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An important feature of panel data is that it allows the estimation of parameters characterizing dynamics from individual level data. Several authors argue that such parameters can also be identified from repeated cross-section data and present estimators to do so. This paper reviews the identification conditions underlying these estimators. As grouping data to obtain a pseudo-panel is an application of instrumental variables (IV), identification requires that standard IV conditions are met. This paper explicitly discusses the implications of these conditions for empirical analyses. We also propose a computationally attractive IV estimator that is consistent under essentially the same conditions as existing estimators. While a Monte Carlo study indicates that this estimator may work well under relatively weak conditions, these conditions are not trivially satisfied in applied work. Accordingly, a key conclusion of the paper is that these estimators cannot be implemented under general conditions. JEL classification: C21; C23; C81 Keywords: Repeated cross-sections; Pseudo-panel data; Cohorts; Instrumental variables; Individual dynamics

This paper deals with the testing of autoregressive conditional duration (ACD) models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non-parametric estimates. We derive the asymptotic justification using the functional delta method for fixed and gamma kernels, and then investigate the finite-sample properties through Monte Carlo simulations. Although our tests display some size distortion, bootstrapping suffices to correct the size without compromising their excellent power. We show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns. JEL classification: C14; C41; C52 Keywords: Duration models; Gamma kernel; Hazard rate; Specification testing

The linear and nonlinear seemingly unrelated regression problem with general error distribution is analyzed using recent likelihood theory that arguably provides the definitive distribution for assessing a scalar parameter; this involves implicit but well defined conditioning and marginalization for determining intrinsic measures of departure. Highly accurate p-values are obtained for the key difference between two regression coefficients of central interest. The p-value gives the statistical position of the data with respect to the key parameter. The theory and the results indicate that this methodology provides substantial improvement on first-order likelihood procedures, both in distributional accuracy, and in precise measurement of the key parameter. JEL classification: C1; C3 Keywords: Asymptotics; Conditioning; Likelihood; p-value; SUR

This paper studies analogs of Granger's representation theorem in the context of a general nonlinear vector autoregressive error correction model. The model allows for nonlinear autoregressive conditional heteroskedasticity and the conditional distribution involved can be a mixture distribution of a rather general type. Mixture models of this kind can be thought of as generalizations of threshold models and they have attracted attention in the recent time series and econometrics literature. The paper develops a useful transformation which shows how the nonlinear error correction model can be transformed to a nonlinear vector autoregressive model so that available results on the stationarity or nonstationarity of the latter can be used for the former. The most satisfactory results are obtained in a model in which a specific structural relation between the nonlinearity and equilibrium correction prevails. Without this structural relation only a lower bound for the number of long-run equilibrium relations can explicitly be determined because the exact number depends on properties of the first and second moments of a nonlinear stationary component of the process. JEL classification: C32 Keywords: Cointegration; Mixing; Nonlinear error correction; Nonstationarity; Stationarity

Within a flexible regression model (J.D. Hamilton, Econometrica 69 (3) (2001) 537) we offer a battery of new Lagrange multiplier statistics that circumvent the problem of unidentified nuisance parameters under the null hypothesis of linearity and that are robust to the specification of the covariance function that defines the random field. These advantages are the result of (i) switching from the [L.sub.2] to the [L.sub.1] norm; and (ii) assuming that the random field is sufficiently smooth for its covariance function to be locally approximated by a high order Taylor expansion. A Monte Carlo simulation suggests that our statistics have superior power performance on detecting bilinear, neural network, and smooth transition autoregressive specifications. We also provide an application to the Industrial Production Index of sixteen OECD countries. JEL classification: C12; C15; C22 Keywords: Flexible regression; Random field; Neglected nonlinearity

This paper re-visits the problem of estimating the regression error variance in a linear multiple regression model after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances. There is an extensive literature that discusses these problems, particularly in terms of the sampling properties of the pre-test estimators using various loss functions as the basis for risk analysis. In this paper, a unified framework for analysing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first-order differentiable losses. Particular consideration is given to the choice of critical values for the pre-tests. Analytical results indicate that an [alpha]-level substantially higher than those normally used may be appropriate for optimal risk properties under a wide range of loss functions. The paper also generalizes some known analytical results in the pre-test literature and proves other results only previously shown numerically. JEL classification: C12; C13 Keywords: Entropy loss; First-order differentiable; Lebesgue integrable; Linear restrictions; LINEX loss; Quadratic loss; Risk; Variance homogeneity

