Question

For a regression of test score (T) on the endogenous variable student-teacher ratio (R), Hoxby (2000) suggests using as an instrument the deviation of potential enrollment from its long-term trend (P), where "potential enrollment" means how many children of kindergarten age there are (whether or not they attend public school). Which of the following arguments would NOT support P as an instrument for R?

a.	Due to high adjustment costs of buildings and teachers and the small/discrete number of classrooms per school, schools cannot perfectly adjust each year to maintain a target student-teacher ratio

b.	Parents with young children are more likely to move into good school districts with low student-teacher ratio

c.	There are fluctuations in birth rate due to sheer random chance

d.	Changes in school district quality are slow and contribute to the long-term enrollment trend, but not deviations from the trend

PLEASE PROVIDE EXPLANATION IN ANSWER

Answer 1

note that

regression analysis tries to capture the pattern in the variation of the independent variables to account for the variation in the dependent variable

Here dependent variable is T

and independent variables are R , P etc.

so something that is purely random cant be captured by the model , any pattern in the data can be captured

a. Due to high adjustment costs of buildings and teachers and the small/discrete number of classrooms per school, schools cannot perfectly adjust each year to maintain a target student-teacher ratio

clear pattern given , hence would support

b. Parents with young children are more likely to move into good school districts with low student-teacher ratio

clear pattern given , hence would support

c. There are fluctuations in birth rate due to sheer random chance

only randomness , hence would not support

d. Changes in school district quality are slow and contribute to the long-term enrollment trend, but not deviations from the trend

clear pattern given , hence would support