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Wooldridge PPT ch7

Keunkwan ryu 11 testing for differences across groups

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Prof. Keunkwan Ryu 11 Testing for Differences Across Groups Testing whether a regression function is different for one group versus another can be thought of as simply testing for the joint significance of the dummy and its interactions with all other x variables So, you can estimate the model with all the interactions and without and form an F statistic, but this could be unwieldy
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 12 The Chow Test Turns out you can compute the proper F statistic without running the unrestricted model with interactions with all k continuous variables If run the restricted model for group one and get SSR 1 , then for group two and get SSR 2 Run the restricted model for all to get SSR, then ( 29 [ ] ( 29 [ ] 1 1 2 2 1 2 1 + + - + + - = k k n SSR SSR SSR SSR SSR F
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 13 The Chow Test (continued) The Chow test is really just a simple F test for exclusion restrictions, but we’ve realized that SSR ur = SSR 1 + SSR 2 Note, we have k + 1 restrictions (each of the slope coefficients and the intercept) Note the unrestricted model would estimate 2 different intercepts and 2 different slope coefficients, so the df is n – 2 k – 2
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 14 Linear Probability Model P( y = 1| x ) = E( y|x ), when y is a binary variable, so we can write our model as P( y = 1| x ) = β 0 + β 1 x 1 + … + β k x k So, the interpretation of β j is the change in the probability of success when x j changes The predicted y is the predicted probability of success Potential problem that can be outside [0,1]
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