The practical problem of Pigovian alcohol beverage taxes

I just finished reading this 2022 article by Preety Srivastava (RMIT University), Ou Yang (University of Melbourne), and Xueyan Zhao (Monash University), published in the journal Economic Record (open access), which had been sitting in my (virtual) to-be-read pile for far too long. They look at the negative consequences of consuming different alcoholic beverages in Australia, and what that implies for the taxation of different beverage types.

First, Srivastava et al. make a good case for why alcohol is taxed:

The economic argument for alcohol tax is the need for correction of market failures and negative externalities that are associated with alcohol consumption...

...there are many reasons to believe that serious market failure exists in alcohol consumption, and the scale of alcohol abuse we observe in many societies is a testament to this. One example of market failure is the incomplete information regarding the long-term health impact and addictive nature of alcohol consumption in binge drinkers’ private decision-making on consumption. Another example is the use of incorrect discount rates to future harms due to the problem of willpower. More importantly, significant external costs of excessive drinking are borne by society. These include health-care costs of alcohol abuse in publicly funded health systems (such as in Australia), road accidents from drink-driving, and antisocial behaviours when intoxicated, including public nuisances, damage to and stealing of property, and physical and verbal abuse of family members and the wider community.

An excise tax, such as the one that is imposed on alcohol, is therefore an example of a Pigovian tax (named after Arthur Pigou), because one of the purposes of the tax (aside from generating revenue for the government), is to correct for the negative externality (because a tax will reduce the quantity consumed - see here, for example). Now, ideally:

...alcohol tax should be targeted at those excessive consumers whose consumption creates negative external costs, and not at moderate consumers who do not generate such negative costs to others. However, ‘excessive consumption’ is hard to measure, and taxing directly by consumer type is difficult to implement due to potential ethical and privacy issues in obtaining the required information.

So, while the government should be aiming to tax consumers based on the amount of negative externality they generate, that isn't possible because the government can't easily determine who the 'excessive drinkers', who generate the most negative externalities are. So, a general alcohol tax might be applied to all alcoholic beverages. The consequence is that:

A general alcohol tax applied to all drink types will reduce consumption for all consumers, achieving an efficiency gain for consumers with excessive consumption. However, this will also result in efficiency loss for consumers with low to moderate levels of consumption who have already accounted for all negative impacts as private costs in their consumption decision-making. Given that taxing heterogeneous consumers is less feasible, taxing the products that are more likely to be associated with negative external costs or consumed by individuals who are more likely to be involved in risky and abusive behaviours would seem to be a more feasible and efficient approach.

It turns out that is what Australia (and to a lesser extent New Zealand) does. But ineffectively, as we will see. In their paper, Srivastava et al. look at the relationship between consumption of different beverage types and various antisocial behaviours. They use data from the National Drug Strategy Household Survey (NDSHS) between 2004 and 2019, which included over 113,000 people (after excluding abstainers, who don't drink). The survey asks respondents whether they engaged in a range of activities "while under the influence of or affected by alcohol". Srivastava et al. focus on a subset of these behaviours, being those likely to result in negative externalities:

In this study, we focus on the following eight antisocial and unlawful behaviours under the influence of alcohol: (1) driving a motor vehicle; (2) operating a boat; (3) operating hazardous machinery; (4) creating a public disturbance or nuisance; (5) causing damage to property; (6) stealing money, goods or property; (7) verbally abusing someone; (8) physically abusing someone.

They look at drink-driving as one category, and merge all of the others into a separate category that they call "hazardous, disturbing or abusive behaviour" or HDA. One thing that isn't clear from the paper is exactly how the HDA measure is constructed (presumably, it is just whether the respondent engaged in any of the seven behaviours while affected by alcohol). In terms of the different alcoholic beverages, the NDSHS:

...has several questions on individuals’ consumption of various drink types. One of the questions relates to their drinking preferences: ‘What types of alcohol do you usually drink? (Mark all the types of drinks that apply)’. We use this information to construct ten dichotomous variables to indicate respondents’ usual drinking preferences. These binary indicator variables are respectively regular-strength beer (RSB), middle strength beer (MSB), low-strength beer (LSB), cask wine (CW), bottled wine (BW), fortified wine (FW), pre-mixed spirits in a can (PMSC), pre-mixed spirits in a bottle (PMSB), bottled spirits and liqueurs (BS), and other alcohol (Other).

