Omitted variable bias and cross section regression

"July 1983."Bibliography: p. 27.by Thomas M. Stoker

On ``A proposed standard set of problems to test finite element accuracy'': the twisted beam

The standard test problem of MacNeal and Harder (Finite Elem. Anal. Des. 1 (1985) 3) for the verification of spatial beam finite elements, i.e. the deflection of the initially twisted beam, is commented through the analysis of three variants of initially twisted beams: (i) a linearly twisted beam with a constant cross-section; (ii) a non-linearly twisted beam with a constant cross-section; and (iii) a non-linearly twisted beam with variable cross-sections. Our numerical results lead to the conclusion that the twisted beam problem (Finite Elem. Anal. Des. 1 (1985) 3) assumes the linearly twisted, curved-edge beam. (C) 2003 Elsevier B.V. All rights reserved

On the Energy Dependence of the Dipole-Proton Cross Section in Deep Inelastic Scattering

We study the dipole picture of high-energy virtual-photon-proton scattering. It is shown that different choices for the energy variable in the dipole cross section used in the literature are not related to each other by simple arguments equating the typical dipole size and the inverse photon virtuality, contrary to what is often stated. We argue that the good quality of fits to structure functions that use Bjorken-x as the energy variable - which is strictly speaking not justified in the dipole picture - can instead be understood as a consequence of the sign of scaling violations that occur for increasing Q^2 at fixed small x. We show that the dipole formula for massless quarks has the structure of a convolution. From this we obtain derivative relations between the structure function F_2 at large and small Q^2 and the dipole-proton cross section at small and large dipole size r, respectively.Comment: 27 page

On The Panel Unit Root Tests Using Nonlinear Instrumental Variables

This paper re-examines the panel unit root tests proposed by Chang (2002). She establishes asymptotic independence of the t-statistics when integrable functions of lagged dependent variable are used as instruments even if the original series are cross sectionally dependent. She claims that her non-linear instrumental variable (NIV) panel unit root test is valid under general error cross correlations for any N (the cross section dimension) as T (the time dimension of the panel) tends to infinity. These results are largely due to her particular choice of the error correlation matrix which results in weak cross section dependence. Also, the asymptotic independence property of the t- statistics disappears when Chang's modified instruments are used. Using a common factor model with a sizeable degree of cross section correlations, we show that Chang's NIV panel unit root test suffers from gross size distortions, even when N is small relative to T

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at √s = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton–proton collisions at a centre-of-mass energy of s=7TeV , using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^(−1). The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20<p T<400 GeV and rapidity in the range |y|<2.1. The bb-dijet cross-section is measured as a function of the dijet invariant mass in the range 110<m_(jj)<760 GeV, the azimuthal angle difference between the two jets and the angular variable χ in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bb-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta

Influence Of Current Leads On Critical Current For Spin Precession In Magnetic Multilayers

In magnetic multilayers, a dc current induces a spin precession above a certain critical current. Drive torques responsible for this can be calculated from the spin accumulation $\bar{\Delta\mu}$. Existing calculations of $\bar{\Delta\mu}$ assume a uniform cross section of conductors. But most multilayer samples are pillars with current leads flaring out immediately to a much wider cross-section area than that of the pillar itself. We write spin-diffusion equations of a form valid for variable cross section, and solve the case of flat electrodes with radial current distribution perpendicular to the axis of the pillar. Because of the increased volume available for conduction-electron spin relaxation in such leads, $\bar{\Delta\mu}$ is reduced in the pillar by at least a factor of 2 below its value for uniform cross section, for given current density in the pillar. Also, $\bar{\Delta\mu}$ and the critical current density for spin precession become nearly independent of the thickness of the pinned magnetic layer, and more dependent on the thickness of the spacer, in better agreement with measurements by Albert et al. (2002).Comment: To appear in J. Magn. Magn. Mate

Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N approaching infinity. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coe.cient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.Autoregression, Bias, Cross section dependence, Dynamic factors, Dynamic panel estimation, Incidental trends, Panel unit root

Manifestly Covariant Analysis of the QED Compton Process in ep→eγpe p\to e \gamma p and ep→eγXe p \to e \gamma X

We calculate the unpolarized QED Compton scattering cross section in a manifestly covariant way. Our approach allows a direct implementation of the specific kinematical cuts imposed in the experiments, {\it e. g.} HERA-H1. We compare the 'exact' cross section in terms of the structure functions $F_{1,2} (x_B,Q^2)$, assuming the Callan-Gross relation, with the one obtained using the equivalent photon approximation (EPA) as well as with the experimental results. We find that the agreement with the EPA is better in $x_{\gamma}$ bins, where $x_{\gamma}$ is the fraction of the longitudinal momentum of the proton carried by the virtual photon, compared to the bins in the leptonic variable $x_l$.Comment: 22 pages, 4 figures, 2 table