An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations
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Methodological development of the Model-implied Instrumental Variable (MIIV) estimation framework has proved fruitful over the last three decades. Major milestones include Bollen's (1996) original development of the MIIV estimator and its robustness properties for continuous endogenous variable SEMs, the extension of the MIIV estimator to ordered categorical endogenous variables (Bollen Maydeu-Olivares, 2007), and the introduction of a Generalized Method of Moments (GMM) estimator (Bollen, Kolenikov Bauldry, 2014). In this paper we continue this development by extending the MIIV estimator to the case of mixed mixed continuous, dichotomous and ordinal indicators. Novel alternative parameterizations for ordinal variable models and analytic derivatives for a general MIIV estimator are also developed. An empirical example using data from the General Social Survey (GSS) is used to illustrate the estimator and the possibilities afforded by the proposed alternative parameterizations. Finally, the finite sample performance of the estimator is evaluated using a Monte Carlo simulation.
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