Do alcohol taxes in Europe and the US rightly correct for externalities?

Abstract

We develop an analytical framework for assessing corrective taxes and other policies to reduce alcohol-related externalities and apply it to the US, UK, Sweden, and Finland. The corrective tax estimates for the European countries fall short of current taxes and vice versa for the US (where drunk-driving externalities are larger and current taxes smaller). Alcohol sales restrictions are more difficult to justify on efficiency grounds as (unlike taxes) they involve large, first-order deadweight losses. For all countries, the efficiency case for stiffer drunk driver fines seems strong (though the same does not necessarily apply to non-pecuniary penalties).

Appendices

Appendix A: Analytical derivations

Preliminaries

Deriving formulas for welfare effects and optimal policies involves two steps. First is to solve the household’s optimization problem, taking policy parameters and externalities as given. Second, is to differentiate household utility with respect to a policy parameter, taking into account induced changes in externalities and the government budget (as households respond to the policy change). Here we go through the first sept and subsequently the second step for different policies.

Using (1a)–(1b) and (2), agents solve the following optimization problem:

$$\begin{aligned} & V ( t,G,k,\alpha,\phi,\gamma,\tau ) \\ &\quad= \operatorname{MAX} u \bigl( A^{R} +A^{N}, A^{F}, Y,k A^{R}, \alpha,\phi, \gamma D, D/\pi \bigr) \\ &\qquad{}+\gamma\bigl[\mathit{INC}+G- \bigl( p^{H} +t \bigr) \bigl( A^{R} + A^{N} \bigr) - p^{F} A^{F} -\tau D-Y\bigr] \end{aligned}$$

(8)

where γ is a Lagrange multiplier and V(⋅) denotes indirect utility. The household choice variables here include A ^R (restricted alcohol consumption), A ^N (non-restricted consumption), A ^F (cross-border or black market consumption), Y (general consumption), D (drunk driver convictions—or equivalently drunk driver trips times the exogenous probability of being apprehended and convicted).

From the first-order conditions for this problem (and the household’s budget constraint) we obtain the household demands as functions of external costs, and policy parameters:

$$A^{N} =A^{N} ( t,G,k,\alpha,\phi,\gamma,\tau ) $$

and similarly for A ^R, A ^F and Y. Substituting the equilibrium conditions $A^{R} = \overline{A}^{R}$ etc. in (1b), and substituting for α and ϕ gives equilibrium consumption (denoted $\hat{\,\,}$) as a function of exogenous policy parameters:

$$ \hat{A}^{N} = \hat{A}^{N} ( t,G,k,\gamma,\tau ) $$

(9)

and so on for A ^R, A ^F and Y. The equilibrium responses of the endogenous variables to the policy parameters are the partial derivatives of $\hat{A}^{N}$ etc., as they account for the possible feedback effects of changes in externalities on demand.

From partially differentiating (8):

$$\begin{aligned} \begin{aligned} &\frac{\partial V}{\partial t} =-\lambda\bigl( A^{N} + A^{N}\ \bigr),\qquad \frac{\partial V}{\partial G} =\lambda,\qquad \frac{\partial V}{\partial k} = u_{k A^{R}} A^{R},\qquad \frac{\partial V}{\partial\alpha} = u_{\alpha} \\ &\frac{\partial V}{\partial\phi} = u_{\phi},\qquad \frac{\partial V}{ \partial\gamma} = u_{\gamma D} D,\qquad \frac{\partial V}{\partial\tau} =-\lambda D \end{aligned} \end{aligned}$$

(10)

Deriving Eq. (4a)–(4c)

Totally differentiating V(⋅) with respect to t, and using (10), gives

$$ \frac{1}{\lambda} \frac{dV}{dt} =- \bigl( A^{N} + A^{R} \bigr) + \frac{dG}{dt} + \frac{u_{\alpha}}{\lambda} \frac{d\alpha}{dt} + \frac{u_{\phi}}{\lambda} \frac{d\phi}{dt} $$

(11)

Totally differentiating the government budget constraint with respect to t gives

$$ \frac{dG}{dt} = A^{N} + A^{R} +t \frac{d( A^{N} + A^{R} )}{d t} + \tau \frac{dD}{dt} $$

(12)

From (11) and (12)

$$ \frac{1}{\lambda} \frac{dV}{dt} =t \frac{d( A^{N} + A^{R} )}{dt} +\tau \frac{dD}{dt} + \frac{u_{\alpha}}{\lambda} \frac{d\alpha}{d t} + \frac{u_{\phi}}{\lambda} \frac{d\phi}{dt} $$

(13)

Using (1b) and (4c)

$$ \begin{aligned} &\frac{d\alpha}{dt} =\alpha' \frac{d( A^{N} + A^{R} + A^{F} )}{dt},\qquad \frac{d\phi}{dt} =\phi'D' \frac{d( A^{N} + A^{R} + A^{F} )}{dt} \\ & {\frac{d( A^{N} + A^{R} + A^{F} )}{dt}} \bigg/ {\frac{d( A^{N} + A^{R} )}{dt}} =1- \beta^{Ft} \end{aligned} $$

(14)

Setting (13) to 0 and substituting (14) gives (4a)–(4c).

