I am using the following fixed effects model:

Log(CEO Compensationi,t) = b1Firmperformancei,t-1+ b2Proportionofnonexecutivedirectorsi,t + b3CEO Tenurei,t+ b4CEOagei,t+ b5Log(CEOshareholdingsi,t) + b6BoardSizei,t+ b7Log(FirmSizei,t) + Time dummy + 𝜀𝑖𝑡

I include a robust clustered standard errors in the fixed effects model. This is my first paper and I want to assess the the robustness of my results. I have already already accounted for heteroskedasticity and/or autocorrelation via clustered standard errors. However I suspect endogeneity from the firm performance variable which is already lagged as according to literature this helps control it. How do I test for this, do I test for reverse causality? Is it simple to use a GMM model? Is it simple to do so? Please let me know any robustness checks I could use. Many thanks