Hi all,

I need your comments on change in sign and significance of linear term after adding quadratic and cubic terms. please see details below:

I am using panel data with 681 firms and 9 years each.

DV: In_roa (firm performance)
IV: ff_d (dummy variable, whether firm is family firm or not, if family then 1)
IV: stdfo_own (shares held by an investment company in a firm, values ranges from 0 to 100, moreover i standardized this variable by egen stdvar=std(var) in order to get standardized coefficients ) ----- quadratic and cubic terms of this variable are also used later.

rest four variables are control variables

DV and all control variables are log transformed

i also add interaction terms of both IVs

When i ran xtreg ,fe only with linear terms and their respective interaction. The results are following

Code:
. xtreg ln_roa ln_age ln_assets ln_leverage ln_ebitda stdfo_own i.ff_d c.stdfo_own#i.ff_d i.year,fe Fixed-effects (within) regression Number of obs = 2,619 Group variable: sr Number of groups = 435 R-sq: Obs per group: within = 0.3449 min = 1 between = 0.0702 avg = 6.0 overall = 0.0961 max = 9 F(15,2169) = 76.14 corr(u_i, Xb) = -0.9166 Prob > F = 0.0000 ln_roa Coef. Std. Err. t P>t [95% Conf. Interval] ln_age -.2425169 .1151951 -2.11 0.035 -.4684213 -.0166125 ln_assets .0968887 .0733825 1.32 0.187 -.0470188 .2407961 ln_leverage -.090931 .0229502 -3.96 0.000 -.1359377 -.0459243 ln_ebitda 1.143277 .0353174 32.37 0.000 1.074017 1.212536 stdfo_own .1853135 .0686506 2.70 0.007 .0506857 .3199414 1.ff_d 1.106262 .4312164 2.57 0.010 .2606212 1.951902 ff_d#c.stdfo_own 1 -.3014559 .1265948 -2.38 0.017 -.5497158 -.0531961 year 2008 -.1011256 .0543446 -1.86 0.063 -.2076986 .0054474 2009 -.1452684 .0588673 -2.47 0.014 -.2607106 -.0298262 2010 -.1071921 .0573892 -1.87 0.062 -.2197355 .0053514 2011 -.0159812 .0603661 -0.26 0.791 -.1343627 .1024002 2012 -.021513 .0640318 -0.34 0.737 -.1470832 .1040571 2013 -.0861119 .0674674 -1.28 0.202 -.2184194 .0461957 2014 -.0374172 .0699141 -0.54 0.593 -.1745228 .0996884 2015 -.0255822 .0741488 -0.35 0.730 -.1709924 .119828 _cons 1.423105 .9439093 1.51 0.132 -.4279559 3.274166 sigma_u 2.2670211 sigma_e .64303764 rho .92553463 (fraction of variance due to u_i) F test that all u_i=0: F(434, 2169) = 10.38 Prob > F = 0.0000
but when i add quadratic and cubic terms with their respective interaction terms, change of sign of main linear effect of Stdfo_own arise and main variable and its interaction term also goes insignificant. Please see below:

Code:
. xtreg ln_roa ln_age ln_assets ln_leverage ln_ebitda stdfo_own i.ff_d c.stdfo_own#i.ff_d c.stdfo_own#c.stdfo_own c.stdfo_own#c.stdfo_own#c.stdfo_own i.ff_d#c.stdfo_own#c.stdfo_own > i.ff_d#c.stdfo_own#c.stdfo_own#c.stdfo_own i.year,fe Fixed-effects (within) regression Number of obs = 2,619 Group variable: sr Number of groups = 435 R-sq: Obs per group: within = 0.3525 min = 1 between = 0.0702 avg = 6.0 overall = 0.0972 max = 9 F(19,2165) = 62.04 corr(u_i, Xb) = -0.9157 Prob > F = 0.0000 ---------------------------------------------------------------------------------------------------------- ln_roa | Coef. Std. Err. t P>|t| [95% Conf. Interval] -----------------------------------------+---------------------------------------------------------------- ln_age | -.2487596 .114643 -2.17 0.030 -.4735815 -.0239377 ln_assets | .1082457 .0732253 1.48 0.139 -.0353535 .2518448 ln_leverage | -.0875726 .0228485 -3.83 0.000 -.1323799 -.0427653 ln_ebitda | 1.147255 .0351986 32.59 0.000 1.078229 1.216282 stdfo_own | -.4299763 .2723444 -1.58 0.115 -.9640601 .1041074 1.ff_d | 1.385639 .5345586 2.59 0.010 .3373372 2.433941 | ff_d#c.stdfo_own | 1 | .1154103 .4098834 0.28 0.778 -.6883959 .9192164 | c.stdfo_own#c.stdfo_own | 1.829437 .3914211 4.67 0.000 1.061837 2.597038 | c.stdfo_own#c.stdfo_own#c.stdfo_own | -.548248 .1106208 -4.96 0.000 -.7651821 -.331314 | ff_d#c.stdfo_own#c.stdfo_own | 1 | -1.62318 .5700911 -2.85 0.004 -2.741162 -.5051965 | ff_d#c.stdfo_own#c.stdfo_own#c.stdfo_own | 1 | .5078677 .1566739 3.24 0.001 .2006207 .8151146 | year | 2008 | -.0976755 .0541075 -1.81 0.071 -.2037836 .0084325 2009 | -.1358211 .0586226 -2.32 0.021 -.2507835 -.0208587 2010 | -.0975943 .0571462 -1.71 0.088 -.2096614 .0144728 2011 | .000361 .0602345 0.01 0.995 -.1177626 .1184846 2012 | -.0069673 .0638666 -0.11 0.913 -.1322135 .118279 2013 | -.076881 .0672857 -1.14 0.253 -.2088323 .0550702 2014 | -.0218242 .0697872 -0.31 0.755 -.1586811 .1150327 2015 | -.0140085 .0739652 -0.19 0.850 -.1590588 .1310417 | _cons | .8776022 .9563418 0.92 0.359 -.9978418 2.753046 -----------------------------------------+---------------------------------------------------------------- sigma_u | 2.2607953 sigma_e | .63990051 rho | .92582914 (fraction of variance due to u_i) ---------------------------------------------------------------------------------------------------------- F test that all u_i=0: F(434, 2165) = 10.46 Prob > F = 0.0000
it would be great if anyone can explain why does this change happens and what does it mean.
regards,