When something is wrong on the Internet, bloggers love to pounce. But since no blogger is infallible, most of us can find ample fodder in our own past writing, if we go back and reread it with a sufficiently critical eye. Over the next few weeks, I plan to revisit some things I got wrong the first time around. (You’ll recognize those posts by the Homer Simpson logo.) I hope others will be inspired to do the same.
To lead off this series: In December, 2009 I blogged about space scientiest James Hansen, who prefers carbon taxation to cap-and-trade. His argument: A carbon tax allows for the possibility of additional carbon abatements through altruism. Under cap-and-trade, if I altruistically decide to buy a fuel-efficient car, someone else gets to buy an SUV. Whereas under a carbon tax, if I altruistically decide to buy a fuel-efficient car, less gas gets consumed.
Wait a second, though. Under a carbon tax, if I decide to buy a fuel-efficient car, I drive the price of gas down, which encourages someone else to buy an SUV. So altruism is equally ineffective under either policy, no?
That’s the argument I made in December, 2009. I now believe that:
- Under a plausible interpretation of Hansen’s argument, I was wrong.
- But Hansen is still unconvincing, though for somewhat subtler reasons.
First, the key economic point. There is a demand curve for gasoline, and neither a carbon tax nor a cap-and-trade program can change that. The demand curve relates prices to quantities, and market forces will keep us on that demand curve. Government policies can move us along the curve but they can’t change the curve. Suppose we’re currently at the black point, and the government wants to move us to the red point. There are two ways to do that. You can have a cap-and-trade regime that moves the quantity to Q or a carbon tax that moves the price to P. Move either the quantity or the price and the other will follow.
In that sense, the two programs are entirely equivalent, as I said in my post. So far, Mr. Hansen has no reason to prefer one over the other.
Now let’s introduce some altruism. This moves the demand curve down, and changes the government’s menu of choices. Without the altruism, they can choose any point on the solid demand curve, and they can get to that point with either policy. with altruism, the same is true for the dashed demand curve. Still no reason to prefer one policy over another, which was the point of my 2009 post.
I realize, now, though, that Hansen (at least if we interpret him charitably, which is usually a good idea) was thinking about unexpected altruism, i.e. altruism that kicks in after the new policy is implemented. In that case, he’s right: If you fix the quantity at Q and then the demand curve shifts, the quantity stays at Q. But if you fix a tax rate that moves the quantity to Q on the original demand curve, and then the curve shifts, you will indeed move to a point on the dashed line where the quantity is less than Q. (I don’t claim to have proved that here, but those who have mastered Principles of Economics will be able to fill in the details.) So if Mr Hansen is concerned about changes in altruism that arise only after the policy is set, then he has a point.
What he seems unaware of is that his point cuts both ways. Whatever your current forecast of altruism, you are as likely to be wrong in one direction as the other. So a post-policy shift in demand is equally likely to be upward or downward. Hansen is right about this: If, after a gas tax is implemented, altruism rises, then gas consumption will fall further. But what he seems to overlook is this: If, after a gas tax is implemented, altruism falls, then gas consumption will rise. Either effect is avoided by cap-and-trade, and either effect is, as far as we know, equally likely. (Remember that we are attempting to forecast not altruism, but a change in altruism, which is much harder to get right.) So while Mr Hansen is not clearly wrong (as I incorrectly said he was), there’s still no particular reason to think he’s right.
What about the altruistic behavior of some environmental groups who buy up permits and never use them? Some groups did exactly that with the SO2 cap-and-trade system. Seems like another way Hansen’s analysis might be incomplete.
(thought I posted this already, did it get eaten?)
Mark, you’re right — I think the analysis has to distinguish between “hard altruism” (buying something and then not using it), and “soft altruism” (declining to buy something that you think has harmful side effects). Obviously, hard altruism under a cap-and-trade system can reduce pollution. The interesting question is under what circumstances “soft altruism” can as well. (Under cap-and-trade, it can’t, since the gas you don’t buy will be bought by someone else.)
Cap-and-trade is better for another reason still.
With a Pigouvian tax, the end result might be the same, but taxes necessarily create excess burden. So we are achieving the same result, but at higher (if hidden) cost.
With cap-and-trade, all costs are internalized and an efficient outcome is reached – that is, without excess burden.
