Econometric Model Selection With More Variables Than Observations

Several algorithms for indicator saturation are compared and found to have low power when there are multiple breaks. A new algorithm is introduced, based on repeated application of an automatic model selection procedure (Autometrics, see Doornik, 2009) which is based on the general-to-specific approach. The new algorithm can also be applied in the general case of more variables than observations. The performance of this new algorithm is investigated through Monte Carlo analysis. The relationship between indicator saturation and robust estimation is explored. Building an the results of Johansen and Nielsen (2009), the asymptotic distribution of multi-step indicator saturation is derived, as well as the efficiency of the two-step variance. Next, the asymptotic distribution of multi-step robust estimation using two different critical values (a low one at first) is derived. The asymptotic distribution of the fully iterated case is conjectured, as is the asymptotic distribution of reweighted least squares based on least trimmed squares (Rousseeuw, 1984)), called RLTS here. This allows for a comparison of the efficiency of indicator saturation with RLTS. Finally, the performance of several robust estimators and the new approach is studied in the presence of a structural break. When there are many irrelevant regressors in the model, the robust estimators break down while the new algorithm is largely unaffected.