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November 24, 2008 | 11 Comments

Which president spent the most?

Just for fun, here’s another way to look at the same data we’ve been playing with (in this post and this one.)

First thing is to calculate the inflation-adjusted spending per capita. Then total up the entire amount spent under each president. We could rank presidents this way, but it’s unfair to people like FDR who spent a lot longer in office then did, say, Ford. So I divided the total (inflation-adjusted per capita) by the number of years in office.

This gives a ranking based on who on average had the highest yearly spending. Everything is in 2008 dollars. Democrats in blue and Republicans in Red as usual.

Everybody is guessing, as we mentioned last week, but if the guesses are close, then Obama will top this list with $9400 per citizen per year.

Bush II 8900
Bush I 8200
Clinton 8000
Reagan 7500
Carter 6600
Ford 6200
Nixon 5400
Johnson 4600
JFK 4000
Truman 3400
Eisenhower 3400
FDR 2200
Wilson 700
Harding 500
Hoover 400
Coolidge 300
T Roosevelt 200
Taft 200

As was pointed out, this list does not take into account Congress.

November 23, 2008 | 4 Comments

Government per capita spending revisted

Reader Stephen Dawson, a writer from Australia, has twice tried to show me where I made a bone-headed error in two of the figures from the original government per capita spending article from a couple of days ago. This time I was smart enough to listen and so reproduce those corrected figures below. They are also now correct in the original article too, but I haven’t changed any of the analysis there.

The first picture is this one:Inflation-adjusted per capita spending

(If you’ve visited this page before, be sure to hit “Reload” to make sure you aren’t using an old image from cache.)

This is dollars spent per citizen adjusted to 2008 dollars. The caveats about our inability to precisely measure inflation, plus the partial confounding of inflation and population growth still hold. What changes from the original is the y-axis is now properly adjusted for inflation (in the original, I multiplied where I should have divided—one of my favorite idiotic errors).

The story for the correct figure isn’t too much different than for the incorrect one. Spending was relatively constant until the first World War hit, where it jumped dramatically. It came down a bit in the post-war years, but started rising again after the Great Depression and the installation of FDR. Then another big jump for the Second World War, this time shown in its proper scale. After the war, we have the same depressingly exponentially increasing trend. What might be surprising, however, is that trend briefly reversed itself during the Clinton years. Also remember that the dark blue section is for Obama, and that these numbers are wild guesses.

The second picture is this one:Inflation-adjusted per capita yearly change in spending

This is the annual change in dollars spent per citizen adjusted to 2008 dollars. Numbers less than 0 mean that the budget decreased per person in that year, numbers greater than 0 mean that the budget increased per person. Note the logarithmic scale on the y-axis. This figure is useful to see what happened on a year-to-year basis, but the overall trend is still in the first picture.

Start with 2001, Bush II’s first year in power. He decreased the budget. Then came the wars in Afghanistan and Iraq, and spending increased. Then also came a host of social spending programs. As said above, the picture for Clinton is more flattering. Two years he increased per capita spending, but six years he decreased it. Bush I also increased spending. Working backwards, we see that the opposite pattern held for Reagan. Even Carter decreased per capita spending for one year. Nixon split, but ended with more spending than he started with: that is, his increases were larger than his decreases. The rest is easy to see.

Who tended to increase spending more, Democrats or Republicans? Not in dollars, but in trend: that is, who had more up than down years? Ignoring the upcoming Obama years, Republicans had 25 years with increased per capita spending, and 35 down years. Or, they increased spending about 42% of the time. Democrats had 20 years with increased spending, and 31 years with decreased years; or they increased per capita spending about 39% of the time. Thus, both parties have roughly the same proclivities towards increasing the per capita spending (especially if you consider Obama has promised to increased spending—who knows whether he will—but if he does, then Democrats will have increased spending about 44% of the years).

That crude analysis obviously ignores all subtleties, such as total cost increase or decrease. It turns out that, over this period, Democrats increased net per capita spending by about $5500, and Republicans increased the net by $4000.

If you are fan of one party over another, these figures are nothing to crow about.

Thanks again to Steve Dawson for keeping us straight!

November 21, 2008 | 25 Comments

Stock market crash, hearing aids, F-train music, and the boom-chhh Combinatoric Theory of Finite Musical Variety

The stock market is crashing and may have even bottomed out. Naturally, people are beginning to look around for buying opportunities. I have the perfect one.

Hearing aids.

