Non linear massive gravity as a gravitational σ\sigma-model

We show the direct analogy between the ghost-free non-linear formulation of massive gravity and the standard $\sigma$-models well understood in the literature. This issue explains why there are two non-trivial family of solutions for the spherically symmetric case inside the non-linear massive gravity formulations with two free-parameters $\alpha$ and $\beta$. In general, the case $\beta<\alpha^2$ has a single physical vacuum state. On the other hand, the case $\beta=\alpha^2$ contains a natural vacuum degeneracy. This is in perfect analogy with the $\sigma$-model for scalar fields where depending on the values taken by the parameters of the theory the vacuum can be single or degenerate.Comment: Journal (Published) version up to some final edition arrangements, 5 pages, references added, one section adde

Isomorphy up to complementation

Considering uniform hypergraphs, we prove that for every non-negative integer $h$ there exist two non-negative integers $k$ and $t$ with $k\leq t$ such that two $h$-uniform hypergraphs ${\mathcal H}$ and ${\mathcal H}'$ on the same set $V$ of vertices, with $| V| \geq t$, are equal up to complementation whenever ${\mathcal H}$ and ${\mathcal H}'$ are $k$-{hypomorphic up to complementation}. Let $s(h)$ be the least integer $k$ such that the conclusion above holds and let $v(h)$ be the least $t$ corresponding to $k=s(h)$. We prove that $s(h)= h+2^{\lfloor \log_2 h\rfloor}$. In the special case $h=2^{\ell}$ or $h=2^{\ell}+1$, we prove that $v(h)\leq s(h)+h$. The values $s(2)=4$ and $v(2)=6$ were obtained in a previous work.Comment: 15 page

A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence

This paper develops a simple test for the null hypothesis of stationarity in heterogeneous panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. Our test is basically the same as the KPSS test but the regression is augmented by cross-sectional average of the observations. We also develop a Lagrange multiplier (LM) test allowing for cross-sectional dependence and, under restrictive assumptions, compare our augmented KPSS test with the extended LM test under the null of stationarity, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. We also extend our test to the more realistic case where the shocks are serially correlated. We use Monte Carlo simulations to examine the finite sample property of the augmented KPSS test.Panel data, stationarity, KPSS test, cross-sectional dependence, LM test, locally best test

A Locally Optimal Test for No Unit Root in Cross-sectionally Dependent Panel Data

This paper develops a simple test for the null hypothesis of no unit root for panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. We show that our test is asymptotically locally optimal, although the optimality is not guaranteed under a wide range of the alternative.KPSS test, unit root, cross-sectional dependence, LM test, locally best test

Efficiency, Environmental Contaminants and Farm Size: Testing for Links Using Stochastic Production Frontiers.

This paper investigates whether there is any relationship between farm size, technical efficiency and the use of agrochemicals which are potentially environmentally contaminating. These questions are pertinent in the context of current EU policy decisions. Using two models of stochastic frontier production and a set of panel data on 35 farms from the South West of England for the years 1987-1991, we obtain an indication, that there is a positive relationship between technical efficiency and use of contaminants, and between technical efficiency and farm size. However, there is a weak negative relationship between farm size and use of contaminants.Frontier production; technical efficiency; panel data; environment; farm size

Estimating Farm Efficiency in the Presence of Double Heteroscedasticity Using Panel Data

The accuracy of technical efficiency measures is important given the interest in such measures in policy discussions. In recent years the use of stochastic frontiers has become popular for estimating technical inefficiency, but estimated inefficiencies are sensitive to specification errors. One source of such errors is heteroscedasticity. This paper addresses this issue by extending the Hadri (1999) correction for heteroscedasticity to stochastic production frontiers and to panel data. It is argued that heteroscedasticity within an estimation can have a significant effect on results, and that correcting for heteroscedasticity yields more accurate measures of technical inefficiency. Using panel data on cereal farms, it is found that the usual technical efficiency measures used in stochastic production frontiers are significantly sensitive to the extended correction for heteroscedasticity.stochastic frontier production, heteroscedasticity, technical efficiency, panel data