That's a lot of acronyms. And you have to pay attention to them if you're reading the paper, because Srivastava et al. keep using them, and don't usually remind you what they refer to (which was a bit exhausting!). 

Now, obviously there are some endogeneity problems in a regression of alcohol harms on beverage consumption, because some of the variables that affect beverage consumption (like demographics - for example, younger drinkers have different drink preferences than older drinkers) also affect alcohol harm. This would bias any estimate of the effect of beverages on harm. Srivastava et al. mitigate this problem by using a Lewbel instrument (see here as well) - the price of beverages should affect beverage consumption, but not directly affect harm, so prices make a good instrument. Essentially, they replace beverage consumption in their main model with estimated beverage consumption based on prices, which won't have the same endogeneity problem. They also run models that don't use the instrument (but which will likely be affected by endogeneity).

Aside from endogeneity, there is one problem with the analysis. Looking at Table 1 in the paper, it is clear that the main dependent variables (drink driving, and HDA) are trended downwards over time - there is lower prevalence of all of these behaviours over time. The alcohol beverage consumption data also appears to be trended over time (from Table 2 in the paper). Srinistava et al. adjust all the prices to 2011/12 dollars, so the most obvious source of trending in the prices (inflation) is removed. However, when running a regression model with trended data in the dependent and explanatory variables, there is a risk of spurious correlation (which Tyler Vigen still does the best job of illustrating). That will clearly be a problem in the models without the Lewbel instruments and it isn't clear to me whether the instrument solves this problem. Srinistava et al. don't mention using time fixed effects or corrections for serial autocorrelation in their models, which would go some way towards mitigating this problem. Anyway, enough pointy-headedness.

Unsurprisingly, Srivastava et al. find that harms differ by beverage type. For drink-driving (DD - yes, another acronym):

RSB, PMSC, MSB, BW, CW and BS are all associated with a higher probability of DD, while LSB, PMSB, FW and Other are related to negative or insignificant effects on the probability of DD. Specifically, in terms of ranking, RSB has the highest positive impact, and is shown to be linked to a 6.5–9.5 percentage points higher probability of DD... Interestingly, CW and BS, the drinks that have drawn much attention in the tax debate, although having a positive impact on DD, both rank behind MSB, with a 1.7–3.3 percentage points higher probability of DD.

And for hazardous, disturbing, or abusive behaviour (HDA):

...RSB, PMSC and CW are ranked as the top three drinks that relate to the highest MEs [marginal effects, yet another acronym] for increasing the probability of HDA behaviours from all three models. CW currently has the lowest tax per LAL across all beverages, which has long been the focus of tax reform discussions...

Finally, LSB, BW and FW are shown to have negative MEs on the probability of HDA across all three models, with LSB having the largest negative effect. A noticeable result is for BW. In contrast to the results for DD, drinking BW is linked to a lower probability of HDA behaviours.

The takeaway from all this analysis is that different beverage types should have different tax rates, with those that are associated with the greatest harm having the highest tax rates. That would mean taxing regular strength beer, pre-mixed spirits in a can, and probably cask wine the most. Unfortunately, that's not at all what Australia does:

When converted to an effective rate per litre of alcohol (LAL), based on the 2007/08 data, the volumetric tax rates vary greatly by beverage... with cask wine paying effectively $3/LAL, bottled wines $14–$33/LAL by prices, beers $19–$31/LAL by alcohol strength, ready-to-drink (RTD) pre-mixed spirits $41–$43/LAL, and straight spirits $66/LAL.

So, while cask wine should be among the beverage types with the highest tax rate, it is taxed the lowest. As Yang and Srinistava note in this article in The Conversation about their paper, the Australian alcohol tax system is "incoherent". It is entirely correct for Australia to charge different tax rates for different beverage types, but those tax rates don't bear appear to bear any relationship to the harms arising from the different beverages. New Zealand's excise system is significantly simpler than Australia's, but again it is unlikely that it bears much resemblance to an optimal set of tax rates across different beverage types. To work efficiently in internalising the negative externalities, Pigovian taxes need to reflect the value of the externalities that they are meant to be correcting. We don't have that now, and some more investigation is needed so that we might hope to in the future.

