Benford's Law As an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)

This paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here. A statistical theorem referred to as Benford's Law states that in many sets of numerical data, the significant digits are not uniformly distributed, as one might expect, but rather adhere to a certain logarithmic probability function. To detect fraud we derive several requirements that should, according to this law, be fulfilled in the case of survey data. We show that in several SOEP subsamples, Benford's Law holds for the available continuous data. For this analysis, we have developed a measure that reflects the plausibility of the digit distribution in interviewer clusters. We are able to demonstrate that several interviews that were known to have been fabricated and therefore deleted in the original user data set can be detected using this method. Furthermore, in one subsample, we use this method to identify a case of an interviewer falsifying ten interviews who had not been detected previously by the fieldwork organization. In the last section of our paper, we try to explain the deviation from Benford's distribution empirically, and show that several factors can influence the test statistic used. To avoid misinterpretations and false conclusions, it is important to take these factors into account when Benford's Law is applied to survey data.Falsification, data quality, Benford's Law, SOEP

Respondent Behavior in Panel Studies: A Case Study for Income-Nonresponse by Means of the German Socio-Economic Panel (GSOEP)

Many validation studies deal with item-nonresponse and measurement error in earnings data. In this paper we explore motives of respondents for the failure to reveal earnings using the German Socio-Economic Panel (GSOEP). GSOEP collects socio-economic information of private households in the Federal Republic of Germany. We explain the evolution of income-nonresponse in the GSOEP and demonstrate the importance of a discrimination between refusing the income-statement or don't know.Respondent behavior; Interviewer effects; Item-Nonresponse; Panel analysis; Multilevel modeling

Shift Radix Systems - A Survey

Let $d\ge 1$ be an integer and ${\bf r}=(r_0,\dots,r_{d-1}) \in \mathbf{R}^d$. The {\em shift radix system} $\tau_\mathbf{r}: \mathbb{Z}^d \to \mathbb{Z}^d$ is defined by $$\tau_{{\bf r}}({\bf z})=(z_1,\dots,z_{d-1},-\lfloor {\bf r} {\bf z}\rfloor)^t \qquad ({\bf z}=(z_0,\dots,z_{d-1})^t).$$ $\tau_\mathbf{r}$ has the {\em finiteness property} if each ${\bf z} \in \mathbb{Z}^d$ is eventually mapped to ${\bf 0}$ under iterations of $\tau_\mathbf{r}$. In the present survey we summarize results on these nearly linear mappings. We discuss how these mappings are related to well-known numeration systems, to rotations with round-offs, and to a conjecture on periodic expansions w.r.t.\ Salem numbers. Moreover, we review the behavior of the orbits of points under iterations of $\tau_\mathbf{r}$ with special emphasis on ultimately periodic orbits and on the finiteness property. We also describe a geometric theory related to shift radix systems.Comment: 45 pages, 16 figure

Driven quantum transport on the nanoscale

We explore the prospects to control by use of time-dependent fields quantum transport phenomena in nanoscale systems. In particular, we study for driven conductors the electron current and its noise properties. We review recent corresponding theoretical descriptions which are based on Floquet theory. Alternative approaches, as well as various limiting approximation schemes are investigated and compared. The general theory is subsequently applied to different representative nanoscale devices, like the non-adiabatic pumps, molecular gates, molecular quantum ratchets, and molecular transistors. Potential applications range from molecular wires under the influence of strong laser fields to microwave-irradiated quantum dots.Comment: 82 pages, 19 figures, elsart.cls, solved LaTeX/hyperref problem

Enhanced nematic fluctuations near an antiferromagnetic Mott insulator and possible application to high-TcT_{c} cuprates

Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays N\'eel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-$d$ and O-$p$ orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the $p$-orbitals inevitably generate a biquadratic coupling between the spins of the $d$-orbitals. The key point revealed by our classical Monte Carlo simulations and large-$N$ calculations is that the biquadratic term favors local stripe-like magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange $J$. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.Comment: 11 pages, 4 figures; includes Supplemental Material (14 pages, 4 figures

Spin-Orbit Coupling and the Evolution of Transverse Spin

We investigate the evolution of transverse spin in tightly focused circularly polarized beams of light, where spin-orbit coupling causes a local rotation of the polarization ellipses upon propagation through the focal volume. The effect can be explained as a relative Gouy-phase shift between the circularly polarized transverse field and the longitudinal field carrying orbital angular momentum. The corresponding rotation of the electric transverse spin density is observed experimentally by utilizing a recently developed reconstruction scheme, which relies on transverse-spin-dependent directional scattering of a nano-probe.Comment: 4 pages, 2 figure

Sick Pay Provision in Experimental Labor Markets

Sick pay is a common provision in most labor contracts. This paper employs an experimental gift-exchange environment to explore two related questions using both managers and undergraduates as subjects. First, do workers reciprocate sick pay in the same way as they reciprocate wage payments? Second, do firms benefit from offering sick pay? Firms may benefit in two different ways: directly, from workers reciprocating higher sick pay with higher efforts; and indirectly, from self-selection of reciprocal workers into contracts with higher sick pay. Our main finding is that the direct effect is rather weak in terms of effort and negative in terms of profits. However, when there is competition among firms for workers, sick pay can become an important advantage. Consequently, competition leads to a higher provision of sick pay relative to a monopsonistic labor market.sick pay, sick leave, experiment, gift exchange