Carbon tax is better because cap-and-trade will be gamed.
Being a person never too afraid to show my ignorance. From my non-extensive search, a carbon tax seems to be a tax on the amount of carbon that is a fuel that is burned. Cap and trade seems to be related to the amount of pollution generated.
Cap and trade (or a pollution tax) would seem to encourage processors/consumers for carbon fuels to develop mechanisms that reduce pollution.
A carbon tax (tax in the amount of carbon in a fuel) would seem to encourage processing/consuming fuels in the most cost efficient way whether or not more pollution is created.
This would seem to be a difference between the two. Or is it a given that the most cost effective way to consume carbon fuels will always be the way that generates the lowest amount of pollution?
Austin: In either case, the excess burden arises entirely from people using less gasoline, therefore in either case the excess burden is the same.
Mr. Landsburg,
That’s not true. The excess burden (or deadweight loss) depends on the incidence of the tax and represents lost resources.
As you well know, if I am taxed on something, I receive less of the good than what the price I paid for it represents – my consumer surplus is decreased. Similarly, the seller of the good receives less revenue than the price the good sold for would suggest – the producer surplus is reduced.
This would be okay if the revenue raised by the tax was completely collected by the government, but it’s not. The government collects revenue equal to the quantity of the unit sold times amount of the tax. This revenue is not equal to the foregone consumer and producer surplus. The difference is excess burden – resources and welfare that are simply lost once a tax is imposed.
With cap-and-trade, all transactions are completely contained within the market for permits. Consumers and producers are both able to realize their full surplus at the selling price. There is no tax, thus no incidence, thus no deadweight loss, thus no wasted resources or welfare.
D’oh.
Austin: If you try drawing a picture, with triangles of social surplus, you will find your mistake.
Austin:
Even if cap and trade contains everything within the system, the deadweight loss must still be exactly equal to what it would be under the tax.
The deadweight loss arises from the fact that less gasoline gets produced and consumed with either policy than would have without either policy. Since each policy (ideally) limits the quantity at Q, the deadweight loss is the same. The fact that the tax sends some of the remaining surplus to external players (government) is irrelevant to determine the amount of deadweight loss.
Cap & Trade or a carbon tax are motivated by the idea that emitting carbon causes an externality. If a policy alters behavior and funnels revenue for the purpose of compensating/mitigating the alleged harm of the externality, do we still refer to it as a “deadweight” social loss?
cmprostreet: Exactly correct.
Just some semantics
IF there is a negative externality, then NOT imposing a tax or a cap’n trade scheme would lead to a dead weigh loss. Without the govt. intervention there would be socially inefficient over-consumption/production. An appropriate tax would then be able to remove the DWL by maximizing social efficiency.
By the way, why are the P and Q axes in the wrong way round in these curves? Is it just convention, or is there a proper reason?
We may prefer carbon tax or cap and trade for political reasons, but it is useful to understand the effects of either policy when making the choice. Hansen has assumed that we can get a lower Q for a given P through altruism. For this to happen, you must move off the current demand curve. He has not offered a very good explation of why this is likely to happen.
However, if we were to suggest that demand curves were not very robust, and could switch from one to another in response to shocks or over time, then he does have a point. All we have to answer is the question which way is the curve most likely to move? The cause, be it altruism or other, is irrelevant.
How much information do we have on the robustness of these curves under different circumstances and over time? If there is a reasonable possibility of a shift in the curve, then the cap and trade is the only way to ensure consumption below a particular value.
The psyche currently responds to gradual changes in price by corresponding movements along the consumption axis. A sudden shock and WHAM! We are suddenly forced to re-think, and decide that our response needs to change. For example, in Europe the fuel price is very much higher than in the USA. Is the Europe demand curve just further along the P axis than the USA? If not, is it all due to geography etc, or is some of it due to a different demand curve? If demand curves can shift, then his point that a fixed Q cannot lead to consumong more fuel, whereas a increase in P may lead to a higher
There is a certain demand curve in the USA, as described above. Fuel in the USA is very cheap compared to many other countries. This is due to low taxes, since petroleum in internationally traded, and costs the same everywhere. I have a feeling that the demand curve in Europe is quite different, with consumption less responsive to price that it is in the USA. Now, this could be the same curve, just further along the P axisThis could be entirely due to immutable differences between Europe and America, such as geography or demographics. But I suspect that it is partly due to individuals responses changing in response to different cercumstances. If thi sis the case, then the current USA demand curve is not as robust as assumed. If fuel in the USA was as expensive as it is in Europe, it is possible that the demand curve could switch to be more similar to those in Europe. It is possible that it could switch in some other way as well, but as we have demonstration that the Europe-like curve occurs in practice, this makes it more likely than some other hypothetical curve.
