title: Non-linear interaction terms in Stata
body: <p>I have a continuous dependent variable <code>polity_diff</code> and a continuous primary independent variable <code>nb_eq</code>. I have hypothesized that the effect of <code>nb_eq</code> will vary with different levels of the continuous variable <code>gini_round</code> in a non-linear manner: The effect of <code>nb_eq</code> will be greatest for mid-range values of <code>gini_round</code> and close to 0 for both low and high levels of <code>gini_round</code> (functional shape as a second-order polynomial).</p>
  
  <p>My question is: How this is modelled in Stata? 
  To this point I've tried with a categorized version of <code>gini_round</code> which allows me to compare the different groups, but obviously this doesn't use data to its fullest. I can't get my head around the inclusion of a single interaction term which allows me to test my hypothesis. My best bet so far is something along the lines of the following (which is simplified by excluding some <code>if</code>-arguments etc.):
  <code>xtreg polity_diff c.nb_eq##c.gini_round_squared, fe vce(cluster countryno)</code>,
  but I have close to 0 confidence that this is even nearly right.</p>