Peak Oil

I suggest in the Welcome below that Peak Rent is like Peak Oil. So what is Peak Oil, and how is it like Peak Rent? Wikipedia describes the idea this way.

In the 1950s, the geologist Marion King Hubbert observed that explorers for oil discovered new reserves in the continental United States less rapidly than Americans consumed existing reserves. He concluded that U.S. production would eventually peak and then decline.

Based on his theoretical modeling of oil discovery and production, Hubbert predicted a peak around 1965. Though he considered a peak in 1965 most likely, his prediction encompassed a range including 1970, so Hubbert's reputation was established when production in the continental U.S. peaked in that year.

Hubbert's theory of a peak in conventional oil production is not based simply upon a presumably finite supply of oil. The amount of oil under the ground is a factor, but so is the difficulty and the cost of discovering ever smaller oil fields as the larger, more easily discovered fields are exhausted.

Small fields, containing even more oil than we've consumed thus far, possibly remain in the continental U.S., but no one knows where they are. The likelihood of finding a small well on a particular square mile is remote, and the cost of searching this area for a well is considerable.

If the product of the likelihood of discovery and the cost of searching an area exceeds the expected return from small wells, oil from these wells, however vast its total supply, will not be produced. Seek and ye shall find ... but not at a profit.

Even now that oil production in the continental U.S is greatly reduced, discovery of a large, new conventional oil reserve is possible. At this point, the discovery would be a Black Swan (see below), but it's conceivable. You might discover this well in your back yard fortuitously tomorrow; however, what we know of the likelihood of discovering the well does not justify the cost of searching for it.

If you happened to discover this Black Swan on your land, the rent you might charge for use of the land would skyrocket; however, searching for this Swan now seems like dropping a quarter in a slot machine. You might win, but if you keep dropping quarters long enough, you'll be a net loser, because this outcome is built into the machine.

In this sense, Peak Oil is a special case of Peak Rent. An oil well is only one of the scarce resources we'd like to own to earn its rents. Earning this rent is difficult, because discovering its source is both unlikely and costly.

I also suggest in the Welcome that Peak Rent is even more inevitable than Peak Oil. Oil is a very valuable resource, but it is not the most valuable resource. Classical liberals from Mises to Simon tell us that human labor, including innovative, intellectual labor, is the most valuable resource. This assertion is not simple politics stroking the human ego. It is sound economic science.

A Black Swan contradicting Peak Oil seems unlikely, but it could be out there. The coming labor shortage is a matter of demographics. We can't go back in time and have more children.

A child could discover an oil substitute or some other innovative resource of unimaginable value, but even if this Black Swan exists, finding it and becoming entitled to its rents is increasingly unlikely, while rents paid by more common humanity decline, relative to demand for them, simply because common humanity declines relatively.

Fat Tailed Distributions,The Law of Large Numbers andBlack Swans

If you hated math class, this post might not be your cup of tea, but give it a chance and ask questions.

The previous post introduced mathematical concepts unfamiliar to most people, even to most economists and certainly to most politicians. I'll try to explain them here. In the preceding post, I try to explain how they relate to Peak Rent.

I'll illustrate "fat tailed distribution" with a concrete example. Below are two, relatively simple, discrete frequency distributions, one thin tailed and one fat tailed.

Thin tailed distribution
Value:	1	2	3	4	5	....	N
Frequency:	1/2	1/4	1/8	1/16	1/32	....	1/2^N
(one over two to the power of N)

Fat tailed distribution
Value:	1	2	3	4	5	....	N
Frequency:	1/2	1/6	1/12	1/20	1/30	....	1/N*(N + 1)
(one over N times (N + 1))

You can verify by googling (or mathematically) that

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... = 1

and

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... = 1,

so both frequency distributions are properly normalized. In other words, I can approximate two populations with these distributions by filling two boxes with tokens, labeled 1, 2, 3 and so on, as follows.

Each box contains roughly a million tokens. In the first box, half a million tokens are labeled 1, a quarter million are labeled 2, an eighth of a million are labeled 3 and so on. In the second box, half a million tokens are labeled 1, a sixth of a million are labeled 2, a twelfth of a million are labeled 3 and so on. I add tokens to each box this way until both boxes contain 999,000 tokens.

I truncate the distributions at 999,000 tokens/box, because I otherwise require fractional tokens. For example, if the total number of tokens is a million, the number of tokens labeled 20 in the first distribution is less than one, because 2 to the 20th power is greater than a million.

If you randomly draw a hundred tokens from the first box and average the numbers labeling them, the average will be very nearly two. If you draw a thousand tokens and average the numbers, the average will almost surely be closer to two. This convergence on two is what Russ meant by "Law of Large Numbers" in the previous post, but mathematicians conventionally use "Law of Large Numbers" differently.

