Why Should PC Ownership Be Correlated With U?
Problem Set 1.
Due Date: 08/02/2015.
1. (Wooldridge, Exercise 15.1) Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university:
GP A = β0 + β1 P C + u where P C is a binary variable indicating PC ownership.
(i) Why might PC ownership be correlated with u?
(ii) Explain why PC is likely to be related to parents’ annual income. does this mean parental income is a good IV for PC? Why or why not?
(iii) Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming students, and the students who received grants were randomly chosen. Carefully explain how you would use this information to construct an instrumental …show more content…
In class, we saw that the validity is not testable (when there are as many instruments as endogenous variables). Here, the R12 obtained in step 2 would be equal to zero always. Obtain this result in a simple regression model with an endogenous regressor X,
Y = β0 + β1 X + U1 and a single instrumental variable Z for X.
5. (Wooldridge, Exercise 16.4) Suppose that annual earnings and alcohol consumption are determined by the SEM log(earnings) = β0 + β1 alcohol + β2 educ + u1 alcohol = γ0 + γ1 log(earnings) + γ2 educ + γ3 log(price) + u2 where price is a local price index for alcohol, which includes state and local taxes. Assume that educ and price are exogenous. If β1 , β2 , γ1 , γ2 and γ3 are all different from zero, which equation is identified? How would you estimate that equation?
2
6. (Wooldridge, Exercise 16.5) A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students is inf rate = β0 + β1 conuse + β2 percmale + β3 avginc + β4 city + u1 where infrate
Due Date: 08/02/2015.
1. (Wooldridge, Exercise 15.1) Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university:
GP A = β0 + β1 P C + u where P C is a binary variable indicating PC ownership.
(i) Why might PC ownership be correlated with u?
(ii) Explain why PC is likely to be related to parents’ annual income. does this mean parental income is a good IV for PC? Why or why not?
(iii) Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming students, and the students who received grants were randomly chosen. Carefully explain how you would use this information to construct an instrumental …show more content…
In class, we saw that the validity is not testable (when there are as many instruments as endogenous variables). Here, the R12 obtained in step 2 would be equal to zero always. Obtain this result in a simple regression model with an endogenous regressor X,
Y = β0 + β1 X + U1 and a single instrumental variable Z for X.
5. (Wooldridge, Exercise 16.4) Suppose that annual earnings and alcohol consumption are determined by the SEM log(earnings) = β0 + β1 alcohol + β2 educ + u1 alcohol = γ0 + γ1 log(earnings) + γ2 educ + γ3 log(price) + u2 where price is a local price index for alcohol, which includes state and local taxes. Assume that educ and price are exogenous. If β1 , β2 , γ1 , γ2 and γ3 are all different from zero, which equation is identified? How would you estimate that equation?
2
6. (Wooldridge, Exercise 16.5) A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students is inf rate = β0 + β1 conuse + β2 percmale + β3 avginc + β4 city + u1 where infrate