lecture notes 6 omitted variable bias

Question 1

What is omitted variable bias?

Answer 1

This is when a variable that can explains a relationship is not taken into account and a coefficient gets biased.

Question 2

How do you work out what type of omitted variable bias?

Answer 2

It is always split into 2 parts:
The coefficient and the Cov
Work out what these signs are and then work out the overall sign to see if positive or negative.

Question 3

What is misspecification in econometrics?

Answer 3

When the model is not specified accurately
Eg if something is non-linear and a linear regression has been used.

Question 4

What is a test that can be used for misspecification

Answer 4

REST TEST
Include non-linear transformations of variables and check if the coefficients are significant or not.

Question 5

What is the equation for omitted variable bias eg Y = B0 + gamma1X1
real equation Y = B0 + b1X1 + B2W

Answer 5

The ols estimate of gamma 1 = the formula

This formula has Y-Y bar in it

Then sub in what that is from the real equation (taking into account the other variable)

When subbed in
gamma hat = B1 + B2 . Cov(X1,W) / V(X)

Question 6

How do you conduct a reset test when estimating a regression function?

Answer 6

You are supposing that the regression function being estimated has been misspecified.

First regress estimated regression and save residuals.
(This saves everything that has not been explained by the model0

Then regress these residuals on all the x variables and the predicted values with ^2 ^3 and so forth.

If the coefficients of the squared and cubic come out as significant this means that the model has been misspecified.

H0 is that all coefficients in front of Y hat are zero

The initial model is the restricted model
The Y hat model is the unrestricted model.

Then calculate F test

d is the number of Y hats used with the polynomial.

The DOF is the N observations - original model parameters + the Y hat polynomial parameters.