OK, I had a momentary lapse of sense and went to see Al Gore's movie, An Inconvenient Truth. Let me get the accolades out first: Al Gore is actually good on camera, and manages to crack a few good ones. The movie will, I suspect, cement the center and left Democratic support for general Democratic party policies and maybe even help Gore if he wants to try another run.
But I am furious over this movie. Absolutely furious. The main prop is the graph of CO2 and temperature over a run of about 650,000 years. This is the well-known temperature, carbon dioxide record recovered from glacial ice cores. Gore makes the most out of it; the chart of the two lines covers the entire screen, and the correlation between temperature and CO2 is obviously close to 1. Then comes the finishing touch (or the grand deception) which is to add the recent CO2 increases (the last 50 years or so) and let the audience draw the obvious and inescapable conclusion that the temperature line will follow the CO2 line upwards into uncharted and cataclysmic territory. Hey, if temperature has been so closely correlated with CO2 over 650,000 years, the pattern is certainly not going to change now is it?? The overall effect of the presentation is quite convincing, and it sets the tone for scary discussion of the climate crisis for the rest of the movie.
My alarm bells started clanging so loudly at this point that I thought I was going to be asked to leave the theatre.
Hmmm....Gore makes a lot out of his college experience in this movie. Did he ever take a course in statistics where they warned about not drawing causal conclusions from mere correlations?
There are a couple things to note about Gore's beloved but deceptively used long term CO2/temperature relationship. First, more careful statistical analysis of the data shows quite convincingly that changes in CO2 concentrations FOLLOW changes in temperature, by something like a lag time of 1000 years. How about that for an inconvenient truth, Al? Don't you think maybe you should have mentioned that?? So some third unknown factor is driving temperature, and then CO2 follows. The reasons for increases in CO2 concentration to follow increases in temperature are varied, but one big one is that the oceans hold less CO2 at higher temperatures. Think of a bottle of Coke on a warm day -- if you shake a bottle, will you get a bigger explosion (release of CO2) on a warm day or a cold day? How about that for a second inconvenient truth, Al?
The biggest issue with these data is, of course, what causes the temperature to increase first, and, I will admit, if there is any subsequent positive feedback of the induced increase in CO2 on temperature. That would be a valid way to put the issue. But if you do that, the point of the movie is going to be lost, right? I mean, how can you say: Well, we don't really know what causes these temperature fluctuations over the last 650,000 years, and all we can really say for sure is that changes in CO2 are caused by the temperature change, not the other way around. But let's not let that get in the way of letting us tell you that we know for sure what has been causing the temperature increase of the last 50 years, and that is the increase in CO2.
I don't know how any self-respecting scientist can let Al Gore get by with such statistical deception. To use that chart in such a deceptive fashion, drawing the CO2 line for current times into the stratosphere and just inviting people to draw the temperature line behind it, that really hits a new low. I am sure that the Hanover audience included a lot of PhDs. Are they so blinded by the propaganda that they don't want to go out and do a little independent thinking??
As I walked into the Hanover theatre, it felt like I was walking into a local Democratic Party get-together. These are all the same people who accuse Bush and Cheney of lying about WMD. Where is their outrage over Al Gore's most convenient and deceptive abuse of the historical climate record? Where is their outrage over the convenient leaving out of the well-accepted finding that CO2 lags behind temperature in that record? Where is their outrage over the convenient lack of mention that the relationship between the oceans and the CO2/temperature record is really critical?
The hypocrisy in the world is going to kill me.
Tuesday, July 25, 2006
Sunday, July 23, 2006
Whither Oil Prices?
There has to be a serious decline in oil prices sometime in the near future. I just don't see how the economics support prices in the $70 range.
Here are just a few things to consider. Iran produces about 3.8 mbd (millions barrels per day).
China consumes about 7mbd.
The world produces and consumes about 85 mbd.
The price elasticity of demand for oil is at least .1, with the time horizon for this being not real short term but not real long term either -- say in the vicinity of one year. A shorter time period will give a smaller elasticity, a longer time period will give a higher one.
The spot price of crude on July 14, 2006 was $68. The spot price in July 04 was $34 -- that is a one hundred percent increase.
With the elasticity of demand at .1, that should give us a 10% reduction in demand for oil, or a decrease of 8.5 million barrels.
Now I grant that the price increase was somewhat gradual over this two year period, so we have not yet had the time for even this very small elasticity adjustment to take place. But it is, and it will continue.
A decrease of 8.5 million barrels is equivalent to taking out all of China's consumption. Or looked at another way, it is equivalent to losing all of Iran's production, plus Kuwait and Iraq as well.
