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120_spring08_pset1_solutions

# 120_spring08_pset1_solutions - ECO 120 Spring 2008 Problem...

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ECO 120, Spring 2008 Problem Set 1 Solutions Jon Robinson 1. (a) The t-statistic for c ° 0 is 0.814/0.347 = 2.35, which is greater than 2. This means that c ° 0 is statistically signi°cant. The t-statistic for c ° 1 is 0.126/0.058=2.17. c ° 1 is statistically signi°cant. (b) The predicted probability is \ malaria = c ° 0 + c ° 1 net (1) so the prediction for someone in a household with a net is \ healthy = c ° 0 + c ° 1 (since net=1 for these people), which is 0.814+.126=0.940. The prediction for someone in a household without a net is \ health = c ° 0 (since net=0 for these people), which is 0.814. The di/erence between the 2 groups is c ° 1 , which is statistically signi°cant (from part a). (c) Malaria prevalence for people without bednets is 1-0.814=0.186. Prevalence for people with bednets is 1-0.814-0.126=0.06. (d) i. The sign of omitted variable bias is the same as the sign of ° 2 ° corr ( net; income ) . ii. We±d probably expect that richer people are less likely to have malaria, because, for instance, they might be able to a/ord anti-malarial drugs or because they might be less likely to have other diseases which would make their immune system vulnerable to malaria. This means that ° 2 is likely to be positive. We±d also expect that richer people are more likely to own nets, so corr ( net; income ) is likely to be positive. Since ° 2 is positive and corr ( net; income ) is positive, ° 2 ° corr ( net; income ) - the omitted variable bias - is positive. This means that the c ° 1 we estimated in (1) is too big . In words, what this means is that people with nets are also likely to be richer, and richer people are less likely to have 1

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malaria even aside from the fact that they have nets. If we don±t control for income, we±ll be giving too much credit to the nets. For instance, the true ° 1 might be 0.100, as opposed to the c ° 1 we estimated. iii. If income had no e/ect on the probability of getting malaria (aside from the fact that richer people are more likely to have nets), then ° 2 = 0 and there is no omitted variable bias at all (even though corr ( net; income ) 6 = 0 ). iv. One way the omitted variable bias in (ii) could be reversed would be if poorer people were more likely to have mosquito nets than richer people. This could happen if, for instance, the government had started an anti-malaria campaign and had given out nets to the very poorest people. Then corr ( net; income ) might be negative, ° 2 would still be positive, and so ° 2 ° corr ( net; income ) would be negative. In words, poorer people are more likely than richer people to have nets, but poorer people are less healthy than other people, so (aside from the impact
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120_spring08_pset1_solutions - ECO 120 Spring 2008 Problem...

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