99% 1 1 Kurtosis 2.400947
I tried using R2 to select levels, but only the second spec had an interior solution (at level 3):
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l nosinglemulti nosinglemultisq nohull nohullsq nopair nopairsq avghulldensity avghulldensitysq avgpairlength avgpairlengthsq avgdisthm avgdisthmsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 1 level: " `i' " r2-within: " `e(r2_w)'
}
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l nosinglemulti nosinglemultisq nohull nohullsq nopair nopairsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 2 level: " `i' " r2-within: " `e(r2_w)'
}
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l numstartups numstartupssq fracsinglemulti fracsinglemultisq fracpair fracpairsq frachull frachullsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 3 level: " `i' " r2-within: " `e(r2_w)'
}
Reg: 2 level: 1 r2-within: .39552569
Reg: 2 level: 2 r2-within: .3998779
Reg: 2 level: 3 r2-within: .40348691
Reg: 2 level: 4 r2-within: .40130097
Reg: 2 level: 5 r2-within: .39931203
Reg: 2 level: 6 r2-within: .39707046
Reg: 2 level: 7 r2-within: .39366909
Reg: 2 level: 8 r2-within: .38957831
Reg: 2 level: 9 r2-within: .38398108
Reg: 2 level: 10 r2-within: .37662604
Reg: 2 level: 11 r2-within: .36999057
Reg: 2 level: 12 r2-within: .38393843
However, doing this by exgroup (0 t0 3), gives the same result - level 3 - for each exgroup.
Alternative approaches are to use AIC/BIC, or maybe entropy. For the same set of variables, in the same model, AIC/BIC are minimized when R2 is maximized, they are only useful when choosing the combination of the variables/estimation and the level. And it seems we can only do entropy one variable at a time:
entropyetc nohull if level==1
===Other===