Any company that sells or markets hearing aids is positioned for rapid growth over the next ten to thirty years. My scientific estimate is that a dollar invested today will bring twenty a few years from now. I give you this hot tip for free, my friends, just for being a loyal reader of this blog. You simply cannot go wrong.

My evidence for this stunning opportunity is based on my experiences commuting via the F train. My insight arrived suddenly, when yesterday I was surrounded by at least seven people wearing Thinking Suppression Devices (TSDs). I had to give up on reading James Fitzjames Stephen because each commuter’s device was louder than the others’. Everybody was wearing earphones, but even still, I was assailed by various booms and crashes which were clearly audible to anybody—to anybody not wearing a TSD themselves. These people are obviously going to lose a significant part of their hearing, if not go deaf, hence my advice about buying stock in hearing aid companies.

But I decided to make this an opportunity instead of despairing and following my usual approach of looking at my fellow passengers like they had just stepped in what they were listening to.

Now, the only distinct sounds I could make out—and I listened attentively—were various combinations of booms and chhhs (electronic cymbal crashes). This was my first important clue.

I asked the guy sitting next to me, who was fiddling with his TSD, “How many songs does that thing hold?” He said a number in the thousands, and that he had just about filled it up and was looking into getting a better model. I asked, “Got any Duke Ellington on it?” When he said “Who?”, I had my second clue, and realized that my boomchhh observation was not an accident. I therefore told him that he didn’t need a larger device, because there were only about 100 pop songs in the world anyway.

“Yes,” I sagaciously intoned, “based on my scientific measurements of your music—this is only an estimate, to be confirmed later, mind you—there are only about 100 possible songs that can be made. You don’t need a more expensive device. Think of the money I have just saved you!”

The look he gave me told me he was deeply aware of my genius. The fact that he edged toward the door as fast as he could, so that he could jump out at the next stop told me how excited he was to pass on his new knowledge to his friends and family.

It was on that train ride that I devised the Combinatorial Theory of Finite Musical Variety. This theory states that there are exactly, and only, 124 possible pop songs. Here is how it is proved.

Our first piece of evidence is that every popular song is comprised solely of combinations of booms and chhhs. There are other trivial elements, related to the outmoded and ancient theories of melody, harmony, point and counterpoint, and lyricism, but these can be, like they now always are, ignored.

The second piece of evidence is that, to build a pop song, you must have either three, four, or five booms and chhhs in combination and that at least one of these must be a special boom. Examples:

  • boom boom chhh
  • boom boom boom chhh
  • boom chhh chhh boom chhh

Ready? Let’s start counting. Begin with the three combination, with one mandatory boom. Suppose first that the boom is at the end. The other two slots must be filled with booms and chhhs. We could have two booms, two chhhs, or one of each with either leading the way. That’s 4 possibilities. But then we remember that we have the mandatory boom at the end, which could be placed in any of the three available slots (it could have come first, second, or third), and then the other booms and chhhs would fill in the other two slots. This makes 3 x 4 = 12 possibilities.

What if there were 4 slots and one mandatory boom? Suppose again that the regulated boom is at the end, and the booms and chhhs fill in the other three slots. They could all be booms or all chhhs, or various combinations. We could list them all, but that gets to be a pain, so let’s use some math. We have three slots and we could put 0, 1, 2, or 3 booms in those slots, with chhhs filling in the blanks.

There is a formula for this called choose. If we say “3 choose 0”, we say we have three slots and we choose no booms to go in them. The choose formula tells you the number of ways we can do this. It should be obvious to you that the only way to place no booms out of three is 1; namely, you choose no booms. Formally, the answer is

(n-k)! k!

where n! is read “n factorial” and means “n x n-1 x n-2 x … x 2 x 1”. In our example, n = 3 for three slots. At first, k = 0 for no booms. The formula works out to be

  3 x 2 x 1
(3 x 2 x 1) x 0!

where you have to know that “0! = 1” (there are good, technical, mathematical reasons for this, which I’ll skip). There answer equals 1. Then you work this formula out for k = 1, k = 2, and k = 3 because we want to know how many different booms go into the 3 slots for each possible number of booms.

The answer turns out to be 1 + 3 + 3 + 1 = 8 for k = 0, k = 1, k = 2, and k = 3. But again we have to remember that one mandatory boom could have gone into any of the four slots, so we have to multiply the answer by 4 to get 32.

