Uh…what?!? So I should go with a chart of “# of fireman at a fire” vs. “amount of property damage of a fire” just because that’s two dimensional and can be put on a graph rather controlling for the size of the fire? Whether or not something can be made into a pretty two dimensional graph is what matters rather than actually getting consistent estimates? What are you talking about?

” It is also quite likely to increase the uncertainty in any parameter estimate in your regression.”

Yes, but consistency of your estimate is more important than the size of your standard errors. Otherwise, I have an estimate of the elasticity for you. 143. Don’t like that one? Ok, 13. No? 503.234?
And think about it. If including a possibly relevant variable is unwarranted because “list of regressors is unlimited” then why are you even bothering to normalize these things by the number of households and median income? Why not just graph gas price vs. gas consumption and be done with it? Why not take that as the true elasticity? Because you can still do a two dimensional chart with those variables and you don’t get to make one with inflation in it? I wasn’t aware that statistics were a branch of aesthetics.

“Hardly. My educated guess is that running the regression with or without an additional term for income this will make little difference: CPI adjusted median income hardly budged during the period (less than 2% increase). For ln G to stay fixed while p_g – p increases by a factor of 2, b1 in your formula would have to be equal to about -log_1.02 (2) x b2 or about -35 x b2. So if b2 were even, say -0.1, b2 would have to be 3.5, which would be very hard to believe.”

You’re missing the point again. Even if you ran it with cpi adjused median income (and no, actually average income is what would matter here under many circumstances, since we’re talking aggregate gas consumption not gas consumption of a typical person – but this is another can of worms) you would still have to include inflation as a separate regressor.

“The reason I am “resisting” is that I find it a bad idea to run models without considering whether they make sense – the statistical machinery often obscures rather than illuminates the issues. ”

What makes sense is that demand for a particular good depends on income and relative prices. Thought experiment time – suppose nominal median income goes up 1000-fold, price of everything but gas goes up 1000-fold and price of gas, in $ terms goes up by 1000-fold. Now consider the same thing with price of gas staying constant. What you’re saying is that this makes no difference to gas consumption. There’s no “statistical machinery” here, just plain common sense.

“In fact, as you probably noticed, I didn’t even run a regression for my proposed model.”

Well, yes, you did. Implicitly or not.

” I prefer to let the data speak for itself.”

Now, what the hey does that mean? You know this is like the oldest rhetorical trick in the book, bring out some shoddy statistical analysis and then claim that you’re “letting the data speak for itself”. But you’re not. If anything you’re holding your hand over the data’s mouth forcing it to mumble incoherently so that it sounds like what you wanna hear.
There’s no ‘data speaking for itself’ there’s only a more general analysis and a more restrictive analysis. You’re insisting on the more restrictive one. This is statistical ventriloquism.

“By the way, I listed all the data sources in the linked post – you are quite welcome to run various regressions yourself. I think you will learn very little.”

Yes but see, I don’t have to, because there’s literally hundreds of studies that do this (which is why I linked to meta-studies) and they agree with me (and John Q) and not you.

“According to the standard model, what would matter here is the supply curve – you would in fact expect a decrease in the price of gas, the size of which would depend on the elasticity of supply.”

Well, once again, I am at a loss as to what you are talking about. You set a quota below current market level. This means that at current market price there’s is excess demand. That means price goes up. In fact in this case the quota level becomes the relevant supply curve so elasticity of supply ain’t got nothing to do with this.

(additionally, how do you know that what you graphed above isn’t a series of demand-supply combinations of price and quantity rather than just a demand curve?)

“You, above, claimed that elasticity is about 0.58 and one of the papers that you linked to claimed 0.6. John Quiggin said that he believes elasticity is in the 1-2 range. This is what I call “order of unity”.”

We’re talking about ratios of % changes here. Which means there’s a huge difference between .58 and 1. I don’t know off hand what research John’s referring to and I don’t presume to speak for him. He could be right.

“That is true, but I have not used “the dollar price of gas” – I have normalized the gas price by median household income. It is this ratio (which, btw, tracks CPI adjusted gas price very closely) that made a 2-fold increase over the decade. As I already explained, I think it is clear that adjusting by median household income is safer and more reasonable than adjusting by the CPI, but for the period in question it doesn’t matter – those two adjustment turn out to be very nearly the same.”

Again, you’re missing the point. Which is that prices of other goods need to be controlled in addition to this kind of normalization. Essentially what you’re doing is including either nominal or real income in the relationship. But demand for gas is a function of real income and relative price. It can also be rewritten as a function of nominal income … and relative price. Either way, relative price is in there.

