# equivalence in hypothesis testing

I have the following unrestricted model $y_i=\beta_1+\beta_2x_{2i}+\beta_3x_{3i}+u$ and the restriction $\beta_2+\beta_3=1$ I need to give an equivalent unrestricted model such that if one of its parameters is equal to zero, then the restriction applies.

I had in mind $y_i=(1-\beta_3-\beta_2)+\beta_2x_{2i}+\beta_3x_{3i}+u$ but of course it is incorrect.

• You can try $y_i=\beta_1+(1-\beta_3)x_{2i}+\beta_3x_{3i}+u$ – DornerA Apr 3 '16 at 17:38