Deriving Eq. (5a)–(5c)

Totally differentiating V(⋅) in (8) with respect to k, and using (10) gives

$$ \frac{1}{\lambda} \frac{dV}{dk} = \frac{dG}{dk} + \frac{u_{K A^{R}}}{\lambda} + \frac{u_{\alpha}}{\lambda} \frac{d\alpha}{d k} + \frac{u_{\phi}}{\lambda} \frac{d\phi}{dk} $$

(15)

Totally differentiating the government budget constraint with respect to k gives

$$ \frac{dG}{dk} =t \frac{d( A^{N} + A^{R} )}{dk} +\tau \frac{dD}{dk} $$

(16)

From (15) and (16)

$$ \frac{1}{\lambda} \frac{dV}{dk} = \frac{u_{k A^{R}} A^{R}}{ \lambda} +t \frac{d( A^{N} + A^{R} )}{dk} +\tau \frac{dD}{dk} + \frac{u_{\alpha}}{\lambda} \frac{d\alpha}{dk} + \frac{u_{\phi}}{ \lambda} \frac{d\phi}{dk} $$

(17)

Using (1b) and (4c)

$$ \frac{d\alpha}{dk} = \alpha ' \frac{d A^{R}}{dk} \bigl(1- \beta^{NK} - \beta^{FK} \bigr),\qquad \frac{d\phi}{dk} = \phi ' D' \frac{d A^{N}}{dk} \bigl(1- \beta^{NK} \bigr) $$

(18)

Setting (17) to 0 and substituting (18) gives (5a)–(5c).

Deriving Eq. (6)

Here we ignore the effects of drunk driver penalties on alcohol consumption (see Parry et al. 2009 for some justification).

Differentiating the government budget constraint (3) with respect to τ (holding alcohol consumption fixed) gives

$$ \frac{dD}{d\tau} =D+\tau \frac{dD}{dt} $$

(19)

Following the same derivation as for Eq. (4a)–(4b) but for differentiating with respect to τ rather than t (and with alcohol consumption fixed), in place of (12) we obtain

$$ \frac{1}{\lambda} \frac{dV}{d\tau} =\tau \frac{dD}{d\tau} + \frac{u_{\phi}}{\lambda} \frac{d\phi}{d\tau} $$

(20)

From differentiating (1b)

$$ \frac{d\phi}{d\tau} =\phi' \frac{dD}{d\tau} $$

(21)

Setting (20) to 0 and substituting (21) gives (6).

Deriving Eq. (7)

Differentiating the government budget constraint with respect to γ rather τ than gives

$$ \frac{dG}{d\gamma} =\tau \frac{dD}{d\gamma} $$

(22)

Following the analogous steps to those in deriving (6) yields, in place of (20), the following:

$$ \frac{1}{\lambda} \frac{dV}{d\gamma} =\tau \frac{dD}{ d\gamma} + \frac{u_{\phi}}{\lambda} \phi^{' \frac{dD}{d\gamma}} + \frac{u_{\gamma D}}{\lambda} D $$

(23)

Equating to 0 and substituting Z ^D from (6) gives

$$ Z^{D} =\tau+ \frac{u_{\gamma D} D}{\lambda \frac{dD}{d\gamma}} $$

(24)

Using the definition of Γ, dD/dγ=−(dD/dΓ)u _γD /u _Y . Making this substitution in (24) and using the definition of $\eta_{D}^{D}$, we obtain (7).

Appendix B: Documentation for benchmark parameters in Table 1

Baseline (observed) data with current policies

PPP exchange rate (local currency per US $1) These figures, taken from Heston et al. (2009), are used to convert monetary figures into US dollars.

Population (age 15 and over) These figures, taken from Statistics Finland (2010b), Statistics Sweden (2010), UK ONS (2010), and US Census Bureau (2010), are used to express all quantities in per capita terms.¹⁵

Alcohol consumption This is the sum of beer, wine, and spirits in pure alcohol liters per capita.