We extend the maximum likelihood estimation method of Ait-Sahalia (Econometrica 70 (2002) 223) for time-homogeneous diffusions to time-inhomogeneous ones. We derive a closed-form approximation of the likelihood function for discretely sampled time-inhomogeneous diffusions, and prove that this approximation converges to the true likelihood function and yields consistent parameter estimates. Monte Carlo simulations for several financial models reveal that our method largely outperforms other widely used numerical procedures in approximating the likelihood function. Furthermore, parameter estimates produced by our method are very close to the parameter estimates obtained by maximizing the true likelihood function, and superior to estimates obtained from the Euler approximation. JEL classification: C0; C1; C4; G0 Keywords: Maximum likelihood estimation; Time-inhomogeneous diffusion; Transition density; Hermite expansion

Econometric interest in the possibility of long memory has developed, as a flexible alternative to or compromise between the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We introduce a broad class of such semiparametric estimates that also covers pooling across frequencies. A leading 'Box-Cox' sub-class, indexed by a single tuning parameter, interpolates between the popular local log-periodogram and local Whittle estimates, leading to a smooth interpolation of asymptotic variances. The bias of these two estimates also differs to higher order, and we also show how bias, and asymptotic mean-squared error, can be reduced, across the class of estimates studied, by means of a suitable version of higher-order kernels. We thence calculate an optimal bandwidth (the number of low-frequency periodogram ordinates employed) which minimizes this mean-squared error. Finite sample performance is studied in a small Monte Carlo experiment, and an empirical application to intra-day foreign exchange returns is included. JEL classification: C22 Keywords: Long memory; Semiparametric methods; Higher-order kernel; M-estimation; Bias; Mean-squared error

This paper considers index models, such as simple neural network models and smooth transition regressions, with integrated regressors. The models can be used to analyze various nonlinear relationships among nonstationary economic time series. Asymptotics for the nonlinear least squares (NLS) estimator in such models are fully developed. The estimator is shown to be consistent with a convergence rate that is a mixture of [n.sup.3/4], [n.sup.1/2] and [n.sup.1/4] for simple neural network models, and of [n.sup.5/4], n, [n.sup.3/4] and [n.sup.1/2] for smooth transition regressions. Its limiting distribution is also obtained. Some of its components are mixed normal, with mixing variates depending upon Brownian local time as well as Brownian motion. However, it also has nonGaussian components. It is in particular shown that applications of usual statistical methods in such models generally yield inefficient estimates and/or invalid tests. We develop a new methodology to efficiently estimate and to correctly test in those models. A simple simulation is conducted to investigate the finite sample properties of the (NLS) estimators and the newly proposed efficient estimators. JEL classification: C22; C45 Keywords: Index model; Integrated time series; Neural network model; Smooth transition regression; Brownian motion and Brownian local time

We establish relationships between certain Bayesian and classical approaches to instrumental variable regression. We determine the form of priors that lead to posteriors for structural parameters that have similar properties as classical 2SLS and LIML and in doing so provide some new insight, especially in the context of weak instruments, to the small sample behavior of Bayesian and classical procedures. Using a reduced rank restriction on a multivariate linear model, we determine the priors that give rise to posteriors that are identical in functional form to the sampling densities of the classical 2SLS and LIML estimators. JEL classification: C11; C20 Keywords: Diffuse prior; Instrumental variables; Posterior distributions; Reduced rank; Weak instruments

Previous papers estimate base-independent equivalence scales and test base-independence using strict parametric assumptions on Engel curves and equivalence scale functions. These parametric tests reject the hypothesis of base independence. I construct a semiparametric estimator of a household equivalence scale under the assumption of base independence without putting any further restrictions on the shape of household Engel curves. This estimator uses cross-equation restrictions on a system of estimated nonparametric engel curves to identify equivalence scale parameters. I test the hypothesis of base independence against a fully nonparametric alternative and find that preferences are consistent with the existence of a base-independent equivalence scale for some interhousehold comparisons. Keywords: Equivalence scales; Semiparametric estimation; Household demand