If you randomly draw a hundred tokens from the second box and average the numbers on them, the average will be around 6.5 but maybe not so close to 6.5. If you draw a thousand tokens and average the numbers, the larger sample average is no more predictable than the smaller sample average. In other words, large sample averages have no expected value.

From both boxes, the proportion of tokens labeled 1 approaches 1/2 in samples of increasing size. This convergence is the Law of Large Numbers.

Because we've truncated the distribution, very large sample averages from the second box (approaching a million in size) do approach 6.5, because the entire truncated distribution has this mean value; however, the untruncated distribution has no mean value.

If we fill a box with roughly a billion tokens and stop when we can no longer add whole tokens, the mean value of the entire box is larger than 6.5. If we use a trillion tokens, the mean value is larger still. If we keep filling larger and larger boxes this way, the mean value increases without limit.

Why do large sample averages from the second box have no expected value (if the samples are much smaller than a million)? Consider how I've filled the boxes. Both boxes have a million tokens, but as I add tokens of increasing value, I fill the first box faster.

For example, I add a quarter million tokens labeled 2 to the first box but only a sixth of a million of these tokens to the second box. As a consequence, the highest label in the second box is much larger than the highest label in the first box.

In fact, the highest label in the first box is only 10, while the highest label in the second box is over 1000, a hundred times larger, and roughly 9000 tokens in the second box are higher than 100.

When you sample from the second box, you occasionally pick one of these rare tokens with a very large label, and these very large values contribute far more to the sample average than other values in the sample. Sample averages from the second box are less predictable for this reason.

The rare but significant tokens are Taleb's Black Swans. See the previous post.

In economic terms, if the tokens represent the wealth of persons, the richest person recorded in the second box is much richer than the richest person in the first box. In reality, wealth is distributed more like tokens in the second box.

Kling on Freddie and Fannie

My interest in Peak Rent is decades old, but this blog is the offspring of my more recent love affair with the blog Cafe Hayek and the podcast EconTalk. I enthusiastically recommend both. A central thesis of this blog is bolded below.

This post replies to now obsessive talk of the credit crunch following the deflation of the housing bubble and the mortgage backed securities that propelled it, but this blog places these events in a broader context.

This episode of EconTalk features Arnold Kling, a former economist at the Federal Home Loan Mortgage Corporation, Freddie Mac, one of the main characters in the Mortgage Backed Securities story.

Kling says, "The mortgages can default, but the bonds cannot, so we (Freddie Mac) are in the middle taking the default risk."

He doesn't continue, "... until we can't bear the risk anymore, whereupon we transfer the risk to taxpayers."

Freddie Mac sells rents to rent seekers. Seeking rents was always its business, even before the subprime debacle. If it doesn't sell rents to rent seekers, it needn't sell bonds at all.

With Congressional authority, GSEs could simply create money to lend and then remove this money from circulation as it's repaid, or (equivalently) Congress could endow FNMA with funds, and FNMA could lend these funds and then relend them as loans are repaid, charging enough interest to keep its funds stable or growing rapidly enough to meet a growing demand for credit. It's only function then would be to police the credit. It would never pass yields to anyone except the growing pool of home sellers.

If the buyers of bonds don't stand to lose when credit is poorly policed, then they play no role in the policing of credit, so they're pure rent seekers; therefore, selling rents to rent seekers is the primary motive of Freddie Mac's business definitively. That's not a theory. It's an observation.

Referring to mortgage backed securities, Russ says, "The law of large numbers is such that it's going to be more predictable ..."

The law of large numbers need not apply in this context at all and presumably does not apply. This point is crucial.

First, "Law of Large Numbers" technically doesn't refer to a statistical average (like the yield of a package of many mortgages); however, this usage apparently is common. Here is Wikipedia's page on the subject.

Techinically, Wikipedia doesn't describe the Law of Large Numbers at all. The page describes a result involving a statistical average when a distribution has a well defined mean. This result is a consequence of the Law of Large Numbers, but it's not the Law of Large Numbers. At least, it's not what I learned to call "the Law of Large Numbers" in graduate school. The Law of Large Numbers does not involve a statistical average or assume a distribution with a well defined mean.

The Law of Large Numbers says that the proportion of outcomes, in random samples, with a particular characteristic approaches the probability (or frequency) of this characteristic, so for example, the proportion of heads approaches one half in a sequence of fair coin tosses. You can verify this usage of "Law of Large Numbers" by googling. Here's a page at Berkeley for example.

