Wooldridge PPT ch15

Testing for endogeneity cont save the residuals from

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Testing for Endogeneity (cont) Save the residuals from the first stage Include the residual in the structural equation (which of course has y 2 in it) If the coefficient on the residual is statistically different from zero, reject the null of exogeneity If multiple endogenous variables, jointly test the residuals from each first stage
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 19 Testing Overidentifying Restrictions If there is just one instrument for our endogenous variable, we can’t test whether the instrument is uncorrelated with the error We say the model is just identified If we have multiple instruments, it is possible to test the overidentifying restrictions – to see if some of the instruments are correlated with the error
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 20 The OverID Test Estimate the structural model using IV and obtain the residuals Regress the residuals on all the exogenous variables and obtain the R 2 to form nR 2 Under the null that all instruments are uncorrelated with the error, LM ~ χ q 2 where q is the number of extra instruments
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 21 Testing for Heteroskedasticity When using 2SLS, we need a slight adjustment to the Breusch-Pagan test Get the residuals from the IV estimation Regress these residuals squared on all of the exogenous variables in the model (including the instruments) Test for the joint significance
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Fall 2008 under Econometrics Prof. Keunkwan Ryu 22 Testing for Serial Correlation When using 2SLS, we need a slight adjustment to the test for serial correlation Get the residuals from the IV estimation Re-estimate the structural model by 2SLS, including the lagged residuals, and using the same instruments as originally Can do 2SLS on a quasi-differenced model, using quasi-differenced instruments
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Testing for Endogeneity cont Save the residuals from the...

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