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# ProblemSet10 Answers - Professor Mumford [email protected]

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Professor Mumford Econ 360 - Fall 2010 [email protected] Problem Set 10 Answers (Advanced Topic: Instrumental Variables) True/False (24 points) 1. FALSE This is not one of the characteristics of a valid instrument. If x and u are uncorrelated there is no need for an instrument. 2. TRUE Consider the regression model y = β 0 + β 1 x + u , where z is a potential instru- ment for x . In order for z to be a valid instrument, it must be the case that z and u are uncorrelated. 3. FALSE Consider the regression model y = β 0 + β 1 x + u , where z is a potential instrument for x . In order for z to be a valid instrument, it must be the case that z and x are correlated (the stronger the correlation the better) . 4. FALSE Consider the regression model y = β 0 + β 1 x + u , where z is an instrument for x . If z is a valid instrument for x we replace x with the fitted value , ˆ x , where ˆ x is a function of z in the regression model in order to obtain a consistent estimate of β 1 . Or, one could use the instrumental variables estimator. 5. TRUE Consider the regression model y = β 0 + β 1 x + u , where z is a an instrument for x . The instrumental variables estimator of β 1 is ˆ β IV 1 = n X i =1 ( z i - ¯ z ) y i n X i =1 ( z i - ¯ z ) ( x i - ¯ x ) 6. FALSE Consider the regression model y = β 0 + β 1 x + u , where z is a an instrument for x . If the correlation between z and x

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