We take a model selection approach to the question of whether a class of adaptive prediction models (artificial neural networks) is useful for predicting future values of nine macroeconomic variables. We use a variety of out-of-sample forecast-based model selection criteria, including forecast error measures and forecast direction accuracy. Ex ante or real-time forecasting results based on rolling window prediction methods indicate that multivariate adaptive linear vector autoregression models often outperform a variety of (1) adaptive and nonadaptive univariate models, (2) nonadaptive multivariate models, (3) adaptive nonlinear models, and (4) professionally available survey predictions. Further, model selection based on the in-sample Schwarz information criterion apparently fails to offer a convenient shortcut to true out-of-sample performance measures.

This paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables (IV) regression when the available instruments are weak and the number of instruments, Kn, goes to infinity with the sample size. We show that consistent estimation depends importantly on the strength of the instruments as measured by rn, the rate of growth of the so-called concentration parameter, and also on Kn. In particular, when Kn→∞, the concentration parameter can grow, even if each individual instrument is only weakly correlated with the endogenous explanatory variables, and consistency of certain estimators can be established under weaker conditions than have previously been assumed in the literature. Hence, the use of many weak instruments may actually improve the performance of certain point estimators. More specifically, we find that the limited information maximum likelihood (LIML) estimator and the bias-corrected two-stage least squares (B2SLS) estimator are consistent when , while the two-stage least squares (2SLS) estimator is consistent only if Kn/rn→0 as n→∞. These consistency results suggest that LIML and B2SLS are more robust to instrument weakness than 2SLS.