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Two-step estimators for hierarchical models can be constructed even when neither stage is a conventional linear regression model. For example, the first stage might consist of probit models, or duration models, or event count models. The second stage might be a nonlinear regression specification. This note sketches some of the considerations that arise in ensuring that two-step estimators are consistent in such cases.
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Christopher H. Achen (2005) studied this question.
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