We consider an additive model with second-order interaction terms. Both marginal integration estimators and a combined backfitting-integration estimator are proposed for all components of the model and their derivatives. The corresponding asymptotic distributions are derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions and local power results are obtained. Because direct implementation of the test procedure based on the asymptotics would produce inaccurate results unless the number of observations is very large, a bootstrap procedure is provided, which is applicable for small or moderate sample sizes. Further, based on these methods a general test for additivity is developed. Estimation and testing methods are shown to work well in simulation studies. Finally, our methods are illustrated on a five-dimensional production function for a set of Wisconsin farm data. In particular, the separability hypothesis for the production function is discussed.

Least squares estimation has casually been dismissed as an inconsistent estimation method for mixed regressive, spatial autoregressive models with or without spatial correlated disturbances. Although this statement is correct for a wide class of models, we show that, in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can be consistent. Indeed, they can even be asymptotically efficient relative to some other estimators. Their computations are easier than alternative instrumental variables and maximum likelihood approaches.

The measurement error problem that we consider in this paper is concerned with the situation where time series data of various kinds—short memory, long memory, and random walk processes—are contaminated by white noise. We suggest a unified approach to testing for the existence of such noise. It is found that the power of our test crucially depends on the underlying process.

Standard methods for analyzing linear-latent variable models rely on the assumption that the observed variables are normally distributed. Normality allows statistical inferences to be carried out based solely on the first-and second-order moments. In general, inferences for nonnormally distributed data require the estimates of matrices of third-and fourth-order moments. In the present paper, we show that inferences based on normal theory retain validity and asymptotic efficiency under general assumptions that allow for considerable departure from normality. In particular, we obtain conditions under which correct asymptotic inferences are attained when replacing a matrix of higher order moments by a matrix that depends only on cross-product moments of the data.

Unit root tests for time series with level shifts of general form are considered when the timing of the shift is unknown. It is proposed to estimate the nuisance parameters of the data generation process including the shift date in a first step and apply standard unit root tests to the residuals. The estimation of the nuisance parameters is done in such a way that the unit root tests on the residuals have the same limiting distributions as for the case of a known break date. Simulations are performed to investigate the small sample properties of the tests, and empirical examples are discussed to illustrate the procedure.

This paper proposes robust M-estimators of dynamic linear models with a structural break of unknown location. Rates of convergence and limiting distributions for the estimated shift point and the estimated regression parameters are derived. The analysis is carried out in the framework of possibly dependent observations and also with trending regressors. The asymptotic distribution of the break location estimator is obtained both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases. The latter is essential for the derivation of feasible confidence intervals for the break location. Monte Carlo simulations illustrate the performance of asymptotic inferences in practice.

This paper considers a continuous time unobserved components model in which the cyclical component follows a differential-difference equation whereas the trend and seasonal components follow more standard differential equations. Estimation of the parameters of the model with either a stock or a flow variable is analyzed using a frequency domain Gaussian estimator whose asymptotic properties are derived paying particular attention to the role of a truncation parameter that arises in the practical computation of the spectral density function. The results of a simulation exercise, which assesses the finite sample performance of the estimator, are also provided.

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form and holds almost surely for all sample realizations. Our development relies upon the strong approximation and the Beveridge–Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickey–Fuller unit root tests for the model driven by a general linear process with independent and identically distributed innovations. We thus provide a theoretical justification on the use of the bootstrap Dickey–Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.

This paper considers generalized method of moment–type estimators for which a criterion function is minimized that is not the “standard” quadratic distance measure but instead is a general Lp distance measure. It is shown that the resulting estimators are root-n consistent but not in general asymptotically normally distributed, and we derive the limit distribution of these estimators. In addition, we prove that it is not possible to obtain estimators that are more efficient than the “usual” L2-GMM estimators by considering Lp-GMM estimators. We also consider the issue of the choice of the weight matrix for Lp-GMM estimators.

The Wald test for linear restrictions on cointegrating vectors is compared in finite samples using the Monte Carlo method. The Wald test is calculated within the vector error-correction based estimation methods of Bewley, Orden, Yang, and Fisher (1994, Journal of Econometrics 64, 3–27) and of Johansen (1991, Econometrica 59, 1551–1580), the canonical cointegration method of Park (1992, Econometrica 60, 119–143), the dynamic ordinary least squares method of Phillips and Loretan (1991, Review of Economic Studies 58, 407–436), Saikkonen (1991, Econometric Theory 7, 1–21), and Stock and Watson (1993, Econometrica 61, 783–820), the fully modified ordinary least squares method of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125), and the band spectral techniques of Phillips (1991, in W. Barnett, J. Powell, & G. E. Tauchen (eds.), Nonparametric and Semiparametric Methods in Economics and Statistics, pp. 413–435). The Wald test performance is also compared to that of the likelihood ratio test suggested by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics 52, 169–210) and to a Bartlett correction of that test as proposed by Johansen (1998, A Small Sample Test for Tests of Hypotheses on Cointegrating Vectors, European University Institute).

In this paper a novel partitioned inversion formula is obtained in terms of the orthogonal complements of off-diagonal blocks, with the emblematic matrix of unit-root econometrics emerging as the leading diagonal block of the inverse. The result paves the way to a straightforward derivation of a key result of vector autoregressive econometrics.

In this paper, we first transform a set of moment conditions into a set of transformed moment conditions, based on which the efficient partial generalized method of moments estimation for part of a parameter vector is defined. Given the set of transformed moment conditions, we then show that the conditions for partial redundancy of an additional set of moment conditions given an original set of moment conditions simply become the conditions for full redundancy of the second subset of transformed moment conditions given the first subset of transformed moment conditions. Thus the transformed moment conditions proposed in this paper unify partial redundancy of moment conditions with full redundancy of moment conditions. Using transformed moment conditions, we then straightforwardly derive necessary and sufficient conditions for partial redundancy of one or two subset(s) of moment conditions given the other when the large set of moment conditions consists of three subsets of moment conditions. The paper also provides several easily checkable sufficient conditions for partial redundancy of one set of moment conditions given other sets of moment conditions.