Estimation and Inference in Models of Cointegration: A Simulation Study

This paper studies the finite sample distributions of estimators of the cointegrating vector of linear regression models with I(1) variables. Attention is concentrated on the least squares (OLS) and instrumental variables (IV) methods analyzed in other recent work (Phillips and Hansen (1988)). The general preference of OLS to IV techniques suggested by asymptotic theory is reinforced by our simulations. An exception arises for cases of low signal to noise, where spurious IV techniques (so named for their use of instruments that are structurally unrelated to the model) outperform uncorrected least squares. We verify the presence of a small sample estimation bias and show that the Park-Phillips bias correction does reduce the magnitude of this problem. We also find that there is substantial distributional divergence of t-statistics from the normal, unless the Phillips-Hansen endogeneity correction is used. Finally, we apply these methods to aggregate consumption and income data. Our empirical results indicate that the endogeneity and serial dependence connections are important and lead to intuitively plausible changes in the estimated coefficients

Statistical Inference in Instrumental Variables Regression with I(1) Processes

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions. The framework of study is based on earlier work by Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). In particular, the results in these papers are extended to allow for IV regressions that accommodate deterministic and stochastic regressors as well as quite general deterministic processes in the data generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a beneficial artifact of spurious regression theory whereby stochastic trends in the instruments ensure their relevance asymptotically. Problems of inference are also addressed and some promising new theoretical results are reported. These involve a class of Wald tests which are modified by semiparametric corrections for serial correlation and for endogeneity. The resulting test statistics which we term fully modified Wald tests have limiting chi-squared distributions, thereby removing the obstacles to inference in cointegrated systems that were presented by the nuisance parameter dependencies in earlier work. Interestingly, IV methods themselves are insufficient to achieve this end and an endogeneity correction is still generally required, again in contrast to traditional theory. Our results therefore provide strong support for the conclusion reached by Hendry (1986) that there is no free lunch in estimating cointegrated systems. Some simulation results are reported which seek to explore the sampling behavior of our suggested procedures. These simulations compare our fully modified (semiparametric) methods with the parametric error correction methodology that has been extensively used in recent empirical research and with conventional least squares regression. Both the fully modified and error correction methods work well in finite samples and the sampling performance of each procedure confirms the relevance of asymptotic distribution theory, as distinct from superconsistency results, in discriminating between different statistical methods

Sorption of dissolved organic C and P to agricultural top- and subsoil

In order to study the mobility of dissolved organic carbon (DOC) and dissolved organic P (DOP) in soil, the pH-dependent sorption of dissolved organic matter to an agricultural top- and subsoil was investigated. In general, sorption isotherms had convex shapes and DOC and DOP sorption increased with time of reaction. There was a very pronounced effect of pH resulting in much higher sorption of DOC at pH 5 than at pH 7; actually extensive desorption was observed at pH 7 especially for the topsoil. Similar sorption patterns were observed for DOP, but they were not as pronounced as for DOC

Bias in Estimating Multivariate and Univariate Diffusions

Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006</p

Temperature and Polarization Patterns in Anisotropic Cosmologies

We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.Comment: 24 pages, 7 Figures, submitted to JCAP. Revised version: numerous references added, text rewritten, and errors corrected

On the stability of the shear-free condition

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear-free condition. The specific case of geodesic fluids is considered in detail, showing that the shear-free condition, in this particular case, may be unstable, the departure from the shear-free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.Comment: 19 pages Latex. To appear in Gen. Rel. Gra