Leaping the Divide

Sharing the cost of carbon mitigation with our grandchildren

laurence kotlikoff is a professor of economics at Boston University.

Illustrations by mitch blunt

Published January 23, 2020


What will it take to prod a complacent America (not to mention a fair portion of the rest of the world) into getting serious about climate change? Greta Thunberg, the determined 16-year-old Swedish activist, has given it a try, making the rounds of the great and powerful with her sobering message. At the UN Climate Summit a few months ago, Greta pleaded with the grown-ups to spare their children: “The eyes of all future generations are upon you. And if you choose to fail us … we will never forgive you. … Right here, right now is where we draw the line.”

But those who needed to listen most, apparently were not. “She seems like a very happy young girl looking forward to a bright and wonderful future,” tweeted President Trump. “So nice to see!”

Indeed, there is little evidence that Greta changed any minds, let alone inspired a radical shift in climate policy. But imagine an alternate universe in which Greta was actually a canny (perhaps even cynical) economist all too aware that calls for sacrifice are not an easy sell. And imagine she had said this instead:

“We children understand you are selfish and disinclined to worry about future generations. So, let’s do some horse-trading. Levy a hefty tax on carbon emissions now — say, $70 per ton — to drive businesses and households toward energy conservation and renewable fuels — and even promise to increase this tax annually. Yes, this will raise your energy prices. But don’t worry: it need not cost you a penny.

“Just simultaneously cut other taxes — Social Security taxes, incomes taxes — by enough to offset the entire carbon tax burden. Then borrow the amount needed to cover the resulting increase in the federal deficit and leave it to us — today’s and tomorrow’s children — to worry about the extra debt. You’ll be no worse off and, on balance, we’ll be better off because the burden of a bigger debt will be smaller than the burden of greater climate change. Or, if you are feeling really, really selfish, cut your own non-carbon-linked taxes by even more than the carbon levy. Yes, at least up to a point, it makes sense for us kids to bribe you if that’s what it takes to prevent climate disaster.”

This might appeal to America’s Dealmaker-in-Chief. But even if it didn’t, it would recast the debate about climate change to focus on how to minimize the cumulative generational cost of living with climate change and making the transition to a low-emissions economy.

A Costly Economic Misunderstanding

Most climate economists have posed the intergenerational problem much the way Greta did at the United Nations. They have viewed the process of limiting carbon emissions as a “zero-sum” game in which current generations have but one option — sacrifice now to spare future generations.

But look again. This framing really implies that the ideal carbon tax is a matter of ethics, not economics: how much we sacrifice today in terms of consumption depends on how much we believe we owe to future generations in terms of a stable climate.

The leading example of this framing is Yale economist William Nordhaus’s seminal and Nobel-Prize-winning work on “optimal” carbon-emissions taxation. Nordhaus presents the problem as one in which an omnipotent social planner arrives on the scene, decides which generations to favor and sets the carbon tax accordingly. The more the planner cares about future generations, the higher they set both the initial carbon tax and its rate of increase.

To be clear, Nordhaus deserved his Nobel Prize. He was the first economist to identify climate change as a man-made, global and enormous economic, health and social problem — a problem demanding significant research and major policy intervention. How​ever, his social-planner solution confounds economics with ethics.

Following his framework logic, each of us is free to imagine a social planner with our own preferences about which generations are most or least deserving. And, since the choice of social planner determines “optimal” policy, Nordhaus is, effectively, telling us the optimal policy is simply the one our preferred planner chooses. In short, anything goes.


Other leading economists have posed the intergenerational climate problem slightly differently, within what economists call a “single-agent” model. Here the world is divided into a large number of infinitely lived dynasties — think of them as extended families across the generations. The sole difference between the single-agent and the social-planner frameworks is that each dynasty in the single-agent model cares only about its own members. This leads the dynasties to attempt to “free ride” by emitting more carbon than would otherwise be the case because most of the cost in terms of climate change is borne by members of other dynasties.

The dynasty model has extremely strong implications that follow from the assumptions. Individuals will share their resources within the dynasty. Hence, if one member gets a pay raise, they’ll share it with both current and future dynasty members, in the latter case by saving part of the raise. Or, if the government cuts the taxes of current dynasty members and demands that future members make up the difference, today’s members will spend not a penny of the tax cut and simply set it aside to give to future members to cover their larger tax bill. Moreover, if members of two dynasties fall in love, the two effectively merge, so that a raise received by anyone in one dynasty is shared with everyone in both dynasties.

Extended-family goodwill is a nice idea, but could not be more removed from reality. When it comes to spending, extended family members in fact act as if they are unrelated — they spend based on their own resources, not on the resources of their children, their parents, their siblings or anyone else on their current, let alone future, family tree. This leaves the economics profession providing carbon-tax policy advice based either on the ethical sensibilities of major climate influencers, like Nordhaus, or on the basis of a model that no one should take remotely seriously.

Why Did Climate Economists Forsake Econ 101?