I think many prefer to use a tax, because they see it would be very difficult politically to set a reasonable value of Q
I seem to have misunderstood deadweight loss. I had thought that part of this was the loss in production caused by people trying to avoid the tax. If a bank sets up a large department employing hundreds of intelligent, creative people to move money around from one invented company to another in several countries to avoid paying tax, is not that deadweight loss? If there was a different system that made such shennanegins useless, could that not lead to less deadweight loss, since all these people could be employed productively?
Apologies for my even more rambling posy above – this was due to failure to edit out my early jottings before hitting submit. It was intende to end after paragraph 4.
Thanks for your dialogue guys. But there is simply no excess burden with cap-and-trade. There can’t be. By your logic, every time the demand curve shifted there would be excess burden. If there is no burden (taxes) there can be no “excess” burden.
If you’re arguing that the shift in the allocation of resources would be identical, that consumer and producer surplus might be fully realized, by by an amount decreased by the same amount that would have caused by the tax, then that is true only if a strong assumption holds.
That would assume the government was able to set the tax at the exact optimal level. With cap-and-trade, we don’t need the government to have this perfect knowledge because the optimal level will be found by the market itself.
So again, the end result might look very similar, but with cap-and-trade we will have gotten there at a lower cost than with a tax. Always.
You may argue that this is simply semantics. I don’t think so and the distinction is important. We do well to realize that taxes should always be our last resort when it comes to influencing the behavior of the market.
The government has very few legitimate functions (but very important ones). While this is a case of market-failure because of externalities, we can solve it through the market. Instead of the government intervening through taxes, it simply implements property rights. While the government is involved, it is only to a minimal extent.
And this is to say nothing of the normative judgment about how it’s wrong to take tax money, by force, from hardworking people. Again, we must hold government very accountable for what it uses our tax money for. If there is a way to achieve the same result (or better) without using taxes, we must choose that alternative every time.
Austin:
You may argue that this is simply semantics.
Not at all. What it is is complete confusion on your part.
The excess burden of a gas tax results from the fact that people consume less gas. Under cap and trade, it is also true that people consume less gas. Same excess burden. That really is all there is to it.
Prof. Landsburg:
Being a person with very little economic understanding would the following be an implication of what you are saying? I’m asking to see if I understand the issue.
We decide that gas at $ 6.00 per gallon is the price that will fix the quantity of consumption to an acceptable level since it will cause consumers to change their behavior. Let’s say the actual cost of the fuel is $ 4.00 and the tax (excess burden) is $ 2.00.
As people start to conserve fuel this will cause the actual cost of the fuel to drop let’s say to $ 3.50. This means that the cost with tax for the gas would be $ 5.50. But since we need to keep the price at $ 6.00, we would need to increase the tax to $ 2.50.
In general, it would seems that the tax (excess burden?) would need to constantly increase in order to fix the quality.
Am I anywhere close to understanding?
Will A:
We decide that gas at $ 6.00 per gallon is the price that will fix the quantity of consumption to an acceptable level since it will cause consumers to change their behavior. Let’s say the actual cost of the fuel is $ 4.00 and the tax (excess burden) is $ 2.00.
As people start to conserve fuel this will cause the actual cost of the fuel to drop let’s say to $ 3.50. This means that the cost with tax for the gas would be $ 5.50
I’m with you up to here.
But since we need to keep the price at $ 6.00, we would need to increase the tax to $ 2.50.
This I don’t get. We don’t care about price, we care about quantity. People have voluntarily decided to conserve fuel, which drops the quantity below what we considered acceptable. Presumably we’re now even happier.
So while Mr Hansen is not clearly wrong (as I incorrectly said he was), there’s still no particular reason to think he’s right.
