In section 5.3 Fixed Effects versus Lagged Dependent Variables,you write that the fixed effect model can deal with the OVB problem caused time-invariant or group-invariant omitted variables,and also give some suggestions on the strategies handing the OVB problem caused by potential omitted variables that may change over time in practice.On whether to employ fixed individual effects model or lagged dependent variable model ,you suggest that the researchers Â…"find broadly similar results using both models".But if the estimated coefficient of the interested explanatory variable from the two models differ tremendously,what shall be done to for the regressions to make sense? Thanks.
The fixed effects and lagged dependent variable models are different models, so can give different results. We discuss this on p. 245-46 in the book. If the results are very different you could consider estimating a model with both fixed effects and a lagged dependent variable. As we discuss in the book, this is a challenging model to estimate. As you can see from our discussion we don’t think the approaches you need to instrument for the lagged dependent variable are all that compelling, so this is not a clean solution. You can also think about the simple FE and LDV results as bracketing the true effect. Of course, if the difference is large this may not be particularly informative. If all else fails there may not be much you can do other than find another approach/other data/a better natural experiment to study the research question you are after.