We first obtain domestic (or documented) alcohol sales (A ^R+A ^N) from liquor and grocery stores, kiosks, gas stations and licensed restaurants.¹⁶ Cross-border consumption (A ^F) is inferred from local estimates of the ratio of undocumented (i.e., cross-border purchases, homebrewing, and illegal distilling/smuggling) to documented consumption. For the US we assume the ratio of undocumented to documented consumption is 11 percent (from Rehm and Monteiro 2005), for the UK 18 percent (from Leifman 2001), for Sweden 31 percent (from Svennson and Selin 2007), and for Finland 15 percent (from NIHW 2009).

Current excise tax Initial alcohol tax rates are calculated by dividing revenues from specific and ad valorem taxes (or, for Sweden, profits to the state monopoly supplier Systembolaget) by domestic alcohol consumption. Revenue for the US (at the federal, state, and local level combined) is from TPC (2010a and 2010b); for the UK from HMRC (2010), Table 1.1; for Sweden from Statens Folkhälsinstitut (2008); and for Finland from OECD (2009a).

Pre-tax price of domestic alcohol This is calculated by domestic alcohol purchases, less tax revenue, divided by domestic consumption. Domestic alcohol expenditures come from US BEA (2010), Table 2.4.5U (lines 97 and 239); UK ONS (2009), Table ALC:CN; Statens Folkhälsinstitut (2008), Table 14; and NIHW (2009), Table 58.

Drunk driver convictions This data was obtained from US BOJS (2010b), Table 4.28, UK MOJ (2010), Table 8.3 (for England and Wales), UK ONS (2008) (for Scotland), Brå (2010b), and Statistics Finland (2010d).¹⁷

Drunk driver fines and non-pecuniary penalties For the US, data is available to assess the fine, license suspension, jail term, and community service per drunk driver conviction, averaged across states and across first-time and repeat-offenders. Without getting into the details, Parry et al. (2009) perform these calculations and make various assumptions to obtain monetary valuations of the non-pecuniary penalties. We simply take their figures, and update them from year 2000 to 2007 based on the growth in average hourly wages (from US BLS 2010b).

For European countries, a comprehensive database for assessing average penalties is not available as penalties vary with income and the discretion of the court. We assume that penalties in Europe are the same as those in the US (alternative assumptions would not have much significance for our results).

External benefits

Value of a statistical life For the US we assume the VSL is $5.8 million, based on the value for auto fatalities in US DOT (2008). To extrapolate this figure to other countries, we multiply it by the ratio of real per capita income in that country to that in the US, where this ratio is raised to the power of the VSL/income elasticity. Income data, measured by Purchasing Power Parity equivalents to account for local purchasing power, is from World Bank (2010). We assume the VSL/income elasticity is 0.75.¹⁸

Third-party medical burdens Most studies estimating the medical costs of alcohol-related illness (e.g., Harwood 2000) use the cost-of-illness (COI) approach. Here estimates of alcohol-attributable fractions (AAFs) are used to apportion instances of different conditions to alcohol abuse and then average costs per condition are applied to these figures. However, this approach does not account for possible health benefits from moderate alcohol consumption or the savings in lifecycle medical and social security costs due to the shorter longevity of heavy drinkers. A rare, but widely, cited study that attempted to account for these factors following individuals over a long period of time, is Manning et al. (1989).

Based on updating Harwood (2000) and Manning et al. (1989) to a common year, Parry et al. (2009) find that the latter amounts to 23 percent of the former. To obtain external costs we therefore use the latest COI study for each country, update it to 2007 using the growth in national health expenditure from OECD (2009a, 2009b), and then multiply by 0.23. The COI studies we use are Harwood (2000) for the US, HIAT (2008) and Scottish Government (2010) for the UK, Johansson et al. (2006) for Sweden, and Salomaa (1995) for Finland. Total external costs are divided by alcohol consumption to obtain unit costs (and for other externalities below).

Violence Here we focus on violent crime—homicide, assault, rape, and armed robbery—which account for a large majority of the social costs of alcohol-related violence.¹⁹ We exclude medical costs of crime since these were accounted for in the third-party medical burden.

We obtain both reported, and actual, violent crime figures, where the actual figures are larger due to under-reporting. Reported figures matter for judicial and public program resource costs while actual figures matter for personal injury costs. For the US, reported figures are from FBI (2008), Table 12, and actual figures from the National Crime Victimization Survey (NCVS) in US BOJS (2010a).²⁰

Next we apply AAFs, which vary between 17 and 21 percent across different crime categories, from Miller et al. (2006) to the reported and actual crime figures. For actual crime figures, we multiply the result by the cost per injury classification: the VSL for a homicide and for non-fatal injuries quality of life, future earnings losses, and property costs for that crime, from Miller et al. (2006). Also from Miller et al. (2006), we apply judicial and public program costs to the reported crime figures, though this cost component is relatively minor.²¹

There are two difficult challenges to gauging the portion of (actual) alcohol-related crimes that are external.

