Use the simple regression as a rule of thumb in the

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use the simple regression as a rule of thumb In the simple regression case, the bias is the same sign as α 2 /( 1 – α 2 α 1 )
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Economics 20 - Prof. Anderson 10 Identification of General SEM Let z 1 be all the exogenous variables in the first equation, and z 2 be all the exogenous variables in the second equation It’s okay for there to be overlap in z 1 and z 2 To identify equation 1, there must be some variables in z 2 that are not in z 1 To identify equation 2, there must be some variables in z 1 that are not in z 2
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Economics 20 - Prof. Anderson 11 Rank and Order Conditions We refer to this as the rank condition Note that the exogenous variable excluded from the first equation must have a non-zero coefficient in the second equation for the rank condition to hold Note that the order condition clearly holds if the rank condition does – there will be an exogenous variable for the endogenous one
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Economics 20 - Prof. Anderson 12 Estimation of the General SEM Estimation of SEM is straightforward The instruments for 2SLS are the exogenous variables from both equations Can extend the idea to systems with more than 2 equations For a given identified equation, the instruments are all of the exogenous variables in the whole system
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