Before revision:  If the spatial correlation structure follows a linear factor model,  we show that inference ignoring such correlation remains reliable when either (i) the second moment of the difference between the pre- and post-treatment averages of common factors is low, or (ii) the distribution of factor loadings has the same expected values for treated and control groups , and do not exhibit significant spatial correlation . Simulations with real datasets corroborate these conclusions.
After revision:  If the spatial correlation structure follows a linear factor model, we show that inference ignoring such correlation remains reliable when either (i) the second moment of the difference between the pre- and post-treatment averages of common factors is large, and (ii) the distribution of factor loadings has the same expected values for treated and control groups , and do not exhibit significant spatial correlation . Simulations with real datasets corroborate these conclusions.