st: Quadratic Interaction Term.

[natasha agarwal <agarwana2@googlemail.com>]

Dear Statalist,

I am estimating an augmented Cobb-Douglas Production function using
the xtreg, fe command.

The estimating equation looks like

VA= f(L,K,FDI, GDP)

All transformed in logs.

I want to interact FDI*GDP and then introduce the quadratic term of
GDP with its interaction with FDI. So now the estimating equation
looks like

lnVA=lnK+Lnl+lnFDI+lnGDP+lnGDP^2+lnFDI*lnGDP+lnFDI*(lnGDP^2)

When I estimate this equation, I get the coefficient on the
lnFDI*(lnGDP^2) is insignificant but when I remove lnGDP^2 and
re-estimate the same lnFDI*(lnGDP^2) becomes significant. However, the
sign and magnitude does not change. The sign, magnitude and
significance does not change as well.

I checked for the joint signigicance of lnFDI lnGDP lnGDP^2
lnFDI*lnGDP lnFDI*(lnGDP^2) and it is significant.

Can anyone please explain me why is this happening?

Many thanks in advance

Natasha
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