For hypotheses on the coefficient values of the lagged-dependent variables in the ARX class of dynamic regression models, test procedures are developed which yield exact inference for given (up to an unknown scale factor) distribution of the innovation errors. They include exact tests on the maximum lag length, for structural change and on the presence of (seasonal or multiple) unit roots, i.e. they cover situations where usually asymptotic and non-exact t, F, AOC, ADF or HEGY tests are employed. The various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed. Key words: ARX model; Exact inference; Monte Carlo test; Order of dynamics; Structural change; Unit root

Computer-intensive bootstrap methods are potentially problematic when applied to biased estimators similar to ridge regression, because biased estimators may lack a pivot. We propose a modification for Efron's bias corrected percentiles and suggest an approximate pivoting transformation for ridge regression. We indicate practical aspects of Beran's double bootstrap designed specifically for situations where there is nonnormality and a lack of a pivot. Econometric applications to estimating consumption functions, a simulation with multicollinear data and new graphical tools are included. Key words: Pivot; Ridge regression; Confidence intervals; Nonnormality; Graphics JEL classification: C10; C20; C52; C8

In panel data four procedures are widely used: pooling, aggregating, averaging group estimates, and cross-section regression. In the static case, if the coefficients differ randomly, all four procedures give unbiased estimates of coefficient means. In the dynamic case, when the coefficients differ across groups, pooling and aggregating give inconsistent and potentially highly misleading estimates of the coefficients, though the cross-section can provide consistent estimates of the long-run effects. The theoretical results on the properties of the four procedures are illustrated by UK labour demand functions for 38 industries over 30 years. Key words: Dynamic panels; Parameter heterogeneity; Data fields; Sectoral employment equations JEL classification: C13; C21; C22; C23

In this paper we construct a number of quality-adjusted price indexes for personal computers in the US marketplace over the 1989-92 time period. We generalize earlier work by incorporating simultaneously the time, age, and vintage effects of computer models and then develop a corresponding specification test procedure. When data on new and surviving models are used in the estimation of hedonic price equations, a variety of quality-adjusted price indexes decline at about 30% per year, with a particularly large price drop occurring in 1992. We conclude that taking quality changes into account has an enormous impact on the time pattern of price indexes for PC's. Key words: Personal computers; Price indexes; Hedonics; Panel data; Divisia index JEL classification: C23; C43; L63

This paper develops a framework for analyzing forecast errors in a panel data setting. The framework provides the means (1) to test for forecast rationality when forecast errors are simultaneously correlated across individuals, across target years, and across forecast horizons using Generalized Method of Moments estimation, (2) to discriminate between forecast errors which arise from unforecastable macroeconomic shocks and forecasts errors which arise from idiosyncratic errors, (3) to measure monthly aggregate shocks and their volatilities independent of data revisions and prior to the actual being realized, and (4) to test for the impact of 'news' on volatility. We use the Blue Chip Survey of Professional Forecasts over the period July 1976 through May 1992 to implement the methodology. Key words: Rational expectations; Aggregate shocks; News; Volatility; GMM estimation; Blue chip survey; Panel data JEL classification: C23; C53; C82; E17; E37

Shively, Ansley, and Kohn (1990) given an O(n) algorithm for computing the p-values of the Durbin - Watson and other invariant test statistics in time series regression. They do so by evaluating the characteristic function of a quadratic form in standard normal random variables and then numerically inverting it. In this paper we obtain a new expression for the characteristic function which simplifies the handling of the independent regressors and so is easier to evaluate. We also obtain general, easily computable bounds on the integration and truncation errors which arise in the numerical inversion of the characteristic function. Empirical results are presented on the speed and accuracy of our algorithm.

Pantula and Hall (1991) proposed instrumental variable based tests for a unit root in an ARMA (p + 1, q) time series under the assumption that (p, q) are known. In this paper we derive conditions under which the Pantula - Hall tests still converge to the Dickey - Fuller distributions when (p, q) are chosen from the data. We propose a simple residual based statistic which can be used to estimate (p, q) and derive conditions under which the asymptotic distribution of the ensuing unit root test are unaffected by this method of choosing (p, q). We also compare the local power properties of a number of unit root tests.

Methods based on linear regression provide an easy way to use the information in control variates to improve the efficiency with which certain features of the distributions of estimators and test statistics are estimated in Monte Carlo experiments. We propose a new technique that allows these methods to be used when the quantities of interest are quantiles. We also propose new ways to obtain approximately optimal control variates in many cases of interest. These methods seem to work well in practice, and can greatly reduce the number of replications required to obtain a given level of accuracy.

