This paper studies the estimation of a semi-strong GARCH(1,1) model when it does not have a stationary solution, where semi-strong means that we do not require the errors to be independent over time. We establish necessary and sufficient conditions for a semi-strong GARCH(1,1) process to have a unique stationary solution. For the nonstationary semi-strong GARCH(1,1) model, we prove that a local minimizer of the least absolute deviations (LAD) criterion converges at the rate to a normal distribution under very mild moment conditions for the errors. Furthermore, when the distributions of the errors are in the domain of attraction of a stable law with the exponent κ ∈ (1, 2), it is shown that the asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is non-Gaussian but is some stable law with the exponent κ ∈ (0, 2). The asymptotic distribution is difficult to estimate using standard parametric methods. Therefore, we propose a percentile-t subsampling bootstrap method to do inference when the errors are independent and identically distributed, as in Hall and Yao (2003). Our result implies that the least absolute deviations estimator (LADE) is always asymptotically normal regardless of whether there exists a stationary solution or not, even when the errors are heavy-tailed. So the LADE is more appealing when the errors are heavy-tailed. Numerical results lend further support to our theoretical results.

Additive coefficient model (Xue and Yang, 2006a, 2006b) is a flexible regression and autoregression tool that circumvents the “curse of dimensionality.” We propose spline-backfitted kernel (SBK) and spline-backfitted local linear (SBLL) estimators for the component functions in the additive coefficient model that are both (i) computationally expedient so they are usable for analyzing high dimensional data, and (ii) theoretically reliable so inference can be made on the component functions with confidence. In addition, they are (iii) intuitively appealing and easy to use for practitioners. The SBLL procedure is applied to a varying coefficient extension of the Cobb-Douglas model for the U.S. GDP that allows nonneutral effects of the R&D on capital and labor as well as in total factor productivity (TFP).

A kernel weighted version of the standard realized integrated volatility estimator is proposed. By different choices of the kernel and bandwidth, the measure allows us to focus on specific characteristics of the volatility process. In particular, as the bandwidth vanishes, an estimator of the realized spot volatility is obtained. We denote this the filtered spot volatility. We show consistency and asymptotic normality of the kernel smoothed realized volatility and the filtered spot volatility. We consider boundary issues and propose two methods to handle these. The choice of bandwidth is discussed and data-driven selection methods are proposed. A simulation study examines the finite sample properties of the estimators.

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.

This paper develops new estimation and inference procedures for dynamic panel data models with fixed effects and incidental trends. A simple consistent GMM estimation method is proposed that avoids the weak moment condition problem that is known to affect conventional GMM estimation when the autoregressive coefficient (ρ) is near unity. In both panel and time series cases, the estimator has standard Gaussian asymptotics for all values of ρ ∈ (−1, 1] irrespective of how the composite cross-section and time series sample sizes pass to infinity. Simulations reveal that the estimator has little bias even in very small samples. The approach is applied to panel unit root testing.

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.

In this paper, we extend the GMM framework for the estimation of the mixed-regressive spatial autoregressive model by Lee(2007a) to estimate a high order mixed-regressive spatial autoregressive model with spatial autoregressive disturbances. Identification of such a general model is considered. The GMM approach has computational advantage over the conventional ML method. The proposed GMM estimators are shown to be consistent and asymptotically normal. The best GMM estimator is derived, within the class of GMM estimators based on linear and quadratic moment conditions of the disturbances. The best GMM estimator is asymptotically as efficient as the ML estimator under normality, more efficient than the QML estimator otherwise, and is efficient relative to the G2SLS estimator.

Most work in the area of nonlinear econometric modeling is based on a single equation and assumes exogeneity of the explanatory variables. Recently, work by Caner and Hansen (2004) and Psaradakis, Sola, and Spagnolo (2005) has considered the possibility of estimating nonlinear models by methods that take into account endogeneity but provide no tests for exogeneity. This paper examines the problem of testing for exogeneity in nonlinear threshold models. We suggest new Hausman-type tests and discuss the use of the bootstrap to improve the properties of asymptotic tests. The theoretical properties of the tests are discussed and an extensive Monte Carlo study is undertaken.

This paper considers the extension of the classical minimum distance approach for the pooling of estimates with various rates of convergence. Under a setting where relatively high rates of convergence can be attained, the minimum distance estimators are shown to be consistent and asymptotically normally distributed. The constrained estimates can be efficient relative to the unconstrained ones. The minimized distance function is shown to be asymptotically χ2-distributed, and can be used as a goodness-of-fit test for the constraints. As the extension is motivated by some social interactions models, which are of interest in their own right, we discuss this approach for the estimation and testing of a social interactions model.

Many regression models have two dimensions, say time (t = 1,…,T) and households (i = 1,…,N), as in panel data, error components, or spatial econometrics. In estimating such models we need to specify the structure of the error variance matrix Ω, which is of dimension T N × T N. If T N is large, then direct computation of the determinant and inverse of Ω is not practical. In this note we define structures of Ω that allow the computation of its determinant and inverse, only using matrices of orders T and N, and at the same time allowing for heteroskedasticity, for household- or station-specific autocorrelation, and for time-specific spatial correlation.

In this note we derive the local asymptotic power function of the standardized averaged Dickey–Fuller panel unit root statistic of Im, Pesaran, and Shin (2003, Journal of Econometrics, 115, 53–74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the magnitude of the initial conditions increases, in direct contrast to what is usually observed in the univariate case. Finite-sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.