And I have not even brought in the idea that there is also a small but positive price elasticity of supply. At $70, how much additional oil will it be profitable for all the world's producers to bring forth? Iran may bluster about cutting its oil exports, but at $70 per barrel, its marginal revenue for each additional barrel it produces is in the $40 range (a marginal revenue calculation based on a residual demand curve; see also my previous post on marginal revenue). The smaller the producer, the closer marginal revenue is to price. For producers of oil from the Alberta oil sands, you might as well take marginal revenue right now to be $70 per barrel.
The sad irony here is that it appears by threatening to cut supplies, some of the producing countries have managed to get prices high and they are probably taking advantage of those high prices by supplying even more! A good trick, but all good things have to come to an end.
One way to think about this market is that both the demand and supply curves are extremely steep. There is then a range of prices that are "almost" equilibrium prices, in that the gaps between supply and demand for any of the prices in that range is not very great. Surpluses that are created at prices high in this range are relatively small and will take time to become visible to traders and others.
But the same holds true for prices on the low end of this equilibrium range. Recall that oil prices back in 1999 were about $13 per barrel. At those prices, the shortage created is also small and takes time to become visible. But it did, and prices increased to more reasonable levels.
Here are just a few things to consider. Iran produces about 3.8 mbd (millions barrels per day).
China consumes about 7mbd.
The world produces and consumes about 85 mbd.
The price elasticity of demand for oil is at least .1, with the time horizon for this being not real short term but not real long term either -- say in the vicinity of one year. A shorter time period will give a smaller elasticity, a longer time period will give a higher one.
The spot price of crude on July 14, 2006 was $68. The spot price in July 04 was $34 -- that is a one hundred percent increase.
With the elasticity of demand at .1, that should give us a 10% reduction in demand for oil, or a decrease of 8.5 million barrels.
Now I grant that the price increase was somewhat gradual over this two year period, so we have not yet had the time for even this very small elasticity adjustment to take place. But it is, and it will continue.
A decrease of 8.5 million barrels is equivalent to taking out all of China's consumption. Or looked at another way, it is equivalent to losing all of Iran's production, plus Kuwait and Iraq as well.
And I have not even brought in the idea that there is also a small but positive price elasticity of supply. At $70, how much additional oil will it be profitable for all the world's producers to bring forth? Iran may bluster about cutting its oil exports, but at $70 per barrel, its marginal revenue for each additional barrel it produces is in the $40 range (a marginal revenue calculation based on a residual demand curve; see also my previous post on marginal revenue). The smaller the producer, the closer marginal revenue is to price. For producers of oil from the Alberta oil sands, you might as well take marginal revenue right now to be $70 per barrel.
The sad irony here is that it appears by threatening to cut supplies, some of the producing countries have managed to get prices high and they are probably taking advantage of those high prices by supplying even more! A good trick, but all good things have to come to an end.
One way to think about this market is that both the demand and supply curves are extremely steep. There is then a range of prices that are "almost" equilibrium prices, in that the gaps between supply and demand for any of the prices in that range is not very great. Surpluses that are created at prices high in this range are relatively small and will take time to become visible to traders and others.
But the same holds true for prices on the low end of this equilibrium range. Recall that oil prices back in 1999 were about $13 per barrel. At those prices, the shortage created is also small and takes time to become visible. But it did, and prices increased to more reasonable levels.
Israel: Looking forward, reasoning back.
The situation in Lebanon is sensitive for me as I know someone who landed in Beirut the day before the airport was bombed and closed. His family was supposed to join him in Beirut in August; that won't happen now. It is a sorry state of affairs.
I've been struggling with a couple related questions. Why did the world sit so quietly while Hezbollah armed itself to the teeth, just miles from the Israeli border? And, in both the Lebanon action and the Gaza action, why does Israel do things that they just have to know are going to play out badly in the world media?
I think I might be able to rationalize what Israel is up to and make a little sense out of the situation. Israel saw that the world ignored its plight, with Hezbollah being armed by outside forces and getting ready to attack Israel. By doing an all-out assault, bombing even civilian structures like the airport, roads and bridges, and TV stations, Israel accomplishes two things. One, it does weaken Hezbollah. But two, and more important, it actually uses the anticipated negative world reaction to its advantage. How can the world sit back and watch the Israelis tear Lebanon apart? It actually looks like we might get French, British, Italian, even German troops on the border of Lebanon and Israel. This is exactly what Israel needed before the war, but could not get the world to take seriously. Now Condoleeza Rice looks like she might be able to get a coalition of countries to keep the peace.