Why have economists invoked social-planner or single-agent models when neither is appropriate? The answer appears to be computational convenience. Both models can be encapsulated in simple mathematical formulas, which can be readily used to solve, either analytically or numerically, for “optimal” carbon tax policy. Unfortunately, using either of these approaches is akin to looking for one’s lost car keys under the nearest streetlight rather than in the unlit places they are likely to be found.

Unlike Greta’s message and that of most climate economists, the climate can in fact be fixed in a manner that makes every generation in every part of the world better off. Understanding this requires the clarification of a key economic issue associated with man-made climate damage: the absence of a market for the benefits generated by a stable climate.

Consider the hypothetical island of Fruits. (Bear with me here for a while — there really is a payoff.)

Fruits is inhabited by the As and the Ps. The As live on half the island; the Ps live on the other side. The two halves are separated by a wide river. On the As’ half, the only food that can be grown is apples. On the Ps’ half, the only source of food is pears. The As, alas, are allergic to apples, but adore pears. The Ps are allergic to pears, but adore apples. (In Fruit world, nobody apparently needs protein in their diet.)

But wait! If the As could build a bridge to trade with the Ps, they’d be in pear heaven. Let’s assume, though, that the costs of building a bridge on their own outweigh the benefits of access to pears. The Ps face a parallel predicament. Misery abounds until the United Nations gets the As and Ps to each build half the bridge. This immediately opens the apple-pear market, dramatically improving the welfare of both the As and Bs.

Economists call the ensuing improvement in everybody’s lives a “Pareto efficiency gain.” Signore Pareto, the 19th-century engineer, sociologist and philosopher who thought up the concept, observed that one could not say changing policy was worthwhile if it meant hurting Peter to help Paul, even if it only hurt Peter a little and helped Paul a lot. What one could do was find “Pareto-improving” policies, like building the bridge, that make at least one person better off and no one worse off.

Climate Change and the Missing Market

Markets may go missing for many reasons. In the above parable, it’s the lack of requisite infrastructure — the bridge. In the climate context, it’s the inability of future generations (Futures) to trade with current generations (Currents).

Imagine that Futures were alive today. Their representatives would sit down with the representatives of the Currents and cut the deal I imagined Greta proposing at the beginning of this screed. Yes, there would be lots of moralizing about the Futures having the right to a temperate climate and the Currents having the right to burn as much coal as West Virginia wished. But, at the end of the day, it would make sense for both to cut a deal, with Futures voluntarily paying Currents for each ton of carbon they didn’t emit — or Currents paying the Futures for each ton they did emit. For the deal to be Pareto-efficient, each extra ton of carbon emitted into the atmosphere would need to be correctly priced based on the extra damage it caused. That way, carbon emissions would have the proper pseudo-market Pigouvian price, which, with appropriate side payments, would benefit both sides, or at least benefit one side while leaving the other side indifferent.

Of course, there is simply no way for unborn generations to bargain with us. Government, which is here now and we assume will be around in the future, is the only party that can make a market between those around today and those around tomorrow. Specifically, it can legislate and enforce, through time, the deal laid out in Greta’s hypothetical speech.

Carbon Taxation that Achieves a Uniform Generational Win-Win

One way to spread the economic gains from taxing carbon is to give all generations an equal stake in the policy. This means not just taxing carbon at, potentially, different levels or rates through time, but simultaneously redistributing between the current elderly, the current middle-aged, the current young and all future generations to ensure that each generation (more precisely, each member within each generation) is made equally better off over the rest of their lives.

Giving all generations an equal claim to the benefits from fixing the climate externality may be the best way to ensure that a Pareto-efficient, carbon-tax policy is actually enacted. The alternative — giving higher (lower) benefits to future generations and lower (higher) benefits to current generations — might lead to so much wrangling that no Pareto-efficient scheme is ever implemented.

Determining the uniform welfare-improving carbon tax coupled with the intergenerational redistribution (side-payment) policy is computationally far more challenging than doing questionable exercises with far simpler models. But, undeterred, four colleagues and I — Felix Kübler of the University of Zurich, Andrey Polbin of the Gaidar Institute, Jeffrey D. Sachs of Columbia University and Simon Scheidegger of the University of Lausanne — have made the requisite calculations.

Our framework assumes neither a social planner nor single-agent dynasties. Instead, it assumes what casual observation confirms — generations are selfish and those alive at any point in time will emit carbon to their pocketbook’s content, absent an economic incentive to do otherwise.

Intergenerational models with selfish generations are called “overlapping generations models.” In ours, households go to work at age 20, retire at 65, and pass away at 75. To make it easier to compare our results with Nordhaus’s carbon tax prescription, our model meshes as closely as possible to his workhorse DICE (dynamic integrated climate economy) model. In particular, we adopt Nordhaus’s assumed relationship between output and the emission of CO2; the manner in which CO2 concentrates in the atmosphere, the upper ocean and the lower ocean; the extent to which CO2 concentration in the upper atmosphere naturally dissipates through time; the manner in which atmospheric CO2 levels affect the average global temperature; and the process by which temperature produces economic damage.

We are selfish and those alive at any point in time will emit carbon to their pocketbook’s content, absent an economic incentive to do otherwise.