Altruism effects are, presumably, about meta-preferences which tend to be cognitive-dissonance driven, and it may be that a tax has a stronger effect than a quantitative restriction- taxes are associated with ‘demerit goods’ and ‘sinful pleasures’. Quantitative restrictions, however, like those an Gasoline or House occupancy during the Second World War have the perverse effect of everybody seeking to justify the largest possible allocation to themselves on the grounds that they were doing work of national importance. Evelyn Waugh’s novels make this point with hilarious effect.
Excess burden is the distortion to the economy ABOVE AND BEYOND the distributional effects of the tax.
What you’re describing is simply the distributional effects of the tax, which is not excess burden.
The point of a corrective tax is to shift the supply curve so the inefficiency of the externality is exactly offset by the amount of the tax. For this to be efficient, the tax must be EXACTLY right for every consumer. If the tax is too high or too low, we have not eliminated these inefficiencies; or we have simply replaced one inefficiency with another.
We can avoid this with cap-and-trade because the market finds the efficient output on its own.
@Will A
“We decide that gas at $ 6.00 per gallon is the price that will fix the quantity of consumption to an acceptable level”
If we decide this, we must have an idea of what the acceptable level of consumption is, and an idea of what the demand curve is.
If gas is $4 and we impose a $2 tax, and this shifts us along the demand and supply curve until the price is $5.50, it means people are still consuming too much gas, and we got the amount of the tax wrong. That means either we didn’t really know what the demand curve was, or we didn’t do our calculations properly.
Or, we did our political calculations correctly. So we don’t have to answer difficult questions like “if the current gas price is $4 and the ideal price is $6, why are you imposing a $3 tax??”
In any event, if you know the acceptable level of consumption, but have os much trouble with the demand and supply curves, the sensible thing is to impose Cap&Trade – that specifies what the consumption should be, and lets the market figure out the prices.
The only problem there is if, say, the market ends up saying “this level of consumption means gas costs $35/gallon”. Then, we will probably have to conclude that our “acceptable” level of consumption is unacceptably low, but by that time we’ve already been voted out of office and our political is wallowing in the gutters of political history.
Typo : for “our political is”, read “our party is”
Austin: This is a standard principles-of-economics problem, and you’re getting it wrong. I’m not sure whether you’re looking for help understanding your error or whether you just want to keep repeating the same wrong analysis over and over. If the former, I’ll be happy to try to help. If the latter, I think you’ve had your say and you can stop now.
“Excess burden is the distortion to the economy ABOVE AND BEYOND the distributional effects of the tax.”
No, it is the cost of the distortion above and beyond the REVENUE of the tax, and it is equal to the value of gasoline not consumed because of the tax minus its cost, That value is the same when gasoline consumption is supressed the same amount by cap and trade.
Either figure it out, or give it up.
Professor Landsburg,
Thank you for engaging with me on this. I assure you it’s not my intention to be controversial for controversy’s sake.
If I’ve frustrated you then I offer my sincerest apologies.
I will wrestle with the material some more, I guess.
Some more on the mutability of the demand curve.
We have just had a recession. Energy consumption has fallen. Fuel, particularly crude oil, is not simply responsive to price signals, as we saw from the Hotelling posts. Is the reduced consumption a shift in the demand curve for fuel? Before the recession there is a demand curve, with a certain P giving a certain Q. After the recession, I think the price and quantity would not lie on that same curve. Is this right?
If we have reason to believe that the demand curve can change, then this will have a significant effect on which policy we want to use, and what effects they will have.
In Europe there is a carbon trading scheme. My understanding is that the permitted emissions were set a few years ago. Since then we have had a recession, so the emissions fell anyway. In fact no-one is emiting more than permitted. There is no value in the permits. The scheme is having no effect in reducing CO2 emissions, although these are lower than anticipated anyway.
A carbon tax would have had a different effect. The tax would reduce demand for fuel even in the recession. This would further reduce CO2 emissions, even in the recession, but may deepen the recession.
What I don’t clearly understand is this. In the above situation the tax and cap-and-trade have a different effect. Is this only because the cap has been set at a level different from the tax, or because the demand curve has shifted? Is setting the cap at a level above actual use the same as setting a tax at zero? And how can we possibly know what the future use is going to be in order to set a cap?
