| Summary: | This paper deals with the problem of choosing the optimum criterion for selecting the best model out of a set of overlapping binary models. The criteria we studied were the well-known AIC and SBIC, and a third one called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>. Special attention was paid to the setting where neither of the competing models was correctly specified. This situation has not been studied very much but it is the most common case in empirical works. The theoretical study we carried out allowed us to conclude that, in general terms, all criteria perform well. A Monte Carlo exercise corroborated those results.
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