the omitted variable problem that arises when including both a predictor variable and its squared term in a regression model

[Eyup TANIL]

I am working on the environmental Kuznets curve. With N:9 T:26, my dependent variable is lnco2 and my independent variables are GDP, GDP^2, and FDI (foreign direct investment). When I run a simple panel regression model regressing lnco2 on lngdp, lngdp^2, and FDI, I get an error message that says 'note: lngdper omitted because of collinearity'. To test the validity of the environmental Kuznets curve, I need to include both GDP and GDP^2. How can I address this issue?"

[Rich Goldstein]

there is much in this question that I don't understand but, if the collinearity is "non-essential", then the simplest way to solve it is to center Ingdp and us the centered version and the square of the centered version in your model - if this does not solve your problem, please provide a -dataex- example in CODE blocks as requested by the FAQ

[Eyup TANIL]

here is my code. these colineratiy is not important me. How can lngdp be centered as you suggest?"

xtreg lnco2 lngdper lngdper2 lnfdi, fe

note: lngdper2 omitted because of collinearity.

Fixed-effects (within) regression Number of obs = 231

Group variable: id Number of groups = 9

R-squared: Obs per group:

Within = 0.4596 min = 24

Between = 0.9063 avg = 25.7

Overall = 0.8457 max = 26

F(2,220) = 93.54

corr(u_i, Xb) = 0.8226 Prob > F = 0.0000

lnco2 Coefficient Std. err. t P>t [95% conf. interval]

lngdper .4925076 .036679 13.43 0.000 .4202205 .5647947

lngdper2 0 (omitted)

lnfdi .000232 .0139738 0.02 0.987 -.0273076 .0277715

_cons -2.798462 .2799846 -10.00 0.000 -3.350257 -2.246667

sigma_u .77794105

sigma_e .19029346

rho .94354321 (fraction of variance due to u_i)

F test that all u_i=0: F(8, 220) = 139.95 Prob > F = 0.0000

[Nick Cox]

I think the problem may lie in that log (GDP squared) is necessarily identical to twice log GDP and therefore (log GDP, log (GDP squared)) are collinear, as reported.

In contrast log GDP and (log GDP)^2 are likely to be quite highly correlated but may still be workable together.

There is in #1 or #3 no data example and no code is given either for how lngdper2 was generated, so like Rich Goldstein I can't be clear on what you've done.

Collinearity is important to you because you can't fit your intended model with the variables as they stand.

[Eyup TANIL]

ı solve my proplem thank you , your post help me to solve