So Israel is using some key lessons from game theory. One: look forward, reason back. What Israel needs is an international force on the border to keep Hezbollah from amassing arms again (or Israel would have to occupy South Lebanon, and they tried that once before). Convincing the world that Hezbollah is the enemy and the crazy force won't work, because the world is afraid to go directly against them. So Israel has to appear to the the crazy force that needs restraining. The second lesson from game theory is a bit of judo economics, or using the other player's incentives against them. Iran and Syria may soon find themselves with a European peacekeeping mission in Lebanon, and it will be much tougher to attack those forces than it would be to attack US forces. Also, even the Europeans are going to be surprised to see that it has somehow become in their interest to step in between Israel and Hizbollah. Who would have thought that would happen?
I am most pleased to see the US letting Israel play this out. Condoleeza Rice is exactly on mark when she says that a ceasefire will not solve anything.
The main conundrum this thinking resolves for me was Israel’s blatant attack of targets that one knew would turn world opinion against it. But that, it appears, may be exactly the plan.
I've been struggling with a couple related questions. Why did the world sit so quietly while Hezbollah armed itself to the teeth, just miles from the Israeli border? And, in both the Lebanon action and the Gaza action, why does Israel do things that they just have to know are going to play out badly in the world media?
I think I might be able to rationalize what Israel is up to and make a little sense out of the situation. Israel saw that the world ignored its plight, with Hezbollah being armed by outside forces and getting ready to attack Israel. By doing an all-out assault, bombing even civilian structures like the airport, roads and bridges, and TV stations, Israel accomplishes two things. One, it does weaken Hezbollah. But two, and more important, it actually uses the anticipated negative world reaction to its advantage. How can the world sit back and watch the Israelis tear Lebanon apart? It actually looks like we might get French, British, Italian, even German troops on the border of Lebanon and Israel. This is exactly what Israel needed before the war, but could not get the world to take seriously. Now Condoleeza Rice looks like she might be able to get a coalition of countries to keep the peace.
So Israel is using some key lessons from game theory. One: look forward, reason back. What Israel needs is an international force on the border to keep Hezbollah from amassing arms again (or Israel would have to occupy South Lebanon, and they tried that once before). Convincing the world that Hezbollah is the enemy and the crazy force won't work, because the world is afraid to go directly against them. So Israel has to appear to the the crazy force that needs restraining. The second lesson from game theory is a bit of judo economics, or using the other player's incentives against them. Iran and Syria may soon find themselves with a European peacekeeping mission in Lebanon, and it will be much tougher to attack those forces than it would be to attack US forces. Also, even the Europeans are going to be surprised to see that it has somehow become in their interest to step in between Israel and Hizbollah. Who would have thought that would happen?
I am most pleased to see the US letting Israel play this out. Condoleeza Rice is exactly on mark when she says that a ceasefire will not solve anything.
The main conundrum this thinking resolves for me was Israel’s blatant attack of targets that one knew would turn world opinion against it. But that, it appears, may be exactly the plan.
Saturday, July 15, 2006
News on the Global Warming Hockey Stick Graph?
I like to stay mildly attuned to the ongoing climate change debate (if we can still call it that). I don't plan, however, on going to see Gore's movie.
It looks like the House Committee on Energy and Commerce will release this week the report by statisticians on the Michael Mann et. al. "hockey stick" study. This is the statistical work that shows our current time to be the warmest period in over 1,000 years -- even though the Medieval Warm Period was previously thought to be a warmer period.
From the early releases, the report looks pretty devastating, even going so far as to question the quality of the peer review process for the papers. Interesting stuff. No doubt it is going to get cast as a Republican slam against good science.
I did look at the resume of the lead statistician, and he looks pretty good.
The full report should be interesting reading.
I still find the work of Richard Lindzen to be especially illuminating on climate change. He accepts some basic findings and predictions, but always brings the argument back to a key point: without positive feedbacks built in, climate models predict relatively minor warming.
It looks like the House Committee on Energy and Commerce will release this week the report by statisticians on the Michael Mann et. al. "hockey stick" study. This is the statistical work that shows our current time to be the warmest period in over 1,000 years -- even though the Medieval Warm Period was previously thought to be a warmer period.
From the early releases, the report looks pretty devastating, even going so far as to question the quality of the peer review process for the papers. Interesting stuff. No doubt it is going to get cast as a Republican slam against good science.
I did look at the resume of the lead statistician, and he looks pretty good.
The full report should be interesting reading.
I still find the work of Richard Lindzen to be especially illuminating on climate change. He accepts some basic findings and predictions, but always brings the argument back to a key point: without positive feedbacks built in, climate models predict relatively minor warming.
