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Using the Kullback-Leibler information criterion to measure the closeness of a model to the truth, the author proposes new likelihood-ratio-based statistics for testing the null hypothesis that the competing models are as close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, the author fully characterizes the asymptotic distribution of the likelihood ratio statistic under the most general conditions. Copyright 1989 by The Econometric Society.