Econometrics: Classical Assumption 7 – The error term is normally distributed.

According to the Gauss Markov Theorem, an Ordinary Least Squares (OLS) model can be considered as the Best Linear Unbiased Estimator (BLUE) as long as the first six classical assumptions are met. However, if you are conducting an econometric analysis and wish to make statistical inferences about the data, such as performing statistical hypothesis testing and generating reliable confidence intervals, this seventh classical assumption is necessary for such statistical hypothesis testing to take place. This seventh classical assumption states that the distribution of the error term needs to be bell shaped or normally distributed.

Just as is the case in general statistics, a set of data has to be normally distributed before statistical observations can be made regarding this information set. This is the same in the case of Ordinary Least Squares (OLS) regression analysis. Considering that the error term is part of the regression equation, then this must be normally distributed before statistical inferences about the linear regression can be made.

In practice, if you were to combine all of the individual, minor errors that occur within a data set, you would arrive at the error term. Due to the central limit theorem* as we increase the number of observations within a given data-set, the number of observations of error will rise to a point where normal distribution is inevitable.

 

*The central limit theorem states that:

The mean (or sum) of a number of independent, identically distributed random variables will tend to be normally distributed, regardless of their distribution, if the number of different random variables is large enough.

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