Deficit Down, Pessimism Up
Last week, the Sunday New York Times ran an article titled, "Surprising Jump in Tax Revenues is Curbing Deficit." The subheadline, though, countered the good news with a warning that the long term outlook was not any better. The article itself spent a lot of effort detailing the grim outlook for the federal budget.
Now there are a lot of issues with the future, but my own view is not nearly as bleak as those who seem to constantly view the world through a pessimistic lens and, of course, cast as much aspersion as possible on President Bush and the Republicans. Perhaps in another post I will look at the future deficit issue, with some sensitivity analysis on some common sense changes, such as a little increase in retirement age; some means-testing for Social Security and/or Medicare; and some enhanced growth through immigration.
But for now, I just want to point out the obvious reasons for the latest reduction in the deficit, and highlight a major error in the NYT's thinking.
The reduction in the deficit is about $100 billion, with the new deficit forecast for this fiscal year being about $300 billion, down from a forecast of over $400 billion just several months ago. By the way, with GDP running at $13 trillion, this means the deficit is 2.3% of GDP, lower than for France, Germany, Italy, and Japan (Japan is at an amazing 5.8%).
The simple reason for the improvement is that nominal and real GDP have been increasing much faster than expected. Here is some simple math. Let's assume that for a one dollar increase in GDP, federal tax revenues increase by 20 cents (20%). This is a bit above the average Federal tax rate for the US, but it could well be an underestimate of the marginal effect on tax revenues from GDP (see my post below on marginal tax rates). Much of the unexpected GDP increase came from incomes of wealthy individuals, and they face higher tax rates than the average person.
Anyway, now we can do a simple calculation. To get an additional $100 billion in tax revenues, with the marginal tax take at 20%, you need another $500 billion in GDP. With total GDP at $13 trillion, that is a 3.8% increase. So have we seen an unexpected increase in GDP of around 3.8%? If you use nominal GDP, which you should because tax revenues are based on nominal GDP, the answer is yes. The last GDP figures gave a real increase of 5.6% for the first quarter and 8.9% in nominal terms. So the increase in tax revenues is simply coming from faster than expected GDP growth.
Now for the NYT's error in logic. The subheadline and much of the article tries to make us think that the reduction in the deficit does nothing for the long term outlook. It is as if a person found $100 on the road; a nice windfall, but don't let yourself get accustomed to it. But this is not the case with the US economy. Growth was several percentage points higher than expected, and this puts us on a new, permanently higher path -- for both GDP and taxes. From finance theory, we know that stock prices are a random walk, so if the price of a stock goes up, you should assume that is now the new level from which the random walk continues. GDP and taxes are the same. My best estimate at this time is that tax revenues are $100 billion higher than before, permanently, because we had a permanent increase in GDP. This means that the budget deficit is permanently lower by $100 billion.
Another proper analogy is with our own yearly salary increases. A bonus of $100 may be a temporary thing, but when your annual salary goes up by, say, 5% on a base of $100,000, that is $5,000 extra per year that you can take to the bank.
One last calculation. With a nominal interest rate of 6%, the $100 billion per year is worth, in present value, $1.7 trillion. With total US federal debt at $8.4 trillion, I would say that the news is indeed quite good.
Let's drop the pessimism, no?
Now there are a lot of issues with the future, but my own view is not nearly as bleak as those who seem to constantly view the world through a pessimistic lens and, of course, cast as much aspersion as possible on President Bush and the Republicans. Perhaps in another post I will look at the future deficit issue, with some sensitivity analysis on some common sense changes, such as a little increase in retirement age; some means-testing for Social Security and/or Medicare; and some enhanced growth through immigration.
But for now, I just want to point out the obvious reasons for the latest reduction in the deficit, and highlight a major error in the NYT's thinking.
The reduction in the deficit is about $100 billion, with the new deficit forecast for this fiscal year being about $300 billion, down from a forecast of over $400 billion just several months ago. By the way, with GDP running at $13 trillion, this means the deficit is 2.3% of GDP, lower than for France, Germany, Italy, and Japan (Japan is at an amazing 5.8%).
The simple reason for the improvement is that nominal and real GDP have been increasing much faster than expected. Here is some simple math. Let's assume that for a one dollar increase in GDP, federal tax revenues increase by 20 cents (20%). This is a bit above the average Federal tax rate for the US, but it could well be an underestimate of the marginal effect on tax revenues from GDP (see my post below on marginal tax rates). Much of the unexpected GDP increase came from incomes of wealthy individuals, and they face higher tax rates than the average person.
