Nonparametric trending regression with cross-sectional dependence

Panel data, whose series length T is large but whose cross-section size N need not be, are assumed to have a common time trend. The time trend is of unknown form, the model includes additive, unknown, individual-specific components, and we allow for spatial or other cross-sectional dependence and/or heteroscedasticity. A simple smoothed nonparametric trend estimate is shown to be dominated by an estimate which exploits the availability of cross-sectional data. Asymptotically optimal choices of bandwidth are justified for both estimates. Feasible optimal bandwidths, and feasible optimal trend estimates, are asymptotically justified, the finite sample performance of the latter being examined in a Monte Carlo study. A number of potential extensions are discussed.

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss application of our conditions to spatial autoregressive models, and models defined on a regular lattice.

DIAGNOSTIC TESTING FOR COINTEGRATION

We develop a sequence of tests for specifying the cointegrating rank of, possiblyfractional, multiple time series. Memory parameters of observables are treated asunknown, as are those of possible cointegrating errors. The individual test statisticshave standard null asymptotics, and are related to Hausman specification teststatistics: when the memory parameter is common to several series, an estimate ofthis parameter based on the assumption of no cointegration achieves an efficiencyimprovement over estimates based on individual series, whereas if the series arecointegrated the former estimate is generally inconsistent. However, acomputationally simpler but asymptotically equivalent approach, which avoidsexplicit computation of the "efficient" estimate, is instead pursued here. Twoversions of it are initially proposed, followed by one that robustifies to possibleinequality between memory parameters of observables. Throughout, asemiparametric approach is pursued, modelling serial dependence only atfrequencies near the origin, with the goal of validity under broad circumstances andcomputational convenience. The main development is in terms of stationary series,but an extension to nonstationary ones is also described. The algorithm forestimating cointegrating rank entails carrying out such tests based on potentially allsubsets of two or more of the series, though outcomes of previous tests mayrender some or all subsequent ones unnecessary. A Monte Carlo study of finitesample performance is included.Fractional cointegration, Diagnostic testing, Specificationtesting, Cointegrating rank, Semiparametric estimation.

Large-sample inference on spatial dependence

We consider cross-sectional data that exhibit no spatial correlation, but are feared to be spatially dependent. We demonstrate that a spatial version of the stochastic volatility model of financial econometrics, entailing a form of spatial autoregression, can explain such behaviour. The parameters are estimated by pseudo Gaussian maximum likelihood based on log-transformed squares, and consistency and asymptotic normality are established. Asymptotically valid tests for spatial independence are developed.

Denis Sargan: some perspectives.

We attempt to present Denis Sargan’s work in some kind of historical perspective, in two ways. First, we discuss some previous members of the Tooke Chair of Economic Science and Statistics, which was founded in 1859 and which Sargan held. Second, we discuss one of his articles “Asymptotic Theory and Large Models” in relation to modern preoccupations with semiparametric econometrics.

The Distance between Rival Nonstationary Fractional Processes

Asymptotic inference on nonstationary fractional time series models, including cointegrated ones, is proceeding along two routes, determined by alternative definitions of nonstationary processes. We derive bounds for the mean squared error of the difference between (possibly tapered) discrete Fourier transforms under two regimes. We apply the results to deduce limit theory for estimates of memory parameters, including ones for cointegrated errors, with mention also of implications for estimates of cointegrating coefficients.Nonstationary fractional processes, memory parameter estimation, fractional cointegration, rates of convergence.

Nursing education and regulation: international profiles and perspectives

This review of nurse education and regulation in selected OECD countries forms part of ongoing work on contemporary nursing careers and working lives, based at the National Nursing Research Unit, King’s College London. The review was commissioned by the Department of Health to inform their work in considering the UK’s position in relation to the Bologna declaration and changes that may emanate from the implementation of Modernising Nursing Careers (DH 2006). While much of the information in the review was obtained from publications and websites, we also contacted key personnel in most of the countries included for an up-to-date review of developments in their country and would like to thank them all for providing this information

ROBUST COVARIANCE MATRIX ESTIMATION: "HAC" Estimates with Long Memory/Antipersistence Correction

Smoothed nonparametric estimates of the spectral density matrix at zero frequency have been widely used in econometric inference, because they can consistently estimate the covariance matrix of a partial sum of a possibly dependent vector process. When elements of the vector process exhibit long memory or antipersistence such estimates are inconsistent. We propose estimates which are still consistent in such circumstances, adapting automatically to memory parameters that can vary across the vector and be unknown.Covariance matrix estimation, long memory, antipersistence correction, "HAC" estimates, vector process, spectral density.