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April 4, 2012
CO2: Tax Now, Pay Later!

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by Étienne Billette de Villemeur and Justin Leroux

Étienne Billette de Villemeur is professor of economics at the University of Lille, France, and research fellow at EQUIPPE, and Justin Leroux is associate professor at the Institute of Applied Economics at HEC Montréal, and research fellow at CIRANO and CIRPÉE.

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Regarding the climate change issue, a tax on greenhouse gas (GHG) emission flows (also dubbed the carbon tax) is arguably the most prominent instrument put forth to correct "the greatest market failure the world has seen" (Stern, 2008). According to the familiar Pigovian argument, the motivation behind carbon taxation is to make emitting GHGs expensive in order to induce a reduction in emissions.

We argue that the carbon tax as we know it suffers from fundamental shortcomings regarding its implementation, and we offer an alternative way to tax emissions that is free of these flaws. Our proposal relates to the timing of taxation: Instead of charging emitters today for the present value of the damage their emissions may cause, we should tax the emissions of countries over time -- albeit at a lower rate -- to reflect the environmental damage actually caused by their emissions. It turns out that this scheme, which we refer to as ex post taxation, is not only cheaper than the carbon tax but avoids the crucially problematic issues of predicting future climate damage and of having to settle the raging debate on how to account for the welfare of future generations. Moreover, it ensures that emitters are held accountable for the real damage incurred, rather than according to some indeterminate ideological stance on what may or may not happen.

Fundamental Problems With the Carbon Tax

To induce the optimal level of emissions reduction, the carbon tax should be set equal to the present value of the environmental damage that carbon emitted today causes -- not only today, but also in the future. The timing of the carbon tax is a major weakness. With carbon dioxide persisting in the atmosphere for up to several centuries (Archer and Brovkin, 2008), the computation of the damage that CO2 emitted today will cause over time is an extremely difficult, if not unreasonable, exercise.

Despite advances in climate science, it is doubtful that our understanding of the climate is accurate enough to predict the impact that a marginal ton of CO2 in the atmosphere will have on the future climate. Furthermore, we do not have any reasonable idea of what types of technology will be available to us in the next centuries to mitigate, or perhaps harness, changes in climate patterns. Worse, predicting future damage requires making explicit forecasts about future emissions patterns, which requires a deep understanding of the interplay between economics, technological development, and climate science that we simply do not have.

That is not all. In order to calculate the present value of future climate damage caused by today's emissions, one must take a stance on how to discount the welfare of future generations. This is the topic of deep philosophical discussions on the ethics of climate change that are beyond the scope of this article.1

It follows from these difficulties that the computation of the carbon tax rate is a highly nebulous exercise. As a result, this makes it subject to interpretation and to political pressures. This partly explains the fact that the carbon tax has been carried out only sporadically and can only be seen in a mere dozen countries. What is perhaps most striking is that the few regions of the world that have a carbon tax differ widely in the tax rate they impose, ranging from $13 to $150/tCO2 (Environmental Tax Policy Institute, 2009). According to the Pigovian principle, however, this would imply that CO2 emitted in Sweden (where the tax rate is the highest) is 10 times more damaging than CO2 emitted in Colorado. This heterogeneity is unsupported by any climate model, quite to the contrary: Wind patterns tend to mix all emissions together so that CO2 concentrations in the atmosphere bear no relationship with their source. In other words, the impact of emissions is roughly the same no matter from where they originate.

Why Delaying Taxation May Help

The timing of the carbon tax creates major obstacles to its implementation. Because it is a forward-looking tax, computation of the carbon tax rate requires making predictions about climate damage far off in the future as well as specifying a social discount rate by which to evaluate the welfare of future generations. By contrast, we argue that delaying tax payments eliminates these obstacles.

