The Review of Financial Studies /v 12 n 2 1999 retains six predictors,whereas PLS and PLS-MDC limit the forecasting model to two variables. Some popular predictors are only occasionally selected.For instance, in 9 of 14 cases,BIC and FIC drop the January dummy. The model selection criteria often retain predictors that are suspected to be unit-root nonstationary,such as the dividend yield,the price- earnings ratio,or even the initial stock price level.Model selection criteria such as FIC,PIC,PLS,and PLS-MDC are robust to unit-root nonstationarities,so this finding should not bother us. For a given country,the model selection criteria agree to a certain ex- tent on the variables to be retained as predictors.The contemporaneous yield on short-term Treasury bills,for instance,is dropped by all se- lection criteria in 4 of 14 cases.It is retained by all selection criteria only for the United States. .FIC and PIC almost universally select lagged bond and stock excess returns.These are often chosen in pairs,so that FIC and PIC effectively construct the moving average predictors that have been popular in professional circles lately. .BIC decides against predictability in five cases(Australia,Canada,Ger- many,Norway,and Spain).This means that all predictors are dropped (only the intercept is retained in the prediction model). PLS almost invariably picks a small model when compared to other criteria,except BIC.PLS-MDC adjusts the choice by changing and/or adding predictors. Overall,however,the predictability that remains after the application of formal selection criteria confirms the evidence of predictability in earlier studies.In other words,the predictability that was uncovered in previous work is clearly not caused by overfitting. Notice that this verdict is uniform across selection criteria.Since each selection criterion starts from a different decision-theoretic framework,it is comforting to observe such an agreement.In other words,our conclusion is not based on the application of a specific,haphazardly chosen criterion. 4.2 External Validation Formal model selection criteria try to determine the model with the best external validity.To verify whether they indeed pick models with external validity in the context of stock market returns,we tested for out-of-sample forecasting power by projecting the excess returns in our testing sample (6/90-5/95)onto the forecasts from each "optimal"model. 6It is well known that the January effect is less pronounced for large stock.As the excess stock return used in this article refers to a subset of large and liquid companies,it should not be too surprising that the January effect often fails to emerge. 416