Using a Pigovian tax to correct for a negative (consumption) externality

In my previous post, I demonstrated that, if left alone, a market with a negative externality produces too much of a good, and creates a deadweight loss. At the end of that post, I noted that, if we wanted to reduce the quantity that is traded in the market, we could use a tax. Such a tax is called a Pigovian tax (named after 20th Century economist Arthur Pigou), and is the focus of this post.

Consider the same market as that previous post (the market for fireplaces, or fireplace use), as shown in the diagram below. The market operates at the point where supply (S) meets demand (D) - that is, the quantity traded will be QM (and the price of fireplaces, or fireplace use) will be PM. Consumer surplus is the area ACPM, producer surplus is the area PMCF, the welfare cost of the negative externality is the area ACHG, and total welfare (which is the sum of consumer surplus and producer surplus, minus the area of the negative externality) is equal to the area (GEF-ECH).[*]

Now consider what happens when the government imposes an excise tax on fireplaces (or fireplace use). We will assume that the per-unit cost of the tax is exactly equal to the marginal external cost (MEC), and that the tax would be paid to the government by the sellers of fireplaces (or fireplace users). We represent the tax with a new curve, S+tax, which is exactly the same distance above the supply curve as the MSB curve is below the demand curve (that's because the tax is exactly equal to MEC). The price that consumers pay increases to PC. The effective price that producers receive (after paying the tax to the government) decreases to PS. The quantity of fireplaces (or fireplace use) decreases to QS.

What happens to economic welfare? The consumer surplus is the area ABPC, and the producer surplus is the area PSEF. The government receives tax revenue equal to the area PCBEPS (this is part of total welfare, because the government can use that revenue to provide services like schools or hospitals). The area of the negative externality is the area ABEG. Total welfare with the tax is equal to GEF. [**]

In other words, the Pigovian tax not only reduces the quantity of fireplaces (or fireplace use), but leads to an increase in total welfare (in fact, it leads to total welfare being maximised and the deadweight loss being eliminated). Economists aren't often in favour of excise taxes, but this is one case where an excise tax can make society better off.

Read more:

• The welfare impacts of a negative (consumption) externality

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[*] For the explanation of these welfare areas, see my previous post.

[**] Note that this is the same total welfare as occurred at the quantity QS in my previous post. To recap, that's because the area of the negative externality ABEG cancels out some of the total welfare that was in the combined consumer and producer surpluses and government revenue (ABEF), leaving the area GEF.

The Greens vs. Labour on carbon emissions, taxes and permits

Brian Fallow wrote an interesting article in the New Zealand Herald on Friday, contrasting the climate policies of Labour and the Greens. It was doubly interesting given that we had just covered this topic in ECON110 last week. Here's what Fallow wrote:

The climate change policies the two parties have recently released overlap a lot, in ways that distinguish them from National and the status quo.

But they are also at odds over which is the better way to put a price on emissions that will influence behaviour in the economy.

Labour wants to restore the emissions trading scheme (ETS), as designed by David Parker and enacted by the fifth Labour Government in the last few weeks of its ninth year in power, then promptly gutted by the incoming National Government.

But the Greens favour a tax on emissions, the proceeds of which would be used to plant trees on erosion-prone land, and the rest (most of it) recycled as an annual payment to everyone over the age of 18.