Anyway, now we can do a simple calculation. To get an additional $100 billion in tax revenues, with the marginal tax take at 20%, you need another $500 billion in GDP. With total GDP at $13 trillion, that is a 3.8% increase. So have we seen an unexpected increase in GDP of around 3.8%? If you use nominal GDP, which you should because tax revenues are based on nominal GDP, the answer is yes. The last GDP figures gave a real increase of 5.6% for the first quarter and 8.9% in nominal terms. So the increase in tax revenues is simply coming from faster than expected GDP growth.
Now for the NYT's error in logic. The subheadline and much of the article tries to make us think that the reduction in the deficit does nothing for the long term outlook. It is as if a person found $100 on the road; a nice windfall, but don't let yourself get accustomed to it. But this is not the case with the US economy. Growth was several percentage points higher than expected, and this puts us on a new, permanently higher path -- for both GDP and taxes. From finance theory, we know that stock prices are a random walk, so if the price of a stock goes up, you should assume that is now the new level from which the random walk continues. GDP and taxes are the same. My best estimate at this time is that tax revenues are $100 billion higher than before, permanently, because we had a permanent increase in GDP. This means that the budget deficit is permanently lower by $100 billion.
Another proper analogy is with our own yearly salary increases. A bonus of $100 may be a temporary thing, but when your annual salary goes up by, say, 5% on a base of $100,000, that is $5,000 extra per year that you can take to the bank.
One last calculation. With a nominal interest rate of 6%, the $100 billion per year is worth, in present value, $1.7 trillion. With total US federal debt at $8.4 trillion, I would say that the news is indeed quite good.
Let's drop the pessimism, no?
Thursday, July 06, 2006
Those Damn Liberal Vandals
Given that I have written two posts somewhat critical of the Bush administration, I should mention one other thing.
If I catch the person who ripped the "Viva Bush" sticker off the bumper of my Tundra, I will definitely prosecute to the full extent of the law.
And that goes for whoever in my neighborhood took one of my Bush/Cheney signs during the last election and threw it in the woods.
Isn't it ironic that the liberals have such disregard for private property and free speech?
I want to replace the bumper sticker with one of those ones that says: Impeach Bush: Cheney for President. That should make them think twice.
If I catch the person who ripped the "Viva Bush" sticker off the bumper of my Tundra, I will definitely prosecute to the full extent of the law.
And that goes for whoever in my neighborhood took one of my Bush/Cheney signs during the last election and threw it in the woods.
Isn't it ironic that the liberals have such disregard for private property and free speech?
I want to replace the bumper sticker with one of those ones that says: Impeach Bush: Cheney for President. That should make them think twice.
Wednesday, July 05, 2006
Our Messed-Up Federal Income Tax: Or, What is Your Marginal Tax Rate?
Last week I wrote about the failure of the Bush administration to apply some of that hard-earned political capital to effect Social Security privatization. Let me move on to another failure to apply political capital, this time to reform of the tax code. I do realize that an advisory group came out with some recommendations, but they did not strike me as cutting to the core of the problem. Here is the real problem.
One of my favorite things on an airplane is to ask people how much they paid for their seat. It is a great lesson in price discrimination and usually gets some good conversation going. Of late, I have been having more fun by asking my friends and colleagues what their marginal (federal) tax rate is. At best, I get an answer related to the 2005 Tax Rate Schedules in that favorite of all publications, 2005 1040 Forms and Instructions – that is, a relatively sophisticated answer is to give the statutory marginal tax rate for an individual’s bracket. The current tax schedule has six different marginal rates: 10%, 15%, 25%, 28%, 33%, and 35%.
The problem is that your statutory marginal rate is not your actual marginal rate because of three major effects and one overpowering effect. The three major effects are: phasing-out of exemptions; the phasing-out of deductions; and the Medicare tax which is 1.45% for the taxpayer no matter how high your income. The overpowering effect involves the AMT, the alternative minimum tax, to which I will return shortly.
Just a quick aside, I focus on the marginal tax rate as being key for incentives and therefore the efficiency of our tax system and of the whole economy. My average tax rate last year was, say, 23%, but that is not what should or did govern my decisions about working additional hours. If I have an opportunity to earn an extra $1,000 by working harder, what I should and do consider is how much of that extra money will end up in my pocket. If my marginal tax rate is 40%, I will get only $600 from the extra effort. My average tax rate might be 23%, but the marginal tax rate is what determines what is happening about additional money that I might be able to bring in. This is key. What we want to minimize to the extent possible is the “wedge” between what I am paid (the $1,000 from the above example) and what I take home (the $600 after-tax cash). The bigger this wedge, the greater effect the tax system will have on economic activity.
