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.     

Institutionalism versus Orthodoxy

A bstract . Orthodox economics has been quite effective in exploiting equilibrium methodology; equilibrium as a heuristic device, as a theoretical norm, and as a prototype of the scientific method. Also, orthodoxy has contrived the dichotomy of equilibrium-anti-equilibrium to depict institutional thought as being muddled and unscientific. Institutionalists have not successfully countered these attacks, nor have they adequately articulated a comprehensive methodological alternative to orthodoxy. Institutionalists have paid too much attention to the methodological components of institutionalism and have neglected the articulation of a guiding, overall methodology. It is proposed that institutionalists recast the methodological debate by expanding the arena from equilibrium-anti-equilibrium analysis to the broader context of closed versus open systems analysis. This would both help expose the methodological weaknesses of orthodox economics, and demonstrate the relevance and power of institutionalism for socioeconomic investigation.     

EFFECT OF GROUPING OF DATA ON THE DIVERGENCE BETWEEN LASPEYRES AND PAASCHE FORMS OF QUANTUM INDEXES*

Historical data for the manufacturing industry in the United States and United Kingdom are quoted, showing in most cases divergences between Laspeyres and Paasche forms of the quantum index that are by no means negligible. When the Paasche index for two of the series is recalculated with quantity indicators for industries instead of for products, the divergence is greatly reduced, and when quantity indicators for industry groups are substituted it almost disappears. This raises some questions about the practices of econometricians and statisticians, which are discussed. In a mathematical appendix by E. R. Coleman it is suggested that the grouping effect referred to does not depend on the particular way in which the data are grouped in most quantum indexes.     

Method in Experiment: Rhetoric and Reality

The methodological ideal of experimentalists, E, is easily stated: derive a testable hypothesis, H, from a well-specified theory, T; implement experiments with a design; implicitly in the latter are auxiliary hypotheses, A, that surface in the review/discussion of completed research reports (payoffs are 'adequate,' Ss are 'relevant,' instructions, context are 'clear,' etc.). We want to be able to conclude, if statistical test outcomes support not-H, that T is 'falsified.' But this is not what we do; rather we ask if there is a flaw in the test, i.e. not-A is supported, and we do more experiments. This is good practice—much better than the statistical rhetoric of falsificationism. Undesigned social processes allow E to accumulate technical and instrumental knowledge that drive the reduction of experimental error and constitute a more coherent methodology than falsificationism.     

Labour Market Structure and Inequality: A Comparison of Italy and the U.S.

Markets with rigid labour regulations and centralized wage setting are often thought to be inefficient but egalitarian. Using a model of off-and on-the-job search and event-history, individual-level data for Italy and the U.S., we show that while the cross-sectional wage distributions of young Italian males are much more compressed than are the comparable distributions for young white U.S. males, the estimated search model implies that the distribution of lifetime welfare is no more disperse in the U.S. than it is in Italy. Our model implies that the high frequency of movements between labour market states leads to both a relatively equitable distribution of "long run" welfare in the U.S. and a high level of cross-sectional inequality.     

Consumer mobility and community tax bases : The financing of local public goods

In a model of economic ‘clubs’, size is fixed and members consuming a public good raise the question of composition; with whom would they rather consume? This depends on the way collective consumption is financed, and three results are proven With a poll tax, clubs must be homogeneous in income for all to be satisfied With a marginal benefit (Lindahl) tax, no consumer is ever satisfied with any composition; and with an income tax, at least one consumer in each club is always dissatisfied. Satisfaction implies there exists no club composition preferred to the existing one.