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Exercise 1

# Exercise 1 - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 140A Exercise 1 1. You are interested in purchasing a home in Santa Barbara. To determine if it is a good time to buy, you collect the selling prices of all homes in the city over the past three years, giving you 497 observations. Let us denote observation t as P t , t=1,...,497 . a) We assume that 497 1 } { t t P is a sequence of independent and identically distributed random variables. Construct an estimator of the mean and median of P t . b) Are your estimators unbiased? What is the variance of each estimator? c) Suppose that you grouped the sales according to years, so you could estimate the mean and median sale price of a home in each of the three years. Suppose further, that our assumption that 497 1 } { t t P is an i.i.d. sequence is erroneous. In fact, there are two types of homes, call them nice with mean price N and average with mean price A , where A N . If the composition of sales over time has shifted toward nice homes, which estimator would shift more over time?

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