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| Type | Working Paper |
| Scope | Discipline-based scholarship |
| Title | Structural Estimation Using Parametric Mathematical Programming with Equilibrium Constraints and Homotopy Path Continuation |
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| Institution | University of Zurich |
| Series Name | Econometrics: Econometric & Statistical Methods - General eJournal - CMBO |
| Number | 12 |
| Date | 2019 |
| Abstract Text | In this paper, we formulate the likelihood function of structural models as a parametric optimization problem, where the model equations enter as constraints, forming a mathematical program with equilibrium constraints (Su and Judd, 2012). We trace the solution to its first-order conditions in dependence on a controlled parameter using homotopy continuation, delivering a relation from the controlled parameter to the corresponding maximum likelihood estimates and their confidence intervals. This enables us to estimate models with identification issues, multiplicity of equilibria, etc. As applications, we first trace the parameter estimates of the bus engine replacement model of Rust (1987), a dynamic discrete choice model, in dependence of the discount factor β. Using relative value iteration, we find that β is well identified and statistically significantly larger than 1. Second, for a simple static binary choice model, we demonstrate how the effects of multiplicity of equilibria and a lack of identification can be mitigated by the tracing method. |
| Free access at | Official URL |
| Official URL | https://ssrn.com/abstract=3303999 |
| Digital Object Identifier | 10.2139/ssrn.3303999 |
| Other Identification Number | merlin-id:17555 |
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