And again, if it shouldn’t the data will tell you so there’s no extra (well, like an epsilon) cost to doing it.

As I already mentioned, the list of things you could add to your list of regressors is unlimited – how about the cost of public transportation? or the weather? Adding regressors is not cost free: at the very least it makes the model more opaque. It is much more difficult to understand a three-dimensional graph than a two-dimensional graph. It is also quite likely to increase the uncertainty in any parameter estimate in your regression.

It seems like you’re resisting this only because that elasticity would increase and that goes against your pre conceived notion.

Hardly. My educated guess is that running the regression with or without an additional term for income this will make little difference: CPI adjusted median income hardly budged during the period (less than 2% increase). For ln G to stay fixed while p_g – p increases by a factor of 2, b1 in your formula would have to be equal to about -log_1.02 (2) x b2 or about -35 x b2. So if b2 were even, say -0.1, b2 would have to be 3.5, which would be very hard to believe.

The reason I am “resisting” is that I find it a bad idea to run models without considering whether they make sense – the statistical machinery often obscures rather than illuminates the issues. In fact, as you probably noticed, I didn’t even run a regression for my proposed model. I prefer to let the data speak for itself.

By the way, I listed all the data sources in the linked post – you are quite welcome to run various regressions yourself. I think you will learn very little.

Well, “less than 1%” is still a negative slope.

Clutching at straws, aren’t we? Beyond the obvious fact that 1% could easily be within the noise in the data, even if we assume there is no noise 1% decrease in consumption over a 2x increase in price would imply elasticity of log_2(.99) = -0.015.

If you slap some quotas on gas consumption what do you think that’s going to do? Particularly with a very price inelastic demand? Raise the prices.

According to the standard model, what would matter here is the supply curve – you would in fact expect a decrease in the price of gas, the size of which would depend on the elasticity of supply.

no one’s claiming that that elasticity is on the order of unity

You, above, claimed that elasticity is about 0.58 and one of the papers that you linked to claimed 0.6. John Quiggin said that he believes elasticity is in the 1-2 range. This is what I call “order of unity”.

the variation in relative price of gas, or in “real” price of gas, or in “inflation adjusted” price of gas simply hasn’t been as large as the variation in the dollar price of gas

That is true, but I have not used “the dollar price of gas” – I have normalized the gas price by median household income. It is this ratio (which, btw, tracks CPI adjusted gas price very closely) that made a 2-fold increase over the decade. As I already explained, I think it is clear that adjusting by median household income is safer and more reasonable than adjusting by the CPI, but for the period in question it doesn’t matter – those two adjustment turn out to be very nearly the same.

Yes and that’s actually part of the point. It’s gotta be a direct or indirect reduction in the relative price of gas. You can get there by lowering the price of gas substitutes which is where all the hybrids, r&d into clean power, fuel efficiency and all that come in. And hopefully all that will be a big part of the adjustment otherwise any kind of reduction in global warming-due-to-gasoline-consumption is going to hurt and there’s just no way around it, whether through taxes or quotas.
But this too, like the changes in the existing vehicle fleet, where people live and how much they commute, etc., is going to be a longer run thing. And if you’re thinking in terms of the longer run then you have a more price elastic demand function to work with which means you probably need a bit of both.
I haven’t said anything specifically about that, because so far it has been outside the scope of the argument.

Lemuel, consumers don’t behave like completely rational economic entities, and so we should design our strategies to take advantage of their economic behavior.

I feel like it would be patriotic for me to buy a Prius, or possibly an american hybrid. But it would cost me a lot of money, and it wouldn’t save me that much in the first few years. My father bought a Prius and the second year he had an accident that totaled it. He replaced it with a different car. How much gasoline did he actually save buying his expensive car?

If gasoline cost me a lot of money, and I also got a lot of money from the government to make up for it, I’d have both a much stronger incentive to buy a new car and also a much stronger ability to do so.

Similarly, I live in a condo and the association pays for the natural gas. Every year they complain more about the cost and tell me they have to raise the rates. But if I use more, it isn’t just the other 9 families in my building that pay for it, it’s the other 90 families in the other buildings. I’ve given very little thought to improving the insulation in my unit. If that cost was mine and taxes increased it a lot, I’d certainly look into ways to reduce it—particularly if I had the money that could go either into paying for heat or for paying to use less heat.

