Chapter 15: Understanding the Standard Error
The previous chapter made clear that a single OLS estimate from one realized sample is like a draw from the probability histogram of the OLS sample estimates. The Gauss–Markov theorem says that, if the requirements of the classical econometric model are met, then the OLS estimator is BLUE – that is, of the class of linear and unbiased estimators, the OLS estimator has the smallest standard error.
This chapter is devoted to more practical concerns about the SE of the OLS
estimator. In the next section, we restate the formulas for the SE in the
univariate and bivariate cases in much simpler language that will allow for
an intuitive understanding of the SE. Section 15.3 shows how to compute the
estimated SE reported by OLS routines such as Excel’s LINEST function.
Section 15.4 illustrates the properties of the SE of the OLS estimator by
a simple discovery exercise. Section 15.5 discusses the concept of consistency
and applies it to a discussion of the estimated RMSE. The final section introduces
another standard error, the SE of forecasted Y. Throughout this chapter, we
work with the classical econometric model of the data generation process.