggregate amount of drunk driving is Y, and [Epsilon] is the cross-price elasticity of the demand for drunk driving with respect to the price of alcohol. The first term in equation (1) gives the deadweight consumer's surplus lost by moderate drinkers, the next two terms are the net welfare gains from taxing informed heavy drinkers, the next to last term gives the welfare gain from taxing uninformed heavy drinkers and the last term is the welfare gain from reducing drunk driving.

To find the optimal tax, T is chosen to maximize the welfare gains W given by equation (1). Solving the first-order condition for T/P [equivalent to] t yields the optimal tax rate:

(2) t = ([E.sub.B]/P){1/[[[Eta].sub.A][X.sub.A]/[[Eta].sub.B] [X.sub.B]) + 1]} + [([E.sub.C] + [H.sub.C])/P]{1/[([[Eta].sub.A][X.sub.A]/[[Eta].sub.C][X.sub.C]) + ([[Eta].sub.B][X.sub.B]/[[Eta].sub.C][X.sub.C])]} + [(F - [Q.sub.1])/P] {1/[([[Eta].sub.A][X.sub.A]/[Epsilon]Y) + ([[Eta].sub.B][X.sub.B]/[Epsilon]Y)]}.

As can be seen in equation (2) the optimal tax rate depends on the relative sizes of the different categories of drinking (where size is measured by the categories' aggregate alcohol consumption) and the relative elasticities of demand. Since taxation creates only welfare losses for moderate drinkers, the optimal tax rate is lower when moderate drinking accounts for a greater share of the alcohol consumption, or is relatively more responsive to price than the other types of drinking. The optimal tax rate is higher when uninformed heavy drinking or drunk driving is high, and when uninformed heavy drinking and drunk driving are relatively responsive to price. The optimal tax also increases with the external costs of heavy alcohol consumption by informed and uninformed heavy drinkers ([E.sub.B] and [E.sub.C]), the health costs uninformed drinkers fail to recognize ([H.sub.C]), and the uninternalized external costs of drunk driving (F - [Q.sub.1]).

If there were no uninformed heavy drinkers and the external costs of drunk driving are measured in the alcohol market, equation (2) reduces to Pogue and Sgontz's [1989] equation (6). As they note, if it were possible to tax only those drinkers that create external costs, the formula simplifies further to the standard Pigovian tax rate for correcting an externality.

III. THE DEMAND FOR ALCOHOL BY CATEGORY OF DRINKING

This section presents the empirical estimates of the demand for alcohol by category of drinking, developed to correspond to the model of section II. First, the data and empirical approach are described. The discussion of results that follows focuses mainly on the new price-elasticity estimates and on the role consumer information plays in the demand for alcohol.

The Data

The primary data source used is the Health Promotion and Disease Prevention (HPDP) supplement to the 1985 Health Interview Survey. The Health Interview Survey is a continuing survey of the adult civilian noninstitutionalized population of the U.S., but the 1985 supplement includes special questions on drinking and other health behaviors, and on health knowledge. Alcohol consumption is measured using responses to questions about occasions of heavy drinking in the past year and consumption in the past two weeks. Although the self-reported measures are probably underestimates, Anda et al. [1987; 1988] find that self-reported measures similar to these are well correlated with objective measures of alcohol-related crashes and injuries. Similarly, I find that estimates of the prevalence of heavy drinking by state based on self-reported measures are reasonably well-correlated with objective measures of alcohol consumption and liver cirrhosis rates.(12)

Since the Health Survey data do not include alcoholic beverage prices, the micro data were merged with state-level estimates of average prices. The price estimates are based on data collected by the American Chamber of Commerce Research Association; see Nelson [1990]. The state-average price measures with error the price faced by individual consumers. The empirical analysis uses a border-price measure to address the problem that some consumers may make their purchases in adjacent states with lower taxes. For respondents living within twenty-five miles of a state with lower alcohol prices, the border-price measure is equal to the difference between the state-of-residence price and the adjacent-state price; for all other respondents the measure equals zero. Aside from border crossing, there is remaining price variation within a state depending upon the location of alcohol purchases and consumption. While the resulting measurement error will tend to bias the estimated coefficients on price to zero, the comparisons of price elasticities for different types of drinking crucial for the tax analysis may be unaffected.(13)

As is described more completely in Kenkel [1993b], additional variables related to alcohol availability and state drunk driving laws were also merged with the Health Survey data. Table I contains definitions and means of the variables used in the analysis. After deleting observations with missing values for some of the merged variables from raw samples of about 14,000 males and 19,500 females, the samples used consist of over 12,000 males and 16,000 females.

The Empirical Approach. The empirical counterparts to the categories of drinking used in the model of section II are defined and measured as follows. Moderate drinking is defined as consumption levels below four drinks a day, and heavy drinking [TABULAR DATA FOR TABLE I OMITTED] is defined as drinking five or more drinks in one day. Consumer information is measured by responses to questions about whether heavy drinking increases the risks of three illnesses (throat cancer, cirrhosis of the liver, and cancer of the mouth).