Consumers pay attention to the consumption they get billed for. The closer the relationship between the actual product consumed and the bill, the more they notice. In the best case, consumers have both high enough prices to get their attention, and high enough income to invest in alternatives. That’s the case I want.

It could be argued that free market forces will automatically optimise everything. But I don’t see that free market forces will automatically provide the right discount for future events. It’s right to distort the economy away from fossil fuels because first We’re going to run out of them in short order, and second
They release too much CO2, and third
Alternate energy is homeland security.

I’ve seen the claim that ethanol from corn uses about 1 automobile-mile of fuel to produce 1.3 automobile-miles of fuel. If this is true, then with taxes that bring up fossil fuel prices, farmers could spend $30 on fuel to produce $40 of fuel. That could be profitable if they don’t have too many middlemen. Also, they could convert their equipment to use straight alcohol and pay some of their costs in reduced output rather than cash upfront.

But if corn ethanol actually costs more fuel than it produces, counting all the fuel (making fertilizer, insecticides, everything) a tax would highlight that. If you use $40 worth of fuel to make $30 worth of fuel, you need heavy subsidies. And businesses shouldn’t get money back for their fuel use, they should pass their fuel costs on to their customers.

My guess is that we’d quickly find ways to grow corn that require smaller energy inputs. And we’d use corn for purposes that it’s actually economic.

… or a direct or indirect reduction in the price of gas substitutes, no? Or no changes in prices at all, but changing the factors that make gas a very strong complement to other goods, most importantly housing.

Yes, at the margin there’s some scope for reducing gas consumpton by scheduling trips mroe efficiently, etc., like J Thomas likes to (and his wife doesn’t.) But for the most part it probably doesn’t make sense to think of people as consuming gas, as consuming a package that consists of housing plus car(s) plus gas. In which case even a doubling in the cost of gas may increase the economically relevant price by only a few percent.

Uh, but nominal income is just real income times … CPI? Or real income times the GDP Deflator? The equations above show how it should be done, whether you’re using real or nominal income, and whatever measure of changes in the aggregate price level you wish to use. The point is that that measure of changes in the aggregate price level should be there in addition to real or nominal income (which one you include only changes the interpretation of the coefficients) . And again, if it shouldn’t the data will tell you so there’s no extra (well, like an epsilon) cost to doing it. It seems like you’re resisting this only because that elasticity would increase and that goes against your pre conceived notion. But hey, maybe you put inflation in there and maybe the slope doesn’t change?!? Who knows.

“I do not see any negative slope in the graph. Again – a 2x increase in the real cost of gas (as measured by ratio to median income) since 1998 – produced essentially no decrease (less than 1%) in the household consumption of gas.”

Well, “less than 1%” is still a negative slope.

“I do not doubt that if gas price is, say, $30/gallon, consumption will drop significantly. However, this would involve very serious hardship for the average household. As things stand, there are no easy substitutes for driving.”

But reduction in gasoline consumption has to be achieved through a direct or indirect rise in gas prices. If you slap some quotas on gas consumption what do you think that’s going to do? Particularly with a very price inelastic demand? Raise the prices.
And while there are no easy short term substitutes for driving there are substitutes for the inputs that go into “producing” driving. Like more fuel efficient cars which let one do the same amount of driving with less gasoline, which is what ultimately is causing the problem here.

“The list of things to control for can be made arbitrarily long, but when a decade-long two-fold increase in the cost of gas (as a share of median income) does not generate any decrease in gas consumption, it makes claims of elasticity being on the order of unity very hard to believe.”

First, no one’s claiming that that elasticity is on the order of unity – see for example the papers I linked to above. Like I stated before, pretty much everyone agrees that demand for gas is inelastic. But that doesn’t mean it’s perfectly inelastic or even close to it which is essentially what you’re suggesting. Second, no, the list of things to control for is not arbitrarily long. Usually three or four key variables explain most of the variation in a given variable. But if these three or four variables are correlated with each other in some way (as inflation surely is) then it is essential to include them in the estimate (i.e. control for them) – otherwise you get bunk results. Furthermore, a basic theory suggests which variables need to be included and here it suggests inflation since it’s the relative price that matters. Third, and most importantly the reason why you’re getting this is result is simply because the variation in relative price of gas, or in “real” price of gas, or in “inflation adjusted” price of gas simply hasn’t been as large as the variation in the dollar price of gas (it hasn’t gone up two fold). You adjust for that in the denominator of %dq/%dp and you get a somewhat larger elasticity since %dp goes down. Again, if it doesn’t matter there’s no reason to object to this as quite simply it won’t go down.

