Zeros of Quasi-Orthogonal Jacobi Polynomials

We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by $\alpha>-1$, $-2<\beta<-1$. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials $P_n^{(\alpha, \beta)}$ and $P_{n}^{(\alpha,\beta+2)}$ are interlacing, holds when the parameters $\alpha$ and $\beta$ are in the range $\alpha>-1$ and $-2<\beta<-1$. We prove that the zeros of $P_n^{(\alpha, \beta)}$ and $P_{n+1}^{(\alpha,\beta)}$ do not interlace for any $n\in\mathbb{N}$, $n\geq2$ and any fixed $\alpha$, $\beta$ with $\alpha>-1$, $-2<\beta<-1$. The interlacing of zeros of $P_n^{(\alpha,\beta)}$ and $P_m^{(\alpha,\beta+t)}$ for $m,n\in\mathbb{N}$ is discussed for $\alpha$ and $\beta$ in this range, $t\geq 1$, and new upper and lower bounds are derived for the zero of $P_n^{(\alpha,\beta)}$ that is less than $-1$

Bounds for extreme zeros of some classical orthogonal polynomials

We derive upper bounds for the smallest zero and lower bounds for the largest zero of Laguerre, Jacobi and Gegenbauer polynomials. Our approach uses mixed three term recurrence relations satisfied by polynomials corresponding to different parameter(s) within the same classical family. We prove that interlacing properties of the zeros impose restrictions on the possible location of common zeros of the polynomials involved and deduce strict bounds for the extreme zeros of polynomials belonging to each of these three classical families. We show numerically that the bounds generated by our method improve known lower (upper) bounds for the largest (smallest) zeros of polynomials in these families, notably in the case of Jacobi and Gegenbauer polynomials

Factors Affecting Maize Producers Adoption of Forward Pricing in Price Risk Management: The Case of Vaalharts

Logistic regression is employed to analyse the factors which influence the decision of whether or not the respondent used forward pricing methods during the 2004/05 maize production season. Forward pricing methods include cash forward contracting and hedging with futures contracts and/or options, through the South African Futures Exchange (SAFEX). Based on the results, the use of forward pricing is associated with lower levels of risk aversion and higher levels of human capital. Factor analysis is employed to reduce the dimensionality of the personal reasons which help to interpret the underlying, common factor of the personal reasons why farmers are reluctant to use forward pricing methods. Three factors were extracted and were labelled “Lack of capacityâ€, “Distrust of the marketâ€, and “Bad experiencesâ€. The results from the factor analysis confirm the finding that farmers need higher levels of human capital to use forward pricing methods and that farmers do not believe that the forward pricing market is effective. Education should furthermore, focus more on the practical application of alternative forward pricing methods and not purely on the benefits of the use of forward pricing methods.Forward pricing, Logit, Factor analysis, Agricultural Finance, Risk and Uncertainty,

Does FDI promote regional development? Evidence from local and regional productivity spillovers in Greece

Studies on the productivity spillovers of FDI have concentrated on the nationalsectoral level. As a result, little is known about the impact of FDI on absolute and relative regional economic performance. In this paper we examine this issue by relying on a unique dataset of over 20,000 Greek firms for the period 2002-2006 covering all sectors of economic activity. We examine the spatial distribution of foreign-owned firms in the country and analyse the effect that their presence – at the local, regional and national levels – has on the productivity of domestic firms. We find strong evidence suggesting that foreignowned firms self-select into regions and sectors of high productivity. Net of this selection effect, the impact of foreign presence on domestic productivity is negative – although at the very local level some positive spillover effects are identifiable. The bulk of the effects concentrate in non-manufacturing activities, high-tech sectors, and medium-sized high-productivity firms. Importantly, this effect is not constant across space however. Productivity spillovers tend to be negative in the regions hosting the main urban areas in the country but positive in smaller and more peripheral regions. In this way, despite the tendency of FDI to concentrate in a limited number of areas within the country – those of the highest level of development – the externalities that FDI activity generates to the local economies appear to be of a rather equilibrating character. Key words: regional development, FDI, productivity spillovers, Greece, spatial heterogeneity

ESTIMATING THE TOURISM POTENTIAL IN NAMIBIA

This paper investigates the determinants of tourism in Namibia for the period 1996 to 2005. The results indicate that an increase in trading partners’ income, depreciation of the exchange rate, improvement in Namibia’s infrastructure, sharing a border with Namibia are associated with an increase in tourist arrivals. The results show that there is unexploited tourism potential from Angola, Austria, Botswana, Germany, South Africa and the United States of America. This suggests that it is important to exploit the tourism potential as this would help to accelerate economic growth and generate the much needed employment.