Harold:
What I don’t clearly understand is this. In the above situation the tax and cap-and-trade have a different effect. Is this only because the cap has been set at a level different from the tax, or because the demand curve has shifted? Is setting the cap at a level above actual use the same as setting a tax at zero? And how can we possibly know what the future use is going to be in order to set a cap?
Taking the demand curve as given, for any given tax level, there is a cap level that is equivalent to that tax, and vice versa. If the demand curve shifts, the cap level equivalent to a given tax (and the tax level equivalent to a given cap) can shift. The fact that demand curves shift unpredictably does factor into the choice between the two policies. (So, for that matter, does the fact that we might have some uncertainty about the location of the demand curve, even when it’s not shifting.) In my opinion, for somewhat technical reasons, those considerations end up making the tax the more desirable policy —- though I can also see good arguments to the contrary.
And yes, setting the cap at a level above actual use is equivalent to a tax of zero.
As to your earlier question about why we reverse the axes, there’s actually a very good reason for that. We have occasion to consider the marginal value function — the function that assoicates to each gallon of gasoline its value to the consumer who buys it. This is a function that takes quantities to prices. We also have occasion to consider the demand curve, which takes prices to quantities. These two functions are inverse to each other, so ordinarily their graphs would appear as mirror images of each other. By switching the axes on the demand curve, we make the curves look identical, and cut in half the number of curves we have to draw.
@Harold, the impact of a tax and of a cap-and-trade are identical for known, certain markets, such as the graph in the discussion here. Uncertainty changes both the actual outcome and the optimal outcome. Thus, an unexpected event like the recession of 2008/9 would make the outcomes of the two policies change. It would also change the “optimal” policy, though, since the optimal quantity of carbon is not merely scientifically determined but also depends on the economic costs and preferences that shocks such as recessions bring.
Thanks for the answers –
I see it like this. Neither cap-and-trade or a tax will shift the demand curve by itself. There is therefore no particular reason to favor one over the other.
It is possible to change the curve, through policy or “events”. However, these are independent of the tax or cap-and-trade policy, so there is still no reason to favor one over the other.
If we could predict the effect of our other policies (or “events”) on the demand curve, we could “build in” a correction for the new curve into our tax or cap, so still no reason to prefer one over the other.
We can predict the effects of a shifting (or unknown) demand curve. A tax allows the quantity to move up or down if the demand curve shifts. A cap prevents quantity rising above the cap, but has no effect if the demand falls below the cap, and I am sure there are other effects too. We may prefer one effect over another, and thus prefer one policy over another, but the difference is subtle.
So, from a purely economic perspective, there is little to choose.
Now we come to politics. There is likely to be huge political differences in passing and implementing the different policies. It may be much easier to arrive at a particular Q with one than another. It may be much easier to “build in” a correction for a predictable shift in demand curve, for example. This could lead us to prefer one policy over another. If the similarities were more widely understood, then there may be less political difference.
Regarding the axes, I suppose there is not really any “right” way – it is just convention that the independent goes along the bottom.
Prof. Landburg:
The following is an explanation of how I see things and I’m interested in knowing where I’m wrong.
If the cost of fuel to me drops from $ 6.00 to $ 5.50 because we are conserving more (I’m glad I was at least correct on this point), then I can now buy a car that gets 10% worse gas mileage or have my Air Conditioner be 10% cooler without any additional cost to me.
So our conserving habits might start to wane and we might start to use more fuel since it is cheaper to us. So if we are using a fixed price to set a point on the demand curve, the cost of gas should always be $ 6.00 (or whatever point we decide).
This would seem to imply that the tax on gas would need to be somewhat fluid. E.g. if the base cost of gas was $ 3.50, then the tax should be $ 2.50. If the base cost of gas was $ 5.75, then the tax should be $ .25.
Another point is that there is some dynamism due to the introduction of a tax also. Say that under a static analysis it is decided that in order to lower the Q to the appropriate level a tax of $2 is required. That higher price will then have a dynamic-long term effect in which people to continuously seek ways to save money. So even as Q is immediately lowered it will continue to fall under that same tax as people move closer to work, buy smaller cars, research better engines, etc. Whereas with cap’n trade as the same dynamic occurs the price of the permit will fall thus keeping pollution at the Q initially selected. Thus for cap’n trade to be have the same effect in the long term requires continuous govt. intervention through lowering the amount of permits. Or then maybe we would green peace continually buy more and more permits, which is kind of a good political outcome as it lets people put their money where their mouth is.
