How antitrust economists are getting better at spotting cartels
反垄断经济学家如何更灵敏的察觉垄断利益集团
Dec 15th 2012 | from the print edition
2012年12月15日 | 印刷版
THESE are nervy times for price-fixers . Banks that allegedly manipulated LIBOR, an interbank interest rate, are awaiting their punishment. At $800 trillion, the market is the largest ever to have been rigged. Fines to follow that imposed on Barclays in the summer are expected soon for other rate-fixing banks; this week saw the first arrests connected with the LIBOR scandal. Other cartels also have reason to be jumpy . The LIBOR case provides a good example of how competition authorities can use price data to scan markets, quickly spotting even small-scale collusion .
对于价格操纵者来说最近着实令人惶恐不安。那些据称操纵伦敦银行同业拆借利率（London Interbank Offered Rate，简称LIBOR）的银行正等待着监管机构对它们的惩戒。价值800万亿，这是迄今为止被操纵的最大的市场。今夏巴克莱银行受到的了惩罚，紧随其后而来的罚单对其它利率操纵银行来说估计仅有咫尺之遥；本周监管机构逮捕了首批与LIBOR丑闻有关的嫌疑人员。其它垄断利益集【1】亦有理由对此感到心神不宁。LIBOR操纵案为竞争监管当局如何使用价格数据来监察市场提供了一个绝佳的案例，使它们能够迅速地察觉到即便是小范围内的企业串通勾结现象。
One way to identify dodgy prices is to use a splendidly counterintuitive phenomenon known as Benford’s law. In a 1938 paper* Frank Benford, a physicist working for General Electric, pointed out a pattern that occurs in large data sets. Across thousands of metrics, including 3,259 different population distribution s and 741 sources of data on firms’ costs, he found that leading digits (for example, the numbers “3” and “7” in 3,259 and 741, respectively) are not distributed evenly , as you might expect. They follow a pattern: “1” is the most common and “9” the rarest.
一个绝好的反常理现象——本福德定律【2】——可以用来作为一种辨明定价伎俩的法门。通用电气公司（General Electric）的物理学家弗兰克•本福德（Frank Benford）在1938年发表的一篇论文中指出了一种出现在大量数据集的数字规律。在数以万计的数据度量中，其中包括了3,259个不同的人口分布数据和741关于企业成本的数据源，他发现首位数（比如说，数字3,259中的3，741中的7）并非如人们想象的那样呈均匀分布。首位数遵循这样一个规律：数字1出现的频率最高，而数字9最低。
For an example of why this should be, take an imaginary country with a population that doubles every year, starting at 1m people. After a year with “1” as the leading digit, it hits 2m and the leading digit changes to “2”. Fast forward another year and the population is 4m. But this means the leading digits “2” and “3” have both passed by in less than a year, occurring for fewer days than “1”. The pattern continues, with digits “4” to “9” spending progressively less time in the lead position. After a little over three years the country’s population is 10m, so that “1” is the leading digit again, where it stays for another year. And so on.
让我们通过一个例子来阐明原因，假设有一个国家，这个国家的人口总数逐年翻番，以100万为人口总数的起始数据。在第一年中，整年人口总数的首位数字都是1，到了第二年人口总数达到了200万，而首位数变成了数字2。很快到了下一年，人口总数变成了400万。而这意味着人口总数的首位数字2和3都在不到一年的时间里相继跳过，比首位数字从1变成2所花费的时间要短。这一规律继续出现，而数字4至9处在首位的时间依次递减。三年多之后，该国的人口总数变成了1000万，因此数字1又一次成为了首位数，这将会持续又一整年的时间。如此循环往复。
Benford’s law holds across a wide range of measures, including naturally occurring data like populations (see left-hand chart) and economic data like stockmarket returns. Such patterns can be used to test economic data: if numbers have been manipulated to give the appearance of randomness, the distribution of the digits will almost certainly violate Benford’s predictions. Forensic accountants have used the technique since the 1970s; a 2011 article showed that Greek economic data strayed further from Benford distributions than those of any other euro-area country.
本福德定律适用于广泛的数据测度中，包括像人口总数这样自然发生的数据以及像股市回报这类的经济数据。此类规律可以被用来检测经济数据：如果数据被人为地操控而表现出随机分布的模式，那么数字的分布几乎定会有悖于本福德的预测。法务会计从上世纪七十年代就开始使用这项技术了；2011年发表的一篇文章显示：较任何其他欧元区国家而言，希腊的经济数据远远偏出了本福德数字分布规律。
The test also works for LIBOR. In a 2011 paper Rosa Abrantes-Metz of New York University’s Stern School of Business and Sofia Villas-Boas and George Judge of the University of California, Berkeley, examined LIBOR data over rolling six-month windows, and found that LIBOR was far likelier than another benchmark interest rate to depart from Benford patterns. A quick Benford test would have pointed to LIBOR anomalies long before one of the colluding banks chose to own up.
