A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

On the accuracy of Latin American trade statistics: A nonparametric test for 1925

This paper proposes a nonparametric test in order to establish the level of accuracy of theforeign trade statistics of 17 Latin American countries when contrasted with the trade statistics of the main partners in 1925. The Wilcoxon Matched-Pairs Ranks test is used to determine whether the differences between the data registered by exporters and importers are meaningful, and if so, whether the differences are systematic in any direction. The paper tests for the reliability of the data registered for two homogeneous products, petroleum and coal, both in volume and value. The conclusion of the several exercises performed is that we cannot accept the existence of statistically significant differences between the data provided by the exporters and the registered by the importing countries in most cases. The qualitative historiography of Latin American describes its foreign trade statistics as mostly unusable. Our quantitative results contest this view.

What is what?: A simple time-domain test of long-memory vs. structural breaks

This paper proposes a new time-domain test of a process being I(d), 0 < d = 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by AB(t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on yt-1 in an OLS regression of ?dyt on a simple transformation of the above-mentioned deterministic components and yt-1, possibly augmented by a suitable number of lags of ?dyt to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey- Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided.

Comparing and validating hypothesis test procedures: Graphical and numerical tools

When the behaviour of a specific hypothesis test statistic is studied by aMonte Carlo experiment, the usual way to describe its quality is by givingthe empirical level of the test. As an alternative to this procedure, we usethe empirical distribution of the obtained \emph{p-}values and exploit itsinformation both graphically and numerically.

Level shifts in a panel data based unit root test : an application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.

Level shifts in a panel data based unit root test : an application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.

Static dipole polarizability of alkali-metal clusters: Electronic exchange and correlation effects

Nonlocal approximations for the electronic exchange and correlation effects are used to compute, within density-functional theory, the polarizability and surface-plasma frequencies of small jelliumlike alkali-metal clusters. The results are compared with those obtained using the local-density approximation and with available experimental data, showing the relevance of these effects in obtaining an accurate description of the surface response of metallic clusters.

Barrier for the reaction X20+ + X20+ -> X402+ in alkali-metal clusters related to electron density at the bond midpoint of the supermolecule (X20+)2

Using the extended Thomas-Fermi version of density-functional theory (DFT), calculations are presented for the barrier for the reaction Na20++Na20+¿Na402+. The deviation from the simple Coulomb barrier is shown to be proportional to the electron density at the bond midpoint of the supermolecule (Na20+)2. An extension of conventional quantum-chemical studies of homonuclear diatomic molecular ions is then effected to apply to the supermolecular ions of the alkali metals. This then allows the Na results to be utilized to make semiquantitative predictions of position and height of the maximum of the fusion barrier for other alkali clusters. These predictions are confirmed by means of similar DFT calculations for the K clusters.

From nonwetting to prewetting: The asymptotic behavior of 4He drops on alkali substrates

We investigate the spreading of 4He droplets on alkali-metal surfaces at zero temperature, within the frame of finite range density-functional theory. The equilibrium configurations of several 4HeN clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects inferring that the asymptotic properties of large droplets correspond to those of the prewetting film.

Condensation of helium in nanoscopic alkali wedges at zero temperature

We present a complete calculation of the structure of liquid 4He confined to a concave nanoscopic wedge, as a function of the opening angle of the walls. This is achieved within a finite-range density functional formalism. The results here presented, restricted to alkali metal substrates, illustrate the change in meniscus shape from rather broad to narrow wedges on weak and strong alkali adsorbers, and we relate this change to the wetting behavior of helium on the corresponding planar substrate. As the wedge angle is varied, we find a sequence of stable states that, in the case of cesium, undergo one filling and one emptying transition at large and small openings, respectively. A computationally unambiguous criterion to determine the contact angle of 4He on cesium is also proposed.

Collective spin excitations of alkali-metal clusters

The response function of alkali-metal clusters, modeled as jellium spheres, to dipole (L=1) and quadrupole (L=2) spin-dependent fields is obtained within the time-dependent local-spin-density approximation of density-functional theory. We predict the existence of low-energy spin modes of surface type, which are identified from the strength function. Their collectivity and evolution with size are discussed.

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Magnesium hydrogen breath test using end-expiratory sampling to assess achlorhydria in pernicious anaemia patients

A modified magnesium hydrogen breath test, using end expiratory breath sampling, is described to investigate achlorhydria. The efficacy of this test in the diagnostic investigation of pernicious anaemia was compared with that of serum pepsinogen I. Twenty one patients with pernicious anaemia--that is, patients with achlorhydria--and 22 with healed duodenal ulcer and normal chlorhydria were studied. Magnesium hydrogen breath test, serum pepsinogen I, serum gastrin, and standard gastric acid secretory tests were performed in all subjects. The mean (SEM) hydrogen peak value was lower in patients with pernicious anaemia than in the duodenal ulcer group (21.7 (1.9) v 71.3 (5.2) ppm; p = 0.00005). The hydrogen peak value had a 95.2% sensitivity and a 100% specificity to detect pentagastrin resistant achlorhydria. Mean serum pepsinogen I concentrations were also significantly lower in patients with pernicious anaemia than in the duodenal ulcer group (10.7 (2.7) v 123.6 (11.8) micrograms/l p = 0.00005). Sensitivity and specificity to detect pernicious anaemia were both 100% for pepsinogen I. It is concluded that this modified magnesium hydrogen breath test is a simple, noninvasive, cost effective, and accurate method to assess achlorhydria and may be useful in the diagnostic investigation of patients with suspected pernicious anaemia.

Performance of correlation functionals in ab initio chemisorption cluster-model calculations: Alkali metals on Si(111)

The performance of different correlation functionals has been tested for alkali metals, Li to Cs, interacting with cluster models simulating different active sites of the Si(111) surface. In all cases, the ab initio Hartree-Fock density has been obtained and used as a starting point. The electronic correlation energy is then introduced as an a posteriori correction to the Hartree-Fock energy using different correlation functionals. By making use of the ionic nature of the interaction and of different dissociation limits we have been able to prove that all functionals tested introduce the right correlation energy, although to a different extent. Hence, correlation functionals appear as an effective and easy way to introduce electronic correlation in the ab initio Hartree-Fock description of the chemisorption bond in complex systems where conventional configuration interaction techniques cannot be used. However, the calculated energies may differ by some tens of eV. Therefore, these methods can be employed to get a qualitative idea of how important correlation effects are, but they have some limitations if accurate binding energies are to be obtained.