@Will A: are you considering the tax you pay on the bigger car?
The effect you identify is a real one though. Safer cars lead to fewer accidents but also then to faster driving which leads to more accidents. In theory making cars safer could cause more accidents; more likely you get something in between.
This effect is more pronounced if it is asymmetrical. Hummers are very safe; you could drive into a wall at speed in a hummer and not muss your hair, but hummers make the rest of us less safe.
After reading all these comments, it seems like taxes actually could be a more appropriate way to deal with pollution than cap-and-trade.
Thanks everybody for setting me straight and making me think in a new way about something I thought I knew. That’s ALWAYS appreciated!
@Harold
yes, for any cap, there exists an equivalent tax, and vice-versa. This is still true if you allow the tax and cap to be functions of time, or of the demand curve.
A cap allows you to specify with certainty how much pollution will be emitted, but you can’t be sure of the price. A tax allows you to be certain how much polluters are charged per ton, but you can’t be certain how much pollution will be reduced.
The “correct” tax rate is equal to the present value of the marginal amount of damage caused by one ton of pollution. However, even if we could perfectly compute the damage from CO2 pollution and agreed on a discount rate, the marginal amount of damage pollution would be a function of the total amount of pollution – which depends on our cap.
Since we don’t know what effective cap arises from any particular tax, we can’t ever be sure we’ve got the tax right. The same argument shows we can never be sure we’ve got the cap right – even if we had perfect knowledge of climate science and its economic effects and the discount rate we should apply to future costs.
Has anyone devised a hybrid tax/cap scheme that is (1) practical, (2) converges on the “ideal” tax/cap, and (3) is politically feasible?
Mike H. From Wikipedia:
“A third option, known as a safety valve, is a hybrid of the price and quantity instruments. The system is essentially an emission cap and permit trading system but the maximum (or minimum) permit price is capped. Emitters have the choice of either obtaining permits in the marketplace or purchasing them from the government at a specified trigger price (which could be adjusted over time). The system is sometimes recommended as a way of overcoming the fundamental disadvantages of both systems by giving governments the flexibility to adjust the system as new information comes to light. It can be shown that by setting the trigger price high enough, or the number of permits low enough, the safety valve can be used to mimic either a pure quantity or pure price mechanism”
It seems that trying to model the effects of the cap and tax is a bit like trying to model the climate – lots of feedbacks that are hard to predict. Also a bit like the climate, we don’t need to get it perfect before we make a start. I think it is clear that CO2 produces changes in climate that will have some cost. Lets start paying for it and it doesn’t matter whether it is tax or cap-and-trade.
After seeing how it has been done in Europe, I prefer a tax because it is simple. Whilst in principle there is a cap for every tax, the level of the cap must be fixed and distributed across all sectors. This is a difficult political task, and subject to much lobbying from the different sectors. How much should transport get? Electricity generation? Cement manufacture? Again from the wikipedia, the disadvantage of cap-and-trade is that the regulator must pick winners and losers, with scope for corruption. No, it seems much easier to say each tonne of CO2 is taxed at X.
More bloggers need to run a “D’oh!” series. So far, so good.
@Harold – the problems you raise for ‘cap’… I don’t see why they don’t disappear for ‘cap&trade‘… perhaps I should read the wikipedia articles you’ve been quoting
The history of Australia’s efforts to introduce either cap or tax have been interesting so far… political reality far outweighs economic reality in terms of its power to influence what gets done… :-(
“So a post-policy shift in demand is equally likely to be upward or downward.”
I do not believe we can just assume this to be true. Simply because there’s two outcomes doesn’t mean the chance of each one happening is 1/2. I don’t have particular data on this, but I would think that it is significantly more likely that the demand curve shifts down rather than up.
In implementing the tax, it is most probable that the government would be trying to persuade the ppl abt how pollution is bad in order to justify their implementation of the tax. Psychologically, this is more likely to make ppl feel that it’s ‘increasingly’ morally wrong to pollute and shift the demand curve down.
I just find it hard to think of a real life scenario why ppl would change their preferences to shift the demand curve up. I know this is more in the realm of psychology rather than economics, but does anyone have opinions on this?