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Jacek Białek

Abstract

As is known, all geo-logarithmic indices enjoy the axiomatic properties of being proportional, commensurable and homogeneous, together with their cofactors (Martini 1992a). Geologarithmic price indices satisfying the axioms of monotonicity, basis reversibility and factor reversibility have been investigated by Marco Fattore (2010), who has shown that the superlative Fisher price index does not belong to this family of indices. In this article, we discuss geo-logarithmic price indices with reference to the Laspeyres-Paasche bounding test and we propose a modification of the considered index family that satisfies this test. We also modify the structure of geo-logarithmic indices by using an additional parameter and, following the economic approach, we list superlative price index formulas that are members of the considered price index family. We obtain a special subfamily that approximates superlative price indices and includes the Fisher, Walsh and Sato-Vartia price indices.

Open access

Elżbieta Roszko-Wójtowicz and Jacek Białek

Abstract

The consumer price index (CPI) is acommon measure of inflation. Similarly to the harmonised index of consumer prices (HICP), it is determined using the Laspeyres index, thus data on the consumption of the basket of goods do not have to be current. The Laspeyres index, using weights only from the base period, may not reflect changes in consumer preferences that occurred in the studied year. This is the reason for the formation of the so-called substitution bias in the measurement of inflation. The aim of the article is to assess the impact of the level of innovativeness of a given country’s economy on the occurrence of the substitution effect. The empirical part of the article is based on basic innovation indices, i.e. the SII, IOI, and GII. The assessment of the relationship between the level of innovativeness and the scale of the substitution effect was carried out based on the methods of multidimensional statistical analysis (including cluster analysis, the PROFIT method).

Open access

Piotr Król, Andrzej Franek, Jacek Durmała, Edward Błaszczak, Krzysztof Ficek, Barbara Król, Ewa Detko, Bartosz Wnuk, Lidia Białek and Jakub Taradaj

Abstract

The purpose of this article was to evaluate and compare the efficacy of radial and focused shock wave therapies applied to treat tennis elbow. Patients with tennis elbow were randomized into two comparative groups: focused shock wave therapy (FSWT; n=25) and radial shock wave therapy (RSWT; n=25). Subjects in the FSWT and RSWT groups were applied with a focused shock wave (3 sessions, 2000 shocks, 4 Hz, 0.2 mJ/mm2) and a radial shock wave (3 sessions, 2000 + 2000 shocks, 8 Hz, 2.5 bar), respectively. The primary study endpoints were pain relief and functional improvement (muscle strength) one week after therapy. The secondary endpoint consisted of the results of the follow-up observation (3, 6 and 12 weeks after the study). Successive measurements showed that the amount of pain patients felt decreased in both groups. At the same time grip strength as well as strength of wrist extensors and flexors of the affected extremity improved significantly. Both focused and radial shock wave therapies can comparably and gradually reduce pain in subjects with tennis elbow. This process is accompanied by steadily improved strength of the affected extremity.