Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 5

Let Y denote a Bernoulli(?) random variable with 0<?<1. Suppose we are interested in estimating the odds ratio, ?= ?/(1- ?), which is the probability of success over the the probability of failure. Given a random sample {Y1, …, Yn}, we know that an unbiased and consistent estimator of ? is , the proportion of successes in n trials. A natural estimator of ? is G = ? /(1 -), the proportion of successes over the proportion of failures in the sample.

(i) Why is G not an unbiased estimator of ?

(ii) Use PLIM.2(iii)

PLIM.2 If plim (Tn) = ?and plim (Un) =?, then

(i) plim(Tn _+Un) = ?+ ?;

(ii) plim(TnUn) = ? ?;

(iii) plim(Tn /Un) = ?/?, provided ?? 0.

to show that G is a consistent estimator of ?.

Step 1 of 3

It is given that a natural estimator of ? is G.