Overview of current population trends in the Federal Republic of Germany and prospects for the future

Current population trends in the Federal Republic of Germany are first reviewed. Topics discussed include demographic aging, ethnic composition, declining fertility, and households. Population projections to the year 2030 are then presented by age group using several different models. Finally, the economic and social policy consequences of long-term population trends are examined, with particular reference to the economically active population and the dependency burden.     

Interpolation,Glättung und Saisonbereinigung von Zeitreihen mit Splinefunktionen

This contribution explains the smoothing method with cubic splines with special regard to the problems of approximation for data points at the historical beginning and the actual end of time series. Seasonal adjustment using spline approximation will be shown. Numerical calculation and the discussion of the assumptions about stochastic disturbances require to distinguish between the spline approximation of data points for economic stock and flow variables. A numerical example for application will be presented for a monthly time series for car purchases in the Federal Republic of Germany. Finally, some properties of the smoothing method with splines in relation to a filter design will be discussed.     

Measurement of disparity from grouped data with different degrees of information

When computing the disparity of a metric variable we frequently have to deal with grouped data. It has been generally assumed that the sums of the values in each class are given. Dropping this assumption we usually resort to working with the class mark as the representative value in each class. This paper presents three approaches to the computation of the bounds of the Gini index from grouped data with incomplete information of different degree. Numerical results based on income distributions of the Federal Republic of Germany demonstrate the effects of different degrees of information on a frequency distribution and, consequently, the problems associated with comparing the disparity of various frequency distributions.     

Up-to-dateness and accuracy of sampling statistics of the population and of the economically active population

The up-to-dateness and accuracy of the population and labor force statistics derived from the micro-census in the Federal Republic of Germany are assessed. The goals, development, and content of micro-censuses carried out between 1957 and 1982 are first reviewed. The next section deals with problems of up-to-dateness, including the speed with which results are produced and their thematic relevance. The remaining sections focus on problems of accuracy, with attention to the sampling plan, random errors, and systematic errors.     

The demographic transformation--a challenge to labor market and social policies

The implications of future demographic trends for labor market and social policies in the Federal Republic of Germany are discussed. The focus is on how trends such as demographic aging and declining fertility will affect the labor market, employment, and old-age security.     

Stochastic population models for the analysis of the effects of demographic processes on social security systems

The aim of this paper is to describe several methods for quantifying the amount of uncertainty inherent in population forecasts used to assess the impact of demographic processes on social security systems. Each method is briefly outlined, and its advantages and disadvantages are discussed. The primary emphasis is on stochastic population models, and the geographic focus is on the Federal Republic of Germany.     

Hierarchical clustering and matrix completion for the reconstruction of world input–output tables

Multi-regional input–output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (parts of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and matrix completion with a LASSO-like nuclear norm penalty, to predict missing entries of a partially unknown I/O matrix. Through analyses based on both real-world and synthetic I/O matrices, we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input–Output Database (WIOD) tables—which are an example of industry-by-industry I/O tables—is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.

     

The future of old-age security in the Federal Republic of Germany

The future aspects of old age security in the Federal Republic of Germany are considered primarily according to the criteria of demographic changes to be expected or presumed. The starting point of our simulations is a strongly declining birth rate which effects a drop in the population growth as well as different criteria concerning the age structure. It is shown that, apart from the demographic structure, the economic development is of decisive importance for old age security. By a model variant obtained by a broad spectrum of simulations, it is shown that an increase in the standard of living affecting all population groups (including pensioners) can be attained provided that the manpower potential is well utilized and the labor productivity is progressing satisfactorily. However, by no means can problems concerning strategies of distribution that are likely to appear be solved by a complete denial of the financing procedure by persons currently employed. The social security of the older persons who no longer are gainfully employed can be financed by the current national product. (author's)     

Some remarks on the duality of continuous time markov chains

A simple proof of Siegmund's result on the relation between dual q-matrices and dual transition functions for Markov chains is given. A byproduct is a uniqueness result for minimal solutions of stochastically monotone q-matrices.     