First, it is not clear that violent crimes committed among people who know each other (at least within a household) should be viewed as fully external. These crimes account for about half of homicides, assaults, and rapes in the US (Truman and Rand 2010). However, there are legitimate reasons for viewing at least some of the violence by non-strangers as external. Johansson et al. (2006, pp. 17) emphasize the lack of information and different bargaining positions of different family members—one could question, for example, whether intoxicated individuals properly internalize the cost of violence to children.

Second, the (actual) crime data is from surveys among inmates about their alcohol consumption prior to committing their crime. However, the counterfactual against which these statistics should be measured is not known—at least some of the crime would likely occur even if no alcohol were consumed. Nonetheless, the well-documented effect of alcohol on decision making suggests that alcohol does cause some violence (for some evidence on this, see, for example, Grossman and Markowitz 1998, 2000 and Markowitz 2000).

In our benchmark case, we assume that 50 percent of alcohol-related crimes are external.

We follow the same procedure for other countries using local data on crime incidence and AAFs.²² To monetize homicides we use the above VSLs. For non-fatal violent crimes we obtain one set of estimates using local values for unit costs. A possible problem here is that methodologies used by country analysts to estimate unit costs may be inconsistent. We therefore obtain a second set of estimates where we use US unit cost estimates extrapolated using the same procedure as for the VSL.²³ Our benchmark estimates in Table 1 for the non-US countries represent an average over the two procedures.

Drunk driving. We collected data on fatal and non-fatal injuries in drunk driver crashes, made assumptions about the external portion of these injuries, and then quantified external costs.

US alcohol-related fatality data for 2007 comes from US NHTSA (2008). To obtain non-fatal injuries of various MAIS (Maximum Abbreviated Injury Scale) classes we assume the ratio of these injuries to fatalities is the same as reported in US NHTSA (2002). For the UK, fatality and injury data is from Transport Statistics (2008) and McEvoy (2010); for Finland from SIKA (2008); and for Sweden fatalities are from Vägverket (2009) and non-fatal injuries are inferred assuming the injury/fatality ratios for 2007 are the same as on average for 2000 to 2004 as reported in UNECE (2007).²⁴ The breakdown of fatalities by driver, passenger of drunk driver, other vehicle occupant, pedestrian, and cyclist is available from our data and we assume this breakdown is the same for the non-fatal injuries.

Following Levitt and Porter (2001), we assume 76.5 percent of alcohol-related injuries are alcohol-caused (i.e., 23.5 percent would have been caused anyway by sober drivers). Of these, all sober drivers, passengers of sober drivers, and bicycle casualties are considered external but only 3.3 percent of injuries to drunk drivers are counted as external—the huge bulk of these injuries occur in single-vehicle accidents where risks are viewed as internal. Again following Levitt and Porter (2001), we assume 86.6 percent of pedestrian injuries are external. To what extent injury risks to passengers of drunk drivers are external is unclear: we assume that half of these alcohol-caused risks are external.

External fatalities are monetized using our VSL values (VSLs swamp any other costs of fatalities).

To monetize other costs we start with US values for non-fatal injuries, classified according to the MAIS, taken from US DOT (2008). For other countries, injuries are typically grouped into ‘slight’ and ‘severe’. We assume a slight injury corresponds to MAIS-1 and a severe injury to a weighted average of MAIS-2 to MAIS-5 injuries, where weights depend on their relative frequencies in the US data. The values of slight and severe injuries for other countries are then obtained from US values for MAIS-1, and an average of MAIS-2 to MAIS-5, multiplied by the same scaling factor as used to extrapolate the VSL.

For non-fatal injuries, potentially significant costs include personal suffering, costs of medical care, property damages, and government resource costs (from apprehending, convicting, and punishing drunk drivers). We make some further assumptions to apportion various social costs as external (though alternative plausible assumptions would not have much effect on our overall results). In particular, 85 percent of medical costs, and 85 percent of property damage costs, incurred in all alcohol-related crashes are taken as external (i.e., borne by third parties).

