Thursday, November 17, 2005

eBay Scandal Exposed!

The online auction site eBay is one of the few internet startups to make it through the dot com bust, and has flourished over the years, posting consistently solid profits. What I am about to expose is so scandalous that I do not expect this success to continue; sell your stock and close your PayPal account, because this post will bring the mega-populist-crap-broker to its knees.

Here's how an auction works on eBay:
  • A person bids on an item by choosing a maximum bid amount, a1, at or above the current bid price plus some bid increment, bi.
  • eBay automatically counterbids for the original holder of the current bid (who bid a maximum of a2) until either bidder reaches their maximum bid amount.
  • The current bid becomes min(a1,a2) + max(|a1-a2|, bi).
What is implied by this description is plainly stated on the eBay website:

[1] The system places bids on your behalf, using only as much of your bid as is necessary to maintain your high bid position (or to meet the reserve price). [emphasis added]

This means that there is no penalty to the bidder for raising their maximum bid unless another bidder drives up the current bid. Here is another statement from eBay's help page:

A bidder may be outbid by less than a full increment. This would happen if the winning bidder's maximum bid beats the second highest maximum by an amount less than the full increment.

In this situation, the difference between the two maximum bids was less than the bid increment, so the current bid becomes the maximum of the two bids. This algorithm, however violates rule [1] because the autobidder will in fact bid "as much of your bid as is necessary" plus one-penny less than the bid increment. For example, if the current bid is $50, and the (secret) maximum bid is $70, and someone else bids a maximum of $80, the current bid will become $71, because the bid increment is $1 in this bid range. However, if the second bid was $70.50, the current bid would be only $70.50, and the second bidder would pay a lower price. In the first instance, where the second bid was $80, the autobidder bid more than the minimum amount necessary to maintain the high position, thus violating rule [1].

This may seem trivial, but imagine a more egregious case. In the same situation, imagine the second bid was placed at $70.50, running the current bid up to $70.50. Now the second bidder has the high bid, and would win if no one places a higher bid. The high bidder may decide to pad his (secret) maximum bid, as a precaution against a challenger, say by raising the maximum bid to $75. Under rule [1], this should never affect the current bid price; the bidder already has the high bid. On eBay, however, raising the maximum bid will actually raise the current bid price to the previous high bid plus the bid increment, in this example to $71. The high bidder can bid against himself! This is an erroneous implementation which violates the rules set forth by eBay and which are firmly established in auction everywhere.

This still may seem somewhat trivial (because it is), but be aware that bid increments are proportional to the size of the current bid, and they increase rapidly. For example, bid over $5000 have a bid increment of $100. This means that this bug could cause clearing prices to be off by as much as two percent. (For smaller prices, the percent can be even higher!)

Sunday, November 13, 2005

Energy efficien....zzzzzzzzzzz

Energy efficiency, or conservation, as it used to be called, is an topic that is so exciting, so sexy, so provocative that the New York Times usually leads at least one section from the Sunday edition with a human interest/pseudo-economic analysis of energy consumption. This week, the article was in the energy-efficiency-is-making-a-comeback-because-it-will-save-you-money style, one of my personal favorites because it combines optimism with weak-but-convincing economic evidence, leaving the reader distracted with thoughts of a utopia where bicycles rule the roads and all windows are double-paned.

Back in reality, the largest step toward increasing energy efficiency taken this year was a small provision in the Energy Policy Act of 2005, passed by Congress on July 29, 2005, which changed the effective dates of Daylight saving time: "Clocks will be set ahead one hour on the second Sunday of March instead of the current first Sunday of April. Clocks will be set back one hour on the first Sunday in November, rather than the last Sunday of October." (wikipedia) This could save as much as one percent of electricity consumption (correct me if I'm wrong; I can't remember the source) by reducing dependence on artificial lighting and other appliances. Not to trivialize this importance provision of the bill, but this is the best energy legislation that congress could come up with? They could save almost as much energy by not hauling the less-than-lean Dick Cheney around in Marine Two, a 1,560 horse power UH-60 Black Hawk, with cupholders.

