Some remarks concerning the quotient of sample median and sample range for a sample of size 2n+1 from a normal distribution

Consider an ordered sample ₍₁₎, ₍₂₎,…, _(2n+1) of size 2 n +1 from the normal distribution with parameters μ and . We then have with probability one
₍₁₎ < ₍₂₎ < … < (2 n +1).
The random variable
_n =_(n+1)/_(2n+1)-(1)
that can be described as the quotient of the sample median and the sample range, provides us with an estimate for μ/, that is easy to calculate. To calculate the distribution of h _n is quite a different matter***. The distribution function of h₁, and the density of h₂ are given in section 1. Our results seem hardly promising for general h_n. In section 2 it is shown that h_n is asymptotically normal.
In the sequel we suppose μ= 0 and = 1, i.e. we consider only the "central" distribution. Note that h_n can be used as a test statistic replacing Student's t. In that case the central h_n is all that is needed.     

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Produktie,kapitaal en interest

Summary As recent discussions show the theory of capital is still an important issue. Surveys by among others Harcourt and Dobb have brought the main themes of this theory before a larger audience. This paper aims at the same purpose. Apart from being written in Dutch the difference with the other surveys lies in the rigourous application of a two-sector model with heterogeneous capital with respect to all the questions raised.Section two of the paper is devoted to the critique of neo-classical theory by J. Robinson and D. G. ChampernowneIs answer in the form of the chain index method to measure capital. P. A. Samuelson's surrogate production function and P. Garegnani's refutation of it are discussed in the next section. The final section on technical matters deals with the relation between capital intensity and the rate of interest. In this setting attention is paid to the famous reswitching debate in the late sixties.In a concluding section the meaning of the central controversy is emphasized. For, as P. Sraffa has shown, it is not only the theory of income distribution which is highly vulnerable but also the whole foundation of micro-economics by the neo-classical authors that goes with it. This is what makes the whole dispute so fascinating.

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Met dank und Drs. A. van Schaik voor de stimulerende kritiek.     

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Enkele vraagstukken van economischen groei in Nederland

Voordracht gehouden op 23 Februari 1956 in de Economische Sectie van het Studentencongres der Nederlanden te Gent.     

Kommunen in der Krise

Die Wirtschaftskrise belastet die Kommunen mit deutlichen Einnahmeausf?llen. Aber auch der Bund hat die Kommunen durch das Wachstumsbeschleunigungsgesetz und andere Bundesgesetze in eine schwierige finanzielle Lage gebracht. Die Kommission zur Neuordnung der Gemeindefinanzen, die Anfang M?rz ihre Arbeit aufgenommen hat, soll Vorschl?ge für eine tragf?hige Finanzierung der Kommunen machen.     

Reforming social security: assessing the effects of alternative funding strategies

Population ageing implies that the large pay-as-you-go social security programmes implemented in many OECD economies will run into severe financial problems. By means of a numerical overlapping generations model, this paper investigates the intergenerational welfare effects of a transition to funded security programmes. Such programmes imply permanent increases in the welfare of the young and unborn generations. It is demonstrated that the size of the welfare gains varies significantly between alternative funding strategies. A nonindividualized funding strategy characterized by increased government asset accumulation triggers considerable welfare gains through increased asset returns in the future. Even larger welfare gains may be realized by an individual funding strategy characterized by increased asset accumulation accompanied by an adoption of actuarial supplementary pensions (i.e. actuarial supplementary pensions combined with a fixed minimum pension) which reduces future tax distortions drastically.     

Layoff taxes and minimum wage: Two complementary public policies

In a matching model in which the job destruction rate and the output are endogenous, we show that the presence of a binding minimum wage prompts firms to choose too risky jobs. Introducing layoff taxes therefore reduces unemployment and improves market efficiency.