This Law of Large Numbers (not the result described at Wikipedia) is always true for any probability distribution, because it's essentially tautological. It's true because of what we mean by "probability" and "random sample". As such, it's more of like a "law", i.e. it's true without exception.

The result described at Wikipedia is what Russ means by "Law of Large Numbers", but this result involves an assumption about the distribution of values, so it's not true in general. The Wikipedia article states this assumption when it says, "Given a random variable with a finite expected value ..."

"Expected value" is a property of a statistical distribution, but some distributions don't have a well defined (finite) expected value. A "fat tailed distribution" doesn't have a finite expected value, by definition.

In a fat tailed distribution, rare values contribute significantly to statistical samples, so that larger and larger sample averages don't converge to a well defined mean value. The standard example is Cauchy's distribution.

We typically study thin tailed distributions in elementary statistics, the standard example being the Gaussian (or Normal) distribution, but fat tailed distributions may be the rule rather than the exception in Economics. See the EconTalk with Nicholas Taleb.

The yield of a mortgage backed security essentially is an average of the yields of mortgages backing the security. If the distribution of the underlying yields is fat tailed, the yield of the security need not be more predictable than the yield of a single mortgage.

So why might the underlying distribution be fat tailed? Can we simply blame politicians encouraging subprime mortgages? I don't think so. The problems we're seeing with mortgage backed securities are not limited to these political influences or to these securities.

Similar problems exist with all CDOs and also with mutual funds and even with corporations, since the yield of a corporation essentially is an average of yields of its factors of production.

The underlying distribution of yields is fat tailed, because Black Swans are everywhere. A particular political influence is only one example. We can't point to one Black Swan and say that we've explained the problem. The next Black Swan could be red.

Kling said, "The creativity of mortgage bankers in delivering fraudulent loans is tremendous ..."

Basically, Kling indicts the "unregulated market" here, but it's a mistake simply to blame criminal "fraud" for the fat tail. This fraud is just another Black Swan. We can't kill all the Black Swans by passing a law. Killing them all is not possible, even in principle, just as a centrally planned economy without market prices can't be more productive than a free market economy in principle.

Kling said, "I'm not sure what made investors willing to buy these securities ..."

Kling asks the right question. It's not about the sellers. It's about the buyers. We have too many buyers. When so many people demand rents, riskier credit is an inevitable outcome, because all the rent seekers exhaust the less risky rents. No political influence is required.

Fundamentally, we're exploring a fat tailed distribution of yields including many negative yields. State regulators can't make the distribution thin tailed without simply commanding unproductive rents. If they could, we'd all be socialists by now, even more than we are.

So what if politicians persuade their cronies in a GSE to package many risky mortgages into still risky "securities"? If less risky securities exist with acceptable yields, who buys the GSE's paper?

We (our pension funds and other institutions) bought the GSE's paper, because we couldn't buy enough rent elsewhere. Just look at the yield on ten year Treasuries. Can you retire on three and a half percent, with inflation at five percent?

Kling said, "Why not subsidize the downpayment?"

Kling hasn't heard of the $7500 tax credit for "first time home buyers" enacted earlier this year. "First time" means that you haven't owned a house in three years.

http://www.federalhousingtaxcredit.com/

Of course, this credit is a pass-thru benefit for rent seekers and has little to do with helping home buyers.

Welcome

Welcome to Peak Rent, the blog and the historically unprecedented event. Mortgage Backed Securities, The Credit Crisis and The Bailout are the Top Story Tonight, but these events only preview a much longer show now opening. The peak in the payroll tax surplus, reportedly this year, is possibly more significant, but we aren't discussing it with the same vigor or much relating it to the Story of the Day. We'll discuss it here, even if most people pay little attention to us.

RDavis provides the following chart to motivate our discussion. I repost it here linked to his site and hope he doesn't mind, since I have no clue who he is. I've researched the same figures, and they've been widely discussed, so you can believe the chart, and even if you don't, the wonders of the internet enable you to verify them yourself.




Why Peak Rent?

It's like Peak Oil, only even more inevitable.

Wikipedia defines "rent seeking" well enough. We'll use the term a lot here. I associate the term with Smith, Ricardo and classically liberal economics, but let's not crowd the boat too much. We're all in it. My libertarian bias will be plain enough, but this blog invites a broad, civil discussion of the issue.

Demography is destiny. The ratio of retirees (persons over 64) to workers (persons between 20 and 64) in the United States will nearly double over the next two decades. The number of workers per retiree will fall to the unprecedented level of roughly 2.5 by 2030, but we'll feel the effects much sooner. The thesis of this blog is that we're feeling them now, but the curtain is only now rising. The show has hardly begun.

Let's talk about it.