But where congress has failed, Fundamint prevails. Fundamint knows that by combining econ 101 market theory with a dash of insight and a splash of simplification, many of the worlds problems can be solved in 1000 words or less. The world's energy woe is no exception.

The most fundamental of all economic theories is that if the consumer does not properly bear the costs associated with consumption, their will be an inefficient outcome in the market. This is why are public services are underfunded and why General Electric consistently outperforms the market. The point is that with the assumption that consumers behave in a self-interested manner (what economists call "rational"), they must pay at least the true cost of the goods they consume or else they will consume too much, resulting in efficiency lost. A good example of this is the all-you-can-eat restaurant: the customer does not pay for each marginal good consumed, so the customer has incentive to eat right up to the point where he feels sick. The tendency is for everyone to eat more than they would if they had to pay some cost for each marginal food item. In the end, this benefits the big eaters and punishes the healthy eaters, which is why it is such a bad system; the restaurant does not bear the cost of your poor health resulting from their harmful system, thus they are creating a negative externality (which is a whole other related topic).

You may be shocked to hear that this all-you-can eat system is prevalent elsewhere in society, and it could even be happening right in your own home. That's right, many apartment buildings include the cost of utilities in the price of the rent, decoupling the cost of energy usage and the consumer. With no incentive for the renter to conserve energy, far more electricity and gas is consumed than is efficient; what's a few more minutes in the shower, or listening to a few more minutes of your favorite radio program, when you don't have to pay it.

So fix it, you say? Require utilities to be metered and paid for by the renter? Here are the problems. First, most apartments which use this method are old and do have individual metering; adding this would be costly. Second, two of the largest energy consumers, heating and air conditioning, are often part of a central system, making it more efficient for the building and making it difficult to divide up expenses. The final, and more subtle problem is that charging renters for energy consumption would have the unintended effect of decoupling the owners from the cost of energy consumption. This means owners would have little incentive to make capital improvements to increase energy efficiency, such as upgrading appliances and improving insulation, an important component in reducing energy consumption. Renters, who do not stand to gain from long-term investment, would not undergo such improvements.

So how do we solve this mess? We make both renters and owners bear the costs of energy consumption. This is tricky because of our notions of fairness, but some reasonable solutions are possible. The simplest would be to create a hybrid system of the two extreme systems, where the renter and the owner each pay a portion of the utilities. Under this system, both parties has incentive to pursue efficiency, although not as strong as if each bore the full cost. The obvious pitfalls of this system is that owners' profits would be somewhat linked to the type of renter they have as a customer; this would discourage renting to families, and other high-energy users.

One method that could be employed to reduce this bias would be to require owners to disclose some measure of the energy efficiency of the rental unit, just as the fuel efficiency is shown on new cars, but still require the renter to bear the full cost of utilities. This would allow the renter to put a value on the energy efficiency of the unit, and the owner would thus have incentive to make investments to improve efficiency so as to make the unit more attractive to potential tenants. The efficiency measure could be done by the utility company, or perhaps more elegantly, by taking a long-run average of past utility costs, something already publicly available in some states.

Another method along the same lines, but providing greater incentive for owners to make investments, would be to have owners pay a percent of the long-run average of past utility costs, and the renter pays the balance. Under this system, both renters and owners have strong incentive to conserve.

Ultimately, there are many market mechanisms which can increase efficiency in energy consumption. Many can also speed technologies already in transition; for example, charging a gas tax proportional to the weight of the vehicle would amplify the existing costs of owning a larger vehicle, precipitating the transition from SUVs to hybrids. The difficulty with all these mechanisms, as we saw in the rental markets is that there is rarely a perfect system, and often transaction costs become prohibitive. Fortunately, technology is making many mechanisms cheaper and easier than we ever thought possible, putting our reveries within practical reach.

Saturday, October 22, 2005

Bush's Quag-Mier

You probably expected a trenchant article about the Harriet Miers confirmation. I've got nothing. I just liked the title.

Sunday, August 21, 2005

Buddy Budgeting

You don’t have to be a fervid egalitarian, or a New York Times regular, to know that the CEO of Walmart makes fourteen quadrillion dollars, or something like that. Actually, you may not know how much he makes, but you’ve probably heard that he takes home about 400-500 times what the company’s most subordinate subordinate does, and that probably even undervalues the CEO’s yacht-friendly pension.