TABLE II

Alcohol Consumption by Type of Drinking

Category of drinking Fraction of Fraction of Fraction of
 males females total drinks

moderate drinking 0.496 0.376 0.638

heavy drinking, consumer 0.010 0.002 0.013
information level 0

heavy drinking, consumer 0.232 0.080 0.217
information level 1

heavy drinking, consumer 0.067 0.025 0.064
information level 2

heavy drinking, consumer 0.073 0.031 0.067
information level 3

Notes: Consumer information level refers to number of illnesses
respondent correctly identified as being associated with heavy
drinking.

Table II provides an overview of the consumption of alcohol due to different types of drinking. By the definition used 38 percent of males and 13 percent of females have engaged in at least one day of heavy drinking. About 50 percent of males and 38 percent of females engaged in moderate drinking. In terms of information, the typical (modal) respondent knew that heavy drinking increased the chances of cirrhosis of the liver, but was unaware of the increased risks of throat cancer and cancer of the mouth. Heavy drinking by the three categories of poorly informed consumers accounts for about 30 percent of all consumption.

Demand equations are estimated using measures of moderate drinking and heavy drinking as dependent variables. Frequency is measured by the number of days of moderate drinking in the past two weeks. Intensity is measured by typical number of daily drinks. To isolate moderate drinking, respondents who report typically consuming five or more drinks are excluded from the samples when the frequency and intensity of moderate drinking demand functions are estimated. The frequency of heavy drinking is measured by the number of days in the past year on which the respondent consumed five or more drinks. It would be better to use different cutoffs for males and females when distinguishing moderate from heavy drinking, say three drinks a day instead of five, to reflect biological differences in average size and metabolism of alcohol. However the data only provide a measure of occasional heavy drinking in the past year using the five drinks cutoff. Less than 5 percent of females reported typically drinking three or more drinks per day of drinking in the past two weeks, so the sample of moderate drinking females would not be very sensitive to a different cutoff. Probably the more important limitation is that the heavy drinking demand function does not reflect the behavior of females who occasionally drink three to four drinks a day. For both males and females, a good measure of the intensity of heavy drinking is not available in the data; the implications of this lack for the optimal tax analysis are discussed below.(14)

Many people report no moderate drinking or heavy drinking, so each of the dependent variables takes a value of zero for fairly large fractions of the sample. To account for this feature of the data, the demand equations are estimated using maximum likelihood tobit. Dubin and Wilde [1991] provide a useful review of a simple consumer optimization problem subject to non-negativity constraints which generates a tobit demand model. An alternative two-part demand model is also used for sensitivity analysis.

The primary explanatory variables of interest are price and consumer information. An interaction term between price and information is included as an explanatory variable in the heavy drinking demand equation to permit different price elasticities for consumers with different information. Additional explanatory variables measure characteristics of the individual and state laws related to alcohol availability and drunk driving countermeasures.

Price Elasticity Estimates. The estimated alcohol demand functions are presented in Table III. The functions are estimated separately for males and females, based on the results of a maximum likelihood ratio test that shows it is inappropriate to pool.(15)

The implied price elasticities from the tobit models are presented in Table IV. Elasticities from tobit models can be calculated in several ways, depending upon the purpose at hand. The optimal tax calculations are based on changes in consumer's surplus. Dubin and Wilde [1991] show that in the tobit model consumer's surplus calculations should be made with reference to changes in observed consumption, to reflect the fact that consumers who purchase a zero quantity before and after the price change experience no loss. All other consumers, including those who change from positive to zero consumption, experience a loss when the price increases. Adjusting the estimated coefficient from the tobit models provides the marginal change in the observed dependent variable, which reflects changes both in the conditional mean of positive consumption and in the probability of positive consumption.(16) The price elasticities in Table IV are based on these marginal changes, calculated at the mean price and quantity.

As shown in Table IV, both the frequency and intensity of moderate drinking are sensitive to price; while demand is usually inelastic the price-elasticity estimates are not that far from -1.0. The results on the effects of price on the frequency and intensity can also be combined to yield the total elasticity of moderate drinking with respect to price. The total price elasticity of moderate drinking is estimated to be -0.828 for males and -0.710 for females; the weighted average total price elasticity is -0.783, where the weights reflect the shares of moderate drinking accounted for by males and females. For comparison, Leung and Phelps [1993] review previous studies that estimate price elasticities of the demand for beer, wine, and liquor ranging from -0.1 to well over -1.0.

For a consumer with average information, the price elasticity of the frequency of heavy drinking is estimated to be -0.522 for males and -1.292 for females. Compared to the price-responsiveness of the frequency of moderate drinking, on average the frequency of male's heavy drinking is less price responsive, but the frequency of female's heavy drinking is more price responsive. As noted above, due to data limitations the price elasticity of the intensity of heavy drinking can not be estimated.

An important result is the significant interaction between consumer information and price, where more-informed consumers are estimated to respond more to changes in price. At the extremes, heavy drinking by the most-informed consumers is much more price elastic than moderate drinking, while the estimated price elasticities of heavy drinking for the least-in-formed consumers are not statistically significantly different from zero. In a general model of alcohol demand it is difficult to predict the sign of this interaction effect. The empirical results are consistent with the argument made by Hochheimer [1981] and others in the health education literature that education programs will have synergistic effects with other policies to regulate alcohol consumption.

