Panel data

6 important questions on Panel data

What is the motivation for multiple regression analysis?

The zero conditional mean in the simple linear regression model can be controversial.
Multiple regression analysis allows to explicitly control for factors that simultaneously affect the dependent variable.

Which estimator to choose when?

We always choose Random effects first because it is more efficient. But only when the assumptions of the RE holds. They are that the individual effect is uncorrelated with x (Cov(x,a)=0). Using the Hausman test.
See exam 2018, task 4 d).

What is the multiple regression model and what differs from SLR?

In the terminology, the variables of multiple regression have possibly nonlinear variables. The assumption of E[u|x1,x2,..,xk]=0 establishes ceteris paribus interpretation of slope parameters.
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What does the first difference help us with?

It removes the bias in POLS. This means that we get rid of a. We need that u2-u1 is uncorrelated with x for OLS to be consistent. This means that the cov(x,u)=0 and we need strict exogeneity, t=1,2.

How do we obtain the OLS estimates in a multiple regression model?

The same way with a simple linear regression model. We take a sample from the population with the function y(i) and calculate the regression function.
Then the OLS estimates minimise the sum of squared residuals (SSR) and the OLS estimates satisfy the OLS first order conditions.

How can we interpret the OLS sample regression function of the multiple regression model?

Intercept equals predicted value y if other variables are 0.
The parameter slopes have partial effect interpretations.

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