ABSTRACT
At several points in this textbook, we have encountered the normal distribution. I have noted that the distribution is frequently encountered in applied econometrics. Its centrality is due in part to its importance in sampling theory. As we will develop in Chapter 6, the normal distribution is typically the limiting distribution of sums of averages. In the vernacular of statistics, this result is referred to as the Central Limit Theorem. However, normality is important apart from its asymptotic nature. Specifically, since the sum of a normal distribution is also a normal distribution, we sometimes invoke the normal distribution function in small samples. For example, since a typical sample average is simply the sum of observations divided by a constant (i.e., the sample size), the mean of a collection of normal random variables is also normal. Extending this notion, since ordinary least squares is simply a weighted sum, then the normal distribution provides small sample statistics for most regression applications.