Private households according to socioeconomic classification in national accounting: the model of the Federal Statistical Office

The author notes that "for calculating income distribution and expenditure by groups of households, annual averages are required concerning the number of private households by household groups and...the structure of the household members in a socio-economic classification." Problems of adjusting such household data so that they are compatible with data from other sources such as employment statistics are discussed, and a procedure for adjusting annual micro-census data on households in the Federal Republic of Germany is described. "Results for the year 1982 are presented, showing the main development trends as compared with the year 1972. Finally, the quality of forecasting with the adjustment procedure is studied." (summary in ENG)     

Effects of future population trends on the labor market--analyses based on projections prepared by the Institute for Research on the Labor Market and Occupations

The effects of future population trends, such as demographic aging, declining fertility, and changes in migration, on the labor market in the Federal Republic of Germany are analyzed up to the year 2000. The study is based on projections prepared by the Institute for Research on the Labor Market and Occupations. Topics discussed include demographic trends as a cause of current unemployment, labor market phases and demographic trends since 1950, the projection model used, age-specific projections of the potential labor force, and labor market projections.     

Performance evaluation of likelihood-ratio tests for assessing similarity of the covariance matrices of two multivariate normal populations

Abstract

In analyzing two multivariate normal data sets, the assumption about equality of covariance matrices is usually used as a default for doing subsequence inferences. If this equality doesn’t hold, later inferences will be more complex and usually approximate. If one detects some identical components between two decomposed non equal covariance matrices and uses this extra information, one expects that subsequence inferences can be more accurately performed. For this purpose, in this article we consider some statistical tests about the equality of components of decomposed covariance matrices of two multivariate normal populations. Our emphasis is on the spectral decomposition of these matrices. Hypotheses about the equalities of sizes, shapes, and set of directions as components of these two covariance matrices are tested by the likelihood ratio test (LRT). Some simulation studies are carried out to investigate the accuracy and power of the LRT. Finally, analyses of two real data sets are illustrated.     

The regression dilemma

A substantial fraction of the statistical analyses and in particular statistical computing is done under the heading of multiple linear regression. That is the fitting of equations to multivariate data using the least squares technique for estimating parameters The optimality properties of these estimates are described in an ideal setting which is not often realized in practice.

Frequently, we do not have "good" data in the sense that the errors are non-normal or the variance is non-homogeneous. The data may contain outliers or extremes which are not easily detectable but variables in the proper functional, and we. may have the linearity

Prior to the mid-sixties regression programs provided just the basic least squares computations plus possibly a step-wise algorithm for variable selection. The increased interest in regression prompted by dramatic improvements in computers has led to a vast amount of literatur describing alternatives to least squares improved variable selection methods and extensive diagnostic procedures

The purpose of this paper is to summarize and illustrate some of these recent developments. In particular we shall review some of the potential problems with regression data discuss the statistics and techniques used to detect these problems and consider some of the proposed solutions. An example is presented to illustrate the effectiveness of these diagnostic methods in revealing such problems and the potential consequences of employing the proposed methods.     

The A-optimal non-saturated weighing designs for n = 15 observations

The problem of constructing A-optimal weighing and first order fractional factorial designs for n ≡ 3 mod 4 observations is considered. The non-existence of the weighing design matrices for n = 15 observations and k = 13, 14 factors, for which the corresponding information matrices have inverses with minimum trace, is proved. These designs are the first non-saturated cases (k < n) in which the unattainability of Sathe and Shenoy's (1989) lower bound on A-optimality is shown. Using an algorithm proposed in Farmakis (1991) we construct 15 × k (+1, −1)-matrices for k = 13, 14 and we prove their A-optimality using the improved (higher) lower bounds on A-optimality established by Chadjiconstantinidis and Kounias (1994). Also the A-optimal designs for n = 15, k ⩽ 12 are given.     

Generating Correlation Matrices With Specified Eigenvalues Using the Method of Alternating Projections

ABSTRACT

This article describes a new algorithm for generating correlation matrices with specified eigenvalues. The algorithm uses the method of alternating projections (MAP) that was first described by Neumann. The MAP algorithm for generating correlation matrices is both easy to understand and to program in higher-level computer languages, making this method accessible to applied researchers with no formal training in advanced mathematics. Simulations indicate that the new algorithm has excellent convergence properties. Correlation matrices with specified eigenvalues can be profitably used in Monte Carlo research in statistics, psychometrics, computer science, and related disciplines. To encourage such use, R code (R Core Team) for implementing the algorithm is provided in the supplementary material.     

