(Solution) An author wants to estimate a model of the form y_i=_0+x_i _1+_i. > Snapessays.com


(Solution) An author wants to estimate a model of the form y_i=_0+x_i _1+_i.


An author wants to estimate a model of the form y_i=?_0+x_i ?_1+?_i. Unfortunately, the author is unable to find exactly the variable for y but instead, they find a variable that has some “measurement error,” that is, the variable they use in the regression is y_i^* and y_i^*=y_i+v_i where v_i is a random error with ?E[v?_i]=0, ?VAR[v?_i]=?_v^2, and Cov(v_i,?_i )=Cov(v_i,x_i )=0. Think of the problem this way. A survey asks people for their usual weekly earnings and instead of responding with their exact earnings, y_i is given as an approximation of y_i^* that varies randomly where the error in their response is given by the random variable v. Suppose the researcher estimates the model using y_i^* instead of y, gets and estimate for ? ?_1=Cov(y_i^* ?,x?_i)/VAR(x_i). Will the researcher estimates be bias? Provide a proof to support your answer.

 


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This question was answered on: Sep 21, 2023

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