I have a question related to 'whether HLM is necessary or not.' 

My data has regions and firms with the time range of 2005 and 2010.
I set each firm (with multiple observations within it) as the first level and regions as the second level. 

However, ICC turned out to be very low at the region level (0.008) while the LR test(chi2(4) = 2981.71) said that the use of the hierarchical model was proper.

Q. Is ICC the best indicator when deciding the use of HLM? Or that clash between ICC and LR test imply something? 

Q. What criteria or tests should I conduct to decide whether to use HLM other than ICC? 

Thank you.