Title: New goodness-of-fit diagnostics for conditional discrete response models,
Abstract: 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-fit 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.