The EU can use a mathematical law as an early warning system for manipulated macroeconomic data, writes Hans Christian Müller in a guest post for “Economics Intelligence”.
If we had known what we know today, Greece would not have been able to enter the Euro area. The macroeconomic data the country reported to Eurostat in Luxembourg were heavily tweaked. Unfortunately, however, this only became clear years after it was too late.
An early warning system could have avoided such a rude awakening – and, astonishingly, it could be set up rather easily. A simple mathematical law delivers circumstantial evidence about data manipulation, as four German economists show in a paper entitled “Fact and Fiction in EU-Governmental Economic Data” that is forthcoming in the “German Economic Review”.
Gernot Brähler (University of Ilmenau), Stefan Engel (University of Eichstätt-Ingolstadt), Max Goettsche and Bernhard Rauch (both: University of Regensburg) apply a rule that is known as “Benford’s Law” among statisticians.
To the statistical layman, this rule appears weird at first glance, but it is mathematically proven. If you want to spot manipulated data, you just have to count how often numbers in a dataset start with a 1 or a 2. Intuitively, one would suspect that all digits from 0 to 9 should be evenly distributed.
However, in reality this is not the case. In sufficiently large datasets the first digit of a number on average is much more often a 1 or a 2 than a 8 or 9. While about 30 percent start with a 1, the frequency decreases the higher the digit. The 9, for instance, occurs in the first place only in less than five percent of the cases.
This law applies to a variety of data, as the US-physicist Frank Benford showed back in 1938: From Baseball results to the lengths of rivers to street numbers from the phonebook – and to macroeconomic data, as recent evidence reveals. According to statisticians, it is almost impossible to manipulate data in a way that a certain outcome is guaranteed and Benford’s Law is met at the same time. Hence, tax authorities in several countries are using Benford’s Law as a default testing device.
In 2009, Karl-Heinz Tödter, a researcher with Bundesbank, suggested that scientific referees could check the coefficient tables within empirical economic studies with this method. This prompted a vivid debate among German economists.
The authors of the forthcoming paper analysed official statistics of the EU member states from the last eleven years by counting the first digits.They looked at 130 different values per country and year. Among other things, they looked at the total level of debt, the cash reserves of the government and the pensions of retired civil servants.
The result is straightforward. Judged by Benford’s Law, Greece produces the dodgiest data. The distribution of the digits differ the most from the Benford distribution. This is a strong indication of creative accounting by the Greek government.
The authors interpret this result carefully and stress that nobody should jump to conclusions:
“In summary, deviation from Benford’s law is only an indicator of manipulation.”
As with every statistical result, the outcome could be pure chance. Nevertheless, the method is well suited as a first routine test for detecting poor data. Asserts Bernhard Rauch:
“The results provide a clear order in which the country data you should then be investigated further.”
There are several signs indicating that the results are not just coincidental. For example, statistics from the Czech Republic, Sweden and the UK meet the Benford distribution particularly close and hence appear unsuspicious. All those countries have no interest in joining the Euro and therefore do not have to meet the convergence criteria. On the other hand, statistics from Latvia, Belgium and Romania (the latter notorious for its corruption) appear very suspicious, as well.
After the Euro zone debt crisis broke out, Brussels expanded Eurostat’s responsibilities. Europe’s statistical office does not have to trust the numbers they receive from the individual member states. Nowadays, Eurostat’s staff is also allowed to visit the national agencies and to inspect all interesting files. However, this is a very tedious and resource consuming effort and Eurostat has only limited manpower. While its tasks were upscaled, its workforce was not.
Benford’s Law could raise a flag with regards to potential manipulation and could guide the supervisory effort. For example, the Benford test shows that in the year of 2000 the Greek statistics were particularly shady. One year later Greece finally joined the Euro area.
Note: This is a guest post written by Hans Christian Müller.