GDP = B0_constant + B1_(GDP/Pop) + B2_X2 + B3_X3
Given that GDP appears on both left- and right-hand side this must certainly be problematic.
What is this particular situation called?
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This is called an opportunity for restructuring your regression equation. For example, why not do this:
$$ GDP/Pop = \beta_0 + \beta_2 X_2 + \beta_3 X_3 $$
Then you only have to multiply to the population to get GDP estimates.
$$ log(GDP / Pop) = \beta_0 + \beta_2 X_2 + \beta_3 X_3 $$
which is effectively:
$$ log(GDP) = log(Pop) + \beta_0 + \beta_2 X_2 + \beta_3 X_3 $$