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The Stata Journal
Volume 18 Number 2: pp. 293-326

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Linear dynamic panel-data estimation using maximum likelihood and structural equation modeling

Richard Williams
University of Notre Dame
Department of Sociology
Notre Dame, IN
Paul D. Allison
University of Pennsylvania
Department of Sociology
Philadelphia, PA
Enrique Moral-Benito
Banco de España
Madrid, Spain
Abstract.  Panel data make it possible both to control for unobserved confounders and to include lagged, endogenous regressors. However, trying to do both simultaneously leads to serious estimation difficulties. In the econometric literature, these problems have been addressed by using lagged instrumental variables together with the generalized method of moments, while in sociology the same problems have been dealt with using maximum likelihood estimation and structural equation modeling. While both approaches have merit, we show that the maximum likelihood–structural equation models method is substantially more efficient than the generalized method of moments method when the normality assumption is met and that the former also suffers less from finite sample biases. We introduce the command xtdpdml, which has syntax similar to other Stata commands for linear dynamic panel-data estimation. xtdpdml greatly simplifies the structural equation model specification process; makes it possible to test and relax many of the constraints that are typically embodied in dynamic panel models; allows one to include time-invariant variables in the model, unlike most related methods; and takes advantage of Stata’s ability to use full-information maximum likelihood for dealing with missing data. The strengths and advantages of xtdpdml are illustrated via examples from both economics and sociology.
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