The Cross Sectional Dependence Puzzle

The analysis of unit roots and cointegration in panel data is becoming a growing research area. A number of issues have been raised in the literature (see Phillips and Moon 1999 and 2000, Banerjee 2000, Maddala and Wu 1999). The aim of the present paper is to contribute to the issue of cross sectional dependence in non-stationary panel data. We review some of the most recent econometric techniques proposed by the literature to dealing with cross sectional dependence and notice a sort of puzzle. We extend the bootstrap methodology proposed by Maddala and Wu (1999) and apply the resulting test to test for PPP. We find no evidence favouring PPP. Finally, we use Monte Carlo simulation to analyse the size distortion of the bootstrap test presented in this paper. The proposed test presents size distortion only when T = 100.

Regression with a Slowly Varying Regressor in the Presence of a Unit Root

This paper considers the regression model with a slowly varying (SV) regressor in the presence of a unit root in serially correlated disturbances. This regressor is known to be asymptotically collinear with the constant term; see Phillips (2007). Under nonstationarity, we find that the estimated coefficients of the constant term and the SV regressor are asymptotically normal, but neither is consistent. Further, we derive the limiting distribution of the unit root test statistic. We may here observe that the finite sample approximation to the limiting one is not monotone and it is poor due to the influence of the collinear regressor. In order to construct a well-behaved test statistic, we recommend dropping the constant term intentionally from the regression and computing the statistics, which are still consistent under the true model having the constant term. The powers and sizes of these statistics are found to be well-behaved through simulation studies. Finally, these results are extended to general Phillips and Perron-type statistics.

SRPT Is 1.86-competitive for Completion Time Scheduling

We consider the classical problem of scheduling preemptible jobs, that ar-rive over time, on identical parallel machines. The goal is to minimize the total completion time of the jobs. In standard scheduling notation of Graham et al. [5], this problem is denoted P | rj,pmtn | j cj. A pop-ular algorithm called SRPT, which always schedules the unfinished jobs with shortest remaining processing time, is known to be 2-competitive, see Phillips et al. [12, 13]. This is also the best known competitive ratio for any online algorithm. However, it is conjectured that the competitive ra-tio of SRPT is significantly less than 2. Even breaking the barrier of 2 is considered a significant step towards the final answer of this classical online problem. We improve on this open problem by showing that SRPT is 1.86-competitive. This result is obtained using the following method, which might be of general interest: We define two dependent random variables that sum up to the difference between the cost of an SRPT schedule and the cost of an optimal schedule. Then we bound the sum of the expected values of these random variables with respect to the cost of the optimal schedule, yielding the claimed competitiveness. Furthermore, we show a lower bound of 21/19 for SRPT, improving on the previously best known 12/11 due to Lu et al. [10]

‘Fixed-axis’ magnetic orientation by an amphibian: non-shoreward-directed compass orientation, misdirected homing or positioning a magnetite-based map detector in a consistent alignment relative to the magnetic field?

Experiments were carried out to investigate the earlier prediction that prolonged exposure to long-wavelength (>500 nm) light would eliminate homing orientation by male Eastern red-spotted newts Notophthalmus viridescens. As in previous experiments, controls held in outdoor tanks under natural lighting conditions and tested in a visually uniform indoor arena under full-spectrum light were homeward oriented. As predicted, however, newts held under long-wavelength light and tested under either full-spectrum or long-wavelength light (>500 nm) failed to show consistent homeward orientation. The newts also did not orient with respect to the shore directions in the outdoor tanks in which they were held prior to testing. Unexpectedly, however, the newts exhibited bimodal orientation along a more-or-less `fixed' north-northeast—south-southwest magnetic axis. The orientation exhibited by newts tested under full-spectrum light was indistinguishable from that of newts tested under long-wavelength light, although these two wavelength conditions have previously been shown to differentially affect both shoreward compass orientation and homing orientation. To investigate the possibility that the `fixed-axis' response of the newts was mediated by a magnetoreception mechanism involving single-domain particles of magnetite, natural remanent magnetism (NRM) was measured from a subset of the newts. The distribution of NRM alignments with respect to the head—body axis of the newts was indistinguishable from random. Furthermore, there was no consistent relationship between the NRM of individual newts and their directional response in the overall sample. However, under full-spectrum, but not long-wavelength, light, the alignment of the NRM when the newts reached the 20 cm radius criterion circle in the indoor testing arena (estimated by adding the NRM alignment measured from each newt to its magnetic bearing) was non-randomly distributed. These findings are consistent with the earlier suggestion that homing newts use the light-dependent magnetic compass to align a magnetite-based `map detector' when obtaining the precise measurements necessary to derive map information from the magnetic field. However, aligning the putative map detector does not explain the fixed-axis response of newts tested under long-wavelength light. Preliminary evidence suggests that, in the absence of reliable directional information from the magnetic compass (caused by the 90° rotation of the response of the magnetic compass under long-wavelength light), newts may resort to a systematic sampling strategy to identify alignment(s) of the map detector that yields reliable magnetic field measurements

On calculating estimates of stratified error-components models

This note provides an AECM (alternating expectation conditional maximization) algorithm for calculating maximum-likelihood estimates of stratified error-components models. An advantage it has over other algorithms is that it can be easily modified to incorporate useful restrictions on the variance components. The new algorithm is applied in an example that illustrates the variance restrictions.

Molecular techniques reveal cryptic life history and demographic processes of a critically endangered marine turtle

The concept of ‘effective population size’ (Ne), which quantifies how quickly a population will lose genetic variability, is one of the most important contributions of theoretical evolutionary biology to practical conservation management. Ne is often much lower than actual population size: how much so depends on key life history and demographic parameters, such as mating systems and population connectivity, that often remain unknown for species of conservation concern. Molecular techniques allow the indirect study of these parameters, as well as the estimation of current and historical Ne. Here, we use genotyping to assess the genetic health of an important population of the critically endangered hawksbill turtle (Eretmochelys imbricata), a slow-to-mature, difficult-to-observe species with a long history of severe overhunting. Our results were surprisingly positive: we found that the study population, located in the Republic of Seychelles, Indian Ocean, has a relatively large Ne, estimated to exceed 1000, and showed no evidence of a recent reduction in Ne (i.e. no genetic bottleneck). Furthermore, molecular inferences suggest the species' mating system is conducive to maintaining a large Ne, with a relatively large and widely distributed male population promoting considerable gene flow amongst nesting sites across the Seychelles area. This may also be reinforced by the movement of females between nesting sites. Our study underlines how molecular techniques can help to inform conservation biology. In this case our results suggest that this important hawksbill population is starting from a relatively strong position as it faces new challenges, such as global climate change

Consumer Expenditure and Cointegration

In this paper we estimate the Almost Ideal Demand System (AIDS) for the Portuguese economy. The budget shares and real per capita income are found to be integrated of order one, I(1), but prices seem to be better classified as I(2). This raises new problems, as it is not possible to test for homogeneity and symmetry in a straightforward way. As cointegration is not rejected after the imposition of homogeneity and symmetry restrictions, we conclude that the AIDS is an acceptable characterisation of the Portuguese data on consumer expenditure.