This shouldn’t be surprising, considering that real wages for the poor and middle class have stagnated for the past forty years, while the upper-class have been abundantly successful in living up to their title. We all know of the flagrant inequality in wealth and income in this and other countries, but since the boom of the late nineties, the CEO has emerged as the American superstar, used ubiquitously to symbolize both the capitalist American dream and the paragon of prodigality.

But is their high pay actually an efficient market outcome, where the company is maximizing profit by paying a single critical employee millions of dollars, or could it be that the company is not acting rationally by hiring the CEO superstar?

The problem with executives in general is that it is often difficult to reward them appropriately: devising a pay package that aligns the goals of shareholders and executives is not an easy task, as has been painfully proved in the recent string of corporate accounting scandals. But even assuming executives have the proper incentives, how much are they really worth? Of course, this value is impossible to quantify, and depends greatly on the company and the specific role of the executive within that organization, but the disparate pay of executives even between similar companies suggests that companies aren’t doing the same cost-benefits analysis before hiring.

The board of non-executive directors is supposed to be an impartial agent, like an outside auditor. The problem is that directors are not outsiders. More importantly, they are often former or future executives themselves, and have a very real incentive to boost compensation for both non-executive and executive positions. The idea of tacit collusion of directors to maintain generous executive wages does not seem far fetched, especially when we acknowledge that executive pay makes up only a fraction of a percent (I made this statistic up, but it seems true; correct me if I’m wrong) of most companies’ expenses, rarefying the incentive (and shareholder pressure) to reduce them.

A recent study revealed what we all suspected: female executives make less than their male counterparts, but are compensated more equitably when their boss is a woman. Looking beyond gender, this same data could be used to see if executives are compensated using the buddy system: is pay positively correlated with the frequency and duration of past contact with board members? We associate mutual back patting with politicians; businessmen are too shrewd to put friends before profits. But why would we expect them to put shareholder income ahead of their own?

Wednesday, June 22, 2005

The Dance of Love

Financial market are innately fickle beasts, precisely because no one person or group has control over them. Their movements are caused by changing expectations, herding, hysteria, and sometimes even economic data. While no one person can predict or control a substantial market, such as the Treasury debt market, certain powerful people seem to be trusted to "guide" the market. And while everyone is familiar with the Gospel of Greenspan, with his "irrational exuberance" and "conundrum," there are others, such as other Fed governors or high-level Treasury officials, who have a sharp effect on markets.

But there are others still, outside of the blind-trust beltway, who seem to guide with bias. For instance, yesterday Bill Gross, managing director of fixed income giant PIMCO, told reporters in a television interview that the Fed "will have to stop (raising rates) shortly" to sustain growth, and will have to start cutting rates after reaching the 3.5% target fed funds rate. While being pessimistic about growth is nothing new to bond traders, his remarks shook the market enough to shake headlines.

His comments paid off: within minutes, the price of Treasuries rose, with the ten-year note up 12/32. Let's do the math. Gross manages $450 billion in assets. Let's pretend that about half of that amount is tied up in long positions of Treasuries. If all that $200 billion in securities went up by the amount that the ten-year did, that's a gain of about $750 million.

Of course, PIMCO's returns are not simply linked to the price of Treasury securities, but I'm assuming they have a net long position. This is also very short term, and not something that can even be capitalized on, but don't think his traders didn't knew what he was going to say in advance.

Thursday, June 09, 2005

Hyper-Rich Hysteria

The Sunday New York Times went front-page last week with the shocking conclusion that the "Richest Are Leaving Even the Rich Far Behind." Looking past the duh-factor inherent in writing about the rich getting richer, David Cay Johnston made some interesting revelations about not just the rich, but the "hyper-rich," those in the top 0.1% and higher:


* Under the Bush tax cuts, the 400 taxpayers with the highest incomes - a minimum of $87 million in 2000, the last year for which the government will release such data - now pay income, Medicare and Social Security taxes amounting to virtually the same percentage of their incomes as people making $50,000 to $75,000.

* Those earning more than $10 million a year now pay a lesser share of their income in these taxes than those making $100,000 to 200,000.

