Abstract
This note provides several remarks relating to the conditional choice probability (CCP) based estimation approaches for dynamic discrete-choice models. Specifically, the Arcidiacono and Miller [2011] estimation procedure relies on the “inverse-CCP” mapping from CCP’s to choice-specific value functions. Exploiting the convex-analytic structure of discrete choice models, we discuss two approaches for computing this, using either linear or convex programming, for models where the utility shocks can follow arbitrary parametric distributions. Furthermore, the inverse-CCP mapping is generally distinct from the “selection adjustment” term (i.e. the expectation of the utility shock for the chosen alternative), so that computational approaches for computing the latter may not be appropriate for computing inverse-CCP mapping.
Highlights
Conditional choice probability (CCP) based estimation approaches for dynamic discrete-choice models have become well-established in the empirical literature on dynamic structural models
For each alternative k the function ψk satisfies ψk (p (z)) = V (z) − vk (z), k = 1, . . . , J, where z denotes the model state, p (z) = (p1 (z), . . . , pJ (z)) ⊺ the choice probabilities implied by the model, vk, k = 1, . . . , J, are the choice-specific value functions, and V is the ex ante value function
The finding that ψ (pt) = e(vt) for the Generalized Extreme Value (GEV) is a special case of the result for additive random utility models (ARUMs) with the invariance property
Summary
Conditional choice probability (CCP) based estimation approaches for dynamic discrete-choice models have become well-established in the empirical literature on dynamic structural models. A crucial step in these procedures involves computing the ‘‘inverse CCP’’ mapping from choice probabilities to choice-specific value functions. This is exemplified by the Arcidiacono and Miller (2011) estimation procedure, which relies on knowing or computing the vector valued function ψ (p) = (ψ1 (p) , . We interpret the quantity ψ based on the convexanalytic properties of additive random utility models (ARUMs). We discuss two general approaches for computing ψ for ARUM models with arbitrary error distributions. It supplements the note with the same title that is forthcoming Economics Letters
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