The result that heavy drinking by the least-informed consumers is unresponsive to price is open to another interpretation: these consumers may be alcoholics. The least-informed consumers responded that heavy drinking does not increase the risks of any of the three illnesses covered in the survey questions, including cirrhosis of the liver. Denial of adverse consequences is sometimes seen as indicating addiction. This interpretation also helps reconcile the results here with the results of Manning, Blumberg and Moulton [1995]. They estimate that the heaviest drinkers are the least price responsive, and cannot reject the hypothesis that the very heaviest drinkers have perfectly price-inelastic demands. The price/information interaction effect estimated here may reflect the same phenomenon found by Manning, Blumberg and Moulton. The uninformed category consists mainly of very heavy drinkers: females in this category on average self-reported over forty-six days of heavy drinking in the past year, while males in the category self-reported sixty-eight days. Viewed in this light, the result that probable alcoholics are not responsive to price is not surprising.(17)

To explore the sensitivity of the price-elasticity estimates to alternative empirical specifications, the alcohol demand models were re-estimated using a two-part model. The first part uses probit to [TABULAR DATA FOR TABLE III OMITTED] estimate the determinants of the probability that demand is non-zero. The second part uses ordinary least squares to estimate the determinants of demand, conditional on non-zero demand.(18) The empirical results (available upon request) of the two-part model are qualitatively similar to those reported in Table III. The price-elasticity estimates corresponding to those reported in Table IV are different, however, which is part of the motivation for the sensitivity analysis undertaken below for the optimal tax rate calculations.

The Role of Consumer Information in Demand. The model provides estimates of the amount of heavy drinking due to incomplete information about the health costs. If all consumers were aware of the three illnesses associated with heavy drinking referred to in the survey, the empirical model predicts that heavy drinking would fall by 18 percent for males and by 15 percent for females. As a result, the share of total consumption accounted for by heavy drinking would fall from 0.361 to 0.299.

The results can be used to infer the dollar value of the health costs uninformed consumers fail to internalize. Comparing the estimated effects of information and price, it is possible to calculate the price change that is equivalent to being aware of an additional illness associated with heavy drinking. Averaging over males and females, consumers unaware of one of the illnesses associated with heavy drinking fail to internalize an estimated $0.06 of internal costs. Consumers unaware of two illnesses are estimated to fail to internalize health costs of $0.56. An additional question explored is the empirical importance of poorly informed consumers who make the opposite type of mistake and believe more illnesses are caused by heavy drinking than actually are. Analysis of the Health Survey data suggests this type of mistake may be fairly common, but it does not seem to have large effects on heavy drinking. About two-thirds of the sample erroneously believed that heavy drinking increases the chances of bladder cancer, and smaller but still substantial numbers erroneously believed that heavy drinking increases the chances of arthritis (15 percent) and blood clots (33 percent).(19) In models ot reported (but available upon request), a variable measuring the number of illnesses the individual incorrectly believes are related to heavy drinking is included as an explanatory variable in the heavy drinking demand equations. For males, the coefficient is insignificantly different from zero, while for females the coefficient is unexpectedly positive and statistically significant at conventional levels. Although the explanation for the positive coefficient is not clear, overall the results imply that this type of misinformation is not an important determinant of heavy drinking. The empirical importance of other types of mistakes, including the possibility that consumers overestimate cure rates, can not be explored with these data.

Other Results. Due to the focus of this paper, the results for the other determinants of alcohol demand will only be briefly summarized. Both moderate and heavy drinking are lower for older individuals. As income and schooling levels increase, moderate drinking increases. In contrast, heavy drinking is not related to income, and decreases with schooling. Compared to whites, both types of drinking are also lower for blacks and hispanics. Compared to singles, married individuals consume less while divorced individuals consume more. Working and unemployed individuals consume more than people not in the labor force. Self-reported stress increases both types of drinking. Finally, several results have additional policy implications. There is little evidence that consumers cross borders into lower-tax states, given existing tax rate differentials. But the results provide consistent evidence that higher legal drinking ages decrease alcohol consumption, and heavy drinking in particular is estimated to respond to state laws that increase the certainty or severity of punishment for drunk driving (see Kenkel [1993b] for a more complete discussion).

A number of the explanatory variables used in the models reported in Table III are potentially endogenous determinants of alcohol demand. For example, recent studies of the socioeconomic consequences of alcohol consumption by Mullahy and Sindelar [1993], Cook and Moore [1993b], and Kenkel and Ribar [1994] explore the extent to which income, schooling, employment status, and marital status are affected by alcohol abuse. Arguments could also be made that the health information and stress variables are endogenous. The alcohol demand models were re-estimated excluding all potentially endogenous variables to explore the possible biases on the price-elasticity estimates. The results (available upon request) are qualitatively similar to those reported, but generally yield price-elasticity estimates that are larger in absolute magnitude.

IV. ESTIMATES OF THE DETERMINANTS OF THE OPTIMAL TAX

This section begins by rederiving the formula for the optimal tax rate for empirical implementation. The discussion then turns to additional sources to find estimates of the remaining determinants of the tax rate: first, the elasticity of drunk driving with respect to the price of alcohol; and second, the external costs of heavy drinking and the uninternalized external costs of drunk driving, [E.sub.B], [E.sub.C], [E.sub.D], and F - [Q.sub.1]. Finally, I present a summary of empirical estimates of the terms of the optimal tax rate.

