Question

We have a theoretical regression model: Yit = a + b1* X1it + b2* X2it + b3* X3it + et

Suppose we have only the data for X1 and X2 while X3 is not observable.

a. What will be the problem if we run a panel data regression using the following form? Yit = a + b1* X1it + b2* X2it + et

b. Under what condition(s) the panel data regression with fixed effect can overcome the problem? (You need to explain why in your answer.)

c. And under what condition(s) running the regression with random effect is a good choice in this case? (You need to explain why in your answer.)

Answer 1

a) As X3 is not observable, we can't include it in the regression model. If we make the model without X3, the problem will be that less variation will be explained by the model. The R-square value might be less because we are not including an important variable X3.

b) Fixed effect model can overcome this problem if X3 variable is correlated with other explanatory variables. The fixed effect model will be helpful in controlling the X3 bias which is the omitted variable. Also, one more condition is that X3 variable should have the same effect on the subject no matter the time. I mean that the effect of variable X3 on the outcome should be the same at t=0 and at a later time t=12.

c) If you believe that the X3 variable is uncorrelated with the explanatory variables (X1, X2), then random effect model will be a good choice in this case.