We propose a semiparametric IGARCH model that allows for persistence in variance but also allows for more flexible functional form. We assume that the difference of the squared process is weakly stationary. We propose an estimation strategy based on the nonparametric instrumental variable method. We establish the rate of convergence of our estimator.

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

In multilevel modeling of clustered survival data, to account for the differences among different clusters, a commonly used approach is to introduce cluster effects, either random or fixed, into the model. Modeling with random effects may lead to difficulties in the implementation of the estimation procedure for the unknown parameters of interest because the numerical computation of multiple integrals may become unavoidable when the cluster effects are not scalars. On the other hand, if fixed effects are used, there is a danger of having estimators with large variances because there are too many nuisance parameters involved in the model. In this article, using the idea of the homogeneity pursuit, we propose a new multilevel modeling approach for clustered survival data. The proposed modeling approach does not have the potential computational problem as modeling with random effects, and it also involves far fewer unknown parameters than modeling with fixed effects. We also establish asymptotic properties to show the advantages of the proposed model and conduct intensive simulation studies to demonstrate the performance of the proposed method. Finally, the proposed method is applied to analyze a dataset on the second-birth interval in Bangladesh. The most interesting finding is the impact of some important factors on the length of the second-birth interval variation over clusters and its homogeneous structure.

New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of marginals. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared with existing procedures involving the multiplier bootstrap.

This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.

This paper proposes a new strategy for the identification of the marginal effects of an endogenous multivalued variable (which can be continuous, or a vector) in a model with an Instrumental Variable (IV) of lower dimension, which may even be a single binary variable, and multiple controls. Despite the failure of the classical order condition, we show that identification may be achieved by exploiting heterogeneity of the “first stage” in the controls through a new rank condition that we term covariance completeness. The identification strategy justifies the use of interactions between instruments and controls as additional exogenous variables and can be straightforwardly implemented by parametric, semiparametric, and nonparametric two-stage least squares estimators, following the same generic algorithm. Monte Carlo simulations show that the estimators have excellent performance in moderate sample sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005, Journal of Political Economy 113, 376–424). All methods are implemented in a companion Stata software package.

In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton–Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are asymptotically equivalent to the infeasible local likelihood estimators [e.g., Aerts and Claeskens (1997) Journal of the American Statistical Association 92, 1536–1545], which require knowledge of the error distribution. Simulation evidence suggests that when the distribution of the error term is different from Gaussian, the adaptive estimators of both conditional mean and variance can often achieve significant efficiency over the conventional local polynomial estimators.

This paper derives the exact distribution and moments of the Stein-ruleestimator in a model where the disturbances follow a non-normal distribution of the Edgeworth or Gram-Charlier type. The results are achieved by combining the approach of Davis [4] for examining non-normality with the fractional calculus techniques of Phillips [11].

The bias-reduced log-periodogram estimator of Andrews and Guggenberger (2003, Econometrica 71, 675–712) for the long-memory parameter d in a stationary long-memory time series reduces the asymptotic bias of the original log-periodogram estimator of Geweke and Porter-Hudak (1983) by an order of magnitude but inflates the asymptotic variance by a multiplicative constant cr, for example, c1 = 2.25 and c2 = 3.52. In this paper, we introduce a new, computationally attractive estimator by taking a weighted average of estimators over different bandwidths. We show that, for each fixed r ≥ 0, the new estimator can be designed to have the same asymptotic bias properties as but its asymptotic variance is changed by a constant cr* that can be chosen to be as small as desired, in particular smaller than cr. The same idea is also applied to the local-polynomial Whittle estimator in Andrews and Sun (2004, Econometrica 72, 569–614) leading to the weighted estimator . We establish the asymptotic bias, variance, and mean-squared error of the weighted estimators and show their asymptotic normality. Furthermore, we introduce a data-dependent adaptive procedure for selecting r and the bandwidth m and show that up to a logarithmic factor, the resulting adaptive weighted estimator achieves the optimal rate of convergence. A Monte Carlo study shows that the adaptive weighted estimator compares very favorably to several other adaptive estimators.We thank a co-editor and three referees for very helpful suggestions. We are grateful for the constructive comments offered by Marc Henry, Javier Hidalgo, and especially Katsumi Shimotsu.