Pigovian taxes (e.g. a tax on carbon emissions) and tradeable pollution permits (e.g. the emissions trading scheme) are essentially two ways of arriving at the same destination - a reduction in emissions. Consider the diagram below, which represents a simple model for the optimal quantity of pollution (or carbon emissions). The MDC curve is the marginal damage cost (the cost to the environment of each additional unit of carbon emitted) and is upward sloping - this is because at low levels of carbon emissions, there is relatively less damage because the environment is able to absorb it. The capacity for the environment to do this is limited, so as carbon emissions increase the damage increases at an accelerated rate. The MAC curve is the marginal abatement cost (the cost to society of each unit of carbon emissions abated, or reduced) and is upward sloping from right to left. This is because, as more resources are applied to reducing carbon emissions, the opportunity costs increase. This may be because less suitable resources (meaning more costly resources) have to begin to be applied to pollution reduction. The optimal quantity of carbon emissions occurs where the MDC and MAC curves intersect - at Q*. Having less carbon emissions than Q* (such as at Q1) means that MAC is greater than MDC. In other words, the cost to society of reducing that last unit of carbon emissions was greater than the cost in terms of environmental damage. Having pollution at Q1 must make us worse off when compared with Q*.

The diagram illustrates that there are two ways of arriving at the optimal quantity of carbon emissions. One way is to regulate the quantity of emissions to be equal to Q*, as you would in an emissions trading scheme. You allocate carbon permits equal to exactly Q*, and legislate that no one is allowed to emit carbon unless they have permits (and have appropriately large penalties in place for those that break the rules).

An alternative is to price emissions at P*, as you would through a carbon tax. If the price of emissions is P*, you will have exactly Q* emissions. This is because no one would want to emit more than Q*, because the MAC is lower than the tax they would have to may (so it is cheaper to abate one unit of carbon emissions than it is to pay the tax, so at quantities above Q* the quantity of emissions would reduce). Similarly no one would want to emit less than Q*, because the MAC is greater than the tax (so it is cheaper to emit one more unit of carbon and pay the tax, rather than pay the cost of abating that unit).

Which should we prefer - an emissions tax, or an emissions trading scheme? There are arguments for and against either (as I have noted before). Neither system is particularly flexible if new cleaner technology becomes available. Both provide incentives to reduce carbon emissions to Q* (and no further). Taxes may be less subject to corrupt practices (such as in deciding who would get any initial allocation of permits). Permits may be more efficient in the economic sense, since the emitters who can reduce their emissions at the lowest cost would sell their permits to those who can only reduce emissions at high cost.

Fallow doesn't conclude that either system is better though. However, one thing is clear, and that is that all countries doing nothing about carbon emissions is unambiguously worse than either system. And both emissions taxes and emissions trading schemes are better than old-school command-and-control regulation.

Read more:

• The inefficiency of New Zealand's emissions trading scheme
• Pigovian taxes vs. tradeable pollution permits when clean technology becomes available

The optimal open road speed limit

A couple of years ago, I wrote a post about speed enforcement. However, it remains an open empirical question as to what the optimal open road speed limit is. When a driver increases their speed, the risk of an accident increases and so does the severity of the accident. That imposes a cost on the driver, and because of the non-linearity of accident damage, the marginal cost is increasing (i.e. the difference in accident severity between an accident at 110 km/hr and one at 100 km/hr is larger than the difference between an accident at 60 km/hr and one at 50 km/hr even though the speed differences are the same in absolute terms). That cost may be offset by benefits in the form lower travel times (i.e. saving the time cost of travel). Marginal benefit decreases with speed (every km/hr faster saves some time, but each km/hr saves less additional time as you go faster). The optimal speed for the driver is the speed where marginal benefit of driving faster is exactly equal to the marginal cost. At this point, driving a little bit faster entails a higher additional cost than the benefit they would receive (which is why they will drive no faster).

However, when setting a speed limit a benevolent social planner doesn't only care about the costs and benefits to drivers. Speeding drivers place additional costs on others (externalities), including risk to other drivers, pedestrians, and increased pollution and its associated health costs. So, if we wanted to know what the optimal open road speed limit is for society (not just for drivers themselves), we need to consider the additional external costs. So the optimal speed limit for society will be lower than the optimal speed limit for each individual driver (which might be one explanation for the number of drivers who consistently drive over the current limits).

