In several chapters we have discussed goodness-of-fit tests to assess the performance of a model with respect to how well it explains the data. However, suppose we want to select from among several candidate models. What criterion can be used to select the best model? In choosing a criterion for model selection, one accepts the fact that models only approximate reality. Given a set of data, the objective is to determine which of the candidate models best approximates the data. This involves trying to minimize the loss of information. Because the field of information theory is used to quantify or measure the expected value of information, the information-theoretic approach is used to derive the two most commonly used criteria in model selection—the Akaike information criterion and the Bayesian information criterion.^{1} These two criteria, as described in this appendix, can be used for the selection of econometric models.^{2}

In 1951, Kullback and Leibler developed a measure to capture the information that is lost when approximating reality; that is, the Kullback and Leibler measure is a criterion for a good model that minimizes the loss of information.^{3} Two decades later, Akaike established a relationship between the Kullback-Leibler measure and maximum likelihood estimation method—an estimation method used in many statistical analyses as described in Chapter 13—to derive a criterion (i.e., formula) for model ...

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