For government resource costs, we follow Parry et al. (2009). We update the judicial costs per conviction using 2006 data from Table 1 of US BOJS (2008) and Table 4.1 of US BOJS (2010b), and the CPI-U from US BLS (2010a), which comes to $2,739. And we update 2000 police costs from Kenkel (1993b) again using the CPI-U from US BLS (2010a), which comes to $433. In the absence of new data, we update costs per sentence from Kenkel (1993a) via Parry et al. (2009) using the CPI-U as well which comes to $1002. The total per conviction is $4175. Multiplying by convictions and dividing by consumption, we get $1.8 per alcohol liter (which is comparable to Parry et al. 2009). Again, this figure is scaled for the three European countries by per capita income and relative tort costs.

For the US, unit costs are taken from US NHTSA (2002), Table 12, updated to 2007 using the CPI-U (from US BLS 2010a). The costs are scaled to account for differences in per capita income. Health related costs are also scaled using health expenditures as a share of GDP from OECD (2009a, 2009b). Legal costs are also scaled using tort costs as a share of GDP from Towers-Perrin Tillinghast (2005). For the UK this figure is roughly one-third of that for the US. For Finland and Sweden, which are not included in the study, we use the figure for Denmark which is roughly one-quarter of that for the US.

Behavioral responses

Based on US evidence, a plausible range for the own-price elasticity for (documented) alcohol consumption is about −0.4 to −1.0 (aggregating over beverages), though perhaps with a ‘most likely’ value closer to the lower end of this range (e.g., Cook and Moore 2000; Parry et al. 2009). We adopt a benchmark value of −0.5 for the US.

A recent meta-analysis by Fogarty (2010) suggests that alcohol elasticity estimates for other countries are broadly similar to those for the US. To be consistent with our model, however, we allow for a (moderately) greater price-responsiveness in countries with more scope for substituting cross-border consumption. To do this, we start by assuming that 90 percent of the domestic alcohol elasticity for the US is due to reduced overall demand for alcohol, and 10 percent reflects switching towards cross-border consumption (based on the latter’s share in total consumption). We assume the former component is the same for all countries, but the switching component is scaled up by the fraction of cross-border alcohol consumption in that country relative to the US fraction.

These assumptions also provide the alcohol leakage fractions, which are given by the share of the switching component in the overall domestic alcohol elasticity.

Although not explicit in Eq. (4a)–(4c), in assessing corrective alcohol taxes, alcohol-related externalities should be weighted by the ratio of the price responsiveness of abusive alcohol consumption to the price sensitivity of alcohol consumption as a whole (e.g., Pogue and Sgontz 1989; Parry et al. 2009). Based on the literature summary in Parry et al. (2009), we assume abusive consumption from domestic alcohol falls in the same proportion to the reduction in domestic alcohol. If there were no substitution towards cross-border consumption, our previous assumption would imply, for all countries, an elasticity of abusive consumption and drunk driving with respect to domestic alcohol prices of −0.45.

However, with switching towards cross-border consumption there is an offsetting increase in abusive consumption. We therefore scale back the assumed elasticity by the switching component of the domestic alcohol elasticity for each country (e.g., for the US this reduces these elasticities to −0.38). Some studies suggest that the price responsiveness of abusive consumption might be significantly less than that for overall alcohol consumption (e.g., Adams et al. 2012). We cover other possibilities in the sensitivity analysis.

We are not aware of any evidence we could use to infer the responsiveness of restricted alcohol consumption to (the virtual tax equivalent of) sales restrictions, though we would expect greater responsiveness than for explicit alcohol taxes, given that sales restrictions are more targeted towards impulsive consumption and the scope (at least in some countries) for substituting non-restrictive for restrictive consumption. We make the assumption that the alcohol elasticity with respect to sales restrictions is 50 percent larger in magnitude than that for explicit tax increases.

Finally, based on the brief review of the literature in Parry et al. (2009), we take the elasticity of drunk driving with respect to penalties to be −0.7.

Remaining parameters pertaining to sales restrictions

Given the difficulty of finding data, we use illustrative values (based on crude judgment) for the remaining parameters relevant for the sales restriction policy. As regards diversion fractions, we assume no substitution into non-restrictive consumption (β ^NK=0) for Finland and Sweden (where essentially all regions are covered by regulations) and that 50 percent of reduced consumption in the US and UK is offset by an increase in other domestic consumption (β ^NK=0.5), given sales restrictions are much less pervasive. The portion of reduced restricted consumption offset by increased cross-border consumption (β ^FK) is taken to be 0.5 in Finland and Sweden and 0.1 in the UK and US. Alternative assumptions concerning β ^NK and β ^FK make little difference to estimated welfare effects of sales restrictions.