This paper characterizes the bandwidth value (h) that is optimal for estimating parameters of the form , where the conditional density of a scalar continuous random variable V, given a random vector U, , is replaced by its kernel estimator. That is, the parameter η is the expectation of ω inversely weighted by , and it is the building block of various semiparametric estimators already proposed in the literature such as Lewbel (1998), Lewbel (2000b), Honoré and Lewbel (2002), Khan and Lewbel (2007), and Lewbel (2007). The optimal bandwidth is derived by minimizing the leading terms of a second-order mean squared error expansion of an in-probability approximation of the resulting estimator with respect to h. The expansion also demonstrates that the bandwidth can be chosen on the basis of bias alone, and that a simple “plug-in” estimator for the optimal bandwidth can be constructed. Finally, the small sample performance of our proposed estimator of the optimal bandwidth is assessed by a Monte Carlo experiment.

Fixed effects estimation of the population-averaged slopes in a panel data random coefficient model.

It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I(d) with d = O(T−1/2), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests include the rescaled-range test. In this sense, despite its widespread use in empirical work, the rescaled-range test is a poor test for fractional integration.

This paper considers the estimation of the parameters of general systems of stochastic differential-difference equations in which the lag parameters themselves are treated as unknown and are not restricted to be integers and therefore form part of the parameter vector to be estimated. The asymptotic properties of an infeasible frequency domain maximum likelihood estimator are established in addition to those of a feasible version based on truncating an infinite series that arises in the computation of the spectral density function of the observed discrete time series. Precise conditions that the truncation parameter must satisfy for the asymptotic results to hold are provided.We are grateful to Gordon Kemp, Andrew Harvey, the Editor, and two anonymous referees for helpful comments on an earlier version of this paper. Any remaining errors are the sole responsibility of the authors. The first author thanks the Economic and Social Research Council for financial support under grant number R00429434216, and the second author thanks the Leverhulme Trust for financial support in the form of a Philip Leverhulme Prize.

Denis Sargan's intellectual influence in econometrics is discussed and some of his visions for the future of econometrics are considered in this memorial article. One of Sargan's favorite topics in econometric theory was finite sample theory, including both exact theory and various types of asymptotic expansions. We provide some summary discussion of asymptotic expansions of the type that Sargan developed in this field and give explicit representations of Sargan's formula for the Edgeworth expansion in the case of an econometric estimator that can be written as a smooth function of sample moments whose distributions themselves have Edgeworth expansions.Parts of Section 1 were presented in March 2002 in the author's Sargan Lecture at the Royal Economics Society Conference, Warwick, UK. My thanks go to John Chao, David Hendry, Essie Maasoumi, Peter Robinson, and Katsumi Shimotsu for helpful comments on the original version of this paper. I learned the Chinese saying that heads this article from Sainan Jin. Thanks also go to the NSF for research support under grant SES 00-92509.

A student is like green grass and a great teacher is like the spring sun. The benefit from the sun is infinite, and little grass can hardly pay it back, although it tries its best.

—Chinese saying

This paper analyzes the large sample behavior of the seasonal unit root tests of Dickey, Hasza, and Fuller (1984, Journal of the American Statistical Association 79, 355–367) when applied to a series that admits a unit root at the zero but not seasonal spectral frequencies. We show that in such cases the Dickey et al. statistics have nondegenerate limiting distributions. Consequently, there is a nonzero probability that, taken in isolation, they will lead the applied researcher to accept the seasonal unit root null hypothesis and hence, incorrectly, take seasonal differences of the series, even asymptotically. The same conclusion holds if the process displays unit root behavior at any of the zero and/or seasonal frequencies. Our results therefore prove a conjecture made on the basis of Monte Carlo simulation evidence, in Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415–442) that the tests of Dickey et al., unlike those of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), are unable to separate between unit roots at the zero and seasonal frequencies.I thank Peter Burridge, Bruce Hansen, and three anonymous referees for helpful comments on earlier drafts of this paper.

In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 12, 705–723), which is based on the standardized number of crossings of a level of a random walk, is extended in two ways, allowing for a deterministic trend in the process and more general innovations. The test has a well-known standard limit distribution. Monte Carlo experiments revealed the good finite-sample properties of the proposed test.The authors appreciate helpful comments from an anonymous referee. We gratefully acknowledge the financial support of the Ministerio de Ciencia y Tecnología and the Conselleria d'Economia, Hisenda i Innovació, grants BEC2002-03769 and PRIB-2004-10095, respectively.