Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 8

How big is the effect of per-student school expenditures on local housing values Let HPRICE be the median housing price in a school district and let EXPEND be per-student expenditures. Using panel data for the years 1992, 1994, and 1996, we postulate the model
lHPRICEit = t + lEXPENDit + 2lPOLICEu + 3lMEDINCit + 4PROPTAXit + ai1 + uit1
where POLICEit is per capita police expenditures, MEDINCit is median income, and PROPTAX t is the property tax rate; l denotes natural logarithm. Expenditures and housing price are simultaneously determined because the value of homes directly affects the revenues available for funding schools.
Suppose that, in 1994, the way schools were funded was drastically changed: rather than being raised by local property taxes, school funding was largely determined at the state level. Let lSTATEALLit denote the log of the state allocation for district i in year t, which is exogenous in the preceding equation, once we control for expenditures and a district fixed effect. How would you estimate the j.