Your description makes a lot of sense to me (btw, I am not an economist, I am a statistician). It shows how woefully simplistic are concepts like “elasticity”. They may still be useful (in the operational sense, at least – what would be the reduction in gas consumption if it is taxed at $5/gallon?), but taking them seriously enough to talk about “precision” can only be explained as a product of indoctrination.

Some comments regarding your last paragraph: As the data I linked to above show, the average American household uses almost 100 gallons of gas per month. Thus the difference between, say, $2/gallon and $4/gallon is about $200/month. This is a non-negligible part of median household income. In fact, the data show that over the period 1998-2007 the cost of gas increased from taking about 3% of the median household income to taking over 6% of the income. Again, this is not a negligible change, and yet, consumption did not decrease.

As I wrote above, I don’t doubt that if the price is high enough (making 100 gallons of gas cost as much as 20% of the median household income) people will consume less – the point is that this is going to be a very painful situation for many people. It is also going to allow the rich to keep polluting. Thus, the carbon tax is not fair and not as effective as a quota system. Your government rebate proposal is much better than a simple tax since, like quotas, it guarantees that every person will have enough money to buy a certain amount of gas.

Say I’m shopping for groceries with my wife at the nearby grocery store. She picks up a can of Spaghettios. I say, “Put that back, we can get it for thirty cents cheaper at WalMart.” Knowing me, she says “But Walmart is 6 miles farther away. That’s an extra 12 miles round trip. And you only save 30 cents. Anyway, it isn’t the same stuff.” And I say, “No, the kids like the WalMart kind more, the sauce has less tomato and more sugar. And I’ll buy two dozen cans and save money. And if we get cheese and bread at the same time that will pay for the extra gas. And if we go the special way I found we save three tenths of a mile both ways.” And she says, “You don’t know how the traffic and the lights will go. You optimise the things that are easy to measure and not the things that are important.” And I have to admit she’s right.

So, my car gets about 20 mpg. That isn’t enough money to justify a new car that got better mileage. I burn about 25 gallons a month. Until recently that cost me about $100/month, but now that’s down to more like $70/month. If I think about driving an extra 12 miles, that costs around $1.50. I have to balance what it costs versus the benefit I get. So I think it out carefully. I arrange triangle trips, when I go in one direction I try to go all the places I need to in that one trip. (Buying frozen food needs to be one of the last things.) I pay a little more to drive less. But my wife doesn’t think that way. If she wants to go to Fresh Foods etc she just gets in the car and goes. Then if the car gets low on gas she expects me to fill it up. It just isn’t worth it to her to figure out complicated plans that will probably save me less than a dollar a day. And neither of us thinks about the indirect costs, the tires that wear out faster, wear-and-tear on the car, etc. Those are hard for me to measure. Should they add up to 50 cents a mile? I don’t know, easier not to think about it.

If gasoline cost me $20/gallon then I’d think differently. At a dollar a mile I’d be much more careful driving long distances or extra trips. If I went to Walmart or Costco I would find people who wanted to carpool with me. It would be a big inconvenience. I would take the shuttlebus more, unless its price went up too much. I would walk more. I’d think carefully about a car that got better mileage—except at those prices I couldn’t afford one.

If I paid $20/gallon but the government gave me $400/month to spend as I pleased, I might just spend $500/month on gasoline and not change anything else. Or if I could lease a car for $250/month that got 40 mpg, I might do that and use half the gasoline. Or I might change my habits considerably. I pay more attention to $500 than I do to $70.

My wife doesn’t like to pay attention to sums of money that are too small. I tell her if we’re very careful and we save $20/month then over the years it will add up. She isn’t interested. But when it’s more money she notices. If gasoline cost $100/gallon but we had an extra $2400 a month to spend on that or on anything, she would get interested in a bicycle or a moped etc. Even though we could keep living exactly the same way, using gasoline would have a great big opportunity cost that it doesn’t have now.

But it wouldn’t work to send everybody enough money to let them buy the same amount of gasoline they buy now. And it wouldn’t seem fair to the people who already conserve it. It would be simple and fair and almost-workable to send everybody the same amount. But then the people who use a lot of gas would be hurt badly.

So anyway, people using gasoline make some big decisions—where to live, how far to commute—that are hard to change. And they make little decisions—one more trip to the grocery store etc—that are individually trivial. And the difference between spending $50/month and $100/month for gasoline is only critical for the poorest people who drive. If your take-home is $1000/month the difference is $5% of your income. If you can’t afford an extra $50/month you can’t really afford a car. So it’s no big surprise if that price doubling had little effect.

