Model selection using AIC in the presence of one-sided information

Abstract In recent decades, econometricians and statisticians have become aware of the benefits of using non-sample information when conducting inference. This is most notable in the field of hypothesis testing where considerable effort has gone into developing tests that utilize non-sample information in the form of inequality constraints—it is now well known that one-sided tests generally have higher power for given size relative to corresponding two-sided tests. In this paper, we extend the principles of one-sided hypothesis testing to the related area of model selection and develop an analogue of Akaike's information criterion that utilizes one-sided information. This criterion is widely applicable in problems where the signs of some or all the parameters are known or can be inferred on the basis of a priori information. Examples of this include selecting between variance components models (such as random effects models for panel data), selecting the order of a (G)ARCH model, selecting between random coefficient models as well as the problem of variable selection in the linear regression framework. Here, we investigate the small sample performance of the new one-sided criterion relative to existing criteria using Monte Carlo simulation. We include two applications—those of variable selection in linear regression and selecting between various random effects models for panel data. We find that the new criterion performs consistently well across a wide variety of model selection problems.