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I have a panel data with unbalanced panel. I am testing a non-linear relationship. I tested a polynomial(quadratic) model for this purpose with following codes in stata.

  xtreg y x x2 z, fe vce(cluster id)

z is a vector of control variables. I want to test if the polynomial model is better than a linear one by omitting x2 from the model. How I can do this?

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I don't know Stata but if the coefficient for x2 is significant then you have evidence for a quadratic component. Alternatively, you could test the significance of the difference between R^2's from a complete model and one without x2 but the result would be the same.

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  • $\begingroup$ A quadratic can be worthwhile even if only one of two terms is significant. The two terms have to be considered jointly. $\endgroup$
    – Nick Cox
    Feb 3, 2017 at 18:17
  • $\begingroup$ I tried different model specifications and different models (OLS, FE, RE etc and changed controls, included and excluded clustered SE and year fixed effects). The coefficient of x2 in all specifications remains significant and different from x1. In Many models both are significant but with different signs. $\endgroup$
    – Ahmed Arif
    Feb 3, 2017 at 22:59

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