In my textbook I often see a quadratic term in the regression. For example let's say I have the regression model: $\log(\mathrm{wage})=\beta_0+\beta_1\mathrm{educ}+\beta_2\mathrm{exp}+\beta_3\mathrm{exp}^2+\varepsilon$. Why is it so common to put the squared term in there? Here's a quote from my book:

It often makes sense to add quadratic terms of any significant variables to a model.

Why is that? And if this is true, then if I'm studying endogeneity and a quadratic variable isn't in there is it likely to be that case the the squared term is endogenous if it's omitted?

• Well, for starters, frequently relationships are not linear. Unless I had a priori reason to, I'd usually only do it if the residual analysis suggested the linear model was clearly inadequate. On the other hand if I had no a priori sense of what form the relationship might take I'd fit something more general from the outset. – Glen_b -Reinstate Monica Nov 26 '12 at 1:10

Often the relationship between y and x is nonlinear. There are a variety of solutions. One solution is to add polynomial terms and the first one to look at is usually $x^2$. But you should first look at a scatterplot of x and y; you should also look at the residuals from the linear model without the quadratic term. But it turns out that many relationships are pretty well fit by $y \sim b_0 + b_1x + b_2x^2$ (plus any other x variables, of course).