So how do we figure out our actual marginal tax rate? Given that my colleagues – business school professors! – could not tell me their marginal rate, I thought I would try to calculate my own. I had an estimate, but I wanted to see if I could pierce that complicated code and get it exact. Now one way of doing this, I suppose, would be to use Quicken or some such tax calculation software and simply do two hypothetical tax returns, one with my actual income and one with $1000 higher income. But I like to do things the old fashioned way – with equations and math. That way I understand a little better of what is actually going on.
Let’s get back to the three major reasons why the statutory marginal rate is not the effective marginal rate. The Medicare one is easy; that is simply an added marginal rate that is not part of the income tax but is certainly a relevant Federal tax. The second two major effects are more interesting, the phasing-out of exemptions and deductions. The key point here lies in those two tables that you have to fill out to complete your Form 1040, the table titled “Deduction for Exemptions Worksheet” and the “Itemized Deductions Worksheet.” As your income increases, the tax system allows you less and less of your exemptions and deductions to be subtracted from your income. As this increases your tax payable, the effects work just like a higher marginal tax rate.
Here is the math of it. I am open to corrections on this, as it is pretty complicated, but I think I have it right. There are a couple minor points not picked up by my equations, but they are not critical (for instance, I do discuss below the issue that deductions do not phase out entirely).
So let’s work with someone in the income bracket for their filing status that would give them a statutory marginal rate of 33%. Then I can write the total tax due, T, as
T = Base Tax + r*(AGI – AE – AD)
In this equation, r is the statutory marginal rate for the income bracket we are dealing with ( for a head of household taxpayer at 33%, this is for taxable income between $166,450 and $326,450). The base tax for such a taxpayer is based on the rates that apply for the first $166,450 of income, which for a single taxpayer would be $39,019.50. AGI is adjusted gross income; AE is allowed exemptions and AD is allowed deductions. Deciphering the tables that calculate AE and AD, we get:
AE = E – ((.02)*(AGI-y')/2500)*E)
where E is your dollar exemption amount before the adjustment and y' is a critical level of income, depending upon filing status (for a head of household taxpayer, y' is $182,450). To take an example, suppose someone has $250,000 of AGI and is filing as head of household, and also has five exemptions. For five exemptions, the statutory amount would be 5*3200 = $16,000. However, from the above equation, you can see that such a taxpayer is going to lose 54% of his exemption amount, leaving him with only $7353.60 of AE to subtract from AGI. Give that taxpayer another $10,000 of income and he is left with only 38% of his exemptions, or a dollar amount of $6073.60. Thought those kids were worth more than that, didn’t you??
Now if this is all getting a bit too complicated, I rest my case: our tax code is a mess.
The equation for AD is not quite so bad:
AD = D – (.03(AGI-y''))
Where AD is allowed deductions; D is statutory deductions; AGI is again adjusted gross income; and y'' is another critical level of income that is $145,950 unless filing status is married filing separately (in which case it is $72,975). (NOTE: I do realize that at worst, you will always get at least 20% of your statutory deductions. The equation above assumes that your income is not so high that you are at the extreme outcome where you will get 20% of your deductions and that is that. This is an interesting aspect of the effective marginal rates, which is that marginal rates actually fall as income gets really high because the phasing-out of exemptions and deductions is done.) Taking another example, let’s have our head of household with $250,000 of income and statutory deductions of say $30,000 (mortgage interest and local property taxes). Then deductions are going to get reduced for this taxpayer by $3125,50.
Now we have it. We can now write total tax payable as
T = Base Tax +r*AGI
-r(E - .02*((AGI-y')/2500)*E)
-r(D-.03*(AGI-y''))
Oh boy! Now we take the derivative of that with respect to AGI to get the marginal tax rate!
dT/dAGI = r + (.02/2500)*E*r + .03r
So the marginal rate depends not only on the statutory rate but also on the level of exemptions…because as your income goes up, the percentage of your total exemptions allowed goes down. Makes sense.
Take again our head of household filer with five exemptions, or an amount of $16,000 in exemptions, and in the 33% statutory bracket. This person would have a marginal income tax rate of
Marginal tax rate = .33 + (.02/2500)*16000*.33 + ,03*(.33)
= .3819.
So these two effects, the phasing-out of exemptions and deductions, increase this taxpayer’s marginal rate by 5.2 percentage points.
On top of that, we have to add the Medicare marginal rate of 1.45%, thereby making this taxpayer’s effective marginal rate a whopping 39.64% -- ah heck, call it 40%.