The Breusch - Pagan test is a popular test for testing zero variances in a random error component model. Realizing the one-sided nature of this problem, Honda (1985) derived the one-sided LM test for the one-way error component model, and suggested a 'handy' one-sided candidate for the two-way error component model. In this paper, we derive a new one-sided test for testing the two-way error component model based upon the results of Gourieroux, Holly, and Monfort (1982). Next, we derive a LM test for testing zero individual (time-specific) effects assuming that the other time period (individual) effects are present. This is in contrast to the usual LM test which assumes that, under the null hypothesis, both effects are absent. Exact power comparisons (whenever possible) as well as Monte Carlo experiments are employed to compare the performance of these tests with the corresponding likelihood ratio and ANOVA F tests.

This paper develops an asymptotic theory of estimation and inference in 'cointegrated' regression models with errors displaying nonstationary variances. Least squares estimates are shown to be consistent at a T to the 1/2 rate. Hypothesis testing requires the use of a robust covariance matrix estimate, in contrast to earlier work on cointegrated regressions. The inference theory is not nuisance-free, but preliminary investigations indicate that approximation by the normal distribution may be adequate in practice.

Although volatility clustering has a long history as a salient empirical regularity characterizing high-frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of explicitly modeling time-varying second-order moments. Instrumental in most of these empirical studies has been the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982). This paper contains an overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data. Several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and the pricing of derivative assets, are also discussed.

The error correction model for seasonal cointegration is analyzed. Conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given. The likelihood function is analyzed and the numerical calculation of the maximum likelihood estimators is discussed. The asymptotic distribution of the likelihood ratio test for cointegrating rank is given. It is shown that the estimated cointegrating vectors are asymptotically mixed Gaussian. The results resemble the results for cointegration at zero frequency when expressed in terms of a complex Brownian motion. Tables are provided for asymptotic inference. Keywords: Autoregressive process; Granger's theorem; Error correction model; Complex Brownian motion

The paper develops Markov Chain Monte Carlo methods to perform exact posterior analysis in models with symmetric stable Paretian disturbances. It is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a Gibbs sampler with Metropolis independence chains. The new method is shown to perform satisfactorily in constructed examples. The method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution. Keywords: Bayesian inference; Stable distributions; Markov chain Monte Carlo; Exchange rate models; Difference stationarity

This paper introduces various consistent tests for the null of stationarity against the alternative of nonstationarity applicable to multiple time series with and without the presence of time trends. The tests are based on the multivariate AR(1) model and derived by the principles of AR unit root tests. An important feature of the tests from the practical viewpoint is that no a priori knowledge about the data generating process of the series under study is required when the lag length for the long-run variance estimation is estimated by using Andrews (1991 Econometrica 59, 812-858) automatic lag selection methods along with a simple inequality restriction. This simple restriction also make the tests diverge at faster rates. The asymptotic distributions of these tests are complex and nonstandard but expressed in a unified manner by using the standard vector Brownian motion. The distributions are tabulated by simulation for some practical cases. The rates of divergence under the alternative are also reported. Further, the asymptotic effects of misspecifying the order of time trends in the regression model are analyzed. Using the regression model which does not detrend time series properly results in rejecting the null hypothesis in large samples even when the null is true. Extensive simulation illustrates the finite same performance of the tests introduced in this paper. The multivariate tests using Andrews' automatic lag selection methods with a restriction work reasonably well in finite samples. In particular, it is illustrated that using the multivariate tests introduced in this paper is a better testing strategy for detrended time series in terms of the finite sample size and power than applying univariate tests several times to each component of a multiple time series. The tests are applied to the real interest rates of the major industrialized nations studied in Kugler and Neusser (1993, Journal of Applied Econometrics 8, 163-174), The null of stationarity is not rejected for the real interest rates at conventional significance levels. Keywords: Null of stationery; LM test; Sargan-Bhargava-Durbin-Hausman test; Multiple time series

Using some standard Hilbert space theory a simplified approach to computing efficiency bounds in semiparametric models is presented. We use some interesting examples to illustrate this approach and also obtain some results which seem to be new to the literature. [C] 2001 Elsevier Science S.A. All rights reserved. JEL classification: C14 Keywords: Efficiency bounds; Semiparametric models