Testing and Fixing Endogeneity/ Simultaneity / Reverse Causation in a multilevel model


I am running a multilevel model using BRMS on some unbalanced panel data. I have ‘fixed’ effects and group-varying ‘random’ effects. I then add group-level predictors to try and predict variation in the random (group-varying) intercepts. I have a AR(1) error structure.

One big issue economics journal referees will raise is revere causality from y_{it} to x_{it} (endogeneity / simultaneity) in two instances: (i) A fixed effect variable of mine is clearly also being caused by the dependant variable, and 9ii) following from this,when I aggregate that same fixed effect variable and use it as a group predictor to `explain’ my group-varying intercept, reverse causality will be present I imagine. Questions:

  • Best Bayesian way to test for endogeneity of this sort?
  • Solutions: Perhaps, I should just try and show model robustness more generally?


  • Finding a good instrument (IV approach) will be tough. Though I am tempted to argue why one of my independant variables serves as an instrument.

Many thanks!

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since no one else answered, I will give it a try, but it is not really within my expertise. Please be skeptical towards what I say and make sure it makes sense to you.

I would say that the inability to determine a direction of causality is usually a property of the data and when it is, no amount of modelling can save you. If your time series is sufficiently detailed and if you see one value lagging behind the other, it is some indication about the more important direction of causality. But even then, I think that in most economic contexts you know for sure that causality flows in both directions (and via numerous feedback loops), at best one direction is much more important than the other. If the effects could be expected to operate on faster timescales than your measurements, you are IMHO completely out of luck and your data cannot help you with determining causality.

You could IMHO somewhat formalize this reasoning by trying to model also the other direction of causality. If the model for one direction is a better fit in most cases (over multiple ways to handle covariates, exclusions, …) this is some support for a preferred direction of causality.

Does that make sense?