Identification in dynamic binary choice models

This paper studies identification in a binary choice panel data model with choice probabilities depending on a lagged outcome, additional observed regressors and an unobserved unit-specific effect. It is shown that with two consecutive periods of data identification is not possible (in a neighborhood of zero), even in the logistic case.

Data" paper was not widely circulated and, to our knowledge, unavailable in any form online.
One version of the 1993 paper included a fifth and final section titled "Binary Response."This material was not published as part of Chamberlain (2022).The "Binary Response" section contained two sets of results.The first, dealing with the identification of static binary choice models, can be found in Chamberlain (2010).The second part, which is reproduced below, deals with the identification of dynamic binary choice models.
Gary establishes that with two consecutive observations of a binary dependent variable, identification is not possible (in a neighborhood of zero), even in the logistic case.This result is not widely known, although it has been cited by, for example, Honoré and Kyriazidou (2000).Publishing this material makes it easily available to researchers worldwide for the first time.
Gary was a great admirer of Manuel Arellano's research, and they engaged in many intellectual exchanges over the years.Gary would no doubt have wanted to celebrate and honor Manuel's considerable achievements and scholarship.Including this short note in this special issue provides a way to do so.Stéphane Bonhomme, Bryan Graham and Laura Hospido.

Identification in dynamic binary response
The outcome variable is binary.There are two periods of observation on each unit (T = 2).The random vector (y i1 , y i2 , x i1 , x i2 , c i ) is independently and identically distributed for i = 1, ..., n.We observe z i = (y i1 , y i2 , x i1 , x i2 ); the (scalar) latent variable c i ∈ R is not observed.The binary variable y it = 0 or 1, and We assume that Pr( The distribution function F is given as part of the prior specification; it is strictly increasing on the whole real line with a bounded, continuous derivative, and with lim s→∞ F(s) = 1 and lim s→−∞ F(s) = 0.The parameter space is = 1 × 2 × 3 , where 1 is an open subset of R, 2 is an open subset of R J , and 3 is an open subset of R, and θ 0 ≡ (α 0 , β 0 , γ 0 ) ∈ .We assume that contains a neighborhood of 0. Define Theorem 1 If X is bounded, then there is a point (α, γ ) ∈ 1 × 3 such that identification fails in (1) for all θ 0 in a neighborhood of (α, 0, γ ).
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