It has been argued that including the lagged dependent variable in panel models will open up unintended back-door paths and bias the estimates of the causal variable. We show that panel analysis in the structural equation modeling framework can get around this issue. Including the lagged dependent variable has the benefit of closing back-door paths due to some unobserved time-varying con-founders. We demonstrate this by looking at simulated data and provide examples in the lavaan package for R as well as Mplus.
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Andersen et al. (2022) studied this question.
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