Empirical Optimal Tax Formula

To correspond exactly to the empirical analysis, the optimal tax formula derived in section II is modified slightly to include additional categories of uninformed consumers. Although empirically it is possible to distinguish three categories of uninformed consumers, the estimated demand functions provide no evidence that the least-informed category is responsive to price. As a result, this category does not contribute to the aggregate welfare gain when alcohol is taxed and drops out of the formula. Compared to the analysis of section II, the modified optimal tax formula therefore involves one more category of uninformed consumers, denoted by subscript D. The optimal tax rate is then derived as in section II, yielding

(3) t = ([E.sub.B]/P) {1/[([[Eta].sub.A][X.sub.A]/[[Eta].sub.b][X.sub.B]) + 1]}

+ [([E.sub.C] + [H.sub.C])/P]{1/[([[Eta].sub.A][X.sub.A]/[[Eta].sub.C][X.sub.C])

+ ([[Eta].sub.B][X.sub.B]/[[Eta].sub.C][X.sub.C])]} + [([E.sub.D] + [H.sub.D]) / P]

{1 / [([[Eta].sub.A][X.sub.A]/[[Eta].sub.D][X.sub.C]) + ([[Eta].sub.B][X.sub.B]/[[Eta].sub.B][X.sub.B]/[[Eta].sub.D][X.sub.D])]}

+ [(F - [Q.sub.1]) / P]{1 / [([[Eta].sub.A][X.sub.A] / [Epsilon]Y)

+ ([[Eta].sub.B][X.sub.B]/[Epsilon]Y)]}.

Many of the determinants of the optimal tax rate given by equation (3) can be calculated based on the results reported in section III. The discussion turns next to developing estimates of the remaining terms that can not be found in section III results.

Drunk Driving and the Price of Alcohol. In other work (Kenkel [1993b]), I have estimated the demand for drunk driving from the same data described in section III. The results provide the cross-price elasticity that shows how drunk driving responds to increases in the price of alcohol. The elasticity of the demand for drunk driving with respect to the price of alcohol is estimated to be -0.74 for males and -0.81 for females; the weighted average elasticity is -0.75. These estimates are consistent with estimates from the studies of Cook [1981], Evans et al. [1991], and Chaloupka, Grossman and Saffer [1993] that use state data on traffic fatalities as a proxy for drunk driving. For adults, fatality price-elasticity estimates from these studies fall in the range from -0.5 to -1.0.

Estimates of External Costs. Estimates of the external costs associated with heavy drinking and drunk driving are required to complete the calculation of the optimal alcohol tax rate. The best source for the external costs of heavy drinking appears to be the study by Manning et al. [1989]. They estimate that the average external cost per excess ounce of alcohol is $1.19. However, this includes $0.58 of external costs reflecting the lives of non-drinkers killed in alcohol - related traffic accidents, so only $0.61 are external costs of heavy drinking as defined here. (The value of the lives of non-drinkers killed is incorporated in the estimate of the external costs of drunk driving, F, described below.) Manning et al.'s estimate of the external cost per excess ounce can be considered as the average for heavy drinkers, so it is necessary to assume that this is equal to the marginal external costs for both informed and uninformed heavy drinkers. Finally, since a typical drink of an alcoholic beverage contains about a half an ounce of alcohol, $0.61 per ounce corresponds to $0.31 per drink.

The estimate of the uninternalized external costs of drunk driving are based on the results of Kenkel [1993a]. The total annual external costs are measured as the value of the risks drunk drivers create for others. The total costs are then divided by an estimate of the amount of drunk driving, from Health Survey responses to a question about how many times in the past year the respondent drove drunk after having had "perhaps too much to drink." Assuming self-reported drunk driving is under-reported by the same amount Giesman [1987] finds that self-reported expenditures on alcohol are under-reported implies 293 million occasions of drunk driving annually. The average risk that an occasion of drunk driving results in the death of a non-drinker is estimated [TABULAR DATA FOR TABLE V OMITTED] to be 0.00002. The dollar value of this small increase in the probability of death is obtained from the extensive literature on the H value of a statistical life. From studies reviewed by Fisher, Chestnut, and Violette [1989], a fairly conservative estimate of the value of a statistical life is $2 million. This implies the average fatal risk created by an occasion of drunk driving is valued at about $40. To this must be added the value of the injury risks, calculated along similar lines. The estimate of the average external costs created by an occasion of drunk driving is $60.16.

By creating additional costs for the potential drunk driver the legal system effectively internalizes some portion of these external costs. The expected cost of a drunk driving offense to the drunk driver is the probability of a sanction times the dollar value of the sanction, where the probability of a sanction is the probability of arrest times the probability of conviction if arrested. The average dollar value of the sanction is calculated to reflect the average imposition of fines, jail terms, license suspensions and higher automobile insurance costs. Based on the results of Kenkel [1993a], I estimate that the average expected cost of a drunk driving offense is $16.15, leaving $44.01 as F - [Q.sub.1], the estimate of the uninternalized external costs of drunk driving.

