Consider the log-linear model
0 1 1 2 2 ln(Y) β0+ β1X1+ β2X2 + u
Suppose you think that the value of β2 (the effect of X2) was not constant, but rather increased when X1 increased.
(a) How would you modify the model to capture this effect?
(b) How would you test the null hypothesis that the value of β2(effect of X2) is constant against the alternative hypothesis that the value of β2(effect of X2) increased when X1 increased.