An Introduction to Econometric Theory

13Introduction to Asymptotics

The statistical results developed in the chapters of this book are powerful and elegant. A comprehensive theory of statistical inference has yielded exact confidence intervals and tests for a range of hypotheses on the regression coefficients. However, there remain major limitations. The independent sampling requirement, as has been discussed extensively in Section 12.4, clearly limits the range of economic data sets that the theory covers. A great deal of econometric work involves time series and panels, yet the theory of the preceding chapters has had nothing to say about these cases.

The assumption of Gaussian disturbances is extremely conventional, and in many textbooks it barely receives comment, but it is well known that some data sets, especially in finance, exhibit a higher probability of outliers than the normal distribution predicts. Skewed disturbances can also be also encountered. However, the major problem with the Gaussianity assumption is that it is made for convenience, to allow the results of Chapter 10 and Section 12.6 to be cited. It is rarely a component of the economic or behavioural model under consideration, and in any case the theory has provided no means of establishing its truth.

These facts present a dilemma, but happily there is resolution at hand, albeit one that involves its own compromises. Asymptotic theory is a collection of approximation results where the adequacy of the approximation is linked to sample size. It is also ...