Summary of Terms for Optimal Tax Formula. Table V presents a summary of the empirical estimates of the terms of the optimal tax formula. The ratios of the price elasticities and the consumption due to different categories of drinking are calculated from the information provided in Tables II and IV. The estimate of the amount of drunk driving described above is used with the drinking measures to calculate the ratio of moderate drinking to occasions of drunk driving, [X.sub.A]/Y, and the ratio of informed heavy drinking to drunk driving, [X.sub.B] / Y.(20)

Finally, the net-of-tax price is estimated to be $0.36 per drink, based on the assumption that the observed average price per drink of $0.45 includes $0.09 of taxes.

V. ESTIMATES OF THE OPTIMAL TAX RATE

The Optimal Tax Rate under Alternative Scenarios

Putting the pieces together, as a benchmark the optimal tax is estimated to be about 106 percent of the net-of-tax price. However, the framework used emphasizes that alcohol taxation is a second-best solution to the problems created by drunk driving and imperfect consumer information. The next step is to explore the relative importance of these two problems in determining the optimal tax rate.

The first exercise explores the importance of the uninternalized costs of drunk driving in determining the optimal tax rate. The extreme case is to assume that the certainty and severity of drunk driving penalties increases enough to fully internalize the risks created by drunk driving, i.e. F - [Q.sub.1] = 0. Holding everything else constant, making this change causes the optimal tax rate to fall to 42 percent of the net-of-tax price. Since this is much closer to the current average tax rate, the implication is that sufficiently large increases in the certainty and severity of punishment for drunk driving would remove some of the need for new alcohol tax increases.

The next exercise explores how the optimal tax rate would change if all consumers were perfectly informed. This has two effects: (i) the second and third terms of equation (3) drop out; and (ii) the proportion of total drinks accounted for by heavy drinking falls from 0.361 to 0.299, so the ratios [X.sub.A] / [X.sub.B] and [X.sub.B] / Y change. Making the required changes, the optimal tax rate that emerges is 78 percent of the net-of-tax price.

Finally, the optimal tax rate can be calculated assuming that both problems are solved, that is, assuming that all of the external costs of drunk driving are internalized through drunk driving penalties and that all consumers are perfectly informed about the health hazards of heavy drinking. The optimal tax rate under this scenario is 41 percent of the net-of-tax price. It seems counterintuitive that this rate, calculated assuming both problems are solved, is about the same as the rate calculated when only one problem - the external costs of drunk driving - is solved. This occurs because heavy drinking is more responsive to price after the information increase due to the estimated interaction between information and price. To some extent, solving the information problem makes taxes more effective and thus more attractive.

Comparisons with Previous Estimates. The benchmark estimate of 106 percent is higher than several previous estimates. Expressed in terms of the net-of-tax price, Phelp's [1988a] most likely values are in range of 30 to 50 percent. An important difference is that Phelps only considers the welfare gains created as alcohol taxes decrease the amount of drunk driving by young adults. As Phelps [1988b] notes, extending the analysis to include the effects of alcohol taxes on older adult drivers implies a larger tax rate. Pogue and Sgontz [1989] present a very wide range of estimates (from 19 to 306 percent), but their best-guess estimate is 51 percent, also lower than the benchmark rate. Since this paper uses an extended version of Pogue and Sgontz's framework, a more detailed comparison of my estimate and their estimate is possible. Closer examination reveals a number of differences which partially cancel each other out.

The benchmark tax rate tends to be higher than Pogue and Sgontz's estimate because it reflects the private welfare gains taxation creates for the uninformed heavy drinker. The best-guess estimate of 51 percent by Pogue and Sgontz only reflects the welfare gains taxation creates for the rest of society. They also analyze the possibility that taxation creates private welfare gains for alcoholics; if so, their best-guess tax rate increases to 306 percent. This estimate in turn is much higher than the benchmark tax rate because Pogue and Sgontz assume that there are large uninternalized internal costs associated with alcoholic's overconsumption. While I estimate that a poorly informed drinker fails to internalize health costs worth at the most $0.56 per drink, Pogue and Sgontz assume the internal abuse costs for an alcoholic are equivalent to $1.72 per drink.

Compared to Pogue and Sgontz, the benchmark tax rate also tends to be higher because a higher value is placed on the fatalities due to drunk driving. At the same time, the benchmark tax rate incorporates a lower estimate of the external cost per drink exclusive of the costs of drunk driving, and assumes a larger fraction of total consumption is accounted for by moderate drinking than do Pogue and Sgontz.(21) The effect of lower external costs and a larger share of moderate drinking is to reduce the optimal tax rate, so the benchmark rate and Pogue and Sgontz's estimate would be further apart if these differences were eliminated.

Some Sensitivity Analysis. That the optimal tax rate is sensitive to changes in assumptions is evident, for example, by the fact that Pogue and Sgontz's estimates range from 19 to 306 percent. This paper attempts to narrow the range of plausible estimates. It is still appropriate to conduct some sensitivity analysis, especially where there is little consensus for the empirical estimates of the determinants of the optimal tax rate.