Cost-benefit analyses of the speed limit are rare. Which is why I was very interested to read this paper in the Journal of Public Economics earlier this year (sorry I don't see an ungated version online) by Arthur van Benthem (Wharton School, University of Pennsylvania). In the paper, van Benthem undertakes a fairly exhaustive evaluation of the costs and benefits of a series of speed limit changes that occurred in 1987 and 1996 in the U.S. (specifically, he looks at the effects in California, Oregon and Washington states). Unlike past studies that have mostly evaluated the costs purely in terms of road accident fatalities (valued using the value of a statistical life, or VSL), this paper looks at a wider range of private and external costs, as shown in the figure below.

van Benthem first evaluates the impact of the speed limit changes on each of the variables above (fatal accidents, non-fatal accidents, infant health, etc.) by comparing roads where the speed limits were raised (mostly from 55 mph to 65 mph) with control roads where speed limits remained unchanged. He tests for and doesn't find any substitution effects, so drivers weren't induced into driving more on the roads with higher speed limits, when compared with the control roads (which is unsurprising because they are generally located in different areas).

What were the effects? In terms of the outcome variables noted in the figure above, he finds:

...that a 10 mph speed limit increase leads to a 3–4 mph increase in travel speed, 9–15% more accidents, 34–60% more fatal accidents, a shift towards more severe accidents, and elevated pollution concentrations of 14–24% (carbon monoxide), 8–15% (nitrogen oxides) and 1–11% (ozone) around the affected freeways. The increased pollution leads to a 0.07 percentage point (9%) increase in the probability of a third trimester fetal death, and a positive but small and statistically insignificant increase in the probability of infant death.

van Benthem then goes on to evaluate the costs and benefits of the speed limit changes, using common measures of the VSL (for accident-related and health-related costs), value of time (for travel time savings) and petrol prices (for increased fuel costs). He finds:

Annual net social benefits are estimated at −$189 million excluding adult health impacts, with a standard deviation of $94 million. The social costs ($345 million) exceed the benefits ($156 million) by a factor of 2.2. Using the adult health impacts from the central health impact scenario, which are admittedly uncertain, the net benefits decrease to −$390 million, with a standard deviation of $102 million... The social costs exceed the benefits 3.5 times.

In other words, the costs of increasing the speed limit outweighed the benefits by a substantial margin - the speed limit should not have been raised. And the results appear to be very robust, even when you consider a range of values for the VSL and the value of time. Of course, any cost-benefit evaluation is necessarily incomplete. It isn't possible to include every cost and benefit that might arise, and many of the costs and benefits will be fairly uncertain (as the quote above notes in the case of adult health impacts). In the paper, van Benthem notes that his analysis omits "marginal excess tax burden from changes in speeding ticket and gas tax revenues, changes in enforcement costs and increased driving pleasure at higher speeds".

So, what was the optimal speed limit? van Benthem suggests that it was not much below 55 mph. Finally, this evaluation was based on somewhat dated data. If the analysis were re-run with more up-to-date data, we might get something different - cars are now more fuel-efficient, safer to drive (even at high speeds), health care has improved (which might reduce some fatal accidents to non-fatal), and petrol prices are higher. van Benthem suggests that:

today's gap between private and social net benefits will be smaller for a 55 to 65 mph speed limit increase. For higher speed limits, the gap is likely to remain substantial because of the steeper speed-emission profile in that range and the external cost component of accidents.

Finally, the paper has a number of additional bits I found interesting:

• The treatment effect of the speed limit changes on travel speeds increased over time - people adjusted their speeds towards the new limit, but this adjustment was not immediate. 
• Carbon monoxide (CO) emissions triple as vehicle speeds increase from 55 mph to 65 mph!
• van Benthem also draws a conclusion about the optimal Pigovian tax on speed, which:

would consist of a combination of a gasoline tax for climate damages, emissions taxes for local air pollutants in exhaust gas (which varywith speed), plus a speed-dependent tax to internalize accident risk imposed on others (which is also a function of traffic conditions).

Pigovian taxes vs. tradeable pollution permits when clean technology becomes available

This week in ECON110 we covered externalities, and pollution. One of the aspects we covered is the difference between Pigovian taxes and tradeable pollution permits. MRUniversity has a useful video describing tradeable permits, and why they are a good idea:

In short, tradeable permits solve the problem of pollution at the least cost, because the producers that could reduce pollution at low cost would do so, and sell their permits to the producers who could only reduce pollution at high cost.

