Estimation of location of discontinuity in a density

Here we propose a few estimators of θ, in addition to those studied in Goria (1978), the point of discontinuity of the probability density $$f(x,\theta ) = \frac{1}{{2\Gamma (\alpha )}}e^{ - |x - \theta |} |x - \theta |^{\alpha - 1} ,$$ for $$0< \alpha< 1, - \infty< x< \infty , - \infty< \theta< \infty .$$ We establish the consistency and the optimality of the Bayes and the maximum probability estimators. Despite their nice properties, these estimators are not easy to compute in this case and their effective computation depends on the knowledge of the exponent α. Hence, we propose another class of estimators, dependent upon the spacings of the observations, computable without actual knowledge of the value of α as long as it is known that α < α₀ < 1: we show that these estimators converge at the best possible rate. We further demonstrate, using a modified version of the maximum probability estimator's technique, that the tails of the density do not substantially effect their efficiency. Finally a bivariate family of densities, having a ridge dependent on the parameter θ, is considered and it is shown that this family exhibits features similar to the univariate case, and thus, the necessary modifications of the arguments of the univariate case are utilized for the estimation of θ in this bivariate example.     

Computerization and Structural Change

I develop three measures of structural change on the basis of U.S. data: changes in occupational composition, changes in input–output technical coefficients, and changes in capital coefficients. Using pooled cross-section, time-series data for 44 industries over the period from 1970 to 1990, I find that computer investment per worker has had a positive and significant effect on the degree of occupational change and changes in input and capital coefficients.     

Symposium on Social Capital: Introduction

This symposium contains three papers that discuss aspects of social capital. Social capital has become a major focus of research in many social sciences. Its increased prominence in economics reflects a general increase in interest in questions that have traditionally been deemed sociological. Regardless of one's opinion of social capital per se , this broadening of questions addressed within economics has been very salutary.     

Analysis and Forecast of the State of Environmental Protection in Russia

The main purpose of the present study is to analyse the emission dynamics of atmospheric and water pollutants in Russia and cost of their removal in the 1980s and early 1990s, and to forecast them by means of a Dynamic Input–Output Model according to different scenarios of future economic development till 1998. Main results of the work are:– methodological principles have been elaborated for singling out the environmental protection sector within the national economy;– a method has been offered for including the ecological block into a Dynamic Input–Output Model of the Russian economy;– a method of data preparation has been elaborated for the ecological block of the above-named model, the data base which characterizes the ecological situation in Russia has been formed and analysed;– calculations for 1994–1998 have been executed for forecasting the economic and ecological development of Russia using the above-mentioned model and the results obtained have been analysed. The results showed that if the existing tendencies towards low environmental protection capital costs remain the same, then the negative environmental impact will increase. In order to implement ecological programs and international agreements, to increase the proportion of removed pollutants, it is necessary to increase substantially expenditures on purifying water and air resources. The proportion of environmental protection investments in the total amount of the national economy capital costs should increase by up to 12–40% according to different scenarios of the economic development and different purposes of the environmental protection policy.     

Problem-solving in teaching/learning packages for Technology

In the project Technology in Secondary Education: Problem-solving in Teaching/learning Packages, two experiments regarding a construction problem and an explanation problem were conducted, in which two variants of a teching/learning package (strongly structuredvs. weakly structured) were compared. Only with the strongly structured instructional variant of the package for the explanation problem did the pupils come to a quick solution of the problem. In both experiments, the factors that influenced the problem-solving processes of the pupils were investigated. The results are of importance for curriculum developers and the authors of teaching/learning packages for Technology but further research into the factors influencing the problem solving process of pupils is necessary.