Jan Tinbergen's Income distribution: Analysis and policies

Summary This paper is a detailed review and critique of Jan Tinbergen'sIncome Distribution: Analysis and Policies. In Part I, the books primary findings and their bases are recounted. This presentation serves as the basis for a number of questions regarding the merits of the overall approach — in particular, the empirical methodology — and the reliability of the findings. These questions are posed in Part II. In Part III, an overall appraisal of the work is offered.North-Holland Publishing Co., Amsterdam, 1975.Professor of Economics and Fellow of the Institute for Research on Poverty, University of Wisconsin-Madison. This article was prepared while the author was a Fellow at the Netherlands Institute for Advanced Study. The work was supported in part by the Netherlands Institute for Advanced Study and by funds granted to the Institute for Research on Poverty at the University of Wisconsin-Madison by the U.S. Department of Health, Education and Welfare pursuant to the Economic Opportunity Act of 1964. Helpful comments on an earlier draft by Hans Daudt, Arthur Goldberger, Victor Halberstadt, Arnold Heertje, and Jan Pen are acknowledged. A discussion with Jan Tinbergen on issues raised in his volume was especially valuable, This review article appeared in a slightly different form in the Winter, 1975 issue of theJournal of Human Resources.     

Redundancy,values and public policy

Although the Industrial Relations Act marks the most significant break with the traditional “abstentionist” role of the law in British labour relations, it is true to say that during the last ten years the development of public policy has entailed a growing involvement of lawyers and the law in the world of work. As Professor Kahn-Freund has written:     

Zur Definition und Schätzung von Mittelwerten für zufällige Variable auf der Sphäre

Zusammenfassung Diese Arbeit ist die gekürzte Fassung einer Dissertation, die vom Autor 1968 unter gleichem Titel in Würzburg ver?ffentlicht wurde. Es ist nicht sinnovll, Mittelwerte für zuf?llige Variable auf der Sph?re in der üblichen Weise, wie z. B. für zuf?llige Variable auf der reellen Achse, zu definieren. W. Uhlmann [1964] bediente sich entscheidungstheoretischer Begriffe, um für zirkul?re zuf?llige Variable mittlere Winkel zu definieren, die ihre Richtung unabh?ngig von der Wahl der Null-Richtung beibehalten. Die analoge Invarianzeigenschaft wird für alle hier definierten Mittelwertbegriffe (mittlere Richtung, mittlerer Gro?kreis, Mittelachse, Mittelkreis) gesichert, indem einfache Forderungen an die zu verwendenden Verlustfunktionen gestellt werden. Da als Sch?tzungen für diese Mittelwerte stets die entsprechenden Mittelwerte der empirischen Verteilung auftreten, haben diese auch die gleiche Invarianzeigenschaft. Um die Diskrepanz zwischen einer solchen Sch?tzung und dem zu sch?tzenden Mittelwert zu messen, werden neue Verlustfunktionen eingeführt. Es wird gezeigt, da? alle eingeführten Sch?tzungen bezüglich mindestens einer Verlustfunktion unverf?lscht sind, d. h. der erwartete Verlust wird minimal, wenn wir aus allen in Frage kommenden Objekten gerade den betreffenden Mittelwert gesch?tzt werden lassen. Dieser minimale Verlust wird die Dispersion der Sch?tzung bezüglich dieser Verlustfunktion genannt. Es wird bewiesen, da? alle ermittelten Dispersionen mindestens wien ^−1/2 gegen Null gehen, wenn n gegen Unendlich strebt.

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Summary This paper is shortened from an equally entitled dissertation which has been published by the author in 1968 at Würzburg. For random variables on the sphere it would make no sense to define means in the usual way as it is done e. g. for random variables on the real line. Introducing concepts of decision theory,W. Uhlmann [1964] defined mean angles for circular random variables the direction of which does not depend on the choice of the zero direction. Setting up simple conditions for the loss functions to be used, we ensure that all the means defined in the paper (mean directions, mean great circles, mean axes, mean circles) have the analogous invariance property. The estimators of these means are always the corresponding means of the empirical distribution, defined with respect to the same loss function and therefore they have the invariance property too. To measure the discrepance between an estimator and the estimated mean, new loss functions are introduced. It is shown that all the established estimators are unbiased with respect to at least one loss function, i. e. the expected loss is a minimum, if we take just the mean from all the things in question to be estimated by the regarded estimator. This minimum loss is called the dispersion of the estimator with respect to this loss function. It is proved, that all the calculated dispersions go to zero at least asn ^−1/2, ifn tends to infinity.