Thus far, we have 12 + 32 = 44 possible songs, but we still have to calculate the number of possibilities if there were 5 slots and one mandatory boom. The math is exactly the same, except n = 4, and k = 0, k = 1, k = 2, k = 3, and k = 4. But it turns out that there is a simplification when you sum up all possible combinations of 2 things (booms and chhhs). The sum of “n choose 0” + “n choose 1” + … + “n choose n” = 2n, which is very easy to calculate.

If n = 4 then 24 works out to 16 different songs with the mandatory boom at the end, but there are 5 possible places for that boom, so we have 5 x 16 = 80 combinations.

In total, then, we have 12 + 32 + 80 = 124.

That’s it, friends! There are only 124 possible pop songs. I was therefore right to harangue my train-mate with this wisdom so that he would not waste his money on a device that holds more than this. It is therefore a matter of great curiosity how people could not have recognized this before now, a fact which can only tell us of the deleterious effect of pop music on the brain.

Incidentally, a corollary to the theory is: Each pop song must be played as loudly as possible, not only to annoy those around you, but to destroy your hearing as quickly as possible.

Incidentally, incidentally, I cannot vouch that the math here is 100% accurate. This is because, as I write this, the beaujolais nouveau arrived in stores this afternoon, and I am liberally sampling this year’s offerings.

November 19, 2008 | 34 Comments

On the growth of government spending: who benefits, the rich or poor?

UPDATE: Reader Stephen Dawson has kindly shown where I made a very stupid error. This error caused me to label the y-axis incorrectly in the third picture below. It also causes the fifth picture to change dramatically. I will leave my original analysis untouched, except to indicate in bold where it is wrong. See the post from 23 November 2008 for an update on these two important figures, where I will give the proper interpretation. Thanks again to Dawson.

It’s obvious that, as time has gone on, the Federal Government has spent more and more and more money. Since a reasonable proxy of government control over the lives of its citizens is the outlay of funds from its treasury, a sane observer might wonder about this increasing trend.

A raw plot of the Federal outlay by year will not do as a measure, however. At least two adjustments have to be made.

A government ruling over 1000 people will obviously have to spend more than one ruling over 10 people, so we have to adjust by population size, which has also been increasing. We can be reasonably sure we are measuring population to, say, the nearest million, which is close enough. The budget is also reasonably well measured.

Then there is inflation, the phenomenon whereby a loaf of bread costs $1.00 ten years ago becomes $1.89 this year. But inflation is difficult to measure because of many reasons. For one, that loaf of bread probably isn’t the same as the loaf now: it has different ingredients, uses changed baking technology, improved packaging—who knows what has changed in that ten years. The population, too, which has increased over this period also tends to drive prices higher because it makes certain commodities scarcer. Plus, nobody knows which are the ideal items to track to measure cost increase: bread? cars? Eliot Spitzer’s hobbies? We’ll use inflation adjusted dollars in some of the plots, but we have to remember that these pictures are a lot more uncertain.

The first picture is the Outlay per Capita: that is, the dollars spent per citizen since 1901 (data from the US Budget Office and the US Census).
Outlay per capita
I have also colored the years red for Republican presidents, and blue for Democrat presidents. The years from 2009-2012 are obviously projections, so should not be taken too seriously. Not too much can be noticed, except for the obvious exponential increase in government control, plus the two blips for World Wars I and II.

Since the rate of increase is exponential, we can see things clearer by showing the picture on a logarithmic scale:
Outlay per capita
The two war-time era increases now pop out, with WW I showing the biggest increase. The after-war decreases are also more obvious. And we can see the small blip for the Korean war and a smaller build-up for Vietnam (all these increases are in the blue areas). The steady increase after Vietnam is also clear: where you can see a higher rate of increase in George W. Bush’s years because of the Iraq/Afghan wars, but certainly not a giant surge. Of course, I do not parse how much of any spending is due to military and civilian funding.

The big, but maybe not so obvious. point is that 2008 spending is about $10,000 per person. That means the government is spending $10-grand per head. That also means, in some loose sense, that if you pay more than this in taxes—if your personal bill is more than $10k—then you are paying more than your equal share. This implies, then, that if you are paying less than $10k you are not paying your equal share. You are requiring those that are better off to support the bulk of the government.

