This question is based on the empirical papers of Acemoglu et al (2001) that estimates the population regression function of the form: Yi = + + ui with the help of an instrumental variable Zi_ The variables are defined as in class. a) b) c) d) e) f) g) h) j) (2 pts.) Briefly explain why the colonizers introduced extractive economic institutions in some colonies and inclusive ones in others. (2 pts.) Briefly explain why the form of the current institutions (extractive vs. inclusive) is highly correlated with the form of institutions introduced by the colonizers. (3 pts.) Show that the PRFYi = + 1Xi + u, could be transformed toyi = Ax, + uzi, where "i, Xi and u, represent the deviations of Yi, Xi and ui respectively from their corresponding sample mean Y, X and _ (3 pts.) Shmu that multiplying both sides of yi 1Xi + ui by Zi across observations yields (2 pts.) Write down the validity and strength assumptions. (2 pts.) Briefly interpret the validity assumption in the context of the Acemoglu et al paper _ (2 pts.) Briefly describe how the violation of the validity assumption relates to selection bias in the context of the Acemoglu et al (2001) paper _ (2 pts.) If both the validity and strength assumptions hold, calculate l_ (2 pts.) If both the validity and strength assumptions hold, briefly describe the implications on the direction of causality between X, Y and Z _ (4 pts.) Given the direction of causality between X, Y and Z, state the key elements of the argument developed by Acemoglu et al (2001).