That's right, our so-called progressive tax structure is actually resulting in an arc (because of tax shelters, deduction, etc); effective total income, Social Security, and Medicare taxation is regressive as income rises above $10 million, and virtually flat between $100,000 and $10 million. In fact, the highest taxed group, $1 to $10 million, is taxed at a rate only 1.7% percentage points higher than the $100,000 to $200,000 group, and still only 4.9% higher than those in the $50,000 to $75,000 range.

The main reason for this regressive taxation at the high high end is that many tax cuts have focused on investment returns which favor mostly the wealthy. Also, Johnston mentions but doesn't pursue the fact that "the very wealthiest find ways, legal and illegal, to shelter a lot of income from taxes." Stephanie Strom outlined one common method: the creation of "supporting organizations" which are a loosely regulated type of foundation, often abused as a tax shelter to the "charitable" donor. The key is that these organizations, unlike foundations, don't actually have to spend any of their endowment, but can serve almost as an investment vehicle for the founder.

The idea for Johnston's analysis must have surfaced because we are used to hearing about income statistics for the "top 1%" or even the "top 10%." He convincingly asserts that the top 1% group is by no means homogeneous: the top 0.1% accounts for almost half the income the top 1%! Perhaps even more amazing is that the top 400 households collect 1.1% of the nation's income. This may not sound like a lot, but that means this top 0.0003% is 45 times richer than the top 0.1%, and a whopping 917 times richer than the top 10%! To put that in comparison, the top 10% is a paltry 7 times richer than the bottom 90%.

Johnston explains this huge gap between the rich and hyper-rich has increased dramatically over time:


From 1950 to 1970, for example, for every additional dollar earned by the bottom 90 percent, those in the top 0.01 percent earned an additional $162, according to the Times analysis. From 1990 to 2002, for every extra dollar earned by those in the bottom 90 percent, each taxpayer at the top brought in an extra $18,000.

The ethical questions of income inequality aside, one fact remains: taxing the top income earners at a few percentage points higher would make up the $450 billion shortfall in the federal budget. That's kinda what John Kerry was telling people during the campaign, but somehow the extraordinary resources available at the top were not seen as a popular source of tax revenue.

Slate contributor Mickey Kaus, also the author of The End of Equality, completely misses the purpose of Johnston's article (which seeks to further divide the top 1%), arguing he "doesn't answer the important question...how much richer would they have gotten if they hadn't gotten the tax cuts?" I guess Kaus is more interested in the moral questions of equality, but Johnston does a better job of sticking to reporting. Kaus says Johnston wrongly asserts that "we really could reverse rising income inequality at the top by reversing the Republican tax cuts." Kaus doesn't even seem to care about the more practical question of how much those cuts have contributed to massive deficits.

Friday, May 27, 2005

The Tight Pants Paradox

Now that there exists scientific evidence that parents give preferential treatment to their more attractive children, it has become apparent that further inquiry into the nature and characteristics of human aesthetics is both timely and necessary. In pursuit of this goal, we investigate the tight pants paradox.

Consider a person who wears pants of constant tension t. In order to solve for the perceived attractiveness function, B(.), we must first determine the relevent parameters. We assume there to be a natural beauty constant, h, which scales B(.) independant of clothing variation. Historically, the clothing-dependent factor of B(.) was assumed to be positively correlated with tension t, following the assumption that a person would self-regulate tension in order to match the purveyance of the buttocks and proximal structures with the desires of the agents of observation. These traditional assumptions would lead to the intuitive conclusion that B(h,t)=ht . While perhaps a reasonable approximation 50 or even 10 years ago, evidence suggests that this functional form is lacking an important term.

Assume a constant wardrobe, and consider a person who has optimized its body mass such that its attractiveness has been maximized, i.e. any other body mass would reduce their overall beauty. Now imagine if that person intentionally or otherwise increased its body mass by a small amount. This person is no longer at a global maximum, and thus has decreased in attractiveness, yet, paradoxically, the tension t of the person's pants has increased. We have shown that there must exist another factor, g>0, that negatively affects B(.). Finally,

B(h,t,g)=t(h-g) .