Where we differ from DICE, apart from positing selfish generations, is in incorporating a more realistic formulation of the energy sector. In particular, we explicitly model the extraction and use of coal, oil and gas, the production of clean energy, and the extent to which clean energy’s cost will decline through time due to technological progress.

Our model is what’s known in economics as a “computable general equilibrium” model. It’s large scale, not simply because it incorporates, at each point in time, 55 overlapping generations, but also because each generation’s decisions about how much to save and spend depends on the economy’s future wages, interest rates, energy prices and fiscal policies. These variables, in turn, are determined by generations’ saving and spending decisions.

The computational solution to our model isn’t, unfortunately, lying under that proverbial streetlight. It requires developing highly precise computer algorithms ensuring that all the model’s equations are solved in an internally consistent manner. How many equations are we talking here? Over 100,000 (no misprint). This reflects, in part, the assumed 3,000 years it takes for carbon in the atmosphere to stabilize once new carbon is no longer being added.

It’s not quite as daunting as it sounds. Our method of solving our big model dates, interestingly enough, back to the 1800s — specifically to the work of mathematicians Carl Friedrich Gauss and Philipp Ludwig von ​Seidel. They showed how one can solve large sets of simultaneous equations, where everything depends on everything else, by guessing the results and then using the equations to update and re-update those guesses.

In our model’s business-as-usual baseline transition path, “dirty” energy represents 97 percent of total energy consumption in year 0, 86 percent in year 50, 46 percent in year 100 and zero after year 130 — when the cost of additional dirty energy extraction exceeds its value. Relative to their initial stocks, coal, oil and gas reserves are depleted by 70, 75 and 85 percent, respectively. Hence, imposing no carbon policy entails burning most of the planet’s fossil fuels.


Given the significant uncertainty surrounding climate damage, we also consider larger climate damages than those assumed by Nordhaus. In our high-damages (but arguably more realistic) scenario, damages initially reduce output by 1 percent, peaking at 18.8 percent in year 2200.

With low damages, the optimal, uniform welfare-increasing carbon tax starts at $30, rises at 1.5 percent per year and raises the welfare of all current and future generations by 0.73 percent. This increase is, by the way, measured in terms of extra consumption. Sharing the gains from our carbon tax evenly across all generations requires taxing future generations by as much as 8.1 percent of output and subsidizing early generations by as much as 1.2 percent of their annual future consumption, precisely by running up government deficits. Without such redistribution, the carbon tax constitutes a lose-win policy, with those now alive experiencing up to a 0.84 percent welfare loss and those born in the medium term (in this case, year 235) experiencing up to a 7.54 percent welfare gain.

This is, in fact, what a Nordhaus social planner would try to do. They would impose essentially the same carbon-tax policy as our model prescribes, at least for this low-damages case. But they’d make no effort to compensate losers by taxing winners. Hence, they would harm early generations in the process of helping future generations. Such a policy might meet someone’s ethical preferences, but can’t be justified as an optimal policy by economics science.

In the high-damages case, the optimal uniform welfare-increasing initial carbon tax is $70 per ton, also rising at 1.5 percent per year. This policy raises all generations’ welfare by almost 5 percent. This is a huge increase as these calculations go. However, achieving this outcome requires taxing certain future generations by as much as 50.1 percent of their annual consumption and subsidizing certain early generations by as much as 10.3 percent of their annual consumption.

The optimal carbon tax materially alters the course of dirty energy production. For example, in the low-damages case, coal production is zero for 25 years, positive for 40 years and zero thereafter. This implies the planet needs to cool down before it is efficient to use coal again in any quantity. However, the reintroduction of coal, when it does occur, is small. Indeed, our low-damages optimal carbon-tax policy entails burning only 10 percent of initial coal reserves, compared to 70 percent with no carbon tax.

With the high-damages scenario, the uniform welfare-improving policy entails an immediate end to coal production. Uniform welfare-improving carbon taxation also shortens the period during which dirty energy of any sort is produced: from 100 to 130 years to 100 years in the low-damages case, and to 80 years in the high-damages case.

When Too Late is Too Little

Another key finding of our study is that waiting, say, 20 years to implement a significant carbon tax is, economically speaking, waiting too long. There will be so much carbon in the atmosphere that most of the potential for Pareto gains from the policy will have been lost. This reflects, in part, the so-called “green paradox”: any policy to tax carbon heavily in the future sends dirty-energy producers a message: use it or lose it! This leads them to extract coal, oil and gas at a faster clip, which produces a faster fossil-fuel burn and heating of the planet.

Getting Carbon Tax Policy on Track

When it comes to carbon taxation, climate economists have put their worst feet forward. They have depicted carbon taxation as inevitably creating a mix of winners and losers, and then taken it upon themselves to play God — to determine the sacrifice that Currents should make on behalf of Futures.

It’s time for climate economics to treat anthropogenic climate change for what it is — a standard, Econ 101, negative externality whose remediation can benefit all of humankind, present and future. Indeed, we now have the technology to calculate the course of carbon taxation and intergenerational (as well as interregional) redistribution that will improve the welfare of all humans, living and prospective, to the same degree. The failure to implement it would be a lose-lose.

main topic: Climate Change
related topics: Tax Policy