Does Benford's law hold in economic research and forecasting?

First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in many business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of leading digits of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content. --Benford's Law,fraud detection,regression coefficients and standard errors,growth and inflation forecasts

DETECTING EVIDENCE OF NON-COMPLIANCE IN SELF-REPORTED POLLUTION EMISSIONS DATA: AN APPLICATION OF BENFORD'S LAW

The paper introduces Digital Frequency Analysis (DFA) based on Benford's Law as a new technique for detecting non-compliance in self-reported pollution emissions data. Public accounting firms are currently adopting DFA to detect fraud in financial data. We argue that DFA can be employed by environmental regulators to detect fraud in self-reported pollution emissions data. The theory of Benford's Law is reviewed, and statistical justifications for its potentially widespread applicability are presented. Several common DFA tests are described and applied to North Carolina air pollution emissions data in an empirical example.Benford, digital frequency analysis, pollution monitoring, pollution regulation, enforcement, Environmental Economics and Policy, Q25, Q28,

Water Quality Reporting Limits, Method Detection Limits, and Censored Values: What Does It All Mean?

The Arkansas Water Resources Center (AWRC) maintains a fee-based water-quality lab that is certified by the Arkansas Department of Environmental Quality (ADEQ). The AWRC Water Quality Lab analyzes water samples for a variety of constituents, using standard methods for the analysis of water samples (APHA 2012). The lab generates a report on the analysis, which is provided to clientele, and reports the concentrations or values as measured. Often times the concentrations or values might be very small, even zero as reported by the lab – what does this mean? How should we use this information? This document is intended to help our clientele understand the analytical report, the values, and how one might interpret information near the lower analytical limits. Every client wants the analysis of their water sample(s) to be accurate and precise, but what do we really mean when we say those two words? These words are often used synonymously or thought of as being the same, but the two words mean two different things. Both are equally important when analyzing water samples for constituent concentrations

Visualizing Magnitude: Graphical Number Representations Help Users Detect Large Number Entry Errors

Nurses frequently have to program infusion pumps to deliver a prescribed quantity of drug over time. Occasional errors are made in the performance of this routine number entry task, resulting in patients receiving the incorrect dose of a drug. While many of these number entry errors are inconsequential, others are not; infusing 100 ml of a drug instead of 10 ml can be fatal. This paper investigates whether a supplementary graphical number representation, depicting the magnitude of a number, can help people detect number entry errors. An experiment was conducted in which 48 participants had to enter numbers from a ‘prescription sheet’ to a computer interface using a keyboard. The graphical representation was supplementary and was shown both on the ‘prescription sheet’ and the device interface. Results show that while overall more errors were made when the graphical representation was visible, the graphical representation helped participants to detect larger number entry errors (i.e., those that were out by at least an order of magnitude). This work suggests that a graphical number entry system that visualizes magnitude of number can help people detect serious number entry errors

Detecting Simultaneous Integer Relations for Several Real Vectors

An algorithm which either finds an nonzero integer vector ${\mathbf m}$ for given $t$ real $n$-dimensional vectors ${\mathbf x}_1,...,{\mathbf x}_t$ such that ${\mathbf x}_i^T{\mathbf m}=0$ or proves that no such integer vector with norm less than a given bound exists is presented in this paper. The cost of the algorithm is at most ${\mathcal O}(n^4 + n^3 \log \lambda(X))$ exact arithmetic operations in dimension $n$ and the least Euclidean norm $\lambda(X)$ of such integer vectors. It matches the best complexity upper bound known for this problem. Experimental data show that the algorithm is better than an already existing algorithm in the literature. In application, the algorithm is used to get a complete method for finding the minimal polynomial of an unknown complex algebraic number from its approximation, which runs even faster than the corresponding \emph{Maple} built-in function.Comment: 10 page

Finite-state Markov Chains obey Benford's Law

A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with probability transition matrix P and limiting matrix P* is Benford if every component of both sequences of matrices (P^n - P*) and (P^{n+1}-P^n) is Benford or eventually zero. Using recent tools that established Benford behavior both for Newton's method and for finite-dimensional linear maps, via the classical theories of uniform distribution modulo 1 and Perron-Frobenius, this paper derives a simple sufficient condition (nonresonant) guaranteeing that P, or the Markov chain associated with it, is Benford. This result in turn is used to show that almost all Markov chains are Benford, in the sense that if the transition probabilities are chosen independently and continuously, then the resulting Markov chain is Benford with probability one. Concrete examples illustrate the various cases that arise, and the theory is complemented with several simulations and potential applications.Comment: 31 pages, no figure