By ex post taxation we intend a scheme that collects payments only once climate damage has occurred and charges countries in proportion to their responsibility in current CO2 concentrations. Hence, the tax rate is calculated based on observed damage, and each country's tax payment reflects the remaining stock of CO2 in the atmosphere for which it is responsible. Data on the latter requires only knowledge of past emissions patterns, which is readily available, and of how fast CO2 decays in the atmosphere. Estimating observed damage, on the other hand, requires some serious work.2 Nevertheless, the ex post tax rate is computed only based on data that is available or that can be estimated, but not on any prediction whatsoever.

At first, it may seem curious that a tax scheme that only rests on information about the past can help us address a problem that is mainly concerned with the future. How can it possibly work? The answer lies in what economists call "rational expectations," a concept for which Bob Lucas was awarded the Nobel Prize in Economics in 1995. Simply put, rational expectations recognize the fact that economic agents take future consequences into consideration when making decisions today. Framed in our context, rational expectations imply that countries will take future tax payments into account when deciding on their current emissions policies. In turn, even though ex post taxation seems only concerned with the past, countries have an incentive to curb today's emissions because those emissions will enter in the calculation of tomorrow's tax base.

Because ex post taxation relies on a farsighted view of the future to motivate curbing emissions today, it most likely requires a shift in the scale of the taxable units, from individuals and businesses to the countries they represent. Given the time durations involved, an important implication of ex post taxation is that future generations will be held accountable for tax payments related to actions about which they have had no say. While this observation may be shocking at first, it is common to all debt-financed policies, which have been around for centuries. In fact, under ex post taxation, emitting CO2 becomes precisely like "emitting" debt.3 Moreover, the scheme fosters decentralization because each country is then free to enact its own emissions policy -- for example, energy taxes, emission quotas, hybrid policies, and so forth -- so long as it complies with the (global) ex post taxation scheme.

Properties of Ex Post Taxation

We now turn to a number of remarkable properties that arise from taxing emissions ex post, in addition to the flexibility just mentioned and the lack of need for predictions.

First, ex post taxation is cheaper than the corresponding carbon tax. This is simply because the carbon tax requires emitters to pay the entire present value of future damage upfront, whereas ex post taxation payments are effectively made in installments. Using business terminology, the carbon tax demands advance payment while the ex post tax is paid on delivery (corresponding to the occurrence of climate damage). Because the present value of payments is the same under both taxes and because ex post taxation delays payment, it is the cheaper of the two.

We illustrate this statement on a simplified numerical example in Figure 1. The graphs show the (future) value of cumulative tax payments over the years brought about by each ton of CO2 emitted today. This value is always lower under the ex post tax, because payments take place over time rather than upfront. Moreover, the gap between the two curves shrinks over time, down to zero in the distant future.

Figure 1. Value of Tax Payments Per Ton of CO2
Emitted Today

Note: CO2 does not remain in the atmosphere forever but decays at a very slow rate that we conservatively take to be 0.98, which corresponds to a half-life of 34 years. Also, in order to evaluate today climate damage that will occur in the future, we must posit a social discount rate (that is, an interest rate of sorts), which we shall take to be r=4% per year. Note that these numbers likely err on the conservative side, meaning that the social discount rate is probably closer to zero and the decay rate of CO2 closer to one. Finally, we assume that the damage caused by CO2 concentrations is constant at $1.73/ton/year. This number was calibrated to fit a present value of carbon damage of $30/ton, which is the current carbon tax rate in the Canadian province of British Columbia.

Another desirable property of ex post taxation is that its rate only depends on observed damage whereas the carbon tax rate depends on predictions of future damage, an understanding of CO2 persistence in the atmosphere, and a specification of a social discount rate. This has major consequences on the sensitivity of the carbon tax rate to small errors in these highly uncertain specifications. Figure 2 illustrates numerically just how sensitive the carbon tax rate is regarding errors in the persistence rate and in the discount rate.