There is still considerable uncertainty over the estimates of the relative price elasticities of different types of drinking. As noted above, using the same data but a different empirical specification (the two-part model instead of the tobit model) yields different point estimates for the price elasticities. In addition, the 95 percent confidence intervals around the point estimates from a given specification are in the range of plus or minus 25 percent of the point estimates reported. Strictly speaking the point estimates are not exactly correct in any case, since they correspond to the elasticity on ordinary (not compensated) demand curves at the current mean price and quantity consumed.(22) Finally, considering the results of other studies using different data sets and empirical approaches further increases the uncertainty. Leung and Phelps [1993, 28] note in the conclusion of their review that "the estimates in the literature contain a wide degree of disagreement about the price responsiveness of alcoholic beverages." Estimates of the relative price responsiveness of different types of drinking should be viewed as preliminary, since this issue has just begun to receive attention.

The optimal tax rate is clearly sensitive to assumptions about the relative price elasticities of different types of drinking. To illustrate, suppose that the price elasticity of moderate drinking is actually 50 percent larger (in absolute value) than assumed for the benchmark estimate, while the price elasticities of the categories of heavy drinking and drunk driving are 50 percent lower. In this case the optimal tax rate is calculated to be only 40 percent instead of 106 percent. This calculation might be viewed as a plausible lower bound, since it assumes moderate drinking is much more price responsive while heavy drinking and drunk driving are much less price responsive than the empirical results suggest.

There is also considerable uncertainty over the uninternalized external costs of drunk driving. The estimate taken from Kenkel [1993a] involves two sets of assumptions: first, estimating the total external costs and total penalties; and second, estimating the external costs and expected penalty per occasion of drunk driving by dividing the totals by an estimate of the amount of drunk driving. The optimal tax rate calculation is sensitive to changes in the assumptions about the total costs and penalties. Based on the range of estimates in Kenkel [1993a], penalties might be high enough that most of the external costs are internalized (F - [Q.sub.1] = $7.32), so the optimal tax rate falls to 55 percent. Under alternative assumptions the uninternalized costs are much higher (F - [Q.sub.1] = $204.07) than assumed in the benchmark case, so the optimal tax rate increases to 414 percent. Perhaps surprisingly, however, the optimal tax rate calculation is not sensitive to changes in the assumed amount of drunk driving. Since the estimates of the per occasion costs and expected penalties (F and [Q.sub.1]) are based on the amount of drunk driving, the assumed amount of drunk driving enters both the numerator and the denominator of the last term of the optimal tax formula (equation (3)). The lack of sensitivity is important, since the amount of drunk driving is extremely difficult to measure; for example, studies by Colquitt, Fielding and Cronan [1987] and Maull et al. [1984] suggest that even the police substantially under-report drunk driving.

Limitations. One limitation of the empirical approach is that it only captures the welfare gains generated as taxation reduces the frequency of heavy drinking. The implicit assumption made in the analysis is that the price elasticity of the intensity of heavy drinking is zero, but intensity may also respond to taxation. If the external costs mainly depend on the frequency of heavy drinking, this limitation is not serious. To the extent the intensity of heavy drinking is price responsive and more intense heavy drinking creates higher external costs, this paper's analysis underestimates the welfare gains of taxation and hence the benchmark tax rate. This limitation is unavoidable, for two separate reasons. First, as noted above, the data used to estimate the price elasticities lack a good measure of the intensity of heavy drinking. Second, I also lack a good estimate of the marginal external costs associated with more or less intense heavy drinking. The study by Manning et al. [1989] provides estimates of the average external costs associated with heavy drinking.

A second problem is the potential for measurement error in the self-reported alcohol consumption measures used in the empirical analysis. Self-reported alcohol consumption probably substantially understates true consumption. Under-reporting might affect the relative sizes of the different categories of drinkers, if, for instance, heavy drinking is more often under-reported than moderate drinking. If so, moderate drinking accounts for a smaller share of total alcohol consumption than estimated above, implying the benchmark optimal tax rate is too low.(23) The benchmark rate would also be biased if measurement error creates bias in the estimates of the relative price elasticities; this remains a subject for future work.

Two of the limitations noted tend to suggest that the optimal alcohol tax rate is above the benchmark tax rate of 106 percent, but the extent of the bias is unknown. The limitations also will affect the quantitative comparisons of tax rates under alternative policy scenarios. The main qualitative results of the analysis would probably be unaffected.

Vl. CONCLUSIONS

Using a new data set, this paper extends previous work on the optimal tax on alcoholic beverages, yielding a benchmark estimate that the optimal tax is over 100 percent of the net-of-tax price. It should be stressed that there are important limitations to the empirical estimates that determine the benchmark rate. These include possible biases from under-reporting of heavy drinking and drunk driving, measurement error in the price variable, and the lack of evidence on the price responsiveness of the intensity of heavy drinking. On balance, this study does not provide a new estimate of the exactly correct tax rate. Instead, taken together with other studies, the results lend support to policy initiatives to restore the real value of alcohol excise taxes to the 1950s levels, or even higher.