这项检测同样也适用于LIBOR。纽约大学斯特恩商学院（New York University’s Stern School of Business）教授罗莎•阿布兰特什-梅斯（Rosa Abrantes-Metz）以及加州大学伯克利分校（University of California, Berkeley）教授索菲亚•薇拉思-博厄斯（Sofia Villas-Boas）和乔治•嘉杰（George Judge）详加分析了LIBOR在连续6个月的窗口期内的数据，并且发现LIBOR悖离本福德规律的可能性远远高于其他基准利率。远在这些相互勾结的银行中的一家选择坦白其存在不法行为之前，快速本福德测试都应当可以指出LIBOR数据存在的异常现象。
Applying Benford’s law is an example of a “price screen”, a quick test that can help spot markets where pricing patterns are odd and warrant further investigation. Although competition authorities would ideally use detailed information on companies’ prices and costs to identify collusion, since the ability to price far above cost is one measure of market power, information on firms’ costs is hard to come by. Hence the value of tests that can be run quickly, across various markets, using just the data at hand.
应用本福德定律的“价格滤网”机制是一个实例，这是一项快速检测方法可以用来检测市场定价模式反常之处并为进一步调查提供明证。由于定价远高于成本的能力是一项衡量市场实力的标准，虽然最为理想的方式是竞争监管当局使用企业价格和成本的详细信息来辨明相互勾结的不法活动，但是它们却很难获取有关企业成本的信息。因此这种测试的价值在于可以快速地应用于各种类型的市场，且无需额外收集数据。
Take the pattern of prices over time. In a competitive market, theory suggests prices are set close to firms’ costs and track those costs over time. Because costs differ between firms, prices should as well. And since the prices of inputs are volatile over time, firms’ selling prices should vary over time, too. Cartels change things. Prices rise far above costs, so small cost increases can simply be absorbed. Once prices are being set collusively, a cartel may not want to raise them further for fear of being caught. And even if a single cartel member does want to change prices, agreeing this with all the others is time-consuming. Colluders don’t just raise prices; they tend to smooth them, too.
以随时间推移的价格所表现出来的规律为例。在竞争市场中，理论表明商品定价接近企业成本并且具有随时间推移的与成本保持一致的趋势。由于企业间成本各异，那么价格应该也是如此。并且由于企业投入的价格随着时间的推移而起伏不定，企业的售价也应该随着时间的推移而不同。但垄断利益集团改变了这种情况。价格涨幅远高于成本，因此企业完全能够吸收成本小幅度的上升。一旦企业相互勾结起来制定价格，垄断利益集团也许会由于担心被监管机构发觉而不愿意进一步提高价格。而且即便是垄断利益集团中的单一成员意欲改变价格，与所有其它企业就这一点达成协议会耗费大量的时间。相互勾结的企业不仅仅提高价格，它们往往也会平抑价格波动。
In a 2006 paper Ms Abrantes-Metz, Luke Froeb of Vanderbilt University, John Geweke of the University of Iowa and Christopher Taylor of the Federal Trade Commission used the price of fish sold to American military bases in the late 1980s to backtest【3】 the theory. A cartel had stitched up the market for cod, flounder, haddock and perch. When the cartel reigned, the prices of perch were oddly stable. But when providers began to compete, prices dropped by 16% and also became choppier, reflecting fluctuations in wholesale fish prices (see right-hand chart). A new paper on a generic-medicines cartel in Mexico found something similar.
在2006年的一篇论文中，阿布兰特什-梅斯教授、范德堡大学（Vanderbilt University）教授卢克•弗吕博（Luke Froeb）、爱荷华大学（University of Iowa）教授约翰•葛维克（John•Geweke）以及美国联邦贸易委员会（Federal Trade Commission）经济学家克里斯托弗•泰勒（Christopher Taylor ）使用上世纪八十年代末出售给美军基地的鲜鱼价格对该理论进行了回测。当时垄断利益集团垄断操纵了鳕鱼，鲽鱼，黑线鳕鱼和鲈鱼市场。当它们支配市场的时，鲈鱼价格异常的稳定。但是当供应商开始相互竞争的时，价格下跌了16%并且变得起伏不定，这反映出鲜鱼批发价格的波动（见右图）。一篇研究墨西哥非专利药品制造商垄断利益集团的论文中也出现了类似的情形。
Clever watchdogs
灵敏的监管机构
All this suggests that one way to direct scarce antitrust resources is to set up automatic scans of market prices, looking for excess price stability. Watchdogs are already moving in this direction. In Italy a screen applied to pharmacies spotted a problem with baby-food prices. In America bids for stimulus-funded projects are checked for signs of collusion. But like any statistical test, scans for prices that are too stable can give “false positives”, implicating firms whose prices are flat for innocent reasons.
