1. IV and 2SLS. Suppose you are interested in estimating the causal effect of increased competition...

 

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1. IV and 2SLS. Suppose you are interested in estimating the causal effect of increased competition among school on student achievement. Your measure of school competition will be the number of school districts per 1,000 students in a city, 2₁, and your measure of student achievement will be the average test score of students in that city, y. The structural relationship you are interested in can be written as: Yi = Bo + B₁₂ + U₂. (a) Give two reasons why Cov(x₁, u₁) may not be zero (that is, why might x; be en- dogenous). (b) Based on these concerns you decide to look for an instrumental variable, 2₁, to obtain a consistent estimate of 3₁. The instrument you settle on is a zero-one indicator for whether or not there is a major stream going through the city. Discuss the possible validity of this instrument (be sure to touch on both conditions). (c) What is the expression for the IV estimator for B₁ in terms of covariances? (d) Show that the IV estimator is equivalent to the two-stage least squares estimator 1. IV and 2SLS. Suppose you are interested in estimating the causal effect of increased competition among school on student achievement. Your measure of school competition will be the number of school districts per 1,000 students in a city, 2₁, and your measure of student achievement will be the average test score of students in that city, y. The structural relationship you are interested in can be written as: Yi = Bo + B₁₂ + U₂. (a) Give two reasons why Cov(x₁, u₁) may not be zero (that is, why might x; be en- dogenous). (b) Based on these concerns you decide to look for an instrumental variable, 2₁, to obtain a consistent estimate of 3₁. The instrument you settle on is a zero-one indicator for whether or not there is a major stream going through the city. Discuss the possible validity of this instrument (be sure to touch on both conditions). (c) What is the expression for the IV estimator for B₁ in terms of covariances? (d) Show that the IV estimator is equivalent to the two-stage least squares estimator

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a Give two reasons why Cov Ti ui may not be zero that is why might x be endogenous Wealthy neighborh... View the full answer