Implementation of substantial tax increases would be problematic, however. In particular, as analyzed by Smith [1976], tax evasion through illegal markets in alcoholic beverages might become a significant factor. Another implementation issue not addressed in this paper is how the tax increase should be allocated across beer, wine, and liquor taxes. Saffer and Chaloupka [1994] suggest that equalizing the tax per unit of alcohol in each of these beverages may be a reasonable policy, which would entail higher relative increases in beer and wine taxes than liquor taxes.

In large part alcohol taxation is a second-best solution to problems associated with alcohol abuse. The analysis of this paper also shows that the optimal tax rate would be much lower if punishment for drunk driving were more certain and severe. One implication is that the optimal tax rate today is much lower than in 1980 because states have enacted hundreds of new laws to combat drunk driving. Similarly, the optimal tax rate may be reduced by government provision of information about the health consequences of heavy drinking, such as warning labels on beverage containers, that removes part of the efficiency rationale for alcohol taxes.

However, stiffer deterrence and improving health information are also socially costly, so it still might be the case that a relatively large tax hike would have a favorable cost-benefit ratio relative to deterrence and health information policies. The best mix of taxation, other alcohol control policies such as the minimum legal drinking age, and drunk driving deterrence policies remains an open question. Kenkel [1993b] provides illustrative calculations that the social costs of alcohol control policies and deterrence policies are not too far apart, but a great deal more work in this area is needed.

1. Figure 1 is based on data for federal, state, and local tax revenues from alcoholic beverages from the Distilled Spirits Council [1991], and data on total sales of alcoholic beverages from the Distilled Spirits Council [1991], Jobson's [1990] and the Beer Institute [1990].

2. The petition to Congress, signed by seventy-nine prominent economists including three Nobel laureates, advocated "substantial excise taxes." Recent empirical studies include Phelps [1988a; 1988b], Pogue and Sgontz [1989], Blumberg [1992] and Saffer and Chaloupka [1994].

3. Leung and Phelps [1993] review studies of the price elasticities for alcoholic beverages. Only a few examine whether heavy drinking is more or less responsive to price than moderate drinking. The most detailed investigation is by Manning, Blumberg, and Moulton [1995], who find that both light and heavy drinkers are less price elastic than moderate drinkers. Studies by Grossman, Coate, and Arluck [1987] and Cook and Tauchen [1982] provide suggestive evidence that heavy drinking may be as price elastic as moderate drinking. Based on the earlier empirical literature, Pogue and Sgontz [1989] argue that it is not implausible that moderate and heavy drinking are equally price elastic.

4. Pogue and Sgontz [1989] refer to the possible role of imperfect consumer information several times, but do not include it in their optimal tax calculations. Phelps [1988a] calculates optimal second-best alcohol taxes under varying assumptions about how well drinkers are informed about the risks of drinking and driving.

5. In general the notation follows that used by Pogue and Sgontz [1989], but for clarity's sake a few notation changes have been made in the process of extending their framework.

6. The demand functions estimated below are ordinary, not income-compensated, demand curves. Using Willig's [1976] results it can be shown that consumer's surplus measured using an ordinary alcohol demand curve will be extremely close to the conceptually correct measure using the compensated demand curve because expenditures on alcohol are a relatively small share of most consumer's budgets.

7. The male pronoun is used advisedly since males are much more likely to engage in heavy drinking; see Table II. The marginal internal and external costs of one evening of heavy drinking may be different for a typically moderate drinker and a chronic heavy drinker. Chronic heavy drinkers may also respond differently to prices than occasional heavy drinkers because of the effects of addiction as in Becker, Grossman and Murphy [1991]. These complications are not pursued here because the data used in the empirical analysis is cross-sectional and does not contain much retrospective data on drinking history.

8. Related analyses of the welfare effects of demand curves shifting in response to consumer information include Peltzman [1973] and Phelps [1992, 434-36].

9. The assumption that a decision made under the influence of alcohol is fully rational can also be questioned, but as Saffer and Chaloupka [1989] argue, even if that decision is not rational, the joint decision to drink and then drive can be modeled as rational. Indirect support for this assumption comes from numerous studies that find that drunk driving can be deterred; recent studies include Chaloupka, Grossman and Saffer [1993], Kenkel [1993b], and Mullahy and Sindelar [1994].

10. In contrast, Perrine et al. [1988] provide evidence that the probability that an occasion of drunk driving results in an accident does depend on how drunk the driver is. It would be desirable to allow F to vary with the severity of drunk driving. Since this can not be done with the available data, F should be considered the external cost of an average occasion of drunk driving.

11. The welfare effects on the uninformed heavy drinker are similar to but not identical to those analyzed by Pogue and Sgontz [1989] under the assumption that alcoholism is a disease. They assume that an alcoholic gains the decrease in his alcohol expenditures plus the decrease in health costs, that is, the entire area under the demand curve. This is equivalent to assuming that at the level of an alcoholic's consumption, a non-alcoholic's willingness to pay for alcohol is zero. While this may be a reasonable assumption with respect to alcoholism, it seems less reasonable for the case of poor information.

12. Detailed results available upon request.

13. In general, the implications for the tax analysis depend upon the nature of the measurement error in the price variable. It is plausible that the measurement error is systematically different for moderate and heavy drinking, if heavy drinkers search out low prices for example. If so, there may be important implications for the empirical comparisons of price elasticities as well.