上述一切都表明：可以通过建立市场价格自动检测机制来监控管理稀缺的反垄断资源，即寻找价格过度稳定的情况。监管机构正朝着这个方向发展。在意大利，应用于审查制药厂家的过滤机制发现了婴儿食物定价方面存在的垄断现象。在美国，监管机会检查经济刺激方案支持项目的竞标，寻找企业勾结迹象。但是正如任何统计统计学检验一样，对过于稳定价格的检测可能会产生“误报”，将那些基于合法的理由而维持价格平稳的企业也牵连进来。
The use of mapping data can refine these tests. In a 2012 paper Pim Heijnen and Marco Haan, both of Groningen University, and Adriaan Soetevent of Amsterdam University analysed location and price data for around 3,300 Dutch petrol stations. Their first step was to calculate the distribution of petrol prices and label the most stable as suspicious. The next step was to use location data and maps. If the cause of smooth prices was something innocent (lazy managers, say) then suspect stations should have been randomly scattered across the country. But they weren’t. Stable pricing patterns often appeared in clusters, suggesting local collusion. Using data in this way promises much. The only problem is that as the watchdogs get better at knowing where to look, cartels are bound to improve at disguising their activities.
映射数据的运用能够完善这些测试方法。格罗宁根大学（Groningen University）的皮姆•荷简（Pim Heijnen）和马克•汉（Marco Haan）与阿姆斯特丹大学（Amsterdam University）的阿德里安•苏伊特伊万特（Adriaan •Soetevent）在2012年的一篇论文中分析了荷兰约3,300家加油站的地理位置数据和价格数据。他们首先计算了汽油价格的分布并且将价格最稳定的加油站标注为有操纵定价嫌疑。接下来他们使用了地理数据和地图。如果平抑价格的原因是合法的（比如说，懒惰的经理），那么有嫌疑的加油站应该是随机分布在全国各地。但事实并非如此。稳定的定价模式常常密集地出现，这表明了当地加油站相互串通起来制定油气的价格。以这种方式使用数据的前景极为乐观。但唯一的难题是：监管机构发现问题的“道”高了一尺，可垄断利益集团在掩盖行为方面的“魔”也定会高出一丈。
Source
参考资料
“The Law of Anomalous Numbers”, by Frank Benford, Proceedings of the American Philosophy Society 78, 551-572 (1938)
“A Variance Screen for Collusion”, by Rosa Abrantes-Metz, Luke Froeb, John Geweke, Christopher Taylor, International Journal of Industrial Organisation, Volume 24, Issue 3, May 2006, Pages 467–486
“Tracking the Libor Rate”, by Rosa Abrantes-Metz, Sofia Villas-Boas, and George Judge,Applied Economics Letters (2011)
“Fact and Fiction in EU-Governmental Economic Data”, by Bernhard Rauch, Max Göttsche, Gernot Brähler and Stefan Engel, German Economic Review, Volume 12, Issue 3, pages 243–255
“Screening for Collusion: A Spatial Statistics Approach”, by Pim Heijnen, Marco Haany and Adriaan Soeteventz, Tinbergen Institute Discussion Papers (2012)
"Mexican Experience in Screens for Bid-Rigging", Carlos Mena-Labarthe, CPI Antitrust Chronicle (2012)
Economist.com/blogs/freeexchange
from the print edition | Finance and economics
印刷版 | 财经版块
A cartel is a formal agreement among competing firms. It's a formal organization where there is a small number of sellers and usually involve homogeneous products. Cartel members may agree on such matters as price fixing, total industry output, market shares, allocation of customers, allocation of territories, bid rigging, establishment of common sales agencies, and the division of profits or combination of these. The aim of such collusion (also called the cartel agreement) is to increase individual members' profits by reducing competition.
One can distinguish private cartels from public cartels. In the public cartel a government is involved to enforce the cartel agreement, and the government's sovereignty shields such cartels from legal actions. Inversely, private cartels are subject to legal liability under the antitrust laws now found in nearly every nation of the world. Furthermore, the purpose of private cartels is to benefit only those individuals who constitute it, public cartels, in theory, work to pass on benefits to the populace as a whole.
Competition laws often forbid private cartels. Identifying and breaking up cartels is an important part of the competition policy in most countries, although proving the existence of a cartel is rarely easy, as firms are usually not so careless as to put collusion agreements on paper.
Several economic studies and legal decisions of antitrust authorities have found that the median price increase achieved by cartels in the last 200 years is around 25%. Private international cartels (those with participants from two or more nations) had an average price increase of 28%, whereas domestic cartels averaged 18%. Fewer than 10% of all cartels in the sample failed to raise market prices.
Benford's law, also called the first-digit law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, the number 1 occurs as the first digit about 30% of the time, while larger numbers occur in that position less frequently, with larger numbers occurring less often: 9 as the first digit less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on a logarithmic scale. Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.
The graph to the right shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization to second digits and later digits.
It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881.
【3】Backtest
A system used to test a trading strategy in which a specially designed computer program is used to examine the success of a series of hypothetical trades after the fact. Backtesting programs apply user-defined entry and exit criteria to historical data and execute simulated trades from which detailed profit and loss statistics are generated.
more: http://en.wikipedia.org/wiki/Backtest
