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The “dynamic” here means the dependence of the dependent variable on its past history, this is usually used to model the “state dependence” in economics. For instance, a person who cannot find a job this year, it will be hard for her to find a job next year because the fact that she doesn’t have a job this year will be a very negative signal for the potential employers. The “unobserved effects” means that one or some of the explanatory variables are unobservable. For example, one’s preference affects quite a lot her consumption choice of the ice cream with a certain taste, but preference is unobservable. A typical dynamic unobserved effects model is represented <ref>Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 495.</ref> as:
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