This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not identified if and only if an independent normally distributed linear combination of regressors can be transferred from the regressors to the errors. Second, we introduce a new estimator for the coefficients using a continuum of moments that are based on second derivatives of the log characteristic function of the observables. In Monte Carlo simulations, the estimator performs well and is robust to the amount of measurement error and number of mismeasured regressors. In an application to firm investment decisions, the estimates are similar to those produced by a generalized method of moments estimator based on third to fifth moments.

We generalize the cumulative sum of squares (CUSQ) test to the case of nonstationary autoregressive distributed lag models with deterministic time trends. The test may be implemented with either ordinary least squares residuals or standardized forecast errors. In explosive cases the asymptotic theory applies more generally for the least squares residuals-based test. Preliminary simulations of the tests suggest a very modest difference between the tests and a very modest variation with nuisance parameters. This supports the use of the tests in explorative analysis.

Despite the fact that it is not correct to speak of Bartlett corrections in the case of nonstationary time series, this paper shows that a Bartlett-type correction to the likelihood ratio test for a unit root can be an effective tool to control size distortions. Using well-known formulae, we obtain second-order (numerical) approximations to the moments and cumulants of the likelihood ratio, which makes it possible to calculate a Bartlett-type factor. It turns out that the cumulants of the corrected statistic are closer to their asymptotic value than the original one. A simulation study is then carried out to assess the quality of these approximations for the first four moments; the size and the power of the original and the corrected statistic are also simulated. Our results suggest that the proposed correction reduces the size distortion without affecting the power too much.

This paper shows that nonparametric identification of latent competing risks models is possible without the usual conditional independence and exclusion restrictions.The authors thank Jinyong Hahn, James Heckman, and Shinichi Sakata for useful discussions on the subject matter of this paper. Any errors are the fault of the authors. Research funding for Rilstone was provided by the Social Sciences and Humanities Research Council of Canada.

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than the domains that have been considered in the existing literature, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring it to satisfy only certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

This paper motivates, exposits, and develops the variable augmentation specification test (VAST) approach from the perspective of generalized linear exponential family, which includes several parametric families widely used in applied econometrics and statistics. The approach is equivalent to score tests and link tests and serves to both unify and simplify the computation of score tests in such models using the Engle-Davidson-MacKinnon technique of artificial regression. Specification tests for both the mean and the variance components are treated symmetrically. Several theoretical applications are discussed.

This paper examines the implications of applying the Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238) (HEGY) seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered, where the zero-frequency unit root t-statistic is shown to converge to the Dickey–Fuller distribution and all seasonal unit root statistics diverge. For periodically integrated processes and a sufficiently high order of augmentation, the HEGY t-statistics for unit roots at the zero and semiannual frequencies both converge to the same Dickey–Fuller distribution. Further, the HEGY joint test statistic for a unit root at the annual frequency and all joint test statistics across frequencies converge to the square of this distribution. Results are also derived for a fixed order of augmentation. Finite-sample Monte Carlo results indicate that, in practice, the zero-frequency HEGY statistic (with augmentation) captures the single unit root of the periodic integrated process, but there may be a high probability of incorrectly concluding that the process is seasonally integrated.

Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditional on the covariates. The impact of the covariates is modelled by an additive model where each component can be written as a linear combination of possibly unknown functions. The focus is on prediction as opposed to variable screening. Conditions are imposed on the coefficients of this linear combination in order to control the estimation error. The rates of convergence are optimal when the number of active covariates is large. As an application, the intensity of the buy and sell trades of the New Zealand Dollar futures is estimated and a test for forecast evaluation is presented. A simulation is included to provide some finite sample intuition on the model and asymptotic properties.

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

This paper considers tests in an instrumental variable (IVs) regression model with IVs that may be weak. Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock (2006, Econometrica 74, 715–752). In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests. Tests with such properties are obtained by introducing rank tests that are analogous to the conditional likelihood ratio test of Moreira (2003, Econometrica 71, 1027–1048). We also introduce a rank test that is analogous to the Lagrange multiplier test of Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, manuscript, University of California, Berkeley).Andrews gratefully acknowledges the research support of the National Science Foundation via grant SES-0417911.

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purposes, we find that the maximum score estimator and smoothed maximum score estimator are at least [square root of n]-consistent. Comparing this rate to the convergence rate of the parametric maximum likelihood estimator (MLE), we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000, Econometrica 68, 1249–1280) parametric MLE converges at a rate of n3/4 and its limiting distribution is a mixed normal. Finally, we show briefly how to apply our estimation method to a nonstationary single-index model.The first draft of the paper was written while Guerre was visiting the economics department of the University of Southern California. We thank Peter C.B. Phillips, a co-editor, and three anonymous referees for helpful comments and John Dolfin for proofreading. Guerre thanks the economics department of the University of Southern California for its hospitality during his visit. Moon appreciates financial support of the University of Southern California faculty development award.

The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (1999, Review of Economics and Statistics 81, 594–607) achieves a second order refinement in the local-to-unity asymptotic approach when compared with a modified version of Stock’s (1991, Journal of Monetary Economics 28, 435–459) and Andrews’ (1993, Econometrica 61, 139–165) grid testing procedures. We establish a second order expansion of the t-statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.

The properties of dynamic conditional correlation (DCC) models, introduced more than a decade ago, are still not entirely known. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a nondegenerate diffusion limit can be obtained. Alternative sets of conditions are considered for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the often used quasi-approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may provide reasonable approximations for sufficiently large frequencies and sample sizes.

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(α) tests, as in Neyman (1959), and shown to be locally asymptotically optimal. These C(α) tests will be contrasted with a new approach to likelihood ratio testing for general mixture models. The latter tests are based on estimation of general nonparametric mixing distribution with the Kiefer and Wolfowitz (1956) maximum likelihood estimator. Recent developments in convex optimization have dramatically improved upon earlier EM methods for computation of these estimators, and recent results on the large sample behavior of likelihood ratios involving such estimators yield a tractable form of asymptotic inference. Improvement in computation efficiency also facilitates the use of a bootstrap method to determine critical values that are shown to work better than the asymptotic critical values in finite samples. Consistency of the bootstrap procedure is also formally established. We compare performance of the two approaches identifying circumstances in which each is preferred.