14. Both the frequency and intensity of heavy drinking could be measured in relation to behavior over the past two weeks. However, the survey question determined the typical number of drinks per day of drinking, so occasional heavy drinking even within the past two weeks is not measured. Only 7 percent of the sample report typically drinking five or more drinks per day of drinking. There are many more occasional heavy drinkers: 24 percent of the sample report at least one occasion of having five or more drinks in the past year. Heavy drinking in the past year therefore appears to be the more useful measure, but the intensity of heavy drinking is not measured.

15. The hypothesis that the estimated tobit parameters in the demand equations are the same for males and females is tested using the likelihood ratio test described by Fomby, Hill, and Johnson [1984, 612-14]. The hypothesis is decisively rejected.

16. See Greene [1993, 694-95]. The estimated tobit coefficient on price shows how the latent index underlying the tobit model responds to a marginal change in price. The response of the observed dependent variable to a marginal change in price is obtained by multiplying the tobit coefficient by [Phi](z). [Phi] is the distribution function of the standard normal, and z = [Beta][prime]X/[Sigma], where, [Beta] is the estimated tobit parameter vector, X is the vector of explanatory variables, and a is the estimated variance. Table III reports [Phi](z) for each demand function estimated, evaluated at the mean of the explanatory variables.

17. However, as emphasized by Becker, Grossman, and Murphy [1991], an implication of the theory of rational addiction is that rational addicts will respond a great deal to price changes in the long run. An alternative explanation is that the result may be partly due to the incomplete measures of heavy drinking available in the data. It is possible for the measured frequency of heavy drinking to remain unchanged even though the intensity of heavy drinking is price responsive. For instance, if a heavy drinker facing a low price consumes ten drinks a day while a heavy drinker facing a higher price consumes seven drinks, since both consume more than five drinks the measured frequency will not change. Since this problem can not be resolved using these data, the result that the least-informed group is unresponsive to price should be viewed with caution. I owe this point to Gary Becker.

18. The two-part model was first applied to medical care demand by Duan et al. [1983], and has recently been used to estimate cigarette and alcohol demand functions by Wasserman et al. [1991] and Manning, Blumberg, and Moulton [1995]. A feature of the two-part model is that the effect an explanatory variable has on the decision to abstain from drinking can differ from its effect on the amount of drinking given non-abstention. The adjusted tobit and sample selection models also allow for this possibility, but Manning, Duan and Rogers [1987] show that the two-part model offers important practical advantages.

19. The consumers' beliefs may not be erroneous, since future research may discover new health risks. For the Health Promotion and Disease Prevention survey, Thornberry et al. [1986] indicate the answers presumed correct based on the determination of Public Health Service agencies. By this standard there were no currently presumed correct answers to the questions regarding bladder cancer, arthritis, and blood clots. Accordingly, I term respondents' answers that the links between these conditions and heavy drinking have been established as erroneous.

20. It is assumed that drunk driving and drinking are under-reported in the same proportion, so the adjustments for under-reporting cancel out of the ratios.

21. Pogue and Sgontz use an estimate of the external costs created by heavy drinking based on a study by Harwood et al. [1984], who use the so-called human capital approach to place a value on fatalities. In estimating the uninternalized external costs of drunk driving, a fatality is valued according to willingness to pay, which Blomquist [1982] shows in general results in much higher values. In calculating the benchmark tax rate, external costs exclusive of the costs created by drunk driving are assumed to be $0.31 per drink. Expressed in the same units, and adjusted to exclude the external costs created by drunk driving, the Pogue and Sgontz estimate is $0.43 per drink, nearly 40 percent larger. Finally, Pogue and Sgontz assume that the ratio of non-abusive consumption to abusive consumption is at most 1.42. From Table II, the ratio of consumption due to moderate drinking over consumption due to all categories of heavy drinking is 1.83.

22. For the optimal tax derivation, demand is approximated as a linear function over the relevant range of price. The empirical elasticities should be the average elasticities over that same range. This is problematic when considering very high tax rates, but possibly less so because the optimal tax rate depends on ratios of elasticities, not the absolute values.

23. Support for this hypothesis is found in evidence reported in footnote 15: the ratio of consumption due to moderate drinking over the ratio of consumption due to all categories of heavy drinking calculated from Table II is larger than a roughly comparable ratio from the study by Pogue and Sgontz [1989]. There are some differences in the definitions used here and in their study, however. Pogue and Sgontz's estimate refers to consumption by heavy drinkers versus moderate drinkers. Here, the ratios are defined in reference to consumption due to heavy drinking versus moderate drinking, on the assumption that it is an occasion of heavy drinking that generates external costs. As defined here, heavy drinkers may also engage in a great deal of moderate drinking, which could explain the different ratios.

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DONALD S. KENKEL, Associate Professor, Department of Consumer Economics and Housing, Cornell University. Financial support through a FIRST award from the National Institute on Alcohol Abuse and Alcoholism, grant number 1R29AA08350-01Al is gratefully acknowledged. I would also like to thank the editor and referees of this journal, participants at workshops at Penn State, the University of Chicago, and the University of Illinois-Chicago, and participants at a session of the Eastern Economics Association for helpful comments.