  I propose Robust Rao's Score (RS) test statistic to determine endogeneity of
spatial weights matrices in a spatial dynamic panel data (SDPD) model (Qu, Lee,
and Yu, 2017). I firstly introduce the bias-corrected score function since the
score function is not centered around zero due to the two-way fixed effects. I
further adjust score functions to rectify the over-rejection of the null
hypothesis under a presence of local misspecification in contemporaneous
dependence over space, dependence over time, or spatial time dependence. I then
derive the explicit forms of our test statistic. A Monte Carlo simulation
supports the analytics and shows nice finite sample properties. Finally, an
empirical illustration is provided using data from Penn World Table version
6.1.
