There has been significant new work published recently on the subject of model selection. Notably Rissanen (1986, 1987, 1988) has introduced new criteria based on the notion of stochastic complexity and Hurvich and Tsai(1989) have introduced a bias corrected version of Akaike's information criterion. In this paper, a Monte Carlo study is conducted to evaluate the relative performance of these new model selection criteria against the commonly used alternatives. In addition, we compare the performance of all the criteria in a number of situations not considered in earlier studies: robustness to distributional assumptions, collinearity among regressors, and non-stationarity in a time series. The evaluation is based on the number of times the correct model is chosen and the out of sample prediction error. The results of this study suggest that Rissanen's criteria are sensitive to the assumptions and choices that need to made in their application, and so are sometimes unreliable. While many of the criteria often perform satisfactorily, across experiments the Schwartz Bayesian Information Criterion (and the related Bayesian Estimation Criterion of Geweke-Meese) seem to consistently outperfom the other alternatives considered.