Hi,

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?

Note:

- 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!