Martin Rosemann

Post-Randomization Under Test: Estimation of the Probit Model

Summary The paper analyzes effects of randomized response with respect to some binary dependent variable on the estimation of the probit model. This approach is used in interviews when asking sensitive questions or if a respondent erroneously chooses the wrong category in an interview leading to ‘misdassification’. Alternatively, randomization can be used for statistical disclosure control and then is called ‘post randomization method’ (PRAM). We consider two variants which are termed ‘ordinary’ and ‘invariant’ PRAM the latter being of importance mainly in descriptive analysis. Maximum likelihood estimation of the corrected likelihood results in consistent estimates although variances increase considerably for ‘strong’ randomization. Moreover a finite sample bias has been observed in the simulation study, but it is much less pronounced than the bias implied from use of the ‘naive’ probit estimator when the binary dependent variable has been randomized. Effects of randomization on the probit estimates are also illustrated by an empirical study using cross-section data from the German ‘ΑΒ establishment panel’ (IAB Betriebspanel). The decision of firms to accept a collective bargaining agreement (‘Tarifvertrag’) is analyzed in a binary probit model using both original data and data masked by ordinary and invariant PRAM. Here, too, a remarkable bias is observed in case of ‘strong’ randomization.

Multiplicative Measurement Error and the Simulation Extrapolation Method

Whereas the literature on additive measurement error has known a considerable treatment, less work has been done for multiplicative noise. In this paper we concentrate on multiplicative measurement error in the covariates, which contrary to additive error not only modi es proportionally the original value, but also conserves the structural zeros. This paper compares three variants to specify the multiplicative measurement error model in the simulation step of the Simulation-Extrapolation (SIMEX) method originally proposed by Cook and Stefanski (1994): i) as an additive one without using a logarithmic transformation, ii) as the well-known logarithmic transformation of the multiplicative error model, and iii) as an approach using the multiplicative measurement error model as such. The aim of the paper is to analyze how well these three approaches reduce the bias caused by the multiplicative measurement error. We apply three variants to the case of data masking by multiplicative measurement error, in order to obtain parameter estimates of the true data generating process. We produce Monte Carlo evidence on how the reduction of data quality can be minimized.

Messung von Ausmaß, Intensität und Konzentration des Einkommens-und Vermögensreichtums in Deutschland (Measuring the Extent, Intensity and Concentration at the Upper Edge of the Income and Wealth Distribution in Germany)

German abstract: In diesem Beitrag wird der obere Rand der Einkommens-und Vermogensverteilung in Deutschland mit Daten des Sozio‐oekonomischen Panels (SOEP) analysiert. In Anlehnung an das von Sen (1976) fur die Armutsmessung vorgeschlagene Vorgehen werden zunachst unterschiedliche Schwellenwerte definiert, oberhalb derer eine Person zum reichen Teil der Gesellschaft gehort. Anschliesend wird untersucht, wie viele Menschen uber diesen Schwellen liegen (Ausmas), uber wie viel Einkommen oder Vermogen diese im Durchschnitt verfugen (Intensitat) und wie diese finanziellen Mittel zwischen den reichen Personen verteilt sind (Konzentration). Eine simultane Analyse von Ausmas, Intensitat und Konzentration ermoglicht ein breites Verstandnis des oberen Rands der Einkommens- und Vermogensverteilung sowie dessen Dynamik. Zum Beispiel ergeben die Untersuchungen, dass im Vergleich zum Durchschnitt in Deutschland Beamte sowohl beim Einkommen als auch beim Vermogen ein hohes Ausmas, aber eine geringe Intensitat aufweisen. Zudem sind ihre finanziellen Ressourcen weniger konzentriert als im deutschen Durchschnitt.English Abstract: In this paper we analyze the upper edge of income and wealth distribution in Germany with data from the German Socio-Economic Panel (SOEP). According to Sens (1976) recommendation for the poverty measurement, we first define different thresholds above which a person belongs to the rich part of society. Then we examine how many people are above these thresholds (extent), how much income or wealth they have on average (intensity), and how these financial resources are distributed among the rich persons (concentration). Analyzing extent, intensity and concentration simultaneously gives a broader understanding of the dynamics of the upper edge of income and wealth distribution. For example, we find that in comparison to the average in Germany, civil servants are more often above the defined thresholds but receive on average less income and own less wealth. In addition, their financial resources are less concentrated then the German average.