But now for the truly overwhelming effect. After going through all of good-old Form 1040, you get to the point where you have to fill out the Worksheet to See if You Should Fill in Form 6251! Form 6251 is the dreaded Alternative Minimum Tax, which in many taxpayers’ cases this year, it turned out they owed. So not only did they have to fill out the form to find out if they should fill in Form 6251, but they actually had to fill in Form 6251. In terms of the discussion here on the effective marginal tax rate, the Alternative Minimum Tax (AMT) really changes thing. In effect, the AMT broadens taxable income, by eliminating completely many deductions and exemptions, but at the same time it lowers the marginal tax rate -- to 26% or 28%. So in the end, the effective marginal tax rate this past year for the hypothetical taxpayer above was 28%, plus the Medicare rate of 1.45%, for a total effective marginal rate of 29.45%.
So she might have thought that she was going to get hit with a marginal tax rate of 40%, per my calculations above, but at the end of the year it would turn out that she should have anticipated getting hit by the AMT and having a marginal rate of only 29.45%. But tell me, how many people think ahead that much?
If anyone in Washington is reading this, can you tell me why we don’t just make the AMT the law of the land? The AMT is essentially a flat tax, with close to one tax rate (26 or 28%) applying to the whole base. Let’s do it and cut out all the confusion! More and more people are getting caught by the AMT. I would have thought that the Bush tax advisory panel would have just said, hey, if all these people are already under a flat tax rate system, let’s just make that the norm. Tell us what you made, with some significant adjustments for really low income taxpayers and to allow for some minor deductions, and pay the government 20-odd percent of it. How sweet and easy!
One of my favorite things on an airplane is to ask people how much they paid for their seat. It is a great lesson in price discrimination and usually gets some good conversation going. Of late, I have been having more fun by asking my friends and colleagues what their marginal (federal) tax rate is. At best, I get an answer related to the 2005 Tax Rate Schedules in that favorite of all publications, 2005 1040 Forms and Instructions – that is, a relatively sophisticated answer is to give the statutory marginal tax rate for an individual’s bracket. The current tax schedule has six different marginal rates: 10%, 15%, 25%, 28%, 33%, and 35%.
The problem is that your statutory marginal rate is not your actual marginal rate because of three major effects and one overpowering effect. The three major effects are: phasing-out of exemptions; the phasing-out of deductions; and the Medicare tax which is 1.45% for the taxpayer no matter how high your income. The overpowering effect involves the AMT, the alternative minimum tax, to which I will return shortly.
Just a quick aside, I focus on the marginal tax rate as being key for incentives and therefore the efficiency of our tax system and of the whole economy. My average tax rate last year was, say, 23%, but that is not what should or did govern my decisions about working additional hours. If I have an opportunity to earn an extra $1,000 by working harder, what I should and do consider is how much of that extra money will end up in my pocket. If my marginal tax rate is 40%, I will get only $600 from the extra effort. My average tax rate might be 23%, but the marginal tax rate is what determines what is happening about additional money that I might be able to bring in. This is key. What we want to minimize to the extent possible is the “wedge” between what I am paid (the $1,000 from the above example) and what I take home (the $600 after-tax cash). The bigger this wedge, the greater effect the tax system will have on economic activity.
So how do we figure out our actual marginal tax rate? Given that my colleagues – business school professors! – could not tell me their marginal rate, I thought I would try to calculate my own. I had an estimate, but I wanted to see if I could pierce that complicated code and get it exact. Now one way of doing this, I suppose, would be to use Quicken or some such tax calculation software and simply do two hypothetical tax returns, one with my actual income and one with $1000 higher income. But I like to do things the old fashioned way – with equations and math. That way I understand a little better of what is actually going on.
Let’s get back to the three major reasons why the statutory marginal rate is not the effective marginal rate. The Medicare one is easy; that is simply an added marginal rate that is not part of the income tax but is certainly a relevant Federal tax. The second two major effects are more interesting, the phasing-out of exemptions and deductions. The key point here lies in those two tables that you have to fill out to complete your Form 1040, the table titled “Deduction for Exemptions Worksheet” and the “Itemized Deductions Worksheet.” As your income increases, the tax system allows you less and less of your exemptions and deductions to be subtracted from your income. As this increases your tax payable, the effects work just like a higher marginal tax rate.
Here is the math of it. I am open to corrections on this, as it is pretty complicated, but I think I have it right. There are a couple minor points not picked up by my equations, but they are not critical (for instance, I do discuss below the issue that deductions do not phase out entirely).