Figure 2. Carbon Tax Rate in Dollar/Ton

Notice how a simple 1 percent variation, say between r=4% and r=3%, results in a change in the carbon tax rate of almost 19 percent, from $29.99/ton to $35.64/ton, respectively. Likewise, a small error in the persistence rate, say between 0.98 and 0.99, results in an error of 20 percent in the carbon tax rate, from $29.99/ton to $35.98/ton, respectively. These are enormous variations for small errors of parameters that we either do not yet understand completely (the persistence rate) or cannot bring ourselves to agree on (the discount rate). Comparatively, the ex post taxation rate is completely unaffected.

Finally, ex post taxation addresses another issue that is increasingly receiving attention, the so-called ramp/springboard debate.4 Proponents of a "ramp" approach to carbon taxation argue that tax rates should be phased in, so that the economy is not disrupted too much. Conversely, the arguments in favor of a "springboard" implementation point to the fact that the stakes are so high that a carbon tax policy should be enacted in full force to immediately induce the optimal level of emissions reduction. Interestingly, ex post taxation answers both desiderata by having initially low-tax payments while implementing the same emission levels as a full-fledged carbon tax.

Note that ex post tax payments will increase with the stock of CO2 in the atmosphere, whereas carbon tax payments follow the pattern of emission flows. Nevertheless, on any given date, the value of cumulated payments is always less under the ex post tax than under the carbon tax. Figure 3 illustrates how the ratio of cumulative tax payments under the both schemes evolves over time.

Figure 3. Ratio of Cumulated Ex Post/Carbon Tax
Payments Over Time

Note: Based on a constant emissions scenario.

Not only is the ratio of cumulative tax payments less than one at all times -- implying that the ex post tax burden is less than that of the carbon tax -- but also it is remarkably low in the early periods. Indeed, the ex post tax burden is a mere 6 percent of that of the carbon tax at the outset. The ratio then takes roughly 25 years to reach 50 percent and catches up to one after 150 years.


We propose an alternative to the carbon tax that is not only cheaper but also easier to implement because it does not rely on controversial estimates of social, economic, and climate parameters. By taxing past emissions on the basis of realized climate damage, ex post taxation amounts to taxing emission stocks rather than emission flows. While taxing stocks may seem surprising at first, it is actually logical that ex post taxation exhibits much nicer properties than the carbon tax. After all, climate change is a stock problem, not a flow problem. In fact, shifting our attention to stock taxes, rather than flow taxes, is a promising avenue to addressing stock problems like climate change.


    Archer, D. and V. Brovkin, "The millennial lifetime of fossil fuel CO2," Climate Change 90, 283-297 (2008).

    Billette de Villemeur, E. and J. Leroux, "Looking Ahead versus Looking Back: Revisiting the Carbon Tax" (2011), available at

    Broome, J., "The Ethics of Climate Change," Scientific American 298, 96-102 (2008).

    Environmental Tax Policy Institute and Vermont Journal of Environmental Law, The Reality of Carbon Taxes in the 21st Century (2009).

    Mason, M., "Tackling Dangerous Climate Change: Slow-Ramp or Springboard?" Global Policy 1, 336-338 (2010).

    Stern, N., "The Economics of Climate Change," American Economic Review: Papers and Proceedings 98, 1-37 (2008).


1 See, e.g., Broome (2008) for a clear presentation of the main arguments.

2 There is no question that correctly estimating current climate damage is a dauntingly ambitious task, especially because it requires disentangling damage caused by human activity from exogenous damage. Yet while it may initially appear foolish to think we can achieve this goal with any satisfactory level of confidence, it is much less so than trying to predict this same damage decades or centuries in the future.

3 It can be shown that ex post taxation can accommodate considerations of intergenerational equity better than the carbon tax because it closely follows the timing of the occurrence of climate damage. See Billette de Villemeur and Leroux (2011) for a discussion of responsibility in the context of climate change.

4 See, e.g., Mason (2010) for an overview of the main arguments.


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