Instrumental variable estimation in a probit measurement error model |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA;2. Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA;1. Faculty of Economics and Management, University of Dschang, Dschang, Cameroon;2. Faculty of Economics and Management Sciences, University of Bamenda, Bamenda, Cameroon;1. Division of Population Medicine, School of Medicine, Neuadd Meirionnydd, Cardiff University, 3rd Floor, Neuadd Meirionnydd, Heath Park, Cardiff CF14 4YS, United Kingdom;2. Public Health Wales NHS Trust, 2 Capital Quarter, Tyndall Street, Cardiff CF10 4BZ, United Kingdom;1. Utrecht School of Economics, Utrecht University, Adam Smith Hall, Office 0.01, Kriekenpitplein 21-22, NL-3584 EC Utrecht, The Netherlands;2. Bordeaux University, GREThA (UMR CNRS 5113), France |
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| Abstract: | Probit regression is studied when normally distributed covariates are subject to normally distributed measurement errors. Under the assumption that surrogate instrumental variables are available, the parameters in the probit model are shown to be identified. The maximum likelihood estimator and an easily computed two-stage estimator are derived and studied. The two-stage estimator is shown to be asymptotically efficient. Simulation results complement the theory and provide evidence of robustness to the normality assumptions. |
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