A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students is
infrate = β0 + β1 conuse + β2 percmale + β3 avginc + β4 city + u1,
where
infrate = the percentage of sexually active students who have contracted venereal disease.
conuse = the percentage of boys who claim to regularly use condoms. avginc = average family income.
city = a dummy variable indicating whether a school is in a city.
The model is at the school level.
(i) Interpreting the preceding equation in a causal, ceteris paribus fashion, what should be the sign of β1?
(ii) Why might infrate and conuse be jointly determined?
(iii) If condom usage increases with the rate of venereal disease, so that -y, > 0 in the equation
conuse = y0 + y1 infrate + other factors,
what is the likely bias in estimating β1 by OLS?
(iv) Let condis be a binary variable equal to unity if a school has a program to distribute condoms. Explain how this can be used to estimate β1 (and the other betas) by IV. What do we have to assume about condis in each equation?