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Challenges and Opportunities in the Estimation of Dynamic Models

Interest in modeling longitudinal processes is increasing rapidly in organizational science. Organizational scholars often employ multilevel or hierarchical linear models (HLMs) to study such processes given that longitudinal data in organizational science typically consist of observations over a relatively small number of time intervals (T) nested within a relatively large number of units (N; e.g., people, teams, organizations). In this paper, we first distinguish change and dynamics as common research foci when modeling longitudinal processes and then demonstrate that a unique set of inferential hazards exists when investigating change or dynamics using multilevel models. Specifically, multilevel models that include one or more time-lagged values of the dependent variable as predictors often result in substantially biased estimates of the model parameters, inflated Type I error rates, and ultimately inaccurate inference. Using Monte Carlo simulations, we investigate the bias and Type I error rates for the standard centered/uncentered hierarchical linear model (HLM) and compare them with two alternative estimation methods: the Bollen and Brand structural equation modeling (SEM) approach and the Arrelano and Bond generalized method of moments using instrumental variables (GMM-IV) approach. We find that the commonly applied hierarchical linear model performs poorly, whereas the SEM and GMM-IV approaches generally perform well, with the SEM approach yielding slightly better performance in small samples with large autoregressive effects. We recommend the Bollen and Brand SEM approach for general use when studying change or dynamics in organizational science.