Every year in Massachusetts, each town sends out local assessors to determine the value of each town's houses. The job of an assessor is to approximate what the sale price of each house would be if it were to be put up for sale this year.
In theory the assessed value of each house (A) and a house's sale price on the market (P) should be very close to each other, but some studies have claimed that there is a "regressive" relationship between A and P. This means that low value houses are systematically over-assessed (so these owners overpay on their property taxes), and high-value houses are systematically under-assessed (so these owners underpay on their property taxes).
A. Suppose you were considering two models to examine this relationship:
(1) Pi = β0 + β1Ai + μi
(2) ln(Pi) = β0 + β1ln(Ai) + μi
What could help you decide between using models (1) and (2)? Explain.
B. If you ran a regression of P on A, would this satisfy all of the Gauss-Markov assumptions for unbiasedness? Explain why or why not.
C. How would issues of assessor accuracy/error impact a regression of P on A? Would assessor error matter if, on average, assessors could correctly appraise the value of houses? Explain.