Now, if you are a Lefty, then you probably like this idea. “Let the rich pay their ‘fair’ share!” But to say this ignores Briggs’s Doctrine of Unintended Consequences. To see what I mean, let’s look at the same picture adjusted for inflation. The inflation adjustment index is from Oregon State University.
Inflation-adjusted Outlay per capita in 2008 $
This is adjusted to 2008 dollars. Suppose I were to declare that every citizen had to pay $10 to the treasury. If you, for example, were Dad and the only worker in a family of four, your bill would be $40. The last time this happened was in the 1940s (remember: this is 2008 dollars, not 1940 dollars, so $40 was affordable).

This analysis is broadly correct, but the y-axis was off. You can see that the cost in 1940 was about $700 per head, or $2800 per family of 4 (all in estimated 2008 dollars). Still affordable, but to as many families as $40.

Everybody can afford this (with the trivial exception of a handful of people). Everybody would contribute an identical amount and would, morally at least, be entitled to an equal say in government. “But, wait! The rich will still have more money, and with money comes influence!” Yes, true. It is a tautology to say the rich will have more money, and it is obvious that with more money comes more influence. But this is not a good argument, my Lefty friend. Because look at 2008, where the bill is $10k per head. Only a small percentage of the population (about 5%) can afford this. Those 5% of course have more money. They further are aware of where that money is going. They will therefore have plenty of motivation to control the outflow, which means controlling the laws, rules, and regulations—controlling the government—which say where the money is to go. This small minority will use their money to align the government to their views.

Now, the rich certainly would have done this to some extent had everybody had to pay the same share, but they will have orders of magnitude more motivation to do it when they are paying nearly all the bill. And—here’s the kicker, so pay attention—they will still have plenty of money left over to have the same influence over other non-governmental matters, influence they already had before this tax structure started asking more of them.

About the only thing this confiscatory tax policy will do is to take enough money from the just-rich, to make them no longer rich. Thus, more control will flow into the hands of fewer and fewer people. This is inevitable. And it’s happening at an exponential pace. The noble idea of having those with more pay for those with less guarantees that those with more will have even more, and those with less will have even less, plus they will suffer a corresponding loss of influence and control over government.

Disproportionately taxing the rich to grow government, and doing so at an increasing, exponential pace, thus guarantees the creation of a oligarchic ruling class. Supporting these tax laws, then, will have the exact opposite effect of your intent.

I use the term “Lefty” not to indicate “Democrat”, as will be clear in the next two pictures:
Change in Outlay per capita in 2008 $
These are the year-to-year change in outlay per captia. The first is unadjusted, the second is adjusted to inflation.

The unadjusted shows the blips due to the wars, plus the accompanying decreases in the budgets after the wars ended. Most of the wars, WW I, WW II, Korea, and Vietnam happened under Democrat administrations. But there was only moderate growth until Nixon was president in 1969, then the increases began with real vigor, and it has rarely abated since (only one year in Reagan’s presidency did the budget not increase significantly).

The scarier picture is this one, adjusted by inflation:
Inflation-adjusted change in Outlay per capita in 2008 $
This shows the contest between R and D more clearly. Nixon (R) had a modest rate of increase, but Carter (D) really showed how it was done with a stellar increase. Reagan (R) did his best, but could never match Carter. Clinton (D) was also just an average player. Bush (R) beat them all. No taxpayer left behind. Again, Obama’s (D) tenure is just a wild guess by the budget office; however he has often boasted of increasing taxes on “the rich”, so we can guess that his rate will be Carter-like.

My comment below about my not being an economist is right on: I am not and made a fundamental error here. The new figure shows the changes more clearly—they bounce around 0 a lot more than I originally thought. Be sure to see the 23 November 2008 post for more on this Figure.

I am not historian or economist enough to say why the rapid increase in government control really got going with Nixon, but we have some hints in his social spending policies. The funny thing is the opposite of common wisdom appears to be true. Most, but not all, of the increases in spending for the military have come from Democrats (the wars just mentioned); and most, but not all, of the increase in spending on social causes have come from Republicans. Each side, as we all know, is continuously accusing the other of the opposite! It might be a case of projected guilt all politicians feel (at some level; I cannot really guess why this is so).

Even if you don’t agree with me on anything, it must be clear that this rate of increase cannot continue indefinitely. It cannot even continue for very much longer. Roughly, every 20 years brings an order of magnitude increase in government control. So in 40 years, in the trend continues, the bill will be about $1 million per head, an impossibly high number. Power would be coalesced into the hands of a very, very few.

I don’t know about you, but I plan a two-pronged strategy: (1) to never vote for anybody, D or R, who I think will raise taxes, and (2) to be one of those who can afford the tax, because I’d rather have the control than not.