But to say more you got to control for other things.

The list of things to control for can be made arbitrarily long, but when a decade-long two-fold increase in the cost of gas (as a share of median income) does not generate any decrease in gas consumption, it makes claims of elasticity being on the order of unity very hard to believe.

If inflation doesn’t matter [...]

Of course inflation matters, but, again, the reliable, reasonable normalizer is not the CPI but the median household income. Taking the ratio between two nominal dollars quantities washes out any change in the value of the dollar.

demand for gas is a) downward sloping

I do not see any negative slope in the graph. Again – a 2x increase in the real cost of gas (as measured by ratio to median income) since 1998 – produced essentially no decrease (less than 1%) in the household consumption of gas.

I do not doubt that if gas price is, say, $30/gallon, consumption will drop significantly. However, this would involve very serious hardship for the average household. As things stand, there are no easy substitutes for driving.

Well, no, that’s not the point, or at least not all of it, since there are two effects when a price changes. First it changes available income to be spend on other goods like you said. But this is probably a small effect for anyone good. The bigger effect, and in fact, the main determinant of consumption is the relative price.
We can just throw all the theoretical stuff out the window for a minute and let the data speak. If inflation doesn’t matter then when you do the above regression, and control for inflation – then IF it doesn’t matter you’ll get a coefficient on it that’s equal to zero, and no change in the gas price coefficient that you had without it. But if it does matter then your estimates will change.

Also, you’re assuming here that all observed variation in price and quantity come from changes in costs and shifts in the supply curve. Maybe.

BTW, I didn’t/don’t mean to sound dismissive or pedantic. I think as a quick heuristic your approach is fine and insightful. It does more or less let one say that demand for gas is a) downward sloping and b) pretty inelastic. But to say more you got to control for other things.

so are you using real median or nominal median income?

I used nominal (current) dollars throughout.

non gas prices are in there and they got to be controlled for

Yes, I imagine that if non-gas prices decreased dramatically that could have somehow increased gas consumption by giving the household more available income to spend on gas. In reality, of course, this did not happen.

I agree that turbine replacement is worth doing wherever it gives good results.

It need not compete with a carbon transfer (it isn’t a tax when you give the money back), which would cost the government very little. Never mind which is better, we can do both.

If I pay-out $100 in the carbon tax and get back $200, I can now go and consume another $100 worth of emitting activities and be no worse off financially.

Sure, but if you find similar things to consume that burn less fossil fuel you’ll get more bang for your $100. Say you live in a city with good mass transit and your apartment is insulated well etc. If you get $200 you probably won’t spend it on gasoline. But if you pay $400 extra in hidden costs for the carbon tax and you get $200 you’ll put it into what you need most, and you’ll be $200 behind. If Rice Krispies cost $12/pound because it takes so much fossil fuel to make them, chances are you’ll eat some other breakfast.

To be effective, the carbon-tax must be onerous, or rather, more onerous than conducting business as usual.

Sure, there’s no way to avoid some of that. But it would only be onerous to those who use more than the average amount of fossil fuels. It would be very hard to tell where the breakeven point was, because the “tax” would be folded into prices like a VAT tax. The inflation would be biggest in the products that use the most fossil fuels, which is as it ought to be.

So sure, the more fossil fuels you use the more onerous it is for you. No way to avoid that. But also, you can find the products you like that needed less fossil fuel to make them, and those will be relatively cheaper. We don’t just bias things to consumers who consume less fossil fuel, we also bias all consumers to buy products that use less fossil fuel. I don’t see how this can be a bad thing.

And that is what raises political hackles.

If we get into a world war civilians will be enthusiastic about conservation to support the war effort. Is that what it takes?

I hope we can do it by getting people to agree that conserving fossil fuels is patriotic and we want to reward that patriotism. And then when it’s hard to tell how much people are paying, it can be like Lake Woebegon where everybody’s kids are above average—almost everybody can think they’re patrioticly using less fossil fuel than average, and there won’t be much sympathy for whiners who use a lot and complain they can’t afford it.

If people get stuck in poorly-insulated houses with long commutes we can look for ways to help them out of their trap. Help them slide out of their mortgages etc. But the way we do it now, oil consumption gets subsidised so that people don’t notice the trap they’re in. Make it clear that what they’re doing is unsustainable and they’ll be glad to grab the lifeline you throw to them. But they won’t care about that while it’s business-as-usual.