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Multiple Regression Analysis: Estimation - Pooled OLS

6 important questions on Multiple Regression Analysis: Estimation - Pooled OLS

What is Pooled OLS?

It is OLS estimation with independently pooled cross-sections, panel data, or cluster samples, where the observations are pooled across time (or group) as well as across the cross-sectional units. For example two years of data. Assuming a is uncorrelated with x (consistency).

What assumptions are needed for unbiasedness of OLS?

MLR1 (Linear in parameters): y = B0 + B1x1 + B2x2 + Bkxk + u
MLR2 (Random sampling): {(x(i)1, x(i)2, .., x(i)k, y(i)); (i) = 1, .., n}
MLR3 (No perfect collinearity): In the sample (and therefore in the population), none of the independent variables is constant, and there are no exact linear relationships among the independent variables
MLR4 (Zero conditional mean): E(u|x1,x2,..,xk)=0
MLR1-MLR4 gives E(^Bj)=Bj, j=0,1,..,k

What is the composite error term and how do we solve cluster correlation?

The composite error term is v=a+u. This implies that v1 and v2 will be correlated. This problem is solved by clustering the standard errors

What are the requirements of POLS?

That v and x are uncorrelated (consistency). Since v=a+u, we need the cov(x,a)=0 and cov(x,u)=0. The first is violated if x is determined based and systematic differences in units (OVB).

What is the omitted variable bias and how can it be shown?

The omitted variable bias can be shown if the model is underspecified. If one parameter doesn't affect the other, they are still unbiased. Otherwise, they are biased.

What can we say about the omitted variable bias in the general case?

With two or more explanatory variables in the estimated (underspecified) model, typically all estimators will be biased, even if only one explanatory variable is correlated with the omitted variable.

The question on the page originate from the summary of the following study material:

Introductory econometrics : a modern approach | 9780324289787 | Jeffrey M Wooldridge

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