I am estimating the following model:
$\ln(y) = \alpha + \beta_1x + \beta_2x^2 $
$\hat\beta_2$ is insignificant while $\hat\beta_1$ is significantly different from zero. However they are jointly significant.
Is it still correct to keep $x^2$ and interpret the semi-elasticity?
Edit: $y$ is a continuous measure of income. $x$ is an ordinal variable measuring numeracy. There is economic evidence of decreasing returns to numeracy hence why I am estimating this model. Unfortunately, the ordinal nature of the variable makes it difficult to plot a relationship.