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Partial Identification and Inference in Binary Choice and Duration Panel Data Models

Jason R. Blevins
The Ohio State University

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Abstract. Many semiparametric fixed effects panel data models, such as binary choice models and duration models, are known to be point identified when at least one regressor has full support on the real line. It is common in practice, however, to have only discrete or continuous, but possibly bounded, regressors. This paper addresses identification, estimation, and inference for the identified set in such cases, when the parameters of interest may only be partially identified. We develop a set of general results for criterion-function-based estimation and inference in partially identified models which can be applied to both regular and irregular models. We apply our general results first to a fixed effects binary choice panel data model where we obtain a sharp characterization of the identified set and propose a consistent set estimator, establishing its rate of convergence under different conditions. Rates arbitrarily close to n−1/3 are possible when a continuous, but possibly bounded, regressor is present. When all regressors are discrete the estimates converge arbitrarily fast to the identified set. We also propose a subsampling-based procedure for constructing confidence regions in the models we consider. Finally, we carry out a series of Monte Carlo experiments to illustrate and evaluate the proposed procedures. We also consider extensions to other fixed effects panel data models such as binary choice models with lagged dependent variables and duration models.

Keywords: partial identification, set estimation, panel data, fixed effects, binary choice, duration, discrete regressors, subsampling.

JEL Classification: C13, C14, C25, C41.

BibTeX Record:

@TechReport{blevins-2011-panel,
  author       = {Jason R. Blevins},
  title        = {Partial Identification and Inference in Binary
                  Choice and Duration Panel Data Models},
  institution  = {Ohio State University},
  year         = 2011,
  type         = {Working Paper}
}

Note: Many of the general results in this paper have been superseded by a newer paper and will be removed in the next revision, which will focus on the application to panel data models.