Anyway, in this post I wanted to compare taxes and permits. Alice Lepissier and Owen Barder at CGD wrote a quite detailed post on this comparison last year. I want to take a different tack to them, and think about what happens when clean technology becomes available.

The diagram below describes the simple model for the optimal quantity of pollution. You might think that the 'optimal' quantity of pollution is zero, but with no pollution we would essentially have no production which wouldn't make us better off at all (or at the extreme, no pollution means no breathing, since we all exhale carbon dioxide). Anyway, the MDC curve is the marginal damage cost (the cost to the environment of each additional unit of pollution) and is upward sloping - this is because at low levels of pollution, there is relatively less damage because the environment is able to absorb it. The capacity for the environment to do this is limited, so as pollution increases the damage increases at an accelerated rate. The MAC curve is the marginal abatement cost (the cost to society of each unit of pollution abated, or reduced) and is upward sloping from right to left. This is because, as more resources get applied to reducing pollution, the opportunity costs increase. Also, less suitable resources (meaning more costly resources) have to begin to be applied to pollution reduction. The optimal quantity of pollution occurs where the MDC and MAC curves intersect - at Q*. Having less pollution than Q* (such as at Q1) means that MAC is greater than MDC. In other words, the cost to society of reducing that last unit of pollution was greater than the cost in terms of environmental damage. Having pollution at Q1 must make us worse off when compared with Q*.

Now consider Pigovian taxes. With a Pigovian tax every firm must pay the government for each unit of pollution they generate. This effectively sets a price for pollution. The optimal price of pollution (which would lead to exactly Q* units of pollution in the diagram above) is P*. Firms would not pollute more than Q*, because the tax (P*) is greater than the MAC - it is cheaper to reduce pollution than it is to pay the tax. On the other hand, firms would not pollute less than Q* either, because the MAC is greater than the tax (P*) - it would be cheaper to pay the tax than to reduce pollution further than Q*.

What about tradeable pollution permits? With tradeable permits, the government sets the number of permits (pollution rights) that are available to the market - one permit allows a firm to emit one unit of pollution. The optimal quantity of permits is Q*, and the market will set the price exactly equal to P*. The price will not rise higher than P*, because then MAC would be less than P* and firms could reduce pollution for less cost than the price of a permit.

So, it is easy to see that both taxes and permits are theoretically equivalent in terms of the market for pollution. Taxes set the market prices, which (if the price is set correctly) results in the optimal quantity of pollution. Permits set the optimal quantity, which leads to the market price. At this point, the argument becomes which system (taxes or permits) would be less costly to administer and which would provide better incentives to adopt cleaner technology - possibly taxes in both cases. Or perhaps the argument is about which system is less risky, which Lepissier and Barder argue is permits.

Now, think about what happens if a new clean technology becomes available that makes it cheaper to reduce pollution. That lowers the marginal abatement cost, so MAC moves to MAC1 in the diagram below. The diagram demonstrates what happens with a Pigovian tax. The price of pollution is fixed at P*, so when MAC decreases to MAC1, the quantity of pollution falls greatly (to Q2). However, Q2 is too little pollution (relative to the new optimal quantity Q1), and at that point MAC is greater than MDC - the cost to society of reducing the last unit of pollution was greater than the cost in terms of environmental damage. We reduce pollution too much, leading to a deadweight loss (the area BEF in the diagram).

The next diagram demonstrates what happens with pollution permits. The quantity of pollution is fixed at Q*, so when MAC decreases to MAC1, the price of pollution permits falls (to P2). Now Q* is too much pollution (relative to the new optimal quantity Q1), and at that point MAC is less than MDC - the cost to society of reducing one more unit of pollution would be less than the cost in terms of environmental damage. We don't reduce pollution enough, leading to a deadweight loss (the area GHJ in the diagram).

So in both cases, when a new clean technology becomes available we end up with a deadweight loss. In this case though, you probably want the clean technology to lead to less pollution rather than the same quantity, so I would argue that this favours taxes over permits, unless it is easy for the government to reduce the number of permits. And when you consider climate risk, it is probably better to over-shoot on pollution reduction, rather than under-shoot.

[Update: Replaced diagrams to fix x-axis labels]