How to Use Statistics to Seek Out Criminals

The discovery of banks’ efforts to manipulate the London interbank offered rate owes a lot to statistical techniques that provided the first indications of wrongdoing. If regulators want to uncover more misdeeds in the markets, they’ll have to use such tools much more actively than they currently do.

Academics and journalists have become adept at employing statistical screens to shed light on a wide range of questionable or illegal activities in the financial markets. Notable examples include collusion among Nasdaq stock dealers, the backdating of stock options and possible insider trading among corporate executives.

Libor is a case in point. In early 2008, the Wall Street Journal published a study showing that the borrowing-cost estimates banks submitted for the calculation of the benchmark interest rate were bunched much too close together and bore little relation to the banks’ riskiness as reflected in the market for default insurance. Together with co-authors Albert Metz, Michael Kraten and Gim Seow, I extended the analysis to show that nonrandom patterns in the banks’ reported borrowing costs started years earlier than the period examined by the Journal and also likely involved coordinated behavior among banks. The studies pointed to the widespread misbehavior that, four years later, is proving to be one of the biggest and most costly financial scandals in history.

Classic Screens

The Libor studies were classic screens, in that they tested for divergence from normal statistical behavior or from markets thought to be functioning properly. To understand how screens work, consider one popular statistical tool: Benford’s law. The law states that the digits in certain types of data from naturally occurring events follow a consistent pattern. The number 1 is by far the most frequent first digit, followed by 2, 3 and so on all the way to 9. The second significant digit is more evenly distributed, and so is the third digit. Such patterns have been observed in financial data such as stock prices, corporate revenue and interest rates. Libor submissions followed Benford’s law closely for about 20 years, but began to diverge sharply in the mid-2000s.

Statistical analysis, by itself, will not usually prove manipulation or other cheating. Rather, it can signal unusual patterns that may require closer investigation. Beyond flagging strange patterns, screens can potentially indicate which actors were involved and when the cheating began.

U.S. regulatory agencies such as the Securities and Exchange Commission, the Commodity Futures Trading Commission, the Department of Transportation and the Internal Revenue Service routinely use screens to help find a variety of illegal behavior, such as insider trading, tax evasion and accounting shenanigans.

The use of screens has been limited, though, in other areas, particularly in antitrust matters. More frequently than not, regulators rely on passive detection policies, in which they wait for complainants or whistle-blowers to come forward. This approach has a track record of success, and it is undoubtedly less resource-intensive than actively engaging in detection. Unfortunately, it probably misses a lot of fraud. Attempts at Libor-rigging, for example, might never have been uncovered without screens.

If regulators were more proactive in their use of screens, they could be more effective in both the detection and deterrence of fraudulent market behavior. The most successful frauds have the biggest effects on prices or quantities, and hence are the most visible to screens. These are precisely the cases in which whistle-blower programs tend to fail -- after all, a conspirator is less likely to come forward if the conspiracy is working effectively from his perspective. The knowledge that authorities were constantly screening for questionable activity would also have a powerful chilling effect on potential perpetrators.

Regulatory agencies can start by enhancing data collection and analysis, and training their staff to monitor those markets they see as most susceptible to illegal behavior.

There have always been those who are naturally skeptical that simple empirical analyses can be brought to bear in complex markets. Hopefully, the Libor scandal will settle the question of whether screens should be more vigorously applied and move the discussion to how that needs to happen.

(Rosa M. Abrantes-Metz is an adjunct associate professor at New York University’s Stern School of Business and a principal in the antitrust, securities and financial regulation practices of Global Economics Group, a consulting firm based in New York. The opinions expressed are her own.)