Author Topic: Misspecification Notes 17: Omitted Variables  (Read 658 times)

cchang46

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Misspecification Notes 17: Omitted Variables
« on: May 07, 2017, 03:34:11 PM »
Hello!


I have a question on how to determine the omitted variable. On page 5, we need to add the term B1(log(x1)-x1) for the first case of misspecification in order to get the true model.


Please correct me if I am wrong, but in class the omitted variable was determined to be log(x1)-x1.


This leaves out B1 when writing the omitted variable--why is that? Is this normal practice?


How then would we specify the omitted variable in the example directly after? In the model this was an addition of [(e^(B1x1+B2x2))-B1x1-B2x2]. Do we omit the betas here as well?


Thank you!

Thomas VanDer Straaten

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Re: Misspecification Notes 17: Omitted Variables
« Reply #1 on: May 07, 2017, 05:45:50 PM »
Hi cchang46, I believe this just means that the "variable" itself is log(x1)-x1, but the whole term to be added to get the true model takes into account the coefficient B1. It is the same as saying x1 is the variable, not B1X1. A much more simple version to see is:

True model: y = B0 + B1X1 + B2X2 + B3X22 + u
Model you run: y = B0 + B1X1 + B2X2 + u

Then B0 + B1X1 + B2X2 + B3X22 + u = B0 + B1X1 + B2X2 + u + A (solve for A)

A = B3X22

"A" is the whole term you need to include; you omitted X22.

Thomas VanDer Straaten

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Re: Misspecification Notes 17: Omitted Variables
« Reply #2 on: May 07, 2017, 05:52:38 PM »
For the second example (#4), this is much more tricky, as the true functional form of the regression is nonlinear. Essentially here, in order to solve for the bias, we need to transform a linear equation into a nonlinear one, so comparing omitted variables isn't going to be strictly identical to how we would do it for the linear case. In this case, I view this as asking "what is the missing specification?"