Eddington-Malmquist bias in a cosmological context

In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. We derived the Malmquist relation within a general cosmological framework, including Friedmann's model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation. The Malmquist formula for the intrinsic difference _m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.Comment: 5 pages, 3 figures, A&A (in press

Aggregation Issues in the Estimation of Linear Programming Productivity Measures

This paper demonstrates the sensitivity of the linear programming approach in the estimation of productivity measures in the primal framework using Malmquist productivity index and Malmquist total factor productivity index models. Specifically, the sensitivity of productivity measure to the number of constraints (level of dis-aggregation) and imposition of returns to scale constraints of linear programing is evaluated. Further, the shadow or dual values are recovered from the linear program and compared to the market prices used in the ideal Fisher index approach to illustrate sensitivity. Empirical application to U.S. state-level time series data from 1960-2004 reveal productivity change decreases with increases in the number of constraints. Further, the input and output shadow or dual values are skewed, leading to the difference in the productivity measures due to aggregation.Aggregation, Share-weights, single and multiple output and input, Malmquist productivity index, Malmquist total factor productivity index, Agribusiness, Production Economics,

On the inconsistency of the Malmquist-Luenberger index

Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist-Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad outputs. In particular, we show that the usual interpretation of the technical change component in terms of production frontier shifts can be inconsistent with its numerical value, thereby resulting in an erroneous interpretation of this component that passes on to the index itself. We illustrate this issue with a simple numerical example. Finally, we propose a solution for this inconsistency issue based on incorporating a new postulate for the technology related to the production of bad output

PRODUCTIVITY GROWTH IN THE CARIBBEAN: A MEASURE OF KEY COMPONENTS

Productivity growth is decomposed into two components: technical change and efficiency change. This assesses their relative importance to the international competitiveness of the agricultural sectors of selected Caribbean countries. A nonparametric programming method is employed to compute Malmquist multifactor productivity indexes, which contrasts the innovation of races of these countries. Keywords: Multifactor productivity, Malmquist indexes, Caribbean agriculture, Relative efficiency, Technical efficiencyMultifactor productivity, Malmquist indexes, Caribbean agriculture, Relative efficiency, Technical efficiency, Productivity Analysis, Research Methods/ Statistical Methods,

Return to Dollar, Generalized Distance Function and the Fisher Productivity Index

Exploring the duality between a return to dollar definition of profit and the generalized distance function we establish the relationship between the Laspeyres, Paasche and Fisher productivity indexes and their alternative Malmquist indexes counterparts. By proceeding this way, we propose a consistent decomposition of these productivity indexes into two mutually exclusive components. A technical component represented by the Malmquist index and an economical component which can be identified with the contribution that allocative criteria make to productivity change. With regard to the Fisher index, we indicate how researchers can further decompose the Malmquist technical component rendering explicit the sources of productivity change. We also show how the proposed model can be implemented by means of Data Envelopment Analysis techniques, and illustrate the empirical process with an example data set.Generalized Distance Function; Return to Dollar; Fisher and Malmquist Productivity Indexes

Optimal Galaxy Distance Estimators

The statistical properties of galaxy distance estimators are studied and a rigorous framework is developed for identifying and removing the effects of Malmquist bias due to obsevational selection. The prescription of Schechter (1980) for defining unbiased distance estimators is extended to more general -- and more realistic -- cases. The derivation of `optimal' unbiased distance estimators of minimum dispersion, by utilising information from additional -- suitably correlated -- observables, is discussed and the results applied to a calibrating sample from the Fornax cluster, as used in the Mathewson spiral galaxy redshift survey. The optimal distance estimator derived from I-band magnitude, diameter and 21cm line width has an intrinsic scatter which is 25 \% smaller than that of the Tully-Fisher relation quoted for this calibrating sample. (Figures are available on request).Comment: Plain Latex, 19 pages, Sussex-AST-93/9-

Agricultural productivity growth in the European Union and transition countries

Malmquist total factor productivity (TFP) index has been extensively applied in the literature to measure productivity growth decomposition. This study applies a parametric decomposition of a Generalized Malmquist TFP index to measure and compare the levels and trends in agricultural productivity in European countries, making use of the most-recent data available from the Food and Agriculture Organization (FAO) of United Nations. The aim of this study is to measure TFP developments in agriculture of transition countries after breakdown of socialism and to compare their TFP growth with other European countries. The Generalized Malmquist productivity index can be decomposed into technological change, technical efficiency change and scale efficiency change. These measures will provide insightful information for policymakers in designing proper policies to promote a higher growth rate in agriculture in transition countries. -- G E R M A N V E R S I O N: Malmquist Total Factor Productivity (TFP) Index gehört zu den meist verwendeten Methoden der Produktivitätsanalyse und ihrer Zerlegung. In diesem Paper wird ein parametrisches Verfahren eingesetzt, um die Produktivitätsentwicklungen in der europäischen Agrarwirtschaft zu analysieren. Die statistische Datenbasis basiert auf der Datenbank der Food and Agriculture Organization (FAO) of United Nations. Das Ziel dieses Forschungsvorhabens ist es, die Produktivitätsentwicklungen in den Agrar- und Ernährungssektoren der Transformationsländern Mittel- und Osteuropas sowie der ehemaligen Sowjetunion zu messen und diese mit dem Wachstum in der Europäischen Union zu vergleichen. Methodisch kann Malmquist Index zerlegt werden in technical change, efficiency change and scale efficiency change. Dieser Zerfall des Indexes kann wichtige Informationen für die Politikgestalter und Forscher hinsichtlich der weiteren Entwicklung des Agrarsektors in betroffenen Ländern bringen.Transition countries,Malmquist,Multifactor Productivity,agriculture,Transformation,Malmquist Index,Agrarsektor,Multifactor Productivity

An Unbiased Estimator of Peculiar Velocity with Gaussian Distributed Errors for Precision Cosmology

We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and that have errors that are Gaussian distributed, thus meeting the assumptions of analyses that rely on individual peculiar velocities. We apply this estimator to the SFI++ and the Cosmicflows-2 catalogs of galaxy distances and, using the fact that peculiar velocity estimates of distant galaxies are error dominated, examine their error distributions, The adoption of the new estimator significantly improves the accuracy and validity of studies of the large-scale peculiar velocity field and eliminates potential systematic biases, thus helping to bring peculiar velocity analysis into the era of precision cosmology. In addition, our method of examining the distribution of velocity errors should provide a useful check of the statistics of large peculiar velocity catalogs, particularly those that are compiled out of data from multiple sources.Comment: 6 Pages, 5 Figure

Evolution of the Ionizing Background at High Redshifts

We use a Maximum-Likelihood analysis to constrain the value and evolution of the ionizing background for 2<z<4.5, taking account of possible systematic errors. (The paper has a more detailed abstract)Comment: 12 figures (9 of those double plots), 17 pages. Accepted by MNRA