# Consistency of estimator

Regression: Wage=b0+b1collegegrad, where collegegrad is a dummy variable. Suppose you want to estimate the wage ratio between college graduates and non-college graduates. Is the estimator theta=b0/b1 consistent?

My thinking is that if we could increase our sample size to infinity, we would cover the entire population and thus get the true ratio, so the estimator is consistent. Am I correct, or am I missing something?

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Doesn't it just follow from Slutsky? –  Glen_b Oct 1 '12 at 4:52
Your intuition is correct in some sense (you have to be a bit careful when talking about what exactly that makes up the population), but probably won't do as an answer to the homework. As @Glen_b suggested, Slutsky's theorem might be of help. –  MånsT Oct 1 '12 at 5:54
Hint: what does $b_0/b_1$ estimate? (Strong hint: it does not estimate the wage ratio.) –  whuber Oct 1 '12 at 14:14
Oh, I see my mistake now. Would the estimator b0/(b0+b1) be an appropriate consistent estimator instead? Since b0 is the wage for non college graduates and b0+b1 is the wage for college graduates? –  user14386 Oct 2 '12 at 16:27