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This paper proposes new speciﬁcation tests for conditional models with discrete responses, which are key to apply eﬀicient maximum likelihood methods, to obtain consistent estimates of partial eﬀects and to get appropriate predictions of the probability of future events. In particular, we test the static and dynamic ordered choice model speciﬁcations and can cover inﬁnite support distributions for e.g. count data. The traditional approach for speciﬁcation testing of discrete response models is based on probability integral transforms of a jittered discrete data which leads to continuous uniform iid series under the true conditional distribution. Then, standard speciﬁcation testing techniques for continuous variables could be applied to the transformed series, but the extra randomness from jitters aﬀects the power properties of these methods. We investigate in this paper an alternative transformation based only on original discrete data that avoids any randomization. We analyze the asymptotic properties of goodness-of- t tests based on this new transformation and explore the properties in ﬁnite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent. We show analytically and in simulations that our approach dominates the methods based on randomization in terms of power. We apply the new tests to models of the monetary policy conducted by the Federal Reserve.
Kheifets, Igor and Velasco, Carlos, "New Goodness-of-fit Diagnostics for Conditional Discrete Response Models" (2013). Cowles Foundation Discussion Papers. 2317.