Dealing with noninvertible, infinite-order moving average (MA) models, we study the asymptotic properties of an estimator of the noninvertible coefficient. The estimator is constructed acting as if the data were generated from a Gaussian MA process. Allowing for two cases on the initial values of the error process, we first discuss the condition for the existence of a consistent estimator. We then compute the probability of the estimator occurring at the boundary of the invertibility region. Some approximations are also suggested to the limiting distribution of the normalized estimator.

For a first-order autoregressive process Yt = βYt−1 + ∈t where the ∈t'S are i.i.d. and belong to the domain of attraction of a stable law, the strong consistency of the ordinary least-squares estimator bn of β is obtained for β = 1, and the limiting distribution of bn is established as a functional of a Lévy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the ∈t'S are heavy-tailed.

We consider several issues related to Durbin-Wu-Hausman tests; that is, tests based on the comparison of two sets of parameter estimates. We first review a number of results about these tests in linear regression models, discuss what determines their power, and propose a simple way to improve power in certain cases. We then show how in a general nonlinear setting they may be computed as “score” tests by means of slightly modified versions of any artificial linear regression that can be used to calculate Lagrange multiplier tests, and explore some of the implications of this result. In particular, we show how to create a variant of the information matrix test that tests for parameter consistency. We examine the conventional information matrix test and our new version in the context of binary-choice models, and provide a simple way to compute both tests using artificial regressions.

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breen's formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

The main aim of the paper is to reevaluate the methodological contributions of Tinbergen and Haavelmo in the context of the current discussions on econometric modeling and propose a reformulation of the Haavelmo methodology. The paper argues that the textbook methodology constitutes a less flexible version of Tinbergen's approach and apart from the probabilistic language, it has little in common with the methodology in Haavelmo's 1944 monograph, commonly acknowledged as having founded modern econometrics. The methodology in this monograph includes several important elements which have either been discarded or never fully integrated within the textbook approach. A re-synthesis of these elements gives rise to an alternative methodological framework. This framework can be used to meet most of the objections to the textbook methodology and provides a framework in the context of which the recent methodological controversies can be evaluated.

The large-sample behavior of one-period-ahead and multiperiod-ahead predictors for a dynamic nonlinear simultaneous system is examined in this paper. Conditional on final values of the endogenous variables, the asymptotic moments of the deterministic, closed-form, Monte Carlo stochastic, and several variations of the residual-based stochastic predictor are analyzed. For one-period-ahead prediction, the results closely parallel our previous findings for static nonlinear systems. For multiperiod-ahead prediction similar results hold, except that the effective number of sample-period residuals available for use with the residual-based predictor is T/m, where T denotes sample size. In an attempt to avoid the problems associated with sample splitting, the complete enumeration predictor is proposed which is a multiperiod-ahead generalization of the one-period-ahead residual-based predictor. A bootstrap predictor is also introduced which is similar to the multiperiod-ahead Monte Carlo except disturbance proxies are drawn from the empirical distribution of the residuals. The bootstrap predictor is found to be asymptotically inefficient relative to both the complete enumeration and Monte Carlo predictors.