
This paper presents a clear and concise discussion of (efficient) instrumental-variable estimators for an error-components-model. The paper starts with a common form of a model with a common form of an instrumental-variable estimator, for which four alternative special assumptions lead to four models, which are discussed in detail: 1. Endogenous variables across equations. 2. Endogenous variables varying across equations and correlated with a source of disturbance. 3. Endogenous variables varying across equations and uncorrelated with this disturbance. 4. The more general case by relaxing variance-covariance restrictions. In an appendix an optimal choice of instrumental variables is proposed which is used in this paper under the given concept of asymptotic efficiency. The proposed instrumental-variable procedures may apply to panel data, where efficient estimation involves the combination of ``within''- and ``between-group'' information for a single estimator.
instrumental-variable estimators, disturbance, panel data, variance-covariance restrictions, optimal choice of instrumental variables, Estimation in multivariate analysis, asymptotic efficiency, simultaneous equations, Endogenous variables across equations, Applications of statistics to economics, error- components-model
instrumental-variable estimators, disturbance, panel data, variance-covariance restrictions, optimal choice of instrumental variables, Estimation in multivariate analysis, asymptotic efficiency, simultaneous equations, Endogenous variables across equations, Applications of statistics to economics, error- components-model
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