So let’s work with someone in the income bracket for their filing status that would give them a statutory marginal rate of 33%. Then I can write the total tax due, T, as
T = Base Tax + r*(AGI – AE – AD)
In this equation, r is the statutory marginal rate for the income bracket we are dealing with ( for a head of household taxpayer at 33%, this is for taxable income between $166,450 and $326,450). The base tax for such a taxpayer is based on the rates that apply for the first $166,450 of income, which for a single taxpayer would be $39,019.50. AGI is adjusted gross income; AE is allowed exemptions and AD is allowed deductions. Deciphering the tables that calculate AE and AD, we get:
AE = E – ((.02)*(AGI-y')/2500)*E)
where E is your dollar exemption amount before the adjustment and y' is a critical level of income, depending upon filing status (for a head of household taxpayer, y' is $182,450). To take an example, suppose someone has $250,000 of AGI and is filing as head of household, and also has five exemptions. For five exemptions, the statutory amount would be 5*3200 = $16,000. However, from the above equation, you can see that such a taxpayer is going to lose 54% of his exemption amount, leaving him with only $7353.60 of AE to subtract from AGI. Give that taxpayer another $10,000 of income and he is left with only 38% of his exemptions, or a dollar amount of $6073.60. Thought those kids were worth more than that, didn’t you??
Now if this is all getting a bit too complicated, I rest my case: our tax code is a mess.
The equation for AD is not quite so bad:
AD = D – (.03(AGI-y''))
Where AD is allowed deductions; D is statutory deductions; AGI is again adjusted gross income; and y'' is another critical level of income that is $145,950 unless filing status is married filing separately (in which case it is $72,975). (NOTE: I do realize that at worst, you will always get at least 20% of your statutory deductions. The equation above assumes that your income is not so high that you are at the extreme outcome where you will get 20% of your deductions and that is that. This is an interesting aspect of the effective marginal rates, which is that marginal rates actually fall as income gets really high because the phasing-out of exemptions and deductions is done.) Taking another example, let’s have our head of household with $250,000 of income and statutory deductions of say $30,000 (mortgage interest and local property taxes). Then deductions are going to get reduced for this taxpayer by $3125,50.
Now we have it. We can now write total tax payable as
T = Base Tax +r*AGI
-r(E - .02*((AGI-y')/2500)*E)
-r(D-.03*(AGI-y''))
Oh boy! Now we take the derivative of that with respect to AGI to get the marginal tax rate!
dT/dAGI = r + (.02/2500)*E*r + .03r
So the marginal rate depends not only on the statutory rate but also on the level of exemptions…because as your income goes up, the percentage of your total exemptions allowed goes down. Makes sense.
Take again our head of household filer with five exemptions, or an amount of $16,000 in exemptions, and in the 33% statutory bracket. This person would have a marginal income tax rate of
Marginal tax rate = .33 + (.02/2500)*16000*.33 + ,03*(.33)
= .3819.
So these two effects, the phasing-out of exemptions and deductions, increase this taxpayer’s marginal rate by 5.2 percentage points.
On top of that, we have to add the Medicare marginal rate of 1.45%, thereby making this taxpayer’s effective marginal rate a whopping 39.64% -- ah heck, call it 40%.
But now for the truly overwhelming effect. After going through all of good-old Form 1040, you get to the point where you have to fill out the Worksheet to See if You Should Fill in Form 6251! Form 6251 is the dreaded Alternative Minimum Tax, which in many taxpayers’ cases this year, it turned out they owed. So not only did they have to fill out the form to find out if they should fill in Form 6251, but they actually had to fill in Form 6251. In terms of the discussion here on the effective marginal tax rate, the Alternative Minimum Tax (AMT) really changes thing. In effect, the AMT broadens taxable income, by eliminating completely many deductions and exemptions, but at the same time it lowers the marginal tax rate -- to 26% or 28%. So in the end, the effective marginal tax rate this past year for the hypothetical taxpayer above was 28%, plus the Medicare rate of 1.45%, for a total effective marginal rate of 29.45%.
So she might have thought that she was going to get hit with a marginal tax rate of 40%, per my calculations above, but at the end of the year it would turn out that she should have anticipated getting hit by the AMT and having a marginal rate of only 29.45%. But tell me, how many people think ahead that much?
If anyone in Washington is reading this, can you tell me why we don’t just make the AMT the law of the land? The AMT is essentially a flat tax, with close to one tax rate (26 or 28%) applying to the whole base. Let’s do it and cut out all the confusion! More and more people are getting caught by the AMT. I would have thought that the Bush tax advisory panel would have just said, hey, if all these people are already under a flat tax rate system, let’s just make that the norm. Tell us what you made, with some significant adjustments for really low income taxpayers and to allow for some minor deductions, and pay the government 20-odd percent of it. How sweet and easy!
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