7. An investigator estimated the following equation by Ordinary Least Squares: Yt= a. — (3 Xt — ut...

Question

7. An investigator estimated the following equation by Ordinary Least Squares: Yt= a. — (3 Xt — ut It was then suspected that ut maybe correlated with its own past values: What are the consequences of this? (ii) What may be the possible causes?
(iii) Suggest a method to estimate the above equation if we assume that the Ut were generated by the following process: Ut P Ut-1 Tet
where p is a parameter whose value is known to be 0.8, and et is an error terns satisfying the classical assumptions.
(iv) How would your answer to pan (iii) be altered if the value of p was not known?

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Robert · Accepted Answer

Ans.  
Let xi be the dependent variable. a and b are the regression parameters. A simple regression 
model  
can then be given by: where y the dependent variable and e is the residual term.   ̂       ̂    ̂ 
  ̂=.   ̂– a-   ̂.  
Taking squares on both sides, 
 ̂     ̂– a-   ̂) ^2,  
Taking summation on both the sides, 
∑ ̂ =∑   ̂– a-   ̂) ^2,

7. An investigator estimated the following equation by Ordinary Least Squares: Yt= a. — (3 Xt — ut It was then suspected that ut maybe correlated with its own past values: What are the consequences of...

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