From Wooldridge, Chapter 3:

What are the statistical properties of the linear regression model?

The four assumptions under which the OLS estimators are unbiased for the population parameters are:

How would MLR.3 fail? U may be correlated with X for the following reasons:

- Functional form misspecification (Ex: x2 or log(x) should have been included)

- Omitted variables that are correlated with the independent variables

- Measurement error in an explanatory variable

- One or more of the explanatory variables is jointly determined with y.

When assumption MLR.3 holds, we have exogenous explanatory variables. If xj is correlated with u for

any reason, then xj is an endogenous explanatory variable.

Assumptions MLR.1 to MLR.5 are collectively known as the Gauss-Markov assumptions for cross-

sectional regression.

Now, let’s take a look at the sampling variances of the slope estimators.

Exercises

Measurement Error

a) Measurement error in the dependent variable

b) Measurement error in an independent (explanatory) variable

The classical errors-in-variables assumption is that the measurement error is uncorrelated with the

unobserved explanatory variable.

Testing hypotheses: t-tests and F-tests

(Read Wooldridge, Sections 4.2, 4.4, 4.5)

The R-squared form of the F statistic:

Constrained regression

Example

Beta coefficients, Wooldridge, chapter 6