Hans-Werner Holub

A general qualitative technique for the comparison of economic structures

Quantitative methods normally do not fully exhaust nor sufficiently show the structural information contained in sets of data. Therefore the authors introduce a new general technique for analyzing structures which is based on qualitative methods. The proposed technique can be divided into several steps. First, the given structural information is prepared with the help of graph theoretical tools. Then the obtained results are condensed in several steps to manageable vectors (key values), the most important step being the construction of graph theoretical decay patterns. These strongly condensed data allow the use of statistical methods and offer the chance to compare even a large number of structures simultaneously. After having introduced the necessary theoretical tools, the authors then present the results of some empirical investigations which showed the usefulness of the proposed technique. Compared with the corresponding quantitative methods, the empirical investigations also showed that our technique is relatively robust with respect to short-comings in the primary material. This result opens up opportunities for obtaining more actual yet costsaving structural information.

Statistical aspects of multilayer perceptrons under data limitations

Based on three case studies, the impact of sample size and sample randomness on the predictive accuracy of multilayer perceptrons (MLP) is investigated. The MLP prove to be useful for classification problems. Although they are dependent on the sample size and the non-linearity of the underlying problem, they achieve predictions superior to the classical methods. A so-called saturation curve describes the dependency of the network performance on the sample size. This function enables the user to evaluate the achieved network performance and the usefulness of additional data. For reliable and generalizable results, the calculation of prediction intervals for the network is essential. It is demonstrated that the network leads to narrower confidence intervals of the performance measures in comparison to classical methods even for small sample sizes. The experiments show the validity of the law, for even relatively small sample sizes, that the standard error of the hit ratio decreases by one over the square root of the sample size. Therefore, the suggestion is to estimate the standard error for a given sample size by randomly drawing smaller sample sizes, and then rescaling the standard error accordingly.

An Extension of Input–Output Employment Models

The usual input–output models of the labour market include some weaknesses which restrict their use with regard to analyses of concrete employment problems. The most important of these weaknesses are: (1) the assumption of an absolutely homogeneous labour force; (2) sectoral final demand is the only starting point for economic policy making; (3) if several types of labour are included, a non-substitutability between these types of labour is assumed; (4) there exists a one-sided direction of analysis from the economic policy parameters to the employment variables. In this article we propose some classes of models which try to overcome the above cited weaknesses. Furthermore these models allow us to take into account different useful economic constraints. To show the applicability of our models at the end of the article some empirical results for a small region are introduced.