Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 18

Refer to Table 8.3.
a. A researcher suspects that the effect of % Eligible for subsidized lunch has a nonlinear effect on test scores. In particular, he conjectures that increases in this variable from 10% to 20% have little effect on test scores, but that changes from 50% to 60% have a much larger effect.
i. Describe a nonlinear specification that can be used to model this form of nonlinearity.
ii. How would you test whether the researcher's conjecture was better than the linear specification in column (7) of Table 8.3
b. A researcher suspects that the effect of income on test scores is different in districts with small classes than in districts with large classes.
i. Describe a nonlinear specification that can be used to model this form of nonlinearity.
ii. How would you test whether the researcher's conjecture was better than the linear specification in column (7) of Table 8.3