Does it matter that low first digits occur more frequently?
First some history.
During the 1920s, Frank Benford, a physicist at GE, noticed that “one” appeared more frequently as the first digit of a number. To test his thesis, he accumulated random lists. He was said to have noted all of the numbers in an issue of Reader’s Digest. He went through demographic and scientific data. Finally he calculated that #1 was the first digit in 31% of the numbers, #2 for 19%, and #9 was the first digit in only 5% of all of his numbers. This brief article about Benford’s conclusions is fascinating.
The current relevance of Benford takes us to Greece. “Undercover Economist” Tim Harford describes it wonderfully. During 2000, just before Greece joined the euro, its deficits deviated considerably from Benford’s Law. As Harford explains, “The criteria were somewhat irksome…but nevertheless the Greeks seemed to comply…Eventually it became clear that the Greek numbers did not quite add up.”
The Economic Lesson
Different from debt which totals all a government owes, the deficit is the amount by which government expenditures exceed revenue during a fiscal year. For Greece, during 2009, the new prime minister said that the deficit appeared to be closer to 12.5% of GDP rather than the previously reported 3.7%.
An Economic Question: How does this Dilbert cartoon relate to Benford’s Law?
The production path of a pair of Levi’s stonewashed 501 jeans could have started in a Mississippi Delta cotton farm, continued with a North Carolina fabric weaver, and included the Dominican Republic and Haiti for cutting, sewing, and finishing. Then, the jeans would have returned to the U.S. to one of countless retail outlets, to a consumer, and maybe even to a recycled life afterwards in some other country.
Commenting on these “production paths” economist Tim Harford says they ultimately lead to economic growth but only if the path is preserved by trust. The trust he refers to is primarily an institutionalized trust. We “trust” that money will have a certain value. We “trust” that a contract will be enforced. We “trust” transactions that involve Visa and American Express. We “trust” that we will receive a package that we order from Amazon.
Correspondingly, in economies where corruption and bribery abound, economic development is constrained. Explaining why Haiti has made little progress rebuilding its main harbor, the Miami Herald points out that the project is “mired in cronyism, waste, scandal, and inertia. They could also have said that there was no institutional trust.
The Economic Lesson
Secretary of the Treasury Alexander Hamilton realized that the sanctity of contracts was essential for U.S. economic development. As a result, when he had to decide who owned Revolutionary War bonds, the benevolent patriots who had sold the bonds at a discount or the ruthless speculators who bought them, he chose the speculators. Why? Government has to enforce a legal contract. A nation has to have “institutional trust.”
Contemporary economists have researched the role of trust in the market system. You might want to look at “Adam Smith’s Essentials: On Trust, Faith, and Free Markets,” and “Trust and Growth“.