Güterverteilungsmatrizen und ihre Bewertung

The distribution of personal income comprises information about the distribution of possible but not actual provisions of households or individuals with goods and services. Value judgements about the actual provisions with goods and services, therefore, should not be confounded on the distribution of personal income. In this paper we are discussing matrices for the distribution with goods and services with m columns (goods and services) and n rows (individuals or households). We distinguish between matrices with columns adding up to personal income and matrices with columns which do not add up to something meaningful. We also analyse problems which arise when either some columns are meant to desire special attention (‘specific egalitarianism’) or when some rows are seperated for special treatment (measurement of relative poverty). Finally, we concentrate on problems of comparing two such matrices. Methodological means are Lorenz-Curves, Concentration-Curves, Gini Coefficients with decompositions and reasonable generalisations thereof.     

Estimating the Nitrous Oxide Emission Rate from the Soil Surface by Means of a Diffusion Model

Soil cover methods are probably the most widely used methods for measuring the nitrous oxide emission rate from the soil surface. The methodology involves estimation of the emission rate from repeated measurements of the nitrous oxide concentration beneath a soil cover. Based on a deterministic model proposed by Hutchinson & Mosier (1981) we propose to use a diffusion process as a stochastic model for the evolution of the nitrous oxide concentrations beneath a soil cover. From this model we derive methods for statistical inference about the emission rate that significantly extend the method proposed by Hutchinson & Mosier (1981). In particular, the derived methods provide solutions to important problems with the method proposed by Hutchinson & Mosier (1981).     

The Equivalence of Neyman Optimum Allocation for Sampling and Equal Proportions for Apportioning the U.S. House of Representatives

We present a surprising though obvious result that seems to have been unnoticed until now. In particular, we demonstrate the equivalence of two well-known problems—the optimal allocation of the fixed overall sample size n among L strata under stratified random sampling and the optimal allocation of the H = 435 seats among the 50 states for apportionment of the U.S. House of Representatives following each decennial census. In spite of the strong similarity manifest in the statements of the two problems, they have not been linked and they have well-known but different solutions; one solution is not explicitly exact (Neyman allocation), and the other (equal proportions) is exact. We give explicit exact solutions for both and note that the solutions are equivalent. In fact, we conclude by showing that both problems are special cases of a general problem. The result is significant for stratified random sampling in that it explicitly shows how to minimize sampling error when estimating a total T_Y while keeping the final overall sample size fixed at n; this is usually not the case in practice with Neyman allocation where the resulting final overall sample size might be near n + L after rounding. An example reveals that controlled rounding with Neyman allocation does not always lead to the optimum allocation, that is, an allocation that minimizes variance.     

Implementation of ridge analysis on quadratic response surfaces

A computer program that performs ridge analysis on quadratic response surfaces is presented in this paper, the primary goal of which is to seek the estimated optimum operating conditions inside a spherical region of experimentation during the stage of process optimization. The computational algorithm is developed based upon the trust-region methods in nonlinear optimization and guarantees the resulting operating conditions to be globally optimal without any priori assumption on the structure of response functions. Under a particular condition termed the "hard case" arising from the trust region literature, the conventional ridge analysis procedure fails to provide a set of acceptable optimum operating settings, yet the proposed algorithm has the capability of locating a pair of non-unique global solutions achieved on an identical estimated response value. Two illustrative examples taken from the response surface methodology (RSM) literature are given to demonstrate the effectiveness and efficiency of the method addressed in the paper.     

On construction of exact experimental designs from discrete ones

In the paper we try to evaluate approximately optimum exact designs of required goodness from a known approximately optimum discrete design. In dependence on this discrete design we define some subsets of the set of all considered exact designs.

Then we look for sufficiency conditions, on which elements of these subsets are approximately optimum (exact) designs of the required goodness. Moreover we offer a method to find such elements, if they exist at all. Finally we prove some statements concerning the existence of such elements for two classes of (optimum) criteria.