Homework 2

Irrelevant Instruments

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1. Consider the following regression
   
   , where is an unknown parameter and are . It is proposed to estimate by instrumental variable (IV) methods using a vector of instruments generated by
   
   Let be the IV estimator of obtained with the instruments

   1. (Due 2/12, a-c) Show that satisfies
      
      and
      
      and interpret them.

   2. Find the limit distribution of the vector
      
      and prove your result.

   3. Find the asymptotic behavior of as

   4. (due 2/19) What happens to the asymptotic distribution of when That is, let after you have passed