Sample Question #127 (statistics – regressions)

What are the assumptions behind OLS estimations?

(Comment: all too many candidates only know how to use regression techniques and other quantitative tools following a cookbook approach, without understanding what conditions must be satisfied before one can use such techniques)

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ANSWER

The necessary assumptions are:

1) The dependent variable must be linearly related to the independent variables and the error term – this is the most fundamental assumption because the L in OLS stands for linear!

2) The indepenent variables are exogenous – this implies, in theory, they are independent of one another (bonus question: if the sample correlation between two independent variables is 35%, can we still use the OLS?)

3) The error term must have zero expectation, constant variance, and no serial correlation

4) There must be more observations than independent variables – this is an important implicit assumption that almost no candidate mentions

Of these assumptions, you should realize the "weakest" are the ones concerning the error term’s variance and serial correlation in the sense that even if they’re violated, you can still use OLS to obtain the estimates, but you just can’t do proper inferences on the OS estimates.

You should also note that normality of the error term is not a necessary assumption of the OLS model. Normality makes calculating the